Finite Group Databasebeta

← #7591019

Subgroups — #7591019

Order 512.

1644 conjugacy classes of subgroups.

The subgroup lattice has 1315 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59274C211yesmaximal, characteristic, complemented
2#59272C211yesmaximal, characteristic
3#32433C211yesmaximal, characteristic, complemented
4#32430C211yesmaximal, characteristic, complemented
5#31934C211yesmaximal, characteristic, complemented
6#31931C211yesmaximal, characteristic, complemented
7#28543C211yesmaximal, characteristic, complemented
8#28025C211yesmaximal, characteristic, complemented
9#28018C211yesmaximal, characteristic, complemented
10#27945C211yesmaximal, characteristic, complemented
11#27795C211yesmaximal, characteristic, complemented
12#27586C211yesmaximal, characteristic, complemented
13#27585C211yesmaximal, characteristic, complemented
14#27497C211yesmaximal, characteristic, complemented
15#27489C211yesmaximal, characteristic, complemented
16#26799C211yesmaximal, characteristic, complemented
17#26791C211yesmaximal, characteristic, complemented
18#26068C211yesmaximal, characteristic, complemented
19#25965C211yesmaximal, characteristic, complemented
20#25950C211yesmaximal, characteristic, complemented
21#25045C211yesmaximal, characteristic, complemented
22#24875C211yesmaximal, characteristic, complemented
23#24861C211yesmaximal, characteristic
24#24269C211yesmaximal, characteristic
25#23041C211yesmaximal, characteristic, complemented
26#22819C211yesmaximal, characteristic, complemented
27#22659C211yesmaximal, characteristic, complemented
28#22437C211yesmaximal, characteristic, complemented
29#21563C211yesmaximal, characteristic, complemented
30C2×#1968C211yesmaximal, characteristic, complemented
31#20817C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#501C2211yescharacteristic, complemented
34C2×#485C2211yescharacteristic, complemented
35C2×#480C2211yescharacteristic
36C2×#479C2211yescharacteristic, complemented
37C2×#474C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C2×#428C2211yescharacteristic, complemented
44C22×#106C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×C4×C8C2211yescharacteristic
48#2763—21no—
49#2761—21no—
50#2755—21no—
51#2753—21no—
52#2597—21no—
53#2589—21no—
54#2586—21no—
55#2567C2211yescharacteristic, complemented
56#2566C2211yescharacteristic
57#2564—21no—
58#2554—21no—
59#2513C2211yescharacteristic
60#2512C2211yescharacteristic
61#2511C2211yescharacteristic, complemented
62#2511C2211yescharacteristic, complemented
63#2505—21no—
64#2502C2211yescharacteristic, complemented
65#2500C2211yescharacteristic
66#2492C2211yescharacteristic, complemented
67#2490C2211yescharacteristic
68#2480—21no—
69#2442C2211yescharacteristic
70#2440C2211yescharacteristic
71#2438—21no—
72#2423C2211yescharacteristic, complemented
73#2422C2211yescharacteristic
74#2412—21no—
75#2411—21no—
76#2409C2211yescharacteristic
77#2408C2211yescharacteristic
78#2363C2211yescharacteristic
79#2360C2211yescharacteristic, complemented
80#2359—21no—
81#2357C2211yescharacteristic
82#2355C2211yescharacteristic, complemented
83#2352C2211yescharacteristic
84D4×C4⋊C4C2211yescharacteristic
85#2342—21no—
86Q8×C22⋊C4C2211yescharacteristic
87D4×C22⋊C4C2211yescharacteristic
88C4×#123C2211yescharacteristic
89C2×#391C2211yescharacteristic
90C2×#390C2211yescharacteristic
91#2285C2211yescharacteristic
92#2285C2211yescharacteristic
93#2097C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2095C2211yescharacteristic, complemented
96#2095C2211yescharacteristic, complemented
97#2094C2211yescharacteristic
98#2094C2211yescharacteristic
99#2093C2211yescharacteristic
100#2093C2211yescharacteristic
101#2085C2211yescharacteristic, complemented
102#2084C2211yescharacteristic, complemented
103#2074C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2072C2211yescharacteristic, complemented
106#2071C2211yescharacteristic
107#2071C2211yescharacteristic
108#2071C2211yescharacteristic
109#2068C2211yescharacteristic, complemented
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2066C2211yescharacteristic, complemented
113#2059C2211yescharacteristic, complemented
114#2058C2211yescharacteristic, complemented
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic
117#2036C2211yescharacteristic, complemented
118#2035C2211yescharacteristic, complemented
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2026C2211yescharacteristic, complemented
122#2023C2211yescharacteristic
123#2000C2211yescharacteristic
124#2000C2211yescharacteristic
125#1973C2211yescharacteristic
126#1973C2211yescharacteristic
