Finite Group Databasebeta

← #6451647

Subgroups — #6451647

Order 512.

1507 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35656C211yesmaximal, characteristic
2#34328C211yesmaximal, characteristic
3#27501C211yesmaximal, characteristic
4#27487C211yesmaximal, characteristic
5#27216C211yesmaximal, characteristic
6#27209C211yesmaximal, characteristic
7#27085C211yesmaximal, characteristic
8#27082C211yesmaximal, characteristic
9#26590C211yesmaximal, characteristic
10#26590C211yesmaximal, characteristic
11#26539C211yesmaximal, characteristic
12#26335C211yesmaximal, characteristic
13#26095C211yesmaximal, characteristic
14#25634C211yesmaximal, characteristic
15#25370C211yesmaximal, characteristic
16#25066C211yesmaximal, characteristic
17#24648C211yesmaximal, characteristic
18#24203C211yesmaximal, characteristic
19#23814C211yesmaximal, characteristic
20#23805C211yesmaximal, characteristic
21#23691C211yesmaximal, characteristic
22#23679C211yesmaximal, characteristic
23#21698C211yesmaximal, characteristic
24#21516C211yesmaximal, characteristic
25#21516C211yesmaximal, characteristic
26#21516C211yesmaximal, characteristic
27C4×#462C211yesmaximal, characteristic
28#21348C211yesmaximal, characteristic
29#21127C211yesmaximal, characteristic
30#21123C211yesmaximal, characteristic
31#20505C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#494C2211yescharacteristic
34C2×#462C2211yescharacteristic
35C2×#462C2211yescharacteristic
36C2×#462C2211yescharacteristic
37C2×#462C2211yescharacteristic
38C2×#441C2211yescharacteristic
39C2×#441C2211yescharacteristic
40C2×#441C2211yescharacteristic
41C2×#441C2211yescharacteristic
42C2×#441C2211yescharacteristic
43C2×#441C2211yescharacteristic
44C2×C4×Q16C2211yescharacteristic
45C2×C4×Q16C2211yescharacteristic
46C2×C4×Q16C2211yescharacteristic
47C2×C4×Q16C2211yescharacteristic
48C2×C4×Q16C2211yescharacteristic
49#2590—21no—
50#2588—21no—
51#2581C2211yescharacteristic
52#2570C2211yescharacteristic
53#2568C2211yescharacteristic
54#2546C2211yescharacteristic
55#2533—21no—
56#2533—21no—
57#2528—21no—
58#2528—21no—
59#2524—21no—
60#2520—21no—
61#2514C2211yescharacteristic
62#2511C2211yescharacteristic
63#2446C2211yescharacteristic
64#2446C2211yescharacteristic
65#2371—21no—
66#2371—21no—
67#2370—21no—
68#2365C2211yescharacteristic
69#2365C2211yescharacteristic
70#2365C2211yescharacteristic
71#2356—21no—
72#2356C2211yescharacteristic
73#2356C2211yescharacteristic
74#2355C2211yescharacteristic
75#2355C2211yescharacteristic
76#2336—21no—
77#2336—21no—
78#2327C2211yescharacteristic
79#2327C2211yescharacteristic
80#2327C2211yescharacteristic
81#2327C2211yescharacteristic
82#2320C2211yescharacteristic
83C4×C4⋊Q8C2211yescharacteristic
84C4×C4⋊Q8C2211yescharacteristic
85C4×#125—21no—
86#2295—21no—
87#2295C2211yescharacteristic
88#2295C2211yescharacteristic
89#2276C2211yescharacteristic
90#2276C2211yescharacteristic
91#2276C2211yescharacteristic
92C42×Q8C2211yescharacteristic
93#2097C2211yescharacteristic
94#2097C2211yescharacteristic
95#2097C2211yescharacteristic
96#2097C2211yescharacteristic
97#2096C2211yescharacteristic
98#2096C2211yescharacteristic
99#2096C2211yescharacteristic
100#2096C2211yescharacteristic
101#2085C2211yescharacteristic
102#2083C2211yescharacteristic
103#2074C2211yescharacteristic
104#2072C2211yescharacteristic
105#2068C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2066C2211yescharacteristic
109#2056C2211yescharacteristic
110#2056C2211yescharacteristic
111#2056C2211yescharacteristic
112#2056C2211yescharacteristic
113#2043C2211yescharacteristic
114#2043C2211yescharacteristic
115#2016C2211yescharacteristic
116#2016C2211yescharacteristic
117#2016C2211yescharacteristic
118#2016C2211yescharacteristic
119#2016C2211yescharacteristic
120#2016C2211yescharacteristic
121#2016C2211yescharacteristic
122#2016C2211yescharacteristic
123#2016C2211yescharacteristic
124#2016C2211yescharacteristic
125#1985C2211yescharacteristic
126#1984C2211yescharacteristic
127#1981C2211yescharacteristic
128#1981C2211yescharacteristic
129#1981C2211yescharacteristic
130#1981C2211yescharacteristic
131#1971C2211yescharacteristic
132#1971C2211yescharacteristic
133#1969C2211yescharacteristic
134#1969C2211yescharacteristic
135#1960C2211yescharacteristic
136#1960C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1947C2211yescharacteristic
