Finite Group Databasebeta

← #6677550

Subgroups — #6677550

Order 512.

1850 conjugacy classes of subgroups.

The subgroup lattice has 1397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3376C211yesmaximal, characteristic, complemented
2C2×#3122C211yesmaximal, characteristic
3#42439C211yesmaximal, characteristic, complemented
4#36033C211yesmaximal, characteristic, complemented
5#32966C211yesmaximal, characteristic, complemented
6#31222C211yesmaximal, characteristic, complemented
7#31209C211yesmaximal, characteristic, complemented
8#31008C211yesmaximal, characteristic, complemented
9#30992C211yesmaximal, characteristic, complemented
10#30831C211yesmaximal, characteristic, complemented
11#30819C211yesmaximal, characteristic, complemented
12#30535C211yesmaximal, characteristic, complemented
13#30523C211yesmaximal, characteristic, complemented
14#29856C211yesmaximal, characteristic, complemented
15#29673C211yesmaximal, characteristic, complemented
16#28429C211yesmaximal, characteristic, complemented
17#28276C211yesmaximal, characteristic, complemented
18#26808C211yesmaximal, characteristic, complemented
19#26794C211yesmaximal, characteristic, complemented
20#26612C211yesmaximal, characteristic, complemented
21#26597C211yesmaximal, characteristic, complemented
22#26569C211yesmaximal, characteristic, complemented
23#26553C211yesmaximal, characteristic, complemented
24#26477C211yesmaximal, characteristic, complemented
25#26470C211yesmaximal, characteristic, complemented
26#24684C211yesmaximal, characteristic, complemented
27#24627C211yesmaximal, characteristic, complemented
28#24335C211yesmaximal, characteristic, complemented
29#24185C211yesmaximal, characteristic, complemented
30#22817C211yesmaximal, characteristic, complemented
31#22109C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#554C2211yescharacteristic, complemented
34C2×#540C2211yescharacteristic
35C2×#518C2211yescharacteristic
36#3376—28no—
37C2×#491C2211yescharacteristic, complemented
38C2×#489C2211yescharacteristic
39C2×#488C2211yescharacteristic
40#3122—28no—
41C2×#482C2211yescharacteristic
42C2×#482C2211yescharacteristic
43C2×#479C2211yescharacteristic, complemented
44C2×#475C2211yescharacteristic, complemented
45C2×#478C2211yescharacteristic
46C2×#478C2211yescharacteristic
47C2×#478C2211yescharacteristic
48C2×#478C2211yescharacteristic
49C2×#463C2211yescharacteristic
50C2×#463C2211yescharacteristic
51C2×#461C2211yescharacteristic, complemented
52C2×#461C2211yescharacteristic, complemented
53C2×#459C2211yescharacteristic
54C2×#459C2211yescharacteristic
55C2×#447C2211yescharacteristic
56C2×#447C2211yescharacteristic
57C2×#446C2211yescharacteristic, complemented
58C2×#442C2211yescharacteristic
59C2×#442C2211yescharacteristic
60C2×#440C2211yescharacteristic, complemented
61C2×C4×SD16C2211yescharacteristic, complemented
62C2×C4×D8C2211yescharacteristic
63C2×C4×D8C2211yescharacteristic
64C2×#433C2211yescharacteristic
65#2814—21no—
66#2687—21no—
67#2681—21no—
68#2680—21no—
69#2672—21no—
70#2638—21no—
71#2629C2211yescharacteristic
72#2621C2211yescharacteristic
73#2620—21no—
74#2618—21no—
75#2580C2211yescharacteristic
76#2566C2211yescharacteristic, complemented
77#2561—21no—
78#2552C2211yescharacteristic, complemented
79#2550C2211yescharacteristic, complemented
80#2547C2211yescharacteristic
81#2538C2211yescharacteristic, complemented
82#2491C2211yescharacteristic
83#2490C2211yescharacteristic
84#2482—21no—
85#2480—21no—
86#2480—21no—
87#2468—21no—
88#2468—21no—
89#2447C2211yescharacteristic
90#2447C2211yescharacteristic
