Finite Group Databasebeta

← #6507339

Subgroups — #6507339

Order 512.

1675 conjugacy classes of subgroups.

The subgroup lattice has 1357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37365C211yesmaximal, characteristic
2#35671C211yesmaximal, characteristic, complemented
3#29563C211yesmaximal, characteristic, complemented
4#29500C211yesmaximal, characteristic, complemented
5#29491C211yesmaximal, characteristic, complemented
6#29450C211yesmaximal, characteristic, complemented
7#29094C211yesmaximal, characteristic, complemented
8#28989C211yesmaximal, characteristic, complemented
9#28918C211yesmaximal, characteristic, complemented
10#28900C211yesmaximal, characteristic, complemented
11#28778C211yesmaximal, characteristic, complemented
12#28619C211yesmaximal, characteristic, complemented
13#28590C211yesmaximal, characteristic, complemented
14#28564C211yesmaximal, characteristic, complemented
15#27283C211yesmaximal, characteristic, complemented
16#27271C211yesmaximal, characteristic, complemented
17#26973C211yesmaximal, characteristic, complemented
18#26839C211yesmaximal, characteristic, complemented
19#26259C211yesmaximal, characteristic, complemented
20#25784C211yesmaximal, characteristic, complemented
21#25612C211yesmaximal, characteristic, complemented
22#25511C211yesmaximal, characteristic, complemented
23#25420C211yesmaximal, characteristic, complemented
24#25120C211yesmaximal, characteristic
25#25118C211yesmaximal, characteristic, complemented
26#24269C211yesmaximal, characteristic
27#22197C211yesmaximal, characteristic, complemented
28#22052C211yesmaximal, characteristic, complemented
29#21463C211yesmaximal, characteristic, complemented
30#20936C211yesmaximal, characteristic, complemented
31#20563C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#541C2211yescharacteristic, complemented
34C2×#519C2211yescharacteristic
35C2×#497C2211yescharacteristic
36C2×#497C2211yescharacteristic
37C2×#491C2211yescharacteristic, complemented
38C2×#488C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#468C2211yescharacteristic
41C2×#467C2211yescharacteristic
42C2×#467C2211yescharacteristic, complemented
43C2×#465C2211yescharacteristic
44C2×#451C2211yescharacteristic
45C2×#450C2211yescharacteristic
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#2611—21no—
65#2604—21no—
66#2601—21no—
67#2584—21no—
68#2512C2211yescharacteristic
69#2490C2211yescharacteristic
70#2479—21no—
71#2475—21no—
72#2469—21no—
73#2462—21no—
74#2453C2211yescharacteristic, complemented
75#2448C2211yescharacteristic
76#2446C2211yescharacteristic, complemented
77#2441C2211yescharacteristic
78#2441C2211yescharacteristic
79#2435C2211yescharacteristic
80#2434C2211yescharacteristic
81#2429C2211yescharacteristic, complemented
82#2426C2211yescharacteristic
83#2423C2211yescharacteristic, complemented
84#2415C2211yescharacteristic
85#2415C2211yescharacteristic
86#2409C2211yescharacteristic
87#2408C2211yescharacteristic
88#2323C2211yescharacteristic
89#2323C2211yescharacteristic
90#2323C2211yescharacteristic, complemented
91#2309C2211yescharacteristic
92C4×C4⋊Q8C2211yescharacteristic, complemented
93#2295C2211yescharacteristic, complemented
94#2293C2211yescharacteristic
95#2087C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2083C2211yescharacteristic, complemented
98#2076C2211yescharacteristic, complemented
99#2072C2211yescharacteristic, complemented
100#2071C2211yescharacteristic
101#2068C2211yescharacteristic, complemented
102#2065C2211yescharacteristic
103#2059C2211yescharacteristic, complemented
104#2059C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2056C2211yescharacteristic, complemented
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2043C2211yescharacteristic, complemented
111#2043C2211yescharacteristic, complemented
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2035C2211yescharacteristic, complemented
115#2033C2211yescharacteristic
116#2026C2211yescharacteristic, complemented
117#2025C2211yescharacteristic
118#2015C2211yescharacteristic
119#2015C2211yescharacteristic
120#2013C2211yescharacteristic
121#2013C2211yescharacteristic
122#2001C2211yescharacteristic, complemented
123#2001C2211yescharacteristic, complemented
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic
