Finite Group Databasebeta

← #7606650

Subgroups — #7606650

Order 512.

1254 conjugacy classes of subgroups.

The subgroup lattice has 1111 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45341C211yesmaximal, characteristic
2#45199C211yesmaximal, characteristic
3#32238C211yesmaximal, characteristic, complemented
4#32229C211yesmaximal, characteristic, complemented
5#31747C211yesmaximal, characteristic
6#31742C211yesmaximal, characteristic
7#29405C211yesmaximal, characteristic, complemented
8#29403C211yesmaximal, characteristic, complemented
9#28815C211yesmaximal, characteristic, complemented
10#28028C211yesmaximal, characteristic, complemented
11#28012C211yesmaximal, characteristic, complemented
12#27850C211yesmaximal, characteristic
13#27793C211yesmaximal, characteristic
14#27793C211yesmaximal, characteristic
15#27356C211yesmaximal, characteristic
16#27346C211yesmaximal, characteristic
17#27146C211yesmaximal, characteristic, complemented
18#27142C211yesmaximal, characteristic, complemented
19#27044C211yesmaximal, characteristic
20#27037C211yesmaximal, characteristic
21#27009C211yesmaximal, characteristic, complemented
22#27000C211yesmaximal, characteristic, complemented
23#26491C211yesmaximal, characteristic, complemented
24#26072C211yesmaximal, characteristic
25#23168C211yesmaximal, characteristic, complemented
26#23156C211yesmaximal, characteristic, complemented
27#23038C211yesmaximal, characteristic
28#22623C211yesmaximal, characteristic
29#21730C211yesmaximal, characteristic, complemented
30#21671C211yesmaximal, characteristic
31#21289C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#501C2211yescharacteristic
34C2×#498C2211yescharacteristic
35C2×#470C2211yescharacteristic
36C2×#441C2211yescharacteristic
37C2×#428C2211yescharacteristic
38#2789—21no—
39#2787—21no—
40#2783—21no—
41#2776—21no—
42#2762—21no—
43#2762—21no—
44#2759—21no—
45#2759—21no—
46#2588—21no—
47#2581—21no—
48#2550C2211yescharacteristic
49#2550C2211yescharacteristic
50#2525—21no—
51#2523—21no—
52#2514—21no—
53#2514—21no—
54#2514C2211yescharacteristic
55#2514C2211yescharacteristic
56#2514C2211yescharacteristic
57#2511C2211yescharacteristic
58#2494C2211yescharacteristic
59#2494C2211yescharacteristic
60#2492C2211yescharacteristic
61#2492C2211yescharacteristic
62#2489C2211yescharacteristic
63#2489C2211yescharacteristic
64#2465—21no—
65#2451C2211yescharacteristic
66#2451C2211yescharacteristic
67#2440C2211yescharacteristic
68#2439C2211yescharacteristic
69#2421—21no—
70#2401C2211yescharacteristic
71#2370C2211yescharacteristic
72#2369C2211yescharacteristic
73#2365C2211yescharacteristic
74#2365C2211yescharacteristic
75#2362C2211yescharacteristic
76#2360C2211yescharacteristic
77#2347C2211yescharacteristic
78#2345C2211yescharacteristic
79#2331C2211yescharacteristic
80#2330C2211yescharacteristic
81#2320C2211yescharacteristic
82#2320C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2085C2211yescharacteristic
86#2084C2211yescharacteristic
87#2077C2211yescharacteristic
88#2077C2211yescharacteristic
89#2074C2211yescharacteristic
90#2074C2211yescharacteristic
91#2074C2211yescharacteristic
92#2072C2211yescharacteristic
93#2068C2211yescharacteristic
94#2066C2211yescharacteristic
95#2066C2211yescharacteristic
96#2066C2211yescharacteristic
97#2066C2211yescharacteristic
98#2066C2211yescharacteristic
99#2059C2211yescharacteristic
100#2059C2211yescharacteristic
101#2058C2211yescharacteristic
102#2058C2211yescharacteristic
103#2058C2211yescharacteristic
104#2057C2211yescharacteristic
105#2036C2211yescharacteristic
106#2036C2211yescharacteristic
107#2035C2211yescharacteristic
