Finite Group Databasebeta

← #6832109

Subgroups — #6832109

Order 512.

1633 conjugacy classes of subgroups.

The subgroup lattice has 1374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42977C211yesmaximal, characteristic
2#42816C211yesmaximal, characteristic, complemented
3#33055C211yesmaximal, characteristic, complemented
4#32610C211yesmaximal, characteristic, complemented
5#32600C211yesmaximal, characteristic, complemented
6#32447C211yesmaximal, characteristic, complemented
7#32442C211yesmaximal, characteristic, complemented
8#31158C211yesmaximal, characteristic, complemented
9#31156C211yesmaximal, characteristic, complemented
10#30892C211yesmaximal, characteristic, complemented
11#30892C211yesmaximal, characteristic, complemented
12#29962C211yesmaximal, characteristic, complemented
13#29722C211yesmaximal, characteristic, complemented
14#29102C211yesmaximal, characteristic, complemented
15#29078C211yesmaximal, characteristic, complemented
16#28435C211yesmaximal, characteristic, complemented
17#28404C211yesmaximal, characteristic, complemented
18#27279C211yesmaximal, characteristic, complemented
19#27273C211yesmaximal, characteristic, complemented
20#26832C211yesmaximal, characteristic, complemented
21#26825C211yesmaximal, characteristic, complemented
22#26345C211yesmaximal, characteristic, complemented
23#26343C211yesmaximal, characteristic, complemented
24#25310C211yesmaximal, characteristic, complemented
25#25303C211yesmaximal, characteristic, complemented
26#24356C211yesmaximal, characteristic, complemented
27#24356C211yesmaximal, characteristic, complemented
28#22885C211yesmaximal, characteristic, complemented
29#22865C211yesmaximal, characteristic, complemented
30#21606C211yesmaximal, characteristic, complemented
31#21231C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#490C2211yescharacteristic
34C2×#490C2211yescharacteristic, complemented
35C2×#486C2211yescharacteristic
36C2×#478C2211yescharacteristic, complemented
37C2×#476C2211yescharacteristic, complemented
38C2×#460C2211yescharacteristic
39C2×#460C2211yescharacteristic
40C2×#460C2211yescharacteristic
41C2×#460C2211yescharacteristic
42C2×#448C2211yescharacteristic
43C2×#448C2211yescharacteristic
44C2×#446C2211yescharacteristic, complemented
45C2×#440C2211yescharacteristic, complemented
46C2×C4×SD16C2211yescharacteristic, complemented
47C2×#427C2211yescharacteristic
48C2×#419C2211yescharacteristic
49C2×#418C2211yescharacteristic
50C2×#405C2211yescharacteristic
51#2841—21no—
52#2828—21no—
53#2809—21no—
54#2806—21no—
55#2806—21no—
56#2799—21no—
57#2678—21no—
58#2678—21no—
59#2670—21no—
60#2668—21no—
61#2667—21no—
62#2665—21no—
63#2661—21no—
64#2661—21no—
65#2629C2211yescharacteristic
66#2619C2211yescharacteristic
67#2608—21no—
68#2582C2211yescharacteristic, complemented
69#2581C2211yescharacteristic, complemented
70#2567C2211yescharacteristic, complemented
71#2565C2211yescharacteristic, complemented
72#2555—21no—
73#2548C2211yescharacteristic
74#2548C2211yescharacteristic
75#2541C2211yescharacteristic
76#2541C2211yescharacteristic
77#2513C2211yescharacteristic
78#2513C2211yescharacteristic
79#2453C2211yescharacteristic, complemented
80#2453C2211yescharacteristic, complemented
81#2453C2211yescharacteristic, complemented
82#2451C2211yescharacteristic, complemented
83#2445C2211yescharacteristic
84#2445C2211yescharacteristic
85#2441C2211yescharacteristic
86#2439C2211yescharacteristic
87#2433C2211yescharacteristic
88#2433C2211yescharacteristic
89#2396C2211yescharacteristic
90#2363C2211yescharacteristic
91#2363C2211yescharacteristic
92Q8×C22⋊C4C2211yescharacteristic
93Q8×C22⋊C4C2211yescharacteristic
94#2310C2211yescharacteristic
95#2309C2211yescharacteristic
96#2094C2211yescharacteristic
97#2094C2211yescharacteristic, complemented
98#2093C2211yescharacteristic
99#2092C2211yescharacteristic, complemented
100#2088C2211yescharacteristic, complemented
101#2088C2211yescharacteristic, complemented
102#2074C2211yescharacteristic, complemented
103#2074C2211yescharacteristic, complemented
104#2073C2211yescharacteristic
105#2071C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic, complemented
109#2067C2211yescharacteristic, complemented
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2059C2211yescharacteristic, complemented
