Finite Group Databasebeta

← #62080

Subgroups — #62080

Order 256.

889 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3552C211yesmaximal, characteristic, complemented
2#3521C211yesmaximal, characteristic, complemented
3#3402C211yesmaximal, characteristic, complemented
4#3398C211yesmaximal, characteristic, complemented
5#3376C211yesmaximal, characteristic, complemented
6#3372C211yesmaximal, characteristic, complemented
7#3328C211yesmaximal, characteristic, complemented
8#3326C211yesmaximal, characteristic, complemented
9#3320C211yesmaximal, characteristic, complemented
10#3315C211yesmaximal, characteristic, complemented
11#3313C211yesmaximal, characteristic, complemented
12#3312C211yesmaximal, characteristic, complemented
13#3276C211yesmaximal, characteristic, complemented
14#3275C211yesmaximal, characteristic, complemented
15#3269C211yesmaximal, characteristic, complemented
16#3267C211yesmaximal, characteristic, complemented
17#3266C211yesmaximal, characteristic, complemented
18#3266C211yesmaximal, characteristic, complemented
19#3261C211yesmaximal, characteristic, complemented
20#3258C211yesmaximal, characteristic, complemented
21#3256C211yesmaximal, characteristic, complemented
22#3225C211yesmaximal, characteristic, complemented
23#3223C211yesmaximal, characteristic, complemented
24#3218C211yesmaximal, characteristic, complemented
25#3123C211yesmaximal, characteristic, complemented
26#3120C211yesmaximal, characteristic, complemented
27#3111C211yesmaximal, characteristic, complemented
28#3046C211yesmaximal, characteristic, complemented
29#3042C211yesmaximal, characteristic, complemented
30#3039C211yesmaximal, characteristic, complemented
31#2995C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic
33C2×#137C2211yescharacteristic
34C2×#137C2211yescharacteristic
35C2×AGL(1,ℤ/8)C2211yescharacteristic
36C2×#135C2211yescharacteristic
37C22×SD16C2211yescharacteristic
38#563—21no—
39#563—21no—
40#557C2211yescharacteristic, complemented
41#556C2211yescharacteristic
42#556C2211yescharacteristic
43#556C2211yescharacteristic, complemented
44#554—21no—
45#554C2211yescharacteristic
46#553—21no—
47#553—21no—
48#553C2211yescharacteristic
49#552—21no—
50#552C2211yescharacteristic
51#551—21no—
52#551—21no—
53D4×Q8C2211yescharacteristic
54D4×Q8C2211yescharacteristic
55D4×Q8C2211yescharacteristic, complemented
56#548C2211yescharacteristic
57#548C2211yescharacteristic, complemented
58#547C2211yescharacteristic
59#547C2211yescharacteristic
60#546C2211yescharacteristic
61#546C2211yescharacteristic
62#544—21no—
63#542—21no—
64#542C2211yescharacteristic
65#541C2211yescharacteristic
66#541C2211yescharacteristic
67#541C2211yescharacteristic, complemented
68#539—21no—
69#539—21no—
70#539—21no—
71#538—21no—
72#536C2211yescharacteristic
73#536C2211yescharacteristic, complemented
74C2×C4⋊Q8C2211yescharacteristic, complemented
75#529—21no—
76#529C2211yescharacteristic
77#529C2211yescharacteristic
78#529C2211yescharacteristic, complemented
79C2×#126—21no—
80#520C2211yescharacteristic
81#518C2211yescharacteristic
82C4×#41C2211yescharacteristic
83#497C2211yescharacteristic
84#497C2211yescharacteristic
85#497C2211yescharacteristic
86#497C2211yescharacteristic, complemented
87#495C2211yescharacteristic
88#494C2211yescharacteristic, complemented
89#491C2211yescharacteristic, complemented
90#491C2211yescharacteristic, complemented
91#491C2211yescharacteristic, complemented
92#489C2211yescharacteristic, complemented
93#488C2211yescharacteristic, complemented
