Finite Group Databasebeta

← #62255

Subgroups — #62255

Order 256.

941 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3506C211yesmaximal, characteristic, complemented
2#3505C211yesmaximal, characteristic, complemented
3#3350C211yesmaximal, characteristic, complemented
4#3349C211yesmaximal, characteristic, complemented
5#3348C211yesmaximal, characteristic, complemented
6#3347C211yesmaximal, characteristic, complemented
7#3321C211yesmaximal, characteristic, complemented
8#3319C211yesmaximal, characteristic, complemented
9#3317C211yesmaximal, characteristic, complemented
10#3315C211yesmaximal, characteristic, complemented
11#3313C211yesmaximal, characteristic, complemented
12#3311C211yesmaximal, characteristic, complemented
13#3309C211yesmaximal, characteristic, complemented
14#3307C211yesmaximal, characteristic, complemented
15#3271C211yesmaximal, characteristic, complemented
16#3269C211yesmaximal, characteristic, complemented
17#3268C211yesmaximal, characteristic, complemented
18#3267C211yesmaximal, characteristic, complemented
19#3248C211yesmaximal, characteristic, complemented
20#3247C211yesmaximal, characteristic, complemented
21#3191C211yesmaximal, characteristic, complemented
22#3191C211yesmaximal, characteristic, complemented
23#3190C211yesmaximal, characteristic, complemented
24#3188C211yesmaximal, characteristic, complemented
25#3181C211yesmaximal, characteristic, complemented
26#3180C211yesmaximal, characteristic, complemented
27#3056C211yesmaximal, characteristic, complemented
28#3055C211yesmaximal, characteristic, complemented
29#3050C211yesmaximal, characteristic, complemented
30#3050C211yesmaximal, characteristic, complemented
31C2×#435C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic, complemented
33C2×AGL(1,ℤ/8)C2211yescharacteristic, complemented
34C2×#135C2211yescharacteristic, complemented
35C2×#135C2211yescharacteristic, complemented
36C22×M16C2211yescharacteristic
37C23×C8C2211yescharacteristic, complemented
38#559—21no—
39#559—21no—
40#556C2211yescharacteristic
41#556C2211yescharacteristic, complemented
42#555C2211yescharacteristic
43#555C2211yescharacteristic, complemented
44#553—21no—
45#553—21no—
46#553—21no—
47#553—21no—
48#553C2211yescharacteristic
49#553C2211yescharacteristic
50#552C2211yescharacteristic
51#552C2211yescharacteristic
52#551—21no—
53#551—21no—
54#550C2211yescharacteristic
55#550C2211yescharacteristic, complemented
56#548C2211yescharacteristic
57#548C2211yescharacteristic
58#547C2211yescharacteristic
59#547C2211yescharacteristic, complemented
60#546C2211yescharacteristic
61#546C2211yescharacteristic
62#539—21no—
63#538—21no—
64#538—21no—
65#538—21no—
66#535—21no—
67#534—21no—
68#533C2211yescharacteristic, complemented
69#532C2211yescharacteristic, complemented
70#529C2211yescharacteristic
71#529C2211yescharacteristic
72#525C2211yescharacteristic
73#525C2211yescharacteristic
74#525C2211yescharacteristic
75#525C2211yescharacteristic
76#525C2211yescharacteristic, complemented
77#525C2211yescharacteristic, complemented
78C2×C22⋊Q8C2211yescharacteristic
79C2×#121C2211yescharacteristic
80#520—21no—
81#518—21no—
82C2×C4×D4C2211yescharacteristic
83#501C2211yescharacteristic, complemented
84#501C2211yescharacteristic, complemented
85#497C2211yescharacteristic, complemented
86#496C2211yescharacteristic, complemented
87#491C2211yescharacteristic, complemented
88#490C2211yescharacteristic, complemented
89#489C2211yescharacteristic, complemented
90#489C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#485C2211yescharacteristic, complemented
97#484C2211yescharacteristic, complemented
98#483C2211yescharacteristic, complemented
