Finite Group Databasebeta

← #62059

Subgroups — #62059

Order 256.

905 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3562C211yesmaximal, characteristic, complemented
2#3521C211yesmaximal, characteristic, complemented
3#3401C211yesmaximal, characteristic, complemented
4#3393C211yesmaximal, characteristic, complemented
5#3376C211yesmaximal, characteristic, complemented
6#3361C211yesmaximal, characteristic, complemented
7#3327C211yesmaximal, characteristic, complemented
8#3313C211yesmaximal, characteristic, complemented
9#3307C211yesmaximal, characteristic, complemented
10#3304C211yesmaximal, characteristic, complemented
11#3297C211yesmaximal, characteristic, complemented
12#3296C211yesmaximal, characteristic, complemented
13#3283C211yesmaximal, characteristic, complemented
14#3282C211yesmaximal, characteristic, complemented
15#3282C211yesmaximal, characteristic, complemented
16#3273C211yesmaximal, characteristic, complemented
17#3268C211yesmaximal, characteristic, complemented
18#3267C211yesmaximal, characteristic, complemented
19#3260C211yesmaximal, characteristic, complemented
20#3258C211yesmaximal, characteristic, complemented
21#3250C211yesmaximal, characteristic, complemented
22#3224C211yesmaximal, characteristic, complemented
23#3223C211yesmaximal, characteristic, complemented
24#3212C211yesmaximal, characteristic, complemented
25#3122C211yesmaximal, characteristic, complemented
26#3120C211yesmaximal, characteristic, complemented
27#3102C211yesmaximal, characteristic, complemented
28#3045C211yesmaximal, characteristic, complemented
29#3042C211yesmaximal, characteristic, complemented
30#3035C211yesmaximal, characteristic, complemented
31#2994C211yesmaximal, characteristic, complemented
32C2×AGL(1,ℤ/8)C2211yescharacteristic
33C2×AGL(1,ℤ/8)C2211yescharacteristic
34C2×#135C2211yescharacteristic
35C2×#135C2211yescharacteristic
36C2×#135C2211yescharacteristic, complemented
37C22×SD16C2211yescharacteristic, complemented
38#562—21no—
39#560—21no—
40#559C2211yescharacteristic, complemented
41#556C2211yescharacteristic, complemented
42#556C2211yescharacteristic, complemented
43#556C2211yescharacteristic, complemented
44#554C2211yescharacteristic, complemented
45#553—21no—
46#553—21no—
47#553C2211yescharacteristic
48#552—21no—
49#552C2211yescharacteristic
50#551—21no—
51#551—21no—
52#551—21no—
53#550C2211yescharacteristic
54#548C2211yescharacteristic
55#548C2211yescharacteristic
56#547C2211yescharacteristic
57#547C2211yescharacteristic, complemented
58#546C2211yescharacteristic
59#546C2211yescharacteristic
60#546C2211yescharacteristic, complemented
61#546C2211yescharacteristic, complemented
62#542C2211yescharacteristic
63#541C2211yescharacteristic, complemented
64#541C2211yescharacteristic, complemented
65#540—21no—
66#540C2211yescharacteristic
67#539—21no—
68#539—21no—
69#538—21no—
70#538—21no—
71#538—21no—
72#536C2211yescharacteristic
73#535C2211yescharacteristic, complemented
74#532C2211yescharacteristic, complemented
75#529—21no—
76#529C2211yescharacteristic
77#529C2211yescharacteristic, complemented
78#529C2211yescharacteristic, complemented
79C2×#126—21no—
80#520C2211yescharacteristic
81#518C2211yescharacteristic, complemented
82C4×#41C2211yescharacteristic, complemented
83#497C2211yescharacteristic, complemented
84#496C2211yescharacteristic
85#495C2211yescharacteristic
86#495C2211yescharacteristic
87#495C2211yescharacteristic, complemented
