Finite Group Databasebeta

← #7603503

Subgroups — #7603503

Order 512.

1646 conjugacy classes of subgroups.

The subgroup lattice has 1321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59245C211yesmaximal, characteristic, complemented
2#59148C211yesmaximal, characteristic
3#32092C211yesmaximal, characteristic, complemented
4#32087C211yesmaximal, characteristic, complemented
5#31649C211yesmaximal, characteristic, complemented
6#31647C211yesmaximal, characteristic, complemented
7#29035C211yesmaximal, characteristic, complemented
8#29014C211yesmaximal, characteristic, complemented
9#28424C211yesmaximal, characteristic, complemented
10#28403C211yesmaximal, characteristic, complemented
11#27785C211yesmaximal, characteristic, complemented
12#27682C211yesmaximal, characteristic, complemented
13#27281C211yesmaximal, characteristic
14#27277C211yesmaximal, characteristic, complemented
15#26478C211yesmaximal, characteristic, complemented
16#26331C211yesmaximal, characteristic, complemented
17#25979C211yesmaximal, characteristic, complemented
18#25966C211yesmaximal, characteristic
19#25307C211yesmaximal, characteristic, complemented
20#25105C211yesmaximal, characteristic
21#25095C211yesmaximal, characteristic, complemented
22#24741C211yesmaximal, characteristic, complemented
23#24217C211yesmaximal, characteristic
24#24207C211yesmaximal, characteristic, complemented
25#23013C211yesmaximal, characteristic, complemented
26#22884C211yesmaximal, characteristic
27#22869C211yesmaximal, characteristic, complemented
28#22548C211yesmaximal, characteristic, complemented
29#21600C211yesmaximal, characteristic, complemented
30#21539C211yesmaximal, characteristic, complemented
31#21204C211yesmaximal, characteristic
32C2×#556C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#487C2211yescharacteristic, complemented
36C2×#477C2211yescharacteristic, complemented
37C2×#474C2211yescharacteristic
38C2×#470C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#464C2211yescharacteristic
42C2×#462C2211yescharacteristic, complemented
43C2×#451C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#446C2211yescharacteristic, complemented
46C2×#441C2211yescharacteristic, complemented
47C2×#441C2211yescharacteristic, complemented
48C2×C4×SD16C2211yescharacteristic
49C2×#419C2211yescharacteristic
50C2×#419C2211yescharacteristic
51C2×#418C2211yescharacteristic
52C2×#418C2211yescharacteristic
53C2×C4×M16C2211yescharacteristic
54#2788—21no—
55#2788—21no—
56#2715—21no—
57#2700—21no—
58#2592C2211yescharacteristic
59#2588—21no—
60#2588—21no—
61#2582C2211yescharacteristic, complemented
62#2568C2211yescharacteristic, complemented
63#2568C2211yescharacteristic, complemented
64#2551C2211yescharacteristic, complemented
65#2547C2211yescharacteristic
66#2545C2211yescharacteristic
67#2545C2211yescharacteristic
68#2521—21no—
69#2511—21no—
70#2509C2211yescharacteristic, complemented
71#2509C2211yescharacteristic, complemented
72#2497—21no—
73#2492—21no—
74#2480—21no—
75#2480—21no—
76#2474—21no—
77#2448C2211yescharacteristic
78#2447C2211yescharacteristic
79#2439C2211yescharacteristic
80#2439C2211yescharacteristic
81#2437—21no—
82#2435C2211yescharacteristic
83#2434C2211yescharacteristic
84#2369—21no—
85#2367C2211yescharacteristic
86#2362C2211yescharacteristic
87#2362C2211yescharacteristic
88#2355C2211yescharacteristic, complemented
89Q8×C4⋊C4C2211yescharacteristic, complemented
90#2342—21no—
91Q8×C22⋊C4C2211yescharacteristic
92D4×C22⋊C4C2211yescharacteristic
93C4×C22⋊Q8C2211yescharacteristic
94C4×C22⋊Q8C2211yescharacteristic
95C4×C22⋊Q8C2211yescharacteristic
96#2285C2211yescharacteristic
97#2101C2211yescharacteristic, complemented
98#2101C2211yescharacteristic, complemented
99#2097C2211yescharacteristic, complemented
100#2097C2211yescharacteristic, complemented
101#2097C2211yescharacteristic, complemented
102#2092C2211yescharacteristic
103#2074C2211yescharacteristic, complemented
104#2073C2211yescharacteristic
105#2068C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2056C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2043C2211yescharacteristic, complemented
114#2043C2211yescharacteristic, complemented
115#2043C2211yescharacteristic, complemented
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic
121#2024C2211yescharacteristic, complemented
122#2024C2211yescharacteristic, complemented
123#2023C2211yescharacteristic
124#2023C2211yescharacteristic
125#2016C2211yescharacteristic, complemented
126#2015C2211yescharacteristic
127#2015C2211yescharacteristic
128#2015C2211yescharacteristic
