Finite Group Databasebeta

← C2×#46946 #7700749

Subgroups — C2×#46946 #7700749

Order 512.

4888 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2793C211yesmaximal, characteristic, complemented
2C2×#2790C211yesmaximal, characteristic, complemented
3C2×#2790C211yesmaximal, characteristic, complemented
4C2×#2786C211yesmaximal, characteristic
5C2×#2783C211yesmaximal, characteristic, complemented
6C2×#2770C211yesmaximal, characteristic, complemented
7C2×#2764C211yesmaximal, characteristic, complemented
8C2×#2725C211yesmaximal, characteristic, complemented
9C2×#2719C211yesmaximal, characteristic, complemented
10C2×#2719C211yesmaximal, characteristic, complemented
11C2×#2719C211yesmaximal, characteristic, complemented
12C2×#2704C211yesmaximal, characteristic, complemented
13#46946C2132yesmaximal, direct product factor
14C2×#2831C211yesmaximal, characteristic, complemented
15C2×#2552C211yesmaximal, characteristic, complemented
16C2×#2566C211yesmaximal, characteristic
17C2×#2573C211yesmaximal, characteristic, complemented
18C2×#2573C211yesmaximal, characteristic, complemented
19C2×#2588C211yesmaximal, characteristic, complemented
20C2×#2560C211yesmaximal, characteristic
21C2×#2558C211yesmaximal, characteristic
22C2×#2558C211yesmaximal, characteristic
23C2×#2515C211yesmaximal, characteristic, complemented
24C2×#2524C211yesmaximal, characteristic, complemented
25C2×#2511C211yesmaximal, characteristic, complemented
26C2×#2497C211yesmaximal, characteristic, complemented
27C2×#2505C211yesmaximal, characteristic, complemented
28C2×#2419C211yesmaximal, characteristic
29C2×#2460C211yesmaximal, characteristic
30C2×#2336C211yesmaximal, characteristic, complemented
31C2×#2334C211yesmaximal, characteristic, complemented
32C2×#2329C211yesmaximal, characteristic, complemented
33C22×#126C2211yescharacteristic
34C22×#125C2211yescharacteristic
35C22×#125C2211yescharacteristic
36C22×#125C2211yescharacteristic
37C22×#125C2211yescharacteristic
38C22×#125C2211yescharacteristic
39C22×#123C2211yescharacteristic
40C22×C22⋊Q8C2211yescharacteristic
41C22×C4×D4C2211yescharacteristic
42#2831C22116yescomplemented
43#2793C22116yescomplemented
44#2790C22116yescomplemented
45#2790C22116yescomplemented
46#2786C22116yes—
47#2783C22116yescomplemented
48#2770C22116yescomplemented
49#2764C22116yescomplemented
50#2725C22116yescomplemented
51#2719C22116yescomplemented
52#2719C22116yescomplemented
53#2719C22116yescomplemented
54#2704C22116yescomplemented
55#2588C22116yescomplemented
56#2573C22116yescomplemented
57#2573C22116yescomplemented
58#2566C22116yes—
59#2560C22116yes—
60#2558C22116yes—
61#2558C22116yes—
62#2552C22116yescomplemented
63#2524C22116yescomplemented
64#2515C22116yescomplemented
65#2511C22116yescomplemented
66#2505C22116yescomplemented
67#2497C22116yescomplemented
68#2460C22116yes—
69#2419C22116yes—
70C2×#400C2211yescharacteristic
71C2×#400C2211yescharacteristic
72C2×#400C2211yescharacteristic
73C2×#400C2211yescharacteristic
74C2×#400C2211yescharacteristic
75C2×#400C2211yescharacteristic
76C2×#400C2211yescharacteristic
77C2×#400C2211yescharacteristic
78C2×#400C2211yescharacteristic
79C2×#400C2211yescharacteristic
80C2×#400C2211yescharacteristic
