Finite Group Databasebeta

← #7194796

Subgroups — #7194796

Order 512.

1196 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45223C211yesmaximal, characteristic, complemented
2#42704C211yesmaximal, characteristic
3#32501C211yesmaximal, characteristic
4#32488C211yesmaximal, characteristic
5#32337C211yesmaximal, characteristic, complemented
6#32334C211yesmaximal, characteristic, complemented
7#32314C211yesmaximal, characteristic, complemented
8#32314C211yesmaximal, characteristic, complemented
9#32253C211yesmaximal, characteristic
10#32241C211yesmaximal, characteristic
11#29228C211yesmaximal, characteristic, complemented
12#28805C211yesmaximal, characteristic, complemented
13#28798C211yesmaximal, characteristic, complemented
14#28698C211yesmaximal, characteristic, complemented
15#28055C211yesmaximal, characteristic
16#28046C211yesmaximal, characteristic
17#27822C211yesmaximal, characteristic
18#27739C211yesmaximal, characteristic
19#27150C211yesmaximal, characteristic
20#27140C211yesmaximal, characteristic
21#26525C211yesmaximal, characteristic, complemented
22#26524C211yesmaximal, characteristic, complemented
23#26508C211yesmaximal, characteristic, complemented
24#26457C211yesmaximal, characteristic, complemented
25#25465C211yesmaximal, characteristic
26#25457C211yesmaximal, characteristic
27#23790C211yesmaximal, characteristic
28#23262C211yesmaximal, characteristic, complemented
29#23167C211yesmaximal, characteristic, complemented
30#23164C211yesmaximal, characteristic, complemented
31#22122C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#499C2211yescharacteristic
34C2×#478C2211yescharacteristic
35#2836—21no—
36#2802—21no—
37#2791—21no—
38#2791—21no—
39#2726—21no—
40#2704—21no—
41#2698—21no—
42#2690—21no—
43#2689—21no—
44#2664—21no—
45#2660C2211yescharacteristic
46#2654—21no—
47#2590—21no—
48#2585—21no—
49#2571C2211yescharacteristic
50#2570C2211yescharacteristic
51#2566C2211yescharacteristic
52#2552—21no—
53#2552C2211yescharacteristic
54#2552C2211yescharacteristic
55#2552C2211yescharacteristic
56#2552C2211yescharacteristic
57#2552C2211yescharacteristic
58#2552C2211yescharacteristic
59#2542C2211yescharacteristic
60#2519—21no—
61#2513C2211yescharacteristic
62#2513C2211yescharacteristic
63#2512C2211yescharacteristic
64#2512C2211yescharacteristic
65#2507C2211yescharacteristic
66#2507C2211yescharacteristic
67#2506—21no—
68#2506C2211yescharacteristic
69#2506C2211yescharacteristic
70#2402C2211yescharacteristic
71#2370C2211yescharacteristic
72#2370C2211yescharacteristic
73#2370C2211yescharacteristic
74#2370C2211yescharacteristic
75#2370C2211yescharacteristic
76#2369C2211yescharacteristic
77#2330C2211yescharacteristic
78#2330C2211yescharacteristic
79#2319C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2100C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2100C2211yescharacteristic
87#2099C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2099C2211yescharacteristic
91#2094C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2088C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2084C2211yescharacteristic
102#2084C2211yescharacteristic
103#2084C2211yescharacteristic
104#2083C2211yescharacteristic
105#2083C2211yescharacteristic
106#2071C2211yescharacteristic
107#2071C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic
114#2059C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2025C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic
120#1992C2211yescharacteristic
121#1992C2211yescharacteristic
122#1992C2211yescharacteristic
123#1992C2211yescharacteristic
124#1991C2211yescharacteristic
125#1990C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1989C2211yescharacteristic
129#1989C2211yescharacteristic
130#1989C2211yescharacteristic
131#1988C2211yescharacteristic
132#1987C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1948C2211yescharacteristic
