Finite Group Databasebeta

← #62322

Subgroups — #62322

Order 256.

897 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#3541C211yesmaximal, characteristic, complemented
2#3539C211yesmaximal, characteristic, complemented
3#3355C211yesmaximal, characteristic, complemented
4#3349C211yesmaximal, characteristic, complemented
5#3344C211yesmaximal, characteristic, complemented
6#3337C211yesmaximal, characteristic, complemented
7#3333C211yesmaximal, characteristic, complemented
8#3327C211yesmaximal, characteristic, complemented
9#3320C211yesmaximal, characteristic, complemented
10#3315C211yesmaximal, characteristic, complemented
11#3307C211yesmaximal, characteristic, complemented
12#3307C211yesmaximal, characteristic, complemented
13#3304C211yesmaximal, characteristic, complemented
14#3300C211yesmaximal, characteristic, complemented
15#3283C211yesmaximal, characteristic, complemented
16#3276C211yesmaximal, characteristic, complemented
17#3271C211yesmaximal, characteristic, complemented
18#3271C211yesmaximal, characteristic, complemented
19#3260C211yesmaximal, characteristic, complemented
20#3258C211yesmaximal, characteristic, complemented
21#3203C211yesmaximal, characteristic, complemented
22#3201C211yesmaximal, characteristic, complemented
23#3191C211yesmaximal, characteristic, complemented
24#3190C211yesmaximal, characteristic, complemented
25#3179C211yesmaximal, characteristic, complemented
26#3177C211yesmaximal, characteristic, complemented
27#3063C211yesmaximal, characteristic, complemented
28#3060C211yesmaximal, characteristic, complemented
29#3056C211yesmaximal, characteristic, complemented
30#3054C211yesmaximal, characteristic, complemented
31#2933C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic
33C2×#137C2211yescharacteristic, complemented
34C2×#135C2211yescharacteristic
35C2×#135C2211yescharacteristic, complemented
36C2×#131C2211yescharacteristic
37C22×M16C2211yescharacteristic
38#563—21no—
39#562—21no—
40#560—21no—
41#560—21no—
42#556C2211yescharacteristic
43#554—21no—
44#554C2211yescharacteristic
45#553—21no—
46#553—21no—
47#553—21no—
48#553C2211yescharacteristic
49#553C2211yescharacteristic
50#553C2211yescharacteristic
51#552C2211yescharacteristic
52#552C2211yescharacteristic
53#552C2211yescharacteristic
54#550C2211yescharacteristic
55#550C2211yescharacteristic
56D4×Q8C2211yescharacteristic
57#548C2211yescharacteristic
58#548C2211yescharacteristic
59#547C2211yescharacteristic
60#547C2211yescharacteristic
61#547C2211yescharacteristic
62#542—21no—
63#542C2211yescharacteristic
64#541C2211yescharacteristic
65#541C2211yescharacteristic
66#540—21no—
67#540—21no—
68#540C2211yescharacteristic
69#539—21no—
70#539—21no—
71#539—21no—
72#538—21no—
73#538—21no—
74#537C2211yescharacteristic
75#537C2211yescharacteristic
76#537C2211yescharacteristic
77#536C2211yescharacteristic
78#525C2211yescharacteristic
79#525C2211yescharacteristic
80#525C2211yescharacteristic
81#525C2211yescharacteristic
82C2×C22⋊Q8C2211yescharacteristic
83#501C2211yescharacteristic, complemented
84#499C2211yescharacteristic, complemented
85#496C2211yescharacteristic, complemented
86#494C2211yescharacteristic, complemented
87#491C2211yescharacteristic, complemented
88#491C2211yescharacteristic, complemented
89#488C2211yescharacteristic, complemented
90#486C2211yescharacteristic, complemented
91#485C2211yescharacteristic
92#485C2211yescharacteristic
93#485C2211yescharacteristic
94#485C2211yescharacteristic
95#485C2211yescharacteristic, complemented
96#484C2211yescharacteristic, complemented
97#484C2211yescharacteristic, complemented
