Finite Group Databasebeta

← #7189028

Subgroups — #7189028

Order 512.

1459 conjugacy classes of subgroups.

The subgroup lattice has 1207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59247C211yesmaximal, characteristic, complemented
2#59036C211yesmaximal, characteristic, complemented
3#32243C211yesmaximal, characteristic, complemented
4#32227C211yesmaximal, characteristic, complemented
5#31819C211yesmaximal, characteristic, complemented
6#31814C211yesmaximal, characteristic, complemented
7#31767C211yesmaximal, characteristic, complemented
8#31751C211yesmaximal, characteristic, complemented
9#31451C211yesmaximal, characteristic, complemented
10#31427C211yesmaximal, characteristic, complemented
11#27826C211yesmaximal, characteristic, complemented
12#27633C211yesmaximal, characteristic, complemented
13#27124C211yesmaximal, characteristic, complemented
14#27106C211yesmaximal, characteristic, complemented
15#27014C211yesmaximal, characteristic, complemented
16#27006C211yesmaximal, characteristic, complemented
17#26747C211yesmaximal, characteristic
18#26729C211yesmaximal, characteristic
19#26455C211yesmaximal, characteristic, complemented
20#26455C211yesmaximal, characteristic, complemented
21#26449C211yesmaximal, characteristic, complemented
22#26293C211yesmaximal, characteristic, complemented
23#25481C211yesmaximal, characteristic, complemented
24#24693C211yesmaximal, characteristic, complemented
25#24338C211yesmaximal, characteristic, complemented
26#24300C211yesmaximal, characteristic, complemented
27#23708C211yesmaximal, characteristic
28#23075C211yesmaximal, characteristic, complemented
29#22523C211yesmaximal, characteristic, complemented
30#22106C211yesmaximal, characteristic, complemented
31#21842C211yesmaximal, characteristic, complemented
32C2×D4×Q8C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#476C2211yescharacteristic
35C2×#474C2211yescharacteristic
36C2×#446C2211yescharacteristic
37C2×#442C2211yescharacteristic
38C2×#432C2211yescharacteristic
39#2740—21no—
40#2700—21no—
41#2692—21no—
42#2692—21no—
43#2604—21no—
44#2580C2211yescharacteristic
45#2573—21no—
46#2567C2211yescharacteristic
47#2563C2211yescharacteristic
48#2550C2211yescharacteristic
49#2550C2211yescharacteristic
50#2550C2211yescharacteristic
51#2538—21no—
52#2532—21no—
53#2523—21no—
54#2513C2211yescharacteristic
55#2512C2211yescharacteristic
56#2497C2211yescharacteristic
57#2495C2211yescharacteristic
58#2491C2211yescharacteristic
59#2490C2211yescharacteristic
60#2466—21no—
61#2465—21no—
62#2465—21no—
63#2454C2211yescharacteristic
64#2454C2211yescharacteristic
65#2439C2211yescharacteristic
66#2439C2211yescharacteristic
67#2423—21no—
68#2409—21no—
69#2370C2211yescharacteristic
70#2367—21no—
71#2365C2211yescharacteristic
72#2365C2211yescharacteristic
73#2363C2211yescharacteristic
74#2363C2211yescharacteristic
75#2357C2211yescharacteristic
76#2355C2211yescharacteristic
77Q8×C22⋊C4—21no—
78C4×C22⋊Q8C2211yescharacteristic
79C4×#121C2211yescharacteristic
80C4×#121C2211yescharacteristic
81#2283C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2100C2211yescharacteristic
86#2088C2211yescharacteristic
87#2088C2211yescharacteristic
88#2087C2211yescharacteristic
89#2086C2211yescharacteristic
90#2086C2211yescharacteristic
91#2085C2211yescharacteristic
92#2083C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2075C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic
100#2065C2211yescharacteristic
101#2065C2211yescharacteristic
102#2059C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2058C2211yescharacteristic
106#2058C2211yescharacteristic
107#2058C2211yescharacteristic
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic
110#2054C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2033C2211yescharacteristic
114#2033C2211yescharacteristic
115#2025C2211yescharacteristic
116#2025C2211yescharacteristic
117#2025C2211yescharacteristic
118#2023C2211yescharacteristic
119#2023C2211yescharacteristic
120#2023C2211yescharacteristic
121#1999C2211yescharacteristic
122#1993C2211yescharacteristic
123#1993C2211yescharacteristic
124#1993C2211yescharacteristic
125#1993C2211yescharacteristic
126#1993C2211yescharacteristic
127#1993C2211yescharacteristic
128#1991C2211yescharacteristic
129#1990C2211yescharacteristic
130#1989C2211yescharacteristic
131#1989C2211yescharacteristic
132#1989C2211yescharacteristic
133#1989C2211yescharacteristic
134#1989C2211yescharacteristic
135#1988C2211yescharacteristic
136#1988C2211yescharacteristic
137#1987C2211yescharacteristic
138#1987C2211yescharacteristic
139#1987C2211yescharacteristic
140#1985C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1949C2211yescharacteristic
144#1949C2211yescharacteristic
145#1944C2211yescharacteristic
146#1942C2211yescharacteristic
147#1940C2211yescharacteristic
148#1940C2211yescharacteristic
149#1939C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic
