Finite Group Databasebeta

← #7308188

Subgroups — #7308188

Order 512.

1690 conjugacy classes of subgroups.

The subgroup lattice has 1434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45094C211yesmaximal, characteristic, complemented
2#42563C211yesmaximal, characteristic, complemented
3#32172C211yesmaximal, characteristic, complemented
4#32125C211yesmaximal, characteristic, complemented
5#31805C211yesmaximal, characteristic, complemented
6#31646C211yesmaximal, characteristic, complemented
7#31506C211yesmaximal, characteristic, complemented
8#31403C211yesmaximal, characteristic, complemented
9#31217C211yesmaximal, characteristic, complemented
10#31020C211yesmaximal, characteristic, complemented
11#30526C211yesmaximal, characteristic, complemented
12#30524C211yesmaximal, characteristic, complemented
13#30452C211yesmaximal, characteristic, complemented
14#30445C211yesmaximal, characteristic, complemented
15#29728C211yesmaximal, characteristic, complemented
16#29675C211yesmaximal, characteristic, complemented
17#28128C211yesmaximal, characteristic, complemented
18#27531C211yesmaximal, characteristic, complemented
19#27227C211yesmaximal, characteristic, complemented
20#26938C211yesmaximal, characteristic, complemented
21#26892C211yesmaximal, characteristic, complemented
22#26730C211yesmaximal, characteristic, complemented
23#26598C211yesmaximal, characteristic, complemented
24#25373C211yesmaximal, characteristic, complemented
25#25327C211yesmaximal, characteristic, complemented
26#24373C211yesmaximal, characteristic, complemented
27#24366C211yesmaximal, characteristic, complemented
28#24246C211yesmaximal, characteristic, complemented
29#24162C211yesmaximal, characteristic, complemented
30#23866C211yesmaximal, characteristic, complemented
31#23317C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#548C2211yescharacteristic
34C2×#540C2211yescharacteristic, complemented
35C2×#495C2211yescharacteristic
36C2×#488C2211yescharacteristic, complemented
37C2×#482C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#464C2211yescharacteristic, complemented
40C2×#463C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#463C2211yescharacteristic
43C2×#463C2211yescharacteristic
44C2×#459C2211yescharacteristic
45C2×#452C2211yescharacteristic
46C2×#451C2211yescharacteristic, complemented
47C2×#448C2211yescharacteristic
48C2×#448C2211yescharacteristic
49C2×#450C2211yescharacteristic
50C2×#447C2211yescharacteristic
51C2×C4×Q16C2211yescharacteristic, complemented
52#2827—21no—
53#2781—21no—
54#2753—21no—
55#2735—21no—
56#2710—21no—
57#2699—21no—
58#2688—21no—
59#2687—21no—
60#2685—21no—
61#2648—21no—
62#2622—21no—
63#2620C2211yescharacteristic
64#2566C2211yescharacteristic
65#2557—21no—
66#2544C2211yescharacteristic, complemented
67#2536C2211yescharacteristic
68#2513C2211yescharacteristic
69#2496C2211yescharacteristic
70#2490C2211yescharacteristic
71#2489C2211yescharacteristic
72#2489C2211yescharacteristic
73#2488—21no—
74#2480—21no—
75#2453C2211yescharacteristic, complemented
76#2448C2211yescharacteristic
77#2447C2211yescharacteristic, complemented
78#2444—21no—
79#2436C2211yescharacteristic, complemented
80#2435C2211yescharacteristic
81#2431C2211yescharacteristic
82#2427C2211yescharacteristic
83#2427C2211yescharacteristic
84#2420—21no—
85#2414C2211yescharacteristic
86#2408C2211yescharacteristic
87#2395C2211yescharacteristic
88#2367C2211yescharacteristic
89#2367C2211yescharacteristic, complemented
90#2363C2211yescharacteristic, complemented
91#2339C2211yescharacteristic
92D4×C22⋊C4C2211yescharacteristic
93#2324C2211yescharacteristic
94#2310C2211yescharacteristic, complemented
95#2101C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2076C2211yescharacteristic
99#2073C2211yescharacteristic, complemented
100#2072C2211yescharacteristic, complemented
101#2072C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2066C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2056C2211yescharacteristic, complemented
