Finite Group Databasebeta

← #6484409

Subgroups — #6484409

Order 512.

1654 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35304C211yesmaximal, characteristic, complemented
2#34070C211yesmaximal, characteristic
3#32961C211yesmaximal, characteristic, complemented
4#32961C211yesmaximal, characteristic, complemented
5#32958C211yesmaximal, characteristic, complemented
6#32955C211yesmaximal, characteristic, complemented
7#29958C211yesmaximal, characteristic, complemented
8#29958C211yesmaximal, characteristic, complemented
9#29955C211yesmaximal, characteristic, complemented
10#29954C211yesmaximal, characteristic, complemented
11#29269C211yesmaximal, characteristic, complemented
12#29268C211yesmaximal, characteristic, complemented
13#29267C211yesmaximal, characteristic, complemented
14#29267C211yesmaximal, characteristic, complemented
15#29205C211yesmaximal, characteristic, complemented
16#29204C211yesmaximal, characteristic, complemented
17#29202C211yesmaximal, characteristic, complemented
18#29201C211yesmaximal, characteristic, complemented
19#29153C211yesmaximal, characteristic, complemented
20#29152C211yesmaximal, characteristic, complemented
21#28526C211yesmaximal, characteristic, complemented
22#28525C211yesmaximal, characteristic, complemented
23#28293C211yesmaximal, characteristic, complemented
24#28293C211yesmaximal, characteristic, complemented
25#28289C211yesmaximal, characteristic, complemented
26#28288C211yesmaximal, characteristic, complemented
27#21988C211yesmaximal, characteristic, complemented
28#21985C211yesmaximal, characteristic, complemented
29#21812C211yesmaximal, characteristic
30#21805C211yesmaximal, characteristic
31#20814C211yesmaximal, characteristic, complemented
32C2×#532C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#477C2211yescharacteristic
38C2×#475C2211yescharacteristic
39C2×#478C2211yescharacteristic
40C2×#478C2211yescharacteristic
41C2×#476C2211yescharacteristic
42C2×#474C2211yescharacteristic
43C2×#432C2211yescharacteristic
44C2×#431C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2851C2211yescharacteristic
48#2851C2211yescharacteristic
49#2660C2211yescharacteristic
50#2660C2211yescharacteristic
51#2647C2211yescharacteristic
52#2647C2211yescharacteristic
53#2612—21no—
54#2612—21no—
55#2606—21no—
56#2605—21no—
57#2569—21no—
58#2549—21no—
59#2438—21no—
60#2438—21no—
61#2331C2211yescharacteristic
62#2331C2211yescharacteristic
63#2330C2211yescharacteristic
64#2330C2211yescharacteristic
65#2328C2211yescharacteristic
66#2328C2211yescharacteristic
67#2327C2211yescharacteristic
68#2327C2211yescharacteristic
69#2326C2211yescharacteristic
70#2326C2211yescharacteristic
71#2326C2211yescharacteristic
72#2326C2211yescharacteristic
73#2325—21no—
74#2325—21no—
75#2325—21no—
76#2325—21no—
77#2297C2211yescharacteristic
78#2297C2211yescharacteristic
79#2290—21no—
80#2290—21no—
81#2290—21no—
82#2290—21no—
83#2285C2211yescharacteristic
84#2285C2211yescharacteristic
85#2283C2211yescharacteristic
86C2×#376C2211yescharacteristic
87#2097C2211yescharacteristic
88#2097C2211yescharacteristic
89#2096C2211yescharacteristic
90#2095C2211yescharacteristic
91#2094C2211yescharacteristic
92#2093C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2068C2211yescharacteristic
96#2068C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2066C2211yescharacteristic
104#2066C2211yescharacteristic
105#2066C2211yescharacteristic
106#2066C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2026C2211yescharacteristic
112#2026C2211yescharacteristic
113#2025C2211yescharacteristic
114#2025C2211yescharacteristic
115#2024C2211yescharacteristic
116#2024C2211yescharacteristic
117#2023C2211yescharacteristic
118#2023C2211yescharacteristic
119#1983C2211yescharacteristic
120#1983C2211yescharacteristic
121#1983C2211yescharacteristic
122#1983C2211yescharacteristic
