Finite Group Databasebeta

← #7038507

Subgroups — #7038507

Order 512.

1487 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45259C211yesmaximal, characteristic, complemented
2#42563C211yesmaximal, characteristic, complemented
3#32431C211yesmaximal, characteristic, complemented
4#32299C211yesmaximal, characteristic, complemented
5#31647C211yesmaximal, characteristic, complemented
6#31136C211yesmaximal, characteristic, complemented
7#31057C211yesmaximal, characteristic
8#31012C211yesmaximal, characteristic, complemented
9#30799C211yesmaximal, characteristic, complemented
10#30422C211yesmaximal, characteristic, complemented
11#28891C211yesmaximal, characteristic, complemented
12#28867C211yesmaximal, characteristic, complemented
13#28547C211yesmaximal, characteristic, complemented
14#28357C211yesmaximal, characteristic, complemented
15#28328C211yesmaximal, characteristic, complemented
16#28022C211yesmaximal, characteristic, complemented
17#27904C211yesmaximal, characteristic, complemented
18#27796C211yesmaximal, characteristic, complemented
19#27489C211yesmaximal, characteristic, complemented
20#27249C211yesmaximal, characteristic, complemented
21#27243C211yesmaximal, characteristic, complemented
22#27072C211yesmaximal, characteristic, complemented
23#26809C211yesmaximal, characteristic, complemented
24#25167C211yesmaximal, characteristic, complemented
25#25021C211yesmaximal, characteristic, complemented
26#24878C211yesmaximal, characteristic, complemented
27#23767C211yesmaximal, characteristic, complemented
28#23303C211yesmaximal, characteristic, complemented
29#23107C211yesmaximal, characteristic, complemented
30#22864C211yesmaximal, characteristic, complemented
31#22055C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic, complemented
33C2×#481C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#483C2211yescharacteristic, complemented
36C2×#479C2211yescharacteristic, complemented
37C2×#476C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#452C2211yescharacteristic, complemented
41C2×#449C2211yescharacteristic
42C2×#449C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#447C2211yescharacteristic
45C2×#440C2211yescharacteristic
46C2×#418C2211yescharacteristic
47#2827—21no—
48#2781—21no—
49#2753—21no—
50#2753—21no—
51#2747—21no—
52#2741—21no—
53#2735—21no—
54#2730—21no—
55#2685—21no—
56#2648—21no—
57#2622—21no—
58#2620C2211yescharacteristic
59#2597—21no—
60#2574—21no—
61#2568C2211yescharacteristic, complemented
62#2566C2211yescharacteristic
63#2560—21no—
64#2536C2211yescharacteristic
65#2521—21no—
66#2513C2211yescharacteristic
67#2513C2211yescharacteristic, complemented
68#2512C2211yescharacteristic, complemented
69#2500C2211yescharacteristic
70#2496C2211yescharacteristic
71#2491C2211yescharacteristic
72#2490C2211yescharacteristic
73#2489C2211yescharacteristic
74#2480—21no—
75#2448C2211yescharacteristic
76#2440C2211yescharacteristic, complemented
77#2435C2211yescharacteristic
78#2427C2211yescharacteristic
79#2423C2211yescharacteristic
80#2408C2211yescharacteristic
81#2407C2211yescharacteristic
82#2395C2211yescharacteristic
83#2367C2211yescharacteristic
84#2362C2211yescharacteristic
85#2355C2211yescharacteristic, complemented
86#2352C2211yescharacteristic
87#2341C2211yescharacteristic, complemented
88D4×C22⋊C4C2211yescharacteristic
89#2324C2211yescharacteristic
90#2314C2211yescharacteristic, complemented
91#2311C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2096C2211yescharacteristic, complemented
95#2094C2211yescharacteristic, complemented
96#2093C2211yescharacteristic
97#2092C2211yescharacteristic
98#2092C2211yescharacteristic
99#2084C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic, complemented
103#2076C2211yescharacteristic, complemented
104#2073C2211yescharacteristic
105#2073C2211yescharacteristic, complemented
106#2071C2211yescharacteristic
107#2068C2211yescharacteristic, complemented
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic, complemented
110#2059C2211yescharacteristic, complemented
111#2055C2211yescharacteristic
112#2054C2211yescharacteristic
113#2054C2211yescharacteristic
114#2042C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic, complemented
118#2035C2211yescharacteristic, complemented
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#2025C2211yescharacteristic, complemented
126#2024C2211yescharacteristic, complemented
127#2023C2211yescharacteristic
128#2015C2211yescharacteristic
129#2012C2211yescharacteristic
130#2012C2211yescharacteristic
131#2001C2211yescharacteristic
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic, complemented
134#1972C2211yescharacteristic
135#1972C2211yescharacteristic
136#1971C2211yescharacteristic, complemented
137#1970C2211yescharacteristic
138#1970C2211yescharacteristic
139#1968C2211yescharacteristic
140#1968C2211yescharacteristic
141#1968C2211yescharacteristic, complemented
142#1959C2211yescharacteristic
143#1959C2211yescharacteristic
144#1958C2211yescharacteristic
145#1954C2211yescharacteristic
146#1949C2211yescharacteristic, complemented
147#1948C2211yescharacteristic, complemented
148#1944C2211yescharacteristic, complemented