91#2445C2211yescharacteristic, complemented
92#2445C2211yescharacteristic, complemented
93#2435C2211yescharacteristic
94#2435C2211yescharacteristic
95#2422C2211yescharacteristic
96#2420C2211yescharacteristic
97#2413—21no—
98#2396C2211yescharacteristic
99#2395—21no—
100#2367C2211yescharacteristic
101#2367C2211yescharacteristic
102#2362C2211yescharacteristic
103#2362C2211yescharacteristic
104#2357C2211yescharacteristic
105#2354C2211yescharacteristic, complemented
106#2097C2211yescharacteristic, complemented
107#2096C2211yescharacteristic, complemented
108#2073C2211yescharacteristic
109#2071C2211yescharacteristic
110#2068C2211yescharacteristic, complemented
111#2068C2211yescharacteristic, complemented
112#2067C2211yescharacteristic
113#2067C2211yescharacteristic, complemented
114#2066C2211yescharacteristic, complemented
115#2066C2211yescharacteristic, complemented
116#2065C2211yescharacteristic
117#2065C2211yescharacteristic, complemented
118#2059C2211yescharacteristic, complemented
119#2057C2211yescharacteristic, complemented
120#2055C2211yescharacteristic, complemented
121#2055C2211yescharacteristic, complemented
122#2054C2211yescharacteristic
123#2054C2211yescharacteristic
124#2042C2211yescharacteristic
125#2042C2211yescharacteristic
126#2036C2211yescharacteristic
127#2036C2211yescharacteristic
128#2035C2211yescharacteristic
129#2035C2211yescharacteristic
130#2026C2211yescharacteristic, complemented
131#2026C2211yescharacteristic, complemented
132#2025C2211yescharacteristic
133#2023C2211yescharacteristic
134#2014C2211yescharacteristic, complemented
135#2014C2211yescharacteristic, complemented
136#2012C2211yescharacteristic
137#2012C2211yescharacteristic
138#2012C2211yescharacteristic
139#2012C2211yescharacteristic
140#2012C2211yescharacteristic
141#2012C2211yescharacteristic
142#2000C2211yescharacteristic
143#2000C2211yescharacteristic
144#2000C2211yescharacteristic
145#2000C2211yescharacteristic
146#1991C2211yescharacteristic, complemented
147#1984C2211yescharacteristic, complemented
148#1983C2211yescharacteristic
149#1983C2211yescharacteristic
150#1973C2211yescharacteristic, complemented
151#1972C2211yescharacteristic
152#1972C2211yescharacteristic
153#1970C2211yescharacteristic
154#1970C2211yescharacteristic
155#1968C2211yescharacteristic, complemented
156#1959C2211yescharacteristic
157#1958C2211yescharacteristic
158#1956C2211yescharacteristic, complemented
159#1949C2211yescharacteristic, complemented
160#1947C2211yescharacteristic, complemented
161#1943C2211yescharacteristic, complemented
162#1941C2211yescharacteristic, complemented
163#1940C2211yescharacteristic, complemented
164#1939C2211yescharacteristic, complemented
165#1939C2211yescharacteristic, complemented
166#1928C2211yescharacteristic, complemented
167#1928C2211yescharacteristic, complemented
168#1926C2211yescharacteristic
169#1926C2211yescharacteristic, complemented
170#1926C2211yescharacteristic, complemented
171#1925C2211yescharacteristic
172#1925C2211yescharacteristic, complemented
173#1925C2211yescharacteristic, complemented
174#1924C2211yescharacteristic
175#1924C2211yescharacteristic
176#1923C2211yescharacteristic
177#1923C2211yescharacteristic
178#1917C2211yescharacteristic, complemented
179#1916C2211yescharacteristic, complemented
180#1880C2211yescharacteristic, complemented
181#1880C2211yescharacteristic, complemented
182#1879C2211yescharacteristic
183#1879C2211yescharacteristic
184#1864C2211yescharacteristic
185#1864C2211yescharacteristic
186#1864C2211yescharacteristic, complemented
187#1863C2211yescharacteristic, complemented
