Finite Group Databasebeta

← #40944

Subgroups — #40944

Order 256.

945 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2827C211yesmaximal, characteristic, complemented
2#2812C211yesmaximal, characteristic, complemented
3#2786C211yesmaximal, characteristic, complemented
4#2781C211yesmaximal, characteristic, complemented
5#2753C211yesmaximal, characteristic, complemented
6#2747C211yesmaximal, characteristic, complemented
7#2746C211yesmaximal, characteristic, complemented
8#2730C211yesmaximal, characteristic, complemented
9#2711C211yesmaximal, characteristic, complemented
10#2676C211yesmaximal, characteristic, complemented
11#2653C211yesmaximal, characteristic, complemented
12#2636C211yesmaximal, characteristic, complemented
13#2635C211yesmaximal, characteristic, complemented
14#2617C211yesmaximal, characteristic, complemented
15#2617C211yesmaximal, characteristic, complemented
16#2600C211yesmaximal, characteristic, complemented
17#2576C211yesmaximal, characteristic, complemented
18#2535C211yesmaximal, characteristic, complemented
19#2517C211yesmaximal, characteristic, complemented
20#2489C211yesmaximal, characteristic, complemented
21#2477C211yesmaximal, characteristic, complemented
22#2476C211yesmaximal, characteristic, complemented
23#2468C211yesmaximal, characteristic, complemented
24#2467C211yesmaximal, characteristic, complemented
25#2460C211yesmaximal, characteristic, complemented
26#2459C211yesmaximal, characteristic, complemented
27#2437C211yesmaximal, characteristic, complemented
28#2392C211yesmaximal, characteristic, complemented
29#2358C211yesmaximal, characteristic, complemented
30#2358C211yesmaximal, characteristic, complemented
31#2321C211yesmaximal, characteristic, complemented
32C2×#126C2211yescharacteristic, complemented
33C2×#125C2211yescharacteristic, complemented
34C2×#124C2211yescharacteristic, complemented
35C2×C22⋊Q8C2211yescharacteristic
36C2×C22⋊Q8C2211yescharacteristic
37C2×#121C2211yescharacteristic
38C2×#121C2211yescharacteristic
39C2×#121C2211yescharacteristic, complemented
40C2×#120C2211yescharacteristic
41C2×#120C2211yescharacteristic
42C2×#120C2211yescharacteristic
43C2×C4×D4C2211yescharacteristic
44C2×C4×D4C2211yescharacteristic
45C2×C4×D4C2211yescharacteristic
46C2×C4×D4C2211yescharacteristic
47C2×C4×D4C2211yescharacteristic
48C2×C4×D4C2211yescharacteristic, complemented
49C2×#117C2211yescharacteristic, complemented
50C22×C22⋊C4C2211yescharacteristic
51C22×C22⋊C4C2211yescharacteristic
52C22×C22⋊C4C2211yescharacteristic
53#401C2211yescharacteristic, complemented
54#400C2211yescharacteristic, complemented
55#400C2211yescharacteristic, complemented
56#400C2211yescharacteristic, complemented
57#400C2211yescharacteristic, complemented
58#399C2211yescharacteristic
59#399C2211yescharacteristic, complemented
60#399C2211yescharacteristic, complemented
61#398C2211yescharacteristic, 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, complemented
73#397C2211yescharacteristic, complemented
74#397C2211yescharacteristic, complemented
75#397C2211yescharacteristic, complemented
76#396C2211yescharacteristic
77#396C2211yescharacteristic
78#396C2211yescharacteristic, complemented
79#396C2211yescharacteristic, complemented
80#396C2211yescharacteristic, 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, complemented
96#394C2211yescharacteristic, complemented
97#394C2211yescharacteristic, complemented
98#394C2211yescharacteristic, complemented
99#394C2211yescharacteristic, complemented
100#393C2211yescharacteristic
101#393C2211yescharacteristic, complemented
102#392C2211yescharacteristic
103#392C2211yescharacteristic
104#392C2211yescharacteristic
105#392C2211yescharacteristic
106#392C2211yescharacteristic
107#392C2211yescharacteristic
108#392C2211yescharacteristic
109#391C2211yescharacteristic, complemented
110#391C2211yescharacteristic, complemented
111#390C2211yescharacteristic
112#390C2211yescharacteristic
113#390C2211yescharacteristic
114#390C2211yescharacteristic
115#388C2211yescharacteristic
116#388C2211yescharacteristic
117#388C2211yescharacteristic
118#388C2211yescharacteristic
119#388C2211yescharacteristic
120#388C2211yescharacteristic
121#388C2211yescharacteristic
122#388C2211yescharacteristic
123#388C2211yescharacteristic, complemented
124#388C2211yescharacteristic, complemented
125#388C2211yescharacteristic, complemented