108#2035C2211yescharacteristic
109#2026C2211yescharacteristic
110#2026C2211yescharacteristic
111#2024C2211yescharacteristic
112#2024C2211yescharacteristic
113#2024C2211yescharacteristic
114#2024C2211yescharacteristic
115#1991C2211yescharacteristic
116#1990C2211yescharacteristic
117#1989C2211yescharacteristic
118#1988C2211yescharacteristic
119#1987C2211yescharacteristic
120#1987C2211yescharacteristic
121#1971C2211yescharacteristic
122#1971C2211yescharacteristic
123#1969C2211yescharacteristic
124#1969C2211yescharacteristic
125#1969C2211yescharacteristic
126#1949C2211yescharacteristic
127#1949C2211yescharacteristic
128#1944C2211yescharacteristic
129#1944C2211yescharacteristic
130#1944C2211yescharacteristic
131#1943C2211yescharacteristic
132#1942C2211yescharacteristic
133#1942C2211yescharacteristic
134#1941C2211yescharacteristic
135#1941C2211yescharacteristic
136#1941C2211yescharacteristic
137#1935C2211yescharacteristic
138#1935C2211yescharacteristic
139#1933C2211yescharacteristic
140#1933C2211yescharacteristic
141#1928C2211yescharacteristic
142#1928C2211yescharacteristic
143#1928C2211yescharacteristic
144#1928C2211yescharacteristic
145#1927C2211yescharacteristic
146#1927C2211yescharacteristic
147#1927C2211yescharacteristic
148#1927C2211yescharacteristic
149#1927C2211yescharacteristic
150#1927C2211yescharacteristic
151#1924C2211yescharacteristic
152#1923C2211yescharacteristic
153#1923C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1920C2211yescharacteristic
160#1920C2211yescharacteristic
161#1919C2211yescharacteristic
162#1919C2211yescharacteristic
163#1919C2211yescharacteristic
164#1919C2211yescharacteristic
165#1919C2211yescharacteristic
166#1918C2211yescharacteristic
167#1918C2211yescharacteristic
168#1917C2211yescharacteristic
169#1916C2211yescharacteristic
170#1916C2211yescharacteristic
171#1873C2211yescharacteristic
172#1872C2211yescharacteristic
173#1865C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1863C2211yescharacteristic
177#1854C2211yescharacteristic
178#1853C2211yescharacteristic
179#1847C2211yescharacteristic
180#1846C2211yescharacteristic
181#1840C2211yescharacteristic
182#1825C2211yescharacteristic
183#1823C2211yescharacteristic
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190C4×#107C2211yescharacteristic
191C4×#106C2211yescharacteristic
192C4×#106C2211yescharacteristic
193C4×#106C2211yescharacteristic
194#1771C2211yescharacteristic
195#1770C2211yescharacteristic
196C8×C4⋊C4C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×C22⋊Q8—21no—
212C2×C22⋊Q8C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×C4×Q8—21no—
215C2×C4×Q8—21no—
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×#117C2311yescharacteristic
219C22×C4⋊C4C2311yescharacteristic
220#501—24no—
221#501—24no—
222#498—24no—
223#470—24no—
224#441—24no—
225#428—24no—
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×C22⋊C8C2311yescharacteristic
263C2×C22⋊C8C2311yescharacteristic
264C2×C22⋊C8C2311yescharacteristic
265C2×#97C2311yescharacteristic
266C2×#97C2311yescharacteristic
267C2×#97C2311yescharacteristic
268C2×#97C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270C2×C4×C8C2311yescharacteristic
271C2×C4×C8C2311yescharacteristic
272C2×C4×C8C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
274#401—21no—
275#401—21no—
276#401—21no—
277#401—21no—
278#401—21no—
279#401D411yescharacteristic
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#400D411yescharacteristic
290#400D411yescharacteristic
291#400D411yescharacteristic
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397D411yescharacteristic
