Finite Group Databasebeta

← #7234085

Subgroups — #7234085

Order 512.

1317 conjugacy classes of subgroups.

The subgroup lattice has 1157 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53113C211yesmaximal, characteristic
2#35957C211yesmaximal, characteristic, complemented
3#33091C211yesmaximal, characteristic, complemented
4#33089C211yesmaximal, characteristic
5#32846C211yesmaximal, characteristic, complemented
6#32845C211yesmaximal, characteristic
7#32695C211yesmaximal, characteristic, complemented
8#32638C211yesmaximal, characteristic
9#32594C211yesmaximal, characteristic, complemented
10#32572C211yesmaximal, characteristic
11#32255C211yesmaximal, characteristic, complemented
12#32241C211yesmaximal, characteristic
13#32160C211yesmaximal, characteristic, complemented
14#32144C211yesmaximal, characteristic, complemented
15#30976C211yesmaximal, characteristic, complemented
16#30967C211yesmaximal, characteristic
17#30830C211yesmaximal, characteristic
18#30823C211yesmaximal, characteristic
19#27580C211yesmaximal, characteristic, complemented
20#27577C211yesmaximal, characteristic
21#27316C211yesmaximal, characteristic, complemented
22#27311C211yesmaximal, characteristic, complemented
23#26385C211yesmaximal, characteristic
24#26369C211yesmaximal, characteristic, complemented
25#26177C211yesmaximal, characteristic
26#26169C211yesmaximal, characteristic
27#25941C211yesmaximal, characteristic
28#25848C211yesmaximal, characteristic, complemented
29#24346C211yesmaximal, characteristic
30#24336C211yesmaximal, characteristic, complemented
31#23368C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#489C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#475C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×C4×Q16C2211yescharacteristic
42#2838—21no—
43#2831—21no—
44#2831—21no—
45#2817—21no—
46#2793—21no—
47#2745—21no—
48#2720—21no—
49#2690—21no—
50#2660—21no—
51#2660C2211yescharacteristic
52#2645C2211yescharacteristic
53#2644C2211yescharacteristic
54#2592C2211yescharacteristic
55#2584—21no—
56#2584C2211yescharacteristic
57#2581C2211yescharacteristic
58#2567—21no—
59#2567C2211yescharacteristic
60#2567C2211yescharacteristic
61#2552—21no—
62#2552—21no—
63#2552C2211yescharacteristic
64#2552C2211yescharacteristic
65#2550—21no—
66#2550—21no—
67#2550C2211yescharacteristic
68#2550C2211yescharacteristic
69#2538C2211yescharacteristic
70#2513C2211yescharacteristic
71#2511C2211yescharacteristic
72#2509C2211yescharacteristic
73#2506C2211yescharacteristic
74#2452C2211yescharacteristic
75#2451C2211yescharacteristic
76#2448C2211yescharacteristic
77#2447C2211yescharacteristic
78#2399—21no—
79#2399C2211yescharacteristic
80#2351C2211yescharacteristic
81#2351C2211yescharacteristic
82Q8×C4⋊C4C2211yescharacteristic
83Q8×C4⋊C4C2211yescharacteristic
84#2276C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2100C2211yescharacteristic
89#2100C2211yescharacteristic
90#2099C2211yescharacteristic
91#2097C2211yescharacteristic
92#2095C2211yescharacteristic
93#2093C2211yescharacteristic
94#2092C2211yescharacteristic
95#2087C2211yescharacteristic
96#2086C2211yescharacteristic
97#2086C2211yescharacteristic
98#2086C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2084C2211yescharacteristic
103#2083C2211yescharacteristic
104#2083C2211yescharacteristic
105#2074C2211yescharacteristic
106#2073C2211yescharacteristic
107#2072C2211yescharacteristic
108#2071C2211yescharacteristic
109#2067C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2065C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2058C2211yescharacteristic
118#2058C2211yescharacteristic
119#2057C2211yescharacteristic
120#2057C2211yescharacteristic
121#2057C2211yescharacteristic
122#2057C2211yescharacteristic
123#2042C2211yescharacteristic
124#2042C2211yescharacteristic
125#2026C2211yescharacteristic
126#2026C2211yescharacteristic
127#2026C2211yescharacteristic
128#2025C2211yescharacteristic
129#2025C2211yescharacteristic
130#2025C2211yescharacteristic
131#2024C2211yescharacteristic
132#2023C2211yescharacteristic
133#1992C2211yescharacteristic
134#1991C2211yescharacteristic
135#1989C2211yescharacteristic
136#1987C2211yescharacteristic
137#1985C2211yescharacteristic
138#1985C2211yescharacteristic
139#1985C2211yescharacteristic
140#1984C2211yescharacteristic
141#1944C2211yescharacteristic
