Finite Group Databasebeta

← #7336525

Subgroups — #7336525

Order 512.

1625 conjugacy classes of subgroups.

The subgroup lattice has 1410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53057C211yesmaximal, characteristic, complemented
2#45187C211yesmaximal, characteristic, complemented
3#32077C211yesmaximal, characteristic, complemented
4#31591C211yesmaximal, characteristic, complemented
5#31538C211yesmaximal, characteristic, complemented
6#31216C211yesmaximal, characteristic, complemented
7#31206C211yesmaximal, characteristic, complemented
8#30992C211yesmaximal, characteristic, complemented
9#30895C211yesmaximal, characteristic, complemented
10#30851C211yesmaximal, characteristic, complemented
11#30658C211yesmaximal, characteristic, complemented
12#30568C211yesmaximal, characteristic, complemented
13#30548C211yesmaximal, characteristic, complemented
14#30535C211yesmaximal, characteristic, complemented
15#29962C211yesmaximal, characteristic, complemented
16#29671C211yesmaximal, characteristic, complemented
17#28426C211yesmaximal, characteristic, complemented
18#28339C211yesmaximal, characteristic, complemented
19#28319C211yesmaximal, characteristic, complemented
20#27790C211yesmaximal, characteristic, complemented
21#26793C211yesmaximal, characteristic, complemented
22#26608C211yesmaximal, characteristic, complemented
23#26568C211yesmaximal, characteristic, complemented
24#26535C211yesmaximal, characteristic, complemented
25#26492C211yesmaximal, characteristic, complemented
26#25959C211yesmaximal, characteristic, complemented
27#25683C211yesmaximal, characteristic, complemented
28#25179C211yesmaximal, characteristic, complemented
29#24428C211yesmaximal, characteristic, complemented
30#24257C211yesmaximal, characteristic, complemented
31#22362C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C2×#499C2211yescharacteristic, complemented
35C2×#491C2211yescharacteristic, complemented
36C2×#489C2211yescharacteristic
37C2×#485C2211yescharacteristic, complemented
38C2×#482C2211yescharacteristic
39C2×#482C2211yescharacteristic
40C2×#477C2211yescharacteristic, complemented
41C2×#466C2211yescharacteristic
42C2×#465C2211yescharacteristic, complemented
43C2×#460C2211yescharacteristic, complemented
44C2×#460C2211yescharacteristic, complemented
45C2×#463C2211yescharacteristic
46C2×#463C2211yescharacteristic
47C2×#449C2211yescharacteristic
48C2×#449C2211yescharacteristic
49C2×#447C2211yescharacteristic
50C2×#447C2211yescharacteristic
51C2×#442C2211yescharacteristic
52C2×#440C2211yescharacteristic, complemented
53C2×#416C2211yescharacteristic
54#2829—21no—
55#2829—21no—
56#2816—21no—
57#2813—21no—
58#2741—21no—
59#2730—21no—
60#2711—21no—
61#2694—21no—
62#2687—21no—
63#2685—21no—
64#2685—21no—
65#2676—21no—
66#2629C2211yescharacteristic
67#2619C2211yescharacteristic
68#2570C2211yescharacteristic, complemented
69#2558—21no—
70#2545C2211yescharacteristic
71#2542C2211yescharacteristic, complemented
72#2537C2211yescharacteristic
73#2500C2211yescharacteristic, complemented
74#2491C2211yescharacteristic
75#2490—21no—
76#2490C2211yescharacteristic
77#2490C2211yescharacteristic, complemented
78#2480—21no—
79#2480—21no—
80#2454C2211yescharacteristic
81#2454C2211yescharacteristic, complemented
82#2448C2211yescharacteristic
83#2445C2211yescharacteristic, complemented
84#2439C2211yescharacteristic, complemented
85#2435C2211yescharacteristic
86#2432C2211yescharacteristic
87#2428C2211yescharacteristic, complemented
88#2426C2211yescharacteristic
89#2420C2211yescharacteristic
90#2415C2211yescharacteristic
91#2414C2211yescharacteristic
92#2395C2211yescharacteristic
93#2367C2211yescharacteristic
94#2362C2211yescharacteristic
95#2341C2211yescharacteristic
96#2309C2211yescharacteristic
97#2097C2211yescharacteristic, complemented
98#2095C2211yescharacteristic, complemented
99#2094C2211yescharacteristic
100#2093C2211yescharacteristic
101#2092C2211yescharacteristic
102#2092C2211yescharacteristic
103#2084C2211yescharacteristic, complemented
104#2073C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic, complemented
113#2058C2211yescharacteristic, complemented
114#2055C2211yescharacteristic, complemented
115#2054C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic, complemented
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic, complemented
125#2033C2211yescharacteristic, complemented
126#2025C2211yescharacteristic
127#2025C2211yescharacteristic
128#2025C2211yescharacteristic, complemented
129#2025C2211yescharacteristic, complemented
130#2023C2211yescharacteristic
