Finite Group Databasebeta

← #6628602

Subgroups — #6628602

Order 512.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36605C211yesmaximal, characteristic, complemented
2#36596C211yesmaximal, characteristic, complemented
3#33183C211yesmaximal, characteristic, complemented
4#33183C211yesmaximal, characteristic, complemented
5#33170C211yesmaximal, characteristic, complemented
6#28902C211yesmaximal, characteristic, complemented
7#28900C211yesmaximal, characteristic, complemented
8#28894C211yesmaximal, characteristic, complemented
9#28893C211yesmaximal, characteristic, complemented
10#28837C211yesmaximal, characteristic, complemented
11#28574C211yesmaximal, characteristic, complemented
12#28573C211yesmaximal, characteristic, complemented
13#28572C211yesmaximal, characteristic, complemented
14#28571C211yesmaximal, characteristic, complemented
15#28480C211yesmaximal, characteristic, complemented
16#28021C211yesmaximal, characteristic, complemented
17#28019C211yesmaximal, characteristic, complemented
18#27765C211yesmaximal, characteristic, complemented
19#27760C211yesmaximal, characteristic, complemented
20#26260C211yesmaximal, characteristic, complemented
21#26258C211yesmaximal, characteristic, complemented
22#24754C211yesmaximal, characteristic, complemented
23#24753C211yesmaximal, characteristic, complemented
24#23195C211yesmaximal, characteristic, complemented
25#23109C211yesmaximal, characteristic, complemented
26#23106C211yesmaximal, characteristic, complemented
27#22820C211yesmaximal, characteristic, complemented
28#21528C211yesmaximal, characteristic, complemented
29#21528C211yesmaximal, characteristic, complemented
30C4×#466C211yesmaximal, characteristic, complemented
31C2×#1771C211yesmaximal, characteristic, complemented
32C2×#553—21no—
33C2×#496C2211yescharacteristic
34C2×#496C2211yescharacteristic
35C2×#492C2211yescharacteristic
36C2×#466C2211yescharacteristic
37C2×#466C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#465C2211yescharacteristic
42C2×#465C2211yescharacteristic
43C2×#465C2211yescharacteristic
44C2×#465C2211yescharacteristic
45C2×#460C2211yescharacteristic
46C2×#463C2211yescharacteristic
47C2×#440C2211yescharacteristic
48C2×#440C2211yescharacteristic
49C2×C4×D8C2211yescharacteristic
50C22×C4⋊C8C2211yescharacteristic
51C22×#97C2211yescharacteristic
52C22×#97C2211yescharacteristic
53C22×C4×C8C2211yescharacteristic
54#2857C2211yescharacteristic
55#2856C2211yescharacteristic
56#2856C2211yescharacteristic
57#2856C2211yescharacteristic
58#2850C2211yescharacteristic
59#2850C2211yescharacteristic
60#2594—21no—
61#2579—21no—
62#2573—21no—
63#2570C2211yescharacteristic
64#2554—21no—
65#2554—21no—
66#2552C2211yescharacteristic
67#2545C2211yescharacteristic
68#2543—21no—
69#2543—21no—
70#2541C2211yescharacteristic
71#2525—21no—
72#2514C2211yescharacteristic
73#2512C2211yescharacteristic
74#2512C2211yescharacteristic
75#2512C2211yescharacteristic
76#2510—21no—
77#2490—21no—
78#2481—21no—
79#2447C2211yescharacteristic
80#2446C2211yescharacteristic
81#2445C2211yescharacteristic
82#2445C2211yescharacteristic
83#2416—21no—
84#2373—21no—
85#2367C2211yescharacteristic
86#2366C2211yescharacteristic
87#2363—21no—
88#2356C2211yescharacteristic
89#2354C2211yescharacteristic
90#2353—21no—
91C4×C22⋊Q8C2211yescharacteristic
92C4×C22⋊Q8C2211yescharacteristic
93C4×#121C2211yescharacteristic
94C4×#121C2211yescharacteristic
95C4×#121C2211yescharacteristic
96C4×#121C2211yescharacteristic
97C2×C4×C4⋊C4C2211yescharacteristic
98#2085C2211yescharacteristic
99#2084C2211yescharacteristic
100#2084C2211yescharacteristic
101#2083C2211yescharacteristic
102#2073C2211yescharacteristic
103#2072C2211yescharacteristic
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic
106#2068C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2054C2211yescharacteristic
114#2043C2211yescharacteristic
115#2042C2211yescharacteristic
116#2041C2211yescharacteristic
117#2041C2211yescharacteristic
118#2014C2211yescharacteristic
119#2013C2211yescharacteristic
120#2012C2211yescharacteristic
121#2011C2211yescharacteristic
122#1983C2211yescharacteristic
123#1982C2211yescharacteristic
124#1973C2211yescharacteristic
125#1973C2211yescharacteristic
126#1973C2211yescharacteristic
127#1973C2211yescharacteristic
128#1973C2211yescharacteristic
129#1973C2211yescharacteristic
130#1972C2211yescharacteristic
131#1972C2211yescharacteristic
132#1972C2211yescharacteristic
133#1972C2211yescharacteristic
134#1970C2211yescharacteristic
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1961C2211yescharacteristic
140#1961C2211yescharacteristic
141#1959C2211yescharacteristic
142#1959C2211yescharacteristic
143#1957C2211yescharacteristic
144#1956C2211yescharacteristic
145#1949C2211yescharacteristic
146#1948C2211yescharacteristic
147#1944C2211yescharacteristic