99#482C2211yescharacteristic, complemented
100#482C2211yescharacteristic, complemented
101#482C2211yescharacteristic, complemented
102#482C2211yescharacteristic, complemented
103#482C2211yescharacteristic, complemented
104#482C2211yescharacteristic, complemented
105#481C2211yescharacteristic, complemented
106#480C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#479C2211yescharacteristic, complemented
109#478C2211yescharacteristic, complemented
110#478C2211yescharacteristic, complemented
111#477C2211yescharacteristic, complemented
112#476C2211yescharacteristic, complemented
113#475C2211yescharacteristic, complemented
114#474C2211yescharacteristic, complemented
115#470C2211yescharacteristic, complemented
116#470C2211yescharacteristic, complemented
117#469C2211yescharacteristic, complemented
118#469C2211yescharacteristic, complemented
119#468C2211yescharacteristic, complemented
120#468C2211yescharacteristic, complemented
121#468C2211yescharacteristic, complemented
122#468C2211yescharacteristic, complemented
123#467C2211yescharacteristic, complemented
124#467C2211yescharacteristic, complemented
125#467C2211yescharacteristic, complemented
126#467C2211yescharacteristic, complemented
127#467C2211yescharacteristic, complemented
128#467C2211yescharacteristic, complemented
129#466C2211yescharacteristic
130#466C2211yescharacteristic
131#466C2211yescharacteristic
132#466C2211yescharacteristic
133#466C2211yescharacteristic, complemented
134#466C2211yescharacteristic, complemented
135#465C2211yescharacteristic
136#465C2211yescharacteristic
137#465C2211yescharacteristic
138#465C2211yescharacteristic
139#465C2211yescharacteristic, complemented
140#465C2211yescharacteristic, complemented
141#465C2211yescharacteristic, complemented
142#465C2211yescharacteristic, complemented
143#465C2211yescharacteristic, complemented
144#465C2211yescharacteristic, complemented
145#465C2211yescharacteristic, complemented
146#465C2211yescharacteristic, complemented
147#464C2211yescharacteristic, complemented
148#464C2211yescharacteristic, complemented
149#463C2211yescharacteristic, complemented
150#463C2211yescharacteristic, complemented
151#462C2211yescharacteristic, complemented
152#461C2211yescharacteristic, complemented
153#460C2211yescharacteristic, complemented
154#459C2211yescharacteristic, complemented
155#452C2211yescharacteristic, complemented
156#452C2211yescharacteristic, complemented
157#452C2211yescharacteristic, complemented
158#452C2211yescharacteristic, complemented
159#452C2211yescharacteristic, complemented
160#452C2211yescharacteristic, complemented
161#451C2211yescharacteristic, complemented
162#450C2211yescharacteristic, complemented
163#449C2211yescharacteristic, complemented
164#449C2211yescharacteristic, complemented
165#449C2211yescharacteristic, complemented
166#449C2211yescharacteristic, complemented
167#449C2211yescharacteristic, complemented
168#449C2211yescharacteristic, complemented
169#448C2211yescharacteristic, complemented
170#447C2211yescharacteristic, complemented
171#442C2211yescharacteristic, complemented
172#442C2211yescharacteristic, complemented
173#441C2211yescharacteristic, complemented
174#441C2211yescharacteristic, complemented
175#440C2211yescharacteristic, complemented
176#440C2211yescharacteristic, complemented
177#440C2211yescharacteristic, complemented
178#440C2211yescharacteristic, complemented
179#435C2211yescharacteristic
180#435C2211yescharacteristic
181#435C2211yescharacteristic
182#435C2211yescharacteristic
183#435C2211yescharacteristic, complemented
184#435C2211yescharacteristic, complemented
185#435C2211yescharacteristic, complemented