129#1985C2211yescharacteristic, complemented
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1981C2211yescharacteristic, complemented
134#1973C2211yescharacteristic
135#1969C2211yescharacteristic, complemented
136#1969C2211yescharacteristic, complemented
137#1960C2211yescharacteristic, complemented
138#1959C2211yescharacteristic
139#1959C2211yescharacteristic
140#1959C2211yescharacteristic
141#1959C2211yescharacteristic
142#1958C2211yescharacteristic
143#1958C2211yescharacteristic
144#1958C2211yescharacteristic
145#1958C2211yescharacteristic
146#1958C2211yescharacteristic
147#1948C2211yescharacteristic, complemented
148#1947C2211yescharacteristic, complemented
149#1941C2211yescharacteristic, complemented
150#1940C2211yescharacteristic, complemented
151#1936C2211yescharacteristic
152#1935C2211yescharacteristic, complemented
153#1935C2211yescharacteristic, complemented
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1933C2211yescharacteristic, complemented
157#1933C2211yescharacteristic, complemented
158#1933C2211yescharacteristic, complemented
159#1927C2211yescharacteristic, complemented
160#1927C2211yescharacteristic, complemented
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic
163#1916C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1894C2211yescharacteristic
166#1894C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1878C2211yescharacteristic, complemented
170#1878C2211yescharacteristic, complemented
171#1878C2211yescharacteristic, complemented
172#1877C2211yescharacteristic
173#1873C2211yescharacteristic
174#1873C2211yescharacteristic
175#1865C2211yescharacteristic, complemented
176#1865C2211yescharacteristic, complemented
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1851C2211yescharacteristic
184#1851C2211yescharacteristic
185#1809C2211yescharacteristic
186#1805C2211yescharacteristic, complemented
187#1804C2211yescharacteristic
188#1803C2211yescharacteristic, complemented
189#1803C2211yescharacteristic, complemented
190#1797C2211yescharacteristic
191#1787C2211yescharacteristic
192#1786C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194#1771C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196C8×C4⋊C4C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200C4×#103C2211yescharacteristic, complemented
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212#556—24no—
213#556—42no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#126—21no—
220C2×#126—21no—
221C2×#124—24no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124—42no—
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8D411yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117—21no—
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C42C2311yescharacteristic
251#489—42no—
252#487—42no—
253#477—42no—
254#474—42no—
255#470—24no—
256#464—24no—
257#464—42no—
258#464—42no—
259#462—42no—
260#451—24no—
261#450—24no—
262#446—42no—
263#441—42no—
264#441—42no—
265C4×SD16—42no—
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279#419—42no—
280#419—42no—
281#418—42no—
282#418—42no—
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×#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×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C4×M16—42no—
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332#400—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#400—21no—
337#400—21no—
338#400—21no—
339#400—21no—
340#399—21no—
341#398—21no—
342#398—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#395—21no—
356#395—21no—
357#395—21no—
358#395—21no—
359#394—21no—
360#394—21no—
361#393—21no—
362#393—21no—
363#393—21no—
364#391—21no—
365#391—21no—
366#391—21no—
367#391—21no—
368#391—21no—
369#391—21no—
370#391—21no—
371#391—21no—
372#391—21no—
373#391—21no—
374#391D411yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#389—21no—
388#389—21no—
389#389—21no—
390#389—21no—
391#389—21no—
392#389—21no—
393#389D411yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
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#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387D411yescharacteristic
427#387D411yescharacteristic
428#386—21no—
429#386—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385D411yescharacteristic
437#385D411yescharacteristic
438#384—21no—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#382C2311yescharacteristic
444#382C2311yescharacteristic
445#381—21no—
446#380—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380—21no—
451#380D411yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#379—21no—
