Finite Group Databasebeta

← C2×#37820 #7635018

Subgroups — C2×#37820 #7635018

Order 512.

9328 conjugacy classes of subgroups.

The subgroup lattice has 1744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#538C211yesmaximal, characteristic, complemented
2C22×#532C211yesmaximal, characteristic, complemented
3C2×#2716C211yesmaximal, characteristic, complemented
4C2×#2709C211yesmaximal, characteristic, complemented
5C2×#2699C211yesmaximal, characteristic, complemented
6C2×#2686C211yesmaximal, characteristic, complemented
7C2×#2678C211yesmaximal, characteristic, complemented
8C2×#2677C211yesmaximal, characteristic, complemented
9C2×#2671C211yesmaximal, characteristic, complemented
10C2×#2669C211yesmaximal, characteristic, complemented
11#37820C2132yesmaximal, direct product factor
12C2×#2853C211yesmaximal, characteristic, complemented
13C2×#2491C211yesmaximal, characteristic, complemented
14C2×#2521C211yesmaximal, characteristic, complemented
15C2×#2430C211yesmaximal, characteristic, complemented
16C2×#2404C211yesmaximal, characteristic, complemented
17C2×#2432C211yesmaximal, characteristic, complemented
18C2×#2407C211yesmaximal, characteristic, complemented
19C2×#2468C211yesmaximal, characteristic, complemented
20C2×#2461C211yesmaximal, characteristic, complemented
21C2×#2419C211yesmaximal, characteristic, complemented
22C2×#2467C211yesmaximal, characteristic, complemented
23C2×#2459C211yesmaximal, characteristic, complemented
24C2×#2472C211yesmaximal, characteristic, complemented
25C2×#2463C211yesmaximal, characteristic, complemented
26C2×#2418C211yesmaximal, characteristic, complemented
27C2×#2661C211yesmaximal, characteristic, complemented
28C2×#2635C211yesmaximal, characteristic, complemented
29C2×#2364C211yesmaximal, characteristic, complemented
30C2×#2358C211yesmaximal, characteristic, complemented
31C2×#2333C211yesmaximal, characteristic, complemented
32C2×C4×#123C211yesmaximal, characteristic, complemented
33C23×#41C2211yescharacteristic
34C23×#41C2211yescharacteristic, complemented
35C2×#538—216no—
36C2×#538C22116yescomplemented
37C2×#532—216no—
38C2×#532C22116yescomplemented
39C22×C4⋊Q8C2211yescharacteristic, complemented
40C22×C4⋊Q8C2211yescharacteristic, complemented
41C22×#127C2211yescharacteristic
42C22×#126C2211yescharacteristic
43C22×#126C2211yescharacteristic
44C22×#124C2211yescharacteristic
45C22×#124C2211yescharacteristic
46C22×#124C2211yescharacteristic
47C22×#124C2211yescharacteristic, complemented
48C22×#123C2211yescharacteristic
49C22×#123C2211yescharacteristic
50C22×#123C2211yescharacteristic
51C22×#123C2211yescharacteristic
52C22×C22⋊Q8C2211yescharacteristic
53C22×C22⋊Q8C2211yescharacteristic
54C22×C22⋊Q8C2211yescharacteristic, complemented
55C22×#121C2211yescharacteristic
56C22×#121C2211yescharacteristic
57C22×#121C2211yescharacteristic
58C22×#121C2211yescharacteristic
59C22×#121C2211yescharacteristic
60C22×#121C2211yescharacteristic
61C22×#121C2211yescharacteristic, complemented
62C22×#121C2211yescharacteristic, complemented
63C22×#120C2211yescharacteristic
64C22×#120C2211yescharacteristic
65C22×#120C2211yescharacteristic
66C22×#120C2211yescharacteristic
67C22×C4×D4C2211yescharacteristic
68C22×C4×D4C2211yescharacteristic
69C22×C4×D4C2211yescharacteristic
70C22×C4×D4C2211yescharacteristic
71C22×C4×D4C2211yescharacteristic
72C22×C4×D4C2211yescharacteristic, complemented
73C22×C4×D4C2211yescharacteristic, complemented
74C23×C22⋊C4C2211yescharacteristic
75C23×C22⋊C4C2211yescharacteristic
76C23×C42C2211yescharacteristic, complemented
77#2853C22116yescomplemented
78#2716C22116yescomplemented
79#2709C22116yescomplemented
80#2699C22116yescomplemented
81#2686C22116yescomplemented
82#2678C22116yescomplemented
83#2677C22116yescomplemented
84#2671C22116yescomplemented
85#2669C22116yescomplemented
86#2661C22116yescomplemented
87#2635C22116yescomplemented
88#2521C22116yescomplemented
89#2491C22116yescomplemented
90#2472C22116yescomplemented
91#2468C22116yescomplemented
92#2467C22116yescomplemented
93#2463C22116yescomplemented
94#2461C22116yescomplemented
95#2459C22116yescomplemented
96#2432C22116yescomplemented
97#2430C22116yescomplemented
98#2419C22116yescomplemented
99#2418C22116yescomplemented
100#2407C22116yescomplemented
101#2404C22116yescomplemented
102C2×#400C2211yescharacteristic, complemented
103C2×#399C2211yescharacteristic
104C2×#399C2211yescharacteristic, complemented
105C2×#398C2211yescharacteristic, complemented
106C2×#398C2211yescharacteristic, complemented
107C2×#398C2211yescharacteristic, complemented
108C2×#397C2211yescharacteristic
109C2×#397C2211yescharacteristic
110C2×#397C2211yescharacteristic
111C2×#396C2211yescharacteristic
112C2×#395C2211yescharacteristic, complemented
113C2×#395C2211yescharacteristic, complemented
114C2×#394C2211yescharacteristic
115C2×#394C2211yescharacteristic
116C2×#394C2211yescharacteristic
117C2×#394C2211yescharacteristic
118C2×#394C2211yescharacteristic
119C2×#394C2211yescharacteristic
120C2×#394C2211yescharacteristic
121C2×#394C2211yescharacteristic
122C2×#394C2211yescharacteristic, complemented
123C2×#394C2211yescharacteristic, complemented
124C2×#394C2211yescharacteristic, complemented