188#1863C2211yescharacteristic, complemented
189#1862C2211yescharacteristic
190#1862C2211yescharacteristic
191#1862C2211yescharacteristic, complemented
192#1854C2211yescharacteristic
193#1854C2211yescharacteristic
194#1847C2211yescharacteristic, complemented
195#1804C2211yescharacteristic, complemented
196#1804C2211yescharacteristic, complemented
197#1802C2211yescharacteristic
198#1802C2211yescharacteristic
199#1798C2211yescharacteristic
200#1786C2211yescharacteristic
201#1786C2211yescharacteristic
202#1776C2211yescharacteristic, complemented
203C4×#106C2211yescharacteristic, complemented
204#1771C2211yescharacteristic, complemented
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214#556—24no—
215#556—42no—
216#554—24no—
217#554—42no—
218#540—24no—
219#540—42no—
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#126—21no—
224C2×#126—21no—
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#124—21no—
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#123—21no—
234C2×#123—21no—
235C2×#123—21no—
236C2×#123—21no—
237C2×#123—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8C2311yescharacteristic
244C2×C22⋊Q8C2311yescharacteristic
245C2×#121—21no—
246C2×#121—21no—
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249#518—24no—
250#518—42no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×D4—21no—
255C2×C4×D4—21no—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×#117—21no—
265C2×#117—21no—
266C2×#117C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C22×C4⋊C4—21no—
269C22×C22⋊C4—21no—
270C22×C22⋊C4—21no—
271#491—24no—
272#489—24no—
273#488—24no—
274#482—24no—
275#482—24no—
276#479—24no—
277#478—24no—
278#478—24no—
279#478—24no—
280#478—42no—
281#475—24no—
282#463—24no—
283#463—24no—
284#461—24no—
285#461—42no—
286#459—24no—
287#459—24no—
288#447—24no—
289#447—24no—
290#446—24no—
291#442—24no—
292#442D418yes—
293#440—24no—
294C4×SD16—24no—
295C4×D8—24no—
296C4×D8—24no—
297#433—24no—
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×C22⋊C8C2311yescharacteristic
352C2×C22⋊C8C2311yescharacteristic
353C2×C22⋊C8C2311yescharacteristic
354C2×#97C2311yescharacteristic
355C2×#97C2311yescharacteristic
356C2×#97C2311yescharacteristic
357C2×C4×C8C2311yescharacteristic
358C2×C4×C8C2311yescharacteristic
359C2×C4×C8C2311yescharacteristic
360#400D411yescharacteristic
361#399—21no—
362#399D411yescharacteristic
363#398—21no—
364#398—21no—
365#398—21no—
366#398—21no—
367#398—21no—
368#398—21no—
369#398—21no—
370#398D411yescharacteristic
371#398D411yescharacteristic
372#397—21no—
373#397—21no—
374#397—21no—
375#397—21no—
376#397—21no—
377#397—21no—
378#397—21no—
379#397—21no—
380#397—21no—
381#397—21no—
382#397—21no—
383#396—21no—
384#396—21no—
385#396—21no—
386#396—21no—
387#396—21no—
388#396—21no—
389#396D411yescharacteristic
390#396D411yescharacteristic
391#395—21no—
392#395D411yescharacteristic
393#394—21no—
394#394—21no—
395#394—21no—
396#394—21no—
397#394—21no—
398#394—21no—
399#394—21no—
400#394—21no—
401#394—21no—
402#394—21no—
403#394—21no—
404#394—21no—
405#393—21no—
406#393—21no—
407#393D411yescharacteristic
408#391—21no—
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#391C2311yescharacteristic
413#390—21no—
414#390C2311yescharacteristic
415#390C2311yescharacteristic
416#390C2311yescharacteristic
417#390C2311yescharacteristic
418#390C2311yescharacteristic
419#390C2311yescharacteristic
420#390C2311yescharacteristic
421#390C2311yescharacteristic
422#390C2311yescharacteristic
423#390C2311yescharacteristic
424#389—21no—
425#389—21no—