455#379—21no—
456#379—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4—21no—
460C4×C4⋊C4—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4—21no—
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2311yescharacteristic
472C4×C22⋊C4—21no—
473C4×C22⋊C4—21no—
474C4×C22⋊C4—21no—
475C4×C22⋊C4—21no—
476C4×C22⋊C4C2311yescharacteristic
477C4×C22⋊C4C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8—21no—
506C22×Q8—22no—
507C22×Q8—22no—
508C22×Q8—22no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8—41no—
512C22×Q8C2×D411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—22no—
520C22×D4—22no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2×D411yescharacteristic
530C23×C4C2×D411yescharacteristic
531C23×C4C2411yescharacteristic
532C2×Q16—22no—
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—22no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×M16—22no—
548C2×M16—22no—
549C2×M16—22no—
550C2×M16—22no—
551C2×M16—41no—
552C2×M16—41no—
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C4⋊Q8—22no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568C4⋊Q8—41no—
569C4⋊Q8—44no—
570#126—44no—
571#126—44no—
572#124—22no—
573#124—22no—
574#124—22no—
575#124—22no—
576#124—22no—
577#124—22no—
578#124—44no—
579#124—44no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124#4114yes—
586C22⋊Q8—22no—
587C22⋊Q8—22no—
588C22⋊Q8—22no—
589C22⋊Q8—42no—
590C22⋊Q8—44no—
591C22⋊Q8#4114yes—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—22no—
598C4×Q8—22no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×D4—22no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610#117—44no—
611#117—41no—
612#117—41no—
613#117—41no—
614#117—41no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
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—44no—
689C2×C22⋊C4—44no—
690C2×C22⋊C4—44no—
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C42—22no—
696C2×C42—22no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42C2×D411yescharacteristic
710C2×C42C2×D411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#107—22no—
718#107—41no—
719#107—41no—
720#106—22no—
721#106—41no—
722#106—41no—
723#106—41no—
724C4⋊C8—22no—
725C4⋊C8—22no—
726C4⋊C8—22no—
727C4⋊C8—22no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730#103—22no—
731#103—22no—
732#103—22no—
733#103—22no—
734#103—22no—
735#103—22no—
736#103—22no—
737#103—22no—
738#103—22no—
739#103—22no—
740#103—22no—
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#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768C22⋊C8—22no—
769C22⋊C8—22no—
770#97—22no—
771#97—22no—
772#97—22no—
773#97—41no—
774C4×C8—22no—
775C4×C8—41no—
776C4×C8—41no—
777C4×C8—41no—
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#95—21no—
815#95—21no—
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826C24—21no—
827C24—21no—
828C24—42no—
829C24—42no—
830C24—42no—
831C24—42no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24C22×D411yescharacteristic
836C2×Q8—22no—
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—21no—
859C2×Q8—41no—
860C2×Q8—41no—
861C2×Q8—42no—
862C2×Q8—42no—
863C2×Q8—44no—
864C2×Q8—44no—
865C2×Q8—42no—
866C2×Q8—42no—
867C2×Q8—81no—
868C2×Q8—81no—
869C2×Q8—81no—
870C2×Q8—81no—
871C2×Q8—81no—
872C2×Q8—82no—
873C2×Q8—82no—
874C2×Q8C2×#4112yes—
875C2×Q8C2×#4112yes—
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—21no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—82no—
892C2×D4—82no—
893C2×D4—81no—
894C2×D4C2×#4112yes—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—22no—
903C22×C4—22no—
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—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C2×#4112yes—
942C22×C42−1+412yes—
943C22×C4C2511yescharacteristic
944Q16—44no—
945Q16—44no—
946Q16—82no—
947SD16—44no—
948SD16—82no—
949M16—44no—
950M16—44no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
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×C8H(5,𝔽2)12yes—
974C2×C8H(5,𝔽2)12yes—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—24no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
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—41no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
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⋊C4C2×#4112yes—
1030C22⋊C4—24no—
1031C22⋊C4—24no—
1032C22⋊C4—24no—
1033C22⋊C4—22no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C42—22no—
1063C42—22no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—42no—
1075C42—42no—
1076C42—42no—
1077C42—42no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C42—81no—
