Finite Group Databasebeta

← #6826927

Subgroups — #6826927

Order 512.

1594 conjugacy classes of subgroups.

The subgroup lattice has 1348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40169C211yesmaximal, characteristic
2#39659C211yesmaximal, characteristic, complemented
3#33184C211yesmaximal, characteristic, complemented
4#31660C211yesmaximal, characteristic, complemented
5#31652C211yesmaximal, characteristic, complemented
6#31316C211yesmaximal, characteristic, complemented
7#31302C211yesmaximal, characteristic, complemented
8#30920C211yesmaximal, characteristic, complemented
9#30910C211yesmaximal, characteristic, complemented
10#30407C211yesmaximal, characteristic, complemented
11#30404C211yesmaximal, characteristic
12#30114C211yesmaximal, characteristic, complemented
13#30113C211yesmaximal, characteristic, complemented
14#28543C211yesmaximal, characteristic, complemented
15#28228C211yesmaximal, characteristic, complemented
16#28025C211yesmaximal, characteristic, complemented
17#27848C211yesmaximal, characteristic, complemented
18#27800C211yesmaximal, characteristic, complemented
19#27797C211yesmaximal, characteristic, complemented
20#27245C211yesmaximal, characteristic, complemented
21#27242C211yesmaximal, characteristic, complemented
22#27088C211yesmaximal, characteristic, complemented
23#27083C211yesmaximal, characteristic, complemented
24#26259C211yesmaximal, characteristic, complemented
25#25784C211yesmaximal, characteristic, complemented
26#25423C211yesmaximal, characteristic, complemented
27#24264C211yesmaximal, characteristic
28#23194C211yesmaximal, characteristic, complemented
29#22437C211yesmaximal, characteristic, complemented
30#21561C211yesmaximal, characteristic, complemented
31#21528C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#501C2211yescharacteristic, complemented
34C2×#497C2211yescharacteristic
35C2×#497C2211yescharacteristic
36C2×#479C2211yescharacteristic, complemented
37C2×#474C2211yescharacteristic
38C2×#467C2211yescharacteristic
39C2×#467C2211yescharacteristic, complemented
40C2×#467C2211yescharacteristic, complemented
41C2×#465C2211yescharacteristic
42C2×#465C2211yescharacteristic
43C2×#465C2211yescharacteristic
44C2×#451C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#440C2211yescharacteristic
47C2×#440C2211yescharacteristic
48C2×C4×Q16C2211yescharacteristic, complemented
49C2×C8×D4C2211yescharacteristic
50C22×#97C2211yescharacteristic, complemented
51#2857C2211yescharacteristic, complemented
52#2850C2211yescharacteristic
53#2805—21no—
54#2788—21no—
55#2788—21no—
56#2784—21no—
57#2779—21no—
58#2749—21no—
59#2735—21no—
60#2697—21no—
61#2665—21no—
62#2636—21no—
63#2587—21no—
64#2586—21no—
65#2567C2211yescharacteristic, complemented
66#2566C2211yescharacteristic
67#2538C2211yescharacteristic
68#2538C2211yescharacteristic
69#2518—21no—
70#2512C2211yescharacteristic
71#2511C2211yescharacteristic, complemented
72#2497C2211yescharacteristic
73#2495C2211yescharacteristic
74#2492C2211yescharacteristic
75#2492C2211yescharacteristic, complemented
76#2490C2211yescharacteristic
77#2489C2211yescharacteristic
78#2480—21no—
79#2448C2211yescharacteristic
80#2446C2211yescharacteristic, complemented
81#2435C2211yescharacteristic
82#2434C2211yescharacteristic
83#2429C2211yescharacteristic, complemented
84#2427C2211yescharacteristic
85#2409C2211yescharacteristic
86#2408C2211yescharacteristic
87#2367C2211yescharacteristic
88#2365C2211yescharacteristic, complemented
89Q8×C22⋊C4C2211yescharacteristic
90D4×C22⋊C4C2211yescharacteristic
91#2335—21no—
92#2321—21no—
93C4×C22⋊Q8C2211yescharacteristic, complemented
94C4×#123C2211yescharacteristic
95C4×#121C2211yescharacteristic
96#2101C2211yescharacteristic, complemented
97#2099C2211yescharacteristic, complemented
98#2097C2211yescharacteristic, complemented
99#2095C2211yescharacteristic, complemented
100#2094C2211yescharacteristic
101#2093C2211yescharacteristic
102#2077C2211yescharacteristic
103#2076C2211yescharacteristic
104#2072C2211yescharacteristic, complemented
105#2071C2211yescharacteristic
106#2068C2211yescharacteristic, complemented
107#2067C2211yescharacteristic