88#494C2211yescharacteristic, complemented
89#491C2211yescharacteristic, complemented
90#489C2211yescharacteristic, complemented
91#488C2211yescharacteristic, complemented
92#488C2211yescharacteristic, complemented
93#488C2211yescharacteristic, complemented
94#486C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#484C2211yescharacteristic, complemented
97#483C2211yescharacteristic, complemented
98#482C2211yescharacteristic
99#482C2211yescharacteristic, complemented
100#482C2211yescharacteristic, complemented
101#479C2211yescharacteristic, complemented
102#479C2211yescharacteristic, complemented
103#479C2211yescharacteristic, complemented
104#478C2211yescharacteristic, complemented
105#478C2211yescharacteristic, complemented
106#478C2211yescharacteristic, complemented
107#478C2211yescharacteristic, complemented
108#478C2211yescharacteristic, complemented
109#477C2211yescharacteristic, complemented
110#475C2211yescharacteristic, complemented
111#470C2211yescharacteristic, complemented
112#468C2211yescharacteristic
113#468C2211yescharacteristic
114#468C2211yescharacteristic, complemented
115#467C2211yescharacteristic, complemented
116#467C2211yescharacteristic, complemented
117#466C2211yescharacteristic
118#465C2211yescharacteristic
119#465C2211yescharacteristic
120#465C2211yescharacteristic, complemented
121#465C2211yescharacteristic, complemented
122#465C2211yescharacteristic, complemented
123#464C2211yescharacteristic, complemented
124#464C2211yescharacteristic, complemented
125#464C2211yescharacteristic, complemented
126#464C2211yescharacteristic, complemented
127#464C2211yescharacteristic, complemented
128#464C2211yescharacteristic, complemented
129#464C2211yescharacteristic, complemented
130#464C2211yescharacteristic, complemented
131#463C2211yescharacteristic
132#463C2211yescharacteristic
133#463C2211yescharacteristic
134#463C2211yescharacteristic
135#463C2211yescharacteristic
136#463C2211yescharacteristic
137#463C2211yescharacteristic
138#463C2211yescharacteristic, complemented
139#462C2211yescharacteristic, complemented
140#462C2211yescharacteristic, complemented
141#461C2211yescharacteristic, complemented
142#461C2211yescharacteristic, complemented
143#461C2211yescharacteristic, complemented
144#461C2211yescharacteristic, complemented
145#461C2211yescharacteristic, complemented
146#461C2211yescharacteristic, complemented
147#460C2211yescharacteristic, complemented
148#460C2211yescharacteristic, complemented
149#460C2211yescharacteristic, complemented
150#459C2211yescharacteristic
151#459C2211yescharacteristic
152#459C2211yescharacteristic
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#452C2211yescharacteristic, complemented
158#452C2211yescharacteristic, complemented
159#452C2211yescharacteristic, complemented
160#452C2211yescharacteristic, complemented
161#451C2211yescharacteristic, complemented
162#451C2211yescharacteristic, complemented
163#450C2211yescharacteristic, complemented
164#449C2211yescharacteristic
165#449C2211yescharacteristic
166#449C2211yescharacteristic
167#449C2211yescharacteristic, complemented
168#447C2211yescharacteristic
169#447C2211yescharacteristic
170#447C2211yescharacteristic, complemented
171#446C2211yescharacteristic, complemented
172C8×Q8C2211yescharacteristic, complemented
173#442C2211yescharacteristic
174#442C2211yescharacteristic, complemented
175#441C2211yescharacteristic, complemented
176#440C2211yescharacteristic, complemented