125C2×#394C2211yescharacteristic, complemented
126C2×#394C2211yescharacteristic, complemented
127C2×#394C2211yescharacteristic, complemented
128C2×#394C2211yescharacteristic, complemented
129C2×#394C2211yescharacteristic, complemented
130C2×#393C2211yescharacteristic
131C2×#393C2211yescharacteristic
132C2×#393C2211yescharacteristic
133C2×#393C2211yescharacteristic, complemented
134C2×#392C2211yescharacteristic
135C2×#392C2211yescharacteristic
136C2×#392C2211yescharacteristic
137C2×#392C2211yescharacteristic
138C2×#392C2211yescharacteristic
139C2×#392C2211yescharacteristic
140C2×#392C2211yescharacteristic
141C2×#392C2211yescharacteristic
142#2364C22116yescomplemented
143#2358C22116yescomplemented
144#2333C22116yescomplemented
145C4×#123C22116yescomplemented
146C2×#391C2211yescharacteristic, complemented
147C2×#391C2211yescharacteristic, complemented
148C2×#390C2211yescharacteristic
149C2×#390C2211yescharacteristic
150C2×#390C2211yescharacteristic
151C2×#390C2211yescharacteristic
152C2×#390C2211yescharacteristic, complemented
153C2×#388C2211yescharacteristic
154C2×#388C2211yescharacteristic
155C2×#388C2211yescharacteristic
156C2×#388C2211yescharacteristic
157C2×#388C2211yescharacteristic
158C2×#388C2211yescharacteristic
159C2×#388C2211yescharacteristic
160C2×#388C2211yescharacteristic
161C2×#388C2211yescharacteristic
162C2×#388C2211yescharacteristic, complemented
163C2×#388C2211yescharacteristic, complemented
164C2×#388C2211yescharacteristic, complemented
165C2×#388C2211yescharacteristic, complemented
166C2×#388C2211yescharacteristic, complemented
167C2×#388C2211yescharacteristic, complemented
168C2×#388C2211yescharacteristic, complemented
169C2×#387C2211yescharacteristic, complemented
170C2×#387C2211yescharacteristic, complemented
171C2×#387C2211yescharacteristic, complemented
172C2×#387C2211yescharacteristic, complemented
173C2×#387C2211yescharacteristic, complemented
174C2×#387C2211yescharacteristic, complemented
175C2×#387C2211yescharacteristic, complemented
176C2×#387C2211yescharacteristic, complemented
177C2×#387C2211yescharacteristic, complemented
178C2×#386C2211yescharacteristic
179C2×#386C2211yescharacteristic
180C2×#386C2211yescharacteristic
181C2×#386C2211yescharacteristic
182C2×#386C2211yescharacteristic
183C2×#386C2211yescharacteristic
184C2×#386C2211yescharacteristic
185C2×#386C2211yescharacteristic
186C2×#386C2211yescharacteristic
187C2×#386C2211yescharacteristic
188C2×#386C2211yescharacteristic
189C2×#386C2211yescharacteristic
190C2×#386C2211yescharacteristic
191C2×#386C2211yescharacteristic
192C2×#386C2211yescharacteristic
193C2×#386C2211yescharacteristic, complemented
194C2×#386C2211yescharacteristic, complemented
195C2×#386C2211yescharacteristic, complemented
196C2×#385C2211yescharacteristic
197C2×#385C2211yescharacteristic
198C2×#385C2211yescharacteristic
199C2×#385C2211yescharacteristic, complemented
200C2×#385C2211yescharacteristic, complemented
201C2×#385C2211yescharacteristic, complemented
202C2×#385C2211yescharacteristic, complemented
203C2×#385C2211yescharacteristic, complemented
204C2×#381C2211yescharacteristic
205C2×#381C2211yescharacteristic, complemented
206C2×#381C2211yescharacteristic, complemented
207C2×#381C2211yescharacteristic, complemented
208C2×#380C2211yescharacteristic
209C2×#380C2211yescharacteristic, complemented
210C2×#380C2211yescharacteristic, complemented
211C2×#379C2211yescharacteristic
212C2×C4×C4⋊C4C2211yescharacteristic, complemented
213C2×C4×C4⋊C4C2211yescharacteristic, complemented
214C2×C4×C22⋊C4C2211yescharacteristic
215C2×C4×C22⋊C4C2211yescharacteristic
216C2×C4×C22⋊C4C2211yescharacteristic
217C2×C4×C22⋊C4C2211yescharacteristic, complemented
218C2×C4×C22⋊C4C2211yescharacteristic, complemented
219C2×C4×C22⋊C4C2211yescharacteristic, complemented
220C22×#95C2211yescharacteristic, complemented
221C26C2311yescharacteristic
222C22×#41—28no—
223C22×#41—28no—
224C22×#41—44no—
225C22×#41—44no—
226C22×#41—44no—
227C22×#41—44no—
228C22×#41C2318yes—
229C22×#41C2318yescomplemented
230C23×Q8C2311yescharacteristic
231C23×Q8C2311yescharacteristic
232C23×Q8C2311yescharacteristic
233C23×D4C2311yescharacteristic
234C23×D4C2311yescharacteristic
235C23×D4C2311yescharacteristic
236C23×D4C2311yescharacteristic
237C23×D4C2311yescharacteristic
238C23×D4C2311yescharacteristic
239C23×D4C2311yescharacteristic
240C23×D4C2311yescharacteristic
241C23×D4C2311yescharacteristic
242C23×D4C2311yescharacteristic
243C23×D4C2311yescharacteristic
244C23×D4C2311yescharacteristic
245C23×D4C2311yescharacteristic
246C23×D4C2311yescharacteristic
247C23×D4C2311yescharacteristic
248C23×D4C2311yescharacteristic
249C23×D4C2311yescharacteristic
250C23×D4C2311yescharacteristic
251C24×C4C2311yescharacteristic
252C24×C4C2311yescharacteristic
253C24×C4C2311yescharacteristic
254C24×C4C2311yescharacteristic
255C24×C4C2311yescharacteristic
256C24×C4C2311yescharacteristic
257C24×C4C2311yescharacteristic
258C24×C4C2311yescharacteristic
259C24×C4C2311yescharacteristic
260C24×C4C2311yescharacteristic
261C24×C4C2311yescharacteristic
262C24×C4C2311yescharacteristic
263#538—2128no—
264#532—2128no—
265C2×C4⋊Q8—28no—
266C2×C4⋊Q8—44no—
267C2×C4⋊Q8C2318yescomplemented
268C2×C4⋊Q8C2318yescomplemented