106#2056C2211yescharacteristic, complemented
107#2056C2211yescharacteristic, complemented
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic, complemented
117#2036C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic, complemented
120#2033C2211yescharacteristic, complemented
121#2026C2211yescharacteristic, complemented
122#2026C2211yescharacteristic, complemented
123#2025C2211yescharacteristic
124#2025C2211yescharacteristic, complemented
125#2015C2211yescharacteristic
126#2015C2211yescharacteristic
127#2015C2211yescharacteristic
128#2015C2211yescharacteristic, complemented
129#2014C2211yescharacteristic, complemented
130#2012C2211yescharacteristic
131#2012C2211yescharacteristic
132#2012C2211yescharacteristic
133#2012C2211yescharacteristic
134#2011C2211yescharacteristic
135#2001C2211yescharacteristic
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic, complemented
138#2000C2211yescharacteristic, complemented
139#1999C2211yescharacteristic
140#1999C2211yescharacteristic
141#1999C2211yescharacteristic
142#1999C2211yescharacteristic
143#1989C2211yescharacteristic, complemented
144#1989C2211yescharacteristic, complemented
145#1983C2211yescharacteristic, complemented
146#1982C2211yescharacteristic, complemented
147#1970C2211yescharacteristic
148#1968C2211yescharacteristic
149#1968C2211yescharacteristic, complemented
150#1958C2211yescharacteristic, complemented
151#1954C2211yescharacteristic
152#1939C2211yescharacteristic, complemented
153#1939C2211yescharacteristic, complemented
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1933C2211yescharacteristic, complemented
157#1928C2211yescharacteristic, complemented
158#1928C2211yescharacteristic, complemented
159#1927C2211yescharacteristic, complemented
160#1927C2211yescharacteristic, complemented
161#1925C2211yescharacteristic
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic
164#1923C2211yescharacteristic, complemented
165#1923C2211yescharacteristic, complemented
166#1921C2211yescharacteristic, complemented
167#1916C2211yescharacteristic, complemented
168#1916C2211yescharacteristic, complemented
169#1895C2211yescharacteristic
170#1894C2211yescharacteristic
171#1894C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic, complemented
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic
182#1875C2211yescharacteristic
183#1873C2211yescharacteristic, complemented
184#1870C2211yescharacteristic
185#1865C2211yescharacteristic, complemented
186#1864C2211yescharacteristic, complemented
187#1862C2211yescharacteristic, complemented
188#1862C2211yescharacteristic, complemented
189#1851C2211yescharacteristic
190#1851C2211yescharacteristic
191#1825C2211yescharacteristic, complemented
192#1805C2211yescharacteristic, complemented
193#1802C2211yescharacteristic, complemented
194#1802C2211yescharacteristic, complemented
195#1798C2211yescharacteristic, complemented
196#1798C2211yescharacteristic, complemented
197#1788C2211yescharacteristic
198#1788C2211yescharacteristic
199#1787C2211yescharacteristic, complemented
200#1786C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×AGL(1,ℤ/8)—42no—
207C2×AGL(1,ℤ/8)—42no—
208C2×AGL(1,ℤ/8)—42no—
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×D8C2311yescharacteristic
218C22×D8C2311yescharacteristic
219C22×D8C2311yescharacteristic
220C22×D8C2311yescharacteristic
221C22×M16C2311yescharacteristic
222#548—42no—
223#548—42no—
224#540—42no—
225#540—42no—
226C2×#127C2311yescharacteristic
227C2×#126—21no—
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#124—21no—
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#123—21no—
237C2×#123—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×#121—21no—
243C2×#121—21no—
244C2×#121—21no—
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#121C2311yescharacteristic
250C2×#120—21no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C22×C22⋊C4—21no—
263#495—42no—
264#488—42no—
265#482—42no—
