Finite Group Databasebeta

← #57960

Subgroups — #57960

Order 256.

962 conjugacy classes of subgroups.

The subgroup lattice has 803 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2831C211yesmaximal, characteristic, complemented
2#2826C211yesmaximal, characteristic, complemented
3#2824C211yesmaximal, characteristic, complemented
4#2804C211yesmaximal, characteristic, complemented
5#2796C211yesmaximal, characteristic, complemented
6#2780C211yesmaximal, characteristic, complemented
7#2771C211yesmaximal, characteristic, complemented
8#2750C211yesmaximal, characteristic, complemented
9#2743C211yesmaximal, characteristic, complemented
10#2731C211yesmaximal, characteristic, complemented
11#2706C211yesmaximal, characteristic, complemented
12#2700C211yesmaximal, characteristic, complemented
13#2696C211yesmaximal, characteristic, complemented
14#2693C211yesmaximal, characteristic, complemented
15#2682C211yesmaximal, characteristic, complemented
16#2681C211yesmaximal, characteristic, complemented
17#2672C211yesmaximal, characteristic, complemented
18#2670C211yesmaximal, characteristic, complemented
19#2668C211yesmaximal, characteristic, complemented
20#2635C211yesmaximal, characteristic, complemented
21#2628C211yesmaximal, characteristic, complemented
22#2626C211yesmaximal, characteristic, complemented
23#2488C211yesmaximal, characteristic, complemented
24#2471C211yesmaximal, characteristic, complemented
25#2450C211yesmaximal, characteristic, complemented
26#2432C211yesmaximal, characteristic, complemented
27#2430C211yesmaximal, characteristic, complemented
28#2418C211yesmaximal, characteristic, complemented
29#2412C211yesmaximal, characteristic, complemented
30#2411C211yesmaximal, characteristic, complemented
31#2404C211yesmaximal, characteristic, complemented
32C22×#41C2211yescharacteristic
33C2×C4⋊Q8C2211yescharacteristic, complemented
34C2×#124C2211yescharacteristic
35C2×#124C2211yescharacteristic
36C2×#123C2211yescharacteristic
37C2×#123C2211yescharacteristic
38C2×#123C2211yescharacteristic
39C2×#123C2211yescharacteristic, complemented
40C2×#123C2211yescharacteristic, complemented
41C2×C22⋊Q8C2211yescharacteristic
42C2×C22⋊Q8C2211yescharacteristic, complemented
43C2×C22⋊Q8C2211yescharacteristic, complemented
44C2×#121C2211yescharacteristic
45C2×#121C2211yescharacteristic
46C2×#121C2211yescharacteristic, complemented
47C2×#120C2211yescharacteristic
48C2×#120C2211yescharacteristic
49C2×#120C2211yescharacteristic
50C2×C4×D4C2211yescharacteristic
51C2×#117C2211yescharacteristic
52C22×C22⋊C4C2211yescharacteristic
53C22×C22⋊C4C2211yescharacteristic
54#400C2211yescharacteristic, complemented
55#400C2211yescharacteristic, complemented
56#400C2211yescharacteristic, complemented
57#400C2211yescharacteristic, complemented
58#400C2211yescharacteristic, complemented
59#400C2211yescharacteristic, complemented
60#400C2211yescharacteristic, complemented
61#400C2211yescharacteristic, complemented
62#400C2211yescharacteristic, complemented
63#400C2211yescharacteristic, complemented
64#399C2211yescharacteristic
65#399C2211yescharacteristic
66#399C2211yescharacteristic
67#399C2211yescharacteristic
68#399C2211yescharacteristic, complemented
69#398C2211yescharacteristic, complemented
70#398C2211yescharacteristic, complemented
71#397C2211yescharacteristic
72#397C2211yescharacteristic
73#397C2211yescharacteristic
74#397C2211yescharacteristic
75#397C2211yescharacteristic
76#397C2211yescharacteristic, complemented
77#397C2211yescharacteristic, complemented
78#397C2211yescharacteristic, complemented
79#396C2211yescharacteristic
80#396C2211yescharacteristic