98#484C2211yescharacteristic, complemented
99#483C2211yescharacteristic
100#483C2211yescharacteristic, complemented
101#482C2211yescharacteristic
102#482C2211yescharacteristic
103#482C2211yescharacteristic, complemented
104#480C2211yescharacteristic
105#480C2211yescharacteristic, complemented
106#480C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#479C2211yescharacteristic, complemented
109#479C2211yescharacteristic, complemented
110#478C2211yescharacteristic, complemented
111#478C2211yescharacteristic, complemented
112#478C2211yescharacteristic, complemented
113#477C2211yescharacteristic, complemented
114#475C2211yescharacteristic, complemented
115#470C2211yescharacteristic
116#470C2211yescharacteristic
117#470C2211yescharacteristic
118#470C2211yescharacteristic
119#470C2211yescharacteristic, complemented
120#470C2211yescharacteristic, complemented
121#469C2211yescharacteristic
122#469C2211yescharacteristic
123#469C2211yescharacteristic, complemented
124#468C2211yescharacteristic
125#468C2211yescharacteristic
126#468C2211yescharacteristic
127#468C2211yescharacteristic
128#468C2211yescharacteristic
129#468C2211yescharacteristic
130#468C2211yescharacteristic, complemented
131#467C2211yescharacteristic
132#467C2211yescharacteristic
133#467C2211yescharacteristic
134#467C2211yescharacteristic
135#467C2211yescharacteristic
136#467C2211yescharacteristic, complemented
137#466C2211yescharacteristic
138#465C2211yescharacteristic
139#465C2211yescharacteristic
140#465C2211yescharacteristic
141#465C2211yescharacteristic
142#465C2211yescharacteristic
143#465C2211yescharacteristic
144#465C2211yescharacteristic, complemented
145#465C2211yescharacteristic, complemented
146#465C2211yescharacteristic, complemented
147#464C2211yescharacteristic, complemented
148#464C2211yescharacteristic, complemented
149#462C2211yescharacteristic, complemented
150#461C2211yescharacteristic, complemented
151#461C2211yescharacteristic, complemented
152#461C2211yescharacteristic, complemented
153#460C2211yescharacteristic, complemented
154#460C2211yescharacteristic, complemented
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#452C2211yescharacteristic
158#452C2211yescharacteristic
159#452C2211yescharacteristic, complemented
160#452C2211yescharacteristic, complemented
161#452C2211yescharacteristic, complemented
162#452C2211yescharacteristic, complemented
163#451C2211yescharacteristic
164#451C2211yescharacteristic, complemented
165#449C2211yescharacteristic
166#449C2211yescharacteristic
167#449C2211yescharacteristic, complemented
168#449C2211yescharacteristic, complemented
169#448C2211yescharacteristic
170#448C2211yescharacteristic, complemented
171#442C2211yescharacteristic, complemented
172#441C2211yescharacteristic, complemented
173#441C2211yescharacteristic, complemented
174#440C2211yescharacteristic, complemented
175C4×Q16C2211yescharacteristic, complemented
176C4×Q16C2211yescharacteristic, complemented
177C4×SD16C2211yescharacteristic, complemented
178C4×D8C2211yescharacteristic, complemented
179#436C2211yescharacteristic
180#436C2211yescharacteristic
181#435C2211yescharacteristic
182#435C2211yescharacteristic
183#435C2211yescharacteristic
184#435C2211yescharacteristic
185C8×D4C2211yescharacteristic
186C8×D4C2211yescharacteristic
187#428C2211yescharacteristic
188#428C2211yescharacteristic, complemented
189#427C2211yescharacteristic
190C2×#106C2211yescharacteristic, complemented
191#424C2211yescharacteristic
192#419C2211yescharacteristic
193#417C2211yescharacteristic
194#417C2211yescharacteristic, complemented
195#417C2211yescharacteristic, complemented