186#435C2211yescharacteristic, complemented
187#428C2211yescharacteristic, complemented
188#428C2211yescharacteristic, complemented
189#427C2211yescharacteristic, complemented
190#427C2211yescharacteristic, complemented
191C2×C4⋊C8C2211yescharacteristic, complemented
192#419C2211yescharacteristic, complemented
193#418C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#417C2211yescharacteristic, complemented
196#416C2211yescharacteristic, complemented
197#416C2211yescharacteristic, complemented
198#416C2211yescharacteristic, complemented
199#416C2211yescharacteristic, complemented
200C2×C22⋊C8C2211yescharacteristic
201C2×C22⋊C8C2211yescharacteristic, complemented
202C2×#97C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C2×#41C2311yescharacteristic
210C22×Q8C2311yescharacteristic
211C22×D4—21no—
212C22×D4D411yescharacteristic
213C22×D4C2311yescharacteristic
214C23×C4C2311yescharacteristic
215C23×C4C2311yescharacteristic
216#137—42no—
217AGL(1,ℤ/8)—42no—
218#135—42no—
219#135—42no—
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×Q16C2311yescharacteristic
224C2×SD16C2311yescharacteristic
225C2×SD16C2311yescharacteristic
226C2×SD16C2311yescharacteristic
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×SD16C2311yescharacteristic
231C2×SD16C2311yescharacteristic
232C2×D8C2311yescharacteristic
233C2×D8C2311yescharacteristic
234C2×D8C2311yescharacteristic
235C2×D8C2311yescharacteristic
236C2×M16—42no—
237C2×M16C2311yescharacteristic
238C2×M16C2311yescharacteristic
239C2×M16C2311yescharacteristic
240C2×M16C2311yescharacteristic
241C22×C8—42no—
242C22×C8C2311yescharacteristic
243C22×C8C2311yescharacteristic
244C22×C8C2311yescharacteristic
245C22×C8C2311yescharacteristic
246C22×C8C2311yescharacteristic
247C22×C8C2311yescharacteristic
248C22×C8C2311yescharacteristic
249C22×C8C2311yescharacteristic
250C4⋊Q8C2311yescharacteristic
251C4⋊Q8C2311yescharacteristic
252C4⋊Q8C2311yescharacteristic
253#127—21no—
254#127—21no—
255#127C2311yescharacteristic
256#126—21no—
257#126—21no—
258#126—21no—
259#126—21no—
260#126—21no—
261#126—21no—
262#126—21no—
263#126—21no—
264#126—21no—
265#126—21no—
266#125—21no—
267#125—21no—
268#125—21no—
269#125C2311yescharacteristic
270#125C2311yescharacteristic
271#124—21no—
272#124—21no—
273#124—21no—
274#124—21no—
275#124—21no—
276#124—21no—
277#124—21no—
278#124—21no—
279#124—21no—
280#124C2311yescharacteristic
281#124C2311yescharacteristic
282#123—21no—
283#123—21no—
284#123—21no—
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123—21no—
290#123—21no—
291#123—21no—
292#123—21no—
293#123—21no—
294#123—21no—
295#123—21no—
296#123—21no—
297#123—21no—
298#123—21no—
299#123—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8C2311yescharacteristic
306C22⋊Q8C2311yescharacteristic
307C22⋊Q8C2311yescharacteristic
308C22⋊Q8C2311yescharacteristic
309C22⋊Q8C2311yescharacteristic
310C22⋊Q8C2311yescharacteristic
311C22⋊Q8C2311yescharacteristic
312C22⋊Q8C2311yescharacteristic
313C22⋊Q8C2311yescharacteristic
314C22⋊Q8C2311yescharacteristic
315C22⋊Q8C2311yescharacteristic
316C22⋊Q8C2311yescharacteristic
317#121—21no—
318#121—21no—
319#121—21no—
320#121—21no—
321#121—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
327#121—21no—
328#121—21no—
329#121—21no—
330#121—21no—
331#121—21no—
332#121—21no—
333#121—21no—
334#121C2311yescharacteristic
335#121C2311yescharacteristic
336#121C2311yescharacteristic
337#121C2311yescharacteristic
338#121C2311yescharacteristic
339#121C2311yescharacteristic
340#121C2311yescharacteristic
341#121C2311yescharacteristic
342#121C2311yescharacteristic
343#121C2311yescharacteristic
344#121C2311yescharacteristic
345#121C2311yescharacteristic