269C2×#127—28no—
270C2×#127C2318yes—
271C2×#126—28no—
272C2×#126—28no—
273C2×#126C2318yes—
274C2×#126C2318yes—
275C2×#124—28no—
276C2×#124—28no—
277C2×#124—28no—
278C2×#124—28no—
279C2×#124C2318yes—
280C2×#124C2318yes—
281C2×#124C2318yes—
282C2×#124C2318yescomplemented
283C2×#123—28no—
284C2×#123—28no—
285C2×#123—28no—
286C2×#123—44no—
287C2×#123C2318yes—
288C2×#123C2318yes—
289C2×#123C2318yes—
290C2×#123C2318yes—
291C2×C22⋊Q8—28no—
292C2×C22⋊Q8—44no—
293C2×C22⋊Q8—44no—
294C2×C22⋊Q8C2318yes—
295C2×C22⋊Q8C2318yes—
296C2×C22⋊Q8C2318yescomplemented
297C2×#121—28no—
298C2×#121—28no—
299C2×#121—28no—
300C2×#121—28no—
301C2×#121—28no—
302C2×#121—28no—
303C2×#121—44no—
304C2×#121D4116yescomplemented
305C2×#121C2318yes—
306C2×#121C2318yes—
307C2×#121C2318yes—
308C2×#121C2318yes—
309C2×#121C2318yes—
310C2×#121C2318yes—
311C2×#121C2318yescomplemented
312C2×#121C2318yescomplemented
313C2×#120—28no—
314C2×#120—28no—
315C2×#120—28no—
316C2×#120—44no—
317C2×#120C2318yes—
318C2×#120C2318yes—
319C2×#120C2318yes—
320C2×#120C2318yes—
321C2×C4×D4—28no—
322C2×C4×D4—28no—
323C2×C4×D4—28no—
324C2×C4×D4—28no—
325C2×C4×D4—28no—
326C2×C4×D4—28no—
327C2×C4×D4—44no—
328C2×C4×D4C2318yes—
329C2×C4×D4C2318yes—
330C2×C4×D4C2318yes—
331C2×C4×D4C2318yes—
332C2×C4×D4C2318yes—
333C2×C4×D4C2318yescomplemented
334C2×C4×D4C2318yescomplemented
335C22×C4⋊C4C2311yescharacteristic
336C22×C4⋊C4C2311yescharacteristic
337C22×C4⋊C4C2311yescharacteristic
338C22×C4⋊C4C2311yescharacteristic
339C22×C4⋊C4C2311yescharacteristic
340C22×C4⋊C4C2311yescharacteristic
341C22×C4⋊C4C2311yescharacteristic
342C22×C4⋊C4C2311yescharacteristic
343C22×C4⋊C4C2311yescharacteristic
344C22×C4⋊C4C2311yescharacteristic
345C22×C4⋊C4C2311yescharacteristic
346C22×C4⋊C4C2311yescharacteristic
347C22×C4⋊C4C2311yescharacteristic
348C22×C4⋊C4C2311yescharacteristic
349C22×C4⋊C4C2311yescharacteristic
350C22×C4⋊C4C2311yescharacteristic
351C22×C4⋊C4C2311yescharacteristic
352C22×C4⋊C4C2311yescharacteristic
353C22×C4⋊C4C2311yescharacteristic
354C22×C4⋊C4C2311yescharacteristic
355C22×C4⋊C4C2311yescharacteristic
356C22×C4⋊C4C2311yescharacteristic
357C22×C4⋊C4C2311yescharacteristic
358C22×C22⋊C4—28no—
359C22×C22⋊C4—44no—
360C22×C22⋊C4C2318yes—
361C22×C22⋊C4C2311yescharacteristic
362C22×C22⋊C4C2311yescharacteristic
363C22×C22⋊C4C2311yescharacteristic
364C22×C22⋊C4C2311yescharacteristic
365C22×C22⋊C4C2311yescharacteristic
366C22×C22⋊C4C2311yescharacteristic
367C22×C22⋊C4C2311yescharacteristic
368C22×C22⋊C4C2311yescharacteristic
369C22×C22⋊C4C2311yescharacteristic
370C22×C22⋊C4C2311yescharacteristic
371C22×C22⋊C4C2311yescharacteristic
372C22×C22⋊C4C2311yescharacteristic
373C22×C22⋊C4C2311yescharacteristic
374C22×C22⋊C4C2311yescharacteristic
375C22×C22⋊C4C2311yescharacteristic
376C22×C22⋊C4C2311yescharacteristic
377C22×C22⋊C4C2311yescharacteristic
378C22×C22⋊C4C2311yescharacteristic
379C22×C22⋊C4C2311yescharacteristic
380C22×C22⋊C4C2311yescharacteristic
381C22×C22⋊C4C2311yescharacteristic
382C22×C22⋊C4C2311yescharacteristic
383C22×C22⋊C4C2311yescharacteristic
384C22×C22⋊C4C2311yescharacteristic
385C22×C22⋊C4C2311yescharacteristic
386C22×C22⋊C4C2311yescharacteristic
387C22×C22⋊C4C2311yescharacteristic
388C22×C22⋊C4C2318yes—
389C22×C22⋊C4C2311yescharacteristic
390C22×C22⋊C4C2311yescharacteristic
391C22×C22⋊C4C2311yescharacteristic
392C22×C22⋊C4C2311yescharacteristic
393C22×C22⋊C4C2311yescharacteristic
394C22×C22⋊C4C2311yescharacteristic
395C22×C22⋊C4C2311yescharacteristic
396C22×C22⋊C4C2311yescharacteristic
397C22×C22⋊C4C2311yescharacteristic
398C22×C22⋊C4C2311yescharacteristic
399C22×C22⋊C4C2311yescharacteristic
400C22×C22⋊C4C2311yescharacteristic
401C22×C22⋊C4C2311yescharacteristic
402C22×C22⋊C4C2311yescharacteristic
403C22×C22⋊C4C2311yescharacteristic
404C22×C22⋊C4C2311yescharacteristic
405C22×C22⋊C4C2311yescharacteristic
406C22×C22⋊C4C2311yescharacteristic
407C22×C22⋊C4C2311yescharacteristic
408C22×C22⋊C4C2311yescharacteristic
409C22×C22⋊C4C2311yescharacteristic
410C22×C22⋊C4C2311yescharacteristic
411C22×C22⋊C4C2311yescharacteristic
412C22×C22⋊C4C2311yescharacteristic
413C22×C22⋊C4C2311yescharacteristic
414C22×C22⋊C4C2311yescharacteristic
415C22×C22⋊C4C2311yescharacteristic
416C22×C42—28no—
417C22×C42C2311yescharacteristic
418C22×C42C2311yescharacteristic
419C22×C42C2311yescharacteristic
420C22×C42C2311yescharacteristic
421C22×C42C2311yescharacteristic
422C22×C42C2311yescharacteristic
423C22×C42C2311yescharacteristic
424C22×C42C2311yescharacteristic
425C22×C42C2311yescharacteristic
426C22×C42C2311yescharacteristic
427C22×C42C2318yescomplemented
428#400C2318yescomplemented
429#399C2318yes—
430#399C2318yescomplemented
431#398C2318yescomplemented
432#398C2318yescomplemented
433#398C2318yescomplemented
434#397C2318yes—
435#397C2318yes—
436#397C2318yes—
437#396C2318yes—
438#395C2318yescomplemented
439#395C2318yescomplemented
440#394C2318yes—
441#394C2318yes—
442#394C2318yes—
443#394C2318yes—
444#394C2318yes—
445#394C2318yes—
446#394C2318yes—
447#394C2318yes—
448#394C2318yescomplemented
449#394C2318yescomplemented
450#394C2318yescomplemented
451#394C2318yescomplemented
452#394C2318yescomplemented
453#394C2318yescomplemented
454#394C2318yescomplemented
455#394C2318yescomplemented
