Finite Group Databasebeta

← #6507209

Subgroups — #6507209

Order 512.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37365C211yesmaximal, characteristic, complemented
2#35675C211yesmaximal, characteristic, complemented
3#29563C211yesmaximal, characteristic, complemented
4#29503C211yesmaximal, characteristic, complemented
5#29474C211yesmaximal, characteristic, complemented
6#29435C211yesmaximal, characteristic, complemented
7#29101C211yesmaximal, characteristic, complemented
8#28982C211yesmaximal, characteristic, complemented
9#28926C211yesmaximal, characteristic, complemented
10#28891C211yesmaximal, characteristic, complemented
11#28773C211yesmaximal, characteristic, complemented
12#28617C211yesmaximal, characteristic, complemented
13#28590C211yesmaximal, characteristic, complemented
14#28566C211yesmaximal, characteristic, complemented
15#27281C211yesmaximal, characteristic, complemented
16#27275C211yesmaximal, characteristic, complemented
17#26989C211yesmaximal, characteristic, complemented
18#26830C211yesmaximal, characteristic, complemented
19#26263C211yesmaximal, characteristic, complemented
20#25776C211yesmaximal, characteristic, complemented
21#25610C211yesmaximal, characteristic, complemented
22#25510C211yesmaximal, characteristic, complemented
23#25412C211yesmaximal, characteristic, complemented
24#25118C211yesmaximal, characteristic, complemented
25#25116C211yesmaximal, characteristic
26#24269C211yesmaximal, characteristic, complemented
27#22194C211yesmaximal, characteristic, complemented
28#22056C211yesmaximal, characteristic, complemented
29#21463C211yesmaximal, characteristic, complemented
30#20936C211yesmaximal, characteristic, complemented
31#20566C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#542C2211yescharacteristic, complemented
34C2×#519C2211yescharacteristic
35C2×#495C2211yescharacteristic
36C2×#495C2211yescharacteristic
37C2×#489C2211yescharacteristic
38C2×#488C2211yescharacteristic, complemented
39C2×#468C2211yescharacteristic
40C2×#468C2211yescharacteristic
41C2×#467C2211yescharacteristic, complemented
42C2×#466C2211yescharacteristic
43C2×#465C2211yescharacteristic
44C2×#451C2211yescharacteristic
45C2×#447C2211yescharacteristic
46C2×#441C2211yescharacteristic, complemented
47C2×C4×Q16C2211yescharacteristic, complemented
48C2×#435C2211yescharacteristic
49C2×#435C2211yescharacteristic
50C2×#419C2211yescharacteristic
51C2×#418C2211yescharacteristic
52#2861C2211yescharacteristic
53#2860C2211yescharacteristic
54#2803—21no—
55#2803—21no—
56#2800—21no—
57#2735—21no—
58#2735—21no—
59#2727—21no—
60#2685—21no—
61#2685—21no—
62#2624C2211yescharacteristic
63#2620C2211yescharacteristic
64#2610—21no—
65#2604—21no—
66#2601—21no—
67#2592—21no—
68#2512C2211yescharacteristic
69#2490C2211yescharacteristic
70#2477—21no—
71#2471—21no—
72#2465—21no—
73#2458—21no—
74#2451C2211yescharacteristic, complemented
75#2448C2211yescharacteristic
76#2448C2211yescharacteristic, complemented
77#2441C2211yescharacteristic
78#2439C2211yescharacteristic
79#2436C2211yescharacteristic
80#2435C2211yescharacteristic
81#2426C2211yescharacteristic
82#2426C2211yescharacteristic, complemented
83#2421C2211yescharacteristic, complemented
84#2415C2211yescharacteristic
85#2414C2211yescharacteristic
86#2409C2211yescharacteristic
87#2408C2211yescharacteristic
88#2324C2211yescharacteristic
89#2323C2211yescharacteristic
90#2323C2211yescharacteristic, complemented
91#2309C2211yescharacteristic
92C4×#124C2211yescharacteristic, complemented
93#2295C2211yescharacteristic, complemented
94#2293C2211yescharacteristic
95#2088C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2083C2211yescharacteristic, complemented
98#2077C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2072C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2067C2211yescharacteristic
103#2059C2211yescharacteristic, complemented
104#2057C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic, complemented
109#2054C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic, complemented
113#2042C2211yescharacteristic, complemented
114#2035C2211yescharacteristic, complemented
115#2034C2211yescharacteristic
116#2026C2211yescharacteristic, complemented
117#2023C2211yescharacteristic
118#2015C2211yescharacteristic
119#2015C2211yescharacteristic
120#2012C2211yescharacteristic
121#2012C2211yescharacteristic
122#2001C2211yescharacteristic, complemented
123#2000C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic, complemented
126#1999C2211yescharacteristic
127#1991C2211yescharacteristic, complemented
