Finite Group Databasebeta

← #7038607

Subgroups — #7038607

Order 512.

1516 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59224C211yesmaximal, characteristic
2#39659C211yesmaximal, characteristic, complemented
3#32442C211yesmaximal, characteristic, complemented
4#32295C211yesmaximal, characteristic, complemented
5#31663C211yesmaximal, characteristic, complemented
6#31122C211yesmaximal, characteristic, complemented
7#31065C211yesmaximal, characteristic
8#31002C211yesmaximal, characteristic, complemented
9#30779C211yesmaximal, characteristic, complemented
10#30420C211yesmaximal, characteristic
11#28883C211yesmaximal, characteristic, complemented
12#28858C211yesmaximal, characteristic, complemented
13#28539C211yesmaximal, characteristic, complemented
14#28367C211yesmaximal, characteristic, complemented
15#28311C211yesmaximal, characteristic, complemented
16#28027C211yesmaximal, characteristic, complemented
17#27896C211yesmaximal, characteristic, complemented
18#27802C211yesmaximal, characteristic, complemented
19#27509C211yesmaximal, characteristic, complemented
20#27239C211yesmaximal, characteristic, complemented
21#27224C211yesmaximal, characteristic, complemented
22#27084C211yesmaximal, characteristic, complemented
23#26814C211yesmaximal, characteristic, complemented
24#25156C211yesmaximal, characteristic, complemented
25#25028C211yesmaximal, characteristic, complemented
26#24880C211yesmaximal, characteristic, complemented
27#23765C211yesmaximal, characteristic, complemented
28#23304C211yesmaximal, characteristic, complemented
29#23100C211yesmaximal, characteristic, complemented
30#22885C211yesmaximal, characteristic, complemented
31#22049C211yesmaximal, characteristic, complemented
32C2×#500C2211yescharacteristic, complemented
33C2×#484C2211yescharacteristic
34C2×#484C2211yescharacteristic
35C2×#485C2211yescharacteristic, complemented
36C2×#477C2211yescharacteristic, complemented
37C2×#476C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#461C2211yescharacteristic
40C2×#448C2211yescharacteristic
41C2×#448C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×C4×SD16C2211yescharacteristic
46C2×#419C2211yescharacteristic, complemented
47#2857C2211yescharacteristic
48#2805—21no—
49#2788—21no—
50#2788—21no—
51#2784—21no—
52#2756—21no—
53#2737—21no—
54#2665—21no—
55#2610—21no—
56#2587—21no—
57#2586—21no—
58#2567C2211yescharacteristic, complemented
59#2563C2211yescharacteristic
60#2561—21no—
61#2538C2211yescharacteristic
62#2531—21no—
63#2513C2211yescharacteristic
64#2513C2211yescharacteristic
65#2511C2211yescharacteristic, complemented
66#2500C2211yescharacteristic
67#2497C2211yescharacteristic, complemented
68#2492C2211yescharacteristic
69#2492C2211yescharacteristic, complemented
70#2491C2211yescharacteristic
71#2472—21no—
72#2446C2211yescharacteristic, complemented
73#2440C2211yescharacteristic
74#2434C2211yescharacteristic, complemented
75#2429C2211yescharacteristic
76#2420C2211yescharacteristic
77#2412—21no—
78#2409C2211yescharacteristic
79#2408C2211yescharacteristic
80#2365C2211yescharacteristic, complemented
81#2363C2211yescharacteristic
82#2354C2211yescharacteristic
83#2352C2211yescharacteristic
84#2342—21no—
85Q8×C22⋊C4C2211yescharacteristic, complemented
86D4×C22⋊C4C2211yescharacteristic
87#2335—21no—
88C4×C22⋊Q8C2211yescharacteristic
89C4×#123C2211yescharacteristic
90C2×#390C2211yescharacteristic
91#2283C2211yescharacteristic
92#2101C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2095C2211yescharacteristic, complemented
96#2093C2211yescharacteristic
97#2093C2211yescharacteristic
98#2093C2211yescharacteristic
99#2085C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2077C2211yescharacteristic
102#2076C2211yescharacteristic
103#2075C2211yescharacteristic, complemented
104#2074C2211yescharacteristic, complemented
105#2074C2211yescharacteristic, complemented
106#2071C2211yescharacteristic
107#2068C2211yescharacteristic, complemented
108#2068C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2057C2211yescharacteristic, complemented
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2043C2211yescharacteristic, complemented
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic, complemented