123#1983C2211yescharacteristic
124#1983C2211yescharacteristic
125#1983C2211yescharacteristic
126#1983C2211yescharacteristic
127#1961C2211yescharacteristic
128#1961C2211yescharacteristic
129#1960C2211yescharacteristic
130#1960C2211yescharacteristic
131#1957C2211yescharacteristic
132#1957C2211yescharacteristic
133#1956C2211yescharacteristic
134#1956C2211yescharacteristic
135#1948C2211yescharacteristic
136#1948C2211yescharacteristic
137#1948C2211yescharacteristic
138#1948C2211yescharacteristic
139#1947C2211yescharacteristic
140#1947C2211yescharacteristic
141#1947C2211yescharacteristic
142#1947C2211yescharacteristic
143#1865C2211yescharacteristic
144#1865C2211yescharacteristic
145#1865C2211yescharacteristic
146#1865C2211yescharacteristic
147#1864C2211yescharacteristic
148#1864C2211yescharacteristic
149#1864C2211yescharacteristic
150#1864C2211yescharacteristic
151#1863C2211yescharacteristic
152#1863C2211yescharacteristic
153#1863C2211yescharacteristic
154#1863C2211yescharacteristic
155#1862C2211yescharacteristic
156#1862C2211yescharacteristic
157#1862C2211yescharacteristic
158#1862C2211yescharacteristic
159#1854C2211yescharacteristic
160#1854C2211yescharacteristic
161#1854C2211yescharacteristic
162#1854C2211yescharacteristic
163#1854C2211yescharacteristic
164#1854C2211yescharacteristic
165#1854C2211yescharacteristic
166#1854C2211yescharacteristic
167#1847C2211yescharacteristic
168#1847C2211yescharacteristic
169#1846C2211yescharacteristic
170#1846C2211yescharacteristic
171#1843C2211yescharacteristic
172#1843C2211yescharacteristic
173#1836C2211yescharacteristic
174#1836C2211yescharacteristic
175#1835C2211yescharacteristic
176#1835C2211yescharacteristic
177#1832C2211yescharacteristic
178#1832C2211yescharacteristic
179#1805C2211yescharacteristic
180#1805C2211yescharacteristic
181#1804C2211yescharacteristic
182#1804C2211yescharacteristic
183#1803C2211yescharacteristic
184#1803C2211yescharacteristic
185#1802C2211yescharacteristic
186#1802C2211yescharacteristic
187#1797C2211yescharacteristic
188#1797C2211yescharacteristic
189#1797C2211yescharacteristic
190#1797C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1788C2211yescharacteristic
198#1788C2211yescharacteristic
199#1768C2211yescharacteristic
200#1768C2211yescharacteristic
201#1768C2211yescharacteristic
202#1768C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205#532—24no—
206#532Q818yescomplemented
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×#121—21no—
218C2×#121—21no—
219C4×#41—42no—
220C4×#41—42no—
221C4×#41—42no—
222C4×#41—42no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4—21no—
228C2×C4×D4—21no—
229C2×C4×D4—21no—
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117—21no—
238C2×#117—21no—
239C2×#117—21no—
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C22×C42—21no—
243C22×C42—21no—
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247#479—42no—
248#479—42no—
249#478—42no—
250#478—42no—
251#477—42no—
252#476—42no—
253#475—42no—
254#474—42no—
255#432—24no—
256#431—24no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#391—21no—
342#391—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391—21no—
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#385—21no—
410#385—21no—
411#385—21no—
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#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#383—21no—
428#382—21no—
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#381—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457#376—21no—
458#376D411yescharacteristic
459#376D411yescharacteristic
460#376D411yescharacteristic
461#376D411yescharacteristic
462#376C2311yescharacteristic
463#376C2311yescharacteristic
464#376C2311yescharacteristic
465#376C2311yescharacteristic
466C2×#95D411yescharacteristic
467C2×#95D411yescharacteristic
468C2×#95D411yescharacteristic