128#1990C2211yescharacteristic, complemented
129#1973C2211yescharacteristic
130#1973C2211yescharacteristic
131#1972C2211yescharacteristic
132#1972C2211yescharacteristic
133#1971C2211yescharacteristic, complemented
134#1970C2211yescharacteristic
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1959C2211yescharacteristic, complemented
138#1958C2211yescharacteristic
139#1942C2211yescharacteristic, complemented
140#1941C2211yescharacteristic, complemented
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1935C2211yescharacteristic, complemented
147#1935C2211yescharacteristic, complemented
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic, complemented
151#1928C2211yescharacteristic, complemented
152#1926C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic, complemented
155#1920C2211yescharacteristic, complemented
156#1919C2211yescharacteristic, complemented
157#1895C2211yescharacteristic
158#1895C2211yescharacteristic, complemented
159#1894C2211yescharacteristic
160#1894C2211yescharacteristic, complemented
161#1893C2211yescharacteristic
162#1892C2211yescharacteristic, complemented
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic, complemented
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1877C2211yescharacteristic, complemented
177#1875C2211yescharacteristic
178#1873C2211yescharacteristic
179#1865C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1862C2211yescharacteristic, complemented
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1808C2211yescharacteristic
186#1787C2211yescharacteristic
187#1786C2211yescharacteristic
188#1771C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190C4×C4⋊C8C2211yescharacteristic, complemented
191#1763C2211yescharacteristic, complemented
192C4×#103C2211yescharacteristic, complemented
193#1753C2211yescharacteristic
194#1753C2211yescharacteristic, complemented
195C8×C22⋊C4C2211yescharacteristic
196C8×C22⋊C4C2211yescharacteristic, complemented
197#1750C2211yescharacteristic
198#1750C2211yescharacteristic, complemented
199#1745C2211yescharacteristic, complemented
200#1735C2211yescharacteristic
201#1729C2211yescharacteristic
202#1729C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16—24no—
208C22×SD16—42no—
209C22×SD16—42no—
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C22×M16C2311yescharacteristic
219C23×C8C2311yescharacteristic
220C23×C8C2311yescharacteristic
221#542—42no—
222#542—42no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×#126—21no—
225C2×#126—21no—
226C2×#126—21no—
227C2×#125C2311yescharacteristic
228C2×#124—21no—
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#123—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#120—21no—
244#519—42no—
245#519—42no—
246C2×C4×Q8—21no—
247C2×C4×Q8—21no—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×#117—21no—
256C2×#117—21no—
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261#495—42no—
262#495—42no—
263#489—42no—
264#488—42no—
265#468—42no—
266#468—42no—
267#467—42no—
268#466—42no—
269#465—24no—
270#451—24no—
271#447—24no—
272#441—42no—
273C4×Q16—42no—
274#435—24no—
275#435—24no—
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285#419—42no—
286#418—42no—
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329#400—21no—
330#399—21no—
331#399—21no—
332#399—21no—
333#399—21no—
334#398—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#395—21no—
350#395—21no—
351#394—21no—
352#394—21no—
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#393—21no—
364#393—21no—
365#393—21no—
366#393—21no—
367#392—21no—
368#392—21no—
369#391—21no—
370#391—21no—
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#390—21no—
378#390—21no—
379#390—21no—
380#390—21no—
381#390—21no—
382#390—21no—
383#390—21no—
384#390D411yescharacteristic
385#390D411yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#389—21no—
397#389—21no—
398#389—21no—
399#389—21no—
400#389D411yescharacteristic
401#389D411yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
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#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388D411yescharacteristic
436#388D411yescharacteristic
437#388D411yescharacteristic
438#388D411yescharacteristic
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#387—21no—
447#386—21no—
448#386—21no—
449#386—21no—
450#386—21no—
451#385—21no—
452#385—21no—
453#384C2311yescharacteristic
454#382C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#379—21no—
460#379—21no—
461#379—21no—
462#379—21no—
463#379—21no—
464C4×C4⋊C4—21no—
