Finite Group Databasebeta

← #7500000

Subgroups — #7500000

Order 512.

1236 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59459C211yesmaximal, characteristic, complemented
2#46347C211yesmaximal, characteristic
3#32689C211yesmaximal, characteristic, complemented
4#32643C211yesmaximal, characteristic
5#32593C211yesmaximal, characteristic
6#32583C211yesmaximal, characteristic, complemented
7#32251C211yesmaximal, characteristic, complemented
8#32231C211yesmaximal, characteristic
9#32156C211yesmaximal, characteristic, complemented
10#32132C211yesmaximal, characteristic, complemented
11#30961C211yesmaximal, characteristic, complemented
12#30959C211yesmaximal, characteristic
13#30832C211yesmaximal, characteristic
14#30823C211yesmaximal, characteristic
15#30153C211yesmaximal, characteristic
16#30147C211yesmaximal, characteristic, complemented
17#29522C211yesmaximal, characteristic, complemented
18#29518C211yesmaximal, characteristic
19#28681C211yesmaximal, characteristic, complemented
20#28651C211yesmaximal, characteristic
21#27139C211yesmaximal, characteristic
22#27128C211yesmaximal, characteristic, complemented
23#27014C211yesmaximal, characteristic
24#27008C211yesmaximal, characteristic, complemented
25#26880C211yesmaximal, characteristic, complemented
26#26875C211yesmaximal, characteristic, complemented
27#26717C211yesmaximal, characteristic
28#26691C211yesmaximal, characteristic
29#25486C211yesmaximal, characteristic
30#25480C211yesmaximal, characteristic, complemented
31#22244C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic
33C2×#489C2211yescharacteristic
34C2×#477C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#446C2211yescharacteristic
37C2×#446C2211yescharacteristic
38#2863C2211yescharacteristic
39#2860C2211yescharacteristic
40#2831—21no—
41#2792—21no—
42#2792—21no—
43#2777—21no—
44#2738—21no—
45#2729—21no—
46#2725—21no—
47#2722—21no—
48#2721—21no—
49#2592C2211yescharacteristic
50#2586—21no—
51#2586—21no—
52#2584C2211yescharacteristic
53#2584C2211yescharacteristic
54#2584C2211yescharacteristic
55#2582C2211yescharacteristic
56#2567—21no—
57#2567C2211yescharacteristic
58#2567C2211yescharacteristic
59#2552C2211yescharacteristic
60#2551C2211yescharacteristic
61#2550C2211yescharacteristic
62#2550C2211yescharacteristic
63#2538C2211yescharacteristic
64#2512C2211yescharacteristic
65#2511C2211yescharacteristic
66#2507C2211yescharacteristic
67#2506C2211yescharacteristic
68#2454C2211yescharacteristic
69#2453C2211yescharacteristic
70#2451—21no—
71#2451—21no—
72#2448C2211yescharacteristic
73#2447C2211yescharacteristic
74#2378—21no—
75#2370C2211yescharacteristic
76#2370C2211yescharacteristic
77#2365C2211yescharacteristic
78#2365C2211yescharacteristic
79Q8×C4⋊C4—21no—
80C4×C4⋊Q8C2211yescharacteristic
81C4×C4⋊Q8C2211yescharacteristic
82C4×#125C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2097C2211yescharacteristic
88#2093C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2086C2211yescharacteristic
95#2086C2211yescharacteristic
96#2086C2211yescharacteristic
97#2085C2211yescharacteristic
98#2084C2211yescharacteristic
99#2084C2211yescharacteristic
100#2083C2211yescharacteristic
101#2073C2211yescharacteristic
102#2072C2211yescharacteristic
103#2068C2211yescharacteristic
104#2067C2211yescharacteristic
105#2066C2211yescharacteristic
106#2066C2211yescharacteristic
107#2066C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2059C2211yescharacteristic
116#2058C2211yescharacteristic
117#2058C2211yescharacteristic
118#2058C2211yescharacteristic
119#2058C2211yescharacteristic
120#2057C2211yescharacteristic