81C2×#400C2211yescharacteristic
82C2×#400C2211yescharacteristic
83C2×#400C2211yescharacteristic
84C2×#398C2211yescharacteristic
85C2×#398C2211yescharacteristic
86C2×#398C2211yescharacteristic
87C2×#398C2211yescharacteristic
88C2×#398C2211yescharacteristic
89C2×#398C2211yescharacteristic
90C2×#398C2211yescharacteristic
91C2×#398C2211yescharacteristic
92C2×#398C2211yescharacteristic
93C2×#398C2211yescharacteristic
94C2×#398C2211yescharacteristic
95C2×#398C2211yescharacteristic
96C2×#398C2211yescharacteristic
97C2×#397C2211yescharacteristic
98C2×#397C2211yescharacteristic
99C2×#397C2211yescharacteristic
100C2×#397C2211yescharacteristic
101C2×#397C2211yescharacteristic
102C2×#397C2211yescharacteristic
103C2×#397C2211yescharacteristic
104C2×#396C2211yescharacteristic
105C2×#396C2211yescharacteristic
106C2×#396C2211yescharacteristic
107C2×#396C2211yescharacteristic
108C2×#396C2211yescharacteristic
109C2×#396C2211yescharacteristic
110C2×#396C2211yescharacteristic
111C2×#396C2211yescharacteristic
112C2×#396C2211yescharacteristic
113C2×#396C2211yescharacteristic
114C2×#395C2211yescharacteristic
115C2×#394C2211yescharacteristic
116C2×#394C2211yescharacteristic
117C2×#393C2211yescharacteristic
118#2336C22116yescomplemented
119#2334C22116yescomplemented
120#2329C22116yescomplemented
121C2×#391C2211yescharacteristic
122C2×#391C2211yescharacteristic
123C2×#391C2211yescharacteristic
124C2×#391C2211yescharacteristic
125C2×#390C2211yescharacteristic
126C2×#390C2211yescharacteristic
127C2×#389C2211yescharacteristic
128C2×#389C2211yescharacteristic
129C2×#389C2211yescharacteristic
130C2×#389C2211yescharacteristic
131C2×#389C2211yescharacteristic
132C2×#389C2211yescharacteristic
133C2×#389C2211yescharacteristic
134C2×#389C2211yescharacteristic
135C2×#389C2211yescharacteristic
136C2×#389C2211yescharacteristic
137C2×#389C2211yescharacteristic
138C2×#389C2211yescharacteristic
139C2×#388C2211yescharacteristic
140C2×#388C2211yescharacteristic
141C2×#388C2211yescharacteristic
142C2×#388C2211yescharacteristic
143C2×#388C2211yescharacteristic
144C2×#388C2211yescharacteristic
145C2×#388C2211yescharacteristic
146C2×#388C2211yescharacteristic
147C2×#388C2211yescharacteristic
148C2×#388C2211yescharacteristic
149C2×#388C2211yescharacteristic
150C2×#388C2211yescharacteristic
151C2×#388C2211yescharacteristic
152C2×#388C2211yescharacteristic
153C2×#388C2211yescharacteristic
154C2×#387C2211yescharacteristic
155C2×#387C2211yescharacteristic
156C2×#387C2211yescharacteristic
157C2×#387C2211yescharacteristic
158C2×#387C2211yescharacteristic
159C2×#387C2211yescharacteristic
160C2×#387C2211yescharacteristic
161C2×#387C2211yescharacteristic
162C2×#387C2211yescharacteristic
163C2×#387C2211yescharacteristic
164C2×#387C2211yescharacteristic
165C2×#387C2211yescharacteristic
166C2×#387C2211yescharacteristic
167C2×#387C2211yescharacteristic
168C2×#387C2211yescharacteristic
169C2×#387C2211yescharacteristic
170C2×#387C2211yescharacteristic
171C2×#387C2211yescharacteristic
172C2×#387C2211yescharacteristic
173C2×#387C2211yescharacteristic
174C2×#387C2211yescharacteristic
175C2×#387C2211yescharacteristic
176C2×#387C2211yescharacteristic