137#1948C2211yescharacteristic
138#1948C2211yescharacteristic
139#1948C2211yescharacteristic
140#1948C2211yescharacteristic
141#1947C2211yescharacteristic
142#1947C2211yescharacteristic
143#1947C2211yescharacteristic
144#1943C2211yescharacteristic
145#1943C2211yescharacteristic
146#1943C2211yescharacteristic
147#1943C2211yescharacteristic
148#1941C2211yescharacteristic
149#1941C2211yescharacteristic
150#1940C2211yescharacteristic
151#1940C2211yescharacteristic
152#1940C2211yescharacteristic
153#1939C2211yescharacteristic
154#1936C2211yescharacteristic
155#1936C2211yescharacteristic
156#1936C2211yescharacteristic
157#1936C2211yescharacteristic
158#1934C2211yescharacteristic
159#1934C2211yescharacteristic
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic
163#1926C2211yescharacteristic
164#1926C2211yescharacteristic
165#1925C2211yescharacteristic
166#1921C2211yescharacteristic
167#1920C2211yescharacteristic
168#1920C2211yescharacteristic
169#1920C2211yescharacteristic
170#1920C2211yescharacteristic
171#1919C2211yescharacteristic
172#1919C2211yescharacteristic
173#1919C2211yescharacteristic
174#1919C2211yescharacteristic
175#1919C2211yescharacteristic
176#1919C2211yescharacteristic
177#1919C2211yescharacteristic
178#1918C2211yescharacteristic
179#1918C2211yescharacteristic
180#1917C2211yescharacteristic
181#1917C2211yescharacteristic
182#1916C2211yescharacteristic
183#1916C2211yescharacteristic
184#1836C2211yescharacteristic
185#1836C2211yescharacteristic
186#1834C2211yescharacteristic
187#1834C2211yescharacteristic
188#1802C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192#1776C2211yescharacteristic
193C4×#107C2211yescharacteristic
194C4×#106C2211yescharacteristic
195#1771C2211yescharacteristic
196#1771C2211yescharacteristic
197#1770C2211yescharacteristic
198#1770C2211yescharacteristic
199#1768C2211yescharacteristic
200#1768C2211yescharacteristic
201#1762C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×#126—21no—
205C2×#126—21no—
206C2×#125—21no—
207C2×#125—21no—
208C2×#125—21no—
209C2×#125—21no—
210C2×#125—21no—
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C4×D4C2311yescharacteristic
219#501—24no—
220#499—24no—
221#478—24no—
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#106C2311yescharacteristic
229C2×#106C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×#102C2311yescharacteristic
247C2×#102C2311yescharacteristic
248C2×#102C2311yescharacteristic
249C2×#102C2311yescharacteristic
250C2×#102C2311yescharacteristic
251C2×#102C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×#97C2311yescharacteristic
255C2×#97C2311yescharacteristic
256C2×#97C2311yescharacteristic
257C2×#97C2311yescharacteristic
258C2×#97C2311yescharacteristic
259C2×C4×C8C2311yescharacteristic
260C2×C4×C8C2311yescharacteristic
261C2×C4×C8C2311yescharacteristic
262#400—21no—
263#400—21no—
264#400—21no—
265#400—21no—
266#400—21no—
267#400D411yescharacteristic
268#400D411yescharacteristic
269#400D411yescharacteristic
270#400D411yescharacteristic
271#399—21no—
272#399—21no—
273#398—21no—
274#398—21no—
275#398—21no—
276#398—21no—
277#398—21no—
278#398—21no—
279#398—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398D411yescharacteristic
295#398D411yescharacteristic
296#398D411yescharacteristic
297#398D411yescharacteristic
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#396—21no—
305#396—21no—
306#396—21no—
307#396—21no—
308#395—21no—
309#395—21no—
310#391—21no—
311#391—21no—
312#390C2311yescharacteristic
313#390C2311yescharacteristic
314#390C2311yescharacteristic
315#390C2311yescharacteristic
316#390C2311yescharacteristic
317#390C2311yescharacteristic
318#389—21no—
319#389—21no—
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