469C2×#95D411yescharacteristic
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
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41C2×Q814yes—
505C2×#41C2×Q814yes—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C2×D411yescharacteristic
523C23×C4C2×D411yescharacteristic
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C4⋊Q8—22no—
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542C4⋊Q8C2×Q814yes—
543#127—22no—
544#127C2×Q814yes—
545#125—22no—
546#125—22no—
547#125—41no—
548#125—41no—
549#124—22no—
550#124—22no—
551#124C2×Q814yes—
552#124C2×Q814yes—
553C22⋊Q8—82no—
554C22⋊Q8—82no—
555#121—28no—
556#121—28no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8—22no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×D4—28no—
566C4×D4—28no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—44no—
576C4×D4—44no—
577C4×D4—44no—
578C4×D4—44no—
579#117—44no—
580#117—44no—
581#117—41no—
582#117—41no—
583#117—41no—
584#117—41no—
585#117—82no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
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—21no—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
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×C42—22no—
653C2×C42—22no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—41no—
665C2×C42—41no—
666C2×C42—44no—
667C2×C42—44no—
668C2×C42C2×D411yescharacteristic
669C2×C42C2×D411yescharacteristic
670C2×C42C2×D411yescharacteristic
671C2×C42C2×D411yescharacteristic
672C2×C42C2×D411yescharacteristic
673C2×C42C2×D411yescharacteristic
674C2×C42C2×Q814yes—
675C2×C42#4114yes—
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682#107—41no—
683#107—41no—
684#107—41no—
685#107—41no—
686#107—41no—
687#107—41no—
688#107—41no—
689#107—41no—
690#106—41no—
691#106—41no—
692#106—41no—
693#106—41no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698C4⋊C8—22no—
699C4⋊C8—22no—
700C4⋊C8—22no—
701C4⋊C8—22no—
702C4⋊C8—22no—
703C4⋊C8—22no—
704C4⋊C8—22no—
705C4⋊C8—22no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709C4⋊C8—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742C22⋊C8—22no—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8—22no—
746#97—22no—
747#97—22no—
748C4×C8—22no—
749C4×C8—22no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
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#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
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
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802C24—21no—
803C24—21no—
804C24C22×D411yescharacteristic
805#41—44no—
806#41—44no—
807#41—44no—
808#41—44no—
809#41—44no—
810#41—44no—
811#41—44no—
812#41—44no—
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—42no—
824C2×Q8—42no—
825C2×Q8—81no—
826C2×Q8—81no—
827C2×Q8—81no—
828C2×Q8—81no—
829C2×Q8C22×Q812yes—
830C2×Q8C22×Q812yes—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—24no—
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—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4C22×Q812yes—
854C2×D4C22×Q812yes—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—41no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—41no—
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—41no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
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×C4C22⋊Q814yes—
908C22×C4C22⋊Q814yes—
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×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×Q812yes—
923C22×C4C2×#4112yes—
924C22×C4C2511yescharacteristic
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
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—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—21no—
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—21no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