121#2042C2211yescharacteristic
122#2042C2211yescharacteristic
123#2026C2211yescharacteristic
124#2026C2211yescharacteristic
125#2026C2211yescharacteristic
126#2025C2211yescharacteristic
127#2025C2211yescharacteristic
128#2024C2211yescharacteristic
129#2023C2211yescharacteristic
130#2023C2211yescharacteristic
131#1992C2211yescharacteristic
132#1990C2211yescharacteristic
133#1989C2211yescharacteristic
134#1989C2211yescharacteristic
135#1988C2211yescharacteristic
136#1985C2211yescharacteristic
137#1985C2211yescharacteristic
138#1983C2211yescharacteristic
139#1948C2211yescharacteristic
140#1948C2211yescharacteristic
141#1944C2211yescharacteristic
142#1944C2211yescharacteristic
143#1944C2211yescharacteristic
144#1944C2211yescharacteristic
145#1944C2211yescharacteristic
146#1944C2211yescharacteristic
147#1943C2211yescharacteristic
148#1941C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1935C2211yescharacteristic
152#1935C2211yescharacteristic
153#1935C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1933C2211yescharacteristic
157#1928C2211yescharacteristic
158#1927C2211yescharacteristic
159#1927C2211yescharacteristic
160#1927C2211yescharacteristic
161#1927C2211yescharacteristic
162#1927C2211yescharacteristic
163#1926C2211yescharacteristic
164#1926C2211yescharacteristic
165#1926C2211yescharacteristic
166#1926C2211yescharacteristic
167#1925C2211yescharacteristic
168#1925C2211yescharacteristic
169#1921C2211yescharacteristic
170#1921C2211yescharacteristic
171#1921C2211yescharacteristic
172#1921C2211yescharacteristic
173#1921C2211yescharacteristic
174#1920C2211yescharacteristic
175#1920C2211yescharacteristic
176#1920C2211yescharacteristic
177#1920C2211yescharacteristic
178#1920C2211yescharacteristic
179#1919C2211yescharacteristic
180#1919C2211yescharacteristic
181#1919C2211yescharacteristic
182#1919C2211yescharacteristic
183#1918C2211yescharacteristic
184#1918C2211yescharacteristic
185#1917C2211yescharacteristic
186#1917C2211yescharacteristic
187#1917C2211yescharacteristic
188#1917C2211yescharacteristic
189#1916C2211yescharacteristic
190#1916C2211yescharacteristic
191#1916C2211yescharacteristic
192#1916C2211yescharacteristic
193#1865C2211yescharacteristic
194#1864C2211yescharacteristic
195#1864C2211yescharacteristic
196#1863C2211yescharacteristic
197#1831C2211yescharacteristic
198#1776C2211yescharacteristic
199C4×#106C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#103C2211yescharacteristic
202#1745C2211yescharacteristic
203C2×C4⋊Q8—21no—
204C2×C4⋊Q8D411yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126—21no—
209C2×#126—21no—
210C2×#125—21no—
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×C22⋊Q8—21no—
217C2×C4×Q8—21no—
218C2×C4×Q8—21no—
219C2×C4×Q8—21no—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224#499—42no—
225#489—42no—
226#478—42no—
227#477—42no—
228#446—42no—
229#446—42no—
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#97C2311yescharacteristic
269C2×#97C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×#97C2311yescharacteristic
272C2×C4×C8C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#399—21no—
279#399—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#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#396—21no—
299#396—21no—
300#396—21no—
301#396—21no—
302#395—21no—
303#395—21no—
304#395—21no—
305#395—21no—
306#395—21no—
307#395—21no—
308#395—21no—
309#395—21no—
310#395—21no—
311#395—21no—
312#395—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#391D411yescharacteristic
323#391D411yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389D411yescharacteristic