177C2×#387C2211yescharacteristic
178C2×#387C2211yescharacteristic
179C2×#387C2211yescharacteristic
180C2×#387C2211yescharacteristic
181C2×#386C2211yescharacteristic
182C2×#385C2211yescharacteristic
183C2×#385C2211yescharacteristic
184C2×#385C2211yescharacteristic
185C2×#385C2211yescharacteristic
186C2×#385C2211yescharacteristic
187C2×#385C2211yescharacteristic
188C2×#385C2211yescharacteristic
189C2×#385C2211yescharacteristic
190C2×#385C2211yescharacteristic
191C2×#385C2211yescharacteristic
192C2×#385C2211yescharacteristic
193C2×#384C2211yescharacteristic
194C2×#384C2211yescharacteristic
195C2×#384C2211yescharacteristic
196C2×#383C2211yescharacteristic
197C2×#383C2211yescharacteristic
198C2×#383C2211yescharacteristic
199C2×#382C2211yescharacteristic
200C2×#382C2211yescharacteristic
201C2×#382C2211yescharacteristic
202C2×#381C2211yescharacteristic
203C2×#381C2211yescharacteristic
204C2×#380C2211yescharacteristic
205C2×#380C2211yescharacteristic
206C2×#380C2211yescharacteristic
207C2×C4×C4⋊C4C2211yescharacteristic
208C2×C4×C4⋊C4C2211yescharacteristic
209C2×C4×C4⋊C4C2211yescharacteristic
210C2×C4×C4⋊C4C2211yescharacteristic
211C2×C4×C4⋊C4C2211yescharacteristic
212C2×C4×C4⋊C4C2211yescharacteristic
213C2×C4×C4⋊C4C2211yescharacteristic
214C2×C4×C22⋊C4C2211yescharacteristic
215C2×C4×C22⋊C4C2211yescharacteristic
216C2×C4×C22⋊C4C2211yescharacteristic
217C2×C4×C22⋊C4C2211yescharacteristic
218C22×#95C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C23×D4C2311yescharacteristic
221C24×C4C2311yescharacteristic
222C24×C4C2311yescharacteristic
223C24×C4C2311yescharacteristic
224C24×C4C2311yescharacteristic
225C2×#126—28no—
226C2×#126C2318yes—
227C2×#125—28no—
228C2×#125—44no—
229C2×#125—44no—
230C2×#125—44no—
231C2×#125—44no—
232C2×#125C2318yes—
233C2×#125C2318yes—
234C2×#125C2318yes—
235C2×#125C2318yes—
236C2×#125C2318yes—
237C2×#123—44no—
238C2×#123C2318yes—
239C2×C22⋊Q8—28no—
240C2×C22⋊Q8C2318yes—
241C2×C4×D4—44no—
242C2×C4×D4C2318yes—
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C22⋊C4C2311yescharacteristic
294C22×C22⋊C4C2311yescharacteristic
295C22×C22⋊C4C2311yescharacteristic
296C22×C22⋊C4C2311yescharacteristic
297C22×C22⋊C4C2311yescharacteristic
298C22×C22⋊C4C2311yescharacteristic
299C22×C22⋊C4C2311yescharacteristic
300C22×C22⋊C4C2311yescharacteristic
301C22×C22⋊C4C2311yescharacteristic
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2311yescharacteristic
304C22×C22⋊C4C2311yescharacteristic
305C22×C22⋊C4C2311yescharacteristic
306C22×C22⋊C4C2311yescharacteristic
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2311yescharacteristic
309C22×C22⋊C4C2311yescharacteristic
310C22×C22⋊C4C2311yescharacteristic
311C22×C22⋊C4C2311yescharacteristic
312C22×C22⋊C4C2311yescharacteristic
313C22×C22⋊C4C2311yescharacteristic
314C22×C22⋊C4C2311yescharacteristic
315C22×C22⋊C4C2311yescharacteristic
316C22×C22⋊C4C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322C22×C42C2311yescharacteristic
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325C22×C42C2311yescharacteristic
326C22×C42C2311yescharacteristic
327C22×C42C2311yescharacteristic
328C22×C42C2311yescharacteristic
329C22×C42C2311yescharacteristic
