Finite Group Databasebeta

← #7005078

Subgroups — #7005078

Order 512.

1667 conjugacy classes of subgroups.

The subgroup lattice has 1396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44887C211yesmaximal, characteristic
2#42920C211yesmaximal, characteristic, complemented
3#32295C211yesmaximal, characteristic, complemented
4#32224C211yesmaximal, characteristic, complemented
5#31995C211yesmaximal, characteristic, complemented
6#31931C211yesmaximal, characteristic, complemented
7#31318C211yesmaximal, characteristic, complemented
8#31197C211yesmaximal, characteristic, complemented
9#30681C211yesmaximal, characteristic, complemented
10#30570C211yesmaximal, characteristic, complemented
11#28841C211yesmaximal, characteristic, complemented
12#28235C211yesmaximal, characteristic, complemented
13#27787C211yesmaximal, characteristic, complemented
14#27096C211yesmaximal, characteristic, complemented
15#26571C211yesmaximal, characteristic, complemented
16#26415C211yesmaximal, characteristic, complemented
17#26151C211yesmaximal, characteristic, complemented
18#26072C211yesmaximal, characteristic, complemented
19#25950C211yesmaximal, characteristic, complemented
20#25700C211yesmaximal, characteristic, complemented
21#25536C211yesmaximal, characteristic, complemented
22#25255C211yesmaximal, characteristic, complemented
23#25112C211yesmaximal, characteristic, complemented
24#24890C211yesmaximal, characteristic, complemented
25#24564C211yesmaximal, characteristic, complemented
26#24394C211yesmaximal, characteristic, complemented
27#23483C211yesmaximal, characteristic, complemented
28#22864C211yesmaximal, characteristic, complemented
29#22847C211yesmaximal, characteristic, complemented
30#22707C211yesmaximal, characteristic, complemented
31#21945C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#498C2211yescharacteristic, complemented
35C2×#484C2211yescharacteristic, complemented
36C2×#485C2211yescharacteristic, complemented
37C2×#482C2211yescharacteristic
38C2×#474C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#465C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#440C2211yescharacteristic
44C2×#435C2211yescharacteristic, complemented
45C2×C8×D4C2211yescharacteristic
46C2×#428C2211yescharacteristic
47C2×#418C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C2×#408C2211yescharacteristic
50C2×#408C2211yescharacteristic
51#2831—21no—
52#2797—21no—
53#2779—21no—
54#2730—21no—
55#2712—21no—
56#2702—21no—
57#2684—21no—
58#2673—21no—
59#2670—21no—
60#2662—21no—
61#2651—21no—
62#2616C2211yescharacteristic
63#2586—21no—
64#2547C2211yescharacteristic, complemented
65#2544—21no—
66#2538C2211yescharacteristic, complemented
67#2535C2211yescharacteristic
68#2500C2211yescharacteristic
69#2497C2211yescharacteristic, complemented
70#2496C2211yescharacteristic, complemented
71#2492C2211yescharacteristic, complemented
72#2491C2211yescharacteristic
73#2485C2211yescharacteristic, complemented
74#2474—21no—
75#2440C2211yescharacteristic
76#2439C2211yescharacteristic
77#2424—21no—
78#2423C2211yescharacteristic, complemented
79#2422C2211yescharacteristic
80#2417C2211yescharacteristic
81#2416C2211yescharacteristic
82#2415C2211yescharacteristic, complemented
83#2414C2211yescharacteristic
84#2411—21no—
85#2408C2211yescharacteristic
86#2388C2211yescharacteristic
87#2362C2211yescharacteristic
88#2361C2211yescharacteristic
89#2354C2211yescharacteristic
90#2354C2211yescharacteristic
91D4×C22⋊C4C2211yescharacteristic
92#2311C2211yescharacteristic
93#2311C2211yescharacteristic
94#2101C2211yescharacteristic, complemented
95#2095C2211yescharacteristic, complemented
96#2093C2211yescharacteristic
97#2093C2211yescharacteristic
98#2088C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2084C2211yescharacteristic, complemented
101#2083C2211yescharacteristic, complemented
102#2076C2211yescharacteristic, complemented
103#2075C2211yescharacteristic, complemented
104#2075C2211yescharacteristic, complemented
105#2071C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2066C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2058C2211yescharacteristic, complemented
111#2057C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2036C2211yescharacteristic, complemented
114#2036C2211yescharacteristic, complemented
