Finite Group Databasebeta

← #6999620

Subgroups — #6999620

Order 512.

1660 conjugacy classes of subgroups.

The subgroup lattice has 1345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59096C211yesmaximal, characteristic
2#40100C211yesmaximal, characteristic
3#31521C211yesmaximal, characteristic, complemented
4#31288C211yesmaximal, characteristic, complemented
5#31035C211yesmaximal, characteristic
6#30744C211yesmaximal, characteristic, complemented
7#30569C211yesmaximal, characteristic
8#30550C211yesmaximal, characteristic, complemented
9#30530C211yesmaximal, characteristic, complemented
10#30449C211yesmaximal, characteristic, complemented
11#28934C211yesmaximal, characteristic, complemented
12#28887C211yesmaximal, characteristic, complemented
13#28423C211yesmaximal, characteristic, complemented
14#28313C211yesmaximal, characteristic, complemented
15#28066C211yesmaximal, characteristic, complemented
16#27242C211yesmaximal, characteristic, complemented
17#27082C211yesmaximal, characteristic, complemented
18#26838C211yesmaximal, characteristic, complemented
19#26789C211yesmaximal, characteristic, complemented
20#26636C211yesmaximal, characteristic, complemented
21#26607C211yesmaximal, characteristic, complemented
22#25780C211yesmaximal, characteristic, complemented
23#25600C211yesmaximal, characteristic, complemented
24#25173C211yesmaximal, characteristic, complemented
25#24255C211yesmaximal, characteristic
26#23856C211yesmaximal, characteristic
27#23577C211yesmaximal, characteristic, complemented
28#23300C211yesmaximal, characteristic
29#23187C211yesmaximal, characteristic, complemented
30#22440C211yesmaximal, characteristic, complemented
31#22044C211yesmaximal, characteristic, complemented
32C23×Q16C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#494C2211yescharacteristic
36C2×#494C2211yescharacteristic
37C2×#491C2211yescharacteristic
38C2×#487C2211yescharacteristic
39C2×#483C2211yescharacteristic
40C2×#483C2211yescharacteristic
41C2×#479C2211yescharacteristic
42C2×#467C2211yescharacteristic
43C2×#462C2211yescharacteristic
44C2×#462C2211yescharacteristic
45C2×#451C2211yescharacteristic
46C2×#451C2211yescharacteristic
47C2×#451C2211yescharacteristic
48C2×#451C2211yescharacteristic
49C2×#451C2211yescharacteristic
50C2×#451C2211yescharacteristic
51C2×#441C2211yescharacteristic
52C2×#441C2211yescharacteristic
53C2×#441C2211yescharacteristic
54C2×#441C2211yescharacteristic
55#2857C2211yescharacteristic
56#2787—21no—
57#2774—21no—
58#2745—21no—
59#2713—21no—
60#2704—21no—
61#2695—21no—
62#2666—21no—
63#2578—21no—
64#2574—21no—
65#2565C2211yescharacteristic
66#2549—21no—
67#2546C2211yescharacteristic
68#2536C2211yescharacteristic
69#2514C2211yescharacteristic
70#2496C2211yescharacteristic
71#2492C2211yescharacteristic
72#2489C2211yescharacteristic
73#2489C2211yescharacteristic
74#2465—21no—
75#2451—21no—
76#2451C2211yescharacteristic
77#2450—21no—
78#2446C2211yescharacteristic
79#2446C2211yescharacteristic
80#2438—21no—
81#2434C2211yescharacteristic
82#2434C2211yescharacteristic
83#2434C2211yescharacteristic
84#2429C2211yescharacteristic
85#2429C2211yescharacteristic
86#2417C2211yescharacteristic
87#2409C2211yescharacteristic
88#2365C2211yescharacteristic
89#2365C2211yescharacteristic
90#2360C2211yescharacteristic
91#2359—21no—
92Q8×C22⋊C4C2211yescharacteristic
93Q8×C22⋊C4C2211yescharacteristic
94#2334—21no—
95C4×C22⋊Q8C2211yescharacteristic
96C4×#123C2211yescharacteristic
97C2×#391C2211yescharacteristic
98#2097C2211yescharacteristic
99#2096C2211yescharacteristic
100#2096C2211yescharacteristic