142#1944C2211yescharacteristic
143#1943C2211yescharacteristic
144#1941C2211yescharacteristic
145#1936C2211yescharacteristic
146#1935C2211yescharacteristic
147#1935C2211yescharacteristic
148#1934C2211yescharacteristic
149#1928C2211yescharacteristic
150#1927C2211yescharacteristic
151#1927C2211yescharacteristic
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1921C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1920C2211yescharacteristic
160#1920C2211yescharacteristic
161#1920C2211yescharacteristic
162#1919C2211yescharacteristic
163#1919C2211yescharacteristic
164#1918C2211yescharacteristic
165#1917C2211yescharacteristic
166#1917C2211yescharacteristic
167#1917C2211yescharacteristic
168#1917C2211yescharacteristic
169#1917C2211yescharacteristic
170#1917C2211yescharacteristic
171#1916C2211yescharacteristic
172#1916C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic
177#1880C2211yescharacteristic
178#1878C2211yescharacteristic
179#1878C2211yescharacteristic
180#1878C2211yescharacteristic
181#1878C2211yescharacteristic
182#1878C2211yescharacteristic
183#1865C2211yescharacteristic
184#1865C2211yescharacteristic
185#1865C2211yescharacteristic
186#1865C2211yescharacteristic
187#1865C2211yescharacteristic
188#1865C2211yescharacteristic
189#1864C2211yescharacteristic
190#1863C2211yescharacteristic
191#1863C2211yescharacteristic
192#1863C2211yescharacteristic
193#1863C2211yescharacteristic
194#1863C2211yescharacteristic
195#1863C2211yescharacteristic
196#1862C2211yescharacteristic
197#1840C2211yescharacteristic
198#1840C2211yescharacteristic
199#1805C2211yescharacteristic
200#1803C2211yescharacteristic
201#1763C2211yescharacteristic
202#1763C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205#557—42no—
206#557—42no—
207#557—42no—
208#557—42no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#125—21no—
215C2×#125—21no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#125—21no—
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C4×Q8—21no—
227C2×C4×Q8—21no—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239#501—42no—
240#489—42no—
241#479—42no—
242#478—42no—
243#475—42no—
244#464—42no—
245#440—42no—
246C4×Q16—42no—
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289#401—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#399—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#398D411yescharacteristic
312#398D411yescharacteristic
313#398D411yescharacteristic
314#398D411yescharacteristic
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#395—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#395—21no—
334#395—21no—
335#395—21no—
336#395—21no—
337#395—21no—
338#395—21no—
339#395D411yescharacteristic
340#395D411yescharacteristic
341#395D411yescharacteristic
342#395D411yescharacteristic
343#393—21no—
344#393—21no—
345#391—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#385—21no—
407#385—21no—
408#384—21no—
409#384—21no—
410#384—21no—
411#384—21no—
412#384—21no—
413#384—21no—
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#382—21no—
418#382—21no—
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#381—21no—
423#380—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440#376—21no—
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#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8C2×D411yescharacteristic
494C22×Q8C2×D411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×D4C2411yescharacteristic
498C23×C4—21no—
499C2×Q16—22no—
500C2×Q16—22no—
501C2×Q16—22no—
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—22no—
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C4⋊Q8—22no—
514C4⋊Q8—41no—
515C4⋊Q8—41no—
516C4⋊Q8—41no—
517C4⋊Q8—41no—
518C4⋊Q8—41no—
519C4⋊Q8—44no—
520C4⋊Q8—44no—
521#125—22no—
522#125—22no—
523#125—22no—
524#125—41no—
525#125—41no—
526#125—41no—
527#125—41no—
528#125—41no—
529#125—44no—
530#125—44no—
531#125—44no—
532#125—44no—
533#125—82no—
534#124—41no—
535#124—41no—
536C22⋊Q8—82no—
537C22⋊Q8—82no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×Q8—41no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×Q8—44no—
557C4×Q8—44no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×D4—41no—
561C4×D4—41no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665#107—22no—
666#107—41no—
667#107—41no—
668#107—41no—
669#107—41no—
670#107—41no—
671#107—41no—
672#106—22no—
673#106—22no—