81#396C2211yescharacteristic
82#396C2211yescharacteristic
83#396C2211yescharacteristic
84#396C2211yescharacteristic
85#396C2211yescharacteristic, complemented
86#396C2211yescharacteristic, complemented
87#396C2211yescharacteristic, complemented
88#395C2211yescharacteristic, complemented
89#395C2211yescharacteristic, complemented
90#394C2211yescharacteristic
91#394C2211yescharacteristic
92#394C2211yescharacteristic
93#394C2211yescharacteristic
94#394C2211yescharacteristic
95#394C2211yescharacteristic
96#394C2211yescharacteristic
97#394C2211yescharacteristic
98#394C2211yescharacteristic
99#394C2211yescharacteristic
100#394C2211yescharacteristic, complemented
101#394C2211yescharacteristic, complemented
102#394C2211yescharacteristic, complemented
103#394C2211yescharacteristic, complemented
104#393C2211yescharacteristic
105#393C2211yescharacteristic
106#393C2211yescharacteristic
107#393C2211yescharacteristic
108#393C2211yescharacteristic
109#393C2211yescharacteristic, complemented
110#393C2211yescharacteristic, complemented
111#393C2211yescharacteristic, complemented
112#392C2211yescharacteristic
113#392C2211yescharacteristic
114#392C2211yescharacteristic
115#392C2211yescharacteristic
116#392C2211yescharacteristic
117#392C2211yescharacteristic
118#391C2211yescharacteristic, complemented
119#391C2211yescharacteristic, complemented
120#391C2211yescharacteristic, complemented
121#390C2211yescharacteristic
122#390C2211yescharacteristic
123#390C2211yescharacteristic
124#390C2211yescharacteristic
125#390C2211yescharacteristic, complemented
126#389C2211yescharacteristic, complemented
127#389C2211yescharacteristic, complemented
128#389C2211yescharacteristic, complemented
129#388C2211yescharacteristic
130#388C2211yescharacteristic
131#388C2211yescharacteristic
132#388C2211yescharacteristic
133#388C2211yescharacteristic
134#388C2211yescharacteristic
135#388C2211yescharacteristic, complemented
136#388C2211yescharacteristic, complemented
137#388C2211yescharacteristic, complemented
138#388C2211yescharacteristic, complemented
139#387C2211yescharacteristic, complemented
140#387C2211yescharacteristic, 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
158#386C2211yescharacteristic
159#386C2211yescharacteristic
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#385C2211yescharacteristic, complemented
171#385C2211yescharacteristic, complemented
172#385C2211yescharacteristic, complemented
173#385C2211yescharacteristic, complemented
174#382C2211yescharacteristic, complemented
175#381C2211yescharacteristic
176#381C2211yescharacteristic
177#381C2211yescharacteristic, complemented
178#380C2211yescharacteristic
179#380C2211yescharacteristic
180#380C2211yescharacteristic
181#380C2211yescharacteristic
182#380C2211yescharacteristic, complemented
183#379C2211yescharacteristic
184#379C2211yescharacteristic
185C4×C22⋊C4C2211yescharacteristic, complemented
186C2×#95C2211yescharacteristic, complemented
187C25C2311yescharacteristic
188C2×#41—42no—
189C2×#41—42no—
190C2×#41—42no—
191C22×Q8C2311yescharacteristic
192C22×Q8C2311yescharacteristic
193C22×Q8C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C22×D4C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C22×D4C2311yescharacteristic
198C22×D4C2311yescharacteristic
199C22×D4C2311yescharacteristic
200C22×D4C2311yescharacteristic
201C22×D4C2311yescharacteristic
202C22×D4C2311yescharacteristic
203C22×D4C2311yescharacteristic
204C22×D4C2311yescharacteristic
205C22×D4C2311yescharacteristic
206C23×C4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208C23×C4C2311yescharacteristic
209C23×C4C2311yescharacteristic