126#388C2211yescharacteristic, complemented
127#388C2211yescharacteristic, complemented
128#388C2211yescharacteristic, complemented
129#388C2211yescharacteristic, complemented
130#388C2211yescharacteristic, complemented
131#388C2211yescharacteristic, complemented
132#387C2211yescharacteristic, complemented
133#387C2211yescharacteristic, complemented
134#387C2211yescharacteristic, complemented
135#387C2211yescharacteristic, complemented
136#387C2211yescharacteristic, complemented
137#387C2211yescharacteristic, complemented
138#387C2211yescharacteristic, complemented
139#387C2211yescharacteristic, complemented
140#387C2211yescharacteristic, complemented
141#387C2211yescharacteristic, complemented
142#387C2211yescharacteristic, complemented
143#386C2211yescharacteristic
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, complemented
157#386C2211yescharacteristic, complemented
158#385C2211yescharacteristic
159#385C2211yescharacteristic
160#385C2211yescharacteristic
161#385C2211yescharacteristic
162#385C2211yescharacteristic
163#385C2211yescharacteristic
164#385C2211yescharacteristic
165#385C2211yescharacteristic
166#385C2211yescharacteristic
167#385C2211yescharacteristic, complemented
168#385C2211yescharacteristic, complemented
169#382C2211yescharacteristic, complemented
170#382C2211yescharacteristic, complemented
171#382C2211yescharacteristic, complemented
172#381C2211yescharacteristic, complemented
173#381C2211yescharacteristic, complemented
174#380C2211yescharacteristic
175#380C2211yescharacteristic
176#380C2211yescharacteristic
177#380C2211yescharacteristic
178#380C2211yescharacteristic, complemented
179#379C2211yescharacteristic
180C4×C4⋊C4C2211yescharacteristic, complemented
181C4×C22⋊C4C2211yescharacteristic
182C4×C22⋊C4C2211yescharacteristic
183C4×C22⋊C4C2211yescharacteristic
184C4×C22⋊C4C2211yescharacteristic
185C4×C22⋊C4C2211yescharacteristic
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
201C23×C4C2311yescharacteristic
202C23×C4C2311yescharacteristic
203C23×C4C2311yescharacteristic
204C23×C4C2311yescharacteristic
205C23×C4C2311yescharacteristic
206C23×C4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208C23×C4C2311yescharacteristic
209C23×C4C2311yescharacteristic
210#126—42no—
211#125—42no—
212#124—42no—
213C22⋊Q8—42no—
214C22⋊Q8—42no—
215#121—42no—
216#121—42no—
217#121—42no—
218#120—24no—
219#120—24no—
220#120—24no—
221C4×D4—42no—
222C4×D4—42no—
223C4×D4—42no—
224C4×D4—42no—
225C4×D4—42no—
226C4×D4—42no—
227#117—42no—
228C2×C4⋊C4C2311yescharacteristic
229C2×C4⋊C4C2311yescharacteristic
230C2×C4⋊C4C2311yescharacteristic
231C2×C4⋊C4C2311yescharacteristic
232C2×C4⋊C4C2311yescharacteristic
233C2×C4⋊C4C2311yescharacteristic
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×C22⋊C4—42no—
256C2×C22⋊C4—42no—
257C2×C22⋊C4—42no—
258C2×C22⋊C4C2311yescharacteristic
259C2×C22⋊C4C2311yescharacteristic
260C2×C22⋊C4C2311yescharacteristic
261C2×C22⋊C4C2311yescharacteristic
262C2×C22⋊C4C2311yescharacteristic
263C2×C22⋊C4C2311yescharacteristic
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×C42C2311yescharacteristic
313C2×C42C2311yescharacteristic
314C2×C42C2311yescharacteristic
315C2×C42C2311yescharacteristic
316C2×C42C2311yescharacteristic
317C2×C42C2311yescharacteristic
318C2×C42C2311yescharacteristic
319C2×C42C2311yescharacteristic
320C2×C42C2311yescharacteristic
321#95C2311yescharacteristic
322#95C2311yescharacteristic
323#95C2311yescharacteristic
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
363C24—41no—
364C24—41no—
365C24—41no—
366C24—41no—
367C24—41no—
368C24—41no—
369C24#4114yes—
370C24C2411yescharacteristic
371C24C2411yescharacteristic
372C24C2411yescharacteristic
373C24C2411yescharacteristic
374C24C2411yescharacteristic
375C24C2411yescharacteristic
376C2×Q8—22no—
377C2×Q8—41no—
378C2×Q8—41no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
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—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
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×C4C2411yescharacteristic
443C22×C4C2411yescharacteristic
444C22×C4C2411yescharacteristic
445C22×C4C2411yescharacteristic
446C22×C4C2411yescharacteristic
447C22×C4C2411yescharacteristic
448C22×C4C2411yescharacteristic
449C22×C4C2411yescharacteristic
450C22×C4C2411yescharacteristic