152#1936C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic
166#1921C2211yescharacteristic
167#1921C2211yescharacteristic
168#1920C2211yescharacteristic
169#1920C2211yescharacteristic
170#1920C2211yescharacteristic
171#1920C2211yescharacteristic
172#1919C2211yescharacteristic
173#1919C2211yescharacteristic
174#1918C2211yescharacteristic
175#1918C2211yescharacteristic
176#1917C2211yescharacteristic
177#1916C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic
180#1875C2211yescharacteristic
181#1875C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1854C2211yescharacteristic
185#1854C2211yescharacteristic
186#1825C2211yescharacteristic
187#1825C2211yescharacteristic
188#1825C2211yescharacteristic
189#1825C2211yescharacteristic
190#1804C2211yescharacteristic
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic
193#1802C2211yescharacteristic
194#1797C2211yescharacteristic
195#1776C2211yescharacteristic
196#1776C2211yescharacteristic
197C4×#106C2211yescharacteristic
198#1771C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201#1762C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C23×Q8—21no—
204C22×D8C2311yescharacteristic
205D4×Q8—24no—
206D4×Q8—42no—
207#533—24no—
208#533—42no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#126—21no—
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#124—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8D411yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×C4×Q8—21no—
228C2×C4×Q8—21no—
229C2×C4×Q8—21no—
230C2×C4×Q8—21no—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C22×C42C2311yescharacteristic
241#476—24no—
242#474—42no—
243#446—42no—
244#442—42no—
245#432—42no—
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289#400—21no—
290#400—21no—
291#399—21no—
292#399—21no—
293#399—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#396—21no—
303#396—21no—
304#396—21no—
305#396—21no—
306#396—21no—
307#396—21no—
308#395—21no—
309#395—21no—
310#395—21no—
311#395—21no—
312#395—21no—
313#394—21no—
314#394—21no—
315#393—21no—
316#393—21no—
317#393—21no—
318#393—21no—
319#393—21no—
320#393—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391D411yescharacteristic
331#390—21no—
332#390—21no—
333#390—21no—
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389D411yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—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#387D411yescharacteristic
384#387D411yescharacteristic
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385D411yescharacteristic
394#385D411yescharacteristic
395#384—21no—
396#384C2311yescharacteristic
397#383—21no—
398#383—21no—
399#382C2311yescharacteristic
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#381—21no—
405#381—21no—
406#380—21no—
407#380—21no—
408#380—21no—
409#380—21no—
410#380D411yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
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
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4C2311yescharacteristic
437C4×C22⋊C4C2311yescharacteristic
438#376—21no—
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#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—44no—
493C22×Q8—44no—
494C22×Q8—82no—
495C22×Q8C2×D411yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C2411yescharacteristic
499C22×D4C2411yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4C2×D411yescharacteristic
505C23×C4C2×D411yescharacteristic
506C23×C4C2411yescharacteristic
507C2×D8—22no—
508C2×D8—41no—
509C2×D8—41no—
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C4⋊Q8—22no—
519C4⋊Q8—22no—
520C4⋊Q8—22no—
521C4⋊Q8—22no—
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8#4114yes—
528#126—82no—
529#125—22no—
530#125—22no—
531#125—22no—
532#125—41no—
533#125—41no—
534#125—41no—
535#124—44no—
536C22⋊Q8—42no—
537C22⋊Q8—44no—
538C22⋊Q8—44no—
539C22⋊Q8—44no—
540C22⋊Q8—44no—
541C22⋊Q8—44no—
542#121—22no—
543#121—22no—
544#121—22no—
545#121—41no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—44no—
549C4×Q8—44no—
550C4×Q8—82no—
551C4×Q8—82no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—41no—
559C4×D4—41no—
560C4×D4—82no—
561C4×D4—82no—
562#117—22no—
563#117—22no—
564#117—41no—
565#117—41no—
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⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C42—22no—
647C2×C42—22no—
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×C42—21no—
659C2×C42—21no—
660C2×C42C2×D411yescharacteristic
661C2×C42C2×D411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668#107—22no—
669#107—22no—
670#107—41no—
671#107—41no—
672#107—41no—
673#106—22no—
674#106—22no—
675#106—22no—
676#106—22no—
677#106—41no—
678#106—41no—
679C4⋊C8—22no—
680C4⋊C8—22no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686C4⋊C8—41no—
687#102—22no—
688#102—22no—
689#102—22no—
690#102—22no—
691#102—22no—
692#102—22no—
