Finite Group Databasebeta

← #51964

Subgroups — #51964

Order 256.

1044 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2797C211yesmaximal, characteristic, complemented
2#2782C211yesmaximal, characteristic, complemented
3#2778C211yesmaximal, characteristic, complemented
4#2778C211yesmaximal, characteristic, complemented
5#2750C211yesmaximal, characteristic, complemented
6#2744C211yesmaximal, characteristic, complemented
7#2708C211yesmaximal, characteristic, complemented
8#2688C211yesmaximal, characteristic, complemented
9#2688C211yesmaximal, characteristic, complemented
10#2687C211yesmaximal, characteristic, complemented
11#2673C211yesmaximal, characteristic, complemented
12#2669C211yesmaximal, characteristic, complemented
13#2661C211yesmaximal, characteristic, complemented
14#2648C211yesmaximal, characteristic, complemented
15#2600C211yesmaximal, characteristic, complemented
16#2543C211yesmaximal, characteristic, complemented
17#2531C211yesmaximal, characteristic, complemented
18#2527C211yesmaximal, characteristic, complemented
19#2463C211yesmaximal, characteristic, complemented
20#2450C211yesmaximal, characteristic, complemented
21#2444C211yesmaximal, characteristic, complemented
22#2424C211yesmaximal, characteristic, complemented
23#2424C211yesmaximal, characteristic, complemented
24#2412C211yesmaximal, characteristic, complemented
25#2412C211yesmaximal, characteristic, complemented
26#2407C211yesmaximal, characteristic, complemented
27#2407C211yesmaximal, characteristic, complemented
28#2404C211yesmaximal, characteristic, complemented
29#2377C211yesmaximal, characteristic, complemented
30#2358C211yesmaximal, characteristic, complemented
31#2328C211yesmaximal, characteristic, complemented
32C22×#41C2211yescharacteristic
33C2×#127C2211yescharacteristic
34C2×#123C2211yescharacteristic
35C2×#123C2211yescharacteristic
36C2×C22⋊Q8C2211yescharacteristic, complemented
37C2×C22⋊Q8C2211yescharacteristic, complemented
38C2×#121C2211yescharacteristic
39C2×#121C2211yescharacteristic
40C2×#121C2211yescharacteristic
41C2×#121C2211yescharacteristic
42C2×#121C2211yescharacteristic
43C2×#121C2211yescharacteristic
44C2×#121C2211yescharacteristic, complemented
45C2×#120C2211yescharacteristic
46C2×#120C2211yescharacteristic
47C2×#120C2211yescharacteristic
48C2×#120C2211yescharacteristic
49C2×C4×D4C2211yescharacteristic
50C2×C4×D4C2211yescharacteristic
51C2×C4×D4C2211yescharacteristic
52C2×C4×D4C2211yescharacteristic
53C2×C4×D4C2211yescharacteristic, complemented
54C22×C22⋊C4C2211yescharacteristic
55C22×C22⋊C4C2211yescharacteristic
56C22×C22⋊C4C2211yescharacteristic
57#401C2211yescharacteristic, complemented
58#400C2211yescharacteristic, complemented
59#400C2211yescharacteristic, complemented
60#400C2211yescharacteristic, complemented
61#400C2211yescharacteristic, complemented
62#400C2211yescharacteristic, complemented
63#400C2211yescharacteristic, complemented
64#398C2211yescharacteristic, complemented
65#398C2211yescharacteristic, complemented
66#398C2211yescharacteristic, complemented
67#397C2211yescharacteristic
68#397C2211yescharacteristic
69#397C2211yescharacteristic
70#397C2211yescharacteristic
71#397C2211yescharacteristic, complemented
72#397C2211yescharacteristic, complemented
73#397C2211yescharacteristic, complemented
74#397C2211yescharacteristic, complemented
75#397C2211yescharacteristic, complemented
76#397C2211yescharacteristic, complemented
77#396C2211yescharacteristic
78#396C2211yescharacteristic
79#394C2211yescharacteristic
80#394C2211yescharacteristic
81#394C2211yescharacteristic
82#394C2211yescharacteristic
83#394C2211yescharacteristic
84#394C2211yescharacteristic
85#394C2211yescharacteristic
86#394C2211yescharacteristic
87#394C2211yescharacteristic
88#394C2211yescharacteristic
89#394C2211yescharacteristic, complemented
90#394C2211yescharacteristic, complemented
91#394C2211yescharacteristic, complemented
92#394C2211yescharacteristic, complemented
93#393C2211yescharacteristic
94#393C2211yescharacteristic
95#392C2211yescharacteristic
96#392C2211yescharacteristic
97#392C2211yescharacteristic
98#392C2211yescharacteristic
99#392C2211yescharacteristic
100#392C2211yescharacteristic
101#392C2211yescharacteristic
102#392C2211yescharacteristic
103#392C2211yescharacteristic, complemented
104#392C2211yescharacteristic, complemented
105#391C2211yescharacteristic, complemented
106#391C2211yescharacteristic, complemented
107#390C2211yescharacteristic
