Finite Group Databasebeta

← #43440

Subgroups — #43440

Order 256.

1058 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2803C211yesmaximal, characteristic, complemented
2#2788C211yesmaximal, characteristic, complemented
3#2753C211yesmaximal, characteristic, complemented
4#2749C211yesmaximal, characteristic, complemented
5#2701C211yesmaximal, characteristic, complemented
6#2688C211yesmaximal, characteristic, complemented
7#2670C211yesmaximal, characteristic, complemented
8#2669C211yesmaximal, characteristic, complemented
9#2593C211yesmaximal, characteristic, complemented
10#2591C211yesmaximal, characteristic, complemented
11#2587C211yesmaximal, characteristic, complemented
12#2557C211yesmaximal, characteristic, complemented
13#2555C211yesmaximal, characteristic, complemented
14#2544C211yesmaximal, characteristic, complemented
15#2534C211yesmaximal, characteristic, complemented
16#2518C211yesmaximal, characteristic, complemented
17#2474C211yesmaximal, characteristic, complemented
18#2464C211yesmaximal, characteristic, complemented
19#2456C211yesmaximal, characteristic, complemented
20#2456C211yesmaximal, characteristic, complemented
21#2428C211yesmaximal, characteristic, complemented
22#2424C211yesmaximal, characteristic, complemented
23#2424C211yesmaximal, characteristic, complemented
24#2414C211yesmaximal, characteristic, complemented
25#2392C211yesmaximal, characteristic, complemented
26#2361C211yesmaximal, characteristic, complemented
27#2361C211yesmaximal, characteristic, complemented
28#2358C211yesmaximal, characteristic, complemented
29#2357C211yesmaximal, characteristic, complemented
30#2337C211yesmaximal, characteristic, complemented
31#2321C211yesmaximal, characteristic, complemented
32C2×#127C2211yescharacteristic
33C2×#124C2211yescharacteristic
34C2×#124C2211yescharacteristic
35C2×#124C2211yescharacteristic, complemented
36C2×#123C2211yescharacteristic
37C2×#123C2211yescharacteristic, complemented
38C2×#121C2211yescharacteristic
39C2×#121C2211yescharacteristic
40C2×#121C2211yescharacteristic
41C2×#121C2211yescharacteristic
42C2×#121C2211yescharacteristic
43C2×#121C2211yescharacteristic
44C2×#121C2211yescharacteristic, complemented
45C2×#121C2211yescharacteristic, complemented
46C2×#120C2211yescharacteristic
47C2×#120C2211yescharacteristic
48C2×#120C2211yescharacteristic
49C2×#120C2211yescharacteristic
50C2×C4×D4C2211yescharacteristic
51C2×C4×D4C2211yescharacteristic
52C2×C4×D4C2211yescharacteristic
53C2×C4×D4C2211yescharacteristic
54C2×C4×D4C2211yescharacteristic
55C2×C4×D4C2211yescharacteristic
56C2×C4×D4C2211yescharacteristic, complemented
57C2×C4×D4C2211yescharacteristic, complemented
58C2×#117C2211yescharacteristic, complemented
59C22×C4⋊C4C2211yescharacteristic, complemented
60C22×C22⋊C4C2211yescharacteristic
61C22×C22⋊C4C2211yescharacteristic
62#400C2211yescharacteristic, complemented
63#400C2211yescharacteristic, complemented
64#400C2211yescharacteristic, complemented
65#398C2211yescharacteristic, complemented
66#398C2211yescharacteristic, complemented
