Finite Group Databasebeta

← #7007665

Subgroups — #7007665

Order 512.

1656 conjugacy classes of subgroups.

The subgroup lattice has 1305 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59425C211yesmaximal, characteristic, complemented
2#39367C211yesmaximal, characteristic
3#32621C211yesmaximal, characteristic, complemented
4#32556C211yesmaximal, characteristic, complemented
5#32448C211yesmaximal, characteristic, complemented
6#31827C211yesmaximal, characteristic, complemented
7#31811C211yesmaximal, characteristic, complemented
8#31636C211yesmaximal, characteristic, complemented
9#31165C211yesmaximal, characteristic, complemented
10#31165C211yesmaximal, characteristic, complemented
11#29111C211yesmaximal, characteristic, complemented
12#29091C211yesmaximal, characteristic, complemented
13#28199C211yesmaximal, characteristic, complemented
14#27713C211yesmaximal, characteristic, complemented
15#27435C211yesmaximal, characteristic, complemented
16#27258C211yesmaximal, characteristic, complemented
17#26919C211yesmaximal, characteristic, complemented
18#26836C211yesmaximal, characteristic, complemented
19#25988C211yesmaximal, characteristic, complemented
20#25963C211yesmaximal, characteristic, complemented
21#25320C211yesmaximal, characteristic, complemented
22#25301C211yesmaximal, characteristic, complemented
23#24837C211yesmaximal, characteristic, complemented
24#24694C211yesmaximal, characteristic, complemented
25#24527C211yesmaximal, characteristic
26#24358C211yesmaximal, characteristic
27C2×#2055C211yesmaximal, characteristic
28#22954C211yesmaximal, characteristic, complemented
29#22570C211yesmaximal, characteristic
30#22437C211yesmaximal, characteristic
31#22049C211yesmaximal, characteristic
32C23×SD16C2211yescharacteristic
33C2×#543—21no—
34C2×#487C2211yescharacteristic, complemented
35C2×#477C2211yescharacteristic, complemented
36C2×#477C2211yescharacteristic, complemented
37C2×#461C2211yescharacteristic
38C2×#461C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#446C2211yescharacteristic, complemented
41C2×#440C2211yescharacteristic
42C2×#440C2211yescharacteristic
43C22×C4⋊C8C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#102C2211yescharacteristic
46#2857C2211yescharacteristic
47#2789—21no—
48#2758—21no—
49#2732—21no—
50#2692—21no—
51#2692—21no—
52#2683—21no—
53#2626—21no—
54#2605—21no—
55#2588—21no—
56#2581C2211yescharacteristic, complemented
57#2568C2211yescharacteristic, complemented
58#2542C2211yescharacteristic
59#2542C2211yescharacteristic
60#2538C2211yescharacteristic
61#2538C2211yescharacteristic
62#2514C2211yescharacteristic, complemented
63#2514C2211yescharacteristic, complemented
64#2503C2211yescharacteristic
65#2493—21no—
66#2493—21no—
67#2452C2211yescharacteristic
68#2452C2211yescharacteristic
69#2452C2211yescharacteristic
70#2452C2211yescharacteristic
71#2446C2211yescharacteristic, complemented
72#2446C2211yescharacteristic, complemented
73#2440C2211yescharacteristic
74#2440C2211yescharacteristic
75#2438—21no—
76#2437—21no—
77#2437—21no—
78#2434C2211yescharacteristic
79#2365C2211yescharacteristic, complemented
80#2356C2211yescharacteristic, complemented
81#2344C2211yescharacteristic
82#2343—21no—
83Q8×C22⋊C4C2211yescharacteristic
84D4×C22⋊C4C2211yescharacteristic
85D4×C22⋊C4C2211yescharacteristic
86C4×C22⋊Q8C2211yescharacteristic
87C4×C22⋊Q8C2211yescharacteristic
88C2×#391C2211yescharacteristic
89C2×#390C2211yescharacteristic
90#2101C2211yescharacteristic, complemented
91#2101C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2095C2211yescharacteristic, complemented
94#2087C2211yescharacteristic, complemented
95#2087C2211yescharacteristic, complemented
96#2086C2211yescharacteristic, complemented
97#2086C2211yescharacteristic, complemented
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2072C2211yescharacteristic, complemented
101#2072C2211yescharacteristic, complemented
102#2072C2211yescharacteristic, complemented
103#2072C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2068C2211yescharacteristic, complemented