141#1940C2211yescharacteristic
142#1939C2211yescharacteristic
143#1928C2211yescharacteristic
144#1928C2211yescharacteristic
145#1928C2211yescharacteristic
146#1928C2211yescharacteristic
147#1928C2211yescharacteristic
148#1928C2211yescharacteristic
149#1928C2211yescharacteristic
150#1927C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1920C2211yescharacteristic
156#1920C2211yescharacteristic
157#1919C2211yescharacteristic
158#1919C2211yescharacteristic
159#1917C2211yescharacteristic
160#1917C2211yescharacteristic
161#1916C2211yescharacteristic
162#1916C2211yescharacteristic
163#1878C2211yescharacteristic
164#1878C2211yescharacteristic
165#1878C2211yescharacteristic
166#1878C2211yescharacteristic
167#1878C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1865C2211yescharacteristic
176#1865C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1846C2211yescharacteristic
180#1805C2211yescharacteristic
181#1805C2211yescharacteristic
182#1805C2211yescharacteristic
183#1803C2211yescharacteristic
184#1776C2211yescharacteristic
185#1776C2211yescharacteristic
186C4×#106C2211yescharacteristic
187#1768C2211yescharacteristic
188#1768C2211yescharacteristic
189C4×C4⋊C8C2211yescharacteristic
190#1763C2211yescharacteristic
191#1763C2211yescharacteristic
192#1763C2211yescharacteristic
193#1763C2211yescharacteristic
194C4×#103C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200#1746C2211yescharacteristic
201#1745C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212#557—24no—
213#557—24no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#125—21no—
221C2×#125—21no—
222C2×#125—21no—
223C2×C4×Q8—21no—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239#494—24no—
240#462—24no—
241#462—24no—
242#462—24no—
243#462—24no—
244#441—24no—
245#441—24no—
246#441—24no—
247#441—24no—
248#441—42no—
249#441—42no—
250C4×Q16—24no—
251C4×Q16—42no—
252C4×Q16—42no—
253C4×Q16—42no—
254C4×Q16—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310#401—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#395—21no—
326#391—21no—
327#391—21no—
328#391D411yescharacteristic
329#391D411yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389D411yescharacteristic
356#389D411yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—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#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387D411yescharacteristic
407#387D411yescharacteristic
408#387D411yescharacteristic
409#387D411yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#383—21no—
413#383—21no—
414#383—21no—
415#383—21no—
416#382—21no—
417#382—21no—
418#382—21no—
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
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⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458#376—21no—
459#376—21no—
460#376—21no—
461#376—21no—
462#376—21no—
463#376—21no—
464#376C2311yescharacteristic
465#376C2311yescharacteristic
466C43—21no—
467C43C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
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#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C22×Q8C2×D411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C2×Q16—22no—
504C2×Q16—22no—
505C2×Q16—22no—
506C2×Q16—22no—
507C2×Q16—22no—
508C2×Q16—22no—
509C2×Q16—22no—
510C2×Q16—22no—
511C2×Q16—22no—
512C2×Q16—22no—
513C2×Q16—22no—
514C2×Q16—22no—
515C2×Q16—22no—
516C2×Q16—22no—
517C2×Q16—22no—
518C2×Q16—22no—
519C2×Q16—22no—
520C2×Q16—41no—
521C2×Q16—41no—
522C2×Q16—41no—
523C2×Q16—41no—
524C2×Q16—41no—
525C2×Q16—41no—
526C2×Q16—41no—
527C2×Q16—41no—
528C2×Q16—41no—
529C2×Q16—41no—
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540C4⋊Q8—22no—
541C4⋊Q8—22no—
542C4⋊Q8—22no—
543C4⋊Q8—22no—
544C4⋊Q8—22no—
545C4⋊Q8—22no—
546C4⋊Q8—22no—
547C4⋊Q8—41no—
548C4⋊Q8—41no—
549C4⋊Q8#4114yes—
550#125—28no—
551#125—28no—
552#125—28no—
553C4×Q8—28no—
554C4×Q8—22no—
555C4×Q8—22no—
556C4×Q8—22no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—22no—
564C4×Q8—22no—
565C4×Q8—22no—
566C4×Q8—22no—
567C4×Q8—22no—
568C4×Q8—22no—
569C4×Q8—22no—
570C4×Q8—22no—
571C4×Q8—22no—
572C4×Q8—22no—
573C4×Q8—22no—
574C4×Q8—22no—
575C4×Q8—22no—
576C4×Q8—22no—
577C4×Q8—22no—
578C4×Q8—22no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×Q8—41no—
583C4×Q8#4114yes—