113#2057C2211yescharacteristic, complemented
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2055C2211yescharacteristic, complemented
119#2055C2211yescharacteristic, complemented
120#2055C2211yescharacteristic, complemented
121#2055C2211yescharacteristic, complemented
122#2041C2211yescharacteristic
123#2041C2211yescharacteristic
124#2041C2211yescharacteristic
125#2041C2211yescharacteristic
126#2025C2211yescharacteristic
127#2025C2211yescharacteristic
128#2025C2211yescharacteristic
129#2023C2211yescharacteristic
130#2014C2211yescharacteristic
131#2014C2211yescharacteristic
132#2014C2211yescharacteristic
133#2014C2211yescharacteristic
134#2014C2211yescharacteristic, complemented
135#2014C2211yescharacteristic, complemented
136#1991C2211yescharacteristic, complemented
137#1984C2211yescharacteristic, complemented
138#1973C2211yescharacteristic
139#1973C2211yescharacteristic
140#1973C2211yescharacteristic
141#1973C2211yescharacteristic
142#1973C2211yescharacteristic, complemented
143#1968C2211yescharacteristic
144#1968C2211yescharacteristic
145#1968C2211yescharacteristic
146#1968C2211yescharacteristic
147#1968C2211yescharacteristic, complemented
148#1961C2211yescharacteristic
149#1957C2211yescharacteristic
150#1957C2211yescharacteristic, complemented
151#1949C2211yescharacteristic, complemented
152#1947C2211yescharacteristic, complemented
153#1939C2211yescharacteristic, complemented
154#1936C2211yescharacteristic
155#1936C2211yescharacteristic
156#1936C2211yescharacteristic, complemented
157#1936C2211yescharacteristic, complemented
158#1935C2211yescharacteristic, complemented
159#1934C2211yescharacteristic
160#1934C2211yescharacteristic
161#1934C2211yescharacteristic, complemented
162#1934C2211yescharacteristic, complemented
163#1933C2211yescharacteristic, complemented
164#1928C2211yescharacteristic, complemented
165#1927C2211yescharacteristic, complemented
166#1920C2211yescharacteristic, complemented
167#1919C2211yescharacteristic, complemented
168#1917C2211yescharacteristic, complemented
169#1917C2211yescharacteristic, complemented
170#1895C2211yescharacteristic
171#1895C2211yescharacteristic
172#1893C2211yescharacteristic
173#1893C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic
177#1880C2211yescharacteristic
178#1880C2211yescharacteristic, complemented
179#1880C2211yescharacteristic, complemented
180#1877C2211yescharacteristic, complemented
181#1877C2211yescharacteristic, complemented
182#1875C2211yescharacteristic
183#1875C2211yescharacteristic
184#1865C2211yescharacteristic, complemented
185#1863C2211yescharacteristic, complemented
186#1862C2211yescharacteristic, complemented
187#1862C2211yescharacteristic, complemented
188#1854C2211yescharacteristic
189#1854C2211yescharacteristic
190#1850C2211yescharacteristic
191#1850C2211yescharacteristic
192#1836C2211yescharacteristic, complemented
193#1798C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1771C2211yescharacteristic, complemented
197#1771C2211yescharacteristic, complemented
198C8×C4⋊C4C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200C4×#103C2211yescharacteristic, complemented
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16—24no—
206C22×SD16—42no—
207C22×SD16—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#125C2311yescharacteristic
225C2×#125C2311yescharacteristic
226C2×#124—21no—
227C2×#124—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120—21no—
238C2×#120—21no—
239C2×#120—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250#490—42no—
251#490—42no—
252#486—42no—
253#478—42no—
254#476—42no—
255#460—42no—
256#460—42no—
257#460—42no—
258#460—42no—
259#448—24no—
260#448—24no—
261#446—42no—
262#440—42no—
263C4×SD16—42no—
264#427—42no—
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
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
279#419—42no—
280#418—42no—
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×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315#405—42no—
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400D411yescharacteristic
329#399—21no—
330#399D411yescharacteristic
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398D411yescharacteristic
342#398D411yescharacteristic
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396D411yescharacteristic
352#396D411yescharacteristic
353#395—21no—
