Finite Group Databasebeta

← #6513708

Subgroups — #6513708

Order 512.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1281 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34978C211yesmaximal, characteristic, complemented
2#34240C211yesmaximal, characteristic
3#29262C211yesmaximal, characteristic, complemented
4#29261C211yesmaximal, characteristic, complemented
5#29261C211yesmaximal, characteristic, complemented
6#29260C211yesmaximal, characteristic, complemented
7#28285C211yesmaximal, characteristic, complemented
8#28285C211yesmaximal, characteristic, complemented
9#28282C211yesmaximal, characteristic, complemented
10#28281C211yesmaximal, characteristic, complemented
11#26545C211yesmaximal, characteristic, complemented
12#26544C211yesmaximal, characteristic, complemented
13#26543C211yesmaximal, characteristic, complemented
14#26542C211yesmaximal, characteristic, complemented
15#26479C211yesmaximal, characteristic, complemented
16#26478C211yesmaximal, characteristic, complemented
17#26477C211yesmaximal, characteristic, complemented
18#26476C211yesmaximal, characteristic, complemented
19#25981C211yesmaximal, characteristic, complemented
20#25979C211yesmaximal, characteristic, complemented
21#25976C211yesmaximal, characteristic
22#25974C211yesmaximal, characteristic
23#25973C211yesmaximal, characteristic, complemented
24#25971C211yesmaximal, characteristic, complemented
25#25968C211yesmaximal, characteristic
26#25966C211yesmaximal, characteristic
27#21978C211yesmaximal, characteristic, complemented
28#21963C211yesmaximal, characteristic, complemented
29#21808C211yesmaximal, characteristic
30#21366C211yesmaximal, characteristic, complemented
31#21261C211yesmaximal, characteristic
32C22×#124C2211yescharacteristic
33C2×#479C2211yescharacteristic, complemented
34C2×#479C2211yescharacteristic, complemented
35C2×#477C2211yescharacteristic, complemented
36C2×#475C2211yescharacteristic, complemented
37C2×#478C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#476C2211yescharacteristic
40C2×#474C2211yescharacteristic
41C2×#432C2211yescharacteristic
42C2×#423C2211yescharacteristic
43C2×#419C2211yescharacteristic
44C2×#419C2211yescharacteristic
45C2×#418C2211yescharacteristic
46C2×#418C2211yescharacteristic
47#2612—21no—
48#2612—21no—
49#2571C2211yescharacteristic, complemented
50#2552C2211yescharacteristic, complemented
51#2552C2211yescharacteristic, complemented
52#2551C2211yescharacteristic, complemented
53#2441—21no—
54#2441C2211yescharacteristic
55#2441C2211yescharacteristic
56#2439—21no—
57#2439C2211yescharacteristic
58#2439C2211yescharacteristic
59#2396—21no—
60#2396—21no—
61#2372—21no—
62#2372—21no—
63#2367C2211yescharacteristic
64#2367C2211yescharacteristic
65#2367C2211yescharacteristic
66#2367C2211yescharacteristic
67#2342—21no—
68#2342—21no—
69Q8×C22⋊C4C2211yescharacteristic
70Q8×C22⋊C4C2211yescharacteristic
71D4×C22⋊C4C2211yescharacteristic
72D4×C22⋊C4C2211yescharacteristic
73#2337—21no—
74#2337—21no—
75#2312—21no—
76C4×C4⋊Q8—21no—
77C4×C4⋊Q8C2211yescharacteristic, complemented
78C4×C4⋊Q8C2211yescharacteristic, complemented
79C4×#125—21no—
80C4×#125C2211yescharacteristic, complemented
81C4×#125C2211yescharacteristic, complemented
82C4×#124C2211yescharacteristic
83C4×#124C2211yescharacteristic
84C4×#124C2211yescharacteristic
85C4×#124C2211yescharacteristic
86#2285C2211yescharacteristic
87#2283C2211yescharacteristic
88#2273—21no—
89C4×#117C2211yescharacteristic
90C4×#117C2211yescharacteristic
91#2097C2211yescharacteristic, complemented
92#2097C2211yescharacteristic, complemented
93#2096C2211yescharacteristic, complemented
94#2095C2211yescharacteristic, complemented
95#2094C2211yescharacteristic
96#2093C2211yescharacteristic
97#2092C2211yescharacteristic
98#2092C2211yescharacteristic
99#2068C2211yescharacteristic, complemented
100#2068C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2066C2211yescharacteristic, complemented
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#2026C2211yescharacteristic, complemented
116#2026C2211yescharacteristic, complemented
117#2025C2211yescharacteristic
118#2025C2211yescharacteristic
119#2024C2211yescharacteristic, complemented
120#2024C2211yescharacteristic, complemented
121#2023C2211yescharacteristic
122#2023C2211yescharacteristic
123#1983C2211yescharacteristic
124#1983C2211yescharacteristic
