Finite Group Databasebeta

← #6608244

Subgroups — #6608244

Order 512.

1712 conjugacy classes of subgroups.

The subgroup lattice has 1385 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39069C211yesmaximal, characteristic, complemented
2#39066C211yesmaximal, characteristic, complemented
3#33269C211yesmaximal, characteristic, complemented
4#33248C211yesmaximal, characteristic, complemented
5#33140C211yesmaximal, characteristic, complemented
6#29569C211yesmaximal, characteristic, complemented
7#29564C211yesmaximal, characteristic, complemented
8#29497C211yesmaximal, characteristic, complemented
9#29493C211yesmaximal, characteristic, complemented
10#28891C211yesmaximal, characteristic, complemented
11#28890C211yesmaximal, characteristic, complemented
12#28029C211yesmaximal, characteristic, complemented
13#27264C211yesmaximal, characteristic, complemented
14#27263C211yesmaximal, characteristic, complemented
15#26827C211yesmaximal, characteristic, complemented
16#26825C211yesmaximal, characteristic, complemented
17#26481C211yesmaximal, characteristic, complemented
18#26267C211yesmaximal, characteristic, complemented
19#26254C211yesmaximal, characteristic, complemented
20#26073C211yesmaximal, characteristic, complemented
21#25794C211yesmaximal, characteristic
22#24513C211yesmaximal, characteristic, complemented
23#24512C211yesmaximal, characteristic, complemented
24#23037C211yesmaximal, characteristic, complemented
25#22877C211yesmaximal, characteristic, complemented
26#22870C211yesmaximal, characteristic, complemented
27#22443C211yesmaximal, characteristic, complemented
28C4×#496C211yesmaximal, characteristic, complemented
29#21291C211yesmaximal, characteristic, complemented
30#21235C211yesmaximal, characteristic, complemented
31#20478C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#499C2211yescharacteristic, complemented
34C2×#496C2211yescharacteristic
35C2×#493C2211yescharacteristic
36C2×#490C2211yescharacteristic
37C2×#490C2211yescharacteristic, complemented
38C2×#469C2211yescharacteristic
39C2×#449C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×C4×SD16C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic, complemented
44C2×C4×D8C2211yescharacteristic
45C2×C4×D8C2211yescharacteristic, complemented
46C2×#433C2211yescharacteristic
47C2×#428C2211yescharacteristic
48C2×#416C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C2×#405C2211yescharacteristic
51#2860C2211yescharacteristic
52#2860C2211yescharacteristic, complemented
53#2756—21no—
54#2753—21no—
55#2752—21no—
56#2741—21no—
57#2741—21no—
58#2705—21no—
59#2685—21no—
60#2685—21no—
61#2641C2211yescharacteristic
62#2641C2211yescharacteristic, complemented
63#2624C2211yescharacteristic
64#2624C2211yescharacteristic
65#2602—21no—
66#2602—21no—
67#2578—21no—
68#2553—21no—
69#2534—21no—
70#2513C2211yescharacteristic, complemented
71#2512C2211yescharacteristic
72#2467—21no—
73#2467—21no—
74#2454C2211yescharacteristic
75#2453C2211yescharacteristic, complemented
76#2448C2211yescharacteristic, complemented
77#2445C2211yescharacteristic
78#2445C2211yescharacteristic
79#2445C2211yescharacteristic, complemented
80#2442C2211yescharacteristic
81#2441C2211yescharacteristic
82#2433C2211yescharacteristic
83#2431C2211yescharacteristic
84#2418—21no—
85#2363C2211yescharacteristic
86#2361C2211yescharacteristic
87#2341C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89#2320C2211yescharacteristic, complemented
90#2319C2211yescharacteristic
91#2311C2211yescharacteristic
92#2309C2211yescharacteristic
93C4×#127C2211yescharacteristic
94C4×#124C2211yescharacteristic, complemented
95#2298C2211yescharacteristic
96#2085C2211yescharacteristic, complemented
97#2083C2211yescharacteristic, complemented
98#2073C2211yescharacteristic
99#2071C2211yescharacteristic, complemented
100#2068C2211yescharacteristic, complemented
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic, complemented
103#2065C2211yescharacteristic
104#2059C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2055C2211yescharacteristic, complemented
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic, complemented
110#2042C2211yescharacteristic, complemented
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic, complemented
114#2026C2211yescharacteristic, complemented
115#2025C2211yescharacteristic
116#2014C2211yescharacteristic
117#2012C2211yescharacteristic
118#2011C2211yescharacteristic
119#2011C2211yescharacteristic
120#1973C2211yescharacteristic
121#1973C2211yescharacteristic
122#1973C2211yescharacteristic, complemented
123#1972C2211yescharacteristic
