Finite Group Databasebeta

← #6826941

Subgroups — #6826941

Order 512.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1373 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42835C211yesmaximal, characteristic, complemented
2#42642C211yesmaximal, characteristic, complemented
3#33181C211yesmaximal, characteristic, complemented
4#31656C211yesmaximal, characteristic, complemented
5#31652C211yesmaximal, characteristic, complemented
6#31306C211yesmaximal, characteristic, complemented
7#31305C211yesmaximal, characteristic, complemented
8#30918C211yesmaximal, characteristic, complemented
9#30909C211yesmaximal, characteristic, complemented
10#30410C211yesmaximal, characteristic, complemented
11#30404C211yesmaximal, characteristic, complemented
12#30123C211yesmaximal, characteristic, complemented
13#30117C211yesmaximal, characteristic, complemented
14#28530C211yesmaximal, characteristic, complemented
15#28232C211yesmaximal, characteristic, complemented
16#28021C211yesmaximal, characteristic, complemented
17#27853C211yesmaximal, characteristic, complemented
18#27804C211yesmaximal, characteristic, complemented
19#27803C211yesmaximal, characteristic, complemented
20#27233C211yesmaximal, characteristic, complemented
21#27224C211yesmaximal, characteristic, complemented
22#27071C211yesmaximal, characteristic, complemented
23#27066C211yesmaximal, characteristic, complemented
24#26253C211yesmaximal, characteristic, complemented
25#25796C211yesmaximal, characteristic, complemented
26#25417C211yesmaximal, characteristic, complemented
27#24277C211yesmaximal, characteristic
28#23194C211yesmaximal, characteristic, complemented
29#22443C211yesmaximal, characteristic, complemented
30#21571C211yesmaximal, characteristic, complemented
31#21543C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#498C2211yescharacteristic, complemented
34C2×#497C2211yescharacteristic
35C2×#495C2211yescharacteristic
36C2×#475C2211yescharacteristic, complemented
37C2×#476C2211yescharacteristic
38C2×#470C2211yescharacteristic
39C2×#470C2211yescharacteristic, complemented
40C2×#469C2211yescharacteristic
41C2×#468C2211yescharacteristic
42C2×#465C2211yescharacteristic
43C2×#465C2211yescharacteristic, complemented
44C2×#452C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#440C2211yescharacteristic
47C2×C4×Q16C2211yescharacteristic, complemented
48C2×C4×SD16C2211yescharacteristic
49C2×#436C2211yescharacteristic
50C2×#405C2211yescharacteristic, complemented
51#2830—21no—
52#2826—21no—
53#2803—21no—
54#2788—21no—
55#2735—21no—
56#2730—21no—
57#2727—21no—
58#2715—21no—
59#2702—21no—
60#2685—21no—
61#2662—21no—
62#2649—21no—
63#2649—21no—
64#2626—21no—
65#2620C2211yescharacteristic
66#2620C2211yescharacteristic, complemented
67#2587—21no—
68#2567C2211yescharacteristic, complemented
69#2542C2211yescharacteristic
70#2538C2211yescharacteristic
71#2538C2211yescharacteristic
72#2512C2211yescharacteristic
73#2512C2211yescharacteristic, complemented
74#2497C2211yescharacteristic
75#2496C2211yescharacteristic
76#2492C2211yescharacteristic
77#2492C2211yescharacteristic
78#2491C2211yescharacteristic
79#2491C2211yescharacteristic, complemented
80#2472—21no—
81#2448C2211yescharacteristic
82#2448C2211yescharacteristic, complemented
83#2435C2211yescharacteristic
84#2432C2211yescharacteristic
85#2429C2211yescharacteristic, complemented
86#2427C2211yescharacteristic
87#2408C2211yescharacteristic
88#2407C2211yescharacteristic
89#2395C2211yescharacteristic
90#2367C2211yescharacteristic
91#2365C2211yescharacteristic, complemented
92#2341C2211yescharacteristic
93D4×C22⋊C4C2211yescharacteristic
94#2324C2211yescharacteristic
95#2323C2211yescharacteristic, complemented
96#2100C2211yescharacteristic, complemented
97#2099C2211yescharacteristic, complemented
98#2096C2211yescharacteristic, complemented
99#2096C2211yescharacteristic, complemented
100#2094C2211yescharacteristic
101#2094C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic, complemented
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic, complemented
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic, complemented
111#2054C2211yescharacteristic
112#2043C2211yescharacteristic, complemented
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic, complemented
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic, complemented
121#2035C2211yescharacteristic, complemented
