Finite Group Databasebeta

← #6499362

Subgroups — #6499362

Order 512.

1246 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35304C211yesmaximal, characteristic
2#34638C211yesmaximal, characteristic
3#33262C211yesmaximal, characteristic, complemented
4#33262C211yesmaximal, characteristic, complemented
5#33261C211yesmaximal, characteristic, complemented
6#33260C211yesmaximal, characteristic, complemented
7#30315C211yesmaximal, characteristic, complemented
8#30315C211yesmaximal, characteristic, complemented
9#30314C211yesmaximal, characteristic, complemented
10#30313C211yesmaximal, characteristic, complemented
11#29327C211yesmaximal, characteristic, complemented
12#29326C211yesmaximal, characteristic, complemented
13#29325C211yesmaximal, characteristic, complemented
14#29325C211yesmaximal, characteristic, complemented
15#29324C211yesmaximal, characteristic, complemented
16#29324C211yesmaximal, characteristic, complemented
17#29323C211yesmaximal, characteristic, complemented
18#29322C211yesmaximal, characteristic, complemented
19#29305C211yesmaximal, characteristic
20#29305C211yesmaximal, characteristic
21#29304C211yesmaximal, characteristic
22#29304C211yesmaximal, characteristic
23#29300C211yesmaximal, characteristic
24#29300C211yesmaximal, characteristic
25#29299C211yesmaximal, characteristic
26#29299C211yesmaximal, characteristic
27#21989C211yesmaximal, characteristic
28#21988C211yesmaximal, characteristic
29#21985C211yesmaximal, characteristic
30#21984C211yesmaximal, characteristic
31#20469C211yesmaximal, characteristic
32C2×#432C2211yescharacteristic
33C2×#431C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2851C2211yescharacteristic
37#2851C2211yescharacteristic
38#2660C2211yescharacteristic
39#2660C2211yescharacteristic
40#2647C2211yescharacteristic
41#2647C2211yescharacteristic
42#2647C2211yescharacteristic
43#2647C2211yescharacteristic
44#2647C2211yescharacteristic
45#2647C2211yescharacteristic
46#2647C2211yescharacteristic
47#2647C2211yescharacteristic
48#2647C2211yescharacteristic
49#2647C2211yescharacteristic
50#2646—21no—
51#2646—21no—
52#2646—21no—
53#2646—21no—
54#2612—21no—
55#2612—21no—
56#2606—21no—
57#2605—21no—
58#2569—21no—
59#2549—21no—
60#2438—21no—
61#2438—21no—
62#2402—21no—
63#2402—21no—
64#2402—21no—
65#2402—21no—
66#2331C2211yescharacteristic
67#2331C2211yescharacteristic
68#2330C2211yescharacteristic
69#2330C2211yescharacteristic
70#2296C2211yescharacteristic
71#2296C2211yescharacteristic
72#2296C2211yescharacteristic
73#2296C2211yescharacteristic
74#2285C2211yescharacteristic
75#2285C2211yescharacteristic
76#2285C2211yescharacteristic
77#2283C2211yescharacteristic
78C2×#376C2211yescharacteristic
79#2085C2211yescharacteristic
80#2085C2211yescharacteristic
81#2085C2211yescharacteristic
82#2085C2211yescharacteristic
83#2085C2211yescharacteristic
84#2085C2211yescharacteristic
85#2085C2211yescharacteristic
86#2085C2211yescharacteristic
87#2084C2211yescharacteristic
88#2084C2211yescharacteristic
89#2084C2211yescharacteristic
90#2084C2211yescharacteristic
91#2083C2211yescharacteristic
92#2083C2211yescharacteristic
93#2083C2211yescharacteristic
94#2083C2211yescharacteristic
95#2059C2211yescharacteristic
96#2059C2211yescharacteristic
97#2059C2211yescharacteristic
98#2059C2211yescharacteristic
99#2059C2211yescharacteristic
100#2059C2211yescharacteristic
101#2059C2211yescharacteristic
102#2059C2211yescharacteristic
103#2058C2211yescharacteristic
104#2058C2211yescharacteristic
105#2058C2211yescharacteristic
106#2058C2211yescharacteristic
107#2057C2211yescharacteristic
108#2057C2211yescharacteristic
109#2057C2211yescharacteristic
110#2057C2211yescharacteristic
111#1949C2211yescharacteristic
112#1949C2211yescharacteristic
113#1949C2211yescharacteristic
114#1949C2211yescharacteristic
115#1949C2211yescharacteristic
116#1949C2211yescharacteristic
117#1949C2211yescharacteristic