127#1992C2211yescharacteristic, complemented
128#1992C2211yescharacteristic, complemented
129#1973C2211yescharacteristic
130#1973C2211yescharacteristic
131#1973C2211yescharacteristic
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic
134#1973C2211yescharacteristic
135#1971C2211yescharacteristic, complemented
136#1968C2211yescharacteristic
137#1959C2211yescharacteristic
138#1956C2211yescharacteristic, complemented
139#1944C2211yescharacteristic, complemented
140#1944C2211yescharacteristic, complemented
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1935C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1935C2211yescharacteristic, complemented
147#1935C2211yescharacteristic, complemented
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic, complemented
151#1928C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1925C2211yescharacteristic
155#1918C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1894C2211yescharacteristic
158#1894C2211yescharacteristic
159#1894C2211yescharacteristic, complemented
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
172#1880C2211yescharacteristic
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1878C2211yescharacteristic, complemented
177#1873C2211yescharacteristic
178#1873C2211yescharacteristic
179#1865C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1808C2211yescharacteristic
186#1787C2211yescharacteristic
187#1786C2211yescharacteristic
188#1771C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1767C2211yescharacteristic, complemented
191#1763C2211yescharacteristic, complemented
192C4×#103C2211yescharacteristic, complemented
193#1753C2211yescharacteristic
194#1753C2211yescharacteristic, complemented
195#1752C2211yescharacteristic
196#1752C2211yescharacteristic, 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×Q16C2311yescharacteristic
208C22×SD16—24no—
209C22×SD16—42no—
210C22×SD16—42no—
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C22×M16C2311yescharacteristic
219C23×C8C2311yescharacteristic
220C23×C8C2311yescharacteristic
221#541—42no—
222#541—42no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×#126—21no—
226C2×#126—21no—
227C2×#126—21no—
228C2×#126—21no—
229C2×#125—21no—
230C2×#125—21no—
231C2×#125C2311yescharacteristic
232C2×#125C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
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×Q8C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×#117—21no—
256C2×#117—21no—
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261#497—42no—
262#497—42no—
263#491—42no—
264#488—42no—
265#468—42no—
266#468—42no—
267#467—24no—
268#467—42no—
269#465—42no—
270#451—24no—
271#450—24no—
272#441—42no—
273C4×Q16—42no—
274#435—24no—
275#435—24no—
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
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×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
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×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329#400—21no—
330#400—21no—
331#399—21no—
332#399—21no—
333#399—21no—
334#399—21no—
335#399—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#395—21no—
354#395—21no—
355#395—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#394—21no—
366#394—21no—
367#393—21no—
368#392—21no—
369#391C2311yescharacteristic
370#391C2311yescharacteristic
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#390D411yescharacteristic
382#390D411yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#389—21no—
392#389—21no—
393#389—21no—
394#389—21no—
395#389—21no—
396#389—21no—
397#389—21no—
398#389—21no—
399#389—21no—
400#389—21no—
401#389—21no—
402#389D411yescharacteristic
403#389D411yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
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#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#388D411yescharacteristic
435#388D411yescharacteristic
436#388D411yescharacteristic
437#388D411yescharacteristic
438#387—21no—
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#387—21no—
448#387—21no—
449#386—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#384C2311yescharacteristic
454#384C2311yescharacteristic
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⋊C4—21no—
466C4×C4⋊C4—21no—