108#390C2211yescharacteristic
109#390C2211yescharacteristic
110#390C2211yescharacteristic, complemented
111#390C2211yescharacteristic, complemented
112#388C2211yescharacteristic
113#388C2211yescharacteristic
114#388C2211yescharacteristic
115#388C2211yescharacteristic
116#388C2211yescharacteristic
117#388C2211yescharacteristic
118#388C2211yescharacteristic, complemented
119#388C2211yescharacteristic, complemented
120#388C2211yescharacteristic, complemented
121#388C2211yescharacteristic, complemented
122#388C2211yescharacteristic, complemented
123#388C2211yescharacteristic, complemented
124#388C2211yescharacteristic, complemented
125#388C2211yescharacteristic, complemented
126#387C2211yescharacteristic, complemented
127#387C2211yescharacteristic, complemented
128#387C2211yescharacteristic, complemented
129#387C2211yescharacteristic, complemented
130#387C2211yescharacteristic, complemented
131#387C2211yescharacteristic, complemented
132#387C2211yescharacteristic, complemented
133#386C2211yescharacteristic
134#386C2211yescharacteristic
135#386C2211yescharacteristic
136#386C2211yescharacteristic
137#386C2211yescharacteristic
138#386C2211yescharacteristic
139#386C2211yescharacteristic
140#386C2211yescharacteristic
141#386C2211yescharacteristic
142#386C2211yescharacteristic
143#386C2211yescharacteristic
144#386C2211yescharacteristic
145#386C2211yescharacteristic
146#386C2211yescharacteristic
147#386C2211yescharacteristic
148#386C2211yescharacteristic
149#386C2211yescharacteristic
150#386C2211yescharacteristic
151#386C2211yescharacteristic
152#386C2211yescharacteristic
153#386C2211yescharacteristic, complemented
154#386C2211yescharacteristic, complemented
155#386C2211yescharacteristic, complemented
156#386C2211yescharacteristic, complemented
157#386C2211yescharacteristic, complemented
158#386C2211yescharacteristic, complemented
159#386C2211yescharacteristic, complemented
160#386C2211yescharacteristic, complemented
161#385C2211yescharacteristic
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#382C2211yescharacteristic, complemented
174#381C2211yescharacteristic
175#381C2211yescharacteristic
176#381C2211yescharacteristic
177#381C2211yescharacteristic, complemented
178#380C2211yescharacteristic
179#380C2211yescharacteristic
180#380C2211yescharacteristic
181#380C2211yescharacteristic
182#380C2211yescharacteristic, complemented
183C4×C22⋊C4C2211yescharacteristic
184C4×C22⋊C4C2211yescharacteristic
185#376C2211yescharacteristic, complemented
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
218C23×C4C2311yescharacteristic
219C23×C4C2311yescharacteristic
220C23×C4C2311yescharacteristic
221C23×C4C2311yescharacteristic
222#127—24no—
223#123—42no—
224#123—42no—
225C22⋊Q8—42no—
226C22⋊Q8—42no—
227#121—24no—
228#121—42no—
229#121—42no—
230#121—42no—
231#121—42no—
232#121—42no—
233#121—42no—
234#120—24no—
235#120—42no—
236#120—42no—
237#120—42no—
238C4×D4—42no—
239C4×D4—42no—
240C4×D4—42no—
241C4×D4—42no—
242C4×D4—42no—
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×C4⋊C4C2311yescharacteristic
264C2×C22⋊C4—42no—
265C2×C22⋊C4—42no—
266C2×C22⋊C4—42no—
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×C42C2311yescharacteristic
322C2×C42C2311yescharacteristic
323C2×C42C2311yescharacteristic
324C2×C42C2311yescharacteristic
325C2×C42C2311yescharacteristic
326C2×C42C2311yescharacteristic
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
366#95C2311yescharacteristic
367#95C2311yescharacteristic
368#95C2311yescharacteristic
369C24—22no—
370C24—22no—
371C24—22no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24C2411yescharacteristic
377C24C2411yescharacteristic
378C24C2411yescharacteristic
379C24C2411yescharacteristic
380C24C2411yescharacteristic
381C24C2411yescharacteristic
382C24C2411yescharacteristic
383#41—416no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—41no—
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—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—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—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4#4114yescomplemented
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
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×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×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
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
497C22×C4C2411yescharacteristic
498C22×C4C2411yescharacteristic