67#397C2211yescharacteristic, complemented
68#397C2211yescharacteristic, complemented
69#397C2211yescharacteristic, complemented
70#397C2211yescharacteristic, complemented
71#396C2211yescharacteristic
72#396C2211yescharacteristic
73#396C2211yescharacteristic
74#396C2211yescharacteristic
75#396C2211yescharacteristic, complemented
76#395C2211yescharacteristic, complemented
77#394C2211yescharacteristic
78#394C2211yescharacteristic
79#394C2211yescharacteristic
80#394C2211yescharacteristic
81#394C2211yescharacteristic
82#394C2211yescharacteristic
83#394C2211yescharacteristic
84#394C2211yescharacteristic
85#394C2211yescharacteristic
86#394C2211yescharacteristic
87#394C2211yescharacteristic, complemented
88#394C2211yescharacteristic, complemented
89#394C2211yescharacteristic, complemented
90#394C2211yescharacteristic, complemented
91#393C2211yescharacteristic
92#392C2211yescharacteristic
93#392C2211yescharacteristic
94#392C2211yescharacteristic
95#392C2211yescharacteristic
96#392C2211yescharacteristic
97#392C2211yescharacteristic
98#392C2211yescharacteristic
99#392C2211yescharacteristic
100#392C2211yescharacteristic
101#392C2211yescharacteristic, complemented
102#391C2211yescharacteristic, complemented
103#391C2211yescharacteristic, complemented
104#390C2211yescharacteristic
105#390C2211yescharacteristic
106#390C2211yescharacteristic
107#390C2211yescharacteristic
108#390C2211yescharacteristic
109#390C2211yescharacteristic
110#390C2211yescharacteristic
111#390C2211yescharacteristic, complemented
112#390C2211yescharacteristic, complemented
113#389C2211yescharacteristic, complemented
114#389C2211yescharacteristic, complemented
115#389C2211yescharacteristic, complemented
116#389C2211yescharacteristic, complemented
117#388C2211yescharacteristic
118#388C2211yescharacteristic
119#388C2211yescharacteristic
120#388C2211yescharacteristic
121#388C2211yescharacteristic
122#388C2211yescharacteristic
123#388C2211yescharacteristic
124#388C2211yescharacteristic
125#388C2211yescharacteristic
126#388C2211yescharacteristic
127#388C2211yescharacteristic
128#388C2211yescharacteristic
129#388C2211yescharacteristic
130#388C2211yescharacteristic
131#388C2211yescharacteristic, complemented
132#388C2211yescharacteristic, complemented
133#388C2211yescharacteristic, complemented
134#388C2211yescharacteristic, complemented
135#388C2211yescharacteristic, complemented
136#388C2211yescharacteristic, complemented
137#388C2211yescharacteristic, complemented
138#388C2211yescharacteristic, complemented
139#388C2211yescharacteristic, complemented
140#388C2211yescharacteristic, complemented
141#387C2211yescharacteristic, complemented
142#387C2211yescharacteristic, complemented
143#387C2211yescharacteristic, complemented
144#386C2211yescharacteristic
145#386C2211yescharacteristic
146#386C2211yescharacteristic
147#386C2211yescharacteristic
148#386C2211yescharacteristic
149#386C2211yescharacteristic
150#386C2211yescharacteristic
151#386C2211yescharacteristic
152#386C2211yescharacteristic
153#386C2211yescharacteristic
154#386C2211yescharacteristic
155#386C2211yescharacteristic