101#2085C2211yescharacteristic
102#2077C2211yescharacteristic
103#2066C2211yescharacteristic
104#2066C2211yescharacteristic
105#2066C2211yescharacteristic
106#2059C2211yescharacteristic
107#2058C2211yescharacteristic
108#2056C2211yescharacteristic
109#2056C2211yescharacteristic
110#2056C2211yescharacteristic
111#2043C2211yescharacteristic
112#2043C2211yescharacteristic
113#2036C2211yescharacteristic
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2026C2211yescharacteristic
120#2024C2211yescharacteristic
121#2016C2211yescharacteristic
122#2016C2211yescharacteristic
123#2016C2211yescharacteristic
124#2016C2211yescharacteristic
125#2016C2211yescharacteristic
126#2016C2211yescharacteristic
127#2016C2211yescharacteristic
128#2016C2211yescharacteristic
129#2016C2211yescharacteristic
130#2016C2211yescharacteristic
131#2001C2211yescharacteristic
132#2001C2211yescharacteristic
133#2001C2211yescharacteristic
134#2001C2211yescharacteristic
135#2001C2211yescharacteristic
136#2001C2211yescharacteristic
137#2001C2211yescharacteristic
138#1990C2211yescharacteristic
139#1981C2211yescharacteristic
140#1981C2211yescharacteristic
141#1971C2211yescharacteristic
142#1971C2211yescharacteristic
143#1971C2211yescharacteristic
144#1971C2211yescharacteristic
145#1971C2211yescharacteristic
146#1971C2211yescharacteristic
147#1969C2211yescharacteristic
148#1969C2211yescharacteristic
149#1969C2211yescharacteristic
150#1960C2211yescharacteristic
151#1956C2211yescharacteristic
152#1955C2211yescharacteristic
153#1935C2211yescharacteristic
154#1935C2211yescharacteristic
155#1933C2211yescharacteristic
156#1933C2211yescharacteristic
157#1933C2211yescharacteristic
158#1928C2211yescharacteristic
159#1928C2211yescharacteristic
160#1928C2211yescharacteristic
161#1927C2211yescharacteristic
162#1927C2211yescharacteristic
163#1924C2211yescharacteristic
164#1924C2211yescharacteristic
165#1923C2211yescharacteristic
166#1923C2211yescharacteristic
167#1919C2211yescharacteristic
168#1917C2211yescharacteristic
169#1916C2211yescharacteristic
170#1892C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1878C2211yescharacteristic
180#1878C2211yescharacteristic
181#1878C2211yescharacteristic
182#1878C2211yescharacteristic
183#1872C2211yescharacteristic
184#1869C2211yescharacteristic
185#1865C2211yescharacteristic
186#1865C2211yescharacteristic
187#1852C2211yescharacteristic
188#1807C2211yescharacteristic
189#1805C2211yescharacteristic
190#1787C2211yescharacteristic
191#1787C2211yescharacteristic
192#1787C2211yescharacteristic
193#1787C2211yescharacteristic
194C4×#106C2211yescharacteristic
195#1771C2211yescharacteristic
196#1770C2211yescharacteristic
197#1763C2211yescharacteristic
198#1763C2211yescharacteristic
199#1752C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201#1749C2211yescharacteristic
202C4×C22⋊C8C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×Q8C2311yescharacteristic
206C22×Q16—24no—
207C22×Q16—42no—
208C22×Q16—42no—
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×Q16C2311yescharacteristic
215C22×Q16C2311yescharacteristic
216C22×Q16C2311yescharacteristic
217C22×Q16C2311yescharacteristic
218C22×Q16C2311yescharacteristic
219C22×Q16C2311yescharacteristic
220C22×Q16C2311yescharacteristic
221C23×C8C2311yescharacteristic
222D4×Q8—42no—
223D4×Q8—42no—
224#533—42no—
225#533—42no—
226C2×C4⋊Q8—21no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×#126—21no—
235C2×#125—21no—
236C2×#125C2311yescharacteristic
237C2×#123D411yescharacteristic
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2311yescharacteristic