177C4×Q16C2211yescharacteristic, complemented
178C4×Q16C2211yescharacteristic, complemented
179C4×SD16C2211yescharacteristic, complemented
180C4×SD16C2211yescharacteristic, complemented
181C4×SD16C2211yescharacteristic, complemented
182C4×D8C2211yescharacteristic
183C4×D8C2211yescharacteristic
184C4×D8C2211yescharacteristic, complemented
185#436C2211yescharacteristic
186#435C2211yescharacteristic, complemented
187#435C2211yescharacteristic, complemented
188C8×D4C2211yescharacteristic
189C8×D4C2211yescharacteristic, complemented
190C8×D4C2211yescharacteristic, complemented
191#433C2211yescharacteristic, complemented
192#433C2211yescharacteristic, complemented
193#431C2211yescharacteristic, complemented
194#424C2211yescharacteristic, complemented
195#424C2211yescharacteristic, complemented
196C2×C4⋊C8C2211yescharacteristic, complemented
197#419C2211yescharacteristic, complemented
198#417C2211yescharacteristic, complemented
199#416C2211yescharacteristic
200#416C2211yescharacteristic, complemented
201#416C2211yescharacteristic, complemented
202C2×#102C2211yescharacteristic, complemented
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×D4C2311yescharacteristic
211C22×D4C2311yescharacteristic
212AGL(1,ℤ/8)—42no—
213AGL(1,ℤ/8)—42no—
214#135—42no—
215#135—42no—
216#135—42no—
217C2×Q16C2311yescharacteristic
218C2×Q16C2311yescharacteristic
219C2×Q16C2311yescharacteristic
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×SD16—42no—
224C2×SD16C2311yescharacteristic
225C2×SD16C2311yescharacteristic
226C2×SD16C2311yescharacteristic
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×SD16C2311yescharacteristic
231C2×SD16C2311yescharacteristic
232C2×SD16C2311yescharacteristic
233C2×SD16C2311yescharacteristic
234C2×SD16C2311yescharacteristic
235C2×SD16C2311yescharacteristic
236C2×D8C2311yescharacteristic
237C2×D8C2311yescharacteristic
238C2×D8C2311yescharacteristic
239C2×D8C2311yescharacteristic
240C2×D8C2311yescharacteristic
241C2×D8C2311yescharacteristic
242C2×M16C2311yescharacteristic
243C2×M16C2311yescharacteristic
244C22×C8C2311yescharacteristic
245C22×C8C2311yescharacteristic
246C22×C8C2311yescharacteristic
247C22×C8C2311yescharacteristic
248C4⋊Q8C2311yescharacteristic
249C4⋊Q8C2311yescharacteristic
250C4⋊Q8C2311yescharacteristic
251C4⋊Q8C2311yescharacteristic
252#127—21no—
253#127C2311yescharacteristic
254#127C2311yescharacteristic
255#126—21no—
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#126—21no—
267#126—21no—
268#126—21no—
269#126—21no—
270#126D411yescharacteristic
271#126D411yescharacteristic
272#125—21no—
273#125—21no—
274#125—21no—
275#125—21no—
276#125—21no—
277#125D411yescharacteristic
278#125C2311yescharacteristic
279#125C2311yescharacteristic
280#125C2311yescharacteristic
281#124—21no—
282#124—21no—
283#124—21no—
284#124—21no—
285#124—21no—
286#124D411yescharacteristic
287#124C2311yescharacteristic
288#124C2311yescharacteristic
289#124C2311yescharacteristic
290#124C2311yescharacteristic
291#124C2311yescharacteristic
292#124C2311yescharacteristic
293#124C2311yescharacteristic
294#123—21no—
295#123—21no—
296#123—21no—
297#123—21no—
298#123—21no—
299#123—21no—
300#123—21no—
301#123—21no—
302#123—21no—
303#123—21no—
304#123—21no—
305#123—21no—
306#123—21no—
307#123—21no—
308#123—21no—
309#123—21no—
310#123—21no—
311#123—21no—
312#123—21no—
313#123D411yescharacteristic
314#123D411yescharacteristic
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8D411yescharacteristic