156#386C2211yescharacteristic
157#386C2211yescharacteristic, complemented
158#386C2211yescharacteristic, complemented
159#386C2211yescharacteristic, complemented
160#386C2211yescharacteristic, complemented
161#386C2211yescharacteristic, complemented
162#385C2211yescharacteristic
163#385C2211yescharacteristic
164#385C2211yescharacteristic
165#385C2211yescharacteristic
166#385C2211yescharacteristic
167#385C2211yescharacteristic, complemented
168#385C2211yescharacteristic, complemented
169#385C2211yescharacteristic, complemented
170#383C2211yescharacteristic, complemented
171#382C2211yescharacteristic, complemented
172#381C2211yescharacteristic
173#381C2211yescharacteristic, complemented
174#380C2211yescharacteristic
175#379C2211yescharacteristic
176C4×C4⋊C4C2211yescharacteristic, complemented
177C4×C4⋊C4C2211yescharacteristic, complemented
178C4×C4⋊C4C2211yescharacteristic, complemented
179C4×C4⋊C4C2211yescharacteristic, complemented
180C4×C22⋊C4C2211yescharacteristic
181C4×C22⋊C4C2211yescharacteristic
182C4×C22⋊C4C2211yescharacteristic
183C4×C22⋊C4C2211yescharacteristic, complemented
184C4×C22⋊C4C2211yescharacteristic, complemented
185C4×C22⋊C4C2211yescharacteristic, complemented
186C4×C22⋊C4C2211yescharacteristic, complemented
187C25C2311yescharacteristic
188C22×Q8C2311yescharacteristic
189C22×D4C2311yescharacteristic
190C22×D4C2311yescharacteristic
191C22×D4C2311yescharacteristic
192C22×D4C2311yescharacteristic
193C22×D4C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C22×D4C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C22×D4C2311yescharacteristic
198C22×D4C2311yescharacteristic
199C22×D4C2311yescharacteristic
200C22×D4C2311yescharacteristic
201C22×D4C2311yescharacteristic
202C22×D4C2311yescharacteristic
203C22×D4C2311yescharacteristic
204C22×D4C2311yescharacteristic
205C22×D4C2311yescharacteristic
206C22×D4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208C23×C4C2311yescharacteristic
209C23×C4C2311yescharacteristic
210C23×C4C2311yescharacteristic
211C23×C4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C23×C4C2311yescharacteristic
214C23×C4C2311yescharacteristic
215C23×C4C2311yescharacteristic
216C23×C4C2311yescharacteristic
217#127—42no—
218#124—24no—
219#124—42no—
220#124—42no—
221#123—42no—
222#123—42no—
223#121—24no—
224#121—24no—
225#121—42no—
226#121—42no—
227#121—42no—
228#121—42no—
229#121—42no—
230#121—42no—
231#120—24no—
232#120—24no—
233#120—42no—
234#120—42no—
235C4×D4—24no—
236C4×D4—42no—
237C4×D4—42no—
238C4×D4—42no—
239C4×D4—42no—
240C4×D4—42no—
241C4×D4—42no—
242C4×D4—42no—
243#117—42no—
244C2×C4⋊C4—42no—
245C2×C4⋊C4C2311yescharacteristic
246C2×C4⋊C4C2311yescharacteristic
247C2×C4⋊C4C2311yescharacteristic
248C2×C4⋊C4C2311yescharacteristic
249C2×C4⋊C4C2311yescharacteristic
250C2×C4⋊C4C2311yescharacteristic
251C2×C4⋊C4C2311yescharacteristic
252C2×C4⋊C4C2311yescharacteristic
253C2×C4⋊C4C2311yescharacteristic
254C2×C4⋊C4C2311yescharacteristic
255C2×C4⋊C4C2311yescharacteristic
256C2×C4⋊C4C2311yescharacteristic
257C2×C4⋊C4C2311yescharacteristic