127#1973C2211yescharacteristic
128#1973C2211yescharacteristic
129#1968C2211yescharacteristic
130#1968C2211yescharacteristic
131#1968C2211yescharacteristic
132#1968C2211yescharacteristic
133#1968C2211yescharacteristic
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1949C2211yescharacteristic, complemented
138#1948C2211yescharacteristic, complemented
139#1944C2211yescharacteristic, complemented
140#1943C2211yescharacteristic, complemented
141#1928C2211yescharacteristic, complemented
142#1928C2211yescharacteristic, complemented
143#1928C2211yescharacteristic, complemented
144#1928C2211yescharacteristic, complemented
145#1928C2211yescharacteristic, complemented
146#1927C2211yescharacteristic, complemented
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1923C2211yescharacteristic, complemented
154#1923C2211yescharacteristic, complemented
155#1916C2211yescharacteristic, complemented
156#1916C2211yescharacteristic, complemented
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1877C2211yescharacteristic
160#1877C2211yescharacteristic
161#1874C2211yescharacteristic
162#1873C2211yescharacteristic, complemented
163#1869C2211yescharacteristic
164#1865C2211yescharacteristic, complemented
165#1863C2211yescharacteristic, complemented
166#1862C2211yescharacteristic
167#1862C2211yescharacteristic
168#1854C2211yescharacteristic, complemented
169#1853C2211yescharacteristic
170#1853C2211yescharacteristic
171#1853C2211yescharacteristic, complemented
172#1852C2211yescharacteristic
173#1852C2211yescharacteristic
174#1850C2211yescharacteristic
175#1847C2211yescharacteristic, complemented
176#1847C2211yescharacteristic, complemented
177#1845C2211yescharacteristic, complemented
178#1845C2211yescharacteristic, complemented
179#1834C2211yescharacteristic, complemented
180#1834C2211yescharacteristic, complemented
181#1817C2211yescharacteristic
182#1809C2211yescharacteristic, complemented
183#1808C2211yescharacteristic
184#1808C2211yescharacteristic
185#1808C2211yescharacteristic
186#1808C2211yescharacteristic
187#1805C2211yescharacteristic, complemented
188#1802C2211yescharacteristic
189#1787C2211yescharacteristic
190#1787C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194C4×#107C2211yescharacteristic, complemented
195C4×#107C2211yescharacteristic, complemented
196C4×#107C2211yescharacteristic, complemented
197C4×#107C2211yescharacteristic, complemented
198#1771C2211yescharacteristic, complemented
199#1771C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201#1753C2211yescharacteristic, complemented
202#1752C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16—24no—
206C22×SD16—24no—
207C22×SD16—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#125C2311yescharacteristic
218C2×#123—21no—
219C2×#123D411yescharacteristic
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#120—21no—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×D4—21no—
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×#117—21no—
233C2×#117—21no—
234C2×#117C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C22⋊C4—21no—
239C22×C22⋊C4—21no—
240C22×C22⋊C4—21no—
241C22×C42C2311yescharacteristic
242#501—42no—
243#485—42no—
244#480—42no—
245#479—42no—
246#474—42no—
247#468—24no—
248#468—42no—
249#440—24no—
250#440—42no—
251#435—24no—
252#428—42no—
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106—42no—
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×#103—42no—
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#102—42no—
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×C4×C8—24no—
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#399—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#395—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#393—21no—
346#393—21no—
347#392—21no—
348#391—21no—
349#391—21no—
350#391—21no—
351#391—21no—
352#391—21no—
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#390—21no—
362#390—21no—
363#390—21no—
364#390—21no—
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
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#388D411yescharacteristic
394#388D411yescharacteristic
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387D411yescharacteristic
405#387D411yescharacteristic
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386D411yescharacteristic
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385D411yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#382—21no—
431#382—21no—
432#382—21no—
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#381—21no—
436#381D411yescharacteristic