330C22×C42C2311yescharacteristic
331C22×C42C2311yescharacteristic
332#400C2318yes—
333#400C2318yes—
334#400C2318yes—
335#400C2318yes—
336#400C2318yes—
337#400C2318yes—
338#400C2318yes—
339#400C2318yes—
340#400C2318yes—
341#400C2318yes—
342#400C2318yes—
343#400C2318yes—
344#400C2318yes—
345#400C2318yes—
346#398C2318yes—
347#398C2318yes—
348#398C2318yes—
349#398C2318yes—
350#398C2318yes—
351#398C2318yes—
352#398C2318yes—
353#398C2318yes—
354#398C2318yes—
355#398C2318yes—
356#398C2318yes—
357#398C2318yes—
358#398C2318yes—
359#397C2318yes—
360#397C2318yes—
361#397C2318yes—
362#397C2318yes—
363#397C2318yes—
364#397C2318yes—
365#397C2318yes—
366#396C2318yes—
367#396C2318yes—
368#396C2318yes—
369#396C2318yes—
370#396C2318yes—
371#396C2318yes—
372#396C2318yes—
373#396C2318yes—
374#396C2318yes—
375#396C2318yes—
376#395C2318yes—
377#394C2318yes—
378#394C2318yes—
379#393C2318yes—
380#391C2318yes—
381#391C2318yes—
382#391C2318yes—
383#391C2318yes—
384#390C2318yes—
385#390C2318yes—
386#389C2318yes—
387#389C2318yes—
388#389C2318yes—
389#389C2318yes—
390#389C2318yes—
391#389C2318yes—
392#389C2318yes—
393#389C2318yes—
394#389C2318yes—
395#389C2318yes—
396#389C2318yes—
397#389C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#386C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#384C2318yes—
453#384C2318yes—
454#384C2318yes—
455#383C2318yes—
456#383C2318yes—
457#383C2318yes—
458#382C2318yes—
459#382C2318yes—
460#382C2318yes—
461#381C2318yes—
462#381C2318yes—
463#380C2318yes—
464#380C2318yes—
465#380C2318yes—
466C4×C4⋊C4C2318yes—
467C4×C4⋊C4C2318yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2318yes—
473C4×C22⋊C4C2318yes—
474C4×C22⋊C4C2318yes—
475C4×C22⋊C4C2318yes—
476C4×C22⋊C4C2318yes—
477C2×#95C2318yes—
478C2×#95C2311yescharacteristic
479C2×#95C2311yescharacteristic
480C2×#95C2311yescharacteristic
481C2×#95C2311yescharacteristic
482C2×#95C2311yescharacteristic
483C2×#95C2311yescharacteristic
484C2×#95C2311yescharacteristic
485C2×#95C2311yescharacteristic
486C2×#95C2311yescharacteristic
487C2×#95C2311yescharacteristic
488C2×#95C2311yescharacteristic
489C2×#95C2311yescharacteristic
490C2×#95C2311yescharacteristic
491C2×#95C2311yescharacteristic
492C2×#95C2311yescharacteristic
493C2×#95C2311yescharacteristic
494C2×#95C2311yescharacteristic
495C2×#95C2311yescharacteristic
496C2×#95C2311yescharacteristic
497C2×#95C2311yescharacteristic
498C2×#95C2311yescharacteristic
499C2×#95C2311yescharacteristic
500C2×#95C2311yescharacteristic
501C2×#95C2311yescharacteristic
502C2×#95C2311yescharacteristic
503C2×#95C2311yescharacteristic
504C2×#95C2311yescharacteristic
505C2×#95C2311yescharacteristic
506C2×#95C2311yescharacteristic
507C2×#95C2311yescharacteristic
508C2×#95C2311yescharacteristic
509C2×#95C2311yescharacteristic
510C2×#95C2311yescharacteristic
511C2×#95C2311yescharacteristic
512C2×#95C2311yescharacteristic
513C2×#95C2311yescharacteristic
514C2×#95C2311yescharacteristic
515C2×#95C2311yescharacteristic
516C2×#95C2311yescharacteristic
517C2×#95C2311yescharacteristic
518C2×#95C2311yescharacteristic
519C2×#95C2311yescharacteristic
520C2×#95C2311yescharacteristic
521C2×#95C2311yescharacteristic
522C2×#95C2311yescharacteristic