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#388—21no—
441#388—21no—
442#388—21no—
443#388—21no—
444#388—21no—
445#388—21no—
446#387—21no—
447#387—21no—
448#386—21no—
449#386—21no—
450#386—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#385—21no—
459#385—21no—
460#384—21no—
461#384C2311yescharacteristic
462#384C2311yescharacteristic
463#382C2311yescharacteristic
464#382C2311yescharacteristic
465#381—21no—
466#381—21no—
467#381—21no—
468#381—21no—
469#380—21no—
470#380—21no—
471#380—21no—
472#380—21no—
473#380C2311yescharacteristic
474#380C2311yescharacteristic
475#379—21no—
476#379—21no—
477#379—21no—
478#379—21no—
479C4×C4⋊C4—21no—
480C4×C4⋊C4—21no—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C22⋊C4—21no—
489C4×C22⋊C4—21no—
490C4×C22⋊C4—21no—
491C4×C22⋊C4C2311yescharacteristic
492C4×C22⋊C4C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C25—21no—
516C22×Q8—21no—
517C22×Q8C2×D411yescharacteristic
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4C2411yescharacteristic
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—41no—
547C2×SD16—41no—
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×D8—22no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—22no—
560C2×D8—22no—
561C2×D8—41no—
562C2×D8—41no—
563C2×D8—41no—
564C2×D8—41no—
565C2×D8—41no—
566C2×D8—41no—
567C2×D8C2×D414yes—
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C4⋊Q8—22no—
577C4⋊Q8—22no—
578C4⋊Q8—22no—
579C4⋊Q8—41no—
580#127—22no—
581#127—41no—
582#126—44no—
583#126—44no—
584#125—22no—
585#125—22no—
586#125—22no—
587#125—22no—
588#125—41no—
589#125—41no—
590#124—22no—
591#124—22no—
592#124—22no—
593#124—22no—
594#124—41no—
595#124—41no—
596#124—41no—
597#124—41no—
598#124—82no—
599#123—44no—
600#123—44no—
601#123—82no—
602#123—82no—
603#123—82no—
604C22⋊Q8—44no—
605C22⋊Q8—44no—
606C22⋊Q8—41no—
607C22⋊Q8—41no—
608C22⋊Q8—41no—
609C22⋊Q8—41no—
610C22⋊Q8—44no—
611C22⋊Q8—44no—
612C22⋊Q8—82no—
613#121—22no—
614#121—22no—
615#121—44no—
616#121—44no—
617#121—41no—
618#121—41no—
619C4×Q8—22no—
620C4×Q8—22no—
621C4×Q8—22no—
622C4×Q8—22no—
623C4×Q8—41no—
624C4×Q8—41no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—22no—
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—22no—
634C4×D4—22no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—44no—
640C4×D4—44no—
641C4×D4C2×D414yes—
642C4×D4C2×D414yes—
643#117—22no—
644#117—22no—
645#117—22no—
646#117—41no—
647#117—44no—
648#117—82no—
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—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—44no—
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
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—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—44no—
738C2×C22⋊C4—44no—
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758#107—22no—
759#107—22no—
760#107—22no—
761#107—41no—
762#107—41no—
763#107—41no—
764#106—22no—
765#106—22no—
766#106—41no—
767#106—41no—
768#106—41no—
769#106C2×D414yes—
770C4⋊C8—22no—
771C4⋊C8—22no—
772C4⋊C8—22no—
773C4⋊C8—22no—
774C4⋊C8—22no—
775C4⋊C8—22no—
776C4⋊C8—41no—
777C4⋊C8—41no—
778#103—22no—
779#103—22no—
780#103—22no—
781#103—22no—
782#103—22no—
783#103—22no—
784#103—41no—
785#103—41no—
786#103—41no—
787#103—41no—
788#103—41no—
789#103—41no—
790#102—22no—
791#102—22no—
792#102—22no—
793#102—22no—
794#102—22no—
795#102—22no—
796#102—22no—
797#102—22no—
798#102—41no—
799#102—41no—
800#102—41no—
801#102—41no—
802#102—41no—
803#102—41no—
804#102—41no—
805#102—41no—
806#102—41no—
807#102—41no—
808#102C2×D414yes—
809#102C2×D414yes—
810C22⋊C8—22no—
811C22⋊C8—22no—