266#478—42no—
267#464—42no—
268#463—42no—
269#463—42no—
270#463—42no—
271#463—42no—
272#459—42no—
273#452—42no—
274#451—42no—
275#450—42no—
276#448—42no—
277#448—42no—
278#447—42no—
279C4×Q16—42no—
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333#400—21no—
334#400—21no—
335#400—21no—
336#400—21no—
337#400D411yescharacteristic
338#399—21no—
339#399D411yescharacteristic
340#398—21no—
341#398—21no—
342#398D411yescharacteristic
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397D411yescharacteristic
355#397D411yescharacteristic
356#397D411yescharacteristic
357#396—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394D411yescharacteristic
374#394D411yescharacteristic
375#393—21no—
376#393—21no—
377#392—21no—
378#392—21no—
379#392—21no—
380#392—21no—
381#391—21no—
382#391—21no—
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#390—21no—
392#390—21no—
393#390—21no—
394#390—21no—
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#389—21no—
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
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#388—21no—
424#387—21no—
425#387—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#384C2311yescharacteristic
447#382—21no—
448#382—21no—
449#382C2311yescharacteristic
450#381—21no—
451#381—21no—
452#381—21no—
453#381—21no—
454#380—21no—
455#380—21no—
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#379—21no—
461#379—21no—
462#379—21no—
463#379—21no—
464C4×C4⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
474C4×C22⋊C4C2311yescharacteristic
475C2×#95—21no—
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#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8—21no—
510C22×Q8—22no—
511C22×Q8—41no—
512C22×Q8—41no—
513C22×Q8—41no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×Q8C2411yescharacteristic
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4—41no—
534C22×D4C2×D411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2411yescharacteristic
537C22×D4C2411yescharacteristic
538C22×D4C2411yescharacteristic
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548AGL(1,ℤ/8)—416no—
549C2×Q16—22no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—41no—
578C2×D8—41no—
579C2×D8—41no—
580C2×D8—41no—
581C2×D8—41no—
582C2×D8—41no—
583C2×D8—41no—
584C2×D8—41no—
585C2×M16—41no—
586C2×M16—41no—
587C2×M16—41no—
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C22×C8C2411yescharacteristic
594C22×C8C2411yescharacteristic
595C22×C8C2411yescharacteristic
596#127—22no—
597#127—41no—
598#126—82no—
599#125—22no—
600#125—41no—
601#125—41no—
602#125—41no—
603#124—22no—
604#124—22no—
605#124—22no—
606#124—41no—
607#124—41no—
608#124—41no—
609#124—41no—
610#124—41no—
611#124—41no—
612#124—41no—
613#124—44no—
614#123—44no—
615#123—44no—
616C22⋊Q8—22no—
617C22⋊Q8—44no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—41no—
627#121—41no—
628#121—41no—
629#121—44no—
630#121—44no—
631#121—44no—
632#121—41no—
633#121—41no—
634#121—41no—
635#121—41no—
636#120—82no—
637C4×Q8—22no—
638C4×Q8—41no—
639C4×Q8—41no—
640C4×Q8—41no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—41no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—41no—
648C4×D4—41no—
649C4×D4—41no—
650C4×D4—41no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—44no—
654#117—41no—
655#117—41no—
656#117—41no—
657#117—41no—
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—21no—
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⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
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—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—82no—
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755#107—22no—
756#107—41no—
757#106—41no—
758#106—41no—
759C4⋊C8—41no—
760C4⋊C8—41no—
761C4⋊C8—41no—
762C4⋊C8—41no—
763C4⋊C8—41no—
764C4⋊C8—41no—
765C4⋊C8—41no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—22no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—22no—