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic, complemented
124#2024C2211yescharacteristic, complemented
125#2024C2211yescharacteristic, complemented
126#2023C2211yescharacteristic
127#2023C2211yescharacteristic, complemented
128#2015C2211yescharacteristic
129#2013C2211yescharacteristic
130#2012C2211yescharacteristic
131#2012C2211yescharacteristic
132#2001C2211yescharacteristic, complemented
133#2000C2211yescharacteristic
134#2000C2211yescharacteristic
135#1999C2211yescharacteristic
136#1983C2211yescharacteristic
137#1981C2211yescharacteristic, complemented
138#1972C2211yescharacteristic
139#1972C2211yescharacteristic
140#1971C2211yescharacteristic, complemented
141#1970C2211yescharacteristic
142#1970C2211yescharacteristic
143#1969C2211yescharacteristic, complemented
144#1968C2211yescharacteristic
145#1968C2211yescharacteristic
146#1968C2211yescharacteristic
147#1968C2211yescharacteristic, complemented
148#1959C2211yescharacteristic
149#1959C2211yescharacteristic, complemented
150#1944C2211yescharacteristic, complemented
151#1942C2211yescharacteristic, complemented
152#1936C2211yescharacteristic
153#1935C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1927C2211yescharacteristic, complemented
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic, complemented
159#1926C2211yescharacteristic, complemented
160#1924C2211yescharacteristic
161#1923C2211yescharacteristic
162#1920C2211yescharacteristic, complemented
163#1919C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1893C2211yescharacteristic
167#1892C2211yescharacteristic, complemented
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic, complemented
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1878C2211yescharacteristic, complemented
176#1878C2211yescharacteristic, complemented
177#1878C2211yescharacteristic, complemented
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1869C2211yescharacteristic
181#1850C2211yescharacteristic, complemented
182#1844C2211yescharacteristic, complemented
183#1844C2211yescharacteristic, complemented
184#1818C2211yescharacteristic, complemented
185#1809C2211yescharacteristic
186#1809C2211yescharacteristic
187#1809C2211yescharacteristic, complemented
188#1803C2211yescharacteristic, complemented
189#1803C2211yescharacteristic, complemented
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1776C2211yescharacteristic, complemented
195#1776C2211yescharacteristic, complemented
196#1771C2211yescharacteristic, complemented
197C8×C4⋊C4C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C2×AGL(1,ℤ/8)—42no—
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C22×M16C2311yescharacteristic
219C23×C8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×#126—21no—
224C2×#126—21no—
225C2×#126—21no—
226C2×#124—21no—
227C2×#124—21no—
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#120—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C22×C22⋊C4—21no—
251#498—42no—
252#497—24no—
253#495—42no—
254#476—42no—
255#475—42no—
256#470—42no—
257#470—42no—
258#469—42no—
259#468—24no—
260#465—42no—
261#465—42no—
262#452—42no—
263#450—42no—
264#440—42no—
265C4×Q16—42no—
266C4×SD16—42no—
267#436—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317#405—42no—
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400D411yescharacteristic
330#399—21no—
331#399—21no—
332#399—21no—
333#399—21no—
334#399D411yescharacteristic
335#398—21no—
336#398D411yescharacteristic
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397D411yescharacteristic
344#397D411yescharacteristic
345#397D411yescharacteristic
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#395—21no—
359#395—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394D411yescharacteristic
374#394D411yescharacteristic
375#393—21no—
376#393—21no—
377#393—21no—
378#393—21no—
379#392—21no—
380#392—21no—
381#391—21no—
382#391—21no—
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#390—21no—
390#390—21no—
391#390—21no—
392#390—21no—
393#390—21no—
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#389—21no—
405#389—21no—
406#389—21no—
407#389—21no—
408#389—21no—
409#389—21no—
410#389—21no—
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
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#387—21no—
433#387—21no—
434#387—21no—
435#387—21no—
436#387—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#384C2311yescharacteristic
451#380—21no—
452#380—21no—
