Finite Group Databasebeta

← #6828028

Subgroups — #6828028

Order 512.

1679 conjugacy classes of subgroups.

The subgroup lattice has 1430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42749C211yesmaximal, characteristic, complemented
2#42544C211yesmaximal, characteristic, complemented
3#33246C211yesmaximal, characteristic, complemented
4#32170C211yesmaximal, characteristic, complemented
5#32163C211yesmaximal, characteristic, complemented
6#30996C211yesmaximal, characteristic, complemented
7#30985C211yesmaximal, characteristic, complemented
8#30895C211yesmaximal, characteristic, complemented
9#30891C211yesmaximal, characteristic, complemented
10#30540C211yesmaximal, characteristic, complemented
11#30539C211yesmaximal, characteristic, complemented
12#30054C211yesmaximal, characteristic, complemented
13#30048C211yesmaximal, characteristic, complemented
14#28467C211yesmaximal, characteristic, complemented
15#28464C211yesmaximal, characteristic, complemented
16#28026C211yesmaximal, characteristic, complemented
17#27801C211yesmaximal, characteristic, complemented
18#26594C211yesmaximal, characteristic, complemented
19#26585C211yesmaximal, characteristic, complemented
20#26482C211yesmaximal, characteristic, complemented
21#26261C211yesmaximal, characteristic, complemented
22#25793C211yesmaximal, characteristic, complemented
23#25791C211yesmaximal, characteristic, complemented
24#25429C211yesmaximal, characteristic, complemented
25#25160C211yesmaximal, characteristic, complemented
26#25158C211yesmaximal, characteristic, complemented
27#25036C211yesmaximal, characteristic, complemented
28#23193C211yesmaximal, characteristic, complemented
29#22442C211yesmaximal, characteristic, complemented
30#21704C211yesmaximal, characteristic, complemented
31#21671C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#499C2211yescharacteristic, complemented
34C2×#496C2211yescharacteristic
35C2×#496C2211yescharacteristic
36C2×#495C2211yescharacteristic
37C2×#495C2211yescharacteristic, complemented
38C2×#492C2211yescharacteristic
39C2×#491C2211yescharacteristic, complemented
40C2×#490C2211yescharacteristic
41C2×#468C2211yescharacteristic
42C2×#468C2211yescharacteristic
43C2×#464C2211yescharacteristic
44C2×#463C2211yescharacteristic
45C2×#463C2211yescharacteristic, complemented
46C2×#463C2211yescharacteristic, complemented
47C2×#452C2211yescharacteristic
48C2×#449C2211yescharacteristic
49C2×#450C2211yescharacteristic
50C2×#447C2211yescharacteristic
51C2×#442C2211yescharacteristic
52C2×#440C2211yescharacteristic, complemented
53C2×C4×SD16C2211yescharacteristic, complemented
54C2×C4×SD16C2211yescharacteristic, complemented
55C2×C4×D8C2211yescharacteristic
56C2×C4×D8C2211yescharacteristic
57#2826—21no—
58#2826—21no—
59#2778—21no—
60#2778—21no—
61#2753—21no—
62#2750—21no—
63#2749—21no—
64#2743—21no—
65#2697—21no—
66#2685—21no—
67#2648—21no—
68#2643—21no—
69#2642C2211yescharacteristic, complemented
70#2641C2211yescharacteristic
71#2636—21no—
72#2622—21no—
73#2545C2211yescharacteristic, complemented
74#2544C2211yescharacteristic
75#2544C2211yescharacteristic
76#2544C2211yescharacteristic, complemented
77#2514C2211yescharacteristic, complemented
78#2512C2211yescharacteristic
79#2510—21no—
80#2490C2211yescharacteristic
81#2489C2211yescharacteristic
82#2454C2211yescharacteristic
83#2454C2211yescharacteristic, complemented
84#2448C2211yescharacteristic
85#2447C2211yescharacteristic, complemented
86#2435C2211yescharacteristic
87#2433C2211yescharacteristic
88#2432C2211yescharacteristic
89#2431C2211yescharacteristic
90#2427C2211yescharacteristic
91#2426C2211yescharacteristic
92#2422C2211yescharacteristic
93#2421C2211yescharacteristic
94#2418—21no—
95#2401C2211yescharacteristic
96#2367C2211yescharacteristic, complemented