94#487C2211yescharacteristic, complemented
95#485C2211yescharacteristic
96#485C2211yescharacteristic
97#485C2211yescharacteristic, complemented
98#484C2211yescharacteristic, complemented
99#483C2211yescharacteristic, complemented
100#482C2211yescharacteristic, complemented
101#479C2211yescharacteristic, complemented
102#479C2211yescharacteristic, complemented
103#479C2211yescharacteristic, complemented
104#479C2211yescharacteristic, complemented
105#479C2211yescharacteristic, complemented
106#478C2211yescharacteristic
107#478C2211yescharacteristic
108#478C2211yescharacteristic, complemented
109#477C2211yescharacteristic, complemented
110#475C2211yescharacteristic, complemented
111#470C2211yescharacteristic
112#470C2211yescharacteristic
113#470C2211yescharacteristic, complemented
114#470C2211yescharacteristic, complemented
115#469C2211yescharacteristic
116#468C2211yescharacteristic
117#468C2211yescharacteristic
118#468C2211yescharacteristic, complemented
119#467C2211yescharacteristic
120#467C2211yescharacteristic
121#467C2211yescharacteristic, complemented
122#465C2211yescharacteristic
123#464C2211yescharacteristic
124#464C2211yescharacteristic
125#464C2211yescharacteristic
126#464C2211yescharacteristic, complemented
127#464C2211yescharacteristic, complemented
128#464C2211yescharacteristic, complemented
129#463C2211yescharacteristic
130#463C2211yescharacteristic
131#463C2211yescharacteristic
132#463C2211yescharacteristic
133#463C2211yescharacteristic
134#463C2211yescharacteristic
135#462C2211yescharacteristic, complemented
136#462C2211yescharacteristic, complemented
137#462C2211yescharacteristic, complemented
138#462C2211yescharacteristic, complemented
139#462C2211yescharacteristic, complemented
140#462C2211yescharacteristic, complemented
141#462C2211yescharacteristic, complemented
142#462C2211yescharacteristic, complemented
143#462C2211yescharacteristic, complemented
144#461C2211yescharacteristic
145#461C2211yescharacteristic
146#461C2211yescharacteristic
147#461C2211yescharacteristic
148#461C2211yescharacteristic
149#461C2211yescharacteristic
150#461C2211yescharacteristic
151#461C2211yescharacteristic
152#461C2211yescharacteristic
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#452C2211yescharacteristic
158#452C2211yescharacteristic, complemented
159#451C2211yescharacteristic
160#451C2211yescharacteristic
161#451C2211yescharacteristic, complemented
162#451C2211yescharacteristic, complemented
163#451C2211yescharacteristic, complemented
164#450C2211yescharacteristic
165#450C2211yescharacteristic
166#449C2211yescharacteristic
167#449C2211yescharacteristic
168#448C2211yescharacteristic
169#448C2211yescharacteristic
170#448C2211yescharacteristic
171#446C2211yescharacteristic, complemented
172#446C2211yescharacteristic, complemented
173#442C2211yescharacteristic
174#441C2211yescharacteristic, complemented
175#441C2211yescharacteristic, complemented
176#440C2211yescharacteristic
177#440C2211yescharacteristic
178#440C2211yescharacteristic
179#440C2211yescharacteristic
180#440C2211yescharacteristic, complemented
181C4×Q16C2211yescharacteristic, complemented
182C4×SD16C2211yescharacteristic
183C4×SD16C2211yescharacteristic
184C4×SD16C2211yescharacteristic
185#436C2211yescharacteristic
186#436C2211yescharacteristic, complemented
187#435C2211yescharacteristic
188#435C2211yescharacteristic
189#435C2211yescharacteristic
190#435C2211yescharacteristic, complemented
191#433C2211yescharacteristic
192#433C2211yescharacteristic, complemented