346#120—21no—
347#120—21no—
348#120—21no—
349#120—21no—
350#120—21no—
351#120—21no—
352#120—21no—
353#120—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8C2311yescharacteristic
358C4×Q8C2311yescharacteristic
359C4×Q8C2311yescharacteristic
360C4×Q8C2311yescharacteristic
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4D411yescharacteristic
383C4×D4D411yescharacteristic
384C4×D4D411yescharacteristic
385C4×D4D411yescharacteristic
386C4×D4C2311yescharacteristic
387C4×D4C2311yescharacteristic
388C4×D4C2311yescharacteristic
389C4×D4C2311yescharacteristic
390C4×D4C2311yescharacteristic
391C4×D4C2311yescharacteristic
392C4×D4C2311yescharacteristic
393C4×D4C2311yescharacteristic
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—21no—
401#117C2311yescharacteristic
402#117C2311yescharacteristic
403#117C2311yescharacteristic
404#117C2311yescharacteristic
405#117C2311yescharacteristic
406#117C2311yescharacteristic
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4D411yescharacteristic
411C2×C4⋊C4C2311yescharacteristic
412C2×C4⋊C4C2311yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4D411yescharacteristic
418C2×C22⋊C4D411yescharacteristic
419C2×C42C2311yescharacteristic
420#107C2311yescharacteristic
421#107C2311yescharacteristic
422#107C2311yescharacteristic
423#107C2311yescharacteristic
424#107C2311yescharacteristic
425#107C2311yescharacteristic
426#107C2311yescharacteristic
427#107C2311yescharacteristic
428#106C2311yescharacteristic
429#106C2311yescharacteristic
430#106C2311yescharacteristic
431#106C2311yescharacteristic
432#106C2311yescharacteristic
433#106C2311yescharacteristic
434#106C2311yescharacteristic
435#106C2311yescharacteristic
436C4⋊C8C2311yescharacteristic
437C4⋊C8C2311yescharacteristic
438C4⋊C8C2311yescharacteristic
439C4⋊C8C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
446#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
449#103C2311yescharacteristic
450#103C2311yescharacteristic
451#103C2311yescharacteristic
452#103C2311yescharacteristic
453#103C2311yescharacteristic
454#103C2311yescharacteristic
455#103C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465#102C2311yescharacteristic
466#102C2311yescharacteristic
467#102C2311yescharacteristic
468#102C2311yescharacteristic
469#102C2311yescharacteristic
470#102C2311yescharacteristic
471#102C2311yescharacteristic
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474C22⋊C8C2311yescharacteristic
475C22⋊C8C2311yescharacteristic
476C22⋊C8C2311yescharacteristic
477C22⋊C8C2311yescharacteristic
478C22⋊C8C2311yescharacteristic
479C22⋊C8C2311yescharacteristic
480#97C2311yescharacteristic
481#97C2311yescharacteristic
482#97C2311yescharacteristic
483#97C2311yescharacteristic
484C24—21no—
485C24C2×D411yescharacteristic
486C24C2×D411yescharacteristic
487#41—44no—
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493#41—41no—
494#41—41no—
495#41—41no—
496#41—41no—
497#41—41no—
498#41—41no—
499#41—41no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—41no—
504C2×Q8—41no—
505C2×Q8C2411yescharacteristic
506C2×Q8C2411yescharacteristic
507C2×Q8C2411yescharacteristic
508C2×Q8C2411yescharacteristic
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—42no—
533C2×D4—44no—
534C2×D4C2×D411yescharacteristic
535C2×D4C2×D411yescharacteristic
536C2×D4C2×D411yescharacteristic
537C2×D4C2×D411yescharacteristic
538C2×D4C2411yescharacteristic
539C2×D4C2411yescharacteristic
540C2×D4C2411yescharacteristic
541C2×D4C2411yescharacteristic
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4C2×D411yescharacteristic
560C22×C4C2×D411yescharacteristic
561C22×C4C2×D411yescharacteristic
562C22×C4C2×D411yescharacteristic
