Finite Group Databasebeta

← #62014

Subgroups — #62014

Order 256.

923 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3562C211yesmaximal, characteristic, complemented
2#3517C211yesmaximal, characteristic, complemented
3#3399C211yesmaximal, characteristic, complemented
4#3397C211yesmaximal, characteristic, complemented
5#3377C211yesmaximal, characteristic, complemented
6#3371C211yesmaximal, characteristic, complemented
7#3309C211yesmaximal, characteristic, complemented
8#3308C211yesmaximal, characteristic, complemented
9#3307C211yesmaximal, characteristic, complemented
10#3306C211yesmaximal, characteristic, complemented
11#3301C211yesmaximal, characteristic, complemented
12#3297C211yesmaximal, characteristic, complemented
13#3287C211yesmaximal, characteristic, complemented
14#3284C211yesmaximal, characteristic, complemented
15#3271C211yesmaximal, characteristic, complemented
16#3271C211yesmaximal, characteristic, complemented
17#3268C211yesmaximal, characteristic, complemented
18#3268C211yesmaximal, characteristic, complemented
19#3260C211yesmaximal, characteristic, complemented
20#3259C211yesmaximal, characteristic, complemented
21#3247C211yesmaximal, characteristic, complemented
22#3221C211yesmaximal, characteristic, complemented
23#3220C211yesmaximal, characteristic, complemented
24#3214C211yesmaximal, characteristic, complemented
25#3120C211yesmaximal, characteristic, complemented
26#3119C211yesmaximal, characteristic, complemented
27#3111C211yesmaximal, characteristic, complemented
28#3046C211yesmaximal, characteristic, complemented
29#3045C211yesmaximal, characteristic, complemented
30#3035C211yesmaximal, characteristic, complemented
31#2992C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic, complemented
33C2×AGL(1,ℤ/8)C2211yescharacteristic
34C2×#135C2211yescharacteristic
35C2×#135C2211yescharacteristic
36C2×#135C2211yescharacteristic
37C2×#135C2211yescharacteristic, complemented
38#562—21no—
39#560—21no—
40#559C2211yescharacteristic
41#557C2211yescharacteristic, complemented
42#556C2211yescharacteristic
43#553—21no—
44#553—21no—
45#553—21no—
46#553C2211yescharacteristic
47#553C2211yescharacteristic, complemented
48#551—21no—
49#550—21no—
50#550C2211yescharacteristic
51#550C2211yescharacteristic
52#550C2211yescharacteristic
53#550C2211yescharacteristic, complemented
54#550C2211yescharacteristic, complemented
55#548C2211yescharacteristic
56#548C2211yescharacteristic
57#547—21no—
58#547C2211yescharacteristic
59#547C2211yescharacteristic
60#546C2211yescharacteristic
61#546C2211yescharacteristic
62#541C2211yescharacteristic
63#540—21no—
64#540—21no—
65#540—21no—
66#540C2211yescharacteristic
67#540C2211yescharacteristic
68#540C2211yescharacteristic, complemented
69#539—21no—
70#538—21no—
71#538—21no—
72#536C2211yescharacteristic
73#535C2211yescharacteristic
74#532—21no—
75#532C2211yescharacteristic
76#532C2211yescharacteristic, complemented
77#529—21no—
78#529C2211yescharacteristic
79#529C2211yescharacteristic
80#520C2211yescharacteristic
81#520C2211yescharacteristic, complemented
82C4×#41C2211yescharacteristic, complemented
83#496C2211yescharacteristic
84#496C2211yescharacteristic
85#496C2211yescharacteristic
86#496C2211yescharacteristic, complemented
87#493C2211yescharacteristic
88#492C2211yescharacteristic, complemented
89#491C2211yescharacteristic, complemented
90#490C2211yescharacteristic
91#489C2211yescharacteristic
92#489C2211yescharacteristic, complemented
93#488C2211yescharacteristic
94#488C2211yescharacteristic
95#485C2211yescharacteristic, complemented
96#484C2211yescharacteristic
97#483C2211yescharacteristic
98#482C2211yescharacteristic
99#481C2211yescharacteristic
100#480C2211yescharacteristic, complemented
101#479C2211yescharacteristic, complemented
102#479C2211yescharacteristic, complemented
103#479C2211yescharacteristic, complemented
104#478C2211yescharacteristic
105#478C2211yescharacteristic, complemented
106#478C2211yescharacteristic, complemented
107#478C2211yescharacteristic, complemented
108#478C2211yescharacteristic, complemented
109#477C2211yescharacteristic, complemented
110#476C2211yescharacteristic
111#469C2211yescharacteristic
112#469C2211yescharacteristic, complemented
113#468C2211yescharacteristic
114#468C2211yescharacteristic
115#466C2211yescharacteristic
116#466C2211yescharacteristic