115#2035C2211yescharacteristic, complemented
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2024C2211yescharacteristic, complemented
130#2023C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#1987C2211yescharacteristic, complemented
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1954C2211yescharacteristic, complemented
138#1947C2211yescharacteristic, complemented
139#1947C2211yescharacteristic, complemented
140#1944C2211yescharacteristic, complemented
141#1942C2211yescharacteristic, complemented
142#1936C2211yescharacteristic
143#1934C2211yescharacteristic
144#1927C2211yescharacteristic, complemented
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1925C2211yescharacteristic
148#1924C2211yescharacteristic, complemented
149#1923C2211yescharacteristic, complemented
150#1920C2211yescharacteristic, complemented
151#1918C2211yescharacteristic, complemented
152#1895C2211yescharacteristic
153#1894C2211yescharacteristic
154#1893C2211yescharacteristic
155#1893C2211yescharacteristic
156#1892C2211yescharacteristic
157#1880C2211yescharacteristic
158#1877C2211yescharacteristic
159#1875C2211yescharacteristic
160#1873C2211yescharacteristic
161#1873C2211yescharacteristic, complemented
162#1870C2211yescharacteristic
163#1869C2211yescharacteristic, complemented
164#1869C2211yescharacteristic, complemented
165#1864C2211yescharacteristic
166#1863C2211yescharacteristic, complemented
167#1862C2211yescharacteristic
168#1862C2211yescharacteristic
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic, complemented
173#1854C2211yescharacteristic, complemented
174#1854C2211yescharacteristic, complemented
175#1854C2211yescharacteristic, complemented
176#1854C2211yescharacteristic, complemented
177#1854C2211yescharacteristic, complemented
178#1853C2211yescharacteristic
179#1853C2211yescharacteristic, complemented
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic, complemented
182#1851C2211yescharacteristic, complemented
183#1850C2211yescharacteristic
184#1847C2211yescharacteristic, complemented
185#1834C2211yescharacteristic, complemented
186#1823C2211yescharacteristic, complemented
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic, complemented
189#1809C2211yescharacteristic, complemented
190#1808C2211yescharacteristic
191#1808C2211yescharacteristic, complemented
192#1808C2211yescharacteristic, complemented
193#1807C2211yescharacteristic, complemented
194#1805C2211yescharacteristic, complemented
195#1802C2211yescharacteristic
196#1786C2211yescharacteristic
197C4×#106C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic, complemented
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#555—42no—
213#555—42no—
214#535—42no—
215#535—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127—21no—
219C2×#126—21no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121—21no—
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#120—21no—
240C2×#120—21no—
241C2×#120—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117—21no—
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C22⋊C4—21no—
258#498—42no—
259#485—42no—
260#484—42no—
261#482—42no—
262#474—42no—
263#468—42no—
264#465—42no—
265#465—42no—
266#450—24no—
267#440—42no—
268#435—42no—
269C8×D4—24no—
270#428—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292#418—42no—
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#102—42no—
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314#408—24no—
315#408—42no—
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330#400—21no—
331#400—21no—
332#400—21no—
333#399—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#395—21no—
351#395—21no—
352#395D411yescharacteristic
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394D411yescharacteristic
366#394D411yescharacteristic
367#394D411yescharacteristic
368#393—21no—
369#393—21no—
370#393—21no—
371#393D411yescharacteristic
372#392—21no—
373#392—21no—
374#392—21no—
375#392D411yescharacteristic
376#392D411yescharacteristic
377#392D411yescharacteristic
378#391—21no—
379#391—21no—
380#391—21no—
381#391—21no—
382#391—21no—
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#390—21no—
386#390—21no—
387#390—21no—
388#390—21no—
389#390—21no—
390#390—21no—