106#2068C2211yescharacteristic, complemented
107#2068C2211yescharacteristic, complemented
108#2057C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2055C2211yescharacteristic
119#2055C2211yescharacteristic
120#2055C2211yescharacteristic
121#2043C2211yescharacteristic, complemented
122#2043C2211yescharacteristic, complemented
123#2024C2211yescharacteristic, complemented
124#2024C2211yescharacteristic, complemented
125#2024C2211yescharacteristic, complemented
126#2024C2211yescharacteristic, complemented
127#2024C2211yescharacteristic, complemented
128#2013C2211yescharacteristic
129#2013C2211yescharacteristic
130#1993C2211yescharacteristic, complemented
131#1988C2211yescharacteristic, complemented
132#1987C2211yescharacteristic, complemented
133#1985C2211yescharacteristic, complemented
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic
138#1956C2211yescharacteristic, complemented
139#1947C2211yescharacteristic, complemented
140#1947C2211yescharacteristic, complemented
141#1940C2211yescharacteristic, complemented
142#1940C2211yescharacteristic, complemented
143#1939C2211yescharacteristic, complemented
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1935C2211yescharacteristic, complemented
147#1935C2211yescharacteristic, complemented
148#1935C2211yescharacteristic, complemented
149#1935C2211yescharacteristic, complemented
150#1935C2211yescharacteristic, complemented
151#1935C2211yescharacteristic, complemented
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1933C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1918C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1917C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1892C2211yescharacteristic
165#1892C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1872C2211yescharacteristic
177#1863C2211yescharacteristic, complemented
178#1863C2211yescharacteristic, complemented
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1852C2211yescharacteristic
182#1850C2211yescharacteristic
183#1850C2211yescharacteristic
184#1836C2211yescharacteristic, complemented
185#1823C2211yescharacteristic
186#1823C2211yescharacteristic
187#1808C2211yescharacteristic
188#1808C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1803C2211yescharacteristic, complemented
192#1803C2211yescharacteristic, complemented
193#1787C2211yescharacteristic
194#1787C2211yescharacteristic
195#1786C2211yescharacteristic
196#1771C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1752C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201#1749C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16—24no—
206C22×SD16—42no—
207C22×SD16—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C23×C8C2311yescharacteristic
216#543—48no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8D411yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252C22×C42C2311yescharacteristic
253#487—42no—
254#477—42no—
255#477—42no—
256#461—42no—
257#461—42no—
258#450—24no—
259#446—42no—
260#440—42no—
261#440—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×C4⋊C8—42no—
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×#103—42no—
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#102—24no—
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#401—21no—
316#401—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#399—21no—
327#399—21no—
328#399—21no—
329#399—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#395—21no—
343#395—21no—
344#395—21no—
345#395—21no—
346#395—21no—
347#393—21no—
348#393—21no—
349#393—21no—
350#393—21no—
351#391—21no—
352#391—21no—
353#391—21no—
354#391—21no—
355#391—21no—
356#391—21no—
357#391D411yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#390—21no—
370#390—21no—
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#389—21no—
380#389—21no—
381#389D411yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
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#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387D411yescharacteristic
407#387D411yescharacteristic
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385D411yescharacteristic
