Finite Group Databasebeta

← #7036699

Subgroups — #7036699

Order 512.

1312 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59288C211yesmaximal, characteristic, complemented
2#39529C211yesmaximal, characteristic
3#32464C211yesmaximal, characteristic, complemented
4#32317C211yesmaximal, characteristic, complemented
5#32004C211yesmaximal, characteristic
6#31455C211yesmaximal, characteristic, complemented
7#31432C211yesmaximal, characteristic, complemented
8#31423C211yesmaximal, characteristic, complemented
9#31092C211yesmaximal, characteristic, complemented
10#31088C211yesmaximal, characteristic, complemented
11#29296C211yesmaximal, characteristic, complemented
12#28943C211yesmaximal, characteristic, complemented
13#28841C211yesmaximal, characteristic, complemented
14#28831C211yesmaximal, characteristic, complemented
15#28773C211yesmaximal, characteristic, complemented
16#27992C211yesmaximal, characteristic, complemented
17#27875C211yesmaximal, characteristic, complemented
18#27838C211yesmaximal, characteristic, complemented
19#27462C211yesmaximal, characteristic, complemented
20#27455C211yesmaximal, characteristic, complemented
21#27302C211yesmaximal, characteristic, complemented
22#27159C211yesmaximal, characteristic, complemented
23#27038C211yesmaximal, characteristic, complemented
24#26864C211yesmaximal, characteristic, complemented
25#25018C211yesmaximal, characteristic
26#24934C211yesmaximal, characteristic, complemented
27#23754C211yesmaximal, characteristic, complemented
28#23294C211yesmaximal, characteristic, complemented
29#22966C211yesmaximal, characteristic, complemented
30#22921C211yesmaximal, characteristic, complemented
31#22076C211yesmaximal, characteristic, complemented
32C2×#481C2211yescharacteristic
33C2×#482C2211yescharacteristic
34C2×#478C2211yescharacteristic
35#2857C2211yescharacteristic
36#2773—21no—
37#2767—21no—
38#2757—21no—
39#2739—21no—
40#2728—21no—
41#2696—21no—
42#2630—21no—
43#2570C2211yescharacteristic
44#2570C2211yescharacteristic
45#2535C2211yescharacteristic
46#2533—21no—
47#2523—21no—
48#2519—21no—
49#2508C2211yescharacteristic
50#2508C2211yescharacteristic
51#2506C2211yescharacteristic
52#2498—21no—
53#2496C2211yescharacteristic
54#2495C2211yescharacteristic
55#2495C2211yescharacteristic
56#2495C2211yescharacteristic
57#2488—21no—
58#2487C2211yescharacteristic
59#2485C2211yescharacteristic
60#2481—21no—
61#2452C2211yescharacteristic
62#2442—21no—
63#2442C2211yescharacteristic
64#2441C2211yescharacteristic
65#2439C2211yescharacteristic
66#2422C2211yescharacteristic
67#2420C2211yescharacteristic
68#2370C2211yescharacteristic
69#2363C2211yescharacteristic
70#2352C2211yescharacteristic
71#2349C2211yescharacteristic
72#2346C2211yescharacteristic
73#2345C2211yescharacteristic
74#2343—21no—
75#2318—21no—
76C4×#123C2211yescharacteristic
77C4×#121C2211yescharacteristic
78C2×#389C2211yescharacteristic
79#2285C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2099C2211yescharacteristic
86#2093C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2087C2211yescharacteristic
91#2086C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2083C2211yescharacteristic
97#2083C2211yescharacteristic
98#2083C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2076C2211yescharacteristic
106#2075C2211yescharacteristic
107#2075C2211yescharacteristic
108#2075C2211yescharacteristic
109#2073C2211yescharacteristic
110#2071C2211yescharacteristic
111#2067C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2057C2211yescharacteristic
115#2057C2211yescharacteristic
116#2034C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#1991C2211yescharacteristic
121#1990C2211yescharacteristic
122#1990C2211yescharacteristic
123#1954C2211yescharacteristic
124#1949C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1949C2211yescharacteristic
128#1942C2211yescharacteristic