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—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C22⋊C4—24no—
1006C22⋊C4—24no—
1007C22⋊C4—24no—
1008C22⋊C4—24no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
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—
1027C42—22no—
1028C42—22no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—41no—
1036C42—41no—
1037C42—42no—
1038C42—42no—
1039C42—42no—
1040C42—42no—
1041C42—42no—
1042C42—42no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42C22⋊Q814yes—
1048C42C22⋊Q814yes—
1049C42C22×Q812yes—
1050C42C22×Q812yes—
1051C42C2×#4112yes—
1052C42C2×#4112yes—
1053C42H(5,𝔽2)12yes—
1054C42H(5,𝔽2)12yes—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—22no—
1062C23—22no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23C2×C22⋊Q812yes—
1076C23C23×D411yescharacteristic
1077Q8—22no—
1078Q8—22no—
1079Q8—22no—
1080Q8—22no—
1081Q8—41no—
1082Q8—41no—
1083Q8—41no—
1084Q8—41no—
1085Q8—162no—
1086Q8—162no—
1087D4—22no—
1088D4—22no—
1089D4—22no—
1090D4—22no—
1091D4—48no—
1092D4—48no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—84no—
1098D4—84no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—44no—
1138C2×C4—44no—
1139C2×C4—48no—
1140C2×C4—48no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
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—82no—
1182C2×C4—82no—
1183C2×C4—84no—
1184C2×C4—84no—
1185C2×C4—82no—
1186C2×C4—82no—
1187C2×C4—84no—
1188C2×C4—84no—
1189C2×C4C2×C22⋊Q812yes—
1190C2×C4C2×C22⋊Q812yes—
1191C2×C4C2×C22⋊Q812yes—
1192C2×C4C2×C22⋊Q812yes—
1193C2×C4C2×C22⋊Q812yes—
1194C2×C4#53512yes—
1195C2×C4#53512yes—
1196C2×C4C23×Q811yescharacteristic
1197C2×C4C22×#4111yescharacteristic
1198C2×C4C2×H(5,𝔽2)11yescharacteristic
1199C2×C4C2×H(5,𝔽2)11yescharacteristic
1200C2×C4#58511yescharacteristic
1201C2×C4#58511yescharacteristic
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C8—41no—
1208C8—41no—
1209C8—41no—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22C22×C22⋊Q811yescharacteristic
1232C22C2×#53511yescharacteristic
1233C22#344911yescharacteristic
1234C22#358411yescharacteristic
1235C22#358411yescharacteristic
1236C22#358511yescharacteristic
1237C22#358611yescharacteristic
1238C4—22no—
1239C4—22no—
1240C4—22no—
1241C4—22no—
1242C4—22no—
1243C4—22no—
1244C4—22no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—42no—
1250C4—42no—
1251C4—41no—
1252C4—41no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4#350111yescharacteristic
1266C4#350111yescharacteristic
1267C4#350611yescharacteristic
1268C4#350611yescharacteristic
1269C2—42no—
1270C2—82no—
1271C2—82no—
1272C2#3517211yescharacteristic
1273C2#6048911yescharacteristic
1274C2#6049311yescharacteristic
1275C2#6081511yescharacteristic
1276C2#6081611yescharacteristic
1277C2#6098611yescharacteristic
1278C2#6098711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#376 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35304C2semidirect
3. #32961C2semidirect
4. #32961C2semidirect
5. #32958C2semidirect
6. #32955C2semidirect
7. #29958C2semidirect
8. #29958C2semidirect
9. #29955C2semidirect
10. #29954C2semidirect
11. #29269C2semidirect
12. #29268C2semidirect
13. #29267C2semidirect
14. #29267C2semidirect
15. #29205C2semidirect
16. #29204C2semidirect
17. #29202C2semidirect
18. #29201C2semidirect
19. #29153C2semidirect
20. #29152C2semidirect
21. #28526C2semidirect
22. #28525C2semidirect
23. #28293C2semidirect
24. #28293C2semidirect
25. #28289C2semidirect
26. #28288C2semidirect
27. #21988C2semidirect
28. #21985C2semidirect
31. #20814C2semidirect
206. #532Q8semidirect

Maximal subgroups

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

subgroupindex
#353042
#340702
#329612
#329582
#329552
#299582
#299552
#299542
#292692
#292682
#292672
#292052
#292042
#292022
#292012
#291532
#291522
#285262
#285252
#282932
#282892
#282882
#219882
#219852
#218122
#218052
#208142