193#432C2211yescharacteristic, complemented
194#424C2211yescharacteristic
195#424C2211yescharacteristic, complemented
196#423C2211yescharacteristic, complemented
197#419C2211yescharacteristic
198#419C2211yescharacteristic, complemented
199#419C2211yescharacteristic, complemented
200#417C2211yescharacteristic, complemented
201#416C2211yescharacteristic
202C2×#103C2211yescharacteristic, complemented
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×Q8C2311yescharacteristic
211C22×D4C2311yescharacteristic
212#137—42no—
213#137—42no—
214#137—42no—
215AGL(1,ℤ/8)—42no—
216#135—42no—
217C2×Q16C2311yescharacteristic
218C2×Q16C2311yescharacteristic
219C2×Q16C2311yescharacteristic
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×Q16C2311yescharacteristic
224C2×Q16C2311yescharacteristic
225C2×Q16C2311yescharacteristic
226C2×Q16C2311yescharacteristic
227C2×SD16—42no—
228C2×SD16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×SD16C2311yescharacteristic
231C2×SD16C2311yescharacteristic
232C2×SD16C2311yescharacteristic
233C2×SD16C2311yescharacteristic
234C2×SD16C2311yescharacteristic
235C2×SD16C2311yescharacteristic
236C2×SD16C2311yescharacteristic
237C2×SD16C2311yescharacteristic
238C2×SD16C2311yescharacteristic
239C2×SD16C2311yescharacteristic
240C2×D8C2311yescharacteristic
241C2×D8C2311yescharacteristic
242C2×M16C2311yescharacteristic
243C2×M16C2311yescharacteristic
244C2×M16C2311yescharacteristic
245C2×M16C2311yescharacteristic
246C22×C8C2311yescharacteristic
247C22×C8C2311yescharacteristic
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8C2311yescharacteristic
254C4⋊Q8C2311yescharacteristic
255C4⋊Q8C2311yescharacteristic
256C4⋊Q8C2311yescharacteristic
257C4⋊Q8C2311yescharacteristic
258C4⋊Q8C2311yescharacteristic
259C4⋊Q8C2311yescharacteristic
260C4⋊Q8C2311yescharacteristic
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#126—21no—
271#126—21no—
272#126—21no—
273#126—21no—
274#126—21no—
275#126—21no—
276#126—21no—
277#126—21no—
278#126D411yescharacteristic
279#126D411yescharacteristic
280#125—21no—
281#125—21no—
282#125—21no—
283#125—21no—
284#125—21no—
285#125—21no—
286#125—21no—
287#125—21no—
288#125—21no—
289#125—21no—
290#125D411yescharacteristic
291#125C2311yescharacteristic
292#125C2311yescharacteristic
293#125C2311yescharacteristic
294#124—21no—
295#124—21no—
296#124—21no—
297#124—21no—
298#124D411yescharacteristic
299#124C2311yescharacteristic
300#124C2311yescharacteristic
301#124C2311yescharacteristic
302#124C2311yescharacteristic
303#124C2311yescharacteristic
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#123—21no—
314#123—21no—
315#123—21no—
316#123—21no—
317#123—21no—
318#123—21no—
319#123D411yescharacteristic
320#123D411yescharacteristic
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338C22⋊Q8—21no—
339C22⋊Q8D411yescharacteristic
340C22⋊Q8C2311yescharacteristic
341C22⋊Q8C2311yescharacteristic
342C22⋊Q8C2311yescharacteristic
343C22⋊Q8C2311yescharacteristic
344C22⋊Q8C2311yescharacteristic
345C22⋊Q8C2311yescharacteristic
346C22⋊Q8C2311yescharacteristic
347C22⋊Q8C2311yescharacteristic
348C22⋊Q8C2311yescharacteristic
349#121—21no—
350#121—21no—
351#121—21no—
352#121—21no—
353#121—21no—
354#121—21no—
355#121—21no—
356#121D411yescharacteristic
357#121C2311yescharacteristic
358#121C2311yescharacteristic
359#121C2311yescharacteristic
360#120—21no—
361#120—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8C2311yescharacteristic
365C4×Q8C2311yescharacteristic