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
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—22no—
505C22×Q8—22no—
506C22×Q8—22no—
507C22×Q8—22no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4C2×D411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×Q16—22no—
530C2×Q16—22no—
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—22no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×SD16—22no—
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—41no—
555C2×SD16—41no—
556C2×SD16—416no—
557C2×M16—22no—
558C2×M16—22no—
559C2×M16—41no—
560C2×M16—41no—
561C2×M16—41no—
562C2×M16—41no—
563C22×C8—22no—
564C22×C8—41no—
565C22×C8—41no—
566C22×C8—41no—
567C22×C8—41no—
568C22×C8#4114yes—
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C4⋊Q8—22no—
578C4⋊Q8—22no—
579C4⋊Q8—41no—
580C4⋊Q8—41no—
581#126—44no—
582#126—44no—
583#126—82no—
584#126—82no—
585#125—22no—
586#125—41no—
587#125—41no—
588#125—41no—
589#125—44no—
590#125—44no—
591#124—41no—
592#124—41no—
593#124—41no—
594#124—41no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606C22⋊Q8—41no—
607#121—41no—
608#121—41no—
609#121—41no—
610#121—41no—
611#120—82no—
612C4×Q8—22no—
613C4×Q8—22no—
614C4×Q8—22no—
615C4×Q8—22no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×Q8—41no—
622C4×Q8—44no—
623C4×Q8—41no—
624C4×Q8—41no—
625C4×Q8—44no—
626C4×D4—22no—
627C4×D4—22no—
628#117—22no—
629#117—41no—
630#117—41no—
631#117—41no—
632#117—41no—
633#117—44no—
634#117—41no—
635#117—44no—
636#117—41no—
637#117—41no—
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—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⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42C2×D411yescharacteristic
742C2×C42C2×D411yescharacteristic
743C2×C42C2×D411yescharacteristic
744C2×C42C2×D411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750#107—22no—
751#107—41no—
752#107—41no—
753#107—41no—
754#107—41no—
755#106—22no—
756#106—41no—
757C4⋊C8—22no—
758C4⋊C8—22no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—22no—
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#102—22no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789C22⋊C8—22no—
790C22⋊C8—22no—
791C22⋊C8—22no—
792C22⋊C8#4114yes—
793#97—22no—
794#97—22no—
795#97—41no—
796#97—41no—
797#97—41no—
798#97—41no—
799C4×C8—41no—
800C4×C8—41no—
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#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837C24—21no—
838C24—21no—
839C24—42no—
840C24—81no—
841C24—81no—
842C24—81no—
843C24—81no—
844C24—81no—
845C24—81no—
846C24C22×D411yescharacteristic
847C24C22×D411yescharacteristic
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—28no—
851C2×Q8—21no—
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—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—42no—
872C2×Q8—42no—
873C2×Q8—44no—
874C2×Q8—44no—
875C2×Q8—44no—
876C2×Q8—42no—
877C2×Q8H(5,𝔽2)12yes—
878C2×Q8H(5,𝔽2)12yes—
879C2×D4—22no—
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—44no—
893C2×D4—44no—
894C2×D4—41no—
895C2×D4—41no—
896C2×D4—42no—
897C2×D4—82no—
898C2×D4—82no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
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—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C2×#4112yes—
947C22×C4C2×#4112yes—
948C22×C4C2511yescharacteristic
949Q16—44no—
950Q16—44no—
951Q16—82no—
952SD16—44no—
953SD16—44no—
954SD16—44no—
955SD16—44no—
956SD16—82no—
957SD16—82no—
958M16—82no—
959M16—82no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
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—44no—
981C2×C8—82no—
982C2×C8C2×#4112yes—
983C2×C8C2×#4112yes—
984C2×C8C2×#4112yes—
985C2×C8C2×#4112yes—
986C4⋊C4—24no—
987C4⋊C4—22no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—81no—
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⋊C4H(5,𝔽2)12yes—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
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—
1089C42—24no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—41no—
1101C42—41no—
1102C42—41no—
1103C42—41no—
1104C42—42no—
1105C42—42no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—81no—
1110C42—81no—
1111C42—81no—
1112C42—81no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—84no—
1141C23—162no—