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#379—21no—
448#379—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468C2×#95—21no—
469C2×#95—21no—
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—22no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4C2×D411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—416no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16#4114yes—
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—22no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—22no—
548C22×C8—22no—
549C22×C8—41no—
550C22×C8#4114yes—
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C4⋊Q8—41no—
560C4⋊Q8—41no—
561#126—82no—
562#125—41no—
563#125—41no—
564#123—24no—
565#123—82no—
566C22⋊Q8—22no—
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#120—82no—
576C4×Q8—22no—
577C4×Q8—41no—
578C4×Q8—41no—
579C4×Q8—41no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—82no—
587#117—41no—
588#117—41no—
589#117—82no—
590#117—82no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
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—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
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—44no—
670C2×C22⋊C4—82no—
671C2×C22⋊C4—82no—
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C42—22no—
681C2×C42—22no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42C2×D411yescharacteristic
692C2×C42C2×D411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698#107—22no—
699#107—22no—
700#107—22no—
701#107—22no—
702#107—22no—
703#107—22no—
704#107—41no—
705#107—41no—
706#107—41no—
707#107—41no—
708#107—41no—
709#107—41no—
710#106—22no—
711#106—22no—
712#106—41no—
713#106—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718C4⋊C8—22no—
719C4⋊C8—22no—
720C4⋊C8—41no—
721#103—22no—
722#103—22no—
723#103—22no—
724#103—22no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
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—41no—
750#97—22no—
751#97—22no—
752#97—22no—
753C4×C8—22no—
754C4×C8—22no—
755C4×C8—22no—
756C4×C8—22no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803C24—21no—
804C24—21no—
805C24—42no—
806C24—42no—
807C24—42no—
808C24—42no—
809C24—81no—
810C24—81no—
811C24—81no—
812C24C22×D411yescharacteristic
813C24C22×D411yescharacteristic
814C2×Q8—21no—
815C2×Q8—21no—
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—42no—
826C2×Q8—44no—
827C2×Q8—44no—
828C2×Q8—42no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8—81no—
832C2×Q8—81no—
833C2×Q8—82no—
834C2×Q8—82no—
835C2×Q8C2×#4112yes—
836C2×D4—22no—
837C2×D4—22no—
838C2×D4—22no—
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—21no—
849C2×D4—21no—
850C2×D4—44no—
851C2×D4—44no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—82no—
856C2×D4—82no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4C2×#4112yes—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—22no—
871C22×C4—21no—
872C22×C4—22no—
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—41no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
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×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4#13714yes—
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×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C2×#4112yes—
925C22×C42−1+412yes—
926C22×C4C2511yescharacteristic
927SD16—28no—
928SD16—44no—
929SD16—44no—
930SD16—44no—
931M16—44no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—28no—
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×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—44no—
953C2×C8C2×#4112yes—
954C2×C8C2×#4112yes—
955C2×C8C2×#4112yes—
956C2×C8H(5,𝔽2)12yes—
957C2×C8H(5,𝔽2)12yes—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
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—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—41no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
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—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C22⋊C4—22no—
1014C22⋊C4—22no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—41no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—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—
1050C42—22no—
1051C42—22no—
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—22no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—84no—
1097C23—84no—
1098C23—84no—
1099C23—84no—
1100C23—162no—
1101C23—162no—
1102C23—162no—
1103C23#54712yes—
1104C23C2×#13712yes—
1105C23#57612yes—
1106C23C23×D411yescharacteristic
1107Q8—22no—
1108Q8—22no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—41no—