125#1983C2211yescharacteristic
126#1983C2211yescharacteristic
127#1983C2211yescharacteristic
128#1983C2211yescharacteristic
129#1983C2211yescharacteristic
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1983C2211yescharacteristic
134#1983C2211yescharacteristic
135#1959C2211yescharacteristic
136#1959C2211yescharacteristic
137#1959C2211yescharacteristic
138#1959C2211yescharacteristic
139#1949C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1949C2211yescharacteristic, complemented
142#1949C2211yescharacteristic, complemented
143#1949C2211yescharacteristic, complemented
144#1949C2211yescharacteristic, complemented
145#1949C2211yescharacteristic, complemented
146#1949C2211yescharacteristic, complemented
147#1948C2211yescharacteristic, complemented
148#1948C2211yescharacteristic, complemented
149#1947C2211yescharacteristic, complemented
150#1947C2211yescharacteristic, complemented
151#1940C2211yescharacteristic, complemented
152#1940C2211yescharacteristic, complemented
153#1940C2211yescharacteristic, complemented
154#1940C2211yescharacteristic, complemented
155#1865C2211yescharacteristic, complemented
156#1865C2211yescharacteristic, complemented
157#1865C2211yescharacteristic, complemented
158#1865C2211yescharacteristic, complemented
159#1864C2211yescharacteristic
160#1864C2211yescharacteristic
161#1864C2211yescharacteristic
162#1864C2211yescharacteristic
163#1863C2211yescharacteristic, complemented
164#1863C2211yescharacteristic, complemented
165#1863C2211yescharacteristic, complemented
166#1863C2211yescharacteristic, complemented
167#1862C2211yescharacteristic
168#1862C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1851C2211yescharacteristic
176#1851C2211yescharacteristic
177#1851C2211yescharacteristic
178#1851C2211yescharacteristic
179#1842C2211yescharacteristic, complemented
180#1842C2211yescharacteristic, complemented
181#1831C2211yescharacteristic, complemented
182#1831C2211yescharacteristic, complemented
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic
186#1809C2211yescharacteristic
187#1805C2211yescharacteristic, complemented
188#1805C2211yescharacteristic, complemented
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1803C2211yescharacteristic, complemented
192#1803C2211yescharacteristic, complemented
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1787C2211yescharacteristic
196#1787C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1776C2211yescharacteristic, complemented
200#1776C2211yescharacteristic, complemented
201#1776C2211yescharacteristic, complemented
202#1776C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#125—21no—
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#124—21no—
214C2×#124—21no—
215C2×#124—24no—
216C2×#124Q818yescomplemented
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×C4×Q8—21no—
222C2×C4×Q8—21no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117—21no—
232C2×#117D411yescharacteristic
233C2×#117D411yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C22×C22⋊C4—21no—
237C22×C22⋊C4—21no—
238C22×C22⋊C4—21no—
239C22×C22⋊C4—21no—
240C22×C42C2311yescharacteristic
241#479—42no—
242#479—42no—
243#478—42no—
244#478—42no—
245#477—42no—
246#476—42no—
247#475—42no—
248#474—42no—
249#432—24no—
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266#423—24no—
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281#419—42no—
282#419—42no—
283#418—42no—
284#418—42no—
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×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321#400—21no—
322#400—21no—
323#399—21no—
324#399—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#395—21no—
334#395—21no—
335#393—21no—
336#393—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#391—21no—
344#391—21no—
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#384—21no—
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#383—21no—
407#382—21no—
408#382—21no—
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#381—21no—
414#380—21no—
415#380—21no—
416#380—21no—
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#379—21no—
422#379—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4D411yescharacteristic
431C4×C4⋊C4D411yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4D411yescharacteristic
460C4×C22⋊C4D411yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463#376—21no—
464#376—21no—