108#2056C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2043C2211yescharacteristic, complemented
113#2043C2211yescharacteristic, complemented
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic, complemented
120#2036C2211yescharacteristic, complemented
121#2036C2211yescharacteristic, complemented
122#2035C2211yescharacteristic
123#2034C2211yescharacteristic
124#2026C2211yescharacteristic, complemented
125#2026C2211yescharacteristic, complemented
126#2024C2211yescharacteristic, complemented
127#2023C2211yescharacteristic
128#2015C2211yescharacteristic
129#2015C2211yescharacteristic
130#2013C2211yescharacteristic
131#2013C2211yescharacteristic
132#2001C2211yescharacteristic, complemented
133#2000C2211yescharacteristic
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#1983C2211yescharacteristic
137#1981C2211yescharacteristic, complemented
138#1973C2211yescharacteristic
139#1973C2211yescharacteristic
140#1973C2211yescharacteristic
141#1973C2211yescharacteristic
142#1973C2211yescharacteristic
143#1971C2211yescharacteristic, complemented
144#1971C2211yescharacteristic, complemented
145#1971C2211yescharacteristic, complemented
146#1968C2211yescharacteristic
147#1968C2211yescharacteristic
148#1960C2211yescharacteristic, complemented
149#1959C2211yescharacteristic
150#1944C2211yescharacteristic, complemented
151#1943C2211yescharacteristic, complemented
152#1936C2211yescharacteristic
153#1935C2211yescharacteristic, complemented
154#1928C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1924C2211yescharacteristic
161#1924C2211yescharacteristic
162#1919C2211yescharacteristic, complemented
163#1918C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1893C2211yescharacteristic
167#1892C2211yescharacteristic, complemented
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1869C2211yescharacteristic
181#1850C2211yescharacteristic, complemented
182#1847C2211yescharacteristic, complemented
183#1845C2211yescharacteristic, complemented
184#1817C2211yescharacteristic, complemented
185#1808C2211yescharacteristic
186#1808C2211yescharacteristic, complemented
187#1807C2211yescharacteristic
188#1803C2211yescharacteristic, complemented
189#1803C2211yescharacteristic, complemented
190#1787C2211yescharacteristic
191#1787C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1776C2211yescharacteristic, complemented
195#1776C2211yescharacteristic, complemented
196#1771C2211yescharacteristic, complemented
197#1771C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200#1752C2211yescharacteristic
201#1752C2211yescharacteristic
202#1752C2211yescharacteristic, 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
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C23×C8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×#126—21no—
224C2×#125C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123D411yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C22×C22⋊C4—21no—
246C22×C42C2311yescharacteristic
247#501—42no—
248#497—24no—
249#497—42no—
250#479—42no—
251#474—42no—
252#467—42no—
253#467—42no—
254#467—42no—
255#465—24no—
256#465—42no—
257#465—42no—
258#451—42no—
259#450—42no—
260#440—42no—
261#440—42no—
262C4×Q16—42no—
263C8×D4—42no—
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×#97—42no—
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#399—21no—
330#398—21no—
331#398—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#395—21no—
348#395—21no—
349#395—21no—
350#395—21no—
351#395—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#393—21no—
358#393—21no—
359#393—21no—
360#392—21no—
361#391—21no—
362#391—21no—
363#391—21no—
364#391—21no—
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#390—21no—
376#390—21no—
377#390—21no—
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389—21no—
389#389—21no—
390#389—21no—
391#389—21no—
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388D411yescharacteristic
412#388D411yescharacteristic
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387D411yescharacteristic
422#387D411yescharacteristic
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386D411yescharacteristic
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385D411yescharacteristic