523C2×#95C2311yescharacteristic
524C2×#95C2311yescharacteristic
525C2×#95C2311yescharacteristic
526C2×#95C2311yescharacteristic
527C2×#95C2311yescharacteristic
528C2×#95C2311yescharacteristic
529C2×#95C2311yescharacteristic
530C2×#95C2311yescharacteristic
531C2×#95C2311yescharacteristic
532C2×#95C2311yescharacteristic
533C2×#95C2311yescharacteristic
534C2×#95C2311yescharacteristic
535C2×#95C2311yescharacteristic
536C2×#95C2311yescharacteristic
537C2×#95C2311yescharacteristic
538C25C2411yescharacteristic
539C25C2411yescharacteristic
540C22×Q8—24no—
541C22×Q8—42no—
542C22×Q8—42no—
543C22×Q8C2414yes—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—42no—
547C22×D4C2414yes—
548C23×C4—24no—
549C23×C4—24no—
550C23×C4—42no—
551C23×C4—42no—
552C23×C4—42no—
553C23×C4—42no—
554C23×C4—42no—
555C23×C4—42no—
556C23×C4—42no—
557C23×C4—42no—
558C23×C4—42no—
559C23×C4—42no—
560C23×C4C2411yescharacteristic
561C23×C4C2411yescharacteristic
562C23×C4C2411yescharacteristic
563C23×C4C2411yescharacteristic
564C23×C4C2411yescharacteristic
565C23×C4C2411yescharacteristic
566C23×C4C2411yescharacteristic
567C23×C4C2411yescharacteristic
568C23×C4C2411yescharacteristic
569C23×C4C2411yescharacteristic
570C23×C4C2411yescharacteristic
571C23×C4C2411yescharacteristic
572C23×C4C2411yescharacteristic
573C23×C4C2411yescharacteristic
574C23×C4C2411yescharacteristic
575C23×C4C2411yescharacteristic
576C23×C4C2411yescharacteristic
577C23×C4C2411yescharacteristic
578C23×C4C2411yescharacteristic
579C23×C4C2411yescharacteristic
580C23×C4C2411yescharacteristic
581C23×C4C2411yescharacteristic
582C23×C4C2411yescharacteristic
583C23×C4C2411yescharacteristic
584C23×C4C2411yescharacteristic
585C23×C4C2411yescharacteristic
586C23×C4C2411yescharacteristic
587C23×C4C2411yescharacteristic
588C23×C4C2411yescharacteristic
589C23×C4C2414yes—
590C23×C4C2414yes—
591C23×C4C2414yes—
592C23×C4C2414yes—
593#126—232no—
594#125—232no—
595#125—416no—
596#125—416no—
597#125—416no—
598#125—416no—
599#123—416no—
600C22⋊Q8—232no—
601C4×D4—416no—
602C2×C4⋊C4—24no—
603C2×C4⋊C4—24no—
604C2×C4⋊C4—24no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—24no—
608C2×C4⋊C4—24no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—24no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—24no—
617C2×C4⋊C4—24no—
618C2×C4⋊C4—24no—
619C2×C4⋊C4—24no—
620C2×C4⋊C4—42no—
621C2×C4⋊C4—42no—
622C2×C4⋊C4—42no—
623C2×C4⋊C4—42no—
624C2×C4⋊C4—42no—
625C2×C4⋊C4—42no—
626C2×C4⋊C4—42no—
627C2×C4⋊C4—42no—
628C2×C4⋊C4—42no—
629C2×C4⋊C4—42no—
630C2×C4⋊C4—42no—
631C2×C4⋊C4—42no—
632C2×C4⋊C4—42no—
633C2×C4⋊C4—42no—
634C2×C4⋊C4—42no—
635C2×C4⋊C4—42no—
636C2×C4⋊C4—42no—
637C2×C4⋊C4—42no—
638C2×C4⋊C4—42no—
639C2×C4⋊C4—42no—
640C2×C4⋊C4—42no—
641C2×C4⋊C4—42no—
642C2×C4⋊C4—42no—
643C2×C4⋊C4—42no—
644C2×C4⋊C4—42no—
645C2×C4⋊C4—42no—
646C2×C4⋊C4—42no—
647C2×C4⋊C4—42no—
648C2×C4⋊C4—42no—
649C2×C4⋊C4—42no—
650C2×C4⋊C4—42no—
651C2×C4⋊C4#4118yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C22⋊C4—24no—
703C2×C22⋊C4—24no—
704C2×C22⋊C4—24no—
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—24no—
708C2×C22⋊C4—24no—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—24no—
711C2×C22⋊C4—24no—
712C2×C22⋊C4—42no—
