Finite Group Databasebeta

← #55415

Subgroups — #55415

Order 256.

979 conjugacy classes of subgroups.

The subgroup lattice has 827 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2831C211yesmaximal, characteristic, complemented
2#2828C211yesmaximal, characteristic, complemented
3#2812C211yesmaximal, characteristic, complemented
4#2803C211yesmaximal, characteristic, complemented
5#2781C211yesmaximal, characteristic, complemented
6#2753C211yesmaximal, characteristic, complemented
7#2752C211yesmaximal, characteristic, complemented
8#2751C211yesmaximal, characteristic, complemented
9#2750C211yesmaximal, characteristic, complemented
10#2741C211yesmaximal, characteristic, complemented
11#2723C211yesmaximal, characteristic, complemented
12#2714C211yesmaximal, characteristic, complemented
13#2711C211yesmaximal, characteristic, complemented
14#2699C211yesmaximal, characteristic, complemented
15#2694C211yesmaximal, characteristic, complemented
16#2691C211yesmaximal, characteristic, complemented
17#2678C211yesmaximal, characteristic, complemented
18#2678C211yesmaximal, characteristic, complemented
19#2668C211yesmaximal, characteristic, complemented
20#2635C211yesmaximal, characteristic, complemented
21#2635C211yesmaximal, characteristic, complemented
22#2615C211yesmaximal, characteristic, complemented
23#2561C211yesmaximal, characteristic, complemented
24#2464C211yesmaximal, characteristic, complemented
25#2460C211yesmaximal, characteristic, complemented
26#2444C211yesmaximal, characteristic, complemented
27#2430C211yesmaximal, characteristic, complemented
28#2424C211yesmaximal, characteristic, complemented
29#2424C211yesmaximal, characteristic, complemented
30#2419C211yesmaximal, characteristic, complemented
31#2407C211yesmaximal, characteristic, complemented
32C22×#41C2211yescharacteristic, complemented
33C2×#126C2211yescharacteristic, complemented
34C2×#125C2211yescharacteristic, complemented
35C2×#123C2211yescharacteristic
36C2×#123C2211yescharacteristic
37C2×C22⋊Q8C2211yescharacteristic
38C2×#121C2211yescharacteristic
39C2×#121C2211yescharacteristic
40C2×#121C2211yescharacteristic
41C2×#121C2211yescharacteristic
42C2×#121C2211yescharacteristic
43C2×#121C2211yescharacteristic
44C2×#121C2211yescharacteristic
45C2×#121C2211yescharacteristic
46C2×#120C2211yescharacteristic
47C2×#120C2211yescharacteristic
48C2×#120C2211yescharacteristic
49C2×#120C2211yescharacteristic
50C2×C4×D4C2211yescharacteristic
51C2×C4×D4C2211yescharacteristic
52C2×C4×D4C2211yescharacteristic, complemented
53C22×C22⋊C4C2211yescharacteristic
54#400C2211yescharacteristic, complemented
55#400C2211yescharacteristic, complemented
56#400C2211yescharacteristic, complemented
57#400C2211yescharacteristic, complemented
58#400C2211yescharacteristic, complemented
59#399C2211yescharacteristic
60#399C2211yescharacteristic, complemented
61#399C2211yescharacteristic, complemented
62#398C2211yescharacteristic, complemented
63#398C2211yescharacteristic, complemented
64#398C2211yescharacteristic, complemented
65#397C2211yescharacteristic
66#397C2211yescharacteristic
67#397C2211yescharacteristic
68#397C2211yescharacteristic
69#397C2211yescharacteristic
70#397C2211yescharacteristic
71#397C2211yescharacteristic
72#397C2211yescharacteristic
73#397C2211yescharacteristic
74#397C2211yescharacteristic, complemented
75#397C2211yescharacteristic, complemented
76#396C2211yescharacteristic
77#396C2211yescharacteristic
78#396C2211yescharacteristic
79#396C2211yescharacteristic
80#395C2211yescharacteristic, complemented
81#394C2211yescharacteristic
82#394C2211yescharacteristic
83#394C2211yescharacteristic
84#394C2211yescharacteristic
85#394C2211yescharacteristic
86#394C2211yescharacteristic
87#394C2211yescharacteristic
88#394C2211yescharacteristic
89#394C2211yescharacteristic
90#394C2211yescharacteristic
91#394C2211yescharacteristic
92#394C2211yescharacteristic
93#394C2211yescharacteristic
94#394C2211yescharacteristic
95#394C2211yescharacteristic
96#394C2211yescharacteristic
97#394C2211yescharacteristic, complemented
98#394C2211yescharacteristic, complemented
99#394C2211yescharacteristic, complemented
100#394C2211yescharacteristic, complemented
101#394C2211yescharacteristic, complemented
102#393C2211yescharacteristic
103#393C2211yescharacteristic
104#393C2211yescharacteristic, complemented
105#392C2211yescharacteristic
106#392C2211yescharacteristic
107#392C2211yescharacteristic
108#392C2211yescharacteristic
109#392C2211yescharacteristic
110#392C2211yescharacteristic
111#392C2211yescharacteristic