456#393C2318yes—
457#393C2318yes—
458#393C2318yes—
459#393C2318yescomplemented
460#392C2318yes—
461#392C2318yes—
462#392C2318yes—
463#392C2318yes—
464#392C2318yes—
465#392C2318yes—
466#392C2318yes—
467#392C2318yes—
468#391C2318yescomplemented
469#391C2318yescomplemented
470#390C2318yes—
471#390C2318yes—
472#390C2318yes—
473#390C2318yes—
474#390C2318yescomplemented
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2318yes—
480#388C2318yes—
481#388C2318yes—
482#388C2318yes—
483#388C2318yes—
484#388C2318yescomplemented
485#388C2318yescomplemented
486#388C2318yescomplemented
487#388C2318yescomplemented
488#388C2318yescomplemented
489#388C2318yescomplemented
490#388C2318yescomplemented
491#387C2318yescomplemented
492#387C2318yescomplemented
493#387C2318yescomplemented
494#387C2318yescomplemented
495#387C2318yescomplemented
496#387C2318yescomplemented
497#387C2318yescomplemented
498#387C2318yescomplemented
499#387C2318yescomplemented
500#386C2318yes—
501#386C2318yes—
502#386C2318yes—
503#386C2318yes—
504#386C2318yes—
505#386C2318yes—
506#386C2318yes—
507#386C2318yes—
508#386C2318yes—
509#386C2318yes—
510#386C2318yes—
511#386C2318yes—
512#386C2318yes—
513#386C2318yes—
514#386C2318yes—
515#386C2318yescomplemented
516#386C2318yescomplemented
517#386C2318yescomplemented
518#385C2318yes—
519#385C2318yes—
520#385C2318yes—
521#385C2318yescomplemented
522#385C2318yescomplemented
523#385C2318yescomplemented
524#385C2318yescomplemented
525#385C2318yescomplemented
526#381C2318yes—
527#381C2318yescomplemented
528#381C2318yescomplemented
529#381C2318yescomplemented
530#380C2318yes—
531#380C2318yescomplemented
532#380C2318yescomplemented
533#379C2318yes—
534C4×C4⋊C4C2318yescomplemented
535C4×C4⋊C4C2318yescomplemented
536C4×C22⋊C4C2318yes—
537C4×C22⋊C4C2318yes—
538C4×C22⋊C4C2318yes—
539C4×C22⋊C4C2318yescomplemented
540C4×C22⋊C4C2318yescomplemented
541C4×C22⋊C4C2318yescomplemented
542C2×#95C2311yescharacteristic
543C2×#95C2311yescharacteristic
544C2×#95C2311yescharacteristic
545C2×#95C2311yescharacteristic
546C2×#95C2311yescharacteristic
547C2×#95C2311yescharacteristic
548C2×#95C2311yescharacteristic
549C2×#95C2311yescharacteristic
550C2×#95C2311yescharacteristic
551C2×#95C2311yescharacteristic
552C2×#95C2311yescharacteristic
553C2×#95C2311yescharacteristic
554C2×#95C2311yescharacteristic
555C2×#95C2311yescharacteristic
556C2×#95C2311yescharacteristic
557C2×#95C2311yescharacteristic
558C2×#95C2311yescharacteristic
559C2×#95C2311yescharacteristic
560C2×#95C2311yescharacteristic
561C2×#95C2311yescharacteristic
562C2×#95C2311yescharacteristic
563C2×#95C2311yescharacteristic
564C2×#95C2311yescharacteristic
565C2×#95C2311yescharacteristic
566C2×#95C2311yescharacteristic
567C2×#95C2311yescharacteristic
568C2×#95C2311yescharacteristic
569C2×#95C2311yescharacteristic
570C2×#95C2311yescharacteristic
571C2×#95C2311yescharacteristic
572C2×#95C2311yescharacteristic
573C2×#95C2311yescharacteristic
574C2×#95C2311yescharacteristic
575C2×#95C2311yescharacteristic
576C2×#95C2318yescomplemented
577C25—24no—
578C25—24no—
579C25—42no—
580C25—42no—
581C25—42no—
582C25—42no—
583C25—42no—
584C25C2411yescharacteristic
585C25C2411yescharacteristic
586C25C2411yescharacteristic
587C25C2411yescharacteristic
588C25C2411yescharacteristic
589C25C2411yescharacteristic
590C25C2411yescharacteristic
591C25C2414yes—
592C2×#41—232no—
593C2×#41—232no—
594C2×#41—416no—
595C2×#41—416no—
596C2×#41—416no—
597C2×#41—416no—
598C2×#41—464no—
599C2×#41—464no—
600C22×Q8—24no—
601C22×Q8—24no—
602C22×Q8—24no—
603C22×Q8—24no—
604C22×Q8—24no—
605C22×Q8—42no—
606C22×Q8—42no—
607C22×Q8—42no—
608C22×Q8—42no—
609C22×Q8C2414yes—
610C22×Q8C2414yes—
611C22×Q8C2414yes—
612C22×D4—24no—
613C22×D4—24no—
614C22×D4—24no—
615C22×D4—24no—
616C22×D4—24no—
617C22×D4—24no—
618C22×D4—24no—
619C22×D4—24no—
620C22×D4—24no—
621C22×D4—24no—
622C22×D4—24no—
623C22×D4—24no—
624C22×D4—24no—
625C22×D4—24no—
626C22×D4—24no—
627C22×D4—24no—
628C22×D4—24no—
629C22×D4—24no—
630C22×D4—24no—
631C22×D4—24no—
632C22×D4—42no—
633C22×D4—42no—
634C22×D4—42no—
635C22×D4—42no—
636C22×D4—42no—
637C22×D4—42no—
638C22×D4—42no—
639C22×D4—42no—
640C22×D4—42no—
641C22×D4—42no—
642C22×D4—42no—
643C22×D4—42no—
644C22×D4—42no—
645C22×D4—42no—
646C22×D4—42no—
647C22×D4—42no—
648C22×D4—42no—
649C22×D4—42no—
650C22×D4—42no—
651C22×D4—42no—
652C22×D4—42no—
653C22×D4—42no—
654C22×D4—42no—
655C22×D4—42no—
656C22×D4—42no—
657C22×D4—42no—
658C22×D4—42no—
659C22×D4—42no—
660C22×D4—42no—
661C22×D4—42no—
662C22×D4—42no—
663C22×D4C2×D418yes—
664C22×D4C2×D418yes—
665C22×D4C2×D418yes—
666C22×D4C2414yes—
667C22×D4C2414yes—
668C22×D4C2414yes—
669C22×D4C2414yes—
670C22×D4C2414yes—
671C22×D4C2414yes—
672C22×D4C2414yes—
673C22×D4C2414yes—
674C22×D4C2414yes—
675C22×D4C2414yes—
676C22×D4C2414yes—
677C22×D4C2414yes—
678C22×D4C2414yes—
679C22×D4C2414yes—
680C22×D4C2414yes—
681C22×D4C2414yes—
682C22×D4C2414yes—
683C22×D4C2414yes—
684C23×C4—24no—
685C23×C4—24no—
686C23×C4—24no—
687C23×C4—24no—
688C23×C4—24no—
689C23×C4—24no—
690C23×C4—24no—
691C23×C4—24no—
692C23×C4—24no—
693C23×C4—24no—
694C23×C4—24no—
695C23×C4—24no—
696C23×C4—24no—
697C23×C4—24no—
698C23×C4—24no—
699C23×C4—24no—
700C23×C4—24no—
701C23×C4—42no—