124#1972C2211yescharacteristic
125#1972C2211yescharacteristic
126#1972C2211yescharacteristic
127#1972C2211yescharacteristic
128#1972C2211yescharacteristic, complemented
129#1972C2211yescharacteristic, complemented
130#1970C2211yescharacteristic
131#1970C2211yescharacteristic
132#1970C2211yescharacteristic
133#1970C2211yescharacteristic
134#1970C2211yescharacteristic
135#1970C2211yescharacteristic, complemented
136#1970C2211yescharacteristic, complemented
137#1970C2211yescharacteristic, complemented
138#1968C2211yescharacteristic
139#1968C2211yescharacteristic
140#1968C2211yescharacteristic
141#1961C2211yescharacteristic
142#1959C2211yescharacteristic, complemented
143#1944C2211yescharacteristic, complemented
144#1943C2211yescharacteristic, complemented
145#1942C2211yescharacteristic, complemented
146#1941C2211yescharacteristic, complemented
147#1941C2211yescharacteristic, complemented
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic, complemented
152#1936C2211yescharacteristic, complemented
153#1936C2211yescharacteristic, complemented
154#1936C2211yescharacteristic, complemented
155#1935C2211yescharacteristic, complemented
156#1934C2211yescharacteristic
157#1934C2211yescharacteristic
158#1934C2211yescharacteristic, complemented
159#1934C2211yescharacteristic, complemented
160#1934C2211yescharacteristic, complemented
161#1933C2211yescharacteristic, complemented
162#1926C2211yescharacteristic, complemented
163#1926C2211yescharacteristic, complemented
164#1925C2211yescharacteristic
165#1925C2211yescharacteristic, complemented
166#1893C2211yescharacteristic
167#1893C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic, complemented
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic, complemented
176#1875C2211yescharacteristic
177#1874C2211yescharacteristic
178#1864C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic, complemented
182#1854C2211yescharacteristic
183#1852C2211yescharacteristic
184#1847C2211yescharacteristic, complemented
185#1809C2211yescharacteristic
186#1788C2211yescharacteristic
187#1786C2211yescharacteristic
188#1776C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1771C2211yescharacteristic, complemented
191#1770C2211yescharacteristic, complemented
192C8×C4⋊C4C2211yescharacteristic, complemented
193C4×#103C2211yescharacteristic, complemented
194C4×#102C2211yescharacteristic
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1752C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199#1746C2211yescharacteristic, complemented
200#1744C2211yescharacteristic, complemented
201#1726C2211yescharacteristic, complemented
202C4×#97C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—24no—
207C2×AGL(1,ℤ/8)—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#126—21no—
223C2×#126—21no—
224C2×#126—21no—
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#120—21no—
234C2×#120—21no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C22⋊C4—21no—
248#499—42no—
249#496—24no—
250#493—42no—
251#490—42no—
252#490—42no—
253#469—24no—
254#449—24no—
255#447—24no—
256#440—24no—
257C4×SD16—42no—
258C4×SD16—42no—
259C4×D8—42no—
260C4×D8—42no—
261#433—24no—
262#428—42no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276#416—42no—
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#102—42no—
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310#405—24no—
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325#400—21no—
326#400—21no—
327#399—21no—
328#399—21no—
329#399—21no—
330#399—21no—
331#399—21no—
332#398—21no—
333#398—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#392—21no—
362#392—21no—
363#392—21no—
364#392—21no—
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#390—21no—
369#390—21no—
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#389—21no—
395#389—21no—
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388D411yescharacteristic
424#388D411yescharacteristic
425#388D411yescharacteristic
426#388D411yescharacteristic
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387D411yescharacteristic
432#387D411yescharacteristic
433#387D411yescharacteristic
434#387D411yescharacteristic
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#386—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#384C2311yescharacteristic
450#383—21no—
451#382—21no—
452#382C2311yescharacteristic
453#381—21no—
454#380—21no—
455#380—21no—
456#380—21no—
457#380—21no—
458#380—21no—
459#380—21no—
460#380C2311yescharacteristic
461#380C2311yescharacteristic
462#379—21no—
463#379—21no—
464#379—21no—
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4—21no—
473C4×C22⋊C4C2311yescharacteristic