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⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42C2×D411yescharacteristic
662C2×C42C2×D411yescharacteristic
663C2×C42C2×D411yescharacteristic
664C2×C42C2×D411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672#107—22no—
673#107—41no—
674#107—41no—
675#107—41no—
676#107—41no—
677#106—22no—
678#106—22no—
679#106—22no—
680#106—22no—
681#106—41no—
682#106—41no—
683C4⋊C8—22no—
684C4⋊C8—22no—
685C4⋊C8—22no—
686C4⋊C8—22no—
687C4⋊C8—41no—
688C4⋊C8—41no—
689#103—22no—
690#103—22no—
691#103—22no—
692#103—22no—
693#103—22no—
694#103—22no—
695#103—22no—
696#103—22no—
697#103—22no—
698#103—22no—
699#103—22no—
700#103—22no—
701#103—22no—
702#103—22no—
703#103—22no—
704#103—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103#4114yes—
719#97—22no—
720#97—22no—
721#97—41no—
722#97#4114yes—
723C4×C8—22no—
724C4×C8—22no—
725C4×C8—22no—
726C4×C8—22no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
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#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795C2×Q8—22no—
796C2×Q8—22no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
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—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—41no—
830C2×Q8C2×#4112yes—
831C2×Q8C2×#4112yes—
832C2×Q8C2×#4112yes—
833C2×Q8C2×#4112yes—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C2511yescharacteristic
865Q16—28no—
866Q16—44no—
867Q16—44no—
868Q16—44no—
869Q16—44no—
870Q16—44no—
871Q16—44no—
872Q16—44no—
873Q16—44no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8C2×#4112yes—
896C2×C8C2×#4112yes—
897C2×C8C2×#4112yes—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—22no—
908C4⋊C4—22no—
909C4⋊C4—22no—
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—41no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4C2×#4112yes—
960C4⋊C4C2×#4112yes—
961C42—24no—
962C42—24no—
963C42—24no—
964C42—22no—
965C42—22no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—41no—
977C42—41no—
978C42—42no—
979C42—42no—
980C42—42no—
981C42—42no—
982C42—42no—
983C42—42no—
984C42—42no—
985C42—42no—
986C42—42no—
987C42—42no—
988C42—42no—
989C42—42no—
990C42—42no—
991C42—81no—
992C42—81no—
993C42—81no—
994C42—81no—
995C42—81no—
996C42—81no—
997C42—81no—
998C42—81no—
999C42C2×#4112yes—
1000C42C2×#4112yes—
1001C42C2×#4112yes—
1002C42H(5,𝔽2)12yes—
1003C23C23×D411yescharacteristic
1004Q8—22no—
1005Q8—22no—
1006Q8—22no—
1007Q8—22no—
1008Q8—22no—
1009Q8—22no—
1010Q8—22no—
1011Q8—22no—
1012Q8—44no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—41no—
1017Q8—41no—
1018Q8—41no—
1019Q8—41no—
1020Q8—41no—
1021Q8—41no—
1022Q8—41no—
1023Q8—41no—
1024Q8—41no—
1025Q8—41no—
1026Q8—41no—
1027Q8—41no—
1028Q8—41no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4#52512yes—
1114C2×C4#52512yes—
1115C2×C4#55012yes—
1116C2×C4#55012yes—
1117C2×C4#57812yes—
1118C2×C4#57812yes—
1119C2×C4C22×#4111yescharacteristic
1120C2×C4C22×#4111yescharacteristic
1121C2×C4C22×#4111yescharacteristic
1122C2×C4C22×#4111yescharacteristic
1123C2×C4C2×H(5,𝔽2)11yescharacteristic
1124C2×C4#58511yescharacteristic
1125C8—22no—
1126C8—22no—
1127C8—22no—
1128C8—41no—
1129C8—41no—
1130C8—41no—
1131C8—41no—
1132C8—41no—
1133C22C2×#52511yescharacteristic
1134C22C2×#55011yescharacteristic
1135C22D4×#4111yescharacteristic
1136C22C2×#57811yescharacteristic
1137C22C2×#57811yescharacteristic
1138C22#358611yescharacteristic
1139C22#358611yescharacteristic
1140C4—22no—
1141C4—22no—
1142C4—22no—
1143C4—22no—
1144C4—22no—
1145C4—22no—
1146C4—41no—
1147C4—41no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—41no—
1157C4—41no—
1158C4—41no—
1159C4—42no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4#344411yescharacteristic
1171C4#346011yescharacteristic
1172C4#347511yescharacteristic
1173C4#348111yescharacteristic
1174C2#3472711yescharacteristic
1175C2#6058311yescharacteristic
1176C2#6059411yescharacteristic
1177C2#6142211yescharacteristic
1178C2#6142211yescharacteristic
1179C2#6148411yescharacteristic
1180C2#6151711yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#356562
#343282
#275012
#274872
#272162
#272092
#270852
#270822
#265902
#265392
#263352
#260952
#256342
#253702
#250662
#246482
#242032
#238142
#238052
#236912
#236792
#216982
#215162
C4×#4622
#213482
#211272
#211232
#205052