702C23×C4—42no—
703C23×C4—42no—
704C23×C4—42no—
705C23×C4—42no—
706C23×C4—42no—
707C23×C4—42no—
708C23×C4—42no—
709C23×C4—42no—
710C23×C4—42no—
711C23×C4—42no—
712C23×C4—42no—
713C23×C4—42no—
714C23×C4—42no—
715C23×C4—42no—
716C23×C4—42no—
717C23×C4—42no—
718C23×C4—42no—
719C23×C4C2×D418yes—
720C23×C4C2414yes—
721C23×C4C2411yescharacteristic
722C23×C4C2411yescharacteristic
723C23×C4C2411yescharacteristic
724C23×C4C2411yescharacteristic
725C23×C4C2411yescharacteristic
726C23×C4C2411yescharacteristic
727C23×C4C2411yescharacteristic
728C23×C4C2411yescharacteristic
729C23×C4C2411yescharacteristic
730C23×C4C2411yescharacteristic
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2411yescharacteristic
734C23×C4C2411yescharacteristic
735C23×C4C2411yescharacteristic
736C23×C4C2411yescharacteristic
737C23×C4C2414yes—
738C23×C4C2414yes—
739C23×C4C2414yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2411yescharacteristic
743C23×C4C2411yescharacteristic
744C23×C4C2411yescharacteristic
745C23×C4C2411yescharacteristic
746C23×C4C2411yescharacteristic
747C23×C4C2411yescharacteristic
748C23×C4C2411yescharacteristic
749C23×C4C2411yescharacteristic
750C23×C4C2414yes—
751C23×C4C2414yes—
752C23×C4C2414yes—
753C23×C4C2414yes—
754C23×C4C2414yes—
755C23×C4C2414yes—
756C4⋊Q8—232no—
757C4⋊Q8—416no—
758#127—232no—
759#126—232no—
760#126—232no—
761#124—232no—
762#124—232no—
763#124—232no—
764#124—232no—
765#123—232no—
766#123—232no—
767#123—232no—
768#123—416no—
769C22⋊Q8—232no—
770C22⋊Q8—416no—
771C22⋊Q8—416no—
772#121—232no—
773#121—232no—
774#121—232no—
775#121—232no—
776#121—232no—
777#121—232no—
778#121—416no—
779#121C2×D4164yescomplemented
780#120—232no—
781#120—232no—
782#120—232no—
783#120—416no—
784C4×D4—232no—
785C4×D4—232no—
786C4×D4—232no—
787C4×D4—232no—
788C4×D4—232no—
789C4×D4—232no—
790C4×D4—416no—
791C2×C4⋊C4—24no—
792C2×C4⋊C4—24no—
793C2×C4⋊C4—24no—
794C2×C4⋊C4—24no—
795C2×C4⋊C4—24no—
796C2×C4⋊C4—24no—
797C2×C4⋊C4—24no—
798C2×C4⋊C4—24no—
799C2×C4⋊C4—24no—
800C2×C4⋊C4—24no—
801C2×C4⋊C4—24no—
802C2×C4⋊C4—24no—
803C2×C4⋊C4—24no—
804C2×C4⋊C4—24no—
805C2×C4⋊C4—24no—
806C2×C4⋊C4—42no—
807C2×C4⋊C4—42no—
808C2×C4⋊C4—42no—
809C2×C4⋊C4—42no—
810C2×C4⋊C4—42no—
811C2×C4⋊C4—42no—
812C2×C4⋊C4—42no—
813C2×C4⋊C4C2×D418yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C22⋊C4—24no—
838C2×C22⋊C4—24no—
839C2×C22⋊C4—24no—
840C2×C22⋊C4—24no—
841C2×C22⋊C4—24no—
842C2×C22⋊C4—24no—
843C2×C22⋊C4—24no—
844C2×C22⋊C4—24no—
845C2×C22⋊C4—24no—
846C2×C22⋊C4—24no—
847C2×C22⋊C4—24no—
848C2×C22⋊C4—24no—
849C2×C22⋊C4—24no—
850C2×C22⋊C4—24no—
851C2×C22⋊C4—24no—
852C2×C22⋊C4—24no—
853C2×C22⋊C4—24no—
854C2×C22⋊C4—24no—
855C2×C22⋊C4—24no—
856C2×C22⋊C4—24no—
857C2×C22⋊C4—24no—
858C2×C22⋊C4—24no—
859C2×C22⋊C4—24no—
860C2×C22⋊C4—24no—
861C2×C22⋊C4—24no—
862C2×C22⋊C4—24no—
863C2×C22⋊C4—24no—
864C2×C22⋊C4—232no—
865C2×C22⋊C4—416no—
866C2×C22⋊C4—42no—
867C2×C22⋊C4—42no—
868C2×C22⋊C4—42no—
869C2×C22⋊C4—42no—
870C2×C22⋊C4—42no—
871C2×C22⋊C4—42no—
872C2×C22⋊C4—42no—
873C2×C22⋊C4—42no—
874C2×C22⋊C4—42no—
875C2×C22⋊C4—42no—
876C2×C22⋊C4—42no—
877C2×C22⋊C4—42no—
878C2×C22⋊C4—42no—
879C2×C22⋊C4—42no—
880C2×C22⋊C4—42no—
881C2×C22⋊C4—42no—
882C2×C22⋊C4—42no—
883C2×C22⋊C4—42no—
884C2×C22⋊C4—42no—
885C2×C22⋊C4—42no—
886C2×C22⋊C4—42no—
887C2×C22⋊C4—42no—
888C2×C22⋊C4—42no—
889C2×C22⋊C4—42no—
890C2×C22⋊C4C2×D418yes—
891C2×C22⋊C4C2×D418yes—
892C2×C22⋊C4#4118yescomplemented
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C42—24no—
948C2×C42—24no—
949C2×C42—24no—
950C2×C42—24no—
951C2×C42—24no—
952C2×C42—24no—
953C2×C42—232no—
954C2×C42—42no—
955C2×C42—42no—
956C2×C42—42no—
957C2×C42—42no—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2414yes—
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2414yes—
966C2×C42C2414yes—
967C2×C42C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002C24—22no—
1003C24—22no—
1004C24—22no—
1005C24—22no—
1006C24—22no—
1007C24—22no—
1008C24—22no—
1009C24—22no—
1010C24—22no—
1011C24—22no—
1012C24—22no—
1013C24—22no—
1014C24—22no—
1015C24—22no—
1016C24—22no—
1017C24—22no—
1018C24—22no—
1019C24—22no—
1020C24—22no—
1021C24—22no—
1022C24—22no—
1023C24—22no—
1024C24—22no—
1025C24—22no—
1026C24—22no—
1027C24—22no—
1028C24—22no—
1029C24—22no—
1030C24—22no—
1031C24—22no—
1032C24—22no—
1033C24—22no—
1034C24—22no—
1035C24—22no—
1036C24—22no—
1037C24—22no—
1038C24—22no—
1039C24—22no—
1040C24—22no—
1041C24—22no—
1042C24—22no—
1043C24—22no—
1044C24—22no—
1045C24—22no—
1046C24—22no—
1047C24—28no—
1048C24—28no—
1049C24—44no—
1050C24—44no—
1051C24—44no—
1052C24—44no—
1053C24—44no—
1054C24—416no—
1055C24—416no—
1056C24—88no—
1057C24—88no—
1058C24—88no—
1059C24—88no—
1060C24—88no—
1061C24C22×D414yes—
1062C24C22×D414yes—
1063C24C22×D414yes—
1064C24C2×#4114yes—
1065C24C2512yes—
1066C24C2512yes—
1067C24C2512yes—
1068C24C2512yes—
1069C24C2512yes—
1070C24C2512yes—
1071C24C2512yes—
1072C24C2511yescharacteristic
1073#41—4128no—
1074#41—4128no—
1075C2×Q8—28no—
1076C2×Q8—28no—
1077C2×Q8—28no—
1078C2×Q8—28no—
1079C2×Q8—28no—
1080C2×Q8—44no—
1081C2×Q8—44no—
1082C2×Q8—44no—
1083C2×Q8—44no—
1084C2×Q8—416no—
1085C2×Q8—416no—
1086C2×Q8—88no—
1087C2×D4—28no—
1088C2×D4—28no—
1089C2×D4—28no—
1090C2×D4—28no—
1091C2×D4—28no—