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1928C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic, complemented
160#1925C2211yescharacteristic, complemented
161#1924C2211yescharacteristic
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic, complemented
164#1924C2211yescharacteristic, complemented
165#1919C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1916C2211yescharacteristic, complemented
168#1894C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic, complemented
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1877C2211yescharacteristic
177#1874C2211yescharacteristic
178#1870C2211yescharacteristic
179#1864C2211yescharacteristic
180#1863C2211yescharacteristic, complemented
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1852C2211yescharacteristic, complemented
184#1847C2211yescharacteristic, complemented
185#1846C2211yescharacteristic, complemented
186#1834C2211yescharacteristic, complemented
187#1809C2211yescharacteristic
188#1805C2211yescharacteristic, complemented
189#1788C2211yescharacteristic, complemented
190#1786C2211yescharacteristic
191#1776C2211yescharacteristic, complemented
192C4×#107C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194#1771C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197C4×#103C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1750C2211yescharacteristic, complemented
202#1750C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#126—21no—
214C2×#126—21no—
215C2×#125C2311yescharacteristic
216C2×#124—21no—
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#120—21no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C22⋊C4—21no—
237#501—42no—
238#485—42no—
239#483—42no—
240#481—42no—
241#479—42no—
242#476—42no—
243#468—42no—
244#464—24no—
245#452—42no—
246#450—24no—
247#449—24no—
248#449—42no—
249#447—42no—
250#440—42no—
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268#418—42no—
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400D411yescharacteristic
316#399—21no—
317#399—21no—
318#399D411yescharacteristic
319#398—21no—
320#398—21no—
321#398—21no—
322#398D411yescharacteristic
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397D411yescharacteristic
334#397D411yescharacteristic
335#397D411yescharacteristic
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#395—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394D411yescharacteristic
355#394D411yescharacteristic
356#393—21no—
357#392—21no—
358#392—21no—
359#391—21no—
360#391—21no—
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#390—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
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#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#382—21no—
434#382—21no—
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#380—21no—
439#380—21no—
440#380—21no—
441#380—21no—
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#379—21no—
449#379—21no—
450#379—21no—
451#379—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×D4—22no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4C2×D411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C2×Q16—22no—
525C2×Q16—41no—
526C2×Q16—41no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16#4114yes—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8—41no—
542C2×M16—22no—
543C2×M16—41no—
544C2×M16—41no—
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C4⋊Q8—41no—
554C4⋊Q8—41no—
555#126—82no—
556#126—82no—
557#125—41no—
558#125—41no—
559#124—22no—
560#124—41no—
561#124—41no—
562#124—41no—
563#124—82no—
564C22⋊Q8—22no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—82no—
571#121—22no—
572#121—41no—
573#121—41no—
574#121—41no—
575#121—41no—
576#121—41no—
577#120—82no—
578C4×Q8—22no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×Q8—41no—
583C4×Q8—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590#117—41no—
591#117—41no—
592#117—41no—
593#117—41no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—41no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—82no—
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700#107—22no—
701#107—41no—
702#107—41no—
703#107—41no—
704#107—41no—
705#107—41no—
706#107—41no—
707#106—22no—
708#106—22no—
709#106—22no—
710#106—41no—
711#106—41no—
712#106—41no—
713#106—41no—
714C4⋊C8—22no—
715C4⋊C8—22no—
716C4⋊C8—41no—
717#103—22no—
718#103—22no—
719#103—22no—
720#103—22no—
721#103—22no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745C22⋊C8—22no—
746C22⋊C8—22no—
747C22⋊C8—22no—
748C22⋊C8—22no—
749C22⋊C8—22no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752#97—22no—
753#97—41no—
754#97—41no—
755#97—41no—
756C4×C8—41no—
757C4×C8—41no—
758C4×C8—41no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800C24—21no—
801C24—21no—
802C24—21no—
803C24—42no—
804C24—42no—
805C24—81no—
806C24—81no—
807C24—81no—
808C24—81no—
809C24—81no—
810C24C22×D411yescharacteristic
811C24C22×D411yescharacteristic
812#41—82no—
813#41—82no—
814#41—82no—
815#41—82no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—42no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×Q8C2×#4112yes—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—41no—