326C22⋊Q8C2311yescharacteristic
327C22⋊Q8C2311yescharacteristic
328C22⋊Q8C2311yescharacteristic
329C22⋊Q8C2311yescharacteristic
330C22⋊Q8C2311yescharacteristic
331C22⋊Q8C2311yescharacteristic
332C22⋊Q8C2311yescharacteristic
333#121—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121—21no—
341#121—21no—
342#121—21no—
343#121—21no—
344#121—21no—
345#121—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349#121—21no—
350#121D411yescharacteristic
351#121C2311yescharacteristic
352#121C2311yescharacteristic
353#121C2311yescharacteristic
354#121C2311yescharacteristic
355#121C2311yescharacteristic
356#120—21no—
357#120—21no—
358#120—21no—
359#120—21no—
360#120—21no—
361#120—21no—
362C4×Q8—21no—
363C4×Q8C2311yescharacteristic
364C4×Q8C2311yescharacteristic
365C4×Q8C2311yescharacteristic
366C4×Q8C2311yescharacteristic
367C4×Q8C2311yescharacteristic
368C4×Q8C2311yescharacteristic
369C4×Q8C2311yescharacteristic
370C4×Q8C2311yescharacteristic
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×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4C2311yescharacteristic
387C4×D4C2311yescharacteristic
388C4×D4C2311yescharacteristic
389C4×D4C2311yescharacteristic
390C4×D4C2311yescharacteristic
391C4×D4C2311yescharacteristic
392C4×D4C2311yescharacteristic
393C4×D4C2311yescharacteristic
394C4×D4C2311yescharacteristic
395C4×D4C2311yescharacteristic
396C4×D4C2311yescharacteristic
397C4×D4C2311yescharacteristic
398#117—21no—
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#117—21no—
404#117—21no—
405#117C2311yescharacteristic
406#117C2311yescharacteristic
407#117C2311yescharacteristic
408#117C2311yescharacteristic
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4C2311yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C42—21no—
421C2×C42C2311yescharacteristic
422#107C2311yescharacteristic
423#107C2311yescharacteristic
424#107C2311yescharacteristic
425#107C2311yescharacteristic
426#106C2311yescharacteristic
427#106C2311yescharacteristic
428#106C2311yescharacteristic
429#106C2311yescharacteristic
430C4⋊C8C2311yescharacteristic
431C4⋊C8C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433C4⋊C8C2311yescharacteristic
434C4⋊C8C2311yescharacteristic
435C4⋊C8C2311yescharacteristic
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
478#97C2311yescharacteristic
479#97C2311yescharacteristic
480C4×C8C2311yescharacteristic
481C4×C8C2311yescharacteristic
482C4×C8C2311yescharacteristic
483C4×C8C2311yescharacteristic
484C24—21no—
485C24—21no—
486#41—22no—
487#41—22no—
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—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—41no—
501C2×Q8—41no—
502C2×Q8C2×D411yescharacteristic
503C2×Q8C2411yescharacteristic
504C2×Q8C2411yescharacteristic
505C2×Q8C2411yescharacteristic
506C2×Q8C2411yescharacteristic
507C2×Q8C2411yescharacteristic
508C2×D4—22no—
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—41no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4C2×D411yescharacteristic
530C2×D4C2×D411yescharacteristic
531C2×D4C2×D411yescharacteristic
532C2×D4C2411yescharacteristic
533C2×D4C2411yescharacteristic
534C2×D4C2411yescharacteristic
535C2×D4C2411yescharacteristic
536C2×D4C2411yescharacteristic
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
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×C4C2×D411yescharacteristic
555C22×C4C2×D411yescharacteristic
556C22×C4C2411yescharacteristic