1092C2×D4—28no—
1093C2×D4—28no—
1094C2×D4—28no—
1095C2×D4—28no—
1096C2×D4—28no—
1097C2×D4—28no—
1098C2×D4—28no—
1099C2×D4—28no—
1100C2×D4—28no—
1101C2×D4—28no—
1102C2×D4—28no—
1103C2×D4—28no—
1104C2×D4—28no—
1105C2×D4—28no—
1106C2×D4—28no—
1107C2×D4—44no—
1108C2×D4—416no—
1109C2×D4—416no—
1110C2×D4—416no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C2×D4—44no—
1118C2×D4—44no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—44no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—44no—
1128C2×D4—44no—
1129C2×D4—44no—
1130C2×D4—416no—
1131C2×D4—416no—
1132C2×D4—416no—
1133C2×D4—416no—
1134C2×D4—416no—
1135C2×D4—44no—
1136C2×D4—44no—
1137C2×D4—44no—
1138C2×D4—44no—
1139C2×D4—44no—
1140C2×D4—44no—
1141C2×D4—44no—
1142C2×D4—44no—
1143C2×D4—44no—
1144C2×D4—44no—
1145C2×D4—44no—
1146C2×D4—416no—
1147C2×D4—416no—
1148C2×D4—416no—
1149C2×D4—416no—
1150C2×D4—416no—
1151C2×D4—88no—
1152C2×D4—88no—
1153C2×D4—88no—
1154C2×D4—88no—
1155C2×D4—88no—
1156C2×D4C22×D4116yes—
1157C2×D4C22×D4116yes—
1158C2×D4C22×D4116yes—
1159C22×C4—232no—
1160C22×C4—22no—
1161C22×C4—22no—
1162C22×C4—22no—
1163C22×C4—28no—
1164C22×C4—22no—
1165C22×C4—22no—
1166C22×C4—22no—
1167C22×C4—22no—
1168C22×C4—22no—
1169C22×C4—22no—
1170C22×C4—22no—
1171C22×C4—22no—
1172C22×C4—22no—
1173C22×C4—22no—
1174C22×C4—22no—
1175C22×C4—22no—
1176C22×C4—22no—
1177C22×C4—28no—
1178C22×C4—28no—
1179C22×C4—22no—
1180C22×C4—28no—
1181C22×C4—22no—
1182C22×C4—22no—
1183C22×C4—22no—
1184C22×C4—22no—
1185C22×C4—22no—
1186C22×C4—22no—
1187C22×C4—22no—
1188C22×C4—22no—
1189C22×C4—28no—
1190C22×C4—28no—
1191C22×C4—22no—
1192C22×C4—22no—
1193C22×C4—22no—
1194C22×C4—22no—
1195C22×C4—22no—
1196C22×C4—22no—
1197C22×C4—22no—
1198C22×C4—22no—
1199C22×C4—22no—
1200C22×C4—22no—
1201C22×C4—22no—
1202C22×C4—22no—
1203C22×C4—22no—
1204C22×C4—22no—
1205C22×C4—22no—
1206C22×C4—22no—
1207C22×C4—22no—
1208C22×C4—22no—
1209C22×C4—22no—
1210C22×C4—22no—
1211C22×C4—22no—
1212C22×C4—22no—
1213C22×C4—22no—
1214C22×C4—22no—
1215C22×C4—22no—
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—22no—
1219C22×C4—22no—
1220C22×C4—22no—
1221C22×C4—22no—
1222C22×C4—22no—
1223C22×C4—22no—
1224C22×C4—22no—
1225C22×C4—22no—
1226C22×C4—22no—
1227C22×C4—22no—
1228C22×C4—22no—
1229C22×C4—22no—
1230C22×C4—28no—
1231C22×C4—28no—
1232C22×C4—28no—
1233C22×C4—28no—
1234C22×C4—28no—
1235C22×C4—28no—
1236C22×C4—28no—
1237C22×C4—28no—
1238C22×C4—28no—
1239C22×C4—28no—
1240C22×C4—28no—
1241C22×C4—416no—
1242C22×C4—44no—
1243C22×C4—44no—
1244C22×C4—44no—
1245C22×C4—44no—
1246C22×C4—44no—
1247C22×C4—44no—
1248C22×C4—44no—
1249C22×C4—416no—
1250C22×C4—416no—
1251C22×C4—44no—
1252C22×C4—44no—
1253C22×C4—44no—
1254C22×C4—44no—
1255C22×C4—44no—
1256C22×C4—44no—
1257C22×C4—44no—
1258C22×C4—44no—
1259C22×C4—44no—
1260C22×C4—44no—
1261C22×C4—44no—
1262C22×C4—416no—
1263C22×C4—416no—
1264C22×C4—416no—
1265C22×C4—88no—
1266C22×C4—88no—
1267C22×C4—88no—
1268C22×C4—88no—
1269C22×C4—88no—
1270C22×C4C22×D414yes—
1271C22×C4C22×D414yes—
1272C22×C4C22×D414yes—
1273C22×C4C22×D414yes—
1274C22×C4C22×D4116yes—
1275C22×C4C2×#4114yes—
1276C22×C4C2×#4114yes—
1277C22×C4H(5,𝔽2)14yes—
1278C22×C4H(5,𝔽2)14yes—
1279C22×C4C2512yes—
1280C22×C4C2512yes—
1281C22×C4C2512yes—
1282C22×C4C2512yes—
1283C22×C4C2512yes—
1284C22×C4C2512yes—
1285C22×C4C2512yes—
1286C22×C4C2512yes—
1287C22×C4C2512yes—
1288C22×C4C2512yes—
1289C22×C4C2512yes—
1290C22×C4C2512yes—
1291C22×C4C2512yes—
1292C22×C4C2512yes—
1293C22×C4C2512yes—
1294C22×C4C2512yes—
1295C22×C4C2512yes—
1296C22×C4C2512yes—
1297C22×C4C2512yes—
1298C22×C4C2512yes—
1299C22×C4C2512yes—
1300C22×C4C2512yes—
1301C22×C4C2512yes—
1302C22×C4C2512yes—
1303C4⋊C4—28no—
1304C4⋊C4—28no—
1305C4⋊C4—28no—
1306C4⋊C4—28no—
1307C4⋊C4—28no—
1308C4⋊C4—28no—
1309C4⋊C4—28no—
1310C4⋊C4—28no—
1311C4⋊C4—28no—
1312C4⋊C4—28no—
1313C4⋊C4—28no—
1314C4⋊C4—28no—
1315C4⋊C4—28no—
1316C4⋊C4—28no—
1317C4⋊C4—28no—
1318C4⋊C4—44no—
1319C4⋊C4—44no—
1320C4⋊C4—44no—
1321C4⋊C4—44no—
1322C4⋊C4—44no—
1323C4⋊C4—44no—
1324C4⋊C4—44no—
1325C4⋊C4C22×D4116yes—
1326C22⋊C4—28no—
1327C22⋊C4—28no—
1328C22⋊C4—28no—
1329C22⋊C4—28no—
1330C22⋊C4—28no—
1331C22⋊C4—28no—
1332C22⋊C4—28no—
1333C22⋊C4—28no—
1334C22⋊C4—28no—
1335C22⋊C4—28no—
1336C22⋊C4—28no—
1337C22⋊C4—28no—
1338C22⋊C4—28no—
1339C22⋊C4—28no—
1340C22⋊C4—28no—
1341C22⋊C4—28no—
1342C22⋊C4—28no—
1343C22⋊C4—28no—
1344C22⋊C4—28no—
1345C22⋊C4—28no—
1346C22⋊C4—28no—
1347C22⋊C4—28no—
1348C22⋊C4—28no—
1349C22⋊C4—28no—
1350C22⋊C4—28no—
1351C22⋊C4—28no—
1352C22⋊C4—28no—
1353C22⋊C4—44no—
1354C22⋊C4—44no—
1355C22⋊C4—44no—
1356C22⋊C4—44no—
1357C22⋊C4—44no—
1358C22⋊C4—44no—
1359C22⋊C4—44no—
1360C22⋊C4—44no—
1361C22⋊C4—44no—
1362C22⋊C4—44no—
1363C22⋊C4—44no—
1364C22⋊C4—44no—
1365C22⋊C4—44no—
1366C22⋊C4—44no—
1367C22⋊C4—44no—
1368C22⋊C4—44no—
1369C22⋊C4—44no—
1370C22⋊C4—44no—
1371C22⋊C4—44no—
1372C22⋊C4—44no—
1373C22⋊C4—44no—
1374C22⋊C4—44no—
1375C22⋊C4—44no—
1376C22⋊C4—44no—
1377C22⋊C4C22×D4116yes—
1378C22⋊C4C22×D4116yes—
1379C22⋊C4C2×#41116yescomplemented
1380C42—28no—
1381C42—28no—
1382C42—28no—
1383C42—28no—
1384C42—28no—
1385C42—28no—
1386C42—44no—
1387C42—44no—
1388C42—44no—
1389C42—44no—
1390C23—22no—
1391C23—22no—
1392C23—22no—
1393C23—22no—
1394C23—22no—
1395C23—22no—