131#2013C2211yescharacteristic, complemented
132#2013C2211yescharacteristic, complemented
133#2012C2211yescharacteristic
134#2012C2211yescharacteristic
135#2012C2211yescharacteristic
136#2012C2211yescharacteristic
137#2011C2211yescharacteristic
138#2011C2211yescharacteristic
139#2000C2211yescharacteristic
140#2000C2211yescharacteristic
141#2000C2211yescharacteristic
142#2000C2211yescharacteristic
143#2000C2211yescharacteristic, complemented
144#1999C2211yescharacteristic
145#1992C2211yescharacteristic, complemented
146#1983C2211yescharacteristic
147#1973C2211yescharacteristic, complemented
148#1972C2211yescharacteristic
149#1972C2211yescharacteristic
150#1972C2211yescharacteristic
151#1970C2211yescharacteristic
152#1970C2211yescharacteristic
153#1970C2211yescharacteristic
154#1968C2211yescharacteristic, complemented
155#1959C2211yescharacteristic
156#1958C2211yescharacteristic
157#1956C2211yescharacteristic, complemented
158#1955C2211yescharacteristic
159#1949C2211yescharacteristic, complemented
160#1944C2211yescharacteristic, complemented
161#1943C2211yescharacteristic, complemented
162#1939C2211yescharacteristic, complemented
163#1927C2211yescharacteristic, complemented
164#1926C2211yescharacteristic
165#1926C2211yescharacteristic, complemented
166#1925C2211yescharacteristic, complemented
167#1924C2211yescharacteristic
168#1924C2211yescharacteristic, complemented
169#1924C2211yescharacteristic, complemented
170#1923C2211yescharacteristic
171#1917C2211yescharacteristic, complemented
172#1917C2211yescharacteristic, complemented
173#1880C2211yescharacteristic, complemented
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1877C2211yescharacteristic, complemented
177#1875C2211yescharacteristic
178#1869C2211yescharacteristic
179#1865C2211yescharacteristic, complemented
180#1865C2211yescharacteristic, complemented
181#1865C2211yescharacteristic, complemented
182#1864C2211yescharacteristic, complemented
183#1863C2211yescharacteristic, complemented
184#1863C2211yescharacteristic, complemented
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic, complemented
187#1854C2211yescharacteristic
188#1854C2211yescharacteristic
189#1854C2211yescharacteristic, complemented
190#1850C2211yescharacteristic, complemented
191#1808C2211yescharacteristic, complemented
192#1805C2211yescharacteristic, complemented
193#1805C2211yescharacteristic, complemented
194#1802C2211yescharacteristic
195#1798C2211yescharacteristic
196#1788C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199C4×#107C2211yescharacteristic, complemented
200#1771C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#546—42no—
215#546—42no—
216#541—42no—
217#541—42no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#126—21no—
222C2×#126—21no—
223C2×#125—21no—
224C2×#125—21no—
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#124—21no—
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#123—21no—
232C2×#123—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#120—21no—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C22⋊C4—21no—
258#499—42no—
259#491—42no—
260#489—42no—
261#485—42no—
262#482—42no—
263#482—42no—
264#477—42no—
265#466—42no—
266#465—42no—
267#463—42no—
268#463—42no—
269#460—42no—
270#460—42no—
271#449—42no—
272#449—42no—
273#447—42no—
274#447—42no—
275#442—42no—
276#440—42no—
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294#416—42no—
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×#97C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338C2×C4×C8C2311yescharacteristic
339#400—21no—
340#400D411yescharacteristic
341#399—21no—
342#399—21no—
343#399—21no—
344#399—21no—
345#399—21no—
346#399D411yescharacteristic
347#398—21no—
348#398—21no—
349#398—21no—
350#398D411yescharacteristic
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#397D411yescharacteristic
357#397D411yescharacteristic
358#397D411yescharacteristic
359#396—21no—
360#396—21no—
361#396—21no—
362#396—21no—
363#396—21no—
364#396—21no—
365#396—21no—
366#396—21no—
367#394—21no—
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#394—21no—
387#394D411yescharacteristic
388#394D411yescharacteristic
389#393—21no—
390#393—21no—
391#392—21no—
392#392—21no—
393#392—21no—
394#392—21no—
395#391—21no—
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#390—21no—
399#390—21no—
400#390—21no—
401#390—21no—
402#390—21no—
403#390—21no—
404#390—21no—
405#390—21no—
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#390C2311yescharacteristic
412#390C2311yescharacteristic
413#390C2311yescharacteristic
414#390C2311yescharacteristic
415#390C2311yescharacteristic