112#392C2211yescharacteristic
113#392C2211yescharacteristic
114#392C2211yescharacteristic
115#392C2211yescharacteristic, complemented
116#392C2211yescharacteristic, complemented
117#392C2211yescharacteristic, complemented
118#391C2211yescharacteristic, complemented
119#390C2211yescharacteristic
120#390C2211yescharacteristic
121#390C2211yescharacteristic
122#390C2211yescharacteristic
123#390C2211yescharacteristic
124#390C2211yescharacteristic
125#390C2211yescharacteristic, complemented
126#390C2211yescharacteristic, complemented
127#389C2211yescharacteristic, complemented
128#388C2211yescharacteristic
129#388C2211yescharacteristic
130#388C2211yescharacteristic
131#388C2211yescharacteristic
132#388C2211yescharacteristic
133#388C2211yescharacteristic
134#388C2211yescharacteristic
135#388C2211yescharacteristic
136#388C2211yescharacteristic, complemented
137#388C2211yescharacteristic, complemented
138#388C2211yescharacteristic, complemented
139#388C2211yescharacteristic, complemented
140#388C2211yescharacteristic, complemented
141#388C2211yescharacteristic, complemented
142#388C2211yescharacteristic, complemented
143#388C2211yescharacteristic, complemented
144#388C2211yescharacteristic, complemented
145#387C2211yescharacteristic, complemented
146#387C2211yescharacteristic, complemented
147#387C2211yescharacteristic, complemented
148#387C2211yescharacteristic, complemented
149#387C2211yescharacteristic, complemented
150#387C2211yescharacteristic, complemented
151#387C2211yescharacteristic, complemented
152#386C2211yescharacteristic
153#386C2211yescharacteristic
154#386C2211yescharacteristic
155#386C2211yescharacteristic
156#386C2211yescharacteristic
157#386C2211yescharacteristic
158#386C2211yescharacteristic
159#386C2211yescharacteristic
160#386C2211yescharacteristic
161#386C2211yescharacteristic
162#386C2211yescharacteristic, complemented
163#386C2211yescharacteristic, complemented
164#386C2211yescharacteristic, complemented
165#386C2211yescharacteristic, complemented
166#385C2211yescharacteristic
167#385C2211yescharacteristic
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#381C2211yescharacteristic, complemented
179#380C2211yescharacteristic, complemented
180#380C2211yescharacteristic, complemented
181#380C2211yescharacteristic, complemented
182#380C2211yescharacteristic, complemented
183#379C2211yescharacteristic
184#379C2211yescharacteristic
185C4×C22⋊C4C2211yescharacteristic
186C2×#95C2211yescharacteristic, complemented
187C25C2311yescharacteristic
188C2×#41—42no—
189C2×#41—42no—
190C2×#41—42no—
191C22×Q8C2311yescharacteristic
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
207C22×D4C2311yescharacteristic
208C22×D4C2311yescharacteristic
209C22×D4C2311yescharacteristic
210C23×C4C2311yescharacteristic
211C23×C4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C23×C4C2311yescharacteristic
214C23×C4C2311yescharacteristic
215C23×C4C2311yescharacteristic
216C23×C4C2311yescharacteristic
217C23×C4C2311yescharacteristic
218#126—42no—
219#125—42no—
220#123—42no—
221#123—42no—
222C22⋊Q8—42no—
223#121—42no—
224#121—42no—
225#121—42no—
226#121—42no—
227#121—42no—
228#121—42no—
229#121—42no—
230#121—42no—
231#120—42no—
232#120—42no—
233#120—42no—
234#120—42no—
235C4×D4—42no—
236C4×D4—42no—
237C4×D4—42no—
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⋊C4C2311yescharacteristic
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×C22⋊C4C2311yescharacteristic
320C2×C22⋊C4C2311yescharacteristic
321C2×C22⋊C4C2311yescharacteristic
322C2×C42C2311yescharacteristic
323C2×C42C2311yescharacteristic
324C2×C42C2311yescharacteristic
325C2×C42C2311yescharacteristic
326C2×C42C2311yescharacteristic
327C2×C42C2311yescharacteristic
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—41no—
368C24—41no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24C2411yescharacteristic
374C24C2411yescharacteristic
375C24C2411yescharacteristic
376C24C2411yescharacteristic
377C24C2411yescharacteristic
378C24C2411yescharacteristic
379C24C2411yescharacteristic
380#41—416no—
381C2×Q8—22no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
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—
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—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
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×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
477C22×C4C2411yescharacteristic
478C22×C4C2411yescharacteristic
479C22×C4C2411yescharacteristic
480C22×C4C2411yescharacteristic
