Finite Group Databasebeta

← #7081746

Subgroups — #7081746

Order 512.

1764 conjugacy classes of subgroups.

The subgroup lattice has 1418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44872C211yesmaximal, characteristic
2#42924C211yesmaximal, characteristic, complemented
3#32096C211yesmaximal, characteristic, complemented
4#32059C211yesmaximal, characteristic, complemented
5#31909C211yesmaximal, characteristic, complemented
6#31570C211yesmaximal, characteristic, complemented
7#31534C211yesmaximal, characteristic, complemented
8#31286C211yesmaximal, characteristic, complemented
9#30630C211yesmaximal, characteristic, complemented
10#30612C211yesmaximal, characteristic, complemented
11#28944C211yesmaximal, characteristic, complemented
12#28404C211yesmaximal, characteristic, complemented
13#28365C211yesmaximal, characteristic, complemented
14#28071C211yesmaximal, characteristic, complemented
15#27254C211yesmaximal, characteristic, complemented
16#27063C211yesmaximal, characteristic, complemented
17#26530C211yesmaximal, characteristic, complemented
18#26359C211yesmaximal, characteristic, complemented
19#26141C211yesmaximal, characteristic, complemented
20#25974C211yesmaximal, characteristic, complemented
21#25507C211yesmaximal, characteristic, complemented
22#25093C211yesmaximal, characteristic, complemented
23#24901C211yesmaximal, characteristic, complemented
24#24795C211yesmaximal, characteristic, complemented
25#24516C211yesmaximal, characteristic, complemented
26#24432C211yesmaximal, characteristic, complemented
27#23735C211yesmaximal, characteristic, complemented
28#23023C211yesmaximal, characteristic, complemented
29#22915C211yesmaximal, characteristic, complemented
30#22428C211yesmaximal, characteristic, complemented
31#21872C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#540C2211yescharacteristic
34C2×#486C2211yescharacteristic, complemented
35C2×#482C2211yescharacteristic, complemented
36C2×#476C2211yescharacteristic, complemented
37C2×#468C2211yescharacteristic, complemented
38C2×#468C2211yescharacteristic, complemented
39C2×#465C2211yescharacteristic
40C2×#460C2211yescharacteristic, complemented
41C2×#450C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic, complemented
44C2×#436C2211yescharacteristic
45C2×#433C2211yescharacteristic, complemented
46C2×#428C2211yescharacteristic, complemented
47C2×#427C2211yescharacteristic, complemented
48C2×#418C2211yescharacteristic
49C2×#418C2211yescharacteristic
50C22×#102C2211yescharacteristic
51#2838—21no—
52#2787—21no—
53#2757—21no—
54#2723—21no—
55#2703—21no—
56#2690—21no—
57#2678—21no—
58#2678—21no—
59#2668—21no—
60#2666—21no—
61#2664—21no—
62#2625C2211yescharacteristic, complemented
63#2585—21no—
64#2567C2211yescharacteristic, complemented
65#2552C2211yescharacteristic, complemented
66#2541C2211yescharacteristic
67#2539—21no—
68#2514C2211yescharacteristic, complemented
69#2508C2211yescharacteristic, complemented
70#2499C2211yescharacteristic, complemented
71#2496C2211yescharacteristic, complemented
72#2490C2211yescharacteristic
73#2464—21no—
74#2454C2211yescharacteristic
75#2445C2211yescharacteristic
76#2440C2211yescharacteristic, complemented
77#2439C2211yescharacteristic, complemented
78#2433C2211yescharacteristic
79#2433C2211yescharacteristic
80#2428C2211yescharacteristic
81#2423C2211yescharacteristic, complemented
82#2417C2211yescharacteristic
83#2414C2211yescharacteristic
84#2410—21no—
85#2408—21no—
86#2395C2211yescharacteristic
87#2366C2211yescharacteristic
88#2363C2211yescharacteristic
89#2362C2211yescharacteristic, complemented
90#2354C2211yescharacteristic
91D4×C22⋊C4C2211yescharacteristic
92#2317C2211yescharacteristic, complemented
93#2309C2211yescharacteristic
94#2094C2211yescharacteristic
95#2094C2211yescharacteristic, complemented
96#2094C2211yescharacteristic, complemented
97#2093C2211yescharacteristic
98#2093C2211yescharacteristic, complemented
99#2093C2211yescharacteristic, complemented
100#2092C2211yescharacteristic