97#2366C2211yescharacteristic
98#2339C2211yescharacteristic
99D4×C22⋊C4C2211yescharacteristic
100#2328C2211yescharacteristic, complemented
101#2326C2211yescharacteristic
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2072C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic, complemented
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic, complemented
110#2056C2211yescharacteristic, complemented
111#2054C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic, complemented
114#2042C2211yescharacteristic, complemented
115#2042C2211yescharacteristic, complemented
116#2036C2211yescharacteristic
117#2035C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2026C2211yescharacteristic, complemented
121#2025C2211yescharacteristic
122#2025C2211yescharacteristic, complemented
123#2025C2211yescharacteristic, complemented
124#2016C2211yescharacteristic, complemented
125#2015C2211yescharacteristic
126#2015C2211yescharacteristic
127#2015C2211yescharacteristic, complemented
128#2015C2211yescharacteristic, complemented
129#2014C2211yescharacteristic
130#2013C2211yescharacteristic
131#2012C2211yescharacteristic
132#2012C2211yescharacteristic
133#2012C2211yescharacteristic
134#2012C2211yescharacteristic
135#2011C2211yescharacteristic
136#2011C2211yescharacteristic
137#2011C2211yescharacteristic
138#2011C2211yescharacteristic
139#2011C2211yescharacteristic, complemented
140#2001C2211yescharacteristic
141#1999C2211yescharacteristic
142#1983C2211yescharacteristic, complemented
143#1982C2211yescharacteristic
144#1973C2211yescharacteristic
145#1973C2211yescharacteristic
146#1973C2211yescharacteristic
147#1973C2211yescharacteristic, complemented
148#1973C2211yescharacteristic, complemented
149#1973C2211yescharacteristic, complemented
150#1973C2211yescharacteristic, complemented
151#1972C2211yescharacteristic
152#1970C2211yescharacteristic
153#1970C2211yescharacteristic
154#1968C2211yescharacteristic
155#1968C2211yescharacteristic
156#1968C2211yescharacteristic
157#1968C2211yescharacteristic, complemented
158#1968C2211yescharacteristic, complemented
159#1968C2211yescharacteristic, complemented
160#1958C2211yescharacteristic
161#1957C2211yescharacteristic, complemented
162#1942C2211yescharacteristic, complemented
163#1942C2211yescharacteristic, complemented
164#1928C2211yescharacteristic, complemented
165#1927C2211yescharacteristic, complemented
166#1926C2211yescharacteristic
167#1926C2211yescharacteristic, complemented
168#1924C2211yescharacteristic
169#1923C2211yescharacteristic
170#1923C2211yescharacteristic
171#1917C2211yescharacteristic, complemented
172#1916C2211yescharacteristic, complemented
173#1916C2211yescharacteristic, complemented
174#1880C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic, complemented
179#1879C2211yescharacteristic, complemented
180#1879C2211yescharacteristic, complemented
181#1878C2211yescharacteristic, complemented
182#1878C2211yescharacteristic, complemented
183#1877C2211yescharacteristic
184#1877C2211yescharacteristic
185#1877C2211yescharacteristic
186#1865C2211yescharacteristic, complemented
187#1864C2211yescharacteristic
188#1864C2211yescharacteristic, complemented
189#1862C2211yescharacteristic, complemented
190#1847C2211yescharacteristic, complemented
191#1840C2211yescharacteristic, complemented
192#1809C2211yescharacteristic
193#1788C2211yescharacteristic
194#1786C2211yescharacteristic
195#1776C2211yescharacteristic, complemented
196#1771C2211yescharacteristic, complemented
197#1770C2211yescharacteristic, complemented
198C8×C4⋊C4C2211yescharacteristic, complemented
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1726C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C2×AGL(1,ℤ/8)—42no—
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×D8C2311yescharacteristic