129#1942C2211yescharacteristic
130#1942C2211yescharacteristic
131#1942C2211yescharacteristic
132#1942C2211yescharacteristic
133#1942C2211yescharacteristic
134#1942C2211yescharacteristic
135#1942C2211yescharacteristic
136#1941C2211yescharacteristic
137#1941C2211yescharacteristic
138#1941C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1925C2211yescharacteristic
143#1923C2211yescharacteristic
144#1923C2211yescharacteristic
145#1923C2211yescharacteristic
146#1923C2211yescharacteristic
147#1921C2211yescharacteristic
148#1921C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1920C2211yescharacteristic
155#1920C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1916C2211yescharacteristic
161#1916C2211yescharacteristic
162#1893C2211yescharacteristic
163#1874C2211yescharacteristic
164#1869C2211yescharacteristic
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1864C2211yescharacteristic
168#1862C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1853C2211yescharacteristic
176#1852C2211yescharacteristic
177#1852C2211yescharacteristic
178#1852C2211yescharacteristic
179#1852C2211yescharacteristic
180#1846C2211yescharacteristic
181#1846C2211yescharacteristic
182#1844C2211yescharacteristic
183#1834C2211yescharacteristic
184#1825C2211yescharacteristic
185#1824C2211yescharacteristic
186#1808C2211yescharacteristic
187#1808C2211yescharacteristic
188#1804C2211yescharacteristic
189C4×#107C2211yescharacteristic
190C4×#107C2211yescharacteristic
191C4×#106C2211yescharacteristic
192C8×C4⋊C4C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201C4×C22⋊C8C2211yescharacteristic
202#1735C2211yescharacteristic
203C23×C8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×#126—21no—
206C2×#125—21no—
207C2×#125C2311yescharacteristic
208C2×#123—21no—
209C2×#123D411yescharacteristic
210C2×C22⋊Q8—21no—
211C2×C22⋊Q8—21no—
212C2×#121C2311yescharacteristic
213C2×#121C2311yescharacteristic
214C2×C4×D4—21no—
215C2×C4×D4C2311yescharacteristic
216C2×C4×D4C2311yescharacteristic
217C2×C4×D4C2311yescharacteristic
218C2×C4×D4C2311yescharacteristic
219C2×#117—21no—
220C2×#117C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C22×C4⋊C4—21no—
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C42C2311yescharacteristic
226#482—24no—
227#481—24no—
228#478—24no—
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×C22⋊C8C2311yescharacteristic
261C2×C22⋊C8C2311yescharacteristic
262C2×C22⋊C8C2311yescharacteristic
263C2×C22⋊C8C2311yescharacteristic
264C2×C22⋊C8C2311yescharacteristic
265C2×C22⋊C8C2311yescharacteristic
266C2×C22⋊C8C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270C2×C4×C8C2311yescharacteristic
271C2×C4×C8C2311yescharacteristic
272C2×C4×C8C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
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#399—21no—
286#399—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#396—21no—
302#396—21no—
303#396—21no—
304#394—21no—
305#394—21no—
306#394—21no—
307#393—21no—
308#393—21no—
309#392—21no—
310#391—21no—
311#391—21no—
312#390—21no—
313#390C2311yescharacteristic
314#390C2311yescharacteristic
315#389—21no—
316#389—21no—
317#389—21no—
318#389—21no—
319#389—21no—
320#389C2311yescharacteristic
321#389C2311yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#388—21no—
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388D411yescharacteristic
348#388D411yescharacteristic
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
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#387D411yescharacteristic
366#387D411yescharacteristic
367#386—21no—
368#386—21no—
369#386—21no—
370#386—21no—
371#386—21no—
372#386—21no—
373#386—21no—
374#386D411yescharacteristic
375#385—21no—
376#385—21no—
377#385—21no—
378#385—21no—
379#385—21no—
380#385—21no—
381#385D411yescharacteristic
382#384C2311yescharacteristic
383#384C2311yescharacteristic
384#384C2311yescharacteristic
385#383—21no—