118#1949C2211yescharacteristic
119#1948C2211yescharacteristic
120#1948C2211yescharacteristic
121#1948C2211yescharacteristic
122#1948C2211yescharacteristic
123#1947C2211yescharacteristic
124#1947C2211yescharacteristic
125#1947C2211yescharacteristic
126#1947C2211yescharacteristic
127#1944C2211yescharacteristic
128#1944C2211yescharacteristic
129#1944C2211yescharacteristic
130#1944C2211yescharacteristic
131#1944C2211yescharacteristic
132#1944C2211yescharacteristic
133#1944C2211yescharacteristic
134#1944C2211yescharacteristic
135#1943C2211yescharacteristic
136#1943C2211yescharacteristic
137#1943C2211yescharacteristic
138#1943C2211yescharacteristic
139#1943C2211yescharacteristic
140#1943C2211yescharacteristic
141#1943C2211yescharacteristic
142#1943C2211yescharacteristic
143#1942C2211yescharacteristic
144#1942C2211yescharacteristic
145#1942C2211yescharacteristic
146#1942C2211yescharacteristic
147#1942C2211yescharacteristic
148#1942C2211yescharacteristic
149#1942C2211yescharacteristic
150#1942C2211yescharacteristic
151#1941C2211yescharacteristic
152#1941C2211yescharacteristic
153#1941C2211yescharacteristic
154#1941C2211yescharacteristic
155#1941C2211yescharacteristic
156#1941C2211yescharacteristic
157#1941C2211yescharacteristic
158#1941C2211yescharacteristic
159#1854C2211yescharacteristic
160#1854C2211yescharacteristic
161#1854C2211yescharacteristic
162#1854C2211yescharacteristic
163#1854C2211yescharacteristic
164#1854C2211yescharacteristic
165#1854C2211yescharacteristic
166#1854C2211yescharacteristic
167#1854C2211yescharacteristic
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1847C2211yescharacteristic
176#1847C2211yescharacteristic
177#1847C2211yescharacteristic
178#1847C2211yescharacteristic
179#1846C2211yescharacteristic
180#1846C2211yescharacteristic
181#1845C2211yescharacteristic
182#1844C2211yescharacteristic
183#1836C2211yescharacteristic
184#1836C2211yescharacteristic
185#1836C2211yescharacteristic
186#1836C2211yescharacteristic
187#1835C2211yescharacteristic
188#1835C2211yescharacteristic
189#1834C2211yescharacteristic
190#1834C2211yescharacteristic
191#1768C2211yescharacteristic
192#1768C2211yescharacteristic
193#1768C2211yescharacteristic
194#1768C2211yescharacteristic
195#1749C2211yescharacteristic
196#1749C2211yescharacteristic
197C4×C22⋊C8C2211yescharacteristic
198C4×C22⋊C8C2211yescharacteristic
199#1746C2211yescharacteristic
200#1746C2211yescharacteristic
201#1726C2211yescharacteristic
202#1726C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×#125C2311yescharacteristic
206C2×#125C2311yescharacteristic
207C2×C22⋊Q8—21no—
208C2×C22⋊Q8—21no—
209C2×#117—21no—
210C2×#117C2311yescharacteristic
211C2×#117C2311yescharacteristic
212C2×#117C2311yescharacteristic
213C2×#117C2311yescharacteristic
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217#432Q818yescomplemented
218#431Q818yescomplemented
219C2×#107C2311yescharacteristic
220C2×#107C2311yescharacteristic
221C2×#107C2311yescharacteristic
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C22⋊C8C2311yescharacteristic
256C2×C22⋊C8C2311yescharacteristic
257C2×C22⋊C8C2311yescharacteristic
258C2×C22⋊C8C2311yescharacteristic
259C2×#97C2311yescharacteristic
260C2×#97C2311yescharacteristic
261C2×#97C2311yescharacteristic
262C2×#97C2311yescharacteristic
263C2×#97C2311yescharacteristic
264C2×#97C2311yescharacteristic
265C2×C4×C8C2311yescharacteristic
266C2×C4×C8C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270C2×C4×C8C2311yescharacteristic
271#400—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#395—21no—
316#395—21no—
317#395—21no—
318#395—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#385—21no—
368#385—21no—
369#385—21no—
370#385—21no—
371#385—21no—
372#385—21no—
373#385—21no—
374#385—21no—
375#385—21no—
376#385—21no—
377#385—21no—
378#385—21no—
379#384C2311yescharacteristic
380#384C2311yescharacteristic
381#384C2311yescharacteristic