784#102—22no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795#102—41no—
796#102—41no—
797#102—41no—
798C22⋊C8—41no—
799C22⋊C8—41no—
800C22⋊C8—41no—
801C22⋊C8—41no—
802C22⋊C8—41no—
803C22⋊C8—41no—
804C22⋊C8—41no—
805C4×C8—41no—
806C4×C8—41no—
807C4×C8—41no—
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#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#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—42no—
852C24—42no—
853C24—81no—
854C24—81no—
855C24—81no—
856C24—81no—
857C24—81no—
858C24C22×D411yescharacteristic
859C24C22×D411yescharacteristic
860#41—44no—
861#41—82no—
862#41—82no—
863#41—82no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
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—21no—
880C2×Q8—21no—
881C2×Q8—42no—
882C2×Q8—42no—
883C2×Q8—81no—
884C2×Q8—82no—
885C2×Q8—82no—
886C2×Q8—82no—
887C2×Q8—82no—
888C2×Q8H(5,𝔽2)12yes—
889C2×D4—24no—
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—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—41no—
913C2×D4—41no—
914C2×D4—41no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—44no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—82no—
930C2×D4—82no—
931C2×D4—82no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4—81no—
940C2×D4—81no—
941C2×D4—81no—
942C2×D4—81no—
943C2×D4—81no—
944C2×D4—81no—
945C2×D4H(5,𝔽2)12yes—
946C2×D4H(5,𝔽2)12yes—
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—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C22×D411yescharacteristic
1002C22×C4C22×D411yescharacteristic
1003C22×C4C22×D411yescharacteristic
1004C22×C4C2511yescharacteristic
1005Q16—44no—
1006Q16—82no—
1007SD16—44no—
1008SD16—44no—
1009SD16—82no—
1010SD16—82no—
1011SD16—82no—
1012SD16—82no—
1013D8—44no—
1014D8—44no—
1015D8—82no—
1016D8—82no—
1017M16—44no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4H(5,𝔽2)12yes—
1082C22⋊C4—24no—
1083C22⋊C4—41no—
1084C22⋊C4—41no—
1085C22⋊C4—41no—
1086C22⋊C4—41no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—41no—
1091C22⋊C4—41no—
1092C22⋊C4—41no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
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—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C22⋊C4—81no—
1135C22⋊C4—81no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—21no—
1143C42—21no—
1144C42—21no—
1145C42—21no—
1146C42—42no—
1147C42—81no—
1148C42—81no—
1149C42—81no—
1150C42—81no—
1151C42—81no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—22no—
1161C23—21no—
1162C23—21no—
1163C23—22no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—84no—
1195C23—84no—
1196C23—162no—
1197C23—162no—
1198C23—162no—
1199C23—162no—
1200C23—162no—
1201C23C23×D411yescharacteristic
1202Q8—22no—
1203Q8—22no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—41no—
1209Q8—41no—
1210Q8—41no—
1211Q8—41no—
1212Q8—41no—
1213Q8—41no—
1214Q8—84no—
1215D4—22no—
1216D4—22no—
1217D4—22no—
1218D4—22no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—41no—
1224D4—41no—
1225D4—41no—
1226D4—41no—
1227D4—41no—
1228D4—41no—
1229D4—41no—
1230D4—41no—
1231D4—84no—
1232D4—82no—
1233D4—84no—
1234D4—84no—
1235D4—162no—
1236D4—162no—
1237D4—162no—
1238D4—162no—
1239D4—162no—
1240D4—162no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
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—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—22no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—22no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
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—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—84no—
1322C2×C4—84no—
1323C2×C4—162no—
1324C2×C4—162no—
1325C2×C4—162no—
1326C2×C4—162no—
1327C2×C4—162no—
1328C2×C4C2×H(5,𝔽2)11yescharacteristic
1329C2×C4C2×H(5,𝔽2)11yescharacteristic
1330C2×C4C2×H(5,𝔽2)11yescharacteristic
1331C2×C4C2×H(5,𝔽2)11yescharacteristic
1332C2×C4#58511yescharacteristic
1333C2×C4#58511yescharacteristic
1334C8—41no—
1335C8—41no—
1336C8—41no—
1337C8—41no—