351#389D411yescharacteristic
352#389D411yescharacteristic
353#389D411yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—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#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#385—21no—
403#385—21no—
404#384—21no—
405#384—21no—
406#384—21no—
407#384D411yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#383—21no—
412#382C2311yescharacteristic
413#381—21no—
414#380—21no—
415#380—21no—
416C4×C4⋊C4—21no—
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
435C43C2311yescharacteristic
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#336C2311yescharacteristic
469#336C2311yescharacteristic
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
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8C2×D411yescharacteristic
488C22×Q8C2×D411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4C2411yescharacteristic
491C23×C4—21no—
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C4⋊Q8—22no—
501C4⋊Q8—22no—
502C4⋊Q8—41no—
503C4⋊Q8—41no—
504C4⋊Q8—41no—
505C4⋊Q8—41no—
506C4⋊Q8—42no—
507C4⋊Q8—82no—
508#126—82no—
509#126—82no—
510#125—22no—
511#125—22no—
512#125—41no—
513#125—41no—
514#125—41no—
515#125—41no—
516#125—41no—
517#125—41no—
518#125—82no—
519#124—41no—
520#124—41no—
521C22⋊Q8—44no—
522C4×Q8—41no—
523C4×Q8—41no—
524C4×Q8—41no—
525C4×Q8—41no—
526C4×Q8—41no—
527C4×Q8—41no—
528C4×Q8—44no—
529C4×Q8—82no—
530C4×Q8—82no—
531C4×D4—41no—
532C4×D4—41no—
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⋊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⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
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×C42C2×D411yescharacteristic
626C2×C42C2×D411yescharacteristic
627C2×C42C2×D411yescharacteristic
628C2×C42C2×D411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636#107—22no—
637#107—22no—
638#107—22no—
639#107—22no—
640#107—41no—
641#107—41no—
642#106—22no—
643#106—22no—
644#106—22no—
645#106—22no—
646#106—22no—
647#106—22no—
648#106—41no—
649#106—41no—
650#106—41no—
651#106—41no—
652C4⋊C8—22no—
653C4⋊C8—22no—
654C4⋊C8—41no—
655C4⋊C8—41no—
656C4⋊C8—41no—
657C4⋊C8—41no—
658#103—22no—
659#103—22no—
660#103—22no—
661#103—22no—
662#103—22no—
663#103—41no—
664#103—41no—
665#103—41no—
666#102—22no—
667#102—22no—
668#102—22no—
669#102—22no—
670#102—22no—
671#102—41no—
672#102—41no—
673#102—41no—
674#97—22no—
675#97—22no—
676#97—41no—
677#97—41no—
678C4×C8—22no—
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#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732C24—21no—
733C2×Q8—24no—
734C2×Q8—22no—
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—41no—
742C2×Q8—41no—
743C2×Q8—41no—
744C2×Q8—41no—
745C2×Q8—41no—
746C2×Q8—42no—
747C2×Q8—42no—
748C2×Q8—81no—
749C2×Q8—81no—
750C2×Q8—81no—
751C2×Q8—81no—
752C2×Q8—81no—
753C2×Q8—81no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—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—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—42no—
776C22×C4—81no—
777C22×C4—81no—
778C22×C4C22×D411yescharacteristic
779C22×C4C22×D411yescharacteristic
780C22×C4C22×D411yescharacteristic
781C22×C4C22×D411yescharacteristic
782C22×C4C22×D411yescharacteristic
783C22×C4C22×D411yescharacteristic
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D411yescharacteristic
788C22×C4C22×D411yescharacteristic
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C2511yescharacteristic
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×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×C8H(5,𝔽2)12yes—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—22no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—41no—