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#389—21no—
396#389—21no—
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#382C2311yescharacteristic
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#379—21no—
459#379—21no—
460C4×C4⋊C4—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8C2×D411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—21no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4C2×D411yescharacteristic
524C22×D4C2×D411yescharacteristic
525C22×D4C2×D411yescharacteristic
526C22×D4C2×D411yescharacteristic
527C22×D4C2×D411yescharacteristic
528C22×D4C2×D411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×M16—22no—
546C2×M16—22no—
547C2×M16—22no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16—41no—
551C22×C8—22no—
552C22×C8—22no—
553C22×C8—22no—
554C22×C8—41no—
555C22×C8—41no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C4⋊Q8—22no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572#127—44no—
573#126—82no—
574#124—44no—
575#124—44no—
576#124—44no—
577#124—82no—
578#124—82no—
579#123—82no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—82no—
589#121—22no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—41no—
595#121—41no—
596#121—41no—
597#121—41no—
598#121—41no—
599#121—44no—
600#121—41no—
601#121—41no—
602#121—82no—
603#120—44no—
604#120—44no—
605#120—82no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—82no—
619#117—22no—
620#117—22no—
621#117—44no—
622#117—41no—
623#117—41no—
624#117—41no—
625#117—41no—
626#117—41no—
627#117—41no—
628#117—41no—
629#117—41no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—82no—
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735#107—22no—
736#107—41no—
737#107—41no—
738#107—41no—
739#107—41no—
740#107—41no—
741#107—41no—
742#107—41no—
743#107—41no—
744#107—41no—
745#106—22no—
746#106—22no—
747#106—22no—
748#106—41no—
749#106—41no—
750#106—41no—
751#106—41no—
752#106—41no—
753C4⋊C8—22no—
754C4⋊C8—41no—
755C4⋊C8—41no—
756#103—22no—
757#103—22no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776C22⋊C8—22no—
777C22⋊C8—22no—
778C22⋊C8—22no—
779C22⋊C8—22no—
780C22⋊C8—22no—
781C22⋊C8—22no—
782C22⋊C8—22no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785C22⋊C8—41no—
786C22⋊C8#4114yes—
787#97—22no—
788C4×C8—22no—
789C4×C8—41no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825C24—21no—
826C24—21no—
827C24—42no—
828C24—42no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24C22×D411yescharacteristic
835C24C22×D411yescharacteristic
836C24C22×D411yescharacteristic
837C24C22×D411yescharacteristic
838#41—82no—
839#41—82no—
840#41—82no—
841#41—82no—
842C2×Q8—22no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—41no—
850C2×Q8—41no—
851C2×Q8—42no—
852C2×Q8—42no—
853C2×Q8—81no—
854C2×Q8—81no—
855C2×Q8—81no—
856C2×Q8—81no—
857C2×D4—22no—
858C2×D4—24no—
859C2×D4—22no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—41no—
885C2×D4—41no—
886C2×D4—41no—
887C2×D4—41no—
888C2×D4—41no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—82no—
896C2×D4—82no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4H(5,𝔽2)12yes—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C2×#4112yes—
971C22×C42−1+412yes—
972C22×C4C2511yescharacteristic
973SD16—44no—
974SD16—82no—
975M16—44no—
976M16—82no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—82no—
999C2×C8—82no—
1000C2×C8—82no—
1001C2×C8C2×#4112yes—
1002C2×C8C2×#4112yes—
1003C2×C8H(5,𝔽2)12yes—
1004C4⋊C4—22no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—41no—
1031C4⋊C4—41no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4H(5,𝔽2)12yes—
1054C22⋊C4—24no—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—42no—
1112C42—42no—
1113C42—42no—
1114C42—42no—
1115C42—42no—
1116C42—81no—
1117C42—81no—
1118C42—81no—
1119C42—81no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—22no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—84no—
1162C23—84no—
1163C23—162no—
1164C23—162no—
1165C23—162no—
1166C23—162no—
1167C23—162no—
1168C23#54712yes—
1169C23C23×D411yescharacteristic
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—82no—
1175Q8—162no—
1176Q8—162no—
1177D4—22no—
1178D4—22no—
1179D4—44no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—82no—
1187D4—82no—
1188D4—84no—
1189D4—82no—
1190D4—82no—