117#466C2211yescharacteristic
118#466C2211yescharacteristic, complemented
119#465C2211yescharacteristic
120#465C2211yescharacteristic
121#465C2211yescharacteristic, complemented
122#465C2211yescharacteristic, complemented
123#464C2211yescharacteristic
124#464C2211yescharacteristic
125#464C2211yescharacteristic
126#464C2211yescharacteristic
127#464C2211yescharacteristic, complemented
128#463C2211yescharacteristic
129#463C2211yescharacteristic
130#463C2211yescharacteristic
131#463C2211yescharacteristic
132#463C2211yescharacteristic
133#463C2211yescharacteristic
134#463C2211yescharacteristic, complemented
135#462C2211yescharacteristic, complemented
136#462C2211yescharacteristic, complemented
137#461C2211yescharacteristic, complemented
138#461C2211yescharacteristic, complemented
139#461C2211yescharacteristic, complemented
140#461C2211yescharacteristic, complemented
141#460C2211yescharacteristic
142#460C2211yescharacteristic
143#460C2211yescharacteristic, complemented
144#460C2211yescharacteristic, complemented
145#460C2211yescharacteristic, complemented
146#459C2211yescharacteristic
147#459C2211yescharacteristic
148#459C2211yescharacteristic
149#459C2211yescharacteristic
150#459C2211yescharacteristic
151#459C2211yescharacteristic
152#459C2211yescharacteristic, complemented
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic, complemented
156#449C2211yescharacteristic
157#449C2211yescharacteristic
158#449C2211yescharacteristic
159#449C2211yescharacteristic
160#449C2211yescharacteristic
161#449C2211yescharacteristic
162#449C2211yescharacteristic
163#449C2211yescharacteristic
164#449C2211yescharacteristic, complemented
165#449C2211yescharacteristic, complemented
166#449C2211yescharacteristic, complemented
167#448C2211yescharacteristic, complemented
168#448C2211yescharacteristic, complemented
169#447C2211yescharacteristic
170#447C2211yescharacteristic
171#446C2211yescharacteristic, complemented
172#446C2211yescharacteristic, complemented
173#442C2211yescharacteristic
174#442C2211yescharacteristic, complemented
175#441C2211yescharacteristic, complemented
176#441C2211yescharacteristic, complemented
177#440C2211yescharacteristic
178#440C2211yescharacteristic
179#440C2211yescharacteristic, complemented
180#440C2211yescharacteristic, complemented
181C4×Q16C2211yescharacteristic, complemented
182C4×SD16C2211yescharacteristic, complemented
183C4×SD16C2211yescharacteristic, complemented
184C4×D8C2211yescharacteristic
185#435C2211yescharacteristic
186#435C2211yescharacteristic
187#435C2211yescharacteristic
188#435C2211yescharacteristic, complemented
189C8×D4C2211yescharacteristic
190C8×D4C2211yescharacteristic, complemented
191#433C2211yescharacteristic
192#433C2211yescharacteristic, complemented
193#432C2211yescharacteristic, complemented
194#424C2211yescharacteristic
195#424C2211yescharacteristic, complemented
196C2×C4⋊C8C2211yescharacteristic, complemented
197#417C2211yescharacteristic
198#417C2211yescharacteristic
199#416C2211yescharacteristic
200#416C2211yescharacteristic, complemented
201C2×#103C2211yescharacteristic, complemented
202C2×#102C2211yescharacteristic
203C2×#41—21no—
204C2×#41—21no—
205C2×#41—21no—
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C2×#41C2311yescharacteristic
210C2×#41C2311yescharacteristic
211C2×#41C2311yescharacteristic
212C2×#41C2311yescharacteristic
213C22×Q8C2311yescharacteristic
214C22×D4C2311yescharacteristic
215#137—42no—
216AGL(1,ℤ/8)—42no—
217#135—42no—
218#135—42no—
219#135—42no—
220#135—42no—
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×Q16C2311yescharacteristic
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×D8C2311yescharacteristic
243C2×D8C2311yescharacteristic
244C2×D8C2311yescharacteristic
245C2×M16C2311yescharacteristic
246C2×M16C2311yescharacteristic
247C22×C8C2311yescharacteristic
248C22×C8C2311yescharacteristic
249C22×C8C2311yescharacteristic
250C22×C8C2311yescharacteristic
251C4⋊Q8—21no—
252C4⋊Q8C2311yescharacteristic
253C4⋊Q8C2311yescharacteristic
254C4⋊Q8C2311yescharacteristic
255#127—21no—
256#127—21no—
257#127—21no—
258#127—21no—
259#127C2311yescharacteristic
260#127C2311yescharacteristic
261#127C2311yescharacteristic
262#127C2311yescharacteristic
263#127C2311yescharacteristic
264#126—21no—
265#126—21no—
266#126—21no—
267#126—21no—
268#126—21no—