849C4⋊C4—41no—
850C4⋊C4—41no—
851C4⋊C4—41no—
852C4⋊C4—41no—
853C4⋊C4—41no—
854C4⋊C4—41no—
855C4⋊C4—41no—
856C4⋊C4—41no—
857C4⋊C4—41no—
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—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C42−1+412yes—
896C4⋊C42−1+412yes—
897C4⋊C42−1+412yes—
898C4⋊C42−1+412yes—
899C22⋊C4—42no—
900C22⋊C4—42no—
901C22⋊C4—42no—
902C22⋊C4—42no—
903C22⋊C4—81no—
904C22⋊C4—81no—
905C22⋊C4—81no—
906C22⋊C4—81no—
907C22⋊C4—81no—
908C22⋊C4—81no—
909C22⋊C4—81no—
910C22⋊C4—81no—
911C22⋊C4—81no—
912C42—22no—
913C42—21no—
914C42—21no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—21no—
926C42—21no—
927C42—41no—
928C42—41no—
929C42—41no—
930C42—42no—
931C42—42no—
932C42—42no—
933C42—42no—
934C42—81no—
935C42—81no—
936C42—81no—
937C42—81no—
938C42—81no—
939C42—81no—
940C42—81no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23C23×D411yescharacteristic
949Q8—48no—
950Q8—41no—
951Q8—41no—
952Q8—41no—
953Q8—41no—
954Q8—82no—
955Q8—82no—
956Q8—162no—
957Q8—162no—
958D4—41no—
959D4—41no—
960D4—41no—
961D4—41no—
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—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
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—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
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—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—162no—
1048C2×C4#57512yes—
1049C2×C4#57712yes—
1050C2×C4C2×H(5,𝔽2)11yescharacteristic
1051C2×C4C2×2−1+411yescharacteristic
1052C2×C4C2×2−1+411yescharacteristic
1053C2×C4C2×2−1+411yescharacteristic
1054C2×C4C2×2−1+411yescharacteristic
1055C2×C4#58511yescharacteristic
1056C8—22no—
1057C8—41no—
1058C8—41no—
1059C8—41no—
1060C8—41no—
1061C8—41no—
1062C8—41no—
1063C8—41no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—81no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22#348611yescharacteristic
1072C22#348611yescharacteristic
1073C22#349611yescharacteristic
1074C22C2×#57511yescharacteristic
1075C22C2×#57711yescharacteristic
1076C22#358511yescharacteristic
1077C22#358611yescharacteristic
1078C4—22no—
1079C4—22no—
1080C4—41no—
1081C4—41no—
1082C4—41no—
1083C4—41no—
1084C4—41no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—41no—
1089C4—41no—
1090C4—41no—
1091C4—41no—
1092C4—41no—
1093C4—41no—
1094C4—42no—
1095C4—41no—
1096C4—81no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—81no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4#354411yescharacteristic
1108C4#355011yescharacteristic
1109C4#355511yescharacteristic
1110C4#355511yescharacteristic
1111C2—161no—
1112C2#5207911yescharacteristic
1113C2#6183311yescharacteristic
1114C2#6184111yescharacteristic
1115C2#6185811yescharacteristic
1116C2#6187411yescharacteristic
1117C2#6230211yescharacteristic
1118C2#6235511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59459C2semidirect
3. #32689C2semidirect
6. #32583C2semidirect
7. #32251C2semidirect
9. #32156C2semidirect
10. #32132C2semidirect
11. #30961C2semidirect
16. #30147C2semidirect
17. #29522C2semidirect
19. #28681C2semidirect
22. #27128C2semidirect
24. #27008C2semidirect
25. #26880C2semidirect
26. #26875C2semidirect
30. #25480C2semidirect
31. #22244C2semidirect

Maximal subgroups

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

subgroupindex
#594592
#463472
#326892
#326432
#325932
#325832
#322512
#322312
#321562
#321322
#309612
#309592
#308322
#308232
#301532
#301472
#295222
#295182
#286812
#286512
#271392
#271282
#270142
#270082
#268802
#268752
#267172
#266912
#254862
#254802
#222442