219C22×D8C2311yescharacteristic
220C22×D8C2311yescharacteristic
221C22×D8C2311yescharacteristic
222C22×D8C2311yescharacteristic
223C22×D8C2311yescharacteristic
224C22×M16C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×#127C2311yescharacteristic
227C2×#127C2311yescharacteristic
228C2×#127C2311yescharacteristic
229C2×#126—21no—
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#124C2311yescharacteristic
237C2×#124C2311yescharacteristic
238C2×#123—21no—
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#120—21no—
244C2×#120—21no—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C22×C22⋊C4—21no—
255#499—42no—
256#496—24no—
257#496—24no—
258#495—42no—
259#495—42no—
260#492—42no—
261#491—42no—
262#490—42no—
263#468—42no—
264#468—42no—
265#464—42no—
266#463—42no—
267#463—42no—
268#463—42no—
269#452—42no—
270#450—42no—
271#449—42no—
272#447—42no—
273#442—42no—
274#440—42no—
275C4×SD16—42no—
276C4×SD16—42no—
277C4×D8—42no—
278C4×D8—42no—
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333C2×C4×C8C2311yescharacteristic
334#401—21no—
335#401D411yescharacteristic
336#400—21no—
337#400—21no—
338#400—21no—
339#400—21no—
340#400—21no—
341#400—21no—
342#400—21no—
343#400D411yescharacteristic
344#400D411yescharacteristic
345#400D411yescharacteristic
346#399—21no—
347#399—21no—
348#399—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#397—21no—
357#397—21no—
358#397D411yescharacteristic
359#397D411yescharacteristic
360#397D411yescharacteristic
361#396—21no—
362#396—21no—
363#396—21no—
364#396—21no—
365#396—21no—
366#396—21no—
367#396D411yescharacteristic
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394—21no—
376#394—21no—
377#394—21no—
378#394—21no—
379#394—21no—
380#394—21no—
381#394—21no—
382#394—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#392—21no—
387#392—21no—
388#392—21no—
389#392—21no—
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#391C2311yescharacteristic
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#390—21no—
399#390—21no—
400#390—21no—
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#390C2311yescharacteristic
412#390C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#387—21no—
431#387—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#386—21no—
448#386—21no—
449#386—21no—
450#386—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#385—21no—
459#385—21no—
460#384C2311yescharacteristic
461#383—21no—
462#382—21no—
463#382C2311yescharacteristic
464#381—21no—
465#381—21no—
466#380—21no—
467#380—21no—
468#380—21no—
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#379—21no—
472#379—21no—
473#379—21no—
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C22⋊C4—21no—
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482C4×C22⋊C4C2311yescharacteristic
483#376C2311yescharacteristic
484C2×#95—21no—
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502#336C2311yescharacteristic
503#336C2311yescharacteristic
504#336C2311yescharacteristic
505C25—21no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4C2411yescharacteristic
544AGL(1,ℤ/8)—416no—
545C2×Q16—41no—
546C2×Q16—41no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—41no—
582C2×D8—41no—
583C2×D8—41no—
584C2×D8—41no—
585C2×D8—41no—
586C2×D8—41no—
587C2×D8—41no—
588C2×D8—41no—
589C2×D8—41no—
590C2×D8—41no—
591C2×D8—41no—
592C2×D8#4114yes—
593C2×M16—22no—
594C2×M16—22no—
595C2×M16—22no—
596C22×C8C2411yescharacteristic
597C22×C8C2411yescharacteristic
598C22×C8C2411yescharacteristic
599C22×C8C2411yescharacteristic
600C22×C8C2411yescharacteristic
601C22×C8C2411yescharacteristic
602C22×C8C2411yescharacteristic
603C22×C8C2411yescharacteristic
604C4⋊Q8—41no—
605C4⋊Q8—41no—
606#127—22no—
607#127—22no—
608#127—41no—
609#127—41no—
610#127—41no—
611#127—41no—
612#126—82no—
613#125—41no—