258C2×C4⋊C4C2311yescharacteristic
259C2×C4⋊C4C2311yescharacteristic
260C2×C4⋊C4C2311yescharacteristic
261C2×C4⋊C4C2311yescharacteristic
262C2×C4⋊C4C2311yescharacteristic
263C2×C4⋊C4C2311yescharacteristic
264C2×C4⋊C4C2311yescharacteristic
265C2×C4⋊C4C2311yescharacteristic
266C2×C4⋊C4C2311yescharacteristic
267C2×C4⋊C4C2311yescharacteristic
268C2×C22⋊C4—42no—
269C2×C22⋊C4—42no—
270C2×C22⋊C4C2311yescharacteristic
271C2×C22⋊C4C2311yescharacteristic
272C2×C22⋊C4C2311yescharacteristic
273C2×C22⋊C4C2311yescharacteristic
274C2×C22⋊C4C2311yescharacteristic
275C2×C22⋊C4C2311yescharacteristic
276C2×C22⋊C4C2311yescharacteristic
277C2×C22⋊C4C2311yescharacteristic
278C2×C22⋊C4C2311yescharacteristic
279C2×C22⋊C4C2311yescharacteristic
280C2×C22⋊C4C2311yescharacteristic
281C2×C22⋊C4C2311yescharacteristic
282C2×C22⋊C4C2311yescharacteristic
283C2×C22⋊C4C2311yescharacteristic
284C2×C22⋊C4C2311yescharacteristic
285C2×C22⋊C4C2311yescharacteristic
286C2×C22⋊C4C2311yescharacteristic
287C2×C22⋊C4C2311yescharacteristic
288C2×C22⋊C4C2311yescharacteristic
289C2×C22⋊C4C2311yescharacteristic
290C2×C22⋊C4C2311yescharacteristic
291C2×C22⋊C4C2311yescharacteristic
292C2×C22⋊C4C2311yescharacteristic
293C2×C22⋊C4C2311yescharacteristic
294C2×C22⋊C4C2311yescharacteristic
295C2×C22⋊C4C2311yescharacteristic
296C2×C22⋊C4C2311yescharacteristic
297C2×C22⋊C4C2311yescharacteristic
298C2×C22⋊C4C2311yescharacteristic
299C2×C22⋊C4C2311yescharacteristic
300C2×C22⋊C4C2311yescharacteristic
301C2×C22⋊C4C2311yescharacteristic
302C2×C22⋊C4C2311yescharacteristic
303C2×C22⋊C4C2311yescharacteristic
304C2×C22⋊C4C2311yescharacteristic
305C2×C22⋊C4C2311yescharacteristic
306C2×C22⋊C4C2311yescharacteristic
307C2×C22⋊C4C2311yescharacteristic
308C2×C22⋊C4C2311yescharacteristic
309C2×C22⋊C4C2311yescharacteristic
310C2×C22⋊C4C2311yescharacteristic
311C2×C22⋊C4C2311yescharacteristic
312C2×C22⋊C4C2311yescharacteristic
313C2×C22⋊C4C2311yescharacteristic
314C2×C22⋊C4C2311yescharacteristic
315C2×C22⋊C4C2311yescharacteristic
316C2×C22⋊C4C2311yescharacteristic
317C2×C22⋊C4C2311yescharacteristic
318C2×C22⋊C4C2311yescharacteristic
319C2×C22⋊C4C2311yescharacteristic
320C2×C22⋊C4C2311yescharacteristic
321C2×C22⋊C4C2311yescharacteristic
322C2×C22⋊C4C2311yescharacteristic
323C2×C22⋊C4C2311yescharacteristic
324C2×C22⋊C4C2311yescharacteristic
325C2×C22⋊C4C2311yescharacteristic
326C2×C42C2311yescharacteristic
327C2×C42C2311yescharacteristic
328C2×C42C2311yescharacteristic
329C2×C42C2311yescharacteristic
330C2×C42C2311yescharacteristic
331C2×C42C2311yescharacteristic
332C2×C42C2311yescharacteristic
333C2×C42C2311yescharacteristic
334C2×C42C2311yescharacteristic
335C2×C42C2311yescharacteristic
336C2×C42C2311yescharacteristic
337C2×C42C2311yescharacteristic
338#95C2311yescharacteristic
339#95C2311yescharacteristic
340#95C2311yescharacteristic
341#95C2311yescharacteristic
342#95C2311yescharacteristic
343#95C2311yescharacteristic
344#95C2311yescharacteristic
345#95C2311yescharacteristic
346#95C2311yescharacteristic
347#95C2311yescharacteristic
348#95C2311yescharacteristic