148#1944C2211yescharacteristic
149#1942C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic
152#1935C2211yescharacteristic
153#1935C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1928C2211yescharacteristic
157#1927C2211yescharacteristic
158#1927C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic
167#1893C2211yescharacteristic
168#1892C2211yescharacteristic
169#1892C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1847C2211yescharacteristic
179#1847C2211yescharacteristic
180#1844C2211yescharacteristic
181#1808C2211yescharacteristic
182#1804C2211yescharacteristic
183#1803C2211yescharacteristic
184#1776C2211yescharacteristic
185#1776C2211yescharacteristic
186C4×#107C2211yescharacteristic
187#1771C2211yescharacteristic
188#1771C2211yescharacteristic
189#1771C2211yescharacteristic
190#1771C2211yescharacteristic
191#1771C2211yescharacteristic
192#1771C2211yescharacteristic
193#1771C2211yescharacteristic
194#1771C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C2×#336C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C23×C8C2311yescharacteristic
216#553—48no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#126—21no—
222C2×#126—21no—
223C2×#126—21no—
224C2×#125—21no—
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×#123—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×#121—21no—
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×#117—21no—
255C22×C4⋊C4D411yescharacteristic
256C22×C4⋊C4D411yescharacteristic
257C22×C42C2311yescharacteristic
258C22×C42C2311yescharacteristic
259C22×C42C2311yescharacteristic
260#496—24no—
261#496—42no—
262#492—42no—
263#466—24no—
264#466—42no—
265#466—42no—
266#465—24no—
267#465—24no—
268#465—42no—
269#465—42no—
270#465—42no—
271#465—42no—
272#463—24no—
273#460—24no—
274#440—24no—
275#440—42no—
276C4×D8—42no—
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×C4⋊C8—24no—
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#97—24no—
324C2×#97—42no—
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×#97C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×C4×C8—42no—
334C2×C4×C8C2311yescharacteristic
335C2×C4×C8C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338#401—21no—
339#400—21no—
340#400—21no—
341#400—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#392—21no—
361#392—21no—
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#390—21no—
369#390—21no—
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#389—21no—
388#389—21no—
389#389—21no—
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#383—21no—
443#383—21no—
444#382C2311yescharacteristic
445#382C2311yescharacteristic
446#381—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452C4×C4⋊C4—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4D411yescharacteristic
455C4×C4⋊C4D411yescharacteristic
456C4×C4⋊C4D411yescharacteristic
457C4×C4⋊C4D411yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4—21no—
473C4×C22⋊C4—21no—
474C4×C22⋊C4—21no—
475#376—21no—
476C2×#95D411yescharacteristic
477C2×#95D411yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4C2×D411yescharacteristic
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2×D411yescharacteristic
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2411yescharacteristic
527C2×SD16—22no—
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—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×D8—22no—
546C2×D8—22no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—41no—
551C2×D8—41no—
552C2×D8—41no—
553C2×D8—41no—
554C22×C8—22no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—22no—
561C22×C8—22no—
562C22×C8—41no—
563C22×C8—41no—
564C22×C8—41no—
565C22×C8#4114yes—
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576#127—22no—
577#127—22no—
578#127—41no—
579#127—41no—
580#127—41no—
581#127—41no—
582#126—44no—
583#126—44no—
584#126—44no—
585#125—44no—
586#124—22no—
587#124—22no—
588#124—41no—
589#124—41no—
590#123—44no—
591#123—44no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—44no—
605#121—44no—
606#121—44no—
607#121—44no—
608#121—44no—
609#121—82no—
610#121—82no—
611#121—82no—
612C4×Q8—22no—
613C4×Q8—22no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×D4—22no—
617C4×D4—22no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—44no—
625C4×D4—44no—
626C4×D4—44no—
627C4×D4—44no—
628C4×D4—44no—
629#117—44no—
630C2×C4⋊C4—24no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—42no—
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
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—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—41no—
721C2×C42—41no—
722C2×C42—41no—
723C2×C42—41no—
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D411yescharacteristic
726C2×C42C2×D411yescharacteristic
727C2×C42C2×D411yescharacteristic
728C2×C42C2×D411yescharacteristic