614#125—41no—
615#125—41no—
616#125—41no—
617#124—22no—
618#124—22no—
619#124—41no—
620#124—41no—
621#124—41no—
622#124—41no—
623#124—41no—
624#124—41no—
625#124—41no—
626#124—41no—
627#124—41no—
628#124—41no—
629#123—82no—
630C22⋊Q8—41no—
631C22⋊Q8—41no—
632C22⋊Q8—41no—
633C22⋊Q8—41no—
634#121—41no—
635#121—41no—
636#121—41no—
637#121—41no—
638#120—82no—
639#120—82no—
640C4×Q8—41no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×Q8—41no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—41no—
648C4×D4—41no—
649C4×D4—41no—
650C4×D4—41no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—41no—
654C4×D4—41no—
655C4×D4—41no—
656C4×D4—82no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—82no—
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752#107—22no—
753#107—22no—
754#107—22no—
755#107—41no—
756#106—22no—
757#106—41no—
758#106—41no—
759#106—41no—
760C4⋊C8—22no—
761C4⋊C8—22no—
762C4⋊C8—41no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795C22⋊C8—22no—
796C22⋊C8—22no—
797C22⋊C8—41no—
798#97—22no—
799#97—22no—
800#97—22no—
801#97—22no—
802C4×C8—22no—
803C4×C8—22no—
804C4×C8—22no—
805C4×C8—22no—
806C4×C8—41no—
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#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—42no—
855C24—42no—
856C24—81no—
857C24—81no—
858C24—81no—
859C24—81no—
860C24—81no—
861C24C22×D411yescharacteristic
862#41—44no—
863#41—82no—
864#41—82no—
865#41—82no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—44no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—82no—
937C2×D4—82no—
938C2×D4—82no—
939C2×D4—81no—
940C2×D4—81no—
941C2×D4—81no—
942C2×D4—81no—
943C2×D4—81no—
944C2×D4—81no—
945C2×D4—81no—
946C2×D4C2×#4112yes—
947C2×D4C2×#4112yes—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—42no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C2511yescharacteristic
1000Q16—82no—
1001Q16—82no—
1002SD16—44no—
1003SD16—44no—
1004SD16—44no—
1005SD16—44no—
1006SD16—44no—
1007SD16—82no—
1008SD16—82no—
1009SD16—82no—
1010D8—28no—
1011D8—44no—
1012D8—44no—
1013D8—82no—
1014D8—82no—
1015D8—82no—
1016M16—44no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8C2×#4112yes—
1037C2×C8H(5,𝔽2)12yes—
1038C2×C8H(5,𝔽2)12yes—
1039C2×C8H(5,𝔽2)12yes—
1040C2×C8H(5,𝔽2)12yes—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C22⋊C4—41no—
1080C22⋊C4—41no—
1081C22⋊C4—41no—
1082C22⋊C4—41no—
1083C22⋊C4—41no—
1084C22⋊C4—41no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—21no—
1143C42—21no—
1144C42—21no—
1145C42—42no—
1146C42—81no—
1147C42—81no—
1148C42—81no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—22no—
1154C23—22no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—84no—
1192C23—84no—
1193C23—162no—
1194C23—162no—
1195C23—162no—
1196C23—162no—
1197C23—162no—
1198C23C23×D411yescharacteristic
1199Q8—41no—
1200Q8—41no—
1201Q8—41no—
1202Q8—41no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—41no—
1209Q8—41no—
1210Q8—41no—
1211D4—22no—
1212D4—22no—
1213D4—22no—
1214D4—22no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—41no—
1224D4—41no—
1225D4—41no—
1226D4—41no—
1227D4—41no—
1228D4—41no—
1229D4—41no—
1230D4—41no—
1231D4—84no—
1232D4—84no—
1233D4—84no—
1234D4—162no—
1235D4—162no—
1236D4—162no—
1237D4—162no—
1238D4—162no—
1239D4—162no—
1240D4—162no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—84no—
1318C2×C4—162no—
1319C2×C4—162no—
1320C2×C4—162no—
1321C2×C4—162no—
1322C2×C4—162no—
1323C2×C4—162no—
1324C2×C4C22×#4111yescharacteristic
1325C2×C4C2×H(5,𝔽2)11yescharacteristic
1326C2×C4C2×H(5,𝔽2)11yescharacteristic
1327C2×C4C2×H(5,𝔽2)11yescharacteristic
1328C2×C4C2×H(5,𝔽2)11yescharacteristic
1329C2×C4#58511yescharacteristic
1330C8—22no—
1331C8—22no—
1332C8—41no—
1333C8—41no—
1334C8—41no—
1335C8—41no—
1336C8—41no—
1337C8#53814yes—