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#2024C2211yescharacteristic, complemented
126#2024C2211yescharacteristic, complemented
127#2023C2211yescharacteristic
128#2013C2211yescharacteristic
129#2013C2211yescharacteristic
130#2013C2211yescharacteristic
131#2000C2211yescharacteristic
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic
138#1973C2211yescharacteristic
139#1973C2211yescharacteristic
140#1968C2211yescharacteristic
141#1968C2211yescharacteristic
142#1960C2211yescharacteristic, complemented
143#1960C2211yescharacteristic, complemented
144#1956C2211yescharacteristic, complemented
145#1955C2211yescharacteristic
146#1947C2211yescharacteristic, complemented
147#1947C2211yescharacteristic, complemented
148#1942C2211yescharacteristic, complemented
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1933C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1928C2211yescharacteristic, complemented
154#1928C2211yescharacteristic, complemented
155#1927C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1926C2211yescharacteristic
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1924C2211yescharacteristic, complemented
162#1924C2211yescharacteristic, complemented
163#1923C2211yescharacteristic
164#1923C2211yescharacteristic
165#1921C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1895C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1872C2211yescharacteristic
178#1870C2211yescharacteristic
179#1864C2211yescharacteristic
180#1863C2211yescharacteristic, complemented
181#1854C2211yescharacteristic, complemented
182#1854C2211yescharacteristic, complemented
183#1852C2211yescharacteristic
184#1847C2211yescharacteristic, complemented
185#1847C2211yescharacteristic, complemented
186#1836C2211yescharacteristic, complemented
187#1809C2211yescharacteristic, complemented
188#1805C2211yescharacteristic, complemented
189#1787C2211yescharacteristic, complemented
190#1786C2211yescharacteristic
191#1776C2211yescharacteristic, complemented
192#1776C2211yescharacteristic, complemented
193#1770C2211yescharacteristic, complemented
194#1770C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201#1749C2211yescharacteristic
202#1749C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#124—21no—
217C2×#123D411yescharacteristic
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#120—21no—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×#117—21no—
233C2×#117C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C22⋊C4—21no—
236C22×C22⋊C4—21no—
237C22×C22⋊C4—21no—
238C22×C42C2311yescharacteristic
239#500—42no—
240#485—42no—
241#484—42no—
242#484—42no—
243#477—42no—
244#476—42no—
245#468—42no—
246#461—24no—
247#450—24no—
248#450—42no—
249#450—42no—
250#448—24no—
251#448—42no—
252C4×SD16—42no—
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270#419—42no—
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#396—21no—
331#395—21no—
332#395—21no—
333#395—21no—
334#395—21no—
335#395—21no—
336#395—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#393—21no—
343#393—21no—
344#393—21no—
345#393—21no—
346#393—21no—
347#393—21no—
348#392—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#389—21no—
378#389—21no—
379#389—21no—
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
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#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388D411yescharacteristic
400#388D411yescharacteristic
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387D411yescharacteristic
411#387D411yescharacteristic
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386D411yescharacteristic
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385D411yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#383—21no—
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#381—21no—
433#381—21no—
434#381D411yescharacteristic
435#380—21no—
436#380—21no—
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⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466#376—21no—
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—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8—22no—