210C23×C4C2311yescharacteristic
211C23×C4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C23×C4C2311yescharacteristic
214C23×C4C2311yescharacteristic
215C4⋊Q8—42no—
216#124—42no—
217#124—42no—
218#123—42no—
219#123—42no—
220#123—42no—
221#123—42no—
222#123—42no—
223C22⋊Q8—42no—
224C22⋊Q8—42no—
225C22⋊Q8—42no—
226#121—42no—
227#121—42no—
228#121—42no—
229#120—42no—
230#120—42no—
231#120—42no—
232C4×D4—42no—
233#117—42no—
234C2×C4⋊C4C2311yescharacteristic
235C2×C4⋊C4C2311yescharacteristic
236C2×C4⋊C4C2311yescharacteristic
237C2×C4⋊C4C2311yescharacteristic
238C2×C4⋊C4C2311yescharacteristic
239C2×C4⋊C4C2311yescharacteristic
240C2×C4⋊C4C2311yescharacteristic
241C2×C4⋊C4C2311yescharacteristic
242C2×C4⋊C4C2311yescharacteristic
243C2×C4⋊C4C2311yescharacteristic
244C2×C4⋊C4C2311yescharacteristic
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×C22⋊C4—42no—
264C2×C22⋊C4—42no—
265C2×C22⋊C4C2311yescharacteristic
266C2×C22⋊C4C2311yescharacteristic
267C2×C22⋊C4C2311yescharacteristic
268C2×C22⋊C4C2311yescharacteristic
269C2×C22⋊C4C2311yescharacteristic
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×C42C2311yescharacteristic
320C2×C42C2311yescharacteristic
321C2×C42C2311yescharacteristic
322C2×C42C2311yescharacteristic
323C2×C42C2311yescharacteristic
324#95C2311yescharacteristic
325#95C2311yescharacteristic
326#95C2311yescharacteristic
327#95C2311yescharacteristic
328#95C2311yescharacteristic
329#95C2311yescharacteristic
330#95C2311yescharacteristic
331#95C2311yescharacteristic
332#95C2311yescharacteristic
333#95C2311yescharacteristic
334#95C2311yescharacteristic
335#95C2311yescharacteristic
336#95C2311yescharacteristic
337#95C2311yescharacteristic
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
366C24—22no—
367C24—22no—
368C24—41no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24C2411yescharacteristic
374C24C2411yescharacteristic
375C24C2411yescharacteristic
376C24C2411yescharacteristic
377C24C2411yescharacteristic
378C24C2411yescharacteristic
379#41—416no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8—41no—
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—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
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—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4C2411yescharacteristic
453C22×C4C2411yescharacteristic
454C22×C4C2411yescharacteristic
455C22×C4C2411yescharacteristic
456C22×C4C2411yescharacteristic
457C22×C4C2411yescharacteristic
458C22×C4C2411yescharacteristic
459C22×C4C2411yescharacteristic
460C22×C4C2411yescharacteristic
461C22×C4C2411yescharacteristic
462C22×C4C2411yescharacteristic
463C22×C4C2411yescharacteristic
464C22×C4C2411yescharacteristic
465C22×C4C2411yescharacteristic
466C22×C4C2411yescharacteristic
467C22×C4C2411yescharacteristic
468C22×C4C2411yescharacteristic
469C22×C4C2411yescharacteristic
470C22×C4C2411yescharacteristic
471C22×C4C2411yescharacteristic
472C22×C4C2411yescharacteristic
473C22×C4C2411yescharacteristic
474C22×C4C2411yescharacteristic
475C22×C4C2411yescharacteristic
476C22×C4C2411yescharacteristic
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—41no—
542C22⋊C4—41no—
543C22⋊C4—41no—
544C22⋊C4—41no—
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—
560C42—22no—
561C42—41no—
562C42—41no—
563C42—41no—
564C42—41no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
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—44no—
605C23—44no—
606C23—82no—
607C23—82no—
608C23—82no—
609C23—82no—
610C23—82no—
611C23H(5,𝔽2)12yes—
612C23H(5,𝔽2)12yes—
613C232−1+412yes—
614C23C2511yescharacteristic
615Q8—44no—