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×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⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4C2311yescharacteristic
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#103C2311yescharacteristic
457#103C2311yescharacteristic
458#103C2311yescharacteristic
459#103C2311yescharacteristic
460#103C2311yescharacteristic
461#103C2311yescharacteristic
462#103C2311yescharacteristic
463#103C2311yescharacteristic
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—41no—
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—41no—
499C2×Q8—41no—
500C2×Q8—41no—
501C2×Q8—41no—
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×Q8C2411yescharacteristic
513C2×Q8C2411yescharacteristic
514C2×D4—22no—
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—41no—
524C2×D4C2×D411yescharacteristic
525C2×D4C2×D411yescharacteristic
526C2×D4C2×D411yescharacteristic
527C2×D4C2411yescharacteristic
528C2×D4C2411yescharacteristic
529C2×D4C2411yescharacteristic
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
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×C4C2×D411yescharacteristic
547C22×C4C2×D411yescharacteristic
548C22×C4C2411yescharacteristic
549C22×C4C2411yescharacteristic
550C22×C4C2411yescharacteristic
551Q16—41no—
552Q16—41no—
553Q16—41no—
554Q16—41no—
555Q16—41no—
556Q16—41no—
557Q16—41no—
558Q16—41no—
559Q16—41no—
560Q16—41no—
561SD16—22no—
562SD16—22no—
563SD16—22no—
564SD16—22no—
565SD16—22no—
566SD16—41no—
567SD16—41no—
568SD16—41no—
569SD16—41no—
570SD16—41no—
571SD16—41no—
572SD16—41no—
573D8—22no—
574D8—41no—
575M16—41no—
576M16—41no—
577M16—41no—
578M16—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8C2411yescharacteristic
582C2×C8C2411yescharacteristic
583C2×C8C2411yescharacteristic
584C2×C8C2411yescharacteristic
585C2×C8C2411yescharacteristic
586C2×C8C2411yescharacteristic
587C2×C8C2411yescharacteristic
588C2×C8C2411yescharacteristic
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
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⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4C2×D411yescharacteristic
630C4⋊C4C2×D411yescharacteristic
631C4⋊C4C2×D411yescharacteristic
632C4⋊C4C2×D411yescharacteristic
633C4⋊C4C2×D411yescharacteristic
634C4⋊C4C2×D411yescharacteristic
635C4⋊C4C2×D411yescharacteristic
636C4⋊C4C2×D411yescharacteristic
637C4⋊C4C2×D411yescharacteristic
638C4⋊C4C2×D411yescharacteristic
639C4⋊C4C2411yescharacteristic
640C4⋊C4C2411yescharacteristic
641C4⋊C4C2411yescharacteristic
642C4⋊C4C2411yescharacteristic
643C4⋊C4C2411yescharacteristic
644C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
677C22⋊C4C2×D411yescharacteristic
678C22⋊C4C2×D411yescharacteristic
679C22⋊C4C2×D411yescharacteristic
680C22⋊C4C2×D411yescharacteristic
681C22⋊C4C2×D411yescharacteristic
682C22⋊C4C2×D411yescharacteristic
683C22⋊C4C2×D411yescharacteristic
684C22⋊C4C2×D411yescharacteristic
685C22⋊C4C2×D411yescharacteristic
686C42—21no—
687C42—21no—
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—42no—
707C23—81no—
708C23—81no—
709C23C22×D411yescharacteristic
710C23C22×D411yescharacteristic
711C23C22×D411yescharacteristic
712Q8—21no—
713Q8—21no—
714Q8—21no—
715Q8—21no—
716Q8—21no—
717Q8—21no—
718Q8—21no—
719Q8—21no—
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—41no—
727Q8—81no—
728Q8—81no—
729Q8—81no—
730Q8—81no—
731Q8—81no—
732D4—21no—
733D4—21no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—42no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4H(5,𝔽2)12yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