1142C23—162no—
1143C23—162no—
1144C23—162no—
1145C23—162no—
1146C23—162no—
1147C23#53212yes—
1148C23C23×D411yescharacteristic
1149Q8—22no—
1150Q8—22no—
1151Q8—22no—
1152Q8—22no—
1153Q8—48no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—84no—
1175D4—82no—
1176D4—162no—
1177D4—162no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
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—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—22no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—48no—
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—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4#53212yes—
1265C2×C4C22×#4111yescharacteristic
1266C2×C4C22×#4111yescharacteristic
1267C2×C4C2×H(5,𝔽2)11yescharacteristic
1268C2×C4C2×H(5,𝔽2)11yescharacteristic
1269C2×C4C2×H(5,𝔽2)11yescharacteristic
1270C2×C4#58511yescharacteristic
1271C8—22no—
1272C8—22no—
1273C8—22no—
1274C8—22no—
1275C8—41no—
1276C8—41no—
1277C8—41no—
1278C8—41no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—168no—
1308C22C2×#53211yescharacteristic
1309C22#348411yescharacteristic
1310C22#348811yescharacteristic
1311C22#358511yescharacteristic
1312C22#358611yescharacteristic
1313C22#358611yescharacteristic
1314C22#358611yescharacteristic
1315C4—22no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—42no—
1320C4—42no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—42no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4#349011yescharacteristic
1342C4#350611yescharacteristic
1343C4#351311yescharacteristic
1344C4#351911yescharacteristic
1345C2—42no—
1346C2—81no—
1347C2—161no—
1348C2—161no—
1349C2#3539211yescharacteristic
1350C2#6070911yescharacteristic
1351C2#6072011yescharacteristic
1352C2#6167111yescharacteristic
1353C2#6167611yescharacteristic
1354C2#6207711yescharacteristic
1355C2#6208511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
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
2. #35671C2semidirect
3. #29563C2semidirect
4. #29500C2semidirect
5. #29491C2semidirect
6. #29450C2semidirect
7. #29094C2semidirect
8. #28989C2semidirect
9. #28918C2semidirect
10. #28900C2semidirect
11. #28778C2semidirect
12. #28619C2semidirect
13. #28590C2semidirect
14. #28564C2semidirect
15. #27283C2semidirect
16. #27271C2semidirect
17. #26973C2semidirect
18. #26839C2semidirect
19. #26259C2semidirect
20. #25784C2semidirect
21. #25612C2semidirect
22. #25511C2semidirect
23. #25420C2semidirect
25. #25118C2semidirect
27. #22197C2semidirect
28. #22052C2semidirect
29. #21463C2semidirect
30. #20936C2semidirect
31. #20563C2semidirect
33. C2×#541C22semidirect
37. C2×#491C22semidirect
42. C2×#467C22semidirect
46. C2×#441C22semidirect
47. C2×C4×Q16C22semidirect
74. #2453C22semidirect
76. #2446C22semidirect
81. #2429C22semidirect
83. #2423C22semidirect
90. #2323C22semidirect
92. C4×C4⋊Q8C22semidirect
93. #2295C22semidirect
95. #2087C22semidirect
96. #2083C22semidirect
97. #2083C22semidirect
98. #2076C22semidirect
99. #2072C22semidirect
101. #2068C22semidirect
103. #2059C22semidirect
104. #2059C22semidirect
105. #2056C22semidirect
106. #2056C22semidirect
110. #2043C22semidirect
111. #2043C22semidirect
114. #2035C22semidirect
116. #2026C22semidirect
122. #2001C22semidirect
123. #2001C22semidirect
127. #1992C22semidirect
128. #1992C22semidirect
135. #1971C22semidirect
138. #1956C22semidirect
139. #1944C22semidirect
140. #1944C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
146. #1935C22semidirect
147. #1935C22semidirect
150. #1933C22semidirect
151. #1928C22semidirect
152. #1928C22semidirect
155. #1918C22semidirect
156. #1918C22semidirect
159. #1894C22semidirect
160. #1894C22semidirect
162. #1892C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
176. #1878C22semidirect
179. #1865C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
188. #1771C22semidirect
189. #1771C22semidirect
190. #1767C22semidirect
191. #1763C22semidirect
192. C4×#103C22semidirect
194. #1753C22semidirect
196. #1752C22semidirect
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
#356712
#295632
#295002
#294912
#294502
#290942
#289892
#289182
#289002
#287782
#286192
#285902
#285642
#272832
#272712
#269732
#268392
#262592
#257842
#256122
#255112
#254202
#251202
#251182
#242692
#221972
#220522
#214632
#209362
#205632