101#2092C2211yescharacteristic
102#2092C2211yescharacteristic, complemented
103#2092C2211yescharacteristic, complemented
104#2087C2211yescharacteristic, complemented
105#2083C2211yescharacteristic, complemented
106#2077C2211yescharacteristic, complemented
107#2071C2211yescharacteristic, complemented
108#2068C2211yescharacteristic, complemented
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic, complemented
111#2067C2211yescharacteristic, complemented
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic, complemented
114#2059C2211yescharacteristic, complemented
115#2057C2211yescharacteristic, complemented
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic, complemented
118#2055C2211yescharacteristic, complemented
119#2041C2211yescharacteristic
120#2041C2211yescharacteristic
121#2041C2211yescharacteristic, complemented
122#2041C2211yescharacteristic, complemented
123#2041C2211yescharacteristic, complemented
124#2035C2211yescharacteristic, complemented
125#2034C2211yescharacteristic
126#2033C2211yescharacteristic, complemented
127#2033C2211yescharacteristic, complemented
128#2026C2211yescharacteristic, complemented
129#2023C2211yescharacteristic
130#2014C2211yescharacteristic
131#2014C2211yescharacteristic
132#2014C2211yescharacteristic, complemented
133#2000C2211yescharacteristic
134#1992C2211yescharacteristic, complemented
135#1991C2211yescharacteristic, complemented
136#1982C2211yescharacteristic
137#1982C2211yescharacteristic
138#1973C2211yescharacteristic
139#1968C2211yescharacteristic, complemented
140#1968C2211yescharacteristic, complemented
141#1968C2211yescharacteristic, complemented
142#1961C2211yescharacteristic, complemented
143#1957C2211yescharacteristic
144#1957C2211yescharacteristic
145#1957C2211yescharacteristic, complemented
146#1948C2211yescharacteristic, complemented
147#1942C2211yescharacteristic, complemented
148#1941C2211yescharacteristic, complemented
149#1939C2211yescharacteristic, complemented
150#1936C2211yescharacteristic, complemented
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic, complemented
154#1928C2211yescharacteristic, complemented
155#1925C2211yescharacteristic, complemented
156#1925C2211yescharacteristic, complemented
157#1925C2211yescharacteristic, complemented
158#1923C2211yescharacteristic, complemented
159#1923C2211yescharacteristic, complemented
160#1920C2211yescharacteristic, complemented
161#1919C2211yescharacteristic, complemented
162#1917C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1895C2211yescharacteristic
165#1895C2211yescharacteristic
166#1893C2211yescharacteristic, complemented
167#1880C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic, complemented
170#1877C2211yescharacteristic, complemented
171#1875C2211yescharacteristic
172#1875C2211yescharacteristic
173#1875C2211yescharacteristic, complemented
174#1874C2211yescharacteristic
175#1874C2211yescharacteristic, complemented
176#1873C2211yescharacteristic, complemented
177#1869C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic, complemented
180#1864C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1862C2211yescharacteristic, complemented
183#1862C2211yescharacteristic, complemented
184#1854C2211yescharacteristic, complemented
185#1854C2211yescharacteristic, complemented
186#1851C2211yescharacteristic, complemented
187#1851C2211yescharacteristic, complemented
188#1809C2211yescharacteristic, complemented
189#1804C2211yescharacteristic, complemented
190#1804C2211yescharacteristic, complemented
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic, complemented
193#1802C2211yescharacteristic, complemented
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197C4×#106C2211yescharacteristic, complemented
198C8×C4⋊C4C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213D42—24no—
214D42—42no—
215#540—24no—
216#540—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#126—21no—
223C2×#125—21no—
224C2×#125C2311yescharacteristic