812C22⋊C8—41no—
813C22⋊C8—41no—
814#97—22no—
815#97—41no—
816#97C2×D414yes—
817C4×C8—22no—
818C4×C8—22no—
819C4×C8—41no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850#95C2×D411yescharacteristic
851#95C2×D411yescharacteristic
852#95C2×D411yescharacteristic
853#95C2×D411yescharacteristic
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—42no—
859C24—42no—
860C24—42no—
861C24—81no—
862C24—81no—
863C24—81no—
864C24—81no—
865C24C22×D411yescharacteristic
866C2×Q8—22no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—41no—
880C2×Q8—41no—
881C2×Q8—42no—
882C2×Q8—81no—
883C2×Q8—81no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—42no—
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×D4C22×D412yes—
925C2×D4C22×D412yes—
926C2×D42−1+412yes—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—21no—
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—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C2511yescharacteristic
983SD16—44no—
984SD16—44no—
985SD16—82no—
986SD16—82no—
987D8—44no—
988D8—44no—
989D8—44no—
990D8—44no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
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×C8C22×D412yes—
1014C2×C8C22×D412yes—
1015C4⋊C4—22no—
1016C4⋊C4—22no—
1017C4⋊C4—22no—
1018C4⋊C4—22no—
1019C4⋊C4—22no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
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—41no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—41no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
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⋊C4C22×D412yes—
1068C4⋊C4C22×D412yes—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—22no—
1072C22⋊C4—22no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
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—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
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—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—42no—
1129C42—42no—
1130C42—42no—
1131C42—42no—
1132C42—81no—
1133C42—81no—
1134C42—81no—
1135C42C22×D412yes—
1136C42H(5,𝔽2)12yes—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—22no—
1143C23—22no—
1144C23—21no—
1145C23—22no—
1146C23—21no—
1147C23—48no—
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—162no—
1174C23—162no—
1175C23—162no—
1176C23—162no—
1177C23—162no—
1178C23—162no—
1179C23C23×D411yescharacteristic
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—82no—
1189Q8—162no—
1190D4—22no—
1191D4—22no—
1192D4—22no—
1193D4—22no—
1194D4—22no—
1195D4—22no—
1196D4—48no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—162no—
1208D4—162no—
1209D4—162no—
1210D4—162no—
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—21no—
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—21no—
1240C2×C4—21no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
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—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—84no—
1289C2×C4—84no—
1290C2×C4—84no—
1291C2×C4—162no—
1292C2×C4—162no—
1293C2×C4—162no—
1294C2×C4—162no—
1295C2×C4—162no—
1296C2×C4D4212yes—
1297C2×C4D4212yes—
1298C2×C4C23×D411yescharacteristic
1299C2×C4C2×H(5,𝔽2)11yescharacteristic
1300C2×C4C2×2−1+411yescharacteristic
1301C2×C4#58511yescharacteristic
1302C2×C4#58511yescharacteristic
1303C2×C4#58511yescharacteristic
1304C8—22no—
1305C8—22no—
1306C8—41no—
1307C8—41no—
1308C8—41no—
1309C8—41no—
1310C8—41no—
1311C8—41no—
1312C22—41no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—41no—
1319C22—42no—
1320C22—42no—
1321C22—41no—
1322C22—41no—
1323C22—42no—