693#102—22no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701C22⋊C8—41no—
702C22⋊C8—41no—
703C22⋊C8—41no—
704C22⋊C8—41no—
705#97—22no—
706#97—22no—
707#97—41no—
708#97—41no—
709C4×C8—41no—
710C4×C8—41no—
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#95—21no—
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
757C24—21no—
758C24—21no—
759C24C22×D411yescharacteristic
760C2×Q8—22no—
761C2×Q8—24no—
762C2×Q8—22no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—42no—
767C2×Q8—42no—
768C2×Q8—42no—
769C2×Q8—42no—
770C2×Q8—42no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—81no—
774C2×Q8—81no—
775C2×Q8—81no—
776C2×Q8—81no—
777C2×Q8—81no—
778C2×Q8—816no—
779C2×D4—24no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—42no—
792C2×D4—42no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D42−1+412yes—
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—22no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C2511yescharacteristic
849D8—44no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C4⋊C4—24no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—41no—
904C4⋊C4—41no—
905C4⋊C4—41no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
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⋊C4—81no—
932C4⋊C4C2×#4112yes—
933C4⋊C4C2×#4112yes—
934C4⋊C42−1+412yes—
935C4⋊C42−1+412yes—
936C22⋊C4—24no—
937C22⋊C4—22no—
938C22⋊C4—41no—
939C22⋊C4—41no—
940C22⋊C4—41no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C42—22no—
969C42—22no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—42no—
981C42—42no—
982C42—42no—
983C42—42no—
984C42—42no—
985C42—81no—
986C42—81no—
987C42—81no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42C2×#4112yes—
993C42H(5,𝔽2)12yes—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—22no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23C23×D411yescharacteristic
1016Q8—44no—
1017Q8—48no—
1018Q8—84no—
1019Q8—84no—
1020Q8—84no—
1021Q8—84no—
1022D4—22no—
1023D4—22no—
1024D4—41no—
1025D4—41no—
1026D4—41no—
1027D4—41no—
1028D4—41no—
1029D4—41no—
1030D4—84no—
1031D4—84no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
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—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—82no—
1115C2×C4—82no—
1116C2×C4—84no—
1117C2×C4—84no—
1118C2×C4—84no—
1119C2×C4—162no—
1120C2×C4#54612yes—
1121C2×C4#54612yes—
1122C2×C4#57512yes—
1123C2×C4C22×#4111yescharacteristic
1124C2×C4C2×H(5,𝔽2)11yescharacteristic
1125C2×C4C2×2−1+411yescharacteristic
1126C2×C4C2×2−1+411yescharacteristic
1127C2×C4C2×2−1+411yescharacteristic
1128C2×C4#58511yescharacteristic
1129C8—41no—
1130C8—41no—
1131C8—41no—
1132C8—41no—
1133C8—41no—
1134C8—41no—
1135C8—41no—
1136C8—41no—
1137C22—41no—
1138C22—41no—
1139C22—42no—
1140C22—41no—
1141C22—41no—
1142C22—42no—
1143C22—41no—
1144C22—41no—
1145C22—41no—
1146C22—42no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22—81no—
1154C22—81no—
1155C22—81no—
1156C22—81no—
1157C22—81no—
1158C22C2×#54611yescharacteristic
1159C22#348611yescharacteristic
1160C22#348911yescharacteristic
1161C22C2×#57511yescharacteristic
1162C22#358411yescharacteristic
1163C22#358511yescharacteristic
1164C22#358511yescharacteristic
1165C4—22no—
1166C4—22no—
1167C4—22no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—41no—
1173C4—42no—
1174C4—42no—
1175C4—41no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—42no—
1180C4—42no—
1181C4—41no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4#351811yescharacteristic
1193C4#352311yescharacteristic
1194C4#354111yescharacteristic
1195C4#355011yescharacteristic
1196C2—81no—
1197C2—82no—
1198C2—161no—
1199C2#4529111yescharacteristic
1200C2#6115611yescharacteristic
1201C2#6118911yescharacteristic
1202C2#6183911yescharacteristic
1203C2#6187211yescharacteristic
1204C2#6212211yescharacteristic
1205C2#6217311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#1999C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59247C2semidirect
2. #59036C2semidirect
3. #32243C2semidirect
4. #32227C2semidirect
5. #31819C2semidirect
6. #31814C2semidirect
7. #31767C2semidirect
8. #31751C2semidirect
9. #31451C2semidirect
10. #31427C2semidirect
11. #27826C2semidirect
12. #27633C2semidirect
13. #27124C2semidirect
14. #27106C2semidirect
15. #27014C2semidirect
16. #27006C2semidirect
19. #26455C2semidirect
20. #26455C2semidirect
21. #26449C2semidirect
22. #26293C2semidirect
23. #25481C2semidirect
24. #24693C2semidirect
25. #24338C2semidirect
26. #24300C2semidirect
28. #23075C2semidirect
29. #22523C2semidirect
30. #22106C2semidirect
31. #21842C2semidirect

Maximal subgroups

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

subgroupindex
#592472
#590362
#322432
#322272
#318192
#318142
#317672
#317512
#314512
#314272
#278262
#276332
#271242
#271062
#270142
#270062
#267472
#267292
#264552
#264492
#262932
#254812
#246932
#243382
#243002
#237082
#230752
#225232
#221062
#218422