382#384C2311yescharacteristic
383#384C2311yescharacteristic
384#384C2311yescharacteristic
385#384C2311yescharacteristic
386#384C2311yescharacteristic
387#383—21no—
388#382—21no—
389#382C2311yescharacteristic
390#382C2311yescharacteristic
391#382C2311yescharacteristic
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#382C2311yescharacteristic
395#382C2311yescharacteristic
396#382C2311yescharacteristic
397#381—21no—
398#380—21no—
399#380—21no—
400#380—21no—
401#380—21no—
402#380—21no—
403#380—21no—
404#380—21no—
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C22⋊C4—21no—
427#376—21no—
428#376D411yescharacteristic
429#376D411yescharacteristic
430#376D411yescharacteristic
431#376D411yescharacteristic
432#376C2311yescharacteristic
433#376C2311yescharacteristic
434#376C2311yescharacteristic
435#376C2311yescharacteristic
436C2×#95D411yescharacteristic
437C2×#95D411yescharacteristic
438C2×#95D411yescharacteristic
439C2×#95D411yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480C22×Q8—21no—
481C22×Q8—21no—
482C23×C4C2×D411yescharacteristic
483C23×C4C2×D411yescharacteristic
484C23×C4C2×D411yescharacteristic
485C23×C4C2×D411yescharacteristic
486C23×C4C2×D411yescharacteristic
487C23×C4C2×D411yescharacteristic
488C23×C4C2411yescharacteristic
489C22×C8C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C4⋊Q8—41no—
498C4⋊Q8—41no—
499C4⋊Q8—41no—
500C4⋊Q8—41no—
501#125—41no—
502#125—41no—
503#125—41no—
504#125—41no—
505C22⋊Q8—82no—
506C22⋊Q8—82no—
507#117—41no—
508#117—41no—
509#117—41no—
510#117—41no—
511#117—41no—
512#117—41no—
513#117—41no—
514#117—41no—
515#117—82no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4C2411yescharacteristic
563C2×C4⋊C4C2411yescharacteristic
564C2×C4⋊C4C2411yescharacteristic
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C42—21no—
587C2×C42—21no—
588C2×C42—21no—
589C2×C42—21no—
590C2×C42—21no—
591C2×C42—21no—
592C2×C42—21no—
593C2×C42—21no—
594C2×C42—41no—
595C2×C42—41no—
596C2×C42—41no—
597C2×C42—41no—
598C2×C42C2×D411yescharacteristic
599C2×C42C2×D411yescharacteristic
600C2×C42C2×D411yescharacteristic
601C2×C42C2×D411yescharacteristic
602C2×C42C2×D411yescharacteristic
603C2×C42C2×D411yescharacteristic
604C2×C42C2×Q814yes—
605C2×C42C2×Q814yes—
606C2×C42C2411yescharacteristic
607C2×C42C2411yescharacteristic
608C2×C42C2411yescharacteristic
609C2×C42C2411yescharacteristic
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612#107—41no—
613#107—41no—
614#107—41no—
615#107—41no—
616#107—41no—
617#107—41no—
618#107—41no—
619#107—41no—
620#107—41no—
621#107—41no—
622#107—41no—
623#107—41no—
624#107—41no—
625#107—41no—
626#107—41no—
627#107—41no—
628#106—41no—
629#106—41no—
630#106—41no—
631#106—41no—
632#106—41no—
633#106—41no—
634#106—41no—
635#106—41no—
636#106—41no—
637#106—41no—
638#106—41no—
639#106—41no—
640#106—41no—
641#106—41no—
642#106—41no—
643#106—41no—
644C4⋊C8C2×Q814yes—
645C4⋊C8C2×Q814yes—
646C4⋊C8C2×Q814yes—
647C4⋊C8C2×Q814yes—
648C22⋊C8C2×Q814yes—
649C22⋊C8C2×Q814yes—
650C22⋊C8C2×Q814yes—
651C22⋊C8C2×Q814yes—
652#97—41no—
653#97—41no—
654#97—41no—
655#97—41no—
656#97C2×Q814yes—
657#97C2×Q814yes—
658C4×C8—41no—
659C4×C8—41no—
660C4×C8—41no—
661C4×C8—41no—
662C4×C8C2×Q814yes—
663C4×C8C2×Q814yes—
664#95—21no—
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95C2×D411yescharacteristic
713#95C2×D411yescharacteristic
714#95C2×D411yescharacteristic
715#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728C24C22×D411yescharacteristic
729C2×Q8—42no—
730C2×Q8—42no—
731C2×Q8—81no—
732C2×Q8—81no—
733C2×Q8—81no—
734C2×Q8—81no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—41no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4—41no—
770C22×C4—41no—
771C22×C4C4⋊Q814yes—
772C22×C4C4⋊Q814yes—
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D411yescharacteristic
775C22×C4C22×D411yescharacteristic
776C22×C4C22×D411yescharacteristic
777C22×C4C22×D411yescharacteristic