729C2×C42C2×D411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#107—22no—
737#107—22no—
738#107—22no—
739#107—41no—
740#107—41no—
741#106—22no—
742#106—22no—
743#106—41no—
744#106—41no—
745#106—41no—
746#106—41no—
747C4⋊C8—22no—
748C4⋊C8—22no—
749C4⋊C8—22no—
750C4⋊C8#4114yes—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—22no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#97—22no—
782#97—22no—
783#97—22no—
784#97—22no—
785#97—22no—
786#97—41no—
787#97—41no—
788#97#4114yes—
789C4×C8—22no—
790C4×C8—22no—
791C4×C8—41no—
792C4×C8—41no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24C22×D411yescharacteristic
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
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—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—41no—
932C22×C4—41no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4AGL(1,ℤ/8)14yes—
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C2×#4112yes—
962C22×C4H(5,𝔽2)12yes—
963C22×C4C2511yescharacteristic
964SD16—44no—
965SD16—44no—
966SD16—82no—
967SD16—82no—
968SD16—82no—
969SD16—82no—
970D8—44no—
971D8—82no—
972D8—82no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—28no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—44no—
992C2×C8—44no—
993C2×C8—44no—
994C2×C8C2×#4112yes—
995C2×C8C2×#4112yes—
996C2×C8C2×#4112yes—
997C2×C8C2×#4112yes—
998C2×C8C2×#4112yes—
999C2×C8C2×#4112yes—
1000C2×C8H(5,𝔽2)12yes—
1001C4⋊C4—22no—
1002C4⋊C4—22no—
1003C4⋊C4—22no—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—41no—
1028C4⋊C4—41no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C42—22no—
1090C42—22no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—41no—
1102C42—41no—
1103C42—41no—
1104C42—41no—
1105C42—42no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—42no—
1110C42—42no—
1111C42—81no—
1112C42—81no—
1113C42C2×#4112yes—
1114C42C2×#4112yes—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23#55012yes—
1148C23C2×AGL(1,ℤ/8)12yes—
1149C23#57712yes—
1150C23C23×D411yescharacteristic
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—84no—
1176D4—84no—
1177D4—84no—
1178D4—84no—
1179D4—84no—
1180D4—162no—
1181D4—162no—
1182D4—162no—
1183D4—162no—
1184D4—162no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—44no—
1223C2×C4—44no—
1224C2×C4—44no—
1225C2×C4—44no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—84no—
1263C2×C4—82no—
1264C2×C4—82no—
1265C2×C4—162no—
1266C2×C4—162no—
1267C2×C4—162no—
1268C2×C4#53212yes—
1269C2×C4#53212yes—
1270C2×C4#55012yes—
1271C2×C4C2×AGL(1,ℤ/8)12yes—
1272C2×C4C2×AGL(1,ℤ/8)12yes—
1273C2×C4#57512yes—
1274C2×C4C22×#4111yescharacteristic
1275C2×C4C22×#4111yescharacteristic
1276C2×C4C22×#4111yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4#58511yescharacteristic
1280C8—22no—
1281C8—22no—
1282C8—22no—
1283C8—22no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8#55314yescomplemented
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22#339714yes—
1323C22C2×#53211yescharacteristic
1324C22C2×#55011yescharacteristic
1325C22#349611yescharacteristic
1326C22C22×AGL(1,ℤ/8)11yescharacteristic
1327C22C2×#57511yescharacteristic
1328C22C2×#57711yescharacteristic
1329C22#358411yescharacteristic
1330C4—22no—
1331C4—22no—
1332C4—22no—
1333C4—22no—
1334C4—22no—
1335C4—22no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4C2×#55311yescharacteristic
1356C4#348011yescharacteristic
1357C4#349411yescharacteristic
1358C4#351911yescharacteristic
1359C2—24no—
1360C2—161no—
1361C2—161no—
1362C2—161no—
1363C2—161no—
1364C2#3659611yescharacteristic
1365C2#6070011yescharacteristic
1366C2#6070611yescharacteristic
1367C2C2×#339711yescharacteristic
1368C2#6140111yescharacteristic
1369C2#6225311yescharacteristic
1370C2#6225611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36605C2semidirect
2. #36596C2semidirect
3. #33183C2semidirect
4. #33183C2semidirect
5. #33170C2semidirect
6. #28902C2semidirect
7. #28900C2semidirect
8. #28894C2semidirect
9. #28893C2semidirect
10. #28837C2semidirect
11. #28574C2semidirect
12. #28573C2semidirect
13. #28572C2semidirect
14. #28571C2semidirect
15. #28480C2semidirect
16. #28021C2semidirect
17. #28019C2semidirect
18. #27765C2semidirect
19. #27760C2semidirect
20. #26260C2semidirect
21. #26258C2semidirect
22. #24754C2semidirect
23. #24753C2semidirect
24. #23195C2semidirect
25. #23109C2semidirect
26. #23106C2semidirect
27. #22820C2semidirect
28. #21528C2semidirect
29. #21528C2semidirect
30. C4×#466C2semidirect
31. C2×#1771C2semidirect
1287. C8#553semidirect

Maximal subgroups

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

subgroupindex
#366052
#365962
#331832
#331702
#289022
#289002
#288942
#288932
#288372
#285742
#285732
#285722
#285712
#284802
#280212
#280192
#277652
#277602
#262602
#262582
#247542
#247532
#231952
#231092
#231062
#228202
#215282
C4×#4662
C2×#17712