422#385D411yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#383—21no—
427#383—21no—
428#383—21no—
429#382—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#381—21no—
433#381—21no—
434#381—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380D411yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#379—21no—
444#379—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457#376—21no—
458C2×#95—21no—
459C2×#95—21no—
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#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C25—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—22no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8C2×D411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4#4114yes—
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2411yescharacteristic
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—416no—
547C22×C8—22no—
548C22×C8—22no—
549C22×C8—22no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8—41no—
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C4⋊Q8—22no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C22⋊Q8—24no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—44no—
577C22⋊Q8—44no—
578C22⋊Q8—44no—
579C22⋊Q8—44no—
580C22⋊Q8—44no—
581C22⋊Q8—44no—
582C22⋊Q8—44no—
583C22⋊Q8—44no—
584C22⋊Q8—44no—
585C22⋊Q8—82no—
586C22⋊Q8—82no—
587C4×Q8—22no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603#117—44no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—44no—
681C2×C22⋊C4—44no—
682C2×C22⋊C4—44no—
683C2×C22⋊C4—82no—
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—41no—
695C2×C42—41no—
696C2×C42C2×D411yescharacteristic
697C2×C42C2×D411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704#107—22no—
705#107—41no—
706#107—41no—
707#107—41no—
708#107—41no—
709#107—41no—
710C4⋊C8—22no—
711C4⋊C8—22no—
712C4⋊C8—22no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718#103—22no—
719#103—22no—
720#103—22no—
721#103—22no—
722#103—22no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746C22⋊C8—22no—
747C22⋊C8—22no—
748#97—22no—
749#97—41no—
750#97—41no—
751#97—41no—
752C4×C8—41no—
753C4×C8—41no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805C24—21no—
806C24—21no—
807C24—24no—
808C24—42no—
809C24—42no—
810C24—81no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24C22×D411yescharacteristic
815C2×Q8—22no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—41no—
834C2×Q8—41no—
835C2×Q8—42no—
836C2×Q8—42no—
837C2×Q8—42no—
838C2×Q8—44no—
839C2×Q8—44no—
840C2×Q8—42no—
841C2×Q8—42no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8—81no—
845C2×Q8—81no—
846C2×Q8—81no—
847C2×Q8—81no—
848C2×Q8—81no—
849C2×Q8—82no—
850C2×Q8—82no—
851C2×Q8H(5,𝔽2)12yes—
852C2×D4—24no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—82no—
866C2×D4—82no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4C2×#4112yes—
870C2×D4C2×#4112yes—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—22no—
876C22×C4—21no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C2×#4112yes—
930C22×C42−1+412yes—
931C22×C4C2511yescharacteristic
932SD16—28no—
933SD16—44no—
934SD16—44no—
935SD16—44no—
936SD16—82no—
937SD16—82no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—44no—
962C2×C8—82no—
963C2×C8H(5,𝔽2)12yes—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4AGL(1,ℤ/8)14yes—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—41no—
1064C42—41no—
1065C42—42no—
1066C42—42no—
1067C42—42no—
1068C42—42no—
1069C42—81no—
1070C42—81no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—22no—
1076C23—22no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—48no—
1090C23—84no—
1091C23—84no—
1092C23—162no—
1093C23—162no—
1094C23—162no—
1095C23—162no—
1096C23#54812yes—
1097C23C2×AGL(1,ℤ/8)12yes—
1098C23#57812yes—
1099C23C23×D411yescharacteristic
1100Q8—22no—
1101Q8—22no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—82no—
1113Q8—84no—
1114Q8—162no—
1115Q8—162no—
1116Q8—162no—
1117D4—22no—
1118D4—22no—
1119D4—22no—