196#416C2211yescharacteristic
197#416C2211yescharacteristic
198#416C2211yescharacteristic, complemented
199C2×#103C2211yescharacteristic, complemented
200#408C2211yescharacteristic
201C2×C22⋊C8C2211yescharacteristic
202#405C2211yescharacteristic
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C2×#41C2311yescharacteristic
210C22×Q8C2311yescharacteristic
211C22×Q8C2311yescharacteristic
212C23×C4C2311yescharacteristic
213#137—42no—
214#137—42no—
215#135—42no—
216#135—42no—
217C2×Q16C2311yescharacteristic
218C2×Q16C2311yescharacteristic
219C2×Q16C2311yescharacteristic
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×SD16C2311yescharacteristic
224C2×SD16C2311yescharacteristic
225C2×SD16C2311yescharacteristic
226C2×SD16C2311yescharacteristic
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×SD16C2311yescharacteristic
231C2×D8C2311yescharacteristic
232C2×D8C2311yescharacteristic
233#131—42no—
234C2×M16—42no—
235C2×M16C2311yescharacteristic
236C2×M16C2311yescharacteristic
237C2×M16C2311yescharacteristic
238C2×M16C2311yescharacteristic
239C2×M16C2311yescharacteristic
240C2×M16C2311yescharacteristic
241C22×C8C2311yescharacteristic
242C22×C8C2311yescharacteristic
243C22×C8C2311yescharacteristic
244C22×C8C2311yescharacteristic
245C22×C8C2311yescharacteristic
246C22×C8C2311yescharacteristic
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8C2311yescharacteristic
250C4⋊Q8C2311yescharacteristic
251C4⋊Q8C2311yescharacteristic
252#127—21no—
253#127—21no—
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#125—21no—
269#125—21no—
270#125—21no—
271#125—21no—
272#125—21no—
273#125—21no—
274#125—21no—
275#125—21no—
276#125C2311yescharacteristic
277#125C2311yescharacteristic
278#125C2311yescharacteristic
279#124—21no—
280#124—21no—
281#124—21no—
282#124—21no—
283#124—21no—
284#124C2311yescharacteristic
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—
300#123—21no—
301#123—21no—
302#123—21no—
303#123—21no—
304#123—21no—
305#123D411yescharacteristic
306#123D411yescharacteristic
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8D411yescharacteristic
320C22⋊Q8D411yescharacteristic
321C22⋊Q8C2311yescharacteristic
322C22⋊Q8C2311yescharacteristic
323C22⋊Q8C2311yescharacteristic
324C22⋊Q8C2311yescharacteristic
325C22⋊Q8C2311yescharacteristic
326C22⋊Q8C2311yescharacteristic
327C22⋊Q8C2311yescharacteristic
328C22⋊Q8C2311yescharacteristic
329C22⋊Q8C2311yescharacteristic
330C22⋊Q8C2311yescharacteristic
331C22⋊Q8C2311yescharacteristic
332C22⋊Q8C2311yescharacteristic
333C22⋊Q8C2311yescharacteristic
334C22⋊Q8C2311yescharacteristic
335C22⋊Q8C2311yescharacteristic
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#121—21no—
352#121—21no—
353#121—21no—
354#121—21no—
355#121—21no—
356#121—21no—
357#121—21no—
358#121—21no—
359#121D411yescharacteristic
360#121D411yescharacteristic
361#121C2311yescharacteristic
362#121C2311yescharacteristic
363#121C2311yescharacteristic
364#121C2311yescharacteristic
365#121C2311yescharacteristic
366#121C2311yescharacteristic
367#121C2311yescharacteristic
368#121C2311yescharacteristic
369#121C2311yescharacteristic
370#120—21no—
371#120—21no—
372#120—21no—
373#120D411yescharacteristic
374#120D411yescharacteristic
375C4×Q8—21no—
376C4×Q8C2311yescharacteristic
377C4×Q8C2311yescharacteristic
378C4×Q8C2311yescharacteristic
379C4×Q8C2311yescharacteristic
380C4×Q8C2311yescharacteristic
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×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C2311yescharacteristic
397C4×D4C2311yescharacteristic
398C4×D4C2311yescharacteristic
399C4×D4C2311yescharacteristic