416#390C2311yescharacteristic
417#390C2311yescharacteristic
418#389—21no—
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#388—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#386—21no—
446#386—21no—
447#386—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#382C2311yescharacteristic
456#382C2311yescharacteristic
457#381—21no—
458#380—21no—
459#380—21no—
460#380—21no—
461#380—21no—
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464#380C2311yescharacteristic
465#380C2311yescharacteristic
466#379—21no—
467#379—21no—
468#379—21no—
469#379—21no—
470C4×C4⋊C4—21no—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C22⋊C4—21no—
476C4×C22⋊C4—21no—
477C4×C22⋊C4C2311yescharacteristic
478C4×C22⋊C4C2311yescharacteristic
479C4×C22⋊C4C2311yescharacteristic
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
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8—21no—
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4C2×D411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C22×C8—22no—
563C22×C8—41no—
564C22×C8—41no—
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C4⋊Q8—22no—
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577#127—41no—
578#127—41no—
579#126—44no—
580#126—44no—
581#125—22no—
582#125—41no—
583#125—41no—
584#125—41no—
585#125—44no—
586#125—44no—
587#124—22no—
588#124—22no—
589#124—41no—
590#124—41no—
591#124—41no—
592#124—41no—
593#124—82no—
594#123—44no—
595#123—82no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—82no—
603C22⋊Q8—82no—
604#121—22no—
605#121—41no—
606#121—44no—
607#121—41no—
608#121—41no—
609#121—41no—
610#121—41no—
611#121—41no—
612#121—41no—
613#121—41no—
614#121—41no—
615#121—82no—
616#121—82no—
617#120—44no—
618C4×Q8—22no—
619C4×Q8—22no—
620C4×Q8—41no—
621C4×Q8—41no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×D4—22no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632#117—41no—
633#117—41no—
634#117—41no—
635#117—41no—
636#117—41no—
637#117—41no—
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—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
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×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—44no—
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748#107—22no—
749#107—22no—
750#107—22no—
751#107—41no—
752#107—41no—
753#107—41no—
754#106—22no—
755#106—41no—
756#106—41no—
757#106—41no—
758#106—41no—
759#106—41no—
760C4⋊C8—22no—
761C4⋊C8—41no—
762C4⋊C8—41no—
763C4⋊C8—41no—
764C4⋊C8—41no—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—22no—
770#103—22no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
781#102—22no—
782#102—22no—
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—
795#102—41no—
796#102—41no—
797C22⋊C8—22no—
798C22⋊C8—22no—
799C22⋊C8—22no—
800C22⋊C8—41no—
801C22⋊C8—41no—
802C22⋊C8—41no—
803C22⋊C8—41no—
804#97—22no—
805#97—41no—
806#97—41no—
807C4×C8—41no—
808C4×C8—41no—
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#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—42no—
844C24—42no—
845C24—81no—
846C24—81no—
847C24—81no—
848C24—81no—
849C24—81no—
850C24C22×D411yescharacteristic
851C24C22×D411yescharacteristic
852#41—44no—
853#41—82no—
854#41—82no—
855#41—82no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—42no—
868C2×Q8—81no—
869C2×Q8—81no—
870C2×Q8H(5,𝔽2)12yes—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—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—41no—
895C2×D4—41no—
896C2×D4—41no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—82no—
910C2×D4—82no—
911C2×D4—82no—
912C2×D4—82no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D42−1+412yes—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C2511yescharacteristic
978SD16—44no—
979SD16—82no—
980SD16—82no—
981SD16—82no—
982D8—44no—
983D8—82no—
984D8—82no—
985D8—82no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—82no—
1009C2×C8H(5,𝔽2)12yes—
1010C2×C8H(5,𝔽2)12yes—
1011C4⋊C4—24no—
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—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—41no—
1036C4⋊C4—41no—
1037C4⋊C4—41no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4H(5,𝔽2)12yes—
1061C22⋊C4—24no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
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—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—42no—
1129C42—42no—
1130C42—81no—
1131C42—81no—
1132C42—81no—
1133C42—81no—
1134C42—81no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—22no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
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—84no—