713C2×C22⋊C4—42no—
714C2×C22⋊C4—42no—
715C2×C22⋊C4—42no—
716C2×C22⋊C4—42no—
717C2×C22⋊C4—42no—
718C2×C22⋊C4—42no—
719C2×C22⋊C4—42no—
720C2×C22⋊C4—42no—
721C2×C22⋊C4—42no—
722C2×C22⋊C4—42no—
723C2×C22⋊C4—42no—
724C2×C22⋊C4—42no—
725C2×C22⋊C4—42no—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C42—24no—
751C2×C42—24no—
752C2×C42—24no—
753C2×C42—24no—
754C2×C42—42no—
755C2×C42—42no—
756C2×C42—42no—
757C2×C42—42no—
758C2×C42—42no—
759C2×C42—42no—
760C2×C42—42no—
761C2×C42—42no—
762C2×C42—42no—
763C2×C42—42no—
764C2×C42—42no—
765C2×C42C2414yes—
766C2×C42C2414yes—
767C2×C42C2414yes—
768C2×C42C2414yes—
769C2×C42C2414yes—
770C2×C42C2414yes—
771C2×C42C2414yes—
772C2×C42C2414yes—
773C2×C42C2414yes—
774C2×C42C2414yes—
775C2×C42C2414yes—
776C2×C42C2414yes—
777C2×C42C2414yes—
778C2×C42C2414yes—
779C2×C42C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840C24—22no—
841C24—22no—
842C24—22no—
843C24—22no—
844C24—22no—
845C24—22no—
846C24—22no—
847C24—22no—
848C24—22no—
849C24—22no—
850C24—22no—
851C24—22no—
852C24—22no—
853C242−1+414yes—
854C24C2512yes—
855C24C2512yes—
856C24C2511yescharacteristic
857C2×Q8—28no—
858C2×Q8—44no—
859C2×Q8—44no—
860C2×Q8—88no—
861C2×D4—28no—
862C2×D4—28no—
863C2×D4—44no—
864C2×D4—416no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—22no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—22no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—22no—
935C22×C4—22no—
936C22×C4—22no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—28no—
948C22×C4—28no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—44no—
953C22×C4—44no—
954C22×C4—44no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—88no—
960C22×C4—88no—
961C22×C4—88no—
962C22×C4—88no—
963C22×C4C2×#4114yes—
964C22×C4C2×#4114yes—
965C22×C4C2×#4114yes—
966C22×C4H(5,𝔽2)14yes—
967C22×C42−1+414yes—
968C22×C4C2512yes—
969C22×C4C2512yes—
970C22×C4C2512yes—
971C22×C4C2512yes—
972C22×C4C2512yes—
973C22×C4C2512yes—
974C22×C4C2512yes—
975C22×C4C2512yes—
976C22×C4C2512yes—
977C22×C4C2512yes—
978C22×C4C2512yes—
979C22×C4C2512yes—
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2512yes—
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2512yes—
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2512yes—
995C22×C4C2512yes—
996C22×C4C2512yes—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4C2×#41116yes—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C42—28no—
1072C42—28no—
1073C42—28no—
1074C42—28no—
1075C42—44no—
1076C42—44no—
1077C42—44no—
1078C42—44no—
1079C42—44no—
1080C42—44no—
1081C42—44no—
1082C42—44no—
1083C42—44no—
1084C42—44no—
1085C42—44no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—28no—
1093C23—28no—
1094C23—28no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—44no—
1103C23—44no—
1104C23—44no—
1105C23—44no—
1106C23—44no—
1107C23—44no—
1108C23—44no—
1109C23—44no—
1110C23—44no—
1111C23—44no—
1112C23—44no—
1113C23C22×#4112yes—
1114C23C2×H(5,𝔽2)12yes—
1115C23C2×2−1+414yes—
1116C23C2×2−1+412yes—
1117C23C2×2−1+412yes—
1118C23#58512yes—
1119C23#58512yes—
1120C23#58512yes—
1121C23C2611yescharacteristic
1122Q8—88no—
1123D4—416no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—28no—