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#383—21no—
443#382—21no—
444#382C2311yescharacteristic
445#381D411yescharacteristic
446#380—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#379—21no—
457#379—21no—
458#379—21no—
459#379—21no—
460C4×C4⋊C4—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
474C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—22no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4C2×D411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
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—22no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—416no—
558C2×SD16#4114yes—
559C22×C8—22no—
560C22×C8—22no—
561C22×C8—22no—
562C22×C8—22no—
563C22×C8—22no—
564C22×C8—22no—
565C22×C8—22no—
566C22×C8—41no—
567C22×C8—41no—
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C4⋊Q8—22no—
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579C4⋊Q8—41no—
580C4⋊Q8—41no—
581C4⋊Q8—41no—
582#126—82no—
583#125—41no—
584#125—41no—
585#124—22no—
586#124—41no—
587#124—41no—
588#124—41no—
589#123—24no—
590C22⋊Q8—22no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602#121—22no—
603#121—41no—
604#121—41no—
605#121—41no—
606#120—44no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—82no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—82no—
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—41no—
714C2×C42—41no—
715C2×C42C2×D411yescharacteristic
716C2×C42C2×D411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722#107—22no—
723#107—22no—
724#107—22no—
725#107—22no—
726#107—41no—
727#107—41no—
728#107—41no—
729#106—22no—
730#106—22no—
731#106—22no—
732#106—41no—
733C4⋊C8—22no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736#103—22no—
737#103—22no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#102—22no—
757#102—22no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766C22⋊C8—22no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771#97—22no—
772#97—22no—
773#97—22no—
774#97—22no—
775#97—41no—
776#97—41no—
777C4×C8—22no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824C24—21no—
825C24—21no—
826C24—42no—
827C24—42no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24C22×D411yescharacteristic
834C24C22×D411yescharacteristic
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—42no—
859C2×Q8—44no—
860C2×Q8—81no—
861C2×Q8—81no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8—81no—
865C2×Q8—82no—
866C2×Q8—82no—
867C2×Q8—82no—
868C2×Q8C2×#4112yes—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—42no—
883C2×D4—44no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—82no—
890C2×D4—82no—
891C2×D4—82no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4#13714yes—
896C2×D4C2×#4112yes—
897C22×C4—21no—
898C22×C4—22no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
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—41no—
925C22×C4—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
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×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C2511yescharacteristic
951Q16—44no—
952Q16—82no—
953Q16—82no—
954SD16—28no—
955SD16—44no—
956SD16—44no—
957SD16—44no—
958SD16—82no—
959SD16—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—44no—
982C2×C8—44no—
983C2×C8C2×#4112yes—
984C2×C8H(5,𝔽2)12yes—
985C2×C8H(5,𝔽2)12yes—
986C2×C8H(5,𝔽2)12yes—
987C4⋊C4—22no—
988C4⋊C4—22no—
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—21no—
1008C4⋊C4—21no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C22⋊C4—22no—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
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—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—41no—
1090C42—41no—
1091C42—42no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—22no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—84no—
1126C23—84no—
1127C23—162no—
1128C23—162no—
1129C23—162no—
1130C23—162no—
1131C23—162no—
1132C23C2×#13712yes—
1133C23C2×#13712yes—
1134C23C23×D411yescharacteristic
1135Q8—22no—
1136Q8—22no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—84no—
1152Q8—162no—
1153D4—22no—
1154D4—22no—
1155D4—44no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—84no—
1163D4—84no—