498C22×Q8—41no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—22no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4C2×D411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C2×D411yescharacteristic
523C23×C4C2×D411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16#4114yes—
544C2×M16—22no—
545C2×M16—41no—
546C2×M16—41no—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C4⋊Q8—22no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563#124—82no—
564#123—24no—
565C22⋊Q8—22no—
566C22⋊Q8—41no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—82no—
574#121—22no—
575#121—41no—
576#121—41no—
577#121—41no—
578#120—82no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×Q8—41no—
583C4×Q8—41no—
584C4×Q8—41no—
585C4×D4—22no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591#117—41no—
592#117—41no—
593#117—82no—
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—21no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
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—44no—
668C2×C22⋊C4—82no—
669C2×C22⋊C4—82no—
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—41no—
688C2×C42—41no—
689C2×C42C2×D411yescharacteristic
690C2×C42C2×D411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696#107—22no—
697#107—22no—
698#107—22no—
699#107—41no—
700#107—41no—
701#107—41no—
702#107—41no—
703#107—41no—
704#107—41no—
705#107—41no—
706#106—22no—
707#106—41no—
708#106—41no—
709#106—41no—
710C4⋊C8—22no—
711C4⋊C8—22no—
712C4⋊C8—41no—
713#103—22no—
714#103—22no—
715#103—22no—
716#103—22no—
717#103—22no—
718#103—22no—
719#103—22no—
720#103—22no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
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—
741C22⋊C8—22no—
742C22⋊C8—22no—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8—22no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748#97—41no—
749#97—41no—
750#97—41no—
751#97—41no—
752#97—41no—
753C4×C8—22no—
754C4×C8—41no—
755#95—21no—
756#95—21no—
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#95C2×D411yescharacteristic
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
802C24—21no—
803C24—21no—
804C24—42no—
805C24—42no—
806C24—42no—
807C24—42no—
808C24—81no—
809C24—81no—
810C24—81no—
811C24C22×D411yescharacteristic
812C24C22×D411yescharacteristic
813C2×Q8—21no—
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—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—42no—
831C2×Q8—44no—
832C2×Q8—81no—
833C2×Q8—81no—
834C2×Q8—81no—
835C2×Q8—81no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×Q8—81no—
840C2×Q8—82no—
841C2×Q8—82no—
842C2×Q8—82no—
843C2×Q8C2×#4112yes—
844C2×D4—22no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—81no—
862C2×D4—82no—
863C2×D4—82no—
864C2×D4—82no—
865C2×D4—82no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4C2×#4112yes—
872C22×C4—21no—
873C22×C4—22no—
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—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
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×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C2511yescharacteristic
929SD16—44no—
930SD16—82no—
931SD16—82no—
932SD16—82no—
933SD16—82no—
934SD16—82no—
935M16—82no—
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×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8C2×#4112yes—
958C2×C8H(5,𝔽2)12yes—
959C2×C8H(5,𝔽2)12yes—
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—41no—
985C4⋊C4—41no—
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—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
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#13714yes—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—41no—
1061C42—41no—
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—21no—
1080C23—22no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—41no—
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—84no—
1099C23—84no—
1100C23—84no—
1101C23—84no—
1102C23—162no—
1103C23—162no—
1104C23—162no—
1105C23C2×#13712yes—
1106C23C23×D411yescharacteristic
1107Q8—22no—
1108Q8—22no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—41no—
1115Q8—41no—
1116Q8—41no—
1117Q8—41no—
1118Q8—41no—
1119Q8—84no—
1120Q8—162no—
1121Q8—162no—
1122D4—22no—
1123D4—22no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—82no—
1131D4—84no—
1132D4—162no—