269#126—21no—
270#126—21no—
271#126D411yescharacteristic
272#126D411yescharacteristic
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#124D411yescharacteristic
286#124C2311yescharacteristic
287#124C2311yescharacteristic
288#124C2311yescharacteristic
289#124C2311yescharacteristic
290#124C2311yescharacteristic
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—
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#123D411yescharacteristic
311#123D411yescharacteristic
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8D411yescharacteristic
319C22⋊Q8C2311yescharacteristic
320C22⋊Q8C2311yescharacteristic
321C22⋊Q8C2311yescharacteristic
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#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#121—21no—
351#121D411yescharacteristic
352#121C2311yescharacteristic
353#121C2311yescharacteristic
354#121C2311yescharacteristic
355#121C2311yescharacteristic
356#121C2311yescharacteristic
357#121C2311yescharacteristic
358#121C2311yescharacteristic
359#121C2311yescharacteristic
360#121C2311yescharacteristic
361#120—21no—
362#120—21no—
363#120—21no—
364#120—21no—
365C4×Q8—21no—
366C4×Q8C2311yescharacteristic
367C4×Q8C2311yescharacteristic
368C4×Q8C2311yescharacteristic
369C4×Q8C2311yescharacteristic
370C4×Q8C2311yescharacteristic
371C4×Q8C2311yescharacteristic
372C4×Q8C2311yescharacteristic
373C4×Q8C2311yescharacteristic
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×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4C2311yescharacteristic
394C4×D4C2311yescharacteristic
395C4×D4C2311yescharacteristic
396C4×D4C2311yescharacteristic
397C4×D4C2311yescharacteristic
398C4×D4C2311yescharacteristic
399C4×D4C2311yescharacteristic
400C4×D4C2311yescharacteristic
401C4×D4C2311yescharacteristic
402C4×D4C2311yescharacteristic
403C4×D4C2311yescharacteristic
404C4×D4C2311yescharacteristic
405#117—21no—
406#117—21no—
407#117—21no—
408#117—21no—
409#117—21no—
410#117C2311yescharacteristic
411#117C2311yescharacteristic
412#117C2311yescharacteristic
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4C2311yescharacteristic
417C2×C4⋊C4C2311yescharacteristic
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#102C2311yescharacteristic
455#102C2311yescharacteristic
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
480#97C2311yescharacteristic
481#97C2311yescharacteristic
482C4×C8C2311yescharacteristic
483C4×C8C2311yescharacteristic
484C24—21no—
485#41—22no—
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—
498#41—41no—
499#41—82no—
500#41—82no—
501#41—82no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—41no—
505C2×Q8—41no—
506C2×Q8C2×D411yescharacteristic
507C2×Q8C2411yescharacteristic
508C2×Q8C2411yescharacteristic
509C2×Q8C2411yescharacteristic
510C2×Q8C2411yescharacteristic
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—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—41no—
539C2×D4—41no—
540C2×D4C2×D411yescharacteristic
541C2×D4C2×D411yescharacteristic
542C2×D4C2×D411yescharacteristic
543C2×D4C2411yescharacteristic
544C2×D4C2411yescharacteristic
545C2×D4C2411yescharacteristic
546C2×D4C2411yescharacteristic
547C2×D4C2411yescharacteristic
548C2×D4C2411yescharacteristic
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4C2×D411yescharacteristic
569C22×C4C2×D411yescharacteristic
570C22×C4C2411yescharacteristic
571C22×C4C2411yescharacteristic
572C22×C4C2411yescharacteristic
573Q16—22no—
574Q16—22no—
575Q16—22no—
576SD16—22no—
577SD16—22no—
578SD16—22no—
579SD16—41no—
580SD16—41no—
581SD16—41no—
582SD16—41no—
583SD16—41no—
584SD16—41no—
585SD16—41no—
586SD16—41no—
587SD16—41no—
588D8—41no—
589D8—41no—
590D8—41no—
591D8—41no—
592D8—41no—
593D8—41no—
594D8—41no—
595D8—41no—
596D8—41no—
597M16—41no—
598M16—41no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8C2411yescharacteristic
604C2×C8C2411yescharacteristic
605C2×C8C2411yescharacteristic
606C2×C8C2411yescharacteristic
607C2×C8C2411yescharacteristic
608C2×C8C2411yescharacteristic
609C2×C8C2411yescharacteristic
610C2×C8C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
639C4⋊C4C2×D411yescharacteristic
640C4⋊C4C2×D411yescharacteristic
641C4⋊C4C2×D411yescharacteristic
642C4⋊C4C2×D411yescharacteristic
643C4⋊C4C2×D411yescharacteristic
644C4⋊C4C2411yescharacteristic
645C4⋊C4C2411yescharacteristic