225C2×#123—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#120—21no—
242C2×#120—21no—
243C2×#120—21no—
244C2×#120—21no—
245C2×#120—21no—
246C2×#120—21no—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×D4—21no—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C22⋊C4—21no—
260#486—42no—
261#482—42no—
262#476—42no—
263#468—42no—
264#468—42no—
265#465—24no—
266#460—42no—
267#450—42no—
268#450—42no—
269C4×SD16—42no—
270#436—42no—
271#433—42no—
272#428—42no—
273#427—42no—
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291#418—42no—
292#418—42no—
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#102—42no—
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×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×#97C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333C2×C4×C8C2311yescharacteristic
334C2×C4×C8C2311yescharacteristic
335C2×C4×C8C2311yescharacteristic
336#401—21no—
337#400—21no—
338#400—21no—
339#400—21no—
340#400—21no—
341#400D411yescharacteristic
342#399—21no—
343#399—21no—
344#399D411yescharacteristic
345#398—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#398—21no—
351#398—21no—
352#398D411yescharacteristic
353#397—21no—
354#397—21no—
355#397—21no—
356#397—21no—
357#397—21no—
358#397—21no—
359#397D411yescharacteristic
360#397D411yescharacteristic
361#397D411yescharacteristic
362#396—21no—
363#396—21no—
364#396—21no—
365#395—21no—
366#395—21no—
367#395—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394D411yescharacteristic
374#394D411yescharacteristic
375#393—21no—
376#392—21no—
377#392—21no—
378#392—21no—
379#392—21no—
380#392—21no—
381#392—21no—
382#392—21no—
383#392—21no—
384#391—21no—
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#390—21no—
390#390—21no—
391#390—21no—
392#390—21no—
393#390—21no—
394#390—21no—
395#390—21no—
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#389—21no—
405#389—21no—
406#389—21no—
407#389—21no—
408#389—21no—
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#383—21no—
450#382—21no—
451#382C2311yescharacteristic
452#382C2311yescharacteristic
453#380—21no—
454#380—21no—
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#379—21no—
460#379—21no—
461#379—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
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—
500C25—21no—
501C22×Q8—21no—
502C22×Q8C2411yescharacteristic
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
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—22no—
521C22×D4—22no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—44no—
530C22×D4—82no—
531C22×D4—82no—
532C22×D4C2×D411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2411yescharacteristic
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C2411yescharacteristic
543C23×C4C2411yescharacteristic
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×M16—22no—
557C2×M16—22no—
558C2×M16—22no—
559C2×M16—41no—
560C2×M16—41no—
561C2×M16—41no—
562C22×C8—22no—
563C22×C8—22no—
564C22×C8—41no—
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C4⋊Q8—41no—
574C4⋊Q8—41no—
575#127—22no—
576#127—22no—
577#127—22no—
578#127—41no—
579#127—41no—
580#127—41no—
581#127—41no—
582#127—41no—
583#126—82no—
584#125—22no—
585#125—41no—
586#125—82no—
587#123—44no—
588#123—44no—
589#123—82no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—82no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—44no—
600#121—44no—
601#121—44no—
602#121—41no—
603#121—41no—
604#121—41no—
605#121—82no—
606#121—82no—
607#121—82no—
608#121#4114yes—
609#120—44no—
610#120—44no—
611#120—82no—
612#120—82no—
613#120—82no—
614#120—82no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—82no—
628#117—22no—
629#117—22no—
630#117—41no—
631#117—41no—
632#117—41no—
633#117—41no—
634#117—41no—
635#117—41no—
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⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—82no—
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735#107—22no—
736#107—41no—
737#107—41no—
738#107—41no—