563C22×C4C2×D411yescharacteristic
564C22×C4C2×D411yescharacteristic
565C22×C4C2×D411yescharacteristic
566C22×C4C2×D411yescharacteristic
567C22×C4C2411yescharacteristic
568C22×C4C2411yescharacteristic
569C22×C4C2411yescharacteristic
570C22×C4C2411yescharacteristic
571C22×C4C2411yescharacteristic
572Q16—22no—
573Q16—41no—
574Q16—41no—
575Q16—41no—
576SD16—22no—
577SD16—22no—
578SD16—41no—
579SD16—41no—
580SD16—41no—
581SD16—41no—
582SD16—41no—
583SD16—41no—
584D8—22no—
585D8—41no—
586D8—41no—
587D8—41no—
588M16—22no—
589M16—22no—
590M16—41no—
591M16—41no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8C2411yescharacteristic
601C2×C8C2411yescharacteristic
602C2×C8C2411yescharacteristic
603C2×C8C2411yescharacteristic
604C2×C8C2411yescharacteristic
605C2×C8C2411yescharacteristic
606C2×C8C2411yescharacteristic
607C2×C8C2411yescharacteristic
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4C2×D411yescharacteristic
635C4⋊C4C2×D411yescharacteristic
636C4⋊C4C2×D411yescharacteristic
637C4⋊C4C2×D411yescharacteristic
638C4⋊C4C2411yescharacteristic
639C4⋊C4C2411yescharacteristic
640C4⋊C4C2411yescharacteristic
641C4⋊C4C2411yescharacteristic
642C4⋊C4C2411yescharacteristic
643C4⋊C4C2411yescharacteristic
644C4⋊C4C2411yescharacteristic
645C4⋊C4C2411yescharacteristic
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4C2×D411yescharacteristic
685C22⋊C4C2×D411yescharacteristic
686C22⋊C4C2×D411yescharacteristic
687C22⋊C4C2×D411yescharacteristic
688C22⋊C4C2×D411yescharacteristic
689C22⋊C4C2×D411yescharacteristic
690C22⋊C4C2×D411yescharacteristic
691C22⋊C4C2×D411yescharacteristic
692C42—21no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42C2×D411yescharacteristic
703C42C2×D411yescharacteristic
704C42C2411yescharacteristic
705C42C2411yescharacteristic
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—42no—
717C23—81no—
718C23—81no—
719C23C22×D411yescharacteristic
720C23C22×D411yescharacteristic
721C23C22×D411yescharacteristic
722C23C22×D411yescharacteristic
723C23C22×D411yescharacteristic
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—42no—
733Q8—81no—
734Q8—81no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—21no—
741D4—21no—
742D4—21no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—42no—
748D4—42no—
749D4—42no—
750D4—42no—
751D4—42no—
752D4—42no—
753D4—42no—
754D4—81no—
755D4—81no—
756D4—81no—
757D4—81no—
758D4—81no—
759D4—81no—
760D4—81no—
761D4—81no—
762D4—81no—
763D4—81no—
764D4—81no—
765D4—81no—
766D4—81no—
767D4—81no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4C22×D411yescharacteristic
812C2×C4C22×D411yescharacteristic
813C2×C4C22×D411yescharacteristic
814C2×C4C22×D411yescharacteristic
815C2×C4C22×D411yescharacteristic
816C2×C4C22×D411yescharacteristic
817C2×C4C22×D411yescharacteristic
818C2×C4C22×D411yescharacteristic
819C2×C4C22×D411yescharacteristic
820C2×C4C2511yescharacteristic
821C8—21no—
822C8—21no—
823C8—21no—
824C8—21no—
825C8—21no—
826C8—21no—
827C8—21no—
828C8H(5,𝔽2)12yes—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—44no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—82no—
857C22—162no—
858C22#57512yes—
859C22C23×D411yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—41no—
870C4—41no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4C2×H(5,𝔽2)11yescharacteristic
882C4#58511yescharacteristic
883C2—22no—
884C2—41no—
885C2—41no—
886C2—41no—
887C2—41no—
888C2—81no—
889C2—81no—
890C2—81no—
891C2—81no—
892C2#349611yescharacteristic
893C2C2×#57511yescharacteristic
894C2#358411yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3506C2semidirect
2. #3505C2semidirect
3. #3350C2semidirect
4. #3349C2semidirect