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2311yescharacteristic
249C2×C4×Q8—21no—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×D4—21no—
258C2×C4×D4C2311yescharacteristic
259C2×#117—21no—
260C22×C4⋊C4C2311yescharacteristic
261C22×C42C2311yescharacteristic
262#494—24no—
263#494—42no—
264#491—42no—
265#487—42no—
266#483—42no—
267#483—42no—
268#479—42no—
269#467—42no—
270#462—42no—
271#462—42no—
272#451—24no—
273#451—42no—
274#451—42no—
275#451—42no—
276#451—42no—
277#451—42no—
278#441—42no—
279#441—42no—
280#441—42no—
281#441—42no—
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338C2×C4×C8C2311yescharacteristic
339#401—21no—
340#400—21no—
341#400—21no—
342#400—21no—
343#400—21no—
344#400—21no—
345#400—21no—
346#400—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#398—21no—
351#398—21no—
352#398—21no—
353#398—21no—
354#398—21no—
355#398—21no—
356#398—21no—
357#398—21no—
358#397—21no—
359#397—21no—
360#397—21no—
361#396—21no—
362#396—21no—
363#396—21no—
364#395—21no—
365#395—21no—
366#395—21no—
367#395—21no—
368#395—21no—
369#395—21no—
370#395—21no—
371#395—21no—
372#394—21no—
373#393—21no—
374#393—21no—
375#391—21no—
376#391—21no—
377#391—21no—
378#391—21no—
379#391—21no—
380#391—21no—
381#391—21no—
382#391—21no—
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#391C2311yescharacteristic
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#389—21no—
400#389—21no—
401#389—21no—
402#389—21no—
403#389—21no—
404#389—21no—
405#389—21no—
406#389—21no—
407#389—21no—
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388D411yescharacteristic
420#388D411yescharacteristic
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#387—21no—
436#387D411yescharacteristic
437#387D411yescharacteristic
438#386—21no—
439#386—21no—
440#386D411yescharacteristic
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385D411yescharacteristic
451#384C2311yescharacteristic
452#383—21no—
453#382—21no—
454#382—21no—
455#382C2311yescharacteristic
456#381D411yescharacteristic
457#380—21no—
458#380—21no—
459#380—21no—
460#380—21no—
461#380—21no—
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464#380C2311yescharacteristic
465#380C2311yescharacteristic
466C4×C4⋊C4—21no—
467C4×C4⋊C4—21no—
468C4×C4⋊C4—21no—
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2311yescharacteristic
474C4×C22⋊C4—21no—
475C4×C22⋊C4—21no—
476C4×C22⋊C4—21no—
477C4×C22⋊C4—21no—
478C4×C22⋊C4C2311yescharacteristic
479C4×C22⋊C4C2311yescharacteristic
480C4×C22⋊C4C2311yescharacteristic
481C2×#95—21no—
482C2×#95—21no—
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502#336C2311yescharacteristic
503#336C2311yescharacteristic
504#336C2311yescharacteristic
505C22×Q8—21no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8—21no—
509C22×Q8—22no—
510C22×Q8—22no—
511C22×Q8—22no—
512C22×Q8—22no—
513C22×Q8—41no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8—41no—
517C22×Q8—41no—
518C22×Q8—41no—
519C22×Q8—41no—
520C22×Q8—41no—
521C22×Q8—41no—
522C22×Q8—41no—
523C22×Q8—41no—
524C22×Q8—41no—
525C22×Q8—41no—
526C22×Q8—41no—
527C22×Q8C2411yescharacteristic
528C22×Q8C2411yescharacteristic
529C22×Q8C2411yescharacteristic
530C22×Q8C2411yescharacteristic
531C22×Q8C2411yescharacteristic
532C22×Q8C2411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×D4C2×D411yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4C2×D411yescharacteristic
540C23×C4C2×D411yescharacteristic
541C23×C4C2411yescharacteristic
542C23×C4C2411yescharacteristic
543C2×Q16—22no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—22no—
555C2×Q16—22no—
556C2×Q16—22no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×Q16—41no—