1324C22—41no—
1325C22—41no—
1326C22—42no—
1327C22—41no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—168no—
1348C22C2×D4211yescharacteristic
1349C22#348711yescharacteristic
1350C22#348911yescharacteristic
1351C22#358411yescharacteristic
1352C22#358411yescharacteristic
1353C22#358511yescharacteristic
1354C22#358511yescharacteristic
1355C4—22no—
1356C4—22no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—42no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—42no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4#344911yescharacteristic
1381C4#348911yescharacteristic
1382C4#354011yescharacteristic
1383C4#354111yescharacteristic
1384C2—81no—
1385C2—82no—
1386C2—82no—
1387C2—82no—
1388C2—161no—
1389C2#3765911yescharacteristic
1390C2#6107411yescharacteristic
1391C2#6109211yescharacteristic
1392C2#6193011yescharacteristic
1393C2#6194211yescharacteristic
1394C2#6217111yescharacteristic
1395C2#6219511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3122C2
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
1. C2×#3376C2semidirect
3. #42439C2semidirect
4. #36033C2semidirect
5. #32966C2semidirect
6. #31222C2semidirect
7. #31209C2semidirect
8. #31008C2semidirect
9. #30992C2semidirect
10. #30831C2semidirect
11. #30819C2semidirect
12. #30535C2semidirect
13. #30523C2semidirect
14. #29856C2semidirect
15. #29673C2semidirect
16. #28429C2semidirect
17. #28276C2semidirect
18. #26808C2semidirect
19. #26794C2semidirect
20. #26612C2semidirect
21. #26597C2semidirect
22. #26569C2semidirect
23. #26553C2semidirect
24. #26477C2semidirect
25. #26470C2semidirect
26. #24684C2semidirect
27. #24627C2semidirect
28. #24335C2semidirect
29. #24185C2semidirect
30. #22817C2semidirect
31. #22109C2semidirect
33. C2×#554C22semidirect
37. C2×#491C22semidirect
43. C2×#479C22semidirect
44. C2×#475C22semidirect
51. C2×#461C22semidirect
52. C2×#461C22semidirect
57. C2×#446C22semidirect
60. C2×#440C22semidirect
61. C2×C4×SD16C22semidirect
76. #2566C22semidirect
78. #2552C22semidirect
79. #2550C22semidirect
81. #2538C22semidirect
91. #2445C22semidirect
92. #2445C22semidirect
105. #2354C22semidirect
106. #2097C22semidirect
107. #2096C22semidirect
110. #2068C22semidirect
111. #2068C22semidirect
113. #2067C22semidirect
114. #2066C22semidirect
115. #2066C22semidirect
117. #2065C22semidirect
118. #2059C22semidirect
119. #2057C22semidirect
120. #2055C22semidirect
121. #2055C22semidirect
130. #2026C22semidirect
131. #2026C22semidirect
134. #2014C22semidirect
135. #2014C22semidirect
146. #1991C22semidirect
147. #1984C22semidirect
150. #1973C22semidirect
155. #1968C22semidirect
158. #1956C22semidirect
159. #1949C22semidirect
160. #1947C22semidirect
161. #1943C22semidirect
162. #1941C22semidirect
163. #1940C22semidirect
164. #1939C22semidirect
165. #1939C22semidirect
166. #1928C22semidirect
167. #1928C22semidirect
169. #1926C22semidirect
170. #1926C22semidirect
172. #1925C22semidirect
173. #1925C22semidirect
178. #1917C22semidirect
179. #1916C22semidirect
180. #1880C22semidirect
181. #1880C22semidirect
186. #1864C22semidirect
187. #1863C22semidirect
188. #1863C22semidirect
191. #1862C22semidirect
194. #1847C22semidirect
195. #1804C22semidirect
196. #1804C22semidirect
202. #1776C22semidirect
203. C4×#106C22semidirect
204. #1771C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33762
C2×#31222
#424392
#360332
#329662
#312222
#312092
#310082
#309922
#308312
#308192
#305352
#305232
#298562
#296732
#284292
#282762
#268082
#267942
#266122
#265972
#265692
#265532
#264772
#264702
#246842
#246272
#243352
#241852
#228172
#221092