302#397D411yescharacteristic
303#397D411yescharacteristic
304#396—21no—
305#396D411yescharacteristic
306#395—21no—
307#395—21no—
308#395—21no—
309#395—21no—
310#395—21no—
311#393—21no—
312#393—21no—
313#393—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#391—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—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#385—21no—
397#385—21no—
398#384C2311yescharacteristic
399#383—21no—
400#383—21no—
401#383—21no—
402#383—21no—
403#383—21no—
404#383—21no—
405#382—21no—
406#382—21no—
407#382—21no—
408#382—21no—
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#380—21no—
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441#376C2311yescharacteristic
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
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8—21no—
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C23×C4—21no—
491C23×C4C2411yescharacteristic
492C2×Q16—22no—
493C2×Q16—22no—
494C2×Q16—22no—
495C2×M16—22no—
496C2×M16—22no—
497C2×M16—22no—
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C4⋊Q8—22no—
507C4⋊Q8—22no—
508C4⋊Q8—22no—
509C4⋊Q8—22no—
510C4⋊Q8—41no—
511C4⋊Q8—41no—
512C4⋊Q8—41no—
513C4⋊Q8—41no—
514#125—22no—
515#125—22no—
516#125—41no—
517#125—41no—
518C22⋊Q8—22no—
519C22⋊Q8—22no—
520C22⋊Q8—41no—
521C22⋊Q8—41no—
522C22⋊Q8—82no—
523C4×Q8—22no—
524C4×Q8—22no—
525C4×Q8—41no—
526C4×Q8—41no—
527C4×Q8—82no—
528C4×Q8—82no—
529#117—22no—
530#117—41no—
531C2×C4⋊C4—22no—
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—41no—
562C2×C4⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4C2×D411yescharacteristic
590C2×C22⋊C4C2×D411yescharacteristic
591C2×C22⋊C4C2×D411yescharacteristic
592C2×C22⋊C4C2×D411yescharacteristic
593C2×C22⋊C4C2×D411yescharacteristic
594C2×C22⋊C4C2×D411yescharacteristic
595C2×C42—21no—
596C2×C42—21no—
597C2×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615C2×C42C2411yescharacteristic
616#107—22no—
617#107—22no—
618#107—22no—
619#107—22no—
620#107—22no—
621#107—22no—
622#107—41no—
623#106—22no—
624#106—22no—
625#106—22no—
626#106—22no—
627#106—22no—
628#106—22no—
629#106—22no—
630#106—41no—
631#106—41no—
632#106—41no—
633#106#4114yes—
634#106#4114yes—
635C4⋊C8—22no—
636C4⋊C8—41no—
637C4⋊C8—41no—
638#103—22no—
639#103—22no—
640#103—22no—
641#103—22no—
642#103—22no—
643#103—22no—
644#103—41no—
645#103—41no—
646#103—41no—
647#103—41no—
648#103—41no—
649#103—41no—
650#103—41no—
651#103—41no—
652C22⋊C8—22no—
653C22⋊C8—41no—
654C22⋊C8—41no—
655#97—22no—
656#97—22no—
657#97—22no—
658#97—22no—
659C4×C8—22no—
660C4×C8—22no—
661C4×C8—22no—
662C4×C8—41no—
663C4×C8—41no—
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#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736C24C22×D411yescharacteristic
737C2×Q8—21no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—42no—
750C2×Q8—42no—
751C2×Q8—42no—
752C2×Q8—42no—
753C2×Q8—42no—
754C2×Q8—42no—
755C2×Q8—81no—
756C2×Q8—81no—
757C2×Q8—81no—
758C2×Q8—81no—
759C2×Q8—81no—
760C2×Q8—81no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—42no—
784C22×C4—81no—
785C22×C4—81no—
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D411yescharacteristic
788C22×C4C22×D411yescharacteristic
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C2511yescharacteristic
800Q16—44no—
801M16—44no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8C2×#4112yes—
823C2×C8C2×#4112yes—
824C2×C82−1+412yes—
825C2×C82−1+412yes—
826C4⋊C4—22no—
827C4⋊C4—22no—
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—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—41no—
853C4⋊C4—41no—