349#95C2311yescharacteristic
350#95C2311yescharacteristic
351#95C2311yescharacteristic
352#95C2311yescharacteristic
353#95C2311yescharacteristic
354#95C2311yescharacteristic
355#95C2311yescharacteristic
356#95C2311yescharacteristic
357#95C2311yescharacteristic
358#95C2311yescharacteristic
359#95C2311yescharacteristic
360#95C2311yescharacteristic
361#95C2311yescharacteristic
362#95C2311yescharacteristic
363#95C2311yescharacteristic
364#95C2311yescharacteristic
365#95C2311yescharacteristic
366#95C2311yescharacteristic
367#95C2311yescharacteristic
368#95C2311yescharacteristic
369#95C2311yescharacteristic
370#95C2311yescharacteristic
371#95C2311yescharacteristic
372C24—22no—
373C24—22no—
374C24—41no—
375C24—41no—
376C24—41no—
377C24—41no—
378C24—41no—
379C24C2411yescharacteristic
380C24C2411yescharacteristic
381C24C2411yescharacteristic
382C24C2411yescharacteristic
383C24C2411yescharacteristic
384C24C2411yescharacteristic
385C24C2411yescharacteristic
386C2×Q8—22no—
387C2×Q8—41no—
388C2×Q8—41no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4C2411yescharacteristic
474C22×C4C2411yescharacteristic
475C22×C4C2411yescharacteristic
476C22×C4C2411yescharacteristic
477C22×C4C2411yescharacteristic
478C22×C4C2411yescharacteristic
479C22×C4C2411yescharacteristic
480C22×C4C2411yescharacteristic
481C22×C4C2411yescharacteristic
482C22×C4C2411yescharacteristic
483C22×C4C2411yescharacteristic
484C22×C4C2411yescharacteristic
485C22×C4C2411yescharacteristic
486C22×C4C2411yescharacteristic
487C22×C4C2411yescharacteristic
488C22×C4C2411yescharacteristic
489C22×C4C2411yescharacteristic
490C22×C4C2411yescharacteristic
491C22×C4C2411yescharacteristic
492C22×C4C2411yescharacteristic
493C22×C4C2411yescharacteristic
494C22×C4C2411yescharacteristic
495C22×C4C2411yescharacteristic
496C22×C4C2411yescharacteristic
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C22⋊C4—41no—
553C22⋊C4—41no—
554C22⋊C4—41no—
555C22⋊C4—41no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—41no—
560C22⋊C4—41no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—41no—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4#4114yes—
575C22⋊C4#4114yes—
576C42—22no—
577C42—22no—
578C42—22no—
579C42—22no—
580C42—41no—
581C42—41no—
582C42—41no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—44no—
635C23—44no—
636C23—82no—
637C23—82no—
638C23—82no—
639C23—82no—
640C23—82no—
641C23C2×#4112yes—
642C23C2×#4112yes—
643C23H(5,𝔽2)12yes—
644C23C2511yescharacteristic
645Q8—82no—
646D4—44no—
647D4—44no—
648D4—44no—
649D4—44no—
650D4—44no—
651D4—44no—
652D4—44no—
653D4—44no—
654D4—82no—
655D4—82no—
656D4—82no—
657D4—82no—
658D4—82no—
659D4—82no—
660D4—82no—
661D4—82no—
662D4—82no—
663D4—82no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4—82no—
736C2×C4—82no—
737C2×C4—82no—
738C2×C4—82no—
739C2×C4C2×#4112yes—
740C2×C4C2×#4112yes—
741C2×C4C2×#4112yes—
742C2×C4C2×#4112yes—
743C2×C4H(5,𝔽2)12yes—
744C2×C4H(5,𝔽2)12yes—
745C2×C4H(5,𝔽2)12yes—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—88no—
796C22C22×#4111yescharacteristic
797C22C22×#4111yescharacteristic