1396C23—22no—
1397C23—22no—
1398C23—22no—
1399C23—22no—
1400C23—22no—
1401C23—22no—
1402C23—22no—
1403C23—22no—
1404C23—22no—
1405C23—22no—
1406C23—22no—
1407C23—22no—
1408C23—22no—
1409C23—22no—
1410C23—22no—
1411C23—22no—
1412C23—22no—
1413C23—22no—
1414C23—28no—
1415C23—28no—
1416C23—28no—
1417C23—28no—
1418C23—28no—
1419C23—28no—
1420C23—28no—
1421C23—28no—
1422C23—28no—
1423C23—28no—
1424C23—28no—
1425C23—28no—
1426C23—22no—
1427C23—22no—
1428C23—22no—
1429C23—22no—
1430C23—22no—
1431C23—22no—
1432C23—22no—
1433C23—22no—
1434C23—22no—
1435C23—22no—
1436C23—22no—
1437C23—22no—
1438C23—22no—
1439C23—22no—
1440C23—22no—
1441C23—22no—
1442C23—22no—
1443C23—22no—
1444C23—22no—
1445C23—22no—
1446C23—22no—
1447C23—416no—
1448C23—416no—
1449C23—44no—
1450C23—44no—
1451C23—44no—
1452C23—44no—
1453C23—44no—
1454C23—44no—
1455C23—44no—
1456C23—44no—
1457C23—44no—
1458C23—44no—
1459C23—44no—
1460C23—44no—
1461C23—44no—
1462C23—44no—
1463C23—44no—
1464C23—44no—
1465C23—44no—
1466C23—44no—
1467C23—44no—
1468C23—44no—
1469C23—44no—
1470C23—44no—
1471C23—44no—
1472C23—44no—
1473C23—44no—
1474C23—44no—
1475C23—44no—
1476C23—44no—
1477C23—44no—
1478C23—44no—
1479C23—44no—
1480C23—44no—
1481C23—44no—
1482C23—44no—
1483C23—44no—
1484C23—44no—
1485C23—44no—
1486C23—88no—
1487C23—88no—
1488C23—88no—
1489C23—88no—
1490C23—88no—
1491C23—864no—
1492C23C23×D414yes—
1493C23C23×D414yes—
1494C23C23×D414yes—
1495C23C23×D412yes—
1496C23C22×#4114yes—
1497C23C22×#4112yes—
1498C23C2×H(5,𝔽2)12yes—
1499C23C2×H(5,𝔽2)12yes—
1500C23#58512yes—
1501C23#58512yes—
1502C23#58512yes—
1503C23C2611yescharacteristic
1504Q8—416no—
1505Q8—416no—
1506Q8—88no—
1507D4—416no—
1508D4—416no—
1509D4—416no—
1510D4—416no—
1511D4—416no—
1512D4—416no—
1513D4—416no—
1514D4—416no—
1515D4—416no—
1516D4—416no—
1517D4—416no—
1518D4—416no—
1519D4—416no—
1520D4—88no—
1521D4—88no—
1522D4—88no—
1523D4—88no—
1524D4—88no—
1525C2×C4—232no—
1526C2×C4—22no—
1527C2×C4—22no—
1528C2×C4—22no—
1529C2×C4—22no—
1530C2×C4—22no—
1531C2×C4—22no—
1532C2×C4—22no—
1533C2×C4—22no—
1534C2×C4—22no—
1535C2×C4—22no—
1536C2×C4—22no—
1537C2×C4—22no—
1538C2×C4—22no—
1539C2×C4—22no—
1540C2×C4—22no—
1541C2×C4—22no—
1542C2×C4—28no—
1543C2×C4—28no—
1544C2×C4—28no—
1545C2×C4—28no—
1546C2×C4—28no—
1547C2×C4—28no—
1548C2×C4—28no—
1549C2×C4—28no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—22no—
1554C2×C4—22no—
1555C2×C4—22no—
1556C2×C4—22no—
1557C2×C4—22no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—22no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—22no—
1572C2×C4—22no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—416no—
1599C2×C4—416no—
1600C2×C4—416no—
1601C2×C4—416no—
1602C2×C4—416no—
1603C2×C4—416no—
1604C2×C4—44no—
1605C2×C4—44no—
1606C2×C4—44no—
1607C2×C4—44no—
1608C2×C4—44no—
1609C2×C4—44no—
1610C2×C4—44no—
1611C2×C4—44no—
1612C2×C4—44no—
1613C2×C4—44no—
1614C2×C4—44no—
1615C2×C4—44no—
1616C2×C4—44no—
1617C2×C4—44no—
1618C2×C4—44no—
1619C2×C4—44no—
1620C2×C4—88no—
1621C2×C4—88no—
1622C2×C4—88no—
1623C2×C4—88no—
1624C2×C4—88no—
1625C2×C4C23×D414yes—
1626C2×C4C23×D414yes—
1627C2×C4C23×D414yes—
1628C2×C4C23×D414yes—
1629C2×C4C22×#4114yes—
1630C2×C4C22×#4114yes—
1631C2×C4C2×H(5,𝔽2)14yes—
1632C2×C4C2×H(5,𝔽2)14yes—
1633C22—24no—
1634C22—24no—
1635C22—24no—
1636C22—24no—
1637C22—24no—
1638C22—24no—
1639C22—24no—
1640C22—24no—
1641C22—24no—
1642C22—24no—
1643C22—24no—
1644C22—24no—
1645C22—42no—
1646C22—42no—
1647C22—42no—
1648C22—42no—
1649C22—42no—
1650C22—42no—
1651C22—42no—
1652C22—42no—
1653C22—42no—
1654C22—42no—
1655C22—42no—
1656C22—42no—
1657C22—42no—
1658C22—416no—
1659C22—416no—
1660C22—416no—
1661C22—416no—
1662C22—42no—
1663C22—42no—
1664C22—42no—
1665C22—42no—
1666C22—42no—
1667C22—42no—
1668C22—42no—
1669C22—42no—
1670C22—42no—
1671C22—42no—
1672C22—42no—
1673C22—42no—
1674C22—42no—
1675C22—42no—
1676C22—42no—
1677C22—42no—
1678C22—42no—
1679C22—42no—
1680C22—42no—
1681C22—42no—
1682C22—42no—
1683C22—42no—
1684C22—42no—
1685C22—42no—
1686C22—832no—
1687C22—88no—
1688C22—88no—
1689C22—88no—
1690C22#346014yes—
1691C22D4×#4114yes—
1692C22#348414yes—
1693C22#348514yes—
1694C22#351414yes—
1695C22#355114yes—
1696C22#356214yes—
1697C22C24×D411yescharacteristic
1698C22C23×#4111yescharacteristic
1699C22C22×H(5,𝔽2)11yescharacteristic
1700C22C22×H(5,𝔽2)11yescharacteristic
1701C22C2×#58511yescharacteristic
1702C22C2×#58511yescharacteristic
1703C22C2×#58511yescharacteristic
1704C4—24no—
1705C4—24no—
1706C4—24no—
1707C4—24no—
1708C4—24no—
1709C4—24no—
1710C4—24no—
1711C4—24no—
1712C4—42no—
1713C4—42no—
1714C4—42no—
1715C4—42no—
1716C4—42no—
1717C4—42no—
1718C4—42no—
1719C4—42no—
1720C4—42no—
1721C4—42no—
1722C4—42no—
1723C4—42no—
1724C4—42no—
1725C4—42no—
1726C4—42no—
1727C4—42no—
1728C2—44no—
1729C2—44no—
1730C2—44no—
1731C2—44no—
1732C2—82no—
1733C2—82no—
1734C2—82no—
1735C2#3782018yesdirect product factor
1736C2C2×#346011yescharacteristic
1737C2C2×D4×#4111yescharacteristic
1738C2C2×#355111yescharacteristic
1739C2C2×#356211yescharacteristic
1740C2C2×#348411yescharacteristic
1741C2C2×#348511yescharacteristic
1742C2C2×#351411yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#538C2semidirect
2. C22×#532C2semidirect
3. C2×#2716C2semidirect