854C4⋊C4—41no—
855C4⋊C4—41no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—42no—
860C4⋊C4—42no—
861C4⋊C4—42no—
862C4⋊C4—42no—
863C4⋊C4—42no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—42no—
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⋊C4C2×#4112yes—
886C4⋊C4C2×#4112yes—
887C4⋊C4C2×#4112yes—
888C4⋊C4C2×#4112yes—
889C22⋊C4—22no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C22⋊C4—41no—
893C22⋊C4—41no—
894C22⋊C4—41no—
895C22⋊C4—42no—
896C22⋊C4—42no—
897C22⋊C4—42no—
898C22⋊C4—42no—
899C22⋊C4—81no—
900C22⋊C4—81no—
901C22⋊C4—81no—
902C42—21no—
903C42—21no—
904C42—21no—
905C42—21no—
906C42—21no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42—21no—
912C42—21no—
913C42—21no—
914C42—42no—
915C42—42no—
916C42—42no—
917C42—42no—
918C42—81no—
919C42—81no—
920C42—81no—
921C42—81no—
922C42—81no—
923C42—81no—
924C42—81no—
925C42—81no—
926C42—81no—
927C42—81no—
928C42—81no—
929C23—21no—
930C23—21no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23C23×D411yescharacteristic
937Q8—41no—
938Q8—41no—
939Q8—41no—
940Q8—41no—
941Q8—41no—
942Q8—41no—
943Q8—41no—
944Q8—41no—
945Q8—84no—
946Q8—84no—
947Q8—162no—
948Q8—162no—
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—21no—
974C2×C4—21no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
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—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—162no—
1040C2×C4#57712yes—
1041C2×C4C22×#4111yescharacteristic
1042C2×C4C22×#4111yescharacteristic
1043C2×C4C2×2−1+411yescharacteristic
1044C2×C4C2×2−1+411yescharacteristic
1045C2×C4#58511yescharacteristic
1046C2×C4#58511yescharacteristic
1047C8—22no—
1048C8—41no—
1049C8—41no—
1050C8—41no—
1051C8—41no—
1052C8—41no—
1053C8—41no—
1054C8#55614yes—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—41no—
1059C22—41no—
1060C22—41no—
1061C22—41no—
1062C22D4×#4111yescharacteristic
1063C22D4×#4111yescharacteristic
1064C22#349911yescharacteristic
1065C22C2×#57711yescharacteristic
1066C22#358411yescharacteristic
1067C22#358611yescharacteristic
1068C22#358611yescharacteristic
1069C4—22no—
1070C4—41no—
1071C4—42no—
1072C4—41no—
1073C4—41no—
1074C4—41no—
1075C4—41no—
1076C4—41no—
1077C4—41no—
1078C4—41no—
1079C4—42no—
1080C4—41no—
1081C4—41no—
1082C4—42no—
1083C4—41no—
1084C4—41no—
1085C4—42no—
1086C4—81no—
1087C4—81no—
1088C4—81no—
1089C4—81no—
1090C4—81no—
1091C4—81no—
1092C4—81no—
1093C4—81no—
1094C4—81no—
1095C4—81no—
1096C4—81no—
1097C4—81no—
1098C4C2×#55611yescharacteristic
1099C4#351611yescharacteristic
1100C4#351811yescharacteristic
1101C4#356511yescharacteristic
1102C2—81no—
1103C2#5971111yescharacteristic
1104C2#6149011yescharacteristic
1105C2#6151411yescharacteristic
1106C2#6155011yescharacteristic
1107C2#6155711yescharacteristic
1108C2#6251711yescharacteristic
1109C2#6252211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2401 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32238C2semidirect
4. #32229C2semidirect
7. #29405C2semidirect
8. #29403C2semidirect
9. #28815C2semidirect
10. #28028C2semidirect
11. #28012C2semidirect
17. #27146C2semidirect
18. #27142C2semidirect
21. #27009C2semidirect
22. #27000C2semidirect
23. #26491C2semidirect
25. #23168C2semidirect
26. #23156C2semidirect
29. #21730C2semidirect
31. #21289C2semidirect

Maximal subgroups

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

subgroupindex
#453412
#451992
#322382
#322292
#317472
#317422
#294052
#294032
#288152
#280282
#280122
#278502
#277932
#273562
#273462
#271462
#271422
#270442
#270372
#270092
#270002
#264912
#260722
#231682
#231562
#230382
#226232
#217302
#216712
#212892