499C22×C4C2411yescharacteristic
500C22×C4C2411yescharacteristic
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—41no—
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—
520C4⋊C4—41no—
521C4⋊C4—41no—
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—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—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C42—22no—
577C42—22no—
578C42—41no—
579C42—41no—
580C42—41no—
581C42—41no—
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—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—82no—
631C23—82no—
632C23—82no—
633C23—82no—
634C23C2×#4112yes—
635C23C2×#4112yes—
636C23H(5,𝔽2)12yes—
637C23H(5,𝔽2)12yes—
638C23C2511yescharacteristic
639Q8—44no—
640D4—44no—
641D4—44no—
642D4—44no—
643D4—44no—
644D4—44no—
645D4—44no—
646D4—44no—
647D4—44no—
648D4—82no—
649D4—82no—
650D4—82no—
651D4—82no—
652D4—82no—
653D4—82no—
654D4—82no—
655D4—82no—
656D4—82no—
657D4—82no—
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—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—82no—
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×C4H(5,𝔽2)12yes—
741C2×C4H(5,𝔽2)12yes—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
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—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—88no—
792C22C22×#4111yescharacteristic
793C22C2×H(5,𝔽2)11yescharacteristic
794C22C2×H(5,𝔽2)11yescharacteristic
795C22C2×H(5,𝔽2)11yescharacteristic
796C22C2×H(5,𝔽2)11yescharacteristic
797C22#58511yescharacteristic
798C22#58511yescharacteristic
799C4—22no—
800C4—22no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
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—
823C2—42no—
824C2—42no—
825C2—42no—
826C2—42no—
827C2—81no—
828C2—81no—
829C2—81no—
830C2#350511yescharacteristic
831C2#351311yescharacteristic
832C2#351911yescharacteristic
833C2#353211yescharacteristic
834C2#353411yescharacteristic
835C2#354211yescharacteristic
836C2#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. #2797C2semidirect
2. #2782C2semidirect
3. #2778C2semidirect
4. #2778C2semidirect
5. #2750C2semidirect
6. #2744C2semidirect
7. #2708C2semidirect
8. #2688C2semidirect
9. #2688C2semidirect
10. #2687C2semidirect
11. #2673C2semidirect
12. #2669C2semidirect
13. #2661C2semidirect
14. #2648C2semidirect
15. #2600C2semidirect
16. #2543C2semidirect
17. #2531C2semidirect
18. #2527C2semidirect
19. #2463C2semidirect
20. #2450C2semidirect
21. #2444C2semidirect
22. #2424C2semidirect
23. #2424C2semidirect
24. #2412C2semidirect
25. #2412C2semidirect
26. #2407C2semidirect
27. #2407C2semidirect
28. #2404C2semidirect
29. #2377C2semidirect
30. #2358C2semidirect
31. #2328C2semidirect
36. C2×C22⋊Q8C22semidirect
37. C2×C22⋊Q8C22semidirect
44. C2×#121C22semidirect
53. C2×C4×D4C22semidirect
57. #401C22semidirect
58. #400C22semidirect
59. #400C22semidirect
60. #400C22semidirect
61. #400C22semidirect
62. #400C22semidirect
63. #400C22semidirect
64. #398C22semidirect
65. #398C22semidirect
66. #398C22semidirect
71. #397C22semidirect
72. #397C22semidirect
73. #397C22semidirect
74. #397C22semidirect
75. #397C22semidirect
76. #397C22semidirect
89. #394C22semidirect
90. #394C22semidirect
91. #394C22semidirect
92. #394C22semidirect
103. #392C22semidirect
104. #392C22semidirect
105. #391C22semidirect
106. #391C22semidirect
110. #390C22semidirect
111. #390C22semidirect
118. #388C22semidirect
119. #388C22semidirect
120. #388C22semidirect
121. #388C22semidirect
122. #388C22semidirect
123. #388C22semidirect
124. #388C22semidirect
125. #388C22semidirect
126. #387C22semidirect
127. #387C22semidirect
128. #387C22semidirect
129. #387C22semidirect
130. #387C22semidirect
131. #387C22semidirect
132. #387C22semidirect
153. #386C22semidirect
154. #386C22semidirect
155. #386C22semidirect
156. #386C22semidirect
157. #386C22semidirect
158. #386C22semidirect
159. #386C22semidirect
160. #386C22semidirect
167. #385C22semidirect
168. #385C22semidirect
169. #385C22semidirect
170. #385C22semidirect
171. #385C22semidirect
172. #385C22semidirect
173. #382C22semidirect
177. #381C22semidirect
182. #380C22semidirect
185. #376C22semidirect
186. C2×#95C22semidirect
440. C2×D4#41semidirect

Maximal subgroups

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

subgroupindex
#27972
#27822
#27782
#27502
#27442
#27082
#26882
#26872
#26732
#26692
#26612
#26482
#26002
#25432
#25312
#25272
#24632
#24502
#24442
#24242
#24122
#24072
#24042
#23772
#23582
#23282