354#395—21no—
355#395—21no—
356#395—21no—
357#395D411yescharacteristic
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#393—21no—
369#393D411yescharacteristic
370#392—21no—
371#392—21no—
372#392—21no—
373#392—21no—
374#392—21no—
375#392—21no—
376#392—21no—
377#392—21no—
378#392—21no—
379#392—21no—
380#391—21no—
381#391—21no—
382#391—21no—
383#391—21no—
384#391—21no—
385#391—21no—
386#391—21no—
387#391—21no—
388#391—21no—
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#391C2311yescharacteristic
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#390—21no—
398#390—21no—
399#390—21no—
400#390—21no—
401#390—21no—
402#390—21no—
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#390C2311yescharacteristic
412#390C2311yescharacteristic
413#390C2311yescharacteristic
414#390C2311yescharacteristic
415#389—21no—
416#389—21no—
417#389—21no—
418#389—21no—
419#389—21no—
420#389—21no—
421#389—21no—
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#386—21no—
447#386—21no—
448#386—21no—
449#386—21no—
450#384C2311yescharacteristic
451#384C2311yescharacteristic
452#382C2311yescharacteristic
453#382C2311yescharacteristic
454#381—21no—
455#381—21no—
456#380—21no—
457#380—21no—
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#379—21no—
461#379—21no—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—22no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8C2×D411yescharacteristic
508C22×Q8#4114yes—
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4C2411yescharacteristic
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—416no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×M16—22no—
564C2×M16—22no—
565C2×M16—41no—
566C22×C8—22no—
567C22×C8—22no—
568C22×C8—22no—
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579#127—41no—
580#127—41no—
581#127—41no—
582#127—41no—
583#127—41no—
584#127—41no—
585#127—41no—
586#127—41no—
587#127—41no—
588#127—41no—
589#125—41no—
590#125—41no—
591#125—41no—
592#125—41no—
593#124—82no—
594#124—82no—
595#123—82no—
596#123—82no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—82no—
602#121—82no—
603#121—82no—
604#121—82no—
605#120—82no—
606#120—82no—
607#120—82no—
608#120—82no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623#117—41no—
624#117—41no—
625#117—41no—
626#117—41no—
627#117—41no—
628#117—41no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723#107—41no—
724#107—41no—
725#107—41no—
726#107—41no—
727#106—22no—
728#106—22no—
729#106—41no—
730#106—41no—
731C4⋊C8—22no—
732C4⋊C8—22no—
733C4⋊C8—22no—
734C4⋊C8—22no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737#103—22no—
738#103—22no—
739#103—22no—
740#103—22no—
741#103—22no—
742#103—22no—
743#103—41no—
744#103—41no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769C22⋊C8—22no—
770C22⋊C8—22no—
771#97—22no—
772#97—22no—
773#97—22no—
774#97—41no—
775C4×C8—22no—
776C4×C8—41no—
777C4×C8—41no—
778C4×C8—41no—
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#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—42no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24C22×D411yescharacteristic
833C2×Q8—24no—
834C2×Q8—22no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—41no—
846C2×Q8—41no—
847C2×Q8—44no—
848C2×Q8—44no—
849C2×Q8—81no—
850C2×Q8—81no—
851C2×Q8—81no—
852C2×Q8—81no—
853C2×Q8—81no—
854C2×Q8—82no—
855C2×Q8—82no—
856C2×Q8C2×#4112yes—
857C2×Q8C2×#4112yes—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—82no—
892C2×D4—82no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—24no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C2×#4112yes—
964C22×C42−1+412yes—
965C22×C4C2511yescharacteristic
966SD16—44no—
967SD16—44no—
968SD16—44no—
969SD16—44no—
970SD16—44no—
971SD16—44no—
972SD16—82no—
973SD16—82no—
974M16—44no—
975C2×C8—28no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8H(5,𝔽2)12yes—
998C2×C8H(5,𝔽2)12yes—
999C2×C8H(5,𝔽2)12yes—
1000C4⋊C4—22no—
1001C4⋊C4—22no—
1002C4⋊C4—22no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—41no—
1026C4⋊C4—41no—
1027C4⋊C4—41no—
1028C4⋊C4—41no—
1029C4⋊C4—41no—
1030C4⋊C4—41no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C22⋊C4—22no—
1053C22⋊C4—22no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
1107C42—81no—
1108C42—81no—
1109C42—81no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—84no—
1145C23—162no—