465#376D411yescharacteristic
466#376D411yescharacteristic
467C43—21no—
468C43C2311yescharacteristic
469C43C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C25—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8—21no—
498C22×Q8—22no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8C2×Q814yes—
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4C2×Q814yes—
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4C2×D411yescharacteristic
521C23×C4C2×D411yescharacteristic
522C23×C4C2411yescharacteristic
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16—41no—
528C2×M16—41no—
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C4⋊Q8—22no—
538C4⋊Q8—22no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8—44no—
542#125—22no—
543#125—22no—
544#125—41no—
545#125—41no—
546#125—44no—
547#124—28no—
548#124—28no—
549#124—22no—
550#124—22no—
551#124—22no—
552#124—22no—
553#124C2×Q814yes—
554#124C2×Q814yes—
555#124C2×Q814yes—
556#124C2×Q814yes—
557C4×Q8—41no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—82no—
566C4×Q8—82no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575#117—22no—
576#117—22no—
577#117—42no—
578#117—42no—
579#117—41no—
580#117—41no—
581#117—82no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C22⋊C4—28no—
625C2×C22⋊C4—28no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—44no—
653C2×C22⋊C4—44no—
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42C2×D411yescharacteristic
673C2×C42C2×D411yescharacteristic
674C2×C42C2×D411yescharacteristic
675C2×C42C2×D411yescharacteristic
676C2×C42C2×D411yescharacteristic
677C2×C42C2×D411yescharacteristic
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2×Q814yes—
683C2×C42#4114yes—
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690#107—22no—
691#107—22no—
692#107—41no—
693#107—41no—
694#107—41no—
695#107—41no—
696#107—41no—
697#107—41no—
698#106—22no—
699#106—22no—
700#106—41no—
701#106—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705#106—41no—
706C4⋊C8—22no—
707C4⋊C8—22no—
708C4⋊C8—22no—
709C4⋊C8—22no—
710C4⋊C8—22no—
711C4⋊C8—22no—
712C4⋊C8—41no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720#103—22no—
721#103—22no—
722#103—22no—
723#103—22no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752C22⋊C8—22no—
753C22⋊C8—22no—
754#97—22no—
755#97—22no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
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#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800C24—21no—
801C24—21no—
802C24—24no—
803C24—42no—
804C24—42no—
805C24—81no—
806C24—81no—
807C24—81no—
808C24—81no—
809C24C22×D411yescharacteristic
810C2×Q8—24no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—42no—
822C2×Q8—42no—
823C2×Q8—42no—
824C2×Q8—44no—
825C2×Q8—44no—
826C2×Q8—42no—
827C2×Q8—81no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8—82no—
832C2×Q8—82no—
833C2×Q8C22×Q812yes—
834C2×Q8C22×Q812yes—
835C2×D4—24no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—44no—
847C2×D4—44no—
848C2×D4—82no—
849C2×D4—82no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4C22×Q812yes—
853C2×D4C22×Q812yes—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—24no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4C22⋊Q814yes—
892C22×C4C22⋊Q814yes—
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×Q812yes—
907C22×C4C2×#4112yes—
908C22×C4C2511yescharacteristic
909M16—82no—
910M16—82no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4H(5,𝔽2)12yes—
988C4⋊C4H(5,𝔽2)12yes—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—24no—
994C22⋊C4—24no—
995C22⋊C4—24no—
996C22⋊C4—24no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C42—22no—
1020C42—22no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—41no—
1030C42—41no—
1031C42—41no—
1032C42—41no—
1033C42—41no—
1034C42—41no—
1035C42—42no—
1036C42—42no—
1037C42—42no—
1038C42—42no—
1039C42—42no—
1040C42—42no—
1041C42—42no—
1042C42—42no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C42C22⋊Q814yes—
1050C42C22⋊Q814yes—
1051C42C22×Q812yes—
1052C42C22×Q812yes—
1053C42C2×#4112yes—
1054C42C2×#4112yes—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—22no—
1062C23—22no—
1063C23—48no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—84no—
1077C23—84no—
1078C23—162no—
1079C23—162no—
1080C23—162no—
1081C23—162no—
1082C23C2×C22⋊Q812yes—
1083C23C23×D411yescharacteristic
1084Q8—22no—