561C2×Q16—41no—
562C2×Q16—41no—
563C2×Q16—41no—
564C2×Q16—41no—
565C2×Q16—41no—
566C2×Q16—41no—
567C2×Q16—41no—
568C2×Q16—41no—
569C2×Q16—41no—
570C2×Q16—41no—
571C2×Q16—41no—
572C2×Q16—41no—
573C2×Q16—41no—
574C2×Q16—41no—
575C2×Q16—41no—
576C2×Q16—41no—
577C2×Q16—41no—
578C2×Q16—416no—
579C2×Q16#4114yes—
580C22×C8—22no—
581C22×C8—22no—
582C22×C8—41no—
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C4⋊Q8—22no—
592C4⋊Q8—22no—
593C4⋊Q8—22no—
594C4⋊Q8—22no—
595C4⋊Q8—22no—
596C4⋊Q8—41no—
597C4⋊Q8—41no—
598C4⋊Q8—41no—
599C4⋊Q8—41no—
600C4⋊Q8—41no—
601C4⋊Q8—41no—
602C4⋊Q8—41no—
603C4⋊Q8—41no—
604C4⋊Q8—41no—
605C4⋊Q8—44no—
606#126—44no—
607#125—41no—
608#125—41no—
609#125—44no—
610#123—24no—
611C22⋊Q8—22no—
612C22⋊Q8—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—44no—
616C22⋊Q8—44no—
617C22⋊Q8—41no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—44no—
622C22⋊Q8—41no—
623C22⋊Q8—41no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626C22⋊Q8—41no—
627C22⋊Q8—41no—
628C22⋊Q8—41no—
629C22⋊Q8—41no—
630C4×Q8—22no—
631C4×Q8—22no—
632C4×Q8—22no—
633C4×Q8—41no—
634C4×Q8—41no—
635C4×Q8—41no—
636C4×Q8—41no—
637C4×Q8—41no—
638C4×Q8—41no—
639C4×Q8—41no—
640C4×Q8—41no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×Q8—41no—
644C4×Q8—44no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—44no—
648#117—44no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—41no—
687C2×C4⋊C4—41no—
688C2×C4⋊C4C2×D411yescharacteristic
689C2×C4⋊C4C2×D411yescharacteristic
690C2×C4⋊C4C2×D411yescharacteristic
691C2×C4⋊C4C2×D411yescharacteristic
692C2×C4⋊C4C2×D411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
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—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
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×C42—21no—
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×C42—41no—
733C2×C42—41no—
734C2×C42C2×D411yescharacteristic
735C2×C42C2×D411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741#107—41no—
742#107—41no—
743#106—22no—
744#106—22no—
745#106—22no—
746#106—41no—
747#106—41no—
748#106—41no—
749C4⋊C8—22no—
750C4⋊C8—41no—
751C4⋊C8—41no—
752#103—22no—
753#103—22no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—22no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781#103—41no—
782#103—41no—
783#103—41no—
784C22⋊C8—22no—
785C22⋊C8—22no—
786C22⋊C8—22no—
787C22⋊C8—22no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791#97—22no—
792#97—41no—
793#97—41no—
794#97—41no—
795C4×C8—22no—
796C4×C8—41no—
797C4×C8—41no—
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#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850#95C2×D411yescharacteristic
851#95C2×D411yescharacteristic
852#95C2×D411yescharacteristic
853C24C22×D411yescharacteristic
854C24C22×D411yescharacteristic
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—42no—
895C2×Q8—42no—
896C2×Q8—42no—
897C2×Q8—42no—
898C2×Q8—42no—
899C2×Q8—42no—
900C2×Q8—42no—
901C2×Q8—44no—
902C2×Q8—44no—
903C2×Q8—81no—
904C2×Q8—81no—
905C2×Q8—81no—
906C2×Q8—81no—
907C2×Q8—81no—
908C2×Q8—82no—
909C2×Q8—82no—
910C2×Q8—82no—
911C2×Q8—82no—
912C2×Q8—82no—
913C2×Q8—82no—
914C2×Q8—82no—
915C2×Q8—82no—
916C2×Q8—82no—
917C2×Q8—82no—
918C2×Q8C2×#4112yes—
919C2×Q8C2×#4112yes—
920C2×Q8H(5,𝔽2)12yes—
921C2×D4—22no—
922C2×D4—22no—
923C2×D4—41no—
924C22×C4—22no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—22no—
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—22no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—41no—
956C22×C4—41no—