1146C23—162no—
1147C23—162no—
1148C23—162no—
1149C23—162no—
1150C23—162no—
1151C23#54812yes—
1152C23C23×D411yescharacteristic
1153Q8—22no—
1154Q8—22no—
1155Q8—22no—
1156Q8—22no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—82no—
1162Q8—84no—
1163Q8—162no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—84no—
1181D4—162no—
1182D4—162no—
1183D4—162no—
1184D4—162no—
1185D4—162no—
1186D4—162no—
1187D4—162no—
1188D4—162no—
1189D4—162no—
1190D4—162no—
1191D4—162no—
1192D4—162no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—84no—
1270C2×C4—162no—
1271C2×C4—162no—
1272C2×C4#54812yes—
1273C2×C4#57712yes—
1274C2×C4#57712yes—
1275C2×C4C22×#4111yescharacteristic
1276C2×C4C2×H(5,𝔽2)11yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4C2×2−1+411yescharacteristic
1280C2×C4#58511yescharacteristic
1281C8—22no—
1282C8—22no—
1283C8—22no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—168no—
1325C22C2×#54811yescharacteristic
1326C22#349611yescharacteristic
1327C22#349811yescharacteristic
1328C22C2×#57711yescharacteristic
1329C22C2×#57711yescharacteristic
1330C22#358511yescharacteristic
1331C22#358511yescharacteristic
1332C4—22no—
1333C4—22no—
1334C4—22no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—42no—
1346C4—42no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4#345911yescharacteristic
1358C4#349011yescharacteristic
1359C4#353611yescharacteristic
1360C4#356111yescharacteristic
1361C2—42no—
1362C2—161no—
1363C2—161no—
1364C2—161no—
1365C2—161no—
1366C2#3942011yescharacteristic
1367C2#6134111yescharacteristic
1368C2#6134111yescharacteristic
1369C2#6230811yescharacteristic
1370C2#6234611yescharacteristic
1371C2#6243011yescharacteristic
1372C2#6244111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#42977C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42816C2semidirect
3. #33055C2semidirect
4. #32610C2semidirect
5. #32600C2semidirect
6. #32447C2semidirect
7. #32442C2semidirect
8. #31158C2semidirect
9. #31156C2semidirect
10. #30892C2semidirect
11. #30892C2semidirect
12. #29962C2semidirect
13. #29722C2semidirect
14. #29102C2semidirect
15. #29078C2semidirect
16. #28435C2semidirect
17. #28404C2semidirect
18. #27279C2semidirect
19. #27273C2semidirect
20. #26832C2semidirect
21. #26825C2semidirect
22. #26345C2semidirect
23. #26343C2semidirect
24. #25310C2semidirect
25. #25303C2semidirect
26. #24356C2semidirect
27. #24356C2semidirect
28. #22885C2semidirect
29. #22865C2semidirect
30. #21606C2semidirect
31. #21231C2semidirect
34. C2×#490C22semidirect
36. C2×#478C22semidirect
37. C2×#476C22semidirect
44. C2×#446C22semidirect
45. C2×#440C22semidirect
46. C2×C4×SD16C22semidirect
68. #2582C22semidirect
69. #2581C22semidirect
70. #2567C22semidirect
71. #2565C22semidirect
79. #2453C22semidirect
80. #2453C22semidirect
81. #2453C22semidirect
82. #2451C22semidirect
97. #2094C22semidirect
99. #2092C22semidirect
100. #2088C22semidirect
101. #2088C22semidirect
102. #2074C22semidirect
103. #2074C22semidirect
108. #2067C22semidirect
109. #2067C22semidirect
112. #2059C22semidirect
113. #2057C22semidirect
118. #2055C22semidirect
119. #2055C22semidirect
120. #2055C22semidirect
121. #2055C22semidirect
134. #2014C22semidirect
135. #2014C22semidirect
136. #1991C22semidirect
137. #1984C22semidirect
142. #1973C22semidirect
147. #1968C22semidirect
150. #1957C22semidirect
151. #1949C22semidirect
152. #1947C22semidirect
153. #1939C22semidirect
156. #1936C22semidirect
157. #1936C22semidirect
158. #1935C22semidirect
161. #1934C22semidirect
162. #1934C22semidirect
163. #1933C22semidirect
164. #1928C22semidirect
165. #1927C22semidirect
166. #1920C22semidirect
167. #1919C22semidirect
168. #1917C22semidirect
169. #1917C22semidirect
178. #1880C22semidirect
179. #1880C22semidirect
180. #1877C22semidirect
181. #1877C22semidirect
184. #1865C22semidirect
185. #1863C22semidirect
186. #1862C22semidirect
187. #1862C22semidirect
192. #1836C22semidirect
196. #1771C22semidirect
197. #1771C22semidirect
198. C8×C4⋊C4C22semidirect
199. #1763C22semidirect
200. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#429772
#428162
#330552
#326102
#326002
#324472
#324422
#311582
#311562
#308922
#299622
#297222
#291022
#290782
#284352
#284042
#272792
#272732
#268322
#268252
#263452
#263432
#253102
#253032
#243562
#228852
#228652
#216062
#212312