1164D4—162no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
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—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—22no—
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—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
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—82no—
1251C2×C4—82no—
1252C2×C4—84no—
1253C2×C4—162no—
1254C2×C4—162no—
1255C2×C4C2×#13712yes—
1256C2×C4C22×#4111yescharacteristic
1257C2×C4C2×H(5,𝔽2)11yescharacteristic
1258C2×C4C2×H(5,𝔽2)11yescharacteristic
1259C2×C4C2×H(5,𝔽2)11yescharacteristic
1260C2×C4#58511yescharacteristic
1261C2×C4#58511yescharacteristic
1262C8—22no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C8—41no—
1269C8#53814yes—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—22no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—168no—
1299C22D4×#4111yescharacteristic
1300C22#349611yescharacteristic
1301C22#349811yescharacteristic
1302C22C22×#13711yescharacteristic
1303C22#358411yescharacteristic
1304C22#358511yescharacteristic
1305C22#358611yescharacteristic
1306C4—22no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
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—81no—
1332C4C2×#53811yescharacteristic
1333C4#351411yescharacteristic
1334C4#354211yescharacteristic
1335C4#356211yescharacteristic
1336C2—42no—
1337C2—42no—
1338C2—82no—
1339C2—161no—
1340C2#3940111yescharacteristic
1341C2#6145311yescharacteristic
1342C2#6152811yescharacteristic
1343C2#6225411yescharacteristic
1344C2#6228511yescharacteristic
1345C2#6244811yescharacteristic
1346C2#6246111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
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
2. #39659C2semidirect
3. #33184C2semidirect
4. #31660C2semidirect
5. #31652C2semidirect
6. #31316C2semidirect
7. #31302C2semidirect
8. #30920C2semidirect
9. #30910C2semidirect
10. #30407C2semidirect
12. #30114C2semidirect
13. #30113C2semidirect
14. #28543C2semidirect
15. #28228C2semidirect
16. #28025C2semidirect
17. #27848C2semidirect
18. #27800C2semidirect
19. #27797C2semidirect
20. #27245C2semidirect
21. #27242C2semidirect
22. #27088C2semidirect
23. #27083C2semidirect
24. #26259C2semidirect
25. #25784C2semidirect
26. #25423C2semidirect
28. #23194C2semidirect
29. #22437C2semidirect
30. #21561C2semidirect
31. #21528C2semidirect
33. C2×#501C22semidirect
36. C2×#479C22semidirect
39. C2×#467C22semidirect
40. C2×#467C22semidirect
48. C2×C4×Q16C22semidirect
50. C22×#97C22semidirect
51. #2857C22semidirect
65. #2567C22semidirect
71. #2511C22semidirect
75. #2492C22semidirect
80. #2446C22semidirect
83. #2429C22semidirect
88. #2365C22semidirect
93. C4×C22⋊Q8C22semidirect
96. #2101C22semidirect
97. #2099C22semidirect
98. #2097C22semidirect
99. #2095C22semidirect
104. #2072C22semidirect
106. #2068C22semidirect
108. #2056C22semidirect
112. #2043C22semidirect
113. #2043C22semidirect
119. #2036C22semidirect
120. #2036C22semidirect
121. #2036C22semidirect
124. #2026C22semidirect
125. #2026C22semidirect
126. #2024C22semidirect
132. #2001C22semidirect
137. #1981C22semidirect
143. #1971C22semidirect
144. #1971C22semidirect
145. #1971C22semidirect
148. #1960C22semidirect
150. #1944C22semidirect
151. #1943C22semidirect
153. #1935C22semidirect
154. #1928C22semidirect
155. #1928C22semidirect
156. #1927C22semidirect
157. #1927C22semidirect
162. #1919C22semidirect
163. #1918C22semidirect
164. #1917C22semidirect
165. #1917C22semidirect
167. #1892C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
181. #1850C22semidirect
182. #1847C22semidirect
183. #1845C22semidirect
184. #1817C22semidirect
186. #1808C22semidirect
188. #1803C22semidirect
189. #1803C22semidirect
194. #1776C22semidirect
195. #1776C22semidirect
196. #1771C22semidirect
197. #1771C22semidirect
198. #1763C22semidirect
202. #1752C22semidirect

Maximal subgroups

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

subgroupindex
#401692
#396592
#331842
#316602
#316522
#313162
#313022
#309202
#309102
#304072
#304042
#301142
#301132
#285432
#282282
#280252
#278482
#278002
#277972
#272452
#272422
#270882
#270832
#262592
#257842
#254232
#242642
#231942
#224372
#215612
#215282