1085C42—81no—
1086C42C2×#4112yes—
1087C42H(5,𝔽2)12yes—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—22no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—84no—
1109C23—84no—
1110C23—84no—
1111C23—84no—
1112C23—162no—
1113C23—162no—
1114C23—162no—
1115C23#54812yes—
1116C23C23×D411yescharacteristic
1117Q8—22no—
1118Q8—22no—
1119Q8—22no—
1120Q8—22no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—82no—
1134Q8—84no—
1135Q8—162no—
1136Q8—162no—
1137D4—22no—
1138D4—22no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—84no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
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—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
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—82no—
1228C2×C4—82no—
1229C2×C4—84no—
1230C2×C4—84no—
1231C2×C4—162no—
1232C2×C4#54612yes—
1233C2×C4#54612yes—
1234C2×C4#54812yes—
1235C2×C4#57512yes—
1236C2×C4C22×#4111yescharacteristic
1237C2×C4C22×#4111yescharacteristic
1238C2×C4C2×H(5,𝔽2)11yescharacteristic
1239C2×C4C2×H(5,𝔽2)11yescharacteristic
1240C2×C4C2×H(5,𝔽2)11yescharacteristic
1241C2×C4C2×2−1+411yescharacteristic
1242C8—22no—
1243C8—22no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C22—22no—
1251C22—22no—
1252C22—22no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—168no—
1272C22C2×#54611yescharacteristic
1273C22C2×#54811yescharacteristic
1274C22#349811yescharacteristic
1275C22C2×#57511yescharacteristic
1276C22#358411yescharacteristic
1277C22#358611yescharacteristic
1278C22#358611yescharacteristic
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—42no—
1284C4—42no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—42no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4#348111yescharacteristic
1307C4#351911yescharacteristic
1308C4#352011yescharacteristic
1309C4#353611yescharacteristic
1310C2—42no—
1311C2—82no—
1312C2—161no—
1313C2#5965011yescharacteristic
1314C2#6116511yescharacteristic
1315C2#6119711yescharacteristic
1316C2#6132311yescharacteristic
1317C2#6134411yescharacteristic
1318C2#6242811yescharacteristic
1319C2#6244411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59245C2semidirect
3. #32092C2semidirect
4. #32087C2semidirect
5. #31649C2semidirect
6. #31647C2semidirect
7. #29035C2semidirect
8. #29014C2semidirect
9. #28424C2semidirect
10. #28403C2semidirect
11. #27785C2semidirect
12. #27682C2semidirect
14. #27277C2semidirect
15. #26478C2semidirect
16. #26331C2semidirect
17. #25979C2semidirect
19. #25307C2semidirect
21. #25095C2semidirect
22. #24741C2semidirect
24. #24207C2semidirect
25. #23013C2semidirect
27. #22869C2semidirect
28. #22548C2semidirect
29. #21600C2semidirect
30. #21539C2semidirect
35. C2×#487C22semidirect
36. C2×#477C22semidirect
42. C2×#462C22semidirect
45. C2×#446C22semidirect
46. C2×#441C22semidirect
47. C2×#441C22semidirect
61. #2582C22semidirect
62. #2568C22semidirect
63. #2568C22semidirect
64. #2551C22semidirect
70. #2509C22semidirect
71. #2509C22semidirect
88. #2355C22semidirect
89. Q8×C4⋊C4C22semidirect
97. #2101C22semidirect
98. #2101C22semidirect
99. #2097C22semidirect
100. #2097C22semidirect
101. #2097C22semidirect
103. #2074C22semidirect
105. #2068C22semidirect
107. #2066C22semidirect
108. #2066C22semidirect
111. #2056C22semidirect
113. #2043C22semidirect
114. #2043C22semidirect
115. #2043C22semidirect
121. #2024C22semidirect
122. #2024C22semidirect
125. #2016C22semidirect
129. #1985C22semidirect
133. #1981C22semidirect
135. #1969C22semidirect
136. #1969C22semidirect
137. #1960C22semidirect
147. #1948C22semidirect
148. #1947C22semidirect
149. #1941C22semidirect
150. #1940C22semidirect
152. #1935C22semidirect
153. #1935C22semidirect
156. #1933C22semidirect
157. #1933C22semidirect
158. #1933C22semidirect
159. #1927C22semidirect
160. #1927C22semidirect
163. #1916C22semidirect
164. #1916C22semidirect
169. #1878C22semidirect
170. #1878C22semidirect
171. #1878C22semidirect
175. #1865C22semidirect
176. #1865C22semidirect
179. #1863C22semidirect
186. #1805C22semidirect
188. #1803C22semidirect
189. #1803C22semidirect
193. #1776C22semidirect
194. #1771C22semidirect
195. #1771C22semidirect
196. C8×C4⋊C4C22semidirect
197. #1763C22semidirect
198. #1763C22semidirect
200. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#592452
#591482
#320922
#320872
#316492
#316472
#290352
#290142
#284242
#284032
#277852
#276822
#272812
#272772
#264782
#263312
#259792
#259662
#253072
#251052
#250952
#247412
#242172
#242072
#230132
#228842
#228692
#225482
#216002
#215392
#212042