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—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4C22×D411yescharacteristic
787C2×C4C22×D411yescharacteristic
788C2×C4C22×D411yescharacteristic
789C2×C4C22×D411yescharacteristic
790C2×C4C22×D411yescharacteristic
791C2×C4C22×D411yescharacteristic
792C2×C4C22×D411yescharacteristic
793C2×C4C22×D411yescharacteristic
794C2×C4C22×D411yescharacteristic
795C2×C4C22×D411yescharacteristic
796C2×C4C22×D411yescharacteristic
797C2×C4C2511yescharacteristic
798C8—21no—
799C8—21no—
800C8—21no—
801C8—21no—
802C8—21no—
803C8—21no—
804C8—21no—
805C8—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—22no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—162no—
825C22C23×D411yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4C2×H(5,𝔽2)11yescharacteristic
851C4#58511yescharacteristic
852C2—41no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2#348811yescharacteristic
859C2#358611yescharacteristic
860C2#358611yescharacteristic
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. #3552C2semidirect
2. #3521C2semidirect
3. #3402C2semidirect
4. #3398C2semidirect
5. #3376C2semidirect
6. #3372C2semidirect
7. #3328C2semidirect
8. #3326C2semidirect
9. #3320C2semidirect
10. #3315C2semidirect
11. #3313C2semidirect
12. #3312C2semidirect
13. #3276C2semidirect
14. #3275C2semidirect
15. #3269C2semidirect
16. #3267C2semidirect
17. #3266C2semidirect
18. #3266C2semidirect
19. #3261C2semidirect
20. #3258C2semidirect
21. #3256C2semidirect
22. #3225C2semidirect
23. #3223C2semidirect
24. #3218C2semidirect
25. #3123C2semidirect
26. #3120C2semidirect
27. #3111C2semidirect
28. #3046C2semidirect
29. #3042C2semidirect
30. #3039C2semidirect
31. #2995C2semidirect
40. #557C22semidirect
43. #556C22semidirect
55. D4×Q8C22semidirect
57. #548C22semidirect
67. #541C22semidirect
73. #536C22semidirect
74. C2×C4⋊Q8C22semidirect
78. #529C22semidirect
86. #497C22semidirect
88. #494C22semidirect
89. #491C22semidirect
90. #491C22semidirect
91. #491C22semidirect
92. #489C22semidirect
93. #488C22semidirect
94. #487C22semidirect
97. #485C22semidirect
98. #484C22semidirect
99. #483C22semidirect
100. #482C22semidirect
101. #479C22semidirect
102. #479C22semidirect
103. #479C22semidirect
104. #479C22semidirect
105. #479C22semidirect
108. #478C22semidirect
109. #477C22semidirect
110. #475C22semidirect
113. #470C22semidirect
114. #470C22semidirect
118. #468C22semidirect
121. #467C22semidirect
126. #464C22semidirect
127. #464C22semidirect
128. #464C22semidirect
135. #462C22semidirect
136. #462C22semidirect
137. #462C22semidirect
138. #462C22semidirect
139. #462C22semidirect
140. #462C22semidirect
141. #462C22semidirect
142. #462C22semidirect
143. #462C22semidirect
158. #452C22semidirect
161. #451C22semidirect
162. #451C22semidirect
163. #451C22semidirect
171. #446C22semidirect
172. #446C22semidirect
174. #441C22semidirect
175. #441C22semidirect
180. #440C22semidirect
181. C4×Q16C22semidirect
186. #436C22semidirect
190. #435C22semidirect
192. #433C22semidirect
193. #432C22semidirect
195. #424C22semidirect
196. #423C22semidirect
198. #419C22semidirect
199. #419C22semidirect
200. #417C22semidirect
202. C2×#103C22semidirect

Maximal subgroups

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

subgroupindex
#35522
#35212
#34022
#33982
#33762
#33722
#33282
#33262
#33202
#33152
#33132
#33122
#32762
#32752
#32692
#32672
#32662
#32612
#32582
#32562
#32252
#32232
#32182
#31232
#31202
#31112
#30462
#30422
#30392
#29952