739#107—41no—
740#107—41no—
741#106—22no—
742#106—22no—
743#106—22no—
744#106—22no—
745#106—41no—
746#106—41no—
747C4⋊C8—22no—
748C4⋊C8—41no—
749C4⋊C8—41no—
750C4⋊C8—41no—
751C4⋊C8—41no—
752#103—22no—
753#103—41no—
754#103—41no—
755#103—41no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784C22⋊C8—22no—
785C22⋊C8—22no—
786C22⋊C8—22no—
787C22⋊C8—41no—
788C22⋊C8—41no—
789#97—41no—
790C4×C8—22no—
791C4×C8—41no—
792C4×C8—41no—
793C4×C8—41no—
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#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—42no—
836C24—42no—
837C24—42no—
838C24—42no—
839C24—42no—
840C24—81no—
841C24—81no—
842C24—81no—
843C24—81no—
844C24—81no—
845C24—81no—
846C24—81no—
847C24—81no—
848C24—81no—
849C24C22×D411yescharacteristic
850C24C22×D411yescharacteristic
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—81no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×D4—22no—
861C2×D4—24no—
862C2×D4—22no—
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—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—41no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—44no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—82no—
907C2×D4—82no—
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—
925C2×D4—82no—
926C2×D4—82no—
927C2×D4—82no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—816no—
936C2×D4C2×#4112yes—
937C2×D42−1+412yes—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C2×#4112yes—
988C22×C4H(5,𝔽2)12yes—
989C22×C4C2511yescharacteristic
990SD16—44no—
991SD16—82no—
992SD16—82no—
993SD16—82no—
994M16—44no—
995M16—82no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—44no—
1019C2×C8H(5,𝔽2)12yes—
1020C2×C8H(5,𝔽2)12yes—
1021C4⋊C4—22no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4C2×#4112yes—
1073C22⋊C4—22no—
1074C22⋊C4—22no—
1075C22⋊C4—22no—
1076C22⋊C4—24no—
1077C22⋊C4—22no—
1078C22⋊C4—22no—
1079C22⋊C4—22no—
1080C22⋊C4—22no—
1081C22⋊C4—22no—
1082C22⋊C4—41no—
1083C22⋊C4—41no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—42no—
1127C42—42no—
1128C42—81no—
1129C42—81no—
1130C42—81no—
1131C42—81no—
1132C42—81no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—22no—
1141C23—21no—
1142C23—21no—
1143C23—22no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—84no—
1175C23—84no—
1176C23—84no—
1177C23—84no—
1178C23—84no—
1179C23—162no—
1180C23—162no—
1181C23—162no—
1182C23—162no—
1183C23—162no—
1184C23—162no—
1185C23—162no—
1186C23—162no—
1187C23—162no—
1188C23#54612yes—
1189C23C23×D411yescharacteristic
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—162no—
1195D4—22no—
1196D4—22no—
1197D4—22no—
1198D4—22no—
1199D4—44no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—84no—
1213D4—84no—
1214D4—84no—
1215D4—84no—
1216D4—84no—
1217D4—84no—
1218D4—162no—
1219D4—162no—
1220D4—162no—
1221D4—162no—
1222D4—162no—
1223D4—162no—
1224D4—162no—
1225D4—162no—
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—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—84no—
1303C2×C4—162no—
1304C2×C4—162no—
1305C2×C4—162no—
1306C2×C4—162no—
1307C2×C4#54612yes—
1308C2×C4#57612yes—
1309C2×C4#57712yes—
1310C2×C4#57712yes—
1311C2×C4C22×#4111yescharacteristic
1312C2×C4C2×H(5,𝔽2)11yescharacteristic
1313C2×C4C2×H(5,𝔽2)11yescharacteristic
1314C2×C4C2×H(5,𝔽2)11yescharacteristic
1315C2×C4C2×2−1+411yescharacteristic
1316C2×C4#58511yescharacteristic
1317C8—22no—
1318C8—22no—
1319C8—41no—
1320C8—41no—
1321C8—41no—
1322C8—41no—
1323C8—41no—
1324C8—41no—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—42no—
1334C22—42no—
1335C22—41no—
1336C22—41no—
1337C22—42no—
1338C22—41no—
1339C22—41no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—41no—
1344C22—41no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—168no—
1368C22—168no—
1369C22C2×#54611yescharacteristic
1370C22#348911yescharacteristic
1371C22#349811yescharacteristic
1372C22C2×#57611yescharacteristic
1373C22C2×#57711yescharacteristic
1374C22C2×#57711yescharacteristic
1375C22#358511yescharacteristic