1338C22—41no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—42no—
1349C22—42no—
1350C22—41no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—81no—
1380C22—168no—
1381C22D4×#4111yescharacteristic
1382C22#349811yescharacteristic
1383C22#349811yescharacteristic
1384C22#358411yescharacteristic
1385C22#358411yescharacteristic
1386C22#358511yescharacteristic
1387C22#358511yescharacteristic
1388C4—41no—
1389C4—41no—
1390C4—41no—
1391C4—41no—
1392C4—41no—
1393C4—41no—
1394C4—41no—
1395C4—41no—
1396C4—41no—
1397C4—41no—
1398C4—41no—
1399C4—41no—
1400C4—41no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4—81no—
1408C4—81no—
1409C4—81no—
1410C4—81no—
1411C4—81no—
1412C4C2×#53811yescharacteristic
1413C4#351911yescharacteristic
1414C4#354611yescharacteristic
1415C4#355811yescharacteristic
1416C2—81no—
1417C2—82no—
1418C2—82no—
1419C2—161no—
1420C2—161no—
1421C2—161no—
1422C2#3940511yescharacteristic
1423C2#6154811yescharacteristic
1424C2#6154811yescharacteristic
1425C2#6243311yescharacteristic
1426C2#6244111yescharacteristic
1427C2#6246111yescharacteristic
1428C2#6246811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2401 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42749C2semidirect
2. #42544C2semidirect
3. #33246C2semidirect
4. #32170C2semidirect
5. #32163C2semidirect
6. #30996C2semidirect
7. #30985C2semidirect
8. #30895C2semidirect
9. #30891C2semidirect
10. #30540C2semidirect
11. #30539C2semidirect
12. #30054C2semidirect
13. #30048C2semidirect
14. #28467C2semidirect
15. #28464C2semidirect
16. #28026C2semidirect
17. #27801C2semidirect
18. #26594C2semidirect
19. #26585C2semidirect
20. #26482C2semidirect
21. #26261C2semidirect
22. #25793C2semidirect
23. #25791C2semidirect
24. #25429C2semidirect
25. #25160C2semidirect
26. #25158C2semidirect
27. #25036C2semidirect
28. #23193C2semidirect
29. #22442C2semidirect
30. #21704C2semidirect
31. #21671C2semidirect
33. C2×#499C22semidirect
37. C2×#495C22semidirect
39. C2×#491C22semidirect
45. C2×#463C22semidirect
46. C2×#463C22semidirect
52. C2×#440C22semidirect
53. C2×C4×SD16C22semidirect
54. C2×C4×SD16C22semidirect
69. #2642C22semidirect
73. #2545C22semidirect
76. #2544C22semidirect
77. #2514C22semidirect
83. #2454C22semidirect
85. #2447C22semidirect
96. #2367C22semidirect
100. #2328C22semidirect
103. #2073C22semidirect
104. #2072C22semidirect
105. #2072C22semidirect
107. #2066C22semidirect
109. #2065C22semidirect
110. #2056C22semidirect
113. #2042C22semidirect
114. #2042C22semidirect
115. #2042C22semidirect
120. #2026C22semidirect
122. #2025C22semidirect
123. #2025C22semidirect
124. #2016C22semidirect
127. #2015C22semidirect
128. #2015C22semidirect
139. #2011C22semidirect
142. #1983C22semidirect
147. #1973C22semidirect
148. #1973C22semidirect
149. #1973C22semidirect
150. #1973C22semidirect
157. #1968C22semidirect
158. #1968C22semidirect
159. #1968C22semidirect
161. #1957C22semidirect
162. #1942C22semidirect
163. #1942C22semidirect
164. #1928C22semidirect
165. #1927C22semidirect
167. #1926C22semidirect
171. #1917C22semidirect
172. #1916C22semidirect
173. #1916C22semidirect
178. #1879C22semidirect
179. #1879C22semidirect
180. #1879C22semidirect
181. #1878C22semidirect
182. #1878C22semidirect
186. #1865C22semidirect
188. #1864C22semidirect
189. #1862C22semidirect
190. #1847C22semidirect
191. #1840C22semidirect
195. #1776C22semidirect
196. #1771C22semidirect
197. #1770C22semidirect
198. C8×C4⋊C4C22semidirect
202. #1726C22semidirect

Maximal subgroups

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

subgroupindex
#427492
#425442
#332462
#321702
#321632
#309962
#309852
#308952
#308912
#305402
#305392
#300542
#300482
#284672
#284642
#280262
#278012
#265942
#265852
#264822
#262612
#257932
#257912
#254292
#251602
#251582
#250362
#231932
#224422
#217042
#216712