481C22×C4C2411yescharacteristic
482C22×C4C2411yescharacteristic
483C22×C4C2411yescharacteristic
484C22×C4C2411yescharacteristic
485C22×C4C2411yescharacteristic
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
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—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—41no—
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—22no—
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—
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—
569C42—41no—
570C42—41no—
571C42—41no—
572C42—41no—
573C42—41no—
574C42—41no—
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—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—44no—
623C23—82no—
624C23—82no—
625C23—82no—
626C23—82no—
627C23—82no—
628C23—82no—
629C23H(5,𝔽2)12yes—
630C23H(5,𝔽2)12yes—
631C23C2511yescharacteristic
632Q8—44no—
633D4—44no—
634D4—44no—
635D4—44no—
636D4—44no—
637D4—44no—
638D4—44no—
639D4—82no—
640D4—82no—
641D4—82no—
642D4—82no—
643D4—82no—
644D4—82no—
645D4—82no—
646D4—82no—
647D4—82no—
648D4—82no—
649D4—82no—
650D4—82no—
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—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—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4—82no—
728C2×C4—82no—
729C2×C4H(5,𝔽2)12yes—
730C2×C4H(5,𝔽2)12yes—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
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—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—88no—
781C22C2×H(5,𝔽2)11yescharacteristic
782C22C2×H(5,𝔽2)11yescharacteristic
783C22C2×H(5,𝔽2)11yescharacteristic
784C22C2×H(5,𝔽2)11yescharacteristic
785C22#58511yescharacteristic
786C22#58511yescharacteristic
787C22#58511yescharacteristic
788C4—22no—
789C4—22no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C2—42no—
813C2—42no—
814C2—81no—
815C2—81no—
816C2—81no—
817C2—81no—
818C2—81no—
819C2#353211yescharacteristic
820C2#353311yescharacteristic
821C2#353411yescharacteristic
822C2#353911yescharacteristic
823C2#354211yescharacteristic
824C2#355111yescharacteristic
825C2#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. #2831C2semidirect
2. #2828C2semidirect
3. #2812C2semidirect
4. #2803C2semidirect
5. #2781C2semidirect
6. #2753C2semidirect
7. #2752C2semidirect
8. #2751C2semidirect
9. #2750C2semidirect
10. #2741C2semidirect
11. #2723C2semidirect
12. #2714C2semidirect
13. #2711C2semidirect
14. #2699C2semidirect
15. #2694C2semidirect
16. #2691C2semidirect
17. #2678C2semidirect
18. #2678C2semidirect
19. #2668C2semidirect
20. #2635C2semidirect
21. #2635C2semidirect
22. #2615C2semidirect
23. #2561C2semidirect
24. #2464C2semidirect
25. #2460C2semidirect
26. #2444C2semidirect
27. #2430C2semidirect
28. #2424C2semidirect
29. #2424C2semidirect
30. #2419C2semidirect
31. #2407C2semidirect
32. C22×#41C22semidirect
33. C2×#126C22semidirect
34. C2×#125C22semidirect
52. C2×C4×D4C22semidirect
54. #400C22semidirect
55. #400C22semidirect
56. #400C22semidirect
57. #400C22semidirect
58. #400C22semidirect
60. #399C22semidirect
61. #399C22semidirect
62. #398C22semidirect
63. #398C22semidirect
64. #398C22semidirect
74. #397C22semidirect
75. #397C22semidirect
80. #395C22semidirect
97. #394C22semidirect
98. #394C22semidirect
99. #394C22semidirect
100. #394C22semidirect
101. #394C22semidirect
104. #393C22semidirect
115. #392C22semidirect
116. #392C22semidirect
117. #392C22semidirect
118. #391C22semidirect
125. #390C22semidirect
126. #390C22semidirect
127. #389C22semidirect
136. #388C22semidirect
137. #388C22semidirect
138. #388C22semidirect
139. #388C22semidirect
140. #388C22semidirect
141. #388C22semidirect
142. #388C22semidirect
143. #388C22semidirect
144. #388C22semidirect
145. #387C22semidirect
146. #387C22semidirect
147. #387C22semidirect
148. #387C22semidirect
149. #387C22semidirect
150. #387C22semidirect
151. #387C22semidirect
162. #386C22semidirect
163. #386C22semidirect
164. #386C22semidirect
165. #386C22semidirect
168. #385C22semidirect
169. #385C22semidirect
170. #385C22semidirect
171. #385C22semidirect
172. #385C22semidirect
173. #385C22semidirect
174. #382C22semidirect
177. #381C22semidirect
178. #381C22semidirect
179. #380C22semidirect
180. #380C22semidirect
181. #380C22semidirect
182. #380C22semidirect
186. C2×#95C22semidirect

Maximal subgroups

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

subgroupindex
#28312
#28282
#28122
#28032
#27812
#27532
#27522
#27512
#27502
#27412
#27232
#27142
#27112
#26992
#26942
#26912
#26782
#26682
#26352
#26152
#25612
#24642
#24602
#24442
#24302
#24242
#24192
#24072