1376C4—22no—
1377C4—22no—
1378C4—22no—
1379C4—22no—
1380C4—41no—
1381C4—41no—
1382C4—42no—
1383C4—41no—
1384C4—41no—
1385C4—41no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4#351311yescharacteristic
1401C4#352011yescharacteristic
1402C4#353411yescharacteristic
1403C4#353611yescharacteristic
1404C2—42no—
1405C2—81no—
1406C2—82no—
1407C2—82no—
1408C2—161no—
1409C2—161no—
1410C2#4402211yescharacteristic
1411C2#6118411yescharacteristic
1412C2#6121511yescharacteristic
1413C2#6218811yescharacteristic
1414C2#6220011yescharacteristic
1415C2#6243011yescharacteristic
1416C2#6246311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#44872C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42924C2semidirect
3. #32096C2semidirect
4. #32059C2semidirect
5. #31909C2semidirect
6. #31570C2semidirect
7. #31534C2semidirect
8. #31286C2semidirect
9. #30630C2semidirect
10. #30612C2semidirect
11. #28944C2semidirect
12. #28404C2semidirect
13. #28365C2semidirect
14. #28071C2semidirect
15. #27254C2semidirect
16. #27063C2semidirect
17. #26530C2semidirect
18. #26359C2semidirect
19. #26141C2semidirect
20. #25974C2semidirect
21. #25507C2semidirect
22. #25093C2semidirect
23. #24901C2semidirect
24. #24795C2semidirect
25. #24516C2semidirect
26. #24432C2semidirect
27. #23735C2semidirect
28. #23023C2semidirect
29. #22915C2semidirect
30. #22428C2semidirect
31. #21872C2semidirect
34. C2×#486C22semidirect
35. C2×#482C22semidirect
36. C2×#476C22semidirect
37. C2×#468C22semidirect
38. C2×#468C22semidirect
40. C2×#460C22semidirect
43. C2×C4×SD16C22semidirect
45. C2×#433C22semidirect
46. C2×#428C22semidirect
47. C2×#427C22semidirect
62. #2625C22semidirect
64. #2567C22semidirect
65. #2552C22semidirect
68. #2514C22semidirect
69. #2508C22semidirect
70. #2499C22semidirect
71. #2496C22semidirect
76. #2440C22semidirect
77. #2439C22semidirect
81. #2423C22semidirect
89. #2362C22semidirect
92. #2317C22semidirect
95. #2094C22semidirect
96. #2094C22semidirect
98. #2093C22semidirect
99. #2093C22semidirect
102. #2092C22semidirect
103. #2092C22semidirect
104. #2087C22semidirect
105. #2083C22semidirect
106. #2077C22semidirect
107. #2071C22semidirect
108. #2068C22semidirect
110. #2067C22semidirect
111. #2067C22semidirect
113. #2065C22semidirect
114. #2059C22semidirect
115. #2057C22semidirect
117. #2055C22semidirect
118. #2055C22semidirect
121. #2041C22semidirect
122. #2041C22semidirect
123. #2041C22semidirect
124. #2035C22semidirect
126. #2033C22semidirect
127. #2033C22semidirect
128. #2026C22semidirect
132. #2014C22semidirect
134. #1992C22semidirect
135. #1991C22semidirect
139. #1968C22semidirect
140. #1968C22semidirect
141. #1968C22semidirect
142. #1961C22semidirect
145. #1957C22semidirect
146. #1948C22semidirect
147. #1942C22semidirect
148. #1941C22semidirect
149. #1939C22semidirect
150. #1936C22semidirect
153. #1934C22semidirect
154. #1928C22semidirect
155. #1925C22semidirect
156. #1925C22semidirect
157. #1925C22semidirect
158. #1923C22semidirect
159. #1923C22semidirect
160. #1920C22semidirect
161. #1919C22semidirect
162. #1917C22semidirect
163. #1916C22semidirect
166. #1893C22semidirect
169. #1877C22semidirect
170. #1877C22semidirect
173. #1875C22semidirect
175. #1874C22semidirect
176. #1873C22semidirect
179. #1864C22semidirect
180. #1864C22semidirect
181. #1863C22semidirect
182. #1862C22semidirect
183. #1862C22semidirect
184. #1854C22semidirect
185. #1854C22semidirect
186. #1851C22semidirect
187. #1851C22semidirect
188. #1809C22semidirect
189. #1804C22semidirect
190. #1804C22semidirect
192. #1802C22semidirect
193. #1802C22semidirect
197. C4×#106C22semidirect
198. C8×C4⋊C4C22semidirect
200. #1753C22semidirect
201. C8×C22⋊C4C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#448722
#429242
#320962
#320592
#319092
#315702
#315342
#312862
#306302
#306122
#289442
#284042
#283652
#280712
#272542
#270632
#265302
#263592
#261412
#259742
#255072
#250932
#249012
#247952
#245162
#244322
#237352
#230232
#229152
#224282
#218722