674#106—22no—
675#106—22no—
676#106—22no—
677#106—41no—
678#106—41no—
679C4⋊C8—41no—
680C4⋊C8—41no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683#103—22no—
684#103—22no—
685#103—22no—
686#103—22no—
687#103—22no—
688#103—22no—
689#103—22no—
690#103—22no—
691#103—22no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#97—41no—
704#97—41no—
705#97—41no—
706C4×C8—41no—
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#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758C24—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—41no—
769C2×Q8—41no—
770C2×Q8—41no—
771C2×Q8—41no—
772C2×Q8—41no—
773C2×Q8—41no—
774C2×Q8—42no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×Q8—81no—
778C2×Q8—81no—
779C2×Q8—81no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×Q8H(5,𝔽2)12yes—
784C2×Q82−1+412yes—
785C2×Q82−1+412yes—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—42no—
808C22×C4—81no—
809C22×C4—81no—
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C2511yescharacteristic
825Q16—44no—
826SD16—44no—
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—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
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—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—41no—
878C4⋊C4—41no—
879C4⋊C4—41no—
880C4⋊C4—41no—
881C4⋊C4—41no—
882C4⋊C4—41no—
883C4⋊C4—41no—
884C4⋊C4—41no—
885C4⋊C4—41no—
886C4⋊C4—41no—
887C4⋊C4—41no—
888C4⋊C4—41no—
889C4⋊C4—41no—
890C4⋊C4—41no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4H(5,𝔽2)12yes—
932C4⋊C42−1+412yes—
933C4⋊C42−1+412yes—
934C22⋊C4—42no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—42no—
965C42—42no—
966C42—42no—
967C42—42no—
968C42—81no—
969C42—81no—
970C42—81no—
971C42—81no—
972C42—81no—
973C42—81no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23C23×D411yescharacteristic
982Q8—22no—
983Q8—22no—
984Q8—22no—
985Q8—41no—
986Q8—41no—
987Q8—41no—
988Q8—41no—
989Q8—82no—
990Q8—82no—
991Q8—84no—
992Q8—84no—
993Q8—162no—
994Q8#56314yes—
995D4—41no—
996D4—41no—
997D4—41no—
998D4—41no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—21no—
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—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—22no—
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—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—162no—
1087C2×C4C2×H(5,𝔽2)11yescharacteristic
1088C2×C4C2×H(5,𝔽2)11yescharacteristic
1089C2×C4C2×2−1+411yescharacteristic
1090C2×C4C2×2−1+411yescharacteristic
1091C2×C4C2×2−1+411yescharacteristic
1092C2×C4C2×2−1+411yescharacteristic
1093C8—41no—
1094C8—41no—
1095C8—41no—
1096C8—41no—
1097C8—41no—
1098C8—41no—
1099C8—41no—
1100C8—41no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22#348411yescharacteristic
1109C22#348611yescharacteristic
1110C22#348611yescharacteristic
1111C22#358411yescharacteristic
1112C22#358511yescharacteristic
1113C22#358611yescharacteristic
1114C22#358611yescharacteristic
1115C4—24no—
1116C4—41no—
1117C4—41no—
1118C4—42no—
1119C4—41no—
1120C4—41no—
1121C4—41no—
1122C4—41no—
1123C4—41no—
1124C4—41no—
1125C4—41no—
1126C4—42no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—41no—
1131C4—41no—
1132C4—42no—
1133C4—81no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4C2×#56311yescharacteristic
1145C4#354411yescharacteristic
1146C4#355211yescharacteristic
1147C4#355211yescharacteristic
1148C2—161no—
1149C2#4632511yescharacteristic
1150C2#6161611yescharacteristic
1151C2#6165511yescharacteristic
1152C2#6185611yescharacteristic
1153C2#6186211yescharacteristic
1154C2#6187411yescharacteristic
1155C2#6187811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35957C2semidirect
3. #33091C2semidirect
5. #32846C2semidirect
7. #32695C2semidirect
9. #32594C2semidirect
11. #32255C2semidirect
13. #32160C2semidirect
14. #32144C2semidirect
15. #30976C2semidirect
19. #27580C2semidirect
21. #27316C2semidirect
22. #27311C2semidirect
24. #26369C2semidirect
28. #25848C2semidirect
30. #24336C2semidirect
31. #23368C2semidirect

Maximal subgroups

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

subgroupindex
#531132
#359572
#330912
#330892
#328462
#328452
#326952
#326382
#325942
#325722
#322552
#322412
#321602
#321442
#309762
#309672
#308302
#308232
#275802
#275772
#273162
#273112
#263852
#263692
#261772
#261692
#259412
#258482
#243462
#243362
#233682