1115Q8—84no—
1116Q8—162no—
1117D4—22no—
1118D4—22no—
1119D4—44no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—84no—
1127D4—162no—
1128D4—162no—
1129C2×C4—21no—
1130C2×C4—28no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
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—22no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—44no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—84no—
1214C2×C4—162no—
1215C2×C4—162no—
1216C2×C4—162no—
1217C2×C4—162no—
1218C2×C4—162no—
1219C2×C4#54712yes—
1220C2×C4C2×#13712yes—
1221C2×C4C2×#13712yes—
1222C2×C4#57712yes—
1223C2×C4C22×#4111yescharacteristic
1224C2×C4C22×#4111yescharacteristic
1225C2×C4C2×H(5,𝔽2)11yescharacteristic
1226C2×C4C2×H(5,𝔽2)11yescharacteristic
1227C2×C4C2×2−1+411yescharacteristic
1228C2×C4#58511yescharacteristic
1229C8—22no—
1230C8—22no—
1231C8—41no—
1232C8—41no—
1233C8—41no—
1234C8—41no—
1235C8—41no—
1236C8#55114yes—
1237C22—22no—
1238C22—22no—
1239C22—22no—
1240C22—22no—
1241C22—22no—
1242C22—22no—
1243C22—41no—
1244C22—42no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—42no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—42no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—168no—
1265C22#334614yes—
1266C22C2×#54711yescharacteristic
1267C22D4×#4111yescharacteristic
1268C22#349811yescharacteristic
1269C22C22×#13711yescharacteristic
1270C22C2×#57611yescharacteristic
1271C22C2×#57711yescharacteristic
1272C22#358411yescharacteristic
1273C4—22no—
1274C4—22no—
1275C4—22no—
1276C4—22no—
1277C4—41no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—42no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4C2×#55111yescharacteristic
1300C4#349411yescharacteristic
1301C4#352011yescharacteristic
1302C4#356111yescharacteristic
1303C2—24no—
1304C2—81no—
1305C2—82no—
1306C2—161no—
1307C2#5927311yescharacteristic
1308C2C2×#334611yescharacteristic
1309C2#6126311yescharacteristic
1310C2#6143811yescharacteristic
1311C2#6149811yescharacteristic
1312C2#6242211yescharacteristic
1313C2#6243611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59274C2semidirect
3. #32433C2semidirect
4. #32430C2semidirect
5. #31934C2semidirect
6. #31931C2semidirect
7. #28543C2semidirect
8. #28025C2semidirect
9. #28018C2semidirect
10. #27945C2semidirect
11. #27795C2semidirect
12. #27586C2semidirect
13. #27585C2semidirect
14. #27497C2semidirect
15. #27489C2semidirect
16. #26799C2semidirect
17. #26791C2semidirect
18. #26068C2semidirect
19. #25965C2semidirect
20. #25950C2semidirect
21. #25045C2semidirect
22. #24875C2semidirect
25. #23041C2semidirect
26. #22819C2semidirect
27. #22659C2semidirect
28. #22437C2semidirect
29. #21563C2semidirect
30. C2×#1968C2semidirect
31. #20817C2semidirect
33. C2×#501C22semidirect
34. C2×#485C22semidirect
36. C2×#479C22semidirect
43. C2×#428C22semidirect
55. #2567C22semidirect
61. #2511C22semidirect
62. #2511C22semidirect
64. #2502C22semidirect
66. #2492C22semidirect
72. #2423C22semidirect
79. #2360C22semidirect
82. #2355C22semidirect
93. #2097C22semidirect
94. #2097C22semidirect
95. #2095C22semidirect
96. #2095C22semidirect
101. #2085C22semidirect
102. #2084C22semidirect
103. #2074C22semidirect
104. #2072C22semidirect
105. #2072C22semidirect
109. #2068C22semidirect
112. #2066C22semidirect
113. #2059C22semidirect
114. #2058C22semidirect
117. #2036C22semidirect
118. #2035C22semidirect
121. #2026C22semidirect
137. #1949C22semidirect
138. #1948C22semidirect
139. #1944C22semidirect
140. #1943C22semidirect
141. #1928C22semidirect
142. #1928C22semidirect
143. #1928C22semidirect
144. #1928C22semidirect
145. #1928C22semidirect
146. #1927C22semidirect
153. #1923C22semidirect
154. #1923C22semidirect
155. #1916C22semidirect
156. #1916C22semidirect
162. #1873C22semidirect
164. #1865C22semidirect
165. #1863C22semidirect
168. #1854C22semidirect
171. #1853C22semidirect
175. #1847C22semidirect
176. #1847C22semidirect
177. #1845C22semidirect
178. #1845C22semidirect
179. #1834C22semidirect
180. #1834C22semidirect
182. #1809C22semidirect
187. #1805C22semidirect
193. #1776C22semidirect
194. C4×#107C22semidirect
195. C4×#107C22semidirect
196. C4×#107C22semidirect
197. C4×#107C22semidirect
198. #1771C22semidirect
199. #1771C22semidirect
200. #1753C22semidirect
201. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#592742
#592722
#324332
#324302
#319342
#319312
#285432
#280252
#280182
#279452
#277952
#275862
#275852
#274972
#274892
#267992
#267912
#260682
#259652
#259502
#250452
#248752
#248612
#242692
#230412
#228192
#226592
#224372
#215632
C2×#19682
#208172