778C22×C4C22×D411yescharacteristic
779C22×C4C22×D411yescharacteristic
780C22×C4C22×D411yescharacteristic
781C22×C4C22×D411yescharacteristic
782C22×C4C22×D411yescharacteristic
783C22×C4C22×D411yescharacteristic
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C22×Q812yes—
787C22×C4C22×Q812yes—
788C22×C4C2511yescharacteristic
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8C22×Q812yes—
806C2×C8C22×Q812yes—
807C2×C8C22×Q812yes—
808C2×C8C22×Q812yes—
809C2×C8C22×Q812yes—
810C2×C8C22×Q812yes—
811C2×C8C22×Q812yes—
812C2×C8C22×Q812yes—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—42no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—42no—
849C4⋊C4—42no—
850C4⋊C4—42no—
851C4⋊C4—81no—
852C4⋊C4—81no—
853C4⋊C4—81no—
854C4⋊C4—81no—
855C4⋊C4—81no—
856C4⋊C4—81no—
857C4⋊C4—81no—
858C4⋊C4—81no—
859C4⋊C4—81no—
860C4⋊C4—81no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C22⋊C4—42no—
892C22⋊C4—42no—
893C22⋊C4—42no—
894C22⋊C4—42no—
895C22⋊C4—42no—
896C22⋊C4—42no—
897C22⋊C4—42no—
898C22⋊C4—42no—
899C42—21no—
900C42—21no—
901C42—21no—
902C42—21no—
903C42—21no—
904C42—21no—
905C42—21no—
906C42—21no—
907C42—41no—
908C42—41no—
909C42—41no—
910C42—41no—
911C42—42no—
912C42—42no—
913C42—42no—
914C42—42no—
915C42—81no—
916C42—81no—
917C42—81no—
918C42—81no—
919C42C4⋊Q814yes—
920C42C4⋊Q814yes—
921C42C22×Q812yes—
922C42C22×Q812yes—
923C42C22×Q812yes—
924C42C22×Q812yes—
925C23—21no—
926C23—21no—
927C23—21no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23C2×C4⋊Q812yes—
932C23C23×D411yescharacteristic
933Q8—162no—
934Q8—162no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—82no—
1024C2×C4—82no—
1025C2×C4—82no—
1026C2×C4—82no—
1027C2×C4C2×C4⋊Q812yes—
1028C2×C4C2×C4⋊Q812yes—
1029C2×C4C2×C4⋊Q812yes—
1030C2×C4C2×C4⋊Q812yes—
1031C2×C4C2×C4⋊Q812yes—
1032C2×C4C23×Q811yescharacteristic
1033C2×C4C23×Q811yescharacteristic
1034C2×C4#58511yescharacteristic
1035C2×C4#58511yescharacteristic
1036C2×C4#58511yescharacteristic
1037C2×C4#58511yescharacteristic
1038C8—22no—
1039C8—22no—
1040C8—22no—
1041C8—22no—
1042C8—22no—
1043C8—22no—
1044C8—22no—
1045C8—22no—
1046C22—22no—
1047C22—22no—
1048C22—22no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—41no—
1053C22C22×C4⋊Q811yescharacteristic
1054C22#344911yescharacteristic
1055C22#344911yescharacteristic
1056C22#358411yescharacteristic
1057C22#358411yescharacteristic
1058C22#358511yescharacteristic
1059C22#358611yescharacteristic
1060C4—22no—
1061C4—22no—
1062C4—22no—
1063C4—22no—
1064C4—22no—
1065C4—41no—
1066C4—41no—
1067C4—41no—
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—41no—
1072C4—41no—
1073C4—81no—
1074C4—81no—
1075C4—81no—
1076C4—81no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4—81no—
1086C4—81no—
1087C4—81no—
1088C4—81no—
1089C4#350411yescharacteristic
1090C4#350411yescharacteristic
1091C4#350411yescharacteristic
1092C4#350411yescharacteristic
1093C2—42no—
1094C2#3533511yescharacteristic
1095C2#6066011yescharacteristic
1096C2#6066411yescharacteristic
1097C2#6098411yescharacteristic
1098C2#6098511yescharacteristic
1099C2#6098611yescharacteristic
1100C2#6098711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#376 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33262C2semidirect
4. #33262C2semidirect
5. #33261C2semidirect
6. #33260C2semidirect
7. #30315C2semidirect
8. #30315C2semidirect
9. #30314C2semidirect
10. #30313C2semidirect
11. #29327C2semidirect
12. #29326C2semidirect
13. #29325C2semidirect
14. #29325C2semidirect
15. #29324C2semidirect
16. #29324C2semidirect
17. #29323C2semidirect
18. #29322C2semidirect
217. #432Q8semidirect
218. #431Q8semidirect

Maximal subgroups

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

subgroupindex
#353042
#346382
#332622
#332612
#332602
#303152
#303142
#303132
#293272
#293262
#293252
#293242
#293232
#293222
#293052
#293042
#293002
#292992
#219892
#219882
#219852
#219842
#204692