1338C8—41no—
1339C8—41no—
1340C8—41no—
1341C8—41no—
1342C22—41no—
1343C22—42no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—42no—
1350C22—41no—
1351C22—41no—
1352C22—41no—
1353C22—42no—
1354C22—41no—
1355C22—42no—
1356C22—41no—
1357C22—41no—
1358C22—41no—
1359C22—41no—
1360C22—42no—
1361C22—42no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—168no—
1385C22#348411yescharacteristic
1386C22#348811yescharacteristic
1387C22#348811yescharacteristic
1388C22#358411yescharacteristic
1389C22#358411yescharacteristic
1390C22#358411yescharacteristic
1391C22#358511yescharacteristic
1392C4—41no—
1393C4—41no—
1394C4—41no—
1395C4—41no—
1396C4—41no—
1397C4—41no—
1398C4—41no—
1399C4—42no—
1400C4—41no—
1401C4—41no—
1402C4—41no—
1403C4—41no—
1404C4—41no—
1405C4—42no—
1406C4—81no—
1407C4—81no—
1408C4—81no—
1409C4—81no—
1410C4—81no—
1411C4—81no—
1412C4—81no—
1413C4—81no—
1414C4—81no—
1415C4—81no—
1416C4#353211yescharacteristic
1417C4#354211yescharacteristic
1418C4#355811yescharacteristic
1419C4#356011yescharacteristic
1420C2—81no—
1421C2—81no—
1422C2—82no—
1423C2—82no—
1424C2—161no—
1425C2—161no—
1426C2#4784411yescharacteristic
1427C2#6161411yescharacteristic
1428C2#6166611yescharacteristic
1429C2#6202711yescharacteristic
1430C2#6204911yescharacteristic
1431C2#6206011yescharacteristic
1432C2#6206111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
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
1. #45094C2semidirect
2. #42563C2semidirect
3. #32172C2semidirect
4. #32125C2semidirect
5. #31805C2semidirect
6. #31646C2semidirect
7. #31506C2semidirect
8. #31403C2semidirect
9. #31217C2semidirect
10. #31020C2semidirect
11. #30526C2semidirect
12. #30524C2semidirect
13. #30452C2semidirect
14. #30445C2semidirect
15. #29728C2semidirect
16. #29675C2semidirect
17. #28128C2semidirect
18. #27531C2semidirect
19. #27227C2semidirect
20. #26938C2semidirect
21. #26892C2semidirect
22. #26730C2semidirect
23. #26598C2semidirect
24. #25373C2semidirect
25. #25327C2semidirect
26. #24373C2semidirect
27. #24366C2semidirect
28. #24246C2semidirect
29. #24162C2semidirect
30. #23866C2semidirect
31. #23317C2semidirect
34. C2×#540C22semidirect
36. C2×#488C22semidirect
39. C2×#464C22semidirect
46. C2×#451C22semidirect
51. C2×C4×Q16C22semidirect
66. #2544C22semidirect
75. #2453C22semidirect
77. #2447C22semidirect
79. #2436C22semidirect
89. #2367C22semidirect
90. #2363C22semidirect
94. #2310C22semidirect
95. #2101C22semidirect
96. #2088C22semidirect
99. #2073C22semidirect
100. #2072C22semidirect
101. #2072C22semidirect
102. #2068C22semidirect
103. #2066C22semidirect
105. #2056C22semidirect
106. #2056C22semidirect
107. #2056C22semidirect
116. #2042C22semidirect
119. #2034C22semidirect
120. #2033C22semidirect
121. #2026C22semidirect
122. #2026C22semidirect
124. #2025C22semidirect
128. #2015C22semidirect
129. #2014C22semidirect
137. #2000C22semidirect
138. #2000C22semidirect
143. #1989C22semidirect
144. #1989C22semidirect
145. #1983C22semidirect
146. #1982C22semidirect
149. #1968C22semidirect
150. #1958C22semidirect
152. #1939C22semidirect
153. #1939C22semidirect
156. #1933C22semidirect
157. #1928C22semidirect
158. #1928C22semidirect
159. #1927C22semidirect
160. #1927C22semidirect
164. #1923C22semidirect
165. #1923C22semidirect
166. #1921C22semidirect
167. #1916C22semidirect
168. #1916C22semidirect
174. #1880C22semidirect
183. #1873C22semidirect
185. #1865C22semidirect
186. #1864C22semidirect
187. #1862C22semidirect
188. #1862C22semidirect
191. #1825C22semidirect
192. #1805C22semidirect
193. #1802C22semidirect
194. #1802C22semidirect
195. #1798C22semidirect
196. #1798C22semidirect
199. #1787C22semidirect
202. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#450942
#425632
#321722
#321252
#318052
#316462
#315062
#314032
#312172
#310202
#305262
#305242
#304522
#304452
#297282
#296752
#281282
#275312
#272272
#269382
#268922
#267302
#265982
#253732
#253272
#243732
#243662
#242462
#241622
#238662
#233172