1120D4—22no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—84no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—22no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—44no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—82no—
1209C2×C4—84no—
1210C2×C4—84no—
1211C2×C4—162no—
1212C2×C4—162no—
1213C2×C4—162no—
1214C2×C4—162no—
1215C2×C4—162no—
1216C2×C4#54812yes—
1217C2×C4C2×AGL(1,ℤ/8)12yes—
1218C2×C4C2×AGL(1,ℤ/8)12yes—
1219C2×C4#57712yes—
1220C2×C4C22×#4111yescharacteristic
1221C2×C4C2×H(5,𝔽2)11yescharacteristic
1222C2×C4C2×H(5,𝔽2)11yescharacteristic
1223C2×C4C2×2−1+411yescharacteristic
1224C2×C4#58511yescharacteristic
1225C2×C4#58511yescharacteristic
1226C8—22no—
1227C8—41no—
1228C8—41no—
1229C8—41no—
1230C8—41no—
1231C8—41no—
1232C8—41no—
1233C8—41no—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—22no—
1238C22—22no—
1239C22—22no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—168no—
1255C22#336714yes—
1256C22C2×#54811yescharacteristic
1257C22#348811yescharacteristic
1258C22#349611yescharacteristic
1259C22C22×AGL(1,ℤ/8)11yescharacteristic
1260C22C2×#57711yescharacteristic
1261C22C2×#57811yescharacteristic
1262C22#358611yescharacteristic
1263C4—22no—
1264C4—22no—
1265C4—22no—
1266C4—22no—
1267C4—42no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4#349011yescharacteristic
1291C4#349111yescharacteristic
1292C4#353511yescharacteristic
1293C4#356111yescharacteristic
1294C2—24no—
1295C2—82no—
1296C2—82no—
1297C2#4302411yescharacteristic
1298C2C2×#336711yescharacteristic
1299C2#6134011yescharacteristic
1300C2#6198311yescharacteristic
1301C2#6202011yescharacteristic
1302C2#6228111yescharacteristic
1303C2#6229511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
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. #59425C2semidirect
3. #32621C2semidirect
4. #32556C2semidirect
5. #32448C2semidirect
6. #31827C2semidirect
7. #31811C2semidirect
8. #31636C2semidirect
9. #31165C2semidirect
10. #31165C2semidirect
11. #29111C2semidirect
12. #29091C2semidirect
13. #28199C2semidirect
14. #27713C2semidirect
15. #27435C2semidirect
16. #27258C2semidirect
17. #26919C2semidirect
18. #26836C2semidirect
19. #25988C2semidirect
20. #25963C2semidirect
21. #25320C2semidirect
22. #25301C2semidirect
23. #24837C2semidirect
24. #24694C2semidirect
28. #22954C2semidirect
34. C2×#487C22semidirect
35. C2×#477C22semidirect
36. C2×#477C22semidirect
40. C2×#446C22semidirect
56. #2581C22semidirect
57. #2568C22semidirect
62. #2514C22semidirect
63. #2514C22semidirect
71. #2446C22semidirect
72. #2446C22semidirect
79. #2365C22semidirect
80. #2356C22semidirect
90. #2101C22semidirect
91. #2101C22semidirect
92. #2099C22semidirect
93. #2095C22semidirect
94. #2087C22semidirect
95. #2087C22semidirect
96. #2086C22semidirect
97. #2086C22semidirect
100. #2072C22semidirect
101. #2072C22semidirect
102. #2072C22semidirect
103. #2072C22semidirect
104. #2068C22semidirect
105. #2068C22semidirect
106. #2068C22semidirect
107. #2068C22semidirect
108. #2057C22semidirect
121. #2043C22semidirect
122. #2043C22semidirect
123. #2024C22semidirect
124. #2024C22semidirect
125. #2024C22semidirect
126. #2024C22semidirect
127. #2024C22semidirect
130. #1993C22semidirect
131. #1988C22semidirect
132. #1987C22semidirect
133. #1985C22semidirect
138. #1956C22semidirect
139. #1947C22semidirect
140. #1947C22semidirect
141. #1940C22semidirect
142. #1940C22semidirect
143. #1939C22semidirect
146. #1935C22semidirect
147. #1935C22semidirect
148. #1935C22semidirect
149. #1935C22semidirect
150. #1935C22semidirect
151. #1935C22semidirect
154. #1933C22semidirect
155. #1933C22semidirect
160. #1918C22semidirect
161. #1918C22semidirect
162. #1917C22semidirect
163. #1916C22semidirect
177. #1863C22semidirect
178. #1863C22semidirect
184. #1836C22semidirect
191. #1803C22semidirect
192. #1803C22semidirect
196. #1771C22semidirect

Maximal subgroups

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

subgroupindex
#594252
#393672
#326212
#325562
#324482
#318272
#318112
#316362
#311652
#291112
#290912
#281992
#277132
#274352
#272582
#269192
#268362
#259882
#259632
#253202
#253012
#248372
#246942
#245272
#243582
C2×#20552
#229542
#225702
#224372
#220492