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#379—21no—
460#379—21no—
461#379—21no—
462#379—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
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—
500C2×#41—22no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4C2×D411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531AGL(1,ℤ/8)—416no—
532C2×Q16—22no—
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—22no—
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—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16#4114yes—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—41no—
558C2×D8—41no—
559C2×M16—22no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—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#126—82no—
584#126—82no—
585#124—22no—
586#124—41no—
587#124—41no—
588#124—41no—
589#124—41no—
590#124—41no—
591#124—82no—
592#124—82no—
593C22⋊Q8—22no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—82no—
604C22⋊Q8—82no—
605#121—22no—
606#121—41no—
607#121—41no—
608#121—41no—
609#121—41no—
610#121—41no—
611#120—82no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626#117—41no—
627#117—41no—
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⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×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—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—82no—
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#107—22no—
737#107—22no—
738#106—22no—
739#106—22no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—41no—
744#106—41no—
745#106—41no—
746#106—41no—
747C4⋊C8—22no—
748C4⋊C8—41no—
749C4⋊C8—41no—
750#103—22no—
751#103—22no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103—41no—
765#102—22no—
766#102—22no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780C22⋊C8—22no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785#97—22no—
786#97—22no—
787#97—41no—
788C4×C8—22no—
789C4×C8—22no—
790C4×C8—22no—
791C4×C8—41no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828C24—21no—
829C24—21no—
830C24—21no—
831C24—42no—
832C24—42no—
833C24—81no—
834C24—81no—
835C24—81no—
836C24—81no—
837C24—81no—
838C24C22×D411yescharacteristic
839C24C22×D411yescharacteristic
840#41—44no—
841#41—82no—
842#41—82no—
843#41—82no—
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—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—42no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8—81no—
865C2×Q8—81no—
866C2×Q8—81no—
867C2×Q8C2×#4112yes—
868C2×D4—22no—
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—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—41no—
887C2×D4—41no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—82no—
895C2×D4—82no—
896C2×D4—82no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4C2×#4112yes—
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—21no—
932C22×C4—21no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
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×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C2511yescharacteristic
955Q16—44no—
956Q16—82no—
957SD16—28no—
958SD16—44no—
959SD16—82no—
960SD16—82no—
961SD16—82no—
962D8—44no—
963D8—44no—
964M16—44no—
965M16—44no—
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—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—44no—
987C2×C8C2×#4112yes—
988C2×C8H(5,𝔽2)12yes—
989C2×C8H(5,𝔽2)12yes—
990C2×C8H(5,𝔽2)12yes—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—22no—
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—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
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—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
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—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—42no—
1106C42—81no—
1107C42—81no—
1108C42—81no—
1109C42—81no—
1110C42—81no—
1111C42—81no—
1112C42—81no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—22no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
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—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—84no—
1149C23—84no—
1150C23—162no—
1151C23—162no—
1152C23—162no—
1153C23—162no—
1154C23—162no—
1155C23C23×D411yescharacteristic
1156Q8—22no—
1157Q8—22no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—162no—
1169Q8—162no—
1170D4—22no—
1171D4—22no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—82no—