616Q8—82no—
617Q8—82no—
618D4—44no—
619D4—44no—
620D4—44no—
621D4—44no—
622D4—82no—
623D4—82no—
624D4—82no—
625D4—82no—
626D4—82no—
627D4—82no—
628D4—82no—
629D4—82no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
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—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—82no—
708C2×C4—82no—
709C2×C4—82no—
710C2×C4—82no—
711C2×C4—82no—
712C2×C4H(5,𝔽2)12yes—
713C2×C4H(5,𝔽2)12yes—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—88no—
757C22C2×H(5,𝔽2)11yescharacteristic
758C22C2×H(5,𝔽2)11yescharacteristic
759C22C2×H(5,𝔽2)11yescharacteristic
760C22C2×H(5,𝔽2)11yescharacteristic
761C22C2×2−1+411yescharacteristic
762C22#58511yescharacteristic
763C22#58511yescharacteristic
764C4—22no—
765C4—22no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C2—42no—
790C2—42no—
791C2—42no—
792C2—81no—
793C2—81no—
794C2—81no—
795C2#353211yescharacteristic
796C2#353511yescharacteristic
797C2#353511yescharacteristic
798C2#353611yescharacteristic
799C2#354211yescharacteristic
800C2#355811yescharacteristic
801C2#356211yescharacteristic
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. #2831C2semidirect
2. #2826C2semidirect
3. #2824C2semidirect
4. #2804C2semidirect
5. #2796C2semidirect
6. #2780C2semidirect
7. #2771C2semidirect
8. #2750C2semidirect
9. #2743C2semidirect
10. #2731C2semidirect
11. #2706C2semidirect
12. #2700C2semidirect
13. #2696C2semidirect
14. #2693C2semidirect
15. #2682C2semidirect
16. #2681C2semidirect
17. #2672C2semidirect
18. #2670C2semidirect
19. #2668C2semidirect
20. #2635C2semidirect
21. #2628C2semidirect
22. #2626C2semidirect
23. #2488C2semidirect
24. #2471C2semidirect
25. #2450C2semidirect
26. #2432C2semidirect
27. #2430C2semidirect
28. #2418C2semidirect
29. #2412C2semidirect
30. #2411C2semidirect
31. #2404C2semidirect
33. C2×C4⋊Q8C22semidirect
39. C2×#123C22semidirect
40. C2×#123C22semidirect
42. C2×C22⋊Q8C22semidirect
43. C2×C22⋊Q8C22semidirect
46. C2×#121C22semidirect
54. #400C22semidirect
55. #400C22semidirect
56. #400C22semidirect
57. #400C22semidirect
58. #400C22semidirect
59. #400C22semidirect
60. #400C22semidirect
61. #400C22semidirect
62. #400C22semidirect
63. #400C22semidirect
68. #399C22semidirect
69. #398C22semidirect
70. #398C22semidirect
76. #397C22semidirect
77. #397C22semidirect
78. #397C22semidirect
85. #396C22semidirect
86. #396C22semidirect
87. #396C22semidirect
88. #395C22semidirect
89. #395C22semidirect
100. #394C22semidirect
101. #394C22semidirect
102. #394C22semidirect
103. #394C22semidirect
109. #393C22semidirect
110. #393C22semidirect
111. #393C22semidirect
118. #391C22semidirect
119. #391C22semidirect
120. #391C22semidirect
125. #390C22semidirect
126. #389C22semidirect
127. #389C22semidirect
128. #389C22semidirect
135. #388C22semidirect
136. #388C22semidirect
137. #388C22semidirect
138. #388C22semidirect
139. #387C22semidirect
140. #387C22semidirect
141. #387C22semidirect
142. #387C22semidirect
143. #387C22semidirect
160. #386C22semidirect
161. #386C22semidirect
167. #385C22semidirect
168. #385C22semidirect
169. #385C22semidirect
170. #385C22semidirect
171. #385C22semidirect
172. #385C22semidirect
173. #385C22semidirect
174. #382C22semidirect
177. #381C22semidirect
182. #380C22semidirect
185. C4×C22⋊C4C22semidirect
186. C2×#95C22semidirect

Maximal subgroups

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

subgroupindex
#28312
#28262
#28242
#28042
#27962
#27802
#27712
#27502
#27432
#27312
#27062
#27002
#26962
#26932
#26822
#26812
#26722
#26702
#26682
#26352
#26282
#26262
#24882
#24712
#24502
#24322
#24302
#24182
#24122
#24112
#24042