451C22×C4C2411yescharacteristic
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
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
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—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
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—
548C42—22no—
549C42—22no—
550C42—22no—
551C42—41no—
552C42—41no—
553C42—41no—
554C42—41no—
555C42—41no—
556C42—41no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
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—44no—
597C23—44no—
598C23—44no—
599C23—82no—
600C23—82no—
601C23—82no—
602C23—82no—
603C23C2×#4112yes—
604C23C2×#4112yes—
605C23C2×#4112yes—
606C23C2511yescharacteristic
607Q8—82no—
608D4—44no—
609D4—44no—
610D4—44no—
611D4—44no—
612D4—44no—
613D4—44no—
614D4—82no—
615D4—82no—
616D4—82no—
617D4—82no—
618D4—82no—
619D4—82no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
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—44no—
693C2×C4—82no—
694C2×C4—82no—
695C2×C4—82no—
696C2×C4—82no—
697C2×C4—82no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4H(5,𝔽2)12yes—
702C2×C4H(5,𝔽2)12yes—
703C2×C4H(5,𝔽2)12yes—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
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—88no—
747C22C22×#4111yescharacteristic
748C22C2×H(5,𝔽2)11yescharacteristic
749C22C2×H(5,𝔽2)11yescharacteristic
750C22C2×H(5,𝔽2)11yescharacteristic
751C22#58511yescharacteristic
752C22#58511yescharacteristic
753C22#58511yescharacteristic
754C4—22no—
755C4—22no—
756C4—22no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—41no—
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—
779C2—42no—
780C2—42no—
781C2—42no—
782C2—81no—
783C2—81no—
784C2—81no—
785C2#345911yescharacteristic
786C2#350511yescharacteristic
787C2#350511yescharacteristic
788C2#354211yescharacteristic
789C2#354211yescharacteristic
790C2#355811yescharacteristic
791C2#356611yescharacteristic
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. #2827C2semidirect
2. #2812C2semidirect
3. #2786C2semidirect
4. #2781C2semidirect
5. #2753C2semidirect
6. #2747C2semidirect
7. #2746C2semidirect
8. #2730C2semidirect
9. #2711C2semidirect
10. #2676C2semidirect
11. #2653C2semidirect
12. #2636C2semidirect
13. #2635C2semidirect
14. #2617C2semidirect
15. #2617C2semidirect
16. #2600C2semidirect
17. #2576C2semidirect
18. #2535C2semidirect
19. #2517C2semidirect
20. #2489C2semidirect
21. #2477C2semidirect
22. #2476C2semidirect
23. #2468C2semidirect
24. #2467C2semidirect
25. #2460C2semidirect
26. #2459C2semidirect
27. #2437C2semidirect
28. #2392C2semidirect
29. #2358C2semidirect
30. #2358C2semidirect
31. #2321C2semidirect
32. C2×#126C22semidirect
33. C2×#125C22semidirect
34. C2×#124C22semidirect
39. C2×#121C22semidirect
48. C2×C4×D4C22semidirect
49. C2×#117C22semidirect
53. #401C22semidirect
54. #400C22semidirect
55. #400C22semidirect
56. #400C22semidirect
57. #400C22semidirect
59. #399C22semidirect
60. #399C22semidirect
61. #398C22semidirect
62. #398C22semidirect
63. #398C22semidirect
64. #398C22semidirect
72. #397C22semidirect
73. #397C22semidirect
74. #397C22semidirect
75. #397C22semidirect
78. #396C22semidirect
79. #396C22semidirect
80. #396C22semidirect
95. #394C22semidirect
96. #394C22semidirect
97. #394C22semidirect
98. #394C22semidirect
99. #394C22semidirect
101. #393C22semidirect
109. #391C22semidirect
110. #391C22semidirect
123. #388C22semidirect
124. #388C22semidirect
125. #388C22semidirect
126. #388C22semidirect
127. #388C22semidirect
128. #388C22semidirect
129. #388C22semidirect
130. #388C22semidirect
131. #388C22semidirect
132. #387C22semidirect
133. #387C22semidirect
134. #387C22semidirect
135. #387C22semidirect
136. #387C22semidirect
137. #387C22semidirect
138. #387C22semidirect
139. #387C22semidirect
140. #387C22semidirect
141. #387C22semidirect
142. #387C22semidirect
156. #386C22semidirect
157. #386C22semidirect
167. #385C22semidirect
168. #385C22semidirect
169. #382C22semidirect
170. #382C22semidirect
171. #382C22semidirect
172. #381C22semidirect
173. #381C22semidirect
178. #380C22semidirect
180. C4×C4⋊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
#28272
#28122
#27862
#27812
#27532
#27472
#27462
#27302
#27112
#26762
#26532
#26362
#26352
#26172
#26002
#25762
#25352
#25172
#24892
#24772
#24762
#24682
#24672
#24602
#24592
#24372
#23922
#23582
#23212