798C22C2×H(5,𝔽2)11yescharacteristic
799C22C2×H(5,𝔽2)11yescharacteristic
800C22C2×H(5,𝔽2)11yescharacteristic
801C22C2×H(5,𝔽2)11yescharacteristic
802C22#58511yescharacteristic
803C4—22no—
804C4—22no—
805C4—22no—
806C4—22no—
807C4—22no—
808C4—22no—
809C4—22no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C2—42no—
828C2—42no—
829C2—42no—
830C2—81no—
831C2—81no—
832C2—81no—
833C2—81no—
834C2#348111yescharacteristic
835C2#349411yescharacteristic
836C2#350611yescharacteristic
837C2#351911yescharacteristic
838C2#351911yescharacteristic
839C2#353711yescharacteristic
840C2#355811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #2803C2semidirect
2. #2788C2semidirect
3. #2753C2semidirect
4. #2749C2semidirect
5. #2701C2semidirect
6. #2688C2semidirect
7. #2670C2semidirect
8. #2669C2semidirect
9. #2593C2semidirect
10. #2591C2semidirect
11. #2587C2semidirect
12. #2557C2semidirect
13. #2555C2semidirect
14. #2544C2semidirect
15. #2534C2semidirect
16. #2518C2semidirect
17. #2474C2semidirect
18. #2464C2semidirect
19. #2456C2semidirect
20. #2456C2semidirect
21. #2428C2semidirect
22. #2424C2semidirect
23. #2424C2semidirect
24. #2414C2semidirect
25. #2392C2semidirect
26. #2361C2semidirect
27. #2361C2semidirect
28. #2358C2semidirect
29. #2357C2semidirect
30. #2337C2semidirect
31. #2321C2semidirect
35. C2×#124C22semidirect
37. C2×#123C22semidirect
44. C2×#121C22semidirect
45. C2×#121C22semidirect
56. C2×C4×D4C22semidirect
57. C2×C4×D4C22semidirect
58. C2×#117C22semidirect
59. C22×C4⋊C4C22semidirect
62. #400C22semidirect
63. #400C22semidirect
64. #400C22semidirect
65. #398C22semidirect
66. #398C22semidirect
67. #397C22semidirect
68. #397C22semidirect
69. #397C22semidirect
70. #397C22semidirect
75. #396C22semidirect
76. #395C22semidirect
87. #394C22semidirect
88. #394C22semidirect
89. #394C22semidirect
90. #394C22semidirect
101. #392C22semidirect
102. #391C22semidirect
103. #391C22semidirect
111. #390C22semidirect
112. #390C22semidirect
113. #389C22semidirect
114. #389C22semidirect
115. #389C22semidirect
116. #389C22semidirect
131. #388C22semidirect
132. #388C22semidirect
133. #388C22semidirect
134. #388C22semidirect
135. #388C22semidirect
136. #388C22semidirect
137. #388C22semidirect
138. #388C22semidirect
139. #388C22semidirect
140. #388C22semidirect
141. #387C22semidirect
142. #387C22semidirect
143. #387C22semidirect
157. #386C22semidirect
158. #386C22semidirect
159. #386C22semidirect
160. #386C22semidirect
161. #386C22semidirect
167. #385C22semidirect
168. #385C22semidirect
169. #385C22semidirect
170. #383C22semidirect
171. #382C22semidirect
173. #381C22semidirect
176. C4×C4⋊C4C22semidirect
177. C4×C4⋊C4C22semidirect
178. C4×C4⋊C4C22semidirect
179. C4×C4⋊C4C22semidirect
183. C4×C22⋊C4C22semidirect
184. C4×C22⋊C4C22semidirect
185. C4×C22⋊C4C22semidirect
186. C4×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#28032
#27882
#27532
#27492
#27012
#26882
#26702
#26692
#25932
#25912
#25872
#25572
#25552
#25442
#25342
#25182
#24742
#24642
#24562
#24282
#24242
#24142
#23922
#23612
#23582
#23572
#23372
#23212