4. C2×#2709C2semidirect
5. C2×#2699C2semidirect
6. C2×#2686C2semidirect
7. C2×#2678C2semidirect
8. C2×#2677C2semidirect
9. C2×#2671C2semidirect
10. C2×#2669C2semidirect
11. #37820C2direct (N × H)
12. C2×#2853C2semidirect
13. C2×#2491C2semidirect
14. C2×#2521C2semidirect
15. C2×#2430C2semidirect
16. C2×#2404C2semidirect
17. C2×#2432C2semidirect
18. C2×#2407C2semidirect
19. C2×#2468C2semidirect
20. C2×#2461C2semidirect
21. C2×#2419C2semidirect
22. C2×#2467C2semidirect
23. C2×#2459C2semidirect
24. C2×#2472C2semidirect
25. C2×#2463C2semidirect
26. C2×#2418C2semidirect
27. C2×#2661C2semidirect
28. C2×#2635C2semidirect
29. C2×#2364C2semidirect
30. C2×#2358C2semidirect
31. C2×#2333C2semidirect
32. C2×C4×#123C2semidirect
34. C23×#41C22semidirect
36. C2×#538C22semidirect
38. C2×#532C22semidirect
39. C22×C4⋊Q8C22semidirect
40. C22×C4⋊Q8C22semidirect
47. C22×#124C22semidirect
54. C22×C22⋊Q8C22semidirect
61. C22×#121C22semidirect
62. C22×#121C22semidirect
72. C22×C4×D4C22semidirect
73. C22×C4×D4C22semidirect
76. C23×C42C22semidirect
77. #2853C22semidirect
78. #2716C22semidirect
79. #2709C22semidirect
80. #2699C22semidirect
81. #2686C22semidirect
82. #2678C22semidirect
83. #2677C22semidirect
84. #2671C22semidirect
85. #2669C22semidirect
86. #2661C22semidirect
87. #2635C22semidirect
88. #2521C22semidirect
89. #2491C22semidirect
90. #2472C22semidirect
91. #2468C22semidirect
92. #2467C22semidirect
93. #2463C22semidirect
94. #2461C22semidirect
95. #2459C22semidirect
96. #2432C22semidirect
97. #2430C22semidirect
98. #2419C22semidirect
99. #2418C22semidirect
100. #2407C22semidirect
101. #2404C22semidirect
102. C2×#400C22semidirect
104. C2×#399C22semidirect
105. C2×#398C22semidirect
106. C2×#398C22semidirect
107. C2×#398C22semidirect
112. C2×#395C22semidirect
113. C2×#395C22semidirect
122. C2×#394C22semidirect
123. C2×#394C22semidirect
124. C2×#394C22semidirect
125. C2×#394C22semidirect
126. C2×#394C22semidirect
127. C2×#394C22semidirect
128. C2×#394C22semidirect
129. C2×#394C22semidirect
133. C2×#393C22semidirect
142. #2364C22semidirect
143. #2358C22semidirect
144. #2333C22semidirect
145. C4×#123C22semidirect
146. C2×#391C22semidirect
147. C2×#391C22semidirect
152. C2×#390C22semidirect
162. C2×#388C22semidirect
163. C2×#388C22semidirect
164. C2×#388C22semidirect
165. C2×#388C22semidirect
166. C2×#388C22semidirect
167. C2×#388C22semidirect
168. C2×#388C22semidirect
169. C2×#387C22semidirect
170. C2×#387C22semidirect
171. C2×#387C22semidirect
172. C2×#387C22semidirect
173. C2×#387C22semidirect
174. C2×#387C22semidirect
175. C2×#387C22semidirect
176. C2×#387C22semidirect
177. C2×#387C22semidirect
193. C2×#386C22semidirect
194. C2×#386C22semidirect
195. C2×#386C22semidirect
199. C2×#385C22semidirect
200. C2×#385C22semidirect
201. C2×#385C22semidirect
202. C2×#385C22semidirect
203. C2×#385C22semidirect
205. C2×#381C22semidirect
206. C2×#381C22semidirect
207. C2×#381C22semidirect
209. C2×#380C22semidirect
210. C2×#380C22semidirect
212. C2×C4×C4⋊C4C22semidirect
213. C2×C4×C4⋊C4C22semidirect
217. C2×C4×C22⋊C4C22semidirect
218. C2×C4×C22⋊C4C22semidirect
219. C2×C4×C22⋊C4C22semidirect
220. C22×#95C22semidirect
229. C22×#41C23semidirect
267. C2×C4⋊Q8C23semidirect
268. C2×C4⋊Q8C23semidirect
282. C2×#124C23semidirect
296. C2×C22⋊Q8C23semidirect
304. C2×#121D4semidirect
311. C2×#121C23semidirect
312. C2×#121C23semidirect
333. C2×C4×D4C23semidirect
334. C2×C4×D4C23semidirect
427. C22×C42C23semidirect
428. #400C23semidirect
430. #399C23semidirect
431. #398C23semidirect
432. #398C23semidirect
433. #398C23semidirect
438. #395C23semidirect
439. #395C23semidirect
448. #394C23semidirect
449. #394C23semidirect
450. #394C23semidirect
451. #394C23semidirect
452. #394C23semidirect
453. #394C23semidirect
454. #394C23semidirect
455. #394C23semidirect
459. #393C23semidirect
468. #391C23semidirect
469. #391C23semidirect
474. #390C23semidirect
484. #388C23semidirect
485. #388C23semidirect
486. #388C23semidirect
487. #388C23semidirect
488. #388C23semidirect
489. #388C23semidirect
490. #388C23semidirect
491. #387C23semidirect
492. #387C23semidirect
493. #387C23semidirect
494. #387C23semidirect
495. #387C23semidirect
496. #387C23semidirect
497. #387C23semidirect
498. #387C23semidirect
499. #387C23semidirect
515. #386C23semidirect
516. #386C23semidirect
517. #386C23semidirect
521. #385C23semidirect
522. #385C23semidirect
523. #385C23semidirect
524. #385C23semidirect
525. #385C23semidirect
527. #381C23semidirect
528. #381C23semidirect
529. #381C23semidirect
531. #380C23semidirect
532. #380C23semidirect
534. C4×C4⋊C4C23semidirect
535. C4×C4⋊C4C23semidirect
539. C4×C22⋊C4C23semidirect
540. C4×C22⋊C4C23semidirect
541. C4×C22⋊C4C23semidirect
576. C2×#95C23semidirect
779. #121C2×D4semidirect
892. C2×C22⋊C4#41semidirect
1379. C22⋊C4C2×#41semidirect
1735. C2#37820direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#5382
C22×#5322
C2×#27162
C2×#27092
C2×#26992
C2×#26862
C2×#26782
C2×#26772
C2×#26712
C2×#26692
#378202
C2×#28532
C2×#24912
C2×#25212
C2×#24302
C2×#24042
C2×#24322
C2×#24072
C2×#24682
C2×#24612
C2×#24192
C2×#24672
C2×#24592
C2×#24722
C2×#24632
C2×#24182
C2×#26612
C2×#26352
C2×#23642
C2×#23582
C2×#23332
C2×C4×#1232