5. #3348C2semidirect
6. #3347C2semidirect
7. #3321C2semidirect
8. #3319C2semidirect
9. #3317C2semidirect
10. #3315C2semidirect
11. #3313C2semidirect
12. #3311C2semidirect
13. #3309C2semidirect
14. #3307C2semidirect
15. #3271C2semidirect
16. #3269C2semidirect
17. #3268C2semidirect
18. #3267C2semidirect
19. #3248C2semidirect
20. #3247C2semidirect
21. #3191C2semidirect
22. #3191C2semidirect
23. #3190C2semidirect
24. #3188C2semidirect
25. #3181C2semidirect
26. #3180C2semidirect
27. #3056C2semidirect
28. #3055C2semidirect
29. #3050C2semidirect
30. #3050C2semidirect
31. C2×#435C2semidirect
32. C2×#137C22semidirect
33. C2×AGL(1,ℤ/8)C22semidirect
34. C2×#135C22semidirect
35. C2×#135C22semidirect
37. C23×C8C22semidirect
41. #556C22semidirect
43. #555C22semidirect
55. #550C22semidirect
59. #547C22semidirect
68. #533C22semidirect
69. #532C22semidirect
76. #525C22semidirect
77. #525C22semidirect
83. #501C22semidirect
84. #501C22semidirect
85. #497C22semidirect
86. #496C22semidirect
87. #491C22semidirect
88. #490C22semidirect
89. #489C22semidirect
90. #489C22semidirect
91. #485C22semidirect
92. #485C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #485C22semidirect
96. #485C22semidirect
97. #484C22semidirect
98. #483C22semidirect
99. #482C22semidirect
100. #482C22semidirect
101. #482C22semidirect
102. #482C22semidirect
103. #482C22semidirect
104. #482C22semidirect
105. #481C22semidirect
106. #480C22semidirect
107. #479C22semidirect
108. #479C22semidirect
109. #478C22semidirect
110. #478C22semidirect
111. #477C22semidirect
112. #476C22semidirect
113. #475C22semidirect
114. #474C22semidirect
115. #470C22semidirect
116. #470C22semidirect
117. #469C22semidirect
118. #469C22semidirect
119. #468C22semidirect
120. #468C22semidirect
121. #468C22semidirect
122. #468C22semidirect
123. #467C22semidirect
124. #467C22semidirect
125. #467C22semidirect
126. #467C22semidirect
127. #467C22semidirect
128. #467C22semidirect
133. #466C22semidirect
134. #466C22semidirect
139. #465C22semidirect
140. #465C22semidirect
141. #465C22semidirect
142. #465C22semidirect
143. #465C22semidirect
144. #465C22semidirect
145. #465C22semidirect
146. #465C22semidirect
147. #464C22semidirect
148. #464C22semidirect
149. #463C22semidirect
150. #463C22semidirect
151. #462C22semidirect
152. #461C22semidirect
153. #460C22semidirect
154. #459C22semidirect
155. #452C22semidirect
156. #452C22semidirect
157. #452C22semidirect
158. #452C22semidirect
159. #452C22semidirect
160. #452C22semidirect
161. #451C22semidirect
162. #450C22semidirect
163. #449C22semidirect
164. #449C22semidirect
165. #449C22semidirect
166. #449C22semidirect
167. #449C22semidirect
168. #449C22semidirect
169. #448C22semidirect
170. #447C22semidirect
171. #442C22semidirect
172. #442C22semidirect
173. #441C22semidirect
174. #441C22semidirect
175. #440C22semidirect
176. #440C22semidirect
177. #440C22semidirect
178. #440C22semidirect
183. #435C22semidirect
184. #435C22semidirect
185. #435C22semidirect
186. #435C22semidirect
187. #428C22semidirect
188. #428C22semidirect
189. #427C22semidirect
190. #427C22semidirect
191. C2×C4⋊C8C22semidirect
192. #419C22semidirect
193. #418C22semidirect
194. #417C22semidirect
195. #417C22semidirect
196. #416C22semidirect
197. #416C22semidirect
198. #416C22semidirect
199. #416C22semidirect
201. C2×C22⋊C8C22semidirect
202. C2×#97C22semidirect

Maximal subgroups

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

subgroupindex
#35062
#35052
#33502
#33492
#33482
#33472
#33212
#33192
#33172
#33152
#33132
#33112
#33092
#33072
#32712
#32692
#32682
#32672
#32482
#32472
#31912
#31902
#31882
#31812
#31802
#30562
#30552
#30502
C2×#4352