1085Q8—22no—
1086Q8—22no—
1087Q8—22no—
1088Q8—41no—
1089Q8—41no—
1090Q8—41no—
1091Q8—41no—
1092Q8—84no—
1093Q8—84no—
1094Q8—84no—
1095D4—22no—
1096D4—22no—
1097D4—22no—
1098D4—22no—
1099D4—41no—
1100D4—41no—
1101D4—41no—
1102D4—41no—
1103D4—84no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—44no—
1145C2×C4—44no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—84no—
1185C2×C4—162no—
1186C2×C4—162no—
1187C2×C4—162no—
1188C2×C4—162no—
1189C2×C4C2×C22⋊Q812yes—
1190C2×C4C2×C22⋊Q812yes—
1191C2×C4C2×C22⋊Q812yes—
1192C2×C4C2×C22⋊Q812yes—
1193C2×C4C2×C22⋊Q812yes—
1194C2×C4#57512yes—
1195C2×C4#57512yes—
1196C2×C4C23×Q811yescharacteristic
1197C2×C4C22×#4111yescharacteristic
1198C2×C4C2×H(5,𝔽2)11yescharacteristic
1199C2×C4C2×H(5,𝔽2)11yescharacteristic
1200C2×C4#58511yescharacteristic
1201C2×C4#58511yescharacteristic
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C8—41no—
1208C8—41no—
1209C8—41no—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—168no—
1232C22C22×C22⋊Q811yescharacteristic
1233C22#348811yescharacteristic
1234C22#348811yescharacteristic
1235C22C2×#57511yescharacteristic
1236C22C2×#57511yescharacteristic
1237C22#358511yescharacteristic
1238C22#358611yescharacteristic
1239C4—22no—
1240C4—22no—
1241C4—22no—
1242C4—22no—
1243C4—22no—
1244C4—22no—
1245C4—22no—
1246C4—41no—
1247C4—42no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—42no—
1252C4—41no—
1253C4—41no—
1254C4—42no—
1255C4—42no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4#350111yescharacteristic
1267C4#350111yescharacteristic
1268C4#350811yescharacteristic
1269C4#351011yescharacteristic
1270C2—42no—
1271C2—82no—
1272C2—82no—
1273C2#3551511yescharacteristic
1274C2#6048411yescharacteristic
1275C2#6049311yescharacteristic
1276C2#6197111yescharacteristic
1277C2#6197211yescharacteristic
1278C2#6197311yescharacteristic
1279C2#6197511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #34978C2semidirect
3. #29262C2semidirect
4. #29261C2semidirect
5. #29261C2semidirect
6. #29260C2semidirect
7. #28285C2semidirect
8. #28285C2semidirect
9. #28282C2semidirect
10. #28281C2semidirect
11. #26545C2semidirect
12. #26544C2semidirect
13. #26543C2semidirect
14. #26542C2semidirect
15. #26479C2semidirect
16. #26478C2semidirect
17. #26477C2semidirect
18. #26476C2semidirect
19. #25981C2semidirect
20. #25979C2semidirect
23. #25973C2semidirect
24. #25971C2semidirect
27. #21978C2semidirect
28. #21963C2semidirect
30. #21366C2semidirect
33. C2×#479C22semidirect
34. C2×#479C22semidirect
35. C2×#477C22semidirect
36. C2×#475C22semidirect
49. #2571C22semidirect
50. #2552C22semidirect
51. #2552C22semidirect
52. #2551C22semidirect
77. C4×C4⋊Q8C22semidirect
78. C4×C4⋊Q8C22semidirect
80. C4×#125C22semidirect
81. C4×#125C22semidirect
91. #2097C22semidirect
92. #2097C22semidirect
93. #2096C22semidirect
94. #2095C22semidirect
99. #2068C22semidirect
100. #2068C22semidirect
101. #2068C22semidirect
102. #2068C22semidirect
107. #2066C22semidirect
108. #2066C22semidirect
109. #2066C22semidirect
110. #2066C22semidirect
115. #2026C22semidirect
116. #2026C22semidirect
119. #2024C22semidirect
120. #2024C22semidirect
139. #1949C22semidirect
140. #1949C22semidirect
141. #1949C22semidirect
142. #1949C22semidirect
143. #1949C22semidirect
144. #1949C22semidirect
145. #1949C22semidirect
146. #1949C22semidirect
147. #1948C22semidirect
148. #1948C22semidirect
149. #1947C22semidirect
150. #1947C22semidirect
151. #1940C22semidirect
152. #1940C22semidirect
153. #1940C22semidirect
154. #1940C22semidirect
155. #1865C22semidirect
156. #1865C22semidirect
157. #1865C22semidirect
158. #1865C22semidirect
163. #1863C22semidirect
164. #1863C22semidirect
165. #1863C22semidirect
166. #1863C22semidirect
179. #1842C22semidirect
180. #1842C22semidirect
181. #1831C22semidirect
182. #1831C22semidirect
187. #1805C22semidirect
188. #1805C22semidirect
191. #1803C22semidirect
192. #1803C22semidirect
199. #1776C22semidirect
200. #1776C22semidirect
201. #1776C22semidirect
202. #1776C22semidirect
216. C2×#124Q8semidirect

Maximal subgroups

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

subgroupindex
#349782
#342402
#292622
#292612
#292602
#282852
#282822
#282812
#265452
#265442
#265432
#265422
#264792
#264782
#264772
#264762
#259812
#259792
#259762
#259742
#259732
#259712
#259682
#259662
#219782
#219632
#218082
#213662
#212612