1191D4—84no—
1192D4—82no—
1193D4—162no—
1194D4—162no—
1195D4—162no—
1196D4—162no—
1197D4—162no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—84no—
1284C2×C4—162no—
1285C2×C4—162no—
1286C2×C4—162no—
1287C2×C4#54712yes—
1288C2×C4#57612yes—
1289C2×C4#57712yes—
1290C2×C4C22×#4111yescharacteristic
1291C2×C4C2×H(5,𝔽2)11yescharacteristic
1292C2×C4C2×H(5,𝔽2)11yescharacteristic
1293C2×C4C2×H(5,𝔽2)11yescharacteristic
1294C2×C4C2×2−1+411yescharacteristic
1295C2×C4#58511yescharacteristic
1296C8—22no—
1297C8—22no—
1298C8—22no—
1299C8—41no—
1300C8—41no—
1301C8—41no—
1302C8—41no—
1303C8—41no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—42no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—42no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—42no—
1333C22—41no—
1334C22—41no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—168no—
1347C22C2×#54711yescharacteristic
1348C22#348411yescharacteristic
1349C22#349611yescharacteristic
1350C22C2×#57611yescharacteristic
1351C22C2×#57711yescharacteristic
1352C22#358411yescharacteristic
1353C22#358611yescharacteristic
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—42no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4#351411yescharacteristic
1379C4#351911yescharacteristic
1380C4#353511yescharacteristic
1381C4#353611yescharacteristic
1382C2—42no—
1383C2—81no—
1384C2—81no—
1385C2—81no—
1386C2—82no—
1387C2—161no—
1388C2#4302011yescharacteristic
1389C2#6126311yescharacteristic
1390C2#6127811yescharacteristic
1391C2#6163911yescharacteristic
1392C2#6168011yescharacteristic
1393C2#6231611yescharacteristic
1394C2#6234211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#44887C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2388 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42920C2semidirect
3. #32295C2semidirect
4. #32224C2semidirect
5. #31995C2semidirect
6. #31931C2semidirect
7. #31318C2semidirect
8. #31197C2semidirect
9. #30681C2semidirect
10. #30570C2semidirect
11. #28841C2semidirect
12. #28235C2semidirect
13. #27787C2semidirect
14. #27096C2semidirect
15. #26571C2semidirect
16. #26415C2semidirect
17. #26151C2semidirect
18. #26072C2semidirect
19. #25950C2semidirect
20. #25700C2semidirect
21. #25536C2semidirect
22. #25255C2semidirect
23. #25112C2semidirect
24. #24890C2semidirect
25. #24564C2semidirect
26. #24394C2semidirect
27. #23483C2semidirect
28. #22864C2semidirect
29. #22847C2semidirect
30. #22707C2semidirect
31. #21945C2semidirect
34. C2×#498C22semidirect
35. C2×#484C22semidirect
36. C2×#485C22semidirect
44. C2×#435C22semidirect
64. #2547C22semidirect
66. #2538C22semidirect
69. #2497C22semidirect
70. #2496C22semidirect
71. #2492C22semidirect
73. #2485C22semidirect
78. #2423C22semidirect
82. #2415C22semidirect
94. #2101C22semidirect
95. #2095C22semidirect
98. #2088C22semidirect
99. #2085C22semidirect
100. #2084C22semidirect
101. #2083C22semidirect
102. #2076C22semidirect
103. #2075C22semidirect
104. #2075C22semidirect
108. #2066C22semidirect
110. #2058C22semidirect
111. #2057C22semidirect
113. #2036C22semidirect
114. #2036C22semidirect
115. #2035C22semidirect
129. #2024C22semidirect
134. #1987C22semidirect
137. #1954C22semidirect
138. #1947C22semidirect
139. #1947C22semidirect
140. #1944C22semidirect
141. #1942C22semidirect
144. #1927C22semidirect
148. #1924C22semidirect
149. #1923C22semidirect
150. #1920C22semidirect
151. #1918C22semidirect
161. #1873C22semidirect
163. #1869C22semidirect
164. #1869C22semidirect
166. #1863C22semidirect
172. #1854C22semidirect
173. #1854C22semidirect
174. #1854C22semidirect
175. #1854C22semidirect
176. #1854C22semidirect
177. #1854C22semidirect
179. #1853C22semidirect
181. #1852C22semidirect
182. #1851C22semidirect
184. #1847C22semidirect
185. #1834C22semidirect
186. #1823C22semidirect
188. #1809C22semidirect
189. #1809C22semidirect
191. #1808C22semidirect
192. #1808C22semidirect
193. #1807C22semidirect
194. #1805C22semidirect
197. C4×#106C22semidirect
200. C8×C22⋊C4C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#448872
#429202
#322952
#322242
#319952
#319312
#313182
#311972
#306812
#305702
#288412
#282352
#277872
#270962
#265712
#264152
#261512
#260722
#259502
#257002
#255362
#252552
#251122
#248902
#245642
#243942
#234832
#228642
#228472
#227072
#219452