386#383—21no—
387#383—21no—
388#382—21no—
389#382—21no—
390#382—21no—
391#382—21no—
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#382C2311yescharacteristic
395#382C2311yescharacteristic
396#382C2311yescharacteristic
397#381—21no—
398#381D411yescharacteristic
399#380—21no—
400#380—21no—
401#380—21no—
402#380—21no—
403#380—21no—
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
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×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4C2311yescharacteristic
430C4×C22⋊C4C2311yescharacteristic
431C4×C22⋊C4C2311yescharacteristic
432#376—21no—
433C2×#95—21no—
434C2×#95—21no—
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#340C2311yescharacteristic
470#340C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4C2×D411yescharacteristic
485C22×D4C2411yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4C2×D411yescharacteristic
492C23×C4C2×D411yescharacteristic
493C23×C4C2411yescharacteristic
494C23×C4C2411yescharacteristic
495C22×C8—22no—
496C22×C8—41no—
497C22×C8—41no—
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C4⋊Q8—41no—
507C4⋊Q8—41no—
508#126—82no—
509#125—22no—
510#125—41no—
511#125—82no—
512#123—24no—
513#123—82no—
514C22⋊Q8—82no—
515C22⋊Q8—82no—
516#121—22no—
517#121—22no—
518#121—41no—
519#121—41no—
520C4×D4—22no—
521C4×D4—41no—
522C4×D4—41no—
523C4×D4—41no—
524C4×D4—41no—
525C4×D4—41no—
526C4×D4—41no—
527C4×D4—41no—
528C4×D4—44no—
529#117—22no—
530#117—41no—
531#117—44no—
532#117—41no—
533#117—41no—
534C2×C4⋊C4—22no—
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⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4—82no—
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C22⋊C4—21no—
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×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4C2×D411yescharacteristic
610C2×C22⋊C4C2×D411yescharacteristic
611C2×C22⋊C4C2×D411yescharacteristic
612C2×C22⋊C4C2×D411yescharacteristic
613C2×C22⋊C4C2×D411yescharacteristic
614C2×C22⋊C4C2×D411yescharacteristic
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—41no—
627C2×C42—41no—
628C2×C42C2×D411yescharacteristic
629C2×C42C2×D411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635#107—22no—
636#107—22no—
637#107—22no—
638#107—22no—
639#107—41no—
640#107—41no—
641#107—41no—
642#107—41no—
643#107—41no—
644#107—41no—
645#107—41no—
646#107—41no—
647#106—22no—
648#106—22no—
649#106—22no—
650#106—22no—
651#106—41no—
652#106—41no—
653#106—41no—
654#106—41no—
655C4⋊C8—22no—
656C4⋊C8—22no—
657C4⋊C8—41no—
658#102—22no—
659#102—22no—
660#102—22no—
661#102—22no—
662#102—22no—
663#102—41no—
664#102—41no—
665#102#4114yes—
666C22⋊C8—22no—
667C22⋊C8—22no—
668C22⋊C8—22no—
669C22⋊C8—22no—
670C22⋊C8—22no—
671C22⋊C8—41no—
672C22⋊C8—41no—
673C4×C8—22no—
674C4×C8—41no—
675C4×C8—41no—
676C4×C8—41no—
677C4×C8—41no—
678C4×C8—41no—
679C4×C8—41no—
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#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
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
735C24—21no—
736C24C22×D411yescharacteristic
737C24C22×D411yescharacteristic
738C2×Q8—42no—
739C2×Q8—81no—
740C2×Q8—81no—
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—21no—
746C2×D4—21no—
747C2×D4—41no—
748C2×D4—41no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4C2×#4112yes—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
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—22no—
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—21no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—81no—
794C22×C4—81no—
795C22×C4—81no—
796C22×C4—81no—
797C22×C4—81no—
798C22×C4—81no—
799C22×C4—81no—
800C22×C4—81no—
801C22×C4—81no—
802C22×C4—81no—
803C22×C4#13514yes—
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C2511yescharacteristic
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—82no—
839C2×C8C2×#4112yes—