557C22×C4C2411yescharacteristic
558C22×C4C2411yescharacteristic
559Q16—41no—
560Q16—41no—
561Q16—41no—
562Q16—41no—
563Q16—41no—
564Q16—41no—
565SD16—22no—
566SD16—22no—
567SD16—22no—
568SD16—41no—
569SD16—41no—
570SD16—41no—
571SD16—41no—
572SD16—41no—
573SD16—41no—
574SD16—41no—
575SD16—41no—
576SD16—41no—
577D8—22no—
578D8—22no—
579D8—22no—
580D8—41no—
581D8—41no—
582D8—41no—
583M16—41no—
584M16—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8C2411yescharacteristic
590C2×C8C2411yescharacteristic
591C2×C8C2411yescharacteristic
592C2×C8C2411yescharacteristic
593C2×C8C2411yescharacteristic
594C2×C8C2411yescharacteristic
595C2×C8C2411yescharacteristic
596C2×C8C2411yescharacteristic
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
626C4⋊C4C2×D411yescharacteristic
627C4⋊C4C2×D411yescharacteristic
628C4⋊C4C2×D411yescharacteristic
629C4⋊C4C2×D411yescharacteristic
630C4⋊C4C2×D411yescharacteristic
631C4⋊C4C2×D411yescharacteristic
632C4⋊C4C2×D411yescharacteristic
633C4⋊C4C2×D411yescharacteristic
634C4⋊C4C2×D411yescharacteristic
635C4⋊C4C2411yescharacteristic
636C4⋊C4C2411yescharacteristic
637C4⋊C4C2411yescharacteristic
638C4⋊C4C2411yescharacteristic
639C4⋊C4C2411yescharacteristic
640C4⋊C4C2411yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
679C22⋊C4C2×D411yescharacteristic
680C22⋊C4C2×D411yescharacteristic
681C22⋊C4C2×D411yescharacteristic
682C22⋊C4C2×D411yescharacteristic
683C22⋊C4C2×D411yescharacteristic
684C22⋊C4C2×D411yescharacteristic
685C22⋊C4C2×D411yescharacteristic
686C22⋊C4C2×D411yescharacteristic
687C22⋊C4C2×D411yescharacteristic
688C42—21no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42C2×D411yescharacteristic
698C42C2×D411yescharacteristic
699C42C2411yescharacteristic
700C42C2411yescharacteristic
701C42C2411yescharacteristic
702C42C2411yescharacteristic
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—42no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23C22×D411yescharacteristic
715C23C22×D411yescharacteristic
716C23C22×D411yescharacteristic
717Q8—21no—
718Q8—21no—
719Q8—21no—
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8—41no—
728Q8—81no—
729Q8—81no—
730D4—21no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—42no—
743D4—42no—
744D4—42no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752D4—81no—
753D4—81no—
754D4—81no—
755D4—81no—
756D4—81no—
757D4—81no—
758D4—81no—
759D4H(5,𝔽2)12yes—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
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—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4C22×D411yescharacteristic
797C2×C4C22×D411yescharacteristic
798C2×C4C22×D411yescharacteristic
799C2×C4C22×D411yescharacteristic
800C2×C4C22×D411yescharacteristic
801C2×C4C22×D411yescharacteristic
802C2×C4C22×D411yescharacteristic
803C2×C4C22×D411yescharacteristic
804C2×C4C22×D411yescharacteristic
805C2×C4C22×D411yescharacteristic
806C2×C4C22×D411yescharacteristic
807C2×C4C2511yescharacteristic
808C8—21no—
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—22no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—162no—
841C22—162no—
842C22C23×D411yescharacteristic
843C4—21no—
844C4—21no—
845C4—21no—
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4C2×H(5,𝔽2)11yescharacteristic
866C4#58511yescharacteristic
867C2—41no—
868C2—41no—
869C2—41no—
870C2—42no—
871C2—81no—
872C2—81no—
873C2—81no—
874C2—81no—
875C2#348811yescharacteristic
876C2#358411yescharacteristic