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#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—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#385—21no—
384#385—21no—
385#384—21no—
386#384—21no—
387#384—21no—
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#384C2311yescharacteristic
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#382—21no—
398#382C2311yescharacteristic
399#382C2311yescharacteristic
400#382C2311yescharacteristic
401#381—21no—
402#380—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428#376C2311yescharacteristic
429#340C2311yescharacteristic
430#340C2311yescharacteristic
431#340C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
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#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8—21no—
482C22×D4C2411yescharacteristic
483C23×C4—21no—
484C22×C8C2411yescharacteristic
485C22×C8C2411yescharacteristic
486C22×C8C2411yescharacteristic
487C22×C8C2411yescharacteristic
488C22×C8C2411yescharacteristic
489C22×C8C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C4⋊Q8—22no—
493C4⋊Q8—22no—
494#126—82no—
495#126—82no—
496#125—22no—
497#125—22no—
498#125—22no—
499#125—22no—
500#125—22no—
501#125—22no—
502#125—41no—
503#125—41no—
504#125—41no—
505#125—82no—
506#125—82no—
507#125—82no—
508#125—82no—
509#125—82no—
510#125#4114yes—
511C22⋊Q8—82no—
512C22⋊Q8—82no—
513C4×D4—22no—
514C4×D4—22no—
515C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—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×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617C2×C42C2411yescharacteristic
618C2×C42C2411yescharacteristic
619C2×C42C2411yescharacteristic
620C2×C42C2411yescharacteristic
621C2×C42C2411yescharacteristic
622#107—22no—
623#107—22no—
624#107—22no—
625#107—22no—
626#107—22no—
627#107—22no—
628#106—22no—
629#106—22no—
630#106—22no—
631#106—22no—
632#106—22no—
633#106—22no—
634#106—22no—
635#106—41no—
636#106—41no—
637#106—41no—
638C4⋊C8—22no—
639C4⋊C8—22no—
640C4⋊C8—22no—
641C4⋊C8—22no—
642C4⋊C8—22no—
643C4⋊C8—22no—
644C4⋊C8—41no—
645C4⋊C8—41no—
646#102—22no—
647#102—22no—
648#102—22no—
649#102—22no—
650#102—22no—
651#102—41no—
652#102—41no—
653#102—41no—
654#97—22no—
655#97—22no—
656#97—41no—
657#97—41no—
658#97—41no—
659C4×C8—22no—
660C4×C8—22no—
661C4×C8—41no—
662#95—21no—
663#95—21no—
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#95C2×D411yescharacteristic
700#95C2×D411yescharacteristic
701#95C2×D411yescharacteristic
702#95C2×D411yescharacteristic
703#95C2×D411yescharacteristic
704#95C2×D411yescharacteristic
705#95C2×D411yescharacteristic
706#95C2×D411yescharacteristic
707#95C2×D411yescharacteristic
708#95C2×D411yescharacteristic
709#95C2×D411yescharacteristic
710#95C2×D411yescharacteristic
711#95C2×D411yescharacteristic
712#95C2×D411yescharacteristic
713#95C2×D411yescharacteristic
714#95C2×D411yescharacteristic
715C24—21no—
716C2×Q8—42no—
717C2×Q8—81no—
718C2×Q8—81no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—42no—
741C22×C4—81no—
742C22×C4—81no—
743C22×C4C22×D411yescharacteristic
744C22×C4C22×D411yescharacteristic
745C22×C4C22×D411yescharacteristic
746C22×C4C22×D411yescharacteristic
747C22×C4C22×D411yescharacteristic
748C22×C4C22×D411yescharacteristic
749C22×C4C22×D411yescharacteristic
750C22×C4C22×D411yescharacteristic
751C22×C4C22×D411yescharacteristic
752C22×C4C22×D411yescharacteristic
753C22×C4C22×D411yescharacteristic
754C22×C4C22×D411yescharacteristic
755C22×C4C22×D411yescharacteristic
756C22×C4C22×D411yescharacteristic
757C22×C4C2511yescharacteristic
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C82−1+412yes—
781C2×C82−1+412yes—
782C4⋊C4—24no—
783C4⋊C4—24no—
784C4⋊C4—22no—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—41no—
815C4⋊C4—41no—
816C4⋊C4—41no—
817C4⋊C4—41no—
818C4⋊C4—41no—
819C4⋊C4—41no—
820C4⋊C4—41no—
821C4⋊C4—41no—
822C4⋊C4—41no—