400C4×D4C2311yescharacteristic
401C4×D4C2311yescharacteristic
402C4×D4C2311yescharacteristic
403#117—21no—
404#117—21no—
405#117—21no—
406#117C2311yescharacteristic
407#117C2311yescharacteristic
408#117C2311yescharacteristic
409#117C2311yescharacteristic
410#117C2311yescharacteristic
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4C2311yescharacteristic
416C2×C4⋊C4C2311yescharacteristic
417C2×C4⋊C4C2311yescharacteristic
418C2×C4⋊C4C2311yescharacteristic
419C2×C22⋊C4—21no—
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#103C2311yescharacteristic
457#103C2311yescharacteristic
458#103C2311yescharacteristic
459#103C2311yescharacteristic
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
482C4×C8C2311yescharacteristic
483C4×C8C2311yescharacteristic
484C24C2×D411yescharacteristic
485#41—41no—
486#41—41no—
487#41—41no—
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—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—41no—
503C2×Q8—41no—
504C2×Q8—41no—
505C2×Q8—41no—
506C2×Q8C2×D411yescharacteristic
507C2×Q8C2411yescharacteristic
508C2×Q8C2411yescharacteristic
509C2×Q8C2411yescharacteristic
510C2×Q8C2411yescharacteristic
511C2×Q8C2411yescharacteristic
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×D4C2×D411yescharacteristic
530C2×D4C2×D411yescharacteristic
531C2×D4C2×D411yescharacteristic
532C2×D4C2×D411yescharacteristic
533C2×D4C2×D411yescharacteristic
534C2×D4C2×D411yescharacteristic
535C2×D4C2×D411yescharacteristic
536C2×D4C2411yescharacteristic
537C2×D4C2411yescharacteristic
538C2×D4C2411yescharacteristic
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×C4—41no—
555C22×C4—41no—
556C22×C4C2×D411yescharacteristic
557C22×C4C2×D411yescharacteristic
558C22×C4C2×D411yescharacteristic
559C22×C4C2411yescharacteristic
560C22×C4C2411yescharacteristic
561C22×C4C2411yescharacteristic
562C22×C4C2411yescharacteristic
563C22×C4C2411yescharacteristic
564Q16—22no—
565Q16—22no—
566Q16—41no—
567Q16—41no—
568Q16—41no—
569Q16—41no—
570SD16—22no—
571SD16—41no—
572SD16—41no—
573SD16—41no—
574SD16—41no—
575SD16—41no—
576SD16—41no—
577SD16—41no—
578D8—22no—
579D8—41no—
580M16—22no—
581M16—22no—
582M16—22no—
583M16—41no—
584M16—41no—
585M16—41no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8C2411yescharacteristic
593C2×C8C2411yescharacteristic
594C2×C8C2411yescharacteristic
595C2×C8C2411yescharacteristic
596C2×C8C2411yescharacteristic
597C2×C8C2411yescharacteristic
598C2×C8C2411yescharacteristic
599C2×C8C2411yescharacteristic
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⋊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⋊C4—21no—
635C4⋊C4C2×D411yescharacteristic
636C4⋊C4C2×D411yescharacteristic
637C4⋊C4C2×D411yescharacteristic
638C4⋊C4C2×D411yescharacteristic
639C4⋊C4C2×D411yescharacteristic
640C4⋊C4C2×D411yescharacteristic
641C4⋊C4C2411yescharacteristic
642C4⋊C4C2411yescharacteristic
643C4⋊C4C2411yescharacteristic
644C4⋊C4C2411yescharacteristic
645C4⋊C4C2411yescharacteristic
646C4⋊C4C2411yescharacteristic
647C4⋊C4C2411yescharacteristic
648C4⋊C4C2411yescharacteristic
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⋊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—
700C42—21no—
701C42C2411yescharacteristic
702C42C2411yescharacteristic
703C23—21no—
704C23—21no—
705C23—21no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23C22×D411yescharacteristic
710C23C22×D411yescharacteristic
711C23C22×D411yescharacteristic
712C23C22×D411yescharacteristic
713C23C22×D411yescharacteristic
714Q8—21no—
715Q8—21no—
716Q8—21no—
717Q8—21no—
718Q8—21no—
719Q8—21no—
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—41no—