646C4⋊C4C2411yescharacteristic
647C4⋊C4C2411yescharacteristic
648C4⋊C4C2411yescharacteristic
649C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
683C22⋊C4C2×D411yescharacteristic
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—
700C42C2×D411yescharacteristic
701C42C2×D411yescharacteristic
702C42C2411yescharacteristic
703C42C2411yescharacteristic
704C42C2411yescharacteristic
705C42C2411yescharacteristic
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23C22×D411yescharacteristic
716C23C22×D411yescharacteristic
717C23C22×D411yescharacteristic
718Q8—21no—
719Q8—21no—
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—41no—
726Q8—42no—
727Q8—81no—
728Q8H(5,𝔽2)12yes—
729D4—21no—
730D4—21no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—21no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—42no—
745D4—42no—
746D4—42no—
747D4—42no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752D4—81no—
753D4—81no—
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—
768D4—81no—
769D4—81no—
770D4—81no—
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—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4C22×D411yescharacteristic
809C2×C4C22×D411yescharacteristic
810C2×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
820C8—21no—
821C8—21no—
822C8—21no—
823C8—21no—
824C8—21no—
825C8—21no—
826C8—21no—
827C8—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—162no—
856C22C23×D411yescharacteristic
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—22no—
869C4—41no—
870C4—41no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4C2×H(5,𝔽2)11yescharacteristic
879C4#58511yescharacteristic
880C2—41no—
881C2—41no—
882C2—41no—
883C2—81no—
884C2—81no—
885C2—81no—
886C2—81no—
887C2—81no—
888C2—81no—
889C2#348811yescharacteristic
890C2#358411yescharacteristic
891C2#358511yescharacteristic
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. #3517C2semidirect
3. #3399C2semidirect
4. #3397C2semidirect
5. #3377C2semidirect
6. #3371C2semidirect
7. #3309C2semidirect
8. #3308C2semidirect
9. #3307C2semidirect
10. #3306C2semidirect
11. #3301C2semidirect
12. #3297C2semidirect
13. #3287C2semidirect
14. #3284C2semidirect
15. #3271C2semidirect
16. #3271C2semidirect
17. #3268C2semidirect
18. #3268C2semidirect
19. #3260C2semidirect
20. #3259C2semidirect
21. #3247C2semidirect
22. #3221C2semidirect
23. #3220C2semidirect
24. #3214C2semidirect
25. #3120C2semidirect
26. #3119C2semidirect
27. #3111C2semidirect
28. #3046C2semidirect
29. #3045C2semidirect
30. #3035C2semidirect
31. #2992C2semidirect
32. C2×#137C22semidirect
37. C2×#135C22semidirect
41. #557C22semidirect
47. #553C22semidirect
53. #550C22semidirect
54. #550C22semidirect
68. #540C22semidirect
76. #532C22semidirect
81. #520C22semidirect
82. C4×#41C22semidirect
86. #496C22semidirect
88. #492C22semidirect
89. #491C22semidirect
92. #489C22semidirect
95. #485C22semidirect
100. #480C22semidirect
101. #479C22semidirect
102. #479C22semidirect
103. #479C22semidirect
105. #478C22semidirect
106. #478C22semidirect
107. #478C22semidirect
108. #478C22semidirect
109. #477C22semidirect
112. #469C22semidirect
118. #466C22semidirect
121. #465C22semidirect
122. #465C22semidirect
127. #464C22semidirect
134. #463C22semidirect
135. #462C22semidirect
136. #462C22semidirect
137. #461C22semidirect
138. #461C22semidirect
139. #461C22semidirect
140. #461C22semidirect
143. #460C22semidirect
144. #460C22semidirect
145. #460C22semidirect
152. #459C22semidirect
155. #452C22semidirect
164. #449C22semidirect
165. #449C22semidirect
166. #449C22semidirect
167. #448C22semidirect
168. #448C22semidirect
171. #446C22semidirect
172. #446C22semidirect
174. #442C22semidirect
175. #441C22semidirect
176. #441C22semidirect
179. #440C22semidirect
180. #440C22semidirect
181. C4×Q16C22semidirect
182. C4×SD16C22semidirect
183. C4×SD16C22semidirect
188. #435C22semidirect
190. C8×D4C22semidirect
192. #433C22semidirect
193. #432C22semidirect
195. #424C22semidirect
196. C2×C4⋊C8C22semidirect
200. #416C22semidirect
201. C2×#103C22semidirect

Maximal subgroups

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

subgroupindex
#35622
#35172
#33992
#33972
#33772
#33712
#33092
#33082
#33072
#33062
#33012
#32972
#32872
#32842
#32712
#32682
#32602
#32592
#32472
#32212
#32202
#32142
#31202
#31192
#31112
#30462
#30452
#30352
#29922