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472#376—21no—
473C43C2311yescharacteristic
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#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8—22no—
506C22×Q8—22no—
507C22×Q8—22no—
508C22×Q8—22no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—22no—
520C22×D4—22no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×D411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—22no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—416no—
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×M16—22no—
562C2×M16—22no—
563C2×M16—41no—
564C2×M16—41no—
565C2×M16—41no—
566C2×M16—41no—
567C22×C8—22no—
568C22×C8—41no—
569C22×C8—41no—
570C22×C8—41no—
571C22×C8—41no—
572C22×C8#4114yes—
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C4⋊Q8—22no—
582C4⋊Q8—41no—
583#126—44no—
584#126—82no—
585#126—82no—
586#125—41no—
587#125—41no—
588#124—22no—
589#124—22no—
590#124—41no—
591#124—41no—
592#124—44no—
593#124—41no—
594#124—41no—
595#124—41no—
596#124—41no—
597#123—44no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—44no—
605C22⋊Q8—41no—
606C22⋊Q8—41no—
607#121—22no—
608#121—22no—
609#121—22no—
610#121—41no—
611#121—41no—
612#121—41no—
613#121—41no—
614#121—41no—
615#120—82no—
616C4×Q8—22no—
617C4×Q8—22no—
618C4×Q8—22no—
619C4×Q8—22no—
620C4×Q8—41no—
621C4×Q8—41no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×Q8—44no—
625C4×Q8—41no—
626C4×Q8—41no—
627C4×Q8—44no—
628C4×D4—22no—
629C4×D4—22no—
630C4×D4—41no—
631C4×D4—41no—
632#117—22no—
633#117—41no—
634#117—41no—
635#117—41no—
636#117—41no—
637#117—44no—
638#117—41no—
639#117—44no—
640#117—41no—
641#117—41no—
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—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⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
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—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42C2×D411yescharacteristic
744C2×C42C2×D411yescharacteristic
745C2×C42C2×D411yescharacteristic
746C2×C42C2×D411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752#107—22no—
753#107—41no—
754#107—41no—
755#107—41no—
756#106—22no—
757#106—41no—
758#106—41no—
759C4⋊C8—22no—
760C4⋊C8—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791C22⋊C8—22no—
792C22⋊C8—22no—
793C22⋊C8—22no—
794C22⋊C8#4114yes—
795#97—22no—
796#97—22no—
797#97—41no—
798#97—41no—
799C4×C8—41no—
800C4×C8—41no—
801C4×C8—41no—
802C4×C8—41no—
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#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837C24—21no—
838C24—21no—
839C24—21no—
840C24—42no—
841C24—81no—
842C24—81no—
843C24—81no—
844C24—81no—
845C24—81no—
846C24—81no—
847C24C22×D411yescharacteristic
848C24C22×D411yescharacteristic
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—28no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
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—42no—
867C2×Q8—42no—
868C2×Q8—42no—
869C2×Q8—44no—
870C2×Q8—44no—
871C2×Q8—44no—
872C2×Q8—42no—
873C2×Q8—81no—
874C2×Q8—81no—
875C2×Q8H(5,𝔽2)12yes—
876C2×Q8H(5,𝔽2)12yes—
877C2×D4—22no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—41no—
899C2×D4—41no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—82no—
904C2×D4—82no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
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—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C2×#4112yes—
959C22×C4C2×#4112yes—
960C22×C4C2511yescharacteristic
961Q16—44no—
962Q16—44no—
963SD16—44no—
964SD16—44no—
965SD16—44no—
966SD16—44no—
967SD16—82no—
968D8—82no—
969D8—82no—
970M16—82no—
971M16—82no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
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—44no—
993C2×C8—82no—
994C2×C8C2×#4112yes—
995C2×C8C2×#4112yes—
996C2×C8C2×#4112yes—
997C2×C8C2×#4112yes—
998C4⋊C4—24no—
999C4⋊C4—22no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
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—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
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⋊C4H(5,𝔽2)12yes—
1047C22⋊C4—22no—
1048C22⋊C4—22no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
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—
1100C42—24no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—41no—
1112C42—41no—
1113C42—41no—
1114C42—41no—
1115C42—42no—
1116C42—42no—
1117C42—42no—
1118C42—42no—
1119C42—81no—
1120C42—81no—
1121C42—81no—
1122C42—81no—
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—21no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—84no—