1135C2×C4—28no—
1136C2×C4—28no—
1137C2×C4—28no—
1138C2×C4—28no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—44no—
1212C2×C4—44no—
1213C2×C4—44no—
1214C2×C4—44no—
1215C2×C4—44no—
1216C2×C4—44no—
1217C2×C4—44no—
1218C2×C4—44no—
1219C2×C4—44no—
1220C2×C4—44no—
1221C2×C4—44no—
1222C2×C4—44no—
1223C2×C4—44no—
1224C2×C4—44no—
1225C2×C4—44no—
1226C2×C4—44no—
1227C2×C4—44no—
1228C2×C4—44no—
1229C2×C4—44no—
1230C2×C4—44no—
1231C2×C4—44no—
1232C2×C4—44no—
1233C2×C4—44no—
1234C2×C4—44no—
1235C2×C4—88no—
1236C2×C4—88no—
1237C2×C4—88no—
1238C2×C4—88no—
1239C2×C4C22×#4114yes—
1240C2×C4C22×#4114yes—
1241C2×C4C22×#4114yes—
1242C2×C4C2×H(5,𝔽2)14yes—
1243C2×C4C2×2−1+414yes—
1244C22—24no—
1245C22—24no—
1246C22—24no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—416no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—88no—
1260C22#351114yes—
1261C22#351614yes—
1262C22#352114yes—
1263C22#353514yes—
1264C22#355314yes—
1265C22#356214yes—
1266C22#356314yes—
1267C22C23×#4111yescharacteristic
1268C22C22×H(5,𝔽2)11yescharacteristic
1269C22C22×2−1+411yescharacteristic
1270C22C22×2−1+411yescharacteristic
1271C22C2×#58511yescharacteristic
1272C22C2×#58511yescharacteristic
1273C22C2×#58511yescharacteristic
1274C4—24no—
1275C4—24no—
1276C4—24no—
1277C4—24no—
1278C4—24no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C2—44no—
1304C2—82no—
1305C2#4694618yesdirect product factor
1306C2C2×#353511yescharacteristic
1307C2C2×#356311yescharacteristic
1308C2C2×#356211yescharacteristic
1309C2C2×#355311yescharacteristic
1310C2C2×#352111yescharacteristic
1311C2C2×#351611yescharacteristic
1312C2C2×#351111yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2793C2semidirect
2. C2×#2790C2semidirect
3. C2×#2790C2semidirect
5. C2×#2783C2semidirect
6. C2×#2770C2semidirect
7. C2×#2764C2semidirect
8. C2×#2725C2semidirect
9. C2×#2719C2semidirect
10. C2×#2719C2semidirect
11. C2×#2719C2semidirect
12. C2×#2704C2semidirect
13. #46946C2direct (N × H)
14. C2×#2831C2semidirect
15. C2×#2552C2semidirect
17. C2×#2573C2semidirect
18. C2×#2573C2semidirect
19. C2×#2588C2semidirect
23. C2×#2515C2semidirect
24. C2×#2524C2semidirect
25. C2×#2511C2semidirect
26. C2×#2497C2semidirect
27. C2×#2505C2semidirect
30. C2×#2336C2semidirect
31. C2×#2334C2semidirect
32. C2×#2329C2semidirect
42. #2831C22semidirect
43. #2793C22semidirect
44. #2790C22semidirect
45. #2790C22semidirect
47. #2783C22semidirect
48. #2770C22semidirect
49. #2764C22semidirect
50. #2725C22semidirect
51. #2719C22semidirect
52. #2719C22semidirect
53. #2719C22semidirect
54. #2704C22semidirect
55. #2588C22semidirect
56. #2573C22semidirect
57. #2573C22semidirect
62. #2552C22semidirect
63. #2524C22semidirect
64. #2515C22semidirect
65. #2511C22semidirect
66. #2505C22semidirect
67. #2497C22semidirect
118. #2336C22semidirect
119. #2334C22semidirect
120. #2329C22semidirect
1305. C2#46946direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#27932
C2×#27902
C2×#27862
C2×#27832
C2×#27702
C2×#27642
C2×#27252
C2×#27192
C2×#27042
#469462
C2×#28312
C2×#25522
C2×#25662
C2×#25732
C2×#25882
C2×#25602
C2×#25582
C2×#25152
C2×#25242
C2×#25112
C2×#24972
C2×#25052
C2×#24192
C2×#24602
C2×#23362
C2×#23342
C2×#23292