1183D4—84no—
1184D4—84no—
1185D4—162no—
1186D4—162no—
1187D4—162no—
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—22no—
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—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—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—84no—
1270C2×C4—162no—
1271C2×C4—162no—
1272C2×C4#57712yes—
1273C2×C4#57712yes—
1274C2×C4C22×#4111yescharacteristic
1275C2×C4C2×H(5,𝔽2)11yescharacteristic
1276C2×C4C2×H(5,𝔽2)11yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4#58511yescharacteristic
1279C2×C4#58511yescharacteristic
1280C8—22no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8#53814yes—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—42no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—42no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—42no—
1303C22—41no—
1304C22—41no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
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—168no—
1324C22D4×#4111yescharacteristic
1325C22#349611yescharacteristic
1326C22#349811yescharacteristic
1327C22C2×#57711yescharacteristic
1328C22C2×#57711yescharacteristic
1329C22#358511yescharacteristic
1330C22#358611yescharacteristic
1331C4—22no—
1332C4—22no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—42no—
1343C4—41no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4C2×#53811yescharacteristic
1357C4#351411yescharacteristic
1358C4#354211yescharacteristic
1359C4#356211yescharacteristic
1360C2—81no—
1361C2—81no—
1362C2—82no—
1363C2—161no—
1364C2—161no—
1365C2#3940111yescharacteristic
1366C2#6155411yescharacteristic
1367C2#6155711yescharacteristic
1368C2#6232111yescharacteristic
1369C2#6235511yescharacteristic
1370C2#6243011yescharacteristic
1371C2#6244611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24277C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42835C2semidirect
2. #42642C2semidirect
3. #33181C2semidirect
4. #31656C2semidirect
5. #31652C2semidirect
6. #31306C2semidirect
7. #31305C2semidirect
8. #30918C2semidirect
9. #30909C2semidirect
10. #30410C2semidirect
11. #30404C2semidirect
12. #30123C2semidirect
13. #30117C2semidirect
14. #28530C2semidirect
15. #28232C2semidirect
16. #28021C2semidirect
17. #27853C2semidirect
18. #27804C2semidirect
19. #27803C2semidirect
20. #27233C2semidirect
21. #27224C2semidirect
22. #27071C2semidirect
23. #27066C2semidirect
24. #26253C2semidirect
25. #25796C2semidirect
26. #25417C2semidirect
28. #23194C2semidirect
29. #22443C2semidirect
30. #21571C2semidirect
31. #21543C2semidirect
33. C2×#498C22semidirect
36. C2×#475C22semidirect
39. C2×#470C22semidirect
43. C2×#465C22semidirect
47. C2×C4×Q16C22semidirect
50. C2×#405C22semidirect
66. #2620C22semidirect
68. #2567C22semidirect
73. #2512C22semidirect
79. #2491C22semidirect
82. #2448C22semidirect
85. #2429C22semidirect
91. #2365C22semidirect
95. #2323C22semidirect
96. #2100C22semidirect
97. #2099C22semidirect
98. #2096C22semidirect
99. #2096C22semidirect
105. #2071C22semidirect
107. #2065C22semidirect
110. #2055C22semidirect
112. #2043C22semidirect
115. #2042C22semidirect
120. #2035C22semidirect
121. #2035C22semidirect
123. #2034C22semidirect
124. #2024C22semidirect
125. #2024C22semidirect
127. #2023C22semidirect
132. #2001C22semidirect
137. #1981C22semidirect
140. #1971C22semidirect
143. #1969C22semidirect
147. #1968C22semidirect
149. #1959C22semidirect
150. #1944C22semidirect
151. #1942C22semidirect
153. #1935C22semidirect
154. #1927C22semidirect
155. #1927C22semidirect
158. #1926C22semidirect
159. #1926C22semidirect
162. #1920C22semidirect
163. #1919C22semidirect
164. #1917C22semidirect
165. #1916C22semidirect
167. #1892C22semidirect
172. #1880C22semidirect
175. #1878C22semidirect
176. #1878C22semidirect
177. #1878C22semidirect
181. #1850C22semidirect
182. #1844C22semidirect
183. #1844C22semidirect
184. #1818C22semidirect
187. #1809C22semidirect
188. #1803C22semidirect
189. #1803C22semidirect
194. #1776C22semidirect
195. #1776C22semidirect
196. #1771C22semidirect
197. C8×C4⋊C4C22semidirect
198. C4×#103C22semidirect
202. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#428352
#426422
#331812
#316562
#316522
#313062
#313052
#309182
#309092
#304102
#304042
#301232
#301172
#285302
#282322
#280212
#278532
#278042
#278032
#272332
#272242
#270712
#270662
#262532
#257962
#254172
#242772
#231942
#224432
#215712
#215432