877C2#358411yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3562C2semidirect
2. #3521C2semidirect
3. #3401C2semidirect
4. #3393C2semidirect
5. #3376C2semidirect
6. #3361C2semidirect
7. #3327C2semidirect
8. #3313C2semidirect
9. #3307C2semidirect
10. #3304C2semidirect
11. #3297C2semidirect
12. #3296C2semidirect
13. #3283C2semidirect
14. #3282C2semidirect
15. #3282C2semidirect
16. #3273C2semidirect
17. #3268C2semidirect
18. #3267C2semidirect
19. #3260C2semidirect
20. #3258C2semidirect
21. #3250C2semidirect
22. #3224C2semidirect
23. #3223C2semidirect
24. #3212C2semidirect
25. #3122C2semidirect
26. #3120C2semidirect
27. #3102C2semidirect
28. #3045C2semidirect
29. #3042C2semidirect
30. #3035C2semidirect
31. #2994C2semidirect
36. C2×#135C22semidirect
37. C22×SD16C22semidirect
40. #559C22semidirect
41. #556C22semidirect
42. #556C22semidirect
43. #556C22semidirect
44. #554C22semidirect
57. #547C22semidirect
60. #546C22semidirect
61. #546C22semidirect
63. #541C22semidirect
64. #541C22semidirect
73. #535C22semidirect
74. #532C22semidirect
77. #529C22semidirect
78. #529C22semidirect
81. #518C22semidirect
82. C4×#41C22semidirect
83. #497C22semidirect
87. #495C22semidirect
88. #494C22semidirect
89. #491C22semidirect
90. #489C22semidirect
91. #488C22semidirect
92. #488C22semidirect
93. #488C22semidirect
94. #486C22semidirect
95. #485C22semidirect
96. #484C22semidirect
97. #483C22semidirect
99. #482C22semidirect
100. #482C22semidirect
101. #479C22semidirect
102. #479C22semidirect
103. #479C22semidirect
104. #478C22semidirect
105. #478C22semidirect
106. #478C22semidirect
107. #478C22semidirect
108. #478C22semidirect
109. #477C22semidirect
110. #475C22semidirect
111. #470C22semidirect
114. #468C22semidirect
115. #467C22semidirect
116. #467C22semidirect
120. #465C22semidirect
121. #465C22semidirect
122. #465C22semidirect
123. #464C22semidirect
124. #464C22semidirect
125. #464C22semidirect
126. #464C22semidirect
127. #464C22semidirect
128. #464C22semidirect
129. #464C22semidirect
130. #464C22semidirect
138. #463C22semidirect
139. #462C22semidirect
140. #462C22semidirect
141. #461C22semidirect
142. #461C22semidirect
143. #461C22semidirect
144. #461C22semidirect
145. #461C22semidirect
146. #461C22semidirect
147. #460C22semidirect
148. #460C22semidirect
149. #460C22semidirect
157. #452C22semidirect
158. #452C22semidirect
159. #452C22semidirect
160. #452C22semidirect
161. #451C22semidirect
162. #451C22semidirect
163. #450C22semidirect
167. #449C22semidirect
170. #447C22semidirect
171. #446C22semidirect
172. C8×Q8C22semidirect
174. #442C22semidirect
175. #441C22semidirect
176. #440C22semidirect
177. C4×Q16C22semidirect
178. C4×Q16C22semidirect
179. C4×SD16C22semidirect
180. C4×SD16C22semidirect
181. C4×SD16C22semidirect
184. C4×D8C22semidirect
186. #435C22semidirect
187. #435C22semidirect
189. C8×D4C22semidirect
190. C8×D4C22semidirect
191. #433C22semidirect
192. #433C22semidirect
193. #431C22semidirect
194. #424C22semidirect
195. #424C22semidirect
196. C2×C4⋊C8C22semidirect
197. #419C22semidirect
198. #417C22semidirect
200. #416C22semidirect
201. #416C22semidirect
202. C2×#102C22semidirect

Maximal subgroups

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

subgroupindex
#35622
#35212
#34012
#33932
#33762
#33612
#33272
#33132
#33072
#33042
#32972
#32962
#32832
#32822
#32732
#32682
#32672
#32602
#32582
#32502
#32242
#32232
#32122
#31222
#31202
#31022
#30452
#30422
#30352
#29942