474C4×C22⋊C4C2311yescharacteristic
475#376C2311yescharacteristic
476C43C2311yescharacteristic
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#340C2311yescharacteristic
490#340C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C2411yescharacteristic
507C22×D4—22no—
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—22no—
519C22×D4—22no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4C2411yescharacteristic
535AGL(1,ℤ/8)—416no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16#4114yes—
545C2×D8—22no—
546C2×D8—22no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×D8—41no—
563C2×M16—22no—
564C2×M16—22no—
565C2×M16#4114yes—
566C22×C8—22no—
567C22×C8—22no—
568C22×C8—41no—
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577#127—22no—
578#127—41no—
579#127—41no—
580#127—41no—
581#127—41no—
582#127—41no—
583#126—82no—
584#126—82no—
585#126—82no—
586#125—41no—
587#125—41no—
588#125—41no—
589#125—41no—
590#124—22no—
591#124—41no—
592#123—82no—
593#123—82no—
594#123—82no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#120—82no—
600#120—82no—
601C4×Q8—22no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×Q8—41no—
605C4×D4—22no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—82no—
614C4×D4—82no—
615C4×D4—82no—
616#117—22no—
617#117—22no—
618#117—41no—
619#117—41no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
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—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
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⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—82no—
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42C2×D411yescharacteristic
719C2×C42C2×D411yescharacteristic
720C2×C42C2×D411yescharacteristic
721C2×C42C2×D411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728#107—22no—
729#107—22no—
730#107—41no—
731#107—41no—
732#107—41no—
733#107—41no—
734#106—22no—
735#106—22no—
736#106—22no—
737#106—41no—
738#106—41no—
739C4⋊C8—22no—
740C4⋊C8—22no—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—41no—
745#103—41no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
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—
769#102—41no—
770#102—41no—
771C22⋊C8—22no—
772C22⋊C8#4114yes—
773#97—22no—
774#97—22no—
775#97—22no—
776#97—22no—
777#97—22no—
778#97—22no—
779#97—41no—
780C4×C8—22no—
781C4×C8—22no—
782C4×C8—22no—
783C4×C8—22no—
784C4×C8—22no—
785C4×C8—22no—
786C4×C8—41no—
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#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
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—21no—
826C24—42no—
827C24—42no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24C22×D411yescharacteristic
834#41—44no—
835#41—44no—
836#41—82no—
837#41—82no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8C2×#4112yes—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
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—44no—
874C2×D4—44no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—82no—
886C2×D4—82no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
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×D4C2×#4112yes—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C2×#4112yes—
955C22×C4C2×#4112yes—
956C22×C4C2511yescharacteristic
957SD16—28no—
958SD16—44no—
959SD16—44no—
960D8—44no—
961D8—44no—
962D8—44no—
963D8—44no—
964D8—82no—
965D8—82no—
966M16—28no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
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—44no—
985C2×C8C2×#4112yes—
986C2×C8C2×#4112yes—
987C2×C8C2×#4112yes—
988C2×C8C2×#4112yes—
989C2×C8C2×#4112yes—
990C2×C8H(5,𝔽2)12yes—
991C2×C8H(5,𝔽2)12yes—
992C4⋊C4—22no—
993C4⋊C4—22no—
994C4⋊C4—22no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
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—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C22⋊C4—22no—
1038C22⋊C4—22no—
1039C22⋊C4—22no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
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—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C42—22no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—41no—
1106C42—41no—
1107C42—41no—
1108C42—42no—
1109C42—81no—
1110C42—81no—
1111C42—81no—
1112C42—81no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—22no—
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—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—84no—
1155C23—84no—
1156C23—162no—
1157C23—162no—
1158C23—162no—
1159C23—162no—
1160C23—162no—
1161C23#53212yes—
1162C23C23×D411yescharacteristic
1163Q8—22no—
1164Q8—22no—