849C2×D4—41no—
850C2×D4—41no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—44no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—82no—
859C2×D4—82no—
860C2×D4—82no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4C2×#4112yes—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C2511yescharacteristic
921Q16—82no—
922SD16—44no—
923SD16—82no—
924SD16—82no—
925D8—82no—
926D8—82no—
927M16—82no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8C2×#4112yes—
950C2×C8H(5,𝔽2)12yes—
951C2×C8H(5,𝔽2)12yes—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—42no—
1063C42—81no—
1064C42—81no—
1065C42—81no—
1066C42—81no—
1067C42—81no—
1068C42—81no—
1069C42—81no—
1070C42—81no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—22no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—84no—
1107C23—84no—
1108C23—162no—
1109C23—162no—
1110C23—162no—
1111C23—162no—
1112C23—162no—
1113C23C23×D411yescharacteristic
1114Q8—22no—
1115Q8—22no—
1116Q8—41no—
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—41no—
1122Q8—162no—
1123D4—22no—
1124D4—22no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—82no—
1136D4—84no—
1137D4—84no—
1138D4—162no—
1139D4—162no—
1140D4—162no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—84no—
1225C2×C4—162no—
1226C2×C4—162no—
1227C2×C4—162no—
1228C2×C4C22×#4111yescharacteristic
1229C2×C4C2×H(5,𝔽2)11yescharacteristic
1230C2×C4C2×H(5,𝔽2)11yescharacteristic
1231C2×C4#58511yescharacteristic
1232C2×C4#58511yescharacteristic
1233C2×C4#58511yescharacteristic
1234C8—22no—
1235C8—22no—
1236C8—22no—
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—42no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—42no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—42no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—168no—
1278C22D4×#4111yescharacteristic
1279C22#348511yescharacteristic
1280C22#349811yescharacteristic
1281C22#358411yescharacteristic
1282C22#358511yescharacteristic
1283C22#358511yescharacteristic
1284C22#358611yescharacteristic
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—42no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4#350511yescharacteristic
1311C4#351411yescharacteristic
1312C4#354511yescharacteristic
1313C4#356011yescharacteristic
1314C2—81no—
1315C2—81no—
1316C2—82no—
1317C2—161no—
1318C2—161no—
1319C2#4350211yescharacteristic
1320C2#6150711yescharacteristic
1321C2#6153811yescharacteristic
1322C2#6175111yescharacteristic
1323C2#6179911yescharacteristic
1324C2#6244511yescharacteristic
1325C2#6246811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#31057C2
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. #45259C2semidirect
2. #42563C2semidirect
3. #32431C2semidirect
4. #32299C2semidirect
5. #31647C2semidirect
6. #31136C2semidirect
8. #31012C2semidirect
9. #30799C2semidirect
10. #30422C2semidirect
11. #28891C2semidirect
12. #28867C2semidirect
13. #28547C2semidirect
14. #28357C2semidirect
15. #28328C2semidirect
16. #28022C2semidirect
17. #27904C2semidirect
18. #27796C2semidirect
19. #27489C2semidirect
20. #27249C2semidirect
21. #27243C2semidirect
22. #27072C2semidirect
23. #26809C2semidirect
24. #25167C2semidirect
25. #25021C2semidirect
26. #24878C2semidirect
27. #23767C2semidirect
28. #23303C2semidirect
29. #23107C2semidirect
30. #22864C2semidirect
31. #22055C2semidirect
32. C2×#501C22semidirect
35. C2×#483C22semidirect
36. C2×#479C22semidirect
40. C2×#452C22semidirect
61. #2568C22semidirect
67. #2513C22semidirect
68. #2512C22semidirect
76. #2440C22semidirect
85. #2355C22semidirect
87. #2341C22semidirect
90. #2314C22semidirect
91. #2311C22semidirect
92. #2101C22semidirect
93. #2097C22semidirect
94. #2096C22semidirect
95. #2094C22semidirect
99. #2084C22semidirect
100. #2083C22semidirect
102. #2077C22semidirect
103. #2076C22semidirect
105. #2073C22semidirect
107. #2068C22semidirect
109. #2067C22semidirect
110. #2059C22semidirect
117. #2036C22semidirect
118. #2035C22semidirect
125. #2025C22semidirect
126. #2024C22semidirect
133. #1973C22semidirect
136. #1971C22semidirect
141. #1968C22semidirect
146. #1949C22semidirect
147. #1948C22semidirect
148. #1944C22semidirect
150. #1936C22semidirect
151. #1933C22semidirect
152. #1928C22semidirect
153. #1928C22semidirect
154. #1927C22semidirect
159. #1925C22semidirect
160. #1925C22semidirect
163. #1924C22semidirect
164. #1924C22semidirect
165. #1919C22semidirect
166. #1916C22semidirect
167. #1916C22semidirect
171. #1880C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
180. #1863C22semidirect
183. #1852C22semidirect
184. #1847C22semidirect
185. #1846C22semidirect
186. #1834C22semidirect
188. #1805C22semidirect
189. #1788C22semidirect
191. #1776C22semidirect
192. C4×#107C22semidirect
193. #1771C22semidirect
194. #1771C22semidirect
195. #1763C22semidirect
197. C4×#103C22semidirect
201. #1750C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#452592
#425632
#324312
#322992
#316472
#311362
#310572
#310122
#307992
#304222
#288912
#288672
#285472
#283572
#283282
#280222
#279042
#277962
#274892
#272492
#272432
#270722
#268092
#251672
#250212
#248782
#237672
#233032
#231072
#228642
#220552