957C22×C4—41no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C2511yescharacteristic
983Q16—28no—
984Q16—44no—
985Q16—44no—
986Q16—44no—
987Q16—44no—
988Q16—44no—
989Q16—82no—
990Q16—82no—
991Q16—82no—
992Q16—82no—
993Q16—82no—
994Q16—82no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—44no—
1017C2×C8C2×#4112yes—
1018C2×C8H(5,𝔽2)12yes—
1019C2×C8H(5,𝔽2)12yes—
1020C4⋊C4—24no—
1021C4⋊C4—22no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4H(5,𝔽2)12yes—
1080C22⋊C4—24no—
1081C22⋊C4—22no—
1082C22⋊C4—22no—
1083C22⋊C4—22no—
1084C22⋊C4—22no—
1085C22⋊C4—41no—
1086C22⋊C4—41no—
1087C22⋊C4—41no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4#13714yes—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—41no—
1111C42—41no—
1112C42—42no—
1113C42—42no—
1114C42—42no—
1115C42—42no—
1116C42—42no—
1117C42—81no—
1118C42—81no—
1119C42—81no—
1120C42—81no—
1121C42—81no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23C2×#13712yes—
1135C23#57812yes—
1136C23C23×D411yescharacteristic
1137Q8—22no—
1138Q8—22no—
1139Q8—22no—
1140Q8—22no—
1141Q8—22no—
1142Q8—22no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—84no—
1166Q8—84no—
1167Q8—84no—
1168Q8—84no—
1169D4—44no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—22no—
1189C2×C4—21no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—44no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
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—82no—
1261C2×C4—84no—
1262C2×C4—84no—
1263C2×C4—84no—
1264C2×C4—162no—
1265C2×C4C2×#13712yes—
1266C2×C4C2×#13712yes—
1267C2×C4#57812yes—
1268C2×C4C22×#4111yescharacteristic
1269C2×C4C2×H(5,𝔽2)11yescharacteristic
1270C2×C4C2×H(5,𝔽2)11yescharacteristic
1271C2×C4C2×H(5,𝔽2)11yescharacteristic
1272C2×C4C2×H(5,𝔽2)11yescharacteristic
1273C2×C4#58511yescharacteristic
1274C8—22no—
1275C8—22no—
1276C8—22no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22D4×#4111yescharacteristic
1297C22#348411yescharacteristic
1298C22#349811yescharacteristic
1299C22C22×#13711yescharacteristic
1300C22C2×#57811yescharacteristic
1301C22C2×#57811yescharacteristic
1302C22#358611yescharacteristic
1303C4—22no—
1304C4—22no—
1305C4—22no—
1306C4—41no—
1307C4—41no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—42no—
1317C4—41no—
1318C4—41no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4#349011yescharacteristic
1332C4#351911yescharacteristic
1333C4#354611yescharacteristic
1334C4#355811yescharacteristic
1335C2—42no—
1336C2—42no—
1337C2#4301011yescharacteristic
1338C2#6145711yescharacteristic
1339C2#6148411yescharacteristic
1340C2#6160211yescharacteristic
1341C2#6162211yescharacteristic
1342C2#6242411yescharacteristic
1343C2#6246011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #31521C2semidirect
4. #31288C2semidirect
6. #30744C2semidirect
8. #30550C2semidirect
9. #30530C2semidirect
10. #30449C2semidirect
11. #28934C2semidirect
12. #28887C2semidirect
13. #28423C2semidirect
14. #28313C2semidirect
15. #28066C2semidirect
16. #27242C2semidirect
17. #27082C2semidirect
18. #26838C2semidirect
19. #26789C2semidirect
20. #26636C2semidirect
21. #26607C2semidirect
22. #25780C2semidirect
23. #25600C2semidirect
24. #25173C2semidirect
27. #23577C2semidirect
29. #23187C2semidirect
30. #22440C2semidirect
31. #22044C2semidirect

Maximal subgroups

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

subgroupindex
#590962
#401002
#315212
#312882
#310352
#307442
#305692
#305502
#305302
#304492
#289342
#288872
#284232
#283132
#280662
#272422
#270822
#268382
#267892
#266362
#266072
#257802
#256002
#251732
#242552
#238562
#235772
#233002
#231872
#224402
#220442