1158C23—162no—
1159C23—162no—
1160C23—162no—
1161C23—162no—
1162C23—162no—
1163C23—162no—
1164C23#53212yes—
1165C23C23×D411yescharacteristic
1166Q8—22no—
1167Q8—22no—
1168Q8—22no—
1169Q8—22no—
1170Q8—48no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—162no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—84no—
1193D4—82no—
1194D4—162no—
1195D4—162no—
1196D4—162no—
1197D4—162no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
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—21no—
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—22no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—22no—
1239C2×C4—21no—
1240C2×C4—48no—
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—162no—
1282C2×C4#53212yes—
1283C2×C4C22×#4111yescharacteristic
1284C2×C4C22×#4111yescharacteristic
1285C2×C4C2×H(5,𝔽2)11yescharacteristic
1286C2×C4C2×H(5,𝔽2)11yescharacteristic
1287C2×C4C2×H(5,𝔽2)11yescharacteristic
1288C2×C4#58511yescharacteristic
1289C8—22no—
1290C8—22no—
1291C8—22no—
1292C8—22no—
1293C8—41no—
1294C8—41no—
1295C8—41no—
1296C8—41no—
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—168no—
1333C22C2×#53211yescharacteristic
1334C22#348411yescharacteristic
1335C22#348811yescharacteristic
1336C22#358411yescharacteristic
1337C22#358411yescharacteristic
1338C22#358511yescharacteristic
1339C22#358611yescharacteristic
1340C4—22no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—42no—
1346C4—42no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—42no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4#349011yescharacteristic
1366C4#350611yescharacteristic
1367C4#351311yescharacteristic
1368C4#351911yescharacteristic
1369C2—42no—
1370C2—81no—
1371C2—161no—
1372C2—161no—
1373C2—161no—
1374C2#3539211yescharacteristic
1375C2#6070911yescharacteristic
1376C2#6071311yescharacteristic
1377C2#6168111yescharacteristic
1378C2#6169011yescharacteristic
1379C2#6201311yescharacteristic
1380C2#6202611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25116C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37365C2semidirect
2. #35675C2semidirect
3. #29563C2semidirect
4. #29503C2semidirect
5. #29474C2semidirect
6. #29435C2semidirect
7. #29101C2semidirect
8. #28982C2semidirect
9. #28926C2semidirect
10. #28891C2semidirect
11. #28773C2semidirect
12. #28617C2semidirect
13. #28590C2semidirect
14. #28566C2semidirect
15. #27281C2semidirect
16. #27275C2semidirect
17. #26989C2semidirect
18. #26830C2semidirect
19. #26263C2semidirect
20. #25776C2semidirect
21. #25610C2semidirect
22. #25510C2semidirect
23. #25412C2semidirect
24. #25118C2semidirect
26. #24269C2semidirect
27. #22194C2semidirect
28. #22056C2semidirect
29. #21463C2semidirect
30. #20936C2semidirect
31. #20566C2semidirect
33. C2×#542C22semidirect
38. C2×#488C22semidirect
41. C2×#467C22semidirect
46. C2×#441C22semidirect
47. C2×C4×Q16C22semidirect
74. #2451C22semidirect
76. #2448C22semidirect
82. #2426C22semidirect
83. #2421C22semidirect
90. #2323C22semidirect
92. C4×#124C22semidirect
93. #2295C22semidirect
95. #2088C22semidirect
96. #2085C22semidirect
97. #2083C22semidirect
98. #2077C22semidirect
100. #2072C22semidirect
101. #2068C22semidirect
103. #2059C22semidirect
104. #2057C22semidirect
105. #2056C22semidirect
108. #2055C22semidirect
112. #2042C22semidirect
113. #2042C22semidirect
114. #2035C22semidirect
116. #2026C22semidirect
122. #2001C22semidirect
125. #2000C22semidirect
127. #1991C22semidirect
128. #1990C22semidirect
133. #1971C22semidirect
137. #1959C22semidirect
139. #1942C22semidirect
140. #1941C22semidirect
144. #1936C22semidirect
145. #1935C22semidirect
146. #1935C22semidirect
147. #1935C22semidirect
150. #1933C22semidirect
151. #1928C22semidirect
154. #1925C22semidirect
155. #1920C22semidirect
156. #1919C22semidirect
158. #1895C22semidirect
160. #1894C22semidirect
162. #1892C22semidirect
171. #1880C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
176. #1877C22semidirect
179. #1865C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
182. #1862C22semidirect
188. #1771C22semidirect
189. #1771C22semidirect
190. C4×C4⋊C8C22semidirect
191. #1763C22semidirect
192. C4×#103C22semidirect
194. #1753C22semidirect
196. C8×C22⋊C4C22semidirect
198. #1750C22semidirect
199. #1745C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#373652
#356752
#295632
#295032
#294742
#294352
#291012
#289822
#289262
#288912
#287732
#286172
#285902
#285662
#272812
#272752
#269892
#268302
#262632
#257762
#256102
#255102
#254122
#251182
#251162
#242692
#221942
#220562
#214632
#209362
#205662