1133D4—162no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
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—22no—
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—21no—
1168C2×C4—21no—
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—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—84no—
1219C2×C4—82no—
1220C2×C4—82no—
1221C2×C4—84no—
1222C2×C4—162no—
1223C2×C4—162no—
1224C2×C4C2×#13712yes—
1225C2×C4C2×#13712yes—
1226C2×C4C22×#4111yescharacteristic
1227C2×C4C2×H(5,𝔽2)11yescharacteristic
1228C2×C4C2×H(5,𝔽2)11yescharacteristic
1229C2×C4#58511yescharacteristic
1230C2×C4#58511yescharacteristic
1231C2×C4#58511yescharacteristic
1232C8—22no—
1233C8—22no—
1234C8—22no—
1235C8—41no—
1236C8—41no—
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C22—22no—
1241C22—22no—
1242C22—22no—
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—42no—
1256C22—41no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—168no—
1269C22D4×#4111yescharacteristic
1270C22#348511yescharacteristic
1271C22#349811yescharacteristic
1272C22C22×#13711yescharacteristic
1273C22#358511yescharacteristic
1274C22#358511yescharacteristic
1275C22#358611yescharacteristic
1276C4—22no—
1277C4—22no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—42no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4#350511yescharacteristic
1303C4#351411yescharacteristic
1304C4#354511yescharacteristic
1305C4#356011yescharacteristic
1306C2—42no—
1307C2—81no—
1308C2—82no—
1309C2—161no—
1310C2#4350211yescharacteristic
1311C2#6145311yescharacteristic
1312C2#6150311yescharacteristic
1313C2#6172111yescharacteristic
1314C2#6178211yescharacteristic
1315C2#6244111yescharacteristic
1316C2#6244811yescharacteristic
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
2. #39659C2semidirect
3. #32442C2semidirect
4. #32295C2semidirect
5. #31663C2semidirect
6. #31122C2semidirect
8. #31002C2semidirect
9. #30779C2semidirect
11. #28883C2semidirect
12. #28858C2semidirect
13. #28539C2semidirect
14. #28367C2semidirect
15. #28311C2semidirect
16. #28027C2semidirect
17. #27896C2semidirect
18. #27802C2semidirect
19. #27509C2semidirect
20. #27239C2semidirect
21. #27224C2semidirect
22. #27084C2semidirect
23. #26814C2semidirect
24. #25156C2semidirect
25. #25028C2semidirect
26. #24880C2semidirect
27. #23765C2semidirect
28. #23304C2semidirect
29. #23100C2semidirect
30. #22885C2semidirect
31. #22049C2semidirect
32. C2×#500C22semidirect
35. C2×#485C22semidirect
36. C2×#477C22semidirect
46. C2×#419C22semidirect
58. #2567C22semidirect
65. #2511C22semidirect
67. #2497C22semidirect
69. #2492C22semidirect
72. #2446C22semidirect
74. #2434C22semidirect
80. #2365C22semidirect
85. Q8×C22⋊C4C22semidirect
92. #2101C22semidirect
93. #2097C22semidirect
94. #2097C22semidirect
95. #2095C22semidirect
99. #2085C22semidirect
100. #2083C22semidirect
103. #2075C22semidirect
104. #2074C22semidirect
105. #2074C22semidirect
107. #2068C22semidirect
108. #2068C22semidirect
110. #2057C22semidirect
114. #2043C22semidirect
118. #2036C22semidirect
125. #2024C22semidirect
126. #2024C22semidirect
142. #1960C22semidirect
143. #1960C22semidirect
144. #1956C22semidirect
146. #1947C22semidirect
147. #1947C22semidirect
148. #1942C22semidirect
151. #1933C22semidirect
152. #1928C22semidirect
153. #1928C22semidirect
154. #1928C22semidirect
155. #1927C22semidirect
156. #1927C22semidirect
157. #1927C22semidirect
161. #1924C22semidirect
162. #1924C22semidirect
165. #1921C22semidirect
166. #1917C22semidirect
167. #1917C22semidirect
180. #1863C22semidirect
181. #1854C22semidirect
182. #1854C22semidirect
184. #1847C22semidirect
185. #1847C22semidirect
186. #1836C22semidirect
187. #1809C22semidirect
188. #1805C22semidirect
189. #1787C22semidirect
191. #1776C22semidirect
192. #1776C22semidirect
193. #1770C22semidirect
194. #1770C22semidirect
195. #1763C22semidirect
196. #1763C22semidirect
197. #1763C22semidirect
199. #1753C22semidirect
200. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#592242
#396592
#324422
#322952
#316632
#311222
#310652
#310022
#307792
#304202
#288832
#288582
#285392
#283672
#283112
#280272
#278962
#278022
#275092
#272392
#272242
#270842
#268142
#251562
#250282
#248802
#237652
#233042
#231002
#228852
#220492