1165Q8—41no—
1166Q8—41no—
1167D4—22no—
1168D4—22no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—84no—
1188D4—84no—
1189D4—84no—
1190D4—84no—
1191D4—84no—
1192D4—162no—
1193D4—162no—
1194D4—162no—
1195D4—162no—
1196D4—162no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
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—21no—
1215C2×C4—21no—
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—22no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
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—41no—
1270C2×C4—41no—
1271C2×C4—84no—
1272C2×C4—162no—
1273C2×C4—162no—
1274C2×C4—162no—
1275C2×C4—162no—
1276C2×C4—162no—
1277C2×C4#53212yes—
1278C2×C4#57612yes—
1279C2×C4C22×#4111yescharacteristic
1280C2×C4C22×#4111yescharacteristic
1281C2×C4C22×#4111yescharacteristic
1282C2×C4C2×H(5,𝔽2)11yescharacteristic
1283C2×C4C2×H(5,𝔽2)11yescharacteristic
1284C2×C4#58511yescharacteristic
1285C8—22no—
1286C8—22no—
1287C8—22no—
1288C8—22no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C8#55114yes—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
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—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—168no—
1336C22C2×#53211yescharacteristic
1337C22D4×#4111yescharacteristic
1338C22#349811yescharacteristic
1339C22C2×#57611yescharacteristic
1340C22#358411yescharacteristic
1341C22#358511yescharacteristic
1342C22#358511yescharacteristic
1343C4—22no—
1344C4—22no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C4—42no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4C2×#55111yescharacteristic
1368C4#348111yescharacteristic
1369C4#349411yescharacteristic
1370C4#351411yescharacteristic
1371C2—42no—
1372C2—82no—
1373C2—161no—
1374C2—161no—
1375C2—161no—
1376C2—161no—
1377C2#3626411yescharacteristic
1378C2#6069511yescharacteristic
1379C2#6072511yescharacteristic
1380C2#6154711yescharacteristic
1381C2#6155511yescharacteristic
1382C2#6245911yescharacteristic
1383C2#6246111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25794C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39069C2semidirect
2. #39066C2semidirect
3. #33269C2semidirect
4. #33248C2semidirect
5. #33140C2semidirect
6. #29569C2semidirect
7. #29564C2semidirect
8. #29497C2semidirect
9. #29493C2semidirect
10. #28891C2semidirect
11. #28890C2semidirect
12. #28029C2semidirect
13. #27264C2semidirect
14. #27263C2semidirect
15. #26827C2semidirect
16. #26825C2semidirect
17. #26481C2semidirect
18. #26267C2semidirect
19. #26254C2semidirect
20. #26073C2semidirect
22. #24513C2semidirect
23. #24512C2semidirect
24. #23037C2semidirect
25. #22877C2semidirect
26. #22870C2semidirect
27. #22443C2semidirect
28. C4×#496C2semidirect
29. #21291C2semidirect
30. #21235C2semidirect
31. #20478C2semidirect
33. C2×#499C22semidirect
37. C2×#490C22semidirect
43. C2×C4×SD16C22semidirect
45. C2×C4×D8C22semidirect
52. #2860C22semidirect
62. #2641C22semidirect
70. #2513C22semidirect
75. #2453C22semidirect
76. #2448C22semidirect
79. #2445C22semidirect
89. #2320C22semidirect
94. C4×#124C22semidirect
96. #2085C22semidirect
97. #2083C22semidirect
99. #2071C22semidirect
100. #2068C22semidirect
102. #2067C22semidirect
104. #2059C22semidirect
105. #2059C22semidirect
106. #2055C22semidirect
109. #2054C22semidirect
110. #2042C22semidirect
113. #2041C22semidirect
114. #2026C22semidirect
122. #1973C22semidirect
128. #1972C22semidirect
129. #1972C22semidirect
135. #1970C22semidirect
136. #1970C22semidirect
137. #1970C22semidirect
142. #1959C22semidirect
143. #1944C22semidirect
144. #1943C22semidirect
145. #1942C22semidirect
146. #1941C22semidirect
147. #1941C22semidirect
151. #1936C22semidirect
152. #1936C22semidirect
153. #1936C22semidirect
154. #1936C22semidirect
155. #1935C22semidirect
158. #1934C22semidirect
159. #1934C22semidirect
160. #1934C22semidirect
161. #1933C22semidirect
162. #1926C22semidirect
163. #1926C22semidirect
165. #1925C22semidirect
170. #1880C22semidirect
175. #1879C22semidirect
178. #1864C22semidirect
179. #1863C22semidirect
181. #1862C22semidirect
184. #1847C22semidirect
188. #1776C22semidirect
189. #1771C22semidirect
190. #1771C22semidirect
191. #1770C22semidirect
192. C8×C4⋊C4C22semidirect
193. C4×#103C22semidirect
199. #1746C22semidirect
200. #1744C22semidirect
201. #1726C22semidirect
202. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
#390692
#390662
#332692
#332482
#331402
#295692
#295642
#294972
#294932
#288912
#288902
#280292
#272642
#272632
#268272
#268252
#264812
#262672
#262542
#260732
#257942
#245132
#245122
#230372
#228772
#228702
#224432
C4×#4962
#212912
#212352
#204782