725Q8—81no—
726Q8—81no—
727Q8—81no—
728D4—21no—
729D4—21no—
730D4—21no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—42no—
742D4—81no—
743D4—81no—
744D4—81no—
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—
758C2×C4—21no—
759C2×C4—21no—
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—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
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×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
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×C4C22×D411yescharacteristic
808C2×C4C2511yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—21no—
816C8H(5,𝔽2)12yes—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—82no—
842C22C23×D411yescharacteristic
843C4—21no—
844C4—21no—
845C4—21no—
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—41no—
853C4—41no—
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—41no—
871C2—41no—
872C2—81no—
873C2—81no—
874C2—81no—
875C2#349611yescharacteristic
876C2#358411yescharacteristic
877C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #525 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3541C2semidirect
2. #3539C2semidirect
3. #3355C2semidirect
4. #3349C2semidirect
5. #3344C2semidirect
6. #3337C2semidirect
7. #3333C2semidirect
8. #3327C2semidirect
9. #3320C2semidirect
10. #3315C2semidirect
11. #3307C2semidirect
12. #3307C2semidirect
13. #3304C2semidirect
14. #3300C2semidirect
15. #3283C2semidirect
16. #3276C2semidirect
17. #3271C2semidirect
18. #3271C2semidirect
19. #3260C2semidirect
20. #3258C2semidirect
21. #3203C2semidirect
22. #3201C2semidirect
23. #3191C2semidirect
24. #3190C2semidirect
25. #3179C2semidirect
26. #3177C2semidirect
27. #3063C2semidirect
28. #3060C2semidirect
29. #3056C2semidirect
30. #3054C2semidirect
31. #2933C2semidirect
33. C2×#137C22semidirect
35. C2×#135C22semidirect
83. #501C22semidirect
84. #499C22semidirect
85. #496C22semidirect
86. #494C22semidirect
87. #491C22semidirect
88. #491C22semidirect
89. #488C22semidirect
90. #486C22semidirect
95. #485C22semidirect
96. #484C22semidirect
97. #484C22semidirect
98. #484C22semidirect
100. #483C22semidirect
103. #482C22semidirect
105. #480C22semidirect
106. #480C22semidirect
107. #479C22semidirect
108. #479C22semidirect
109. #479C22semidirect
110. #478C22semidirect
111. #478C22semidirect
112. #478C22semidirect
113. #477C22semidirect
114. #475C22semidirect
119. #470C22semidirect
120. #470C22semidirect
123. #469C22semidirect
130. #468C22semidirect
136. #467C22semidirect
144. #465C22semidirect
145. #465C22semidirect
146. #465C22semidirect
147. #464C22semidirect
148. #464C22semidirect
149. #462C22semidirect
150. #461C22semidirect
151. #461C22semidirect
152. #461C22semidirect
153. #460C22semidirect
154. #460C22semidirect
159. #452C22semidirect
160. #452C22semidirect
161. #452C22semidirect
162. #452C22semidirect
164. #451C22semidirect
167. #449C22semidirect
168. #449C22semidirect
170. #448C22semidirect
171. #442C22semidirect
172. #441C22semidirect
173. #441C22semidirect
174. #440C22semidirect
175. C4×Q16C22semidirect
176. C4×Q16C22semidirect
177. C4×SD16C22semidirect
178. C4×D8C22semidirect
188. #428C22semidirect
190. C2×#106C22semidirect
194. #417C22semidirect
195. #417C22semidirect
198. #416C22semidirect
199. C2×#103C22semidirect

Maximal subgroups

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

subgroupindex
#35412
#35392
#33552
#33492
#33442
#33372
#33332
#33272
#33202
#33152
#33072
#33042
#33002
#32832
#32762
#32712
#32602
#32582
#32032
#32012
#31912
#31902
#31792
#31772
#30632
#30602
#30562
#30542
#29332