823C4⋊C4—42no—
824C4⋊C4—42no—
825C4⋊C4—42no—
826C4⋊C4—42no—
827C4⋊C4—42no—
828C4⋊C4—42no—
829C4⋊C4—42no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C4⋊C4—42no—
834C4⋊C4—42no—
835C4⋊C4—42no—
836C4⋊C4—42no—
837C4⋊C4—42no—
838C4⋊C4—81no—
839C4⋊C4—81no—
840C4⋊C4—81no—
841C4⋊C4—81no—
842C4⋊C4—81no—
843C4⋊C4—81no—
844C4⋊C4—81no—
845C4⋊C4—81no—
846C4⋊C4—81no—
847C4⋊C4—81no—
848C4⋊C4—81no—
849C4⋊C4—81no—
850C4⋊C4—81no—
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⋊C4C2×#4112yes—
869C4⋊C4C2×#4112yes—
870C4⋊C42−1+412yes—
871C22⋊C4—42no—
872C22⋊C4—42no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C22⋊C4—81no—
876C22⋊C4—81no—
877C22⋊C4—81no—
878C22⋊C4—81no—
879C22⋊C4—81no—
880C22⋊C4—81no—
881C22⋊C4—81no—
882C22⋊C4—81no—
883C22⋊C4—81no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42—21no—
889C42—21no—
890C42—21no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—42no—
897C42—42no—
898C42—81no—
899C42—81no—
900C42—81no—
901C42—81no—
902C42—81no—
903C42—81no—
904C42—81no—
905C42—81no—
906C42—81no—
907C42—81no—
908C42—81no—
909C42C2×#4112yes—
910C422−1+412yes—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23C23×D411yescharacteristic
919Q8—162no—
920D4—41no—
921D4—41no—
922D4—41no—
923D4—41no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
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—21no—
946C2×C4—21no—
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—22no—
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—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
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—162no—
1009C2×C4#54812yes—
1010C2×C4#54812yes—
1011C2×C4#57712yes—
1012C2×C4C22×#4111yescharacteristic
1013C2×C4C2×2−1+411yescharacteristic
1014C2×C4C2×2−1+411yescharacteristic
1015C2×C4C2×2−1+411yescharacteristic
1016C2×C4C2×2−1+411yescharacteristic
1017C2×C4#58511yescharacteristic
1018C8—22no—
1019C8—22no—
1020C8—41no—
1021C8—41no—
1022C8—41no—
1023C8—41no—
1024C8—41no—
1025C8—41no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—81no—
1031C22—81no—
1032C22—81no—
1033C22C2×#54811yescharacteristic
1034C22#348911yescharacteristic
1035C22#349911yescharacteristic
1036C22C2×#57711yescharacteristic
1037C22#358511yescharacteristic
1038C22#358511yescharacteristic
1039C22#358611yescharacteristic
1040C4—22no—
1041C4—22no—
1042C4—22no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—42no—
1047C4—41no—
1048C4—41no—
1049C4—41no—
1050C4—41no—
1051C4—41no—
1052C4—42no—
1053C4—42no—
1054C4—41no—
1055C4—41no—
1056C4—41no—
1057C4—81no—
1058C4—81no—
1059C4—81no—
1060C4—81no—
1061C4—81no—
1062C4—81no—
1063C4—81no—
1064C4—81no—
1065C4—81no—
1066C4—81no—
1067C4—81no—
1068C4—81no—
1069C4#351611yescharacteristic
1070C4#352311yescharacteristic
1071C4#355511yescharacteristic
1072C4#355611yescharacteristic
1073C2—161no—
1074C2#4534311yescharacteristic
1075C2#6133711yescharacteristic
1076C2#6134611yescharacteristic
1077C2#6218511yescharacteristic
1078C2#6223811yescharacteristic
1079C2#6250011yescharacteristic
1080C2#6251411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2402 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45223C2semidirect
5. #32337C2semidirect
6. #32334C2semidirect
7. #32314C2semidirect
8. #32314C2semidirect
11. #29228C2semidirect
12. #28805C2semidirect
13. #28798C2semidirect
14. #28698C2semidirect
21. #26525C2semidirect
22. #26524C2semidirect
23. #26508C2semidirect
24. #26457C2semidirect
28. #23262C2semidirect
29. #23167C2semidirect
30. #23164C2semidirect

Maximal subgroups

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

subgroupindex
#452232
#427042
#325012
#324882
#323372
#323342
#323142
#322532
#322412
#292282
#288052
#287982
#286982
#280552
#280462
#278222
#277392
#271502
#271402
#265252
#265242
#265082
#264572
#254652
#254572
#237902
#232622
#231672
#231642
#221222