840C2×C82−1+412yes—
841C2×C82−1+412yes—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—41no—
875C4⋊C4—41no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4C2×#4112yes—
906C22⋊C4—22no—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—22no—
910C22⋊C4—41no—
911C22⋊C4—41no—
912C22⋊C4—41no—
913C22⋊C4—41no—
914C22⋊C4—42no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—42no—
919C22⋊C4—42no—
920C22⋊C4—42no—
921C22⋊C4—42no—
922C22⋊C4—42no—
923C22⋊C4—81no—
924C22⋊C4—81no—
925C22⋊C4—81no—
926C22⋊C4—81no—
927C22⋊C4—81no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—41no—
946C42—41no—
947C42—42no—
948C42—42no—
949C42—42no—
950C42—42no—
951C42—81no—
952C42—81no—
953C42—81no—
954C42—81no—
955C42—81no—
956C23—21no—
957C23—21no—
958C23—21no—
959C23—21no—
960C23—21no—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—22no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23C2×#13512yes—
977C23C23×D411yescharacteristic
978Q8—162no—
979D4—22no—
980D4—22no—
981D4—41no—
982D4—41no—
983D4—82no—
984D4—84no—
985D4—162no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—22no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—44no—
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—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—82no—
1074C2×C4—84no—
1075C2×C4—162no—
1076C2×C4—162no—
1077C2×C4—162no—
1078C2×C4—162no—
1079C2×C4C2×#13512yes—
1080C2×C4C2×#13512yes—
1081C2×C4#57612yes—
1082C2×C4C22×#4111yescharacteristic
1083C2×C4C2×2−1+411yescharacteristic
1084C2×C4C2×2−1+411yescharacteristic
1085C2×C4#58511yescharacteristic
1086C2×C4#58511yescharacteristic
1087C2×C4#58511yescharacteristic
1088C8—22no—
1089C8—22no—
1090C8—22no—
1091C8—41no—
1092C8—41no—
1093C8—41no—
1094C8—41no—
1095C8—41no—
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—41no—
1100C22—41no—
1101C22—41no—
1102C22—41no—
1103C22—41no—
1104C22—41no—
1105C22—41no—
1106C22—41no—
1107C22—42no—
1108C22—41no—
1109C22—41no—
1110C22—42no—
1111C22—42no—
1112C22—41no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22D4×#4111yescharacteristic
1118C22#348511yescharacteristic
1119C22#349911yescharacteristic
1120C22C22×#13511yescharacteristic
1121C22C2×#57611yescharacteristic
1122C22#358411yescharacteristic
1123C22#358611yescharacteristic
1124C4—22no—
1125C4—22no—
1126C4—22no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—41no—
1131C4—41no—
1132C4—41no—
1133C4—42no—
1134C4—41no—
1135C4—41no—
1136C4—41no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4#350711yescharacteristic
1152C4#351511yescharacteristic
1153C4#355311yescharacteristic
1154C4#356411yescharacteristic
1155C2—42no—
1156C2—81no—
1157C2—82no—
1158C2#4349911yescharacteristic
1159C2#6142811yescharacteristic
1160C2#6155311yescharacteristic
1161C2#6169611yescharacteristic
1162C2#6177211yescharacteristic
1163C2#6247411yescharacteristic
1164C2#6252311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59288C2semidirect
3. #32464C2semidirect
4. #32317C2semidirect
6. #31455C2semidirect
7. #31432C2semidirect
8. #31423C2semidirect
9. #31092C2semidirect
10. #31088C2semidirect
11. #29296C2semidirect
12. #28943C2semidirect
13. #28841C2semidirect
14. #28831C2semidirect
15. #28773C2semidirect
16. #27992C2semidirect
17. #27875C2semidirect
18. #27838C2semidirect
19. #27462C2semidirect
20. #27455C2semidirect
21. #27302C2semidirect
22. #27159C2semidirect
23. #27038C2semidirect
24. #26864C2semidirect
26. #24934C2semidirect
27. #23754C2semidirect
28. #23294C2semidirect
29. #22966C2semidirect
30. #22921C2semidirect
31. #22076C2semidirect

Maximal subgroups

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

subgroupindex
#592882
#395292
#324642
#323172
#320042
#314552
#314322
#314232
#310922
#310882
#292962
#289432
#288412
#288312
#287732
#279922
#278752
#278382
#274622
#274552
#273022
#271592
#270382
#268642
#250182
#249342
#237542
#232942
#229662
#229212
#220762