1178C23—84no—
1179C23—162no—
1180C23—162no—
1181C23—162no—
1182C23—162no—
1183C23—162no—
1184C23C23×D411yescharacteristic
1185Q8—22no—
1186Q8—22no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—162no—
1194D4—22no—
1195D4—22no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—82no—
1211D4—84no—
1212D4—84no—
1213D4—162no—
1214D4—162no—
1215D4—162no—
1216D4—162no—
1217D4—162no—
1218D4—162no—
1219D4—162no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—22no—
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—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
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—84no—
1301C2×C4—162no—
1302C2×C4—162no—
1303C2×C4—162no—
1304C2×C4C2×H(5,𝔽2)11yescharacteristic
1305C2×C4C2×H(5,𝔽2)11yescharacteristic
1306C2×C4C2×H(5,𝔽2)11yescharacteristic
1307C2×C4C2×H(5,𝔽2)11yescharacteristic
1308C2×C4C2×2−1+411yescharacteristic
1309C2×C4#58511yescharacteristic
1310C8—22no—
1311C8—22no—
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C22—41no—
1319C22—41no—
1320C22—42no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—42no—
1328C22—42no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—168no—
1361C22#348411yescharacteristic
1362C22#348911yescharacteristic
1363C22#349811yescharacteristic
1364C22#358411yescharacteristic
1365C22#358411yescharacteristic
1366C22#358511yescharacteristic
1367C22#358511yescharacteristic
1368C4—41no—
1369C4—41no—
1370C4—42no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—41no—
1381C4—42no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4#353611yescharacteristic
1393C4#353611yescharacteristic
1394C4#354211yescharacteristic
1395C4#355811yescharacteristic
1396C2—81no—
1397C2—81no—
1398C2—82no—
1399C2—161no—
1400C2—161no—
1401C2—161no—
1402C2#4795111yescharacteristic
1403C2#6161611yescharacteristic
1404C2#6169011yescharacteristic
1405C2#6217111yescharacteristic
1406C2#6217111yescharacteristic
1407C2#6243411yescharacteristic
1408C2#6244111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53057C2semidirect
2. #45187C2semidirect
3. #32077C2semidirect
4. #31591C2semidirect
5. #31538C2semidirect
6. #31216C2semidirect
7. #31206C2semidirect
8. #30992C2semidirect
9. #30895C2semidirect
10. #30851C2semidirect
11. #30658C2semidirect
12. #30568C2semidirect
13. #30548C2semidirect
14. #30535C2semidirect
15. #29962C2semidirect
16. #29671C2semidirect
17. #28426C2semidirect
18. #28339C2semidirect
19. #28319C2semidirect
20. #27790C2semidirect
21. #26793C2semidirect
22. #26608C2semidirect
23. #26568C2semidirect
24. #26535C2semidirect
25. #26492C2semidirect
26. #25959C2semidirect
27. #25683C2semidirect
28. #25179C2semidirect
29. #24428C2semidirect
30. #24257C2semidirect
31. #22362C2semidirect
34. C2×#499C22semidirect
35. C2×#491C22semidirect
37. C2×#485C22semidirect
40. C2×#477C22semidirect
42. C2×#465C22semidirect
43. C2×#460C22semidirect
44. C2×#460C22semidirect
52. C2×#440C22semidirect
68. #2570C22semidirect
71. #2542C22semidirect
73. #2500C22semidirect
77. #2490C22semidirect
81. #2454C22semidirect
83. #2445C22semidirect
84. #2439C22semidirect
87. #2428C22semidirect
97. #2097C22semidirect
98. #2095C22semidirect
103. #2084C22semidirect
108. #2067C22semidirect
109. #2066C22semidirect
112. #2065C22semidirect
113. #2058C22semidirect
114. #2055C22semidirect
122. #2035C22semidirect
124. #2034C22semidirect
125. #2033C22semidirect
128. #2025C22semidirect
129. #2025C22semidirect
131. #2013C22semidirect
132. #2013C22semidirect
143. #2000C22semidirect
145. #1992C22semidirect
147. #1973C22semidirect
154. #1968C22semidirect
157. #1956C22semidirect
159. #1949C22semidirect
160. #1944C22semidirect
161. #1943C22semidirect
162. #1939C22semidirect
163. #1927C22semidirect
165. #1926C22semidirect
166. #1925C22semidirect
168. #1924C22semidirect
169. #1924C22semidirect
171. #1917C22semidirect
172. #1917C22semidirect
173. #1880C22semidirect
176. #1877C22semidirect
179. #1865C22semidirect
180. #1865C22semidirect
181. #1865C22semidirect
182. #1864C22semidirect
183. #1863C22semidirect
184. #1863C22semidirect
186. #1862C22semidirect
189. #1854C22semidirect
190. #1850C22semidirect
191. #1808C22semidirect
192. #1805C22semidirect
193. #1805C22semidirect
199. C4×#107C22semidirect
200. #1771C22semidirect
201. C8×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#530572
#451872
#320772
#315912
#315382
#312162
#312062
#309922
#308952
#308512
#306582
#305682
#305482
#305352
#299622
#296712
#284262
#283392
#283192
#277902
#267932
#266082
#265682
#265352
#264922
#259592
#256832
#251792
#244282
#242572
#223622