Finite Group Databasebeta

← #7308306

Subgroups — #7308306

Order 512.

1683 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
1#59094C211yesmaximal, characteristic
2#39659C211yesmaximal, characteristic, complemented
3#32190C211yesmaximal, characteristic, complemented
4#32126C211yesmaximal, characteristic, complemented
5#31822C211yesmaximal, characteristic, complemented
6#31652C211yesmaximal, characteristic, complemented
7#31504C211yesmaximal, characteristic, complemented
8#31398C211yesmaximal, characteristic, complemented
9#31226C211yesmaximal, characteristic, complemented
10#31035C211yesmaximal, characteristic, complemented
11#30543C211yesmaximal, characteristic, complemented
12#30537C211yesmaximal, characteristic, complemented
13#30465C211yesmaximal, characteristic, complemented
14#30464C211yesmaximal, characteristic, complemented
15#29714C211yesmaximal, characteristic, complemented
16#29664C211yesmaximal, characteristic, complemented
17#28120C211yesmaximal, characteristic, complemented
18#27548C211yesmaximal, characteristic, complemented
19#27239C211yesmaximal, characteristic, complemented
20#26949C211yesmaximal, characteristic, complemented
21#26919C211yesmaximal, characteristic, complemented
22#26743C211yesmaximal, characteristic, complemented
23#26610C211yesmaximal, characteristic, complemented
24#25379C211yesmaximal, characteristic, complemented
25#25336C211yesmaximal, characteristic, complemented
26#24374C211yesmaximal, characteristic, complemented
27#24369C211yesmaximal, characteristic, complemented
28#24259C211yesmaximal, characteristic
29#24155C211yesmaximal, characteristic, complemented
30#23862C211yesmaximal, characteristic
31#23324C211yesmaximal, characteristic, complemented
32C22×#137C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#497C2211yescharacteristic
36C2×#489C2211yescharacteristic
37C2×#483C2211yescharacteristic
38C2×#477C2211yescharacteristic, complemented
39C2×#464C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#462C2211yescharacteristic, complemented
42C2×#462C2211yescharacteristic, complemented
43C2×#462C2211yescharacteristic, complemented
44C2×#462C2211yescharacteristic, complemented
45C2×#452C2211yescharacteristic
46C2×#451C2211yescharacteristic, complemented
47C2×#448C2211yescharacteristic
48C2×#450C2211yescharacteristic
49C2×#450C2211yescharacteristic
50C2×#450C2211yescharacteristic
51C2×#440C2211yescharacteristic
52#2857C2211yescharacteristic
53#2805—21no—
54#2788—21no—
55#2788—21no—
56#2784—21no—
57#2711—21no—
58#2707—21no—
59#2665—21no—
60#2587—21no—
61#2586—21no—
62#2567C2211yescharacteristic, complemented
63#2545C2211yescharacteristic
64#2538C2211yescharacteristic
65#2511C2211yescharacteristic, complemented
66#2497C2211yescharacteristic, complemented
67#2492C2211yescharacteristic
68#2492C2211yescharacteristic, complemented
69#2491C2211yescharacteristic
70#2472—21no—
71#2458—21no—
72#2452C2211yescharacteristic
73#2448C2211yescharacteristic
74#2446C2211yescharacteristic, complemented
75#2437—21no—
76#2435C2211yescharacteristic
77#2434C2211yescharacteristic, complemented
78#2432C2211yescharacteristic
79#2429C2211yescharacteristic
80#2426—21no—
81#2426C2211yescharacteristic
82#2417C2211yescharacteristic
83#2411—21no—
84#2409C2211yescharacteristic
85#2367C2211yescharacteristic
86#2365C2211yescharacteristic, complemented
87#2360C2211yescharacteristic
88#2342—21no—
89#2341C2211yescharacteristic
90Q8×C22⋊C4C2211yescharacteristic, complemented
91#2335—21no—
92C4×C22⋊Q8C2211yescharacteristic
93C4×#123C2211yescharacteristic
94C2×#390C2211yescharacteristic
95#2099C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2075C2211yescharacteristic, complemented
99#2072C2211yescharacteristic, complemented
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2066C2211yescharacteristic, complemented
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2056C2211yescharacteristic, complemented
106#2056C2211yescharacteristic, complemented
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2043C2211yescharacteristic, complemented
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2035C2211yescharacteristic, complemented
120#2033C2211yescharacteristic
121#2024C2211yescharacteristic, complemented
122#2024C2211yescharacteristic, complemented
123#2024C2211yescharacteristic, complemented
124#2023C2211yescharacteristic
125#2016C2211yescharacteristic, complemented
126#2016C2211yescharacteristic, complemented
127#2015C2211yescharacteristic
128#2015C2211yescharacteristic
129#2015C2211yescharacteristic
130#2015C2211yescharacteristic
131#2015C2211yescharacteristic
132#2013C2211yescharacteristic
133#2013C2211yescharacteristic
134#2013C2211yescharacteristic
135#2001C2211yescharacteristic
136#2001C2211yescharacteristic
137#2001C2211yescharacteristic
138#2001C2211yescharacteristic
139#2001C2211yescharacteristic
140#2001C2211yescharacteristic
141#2001C2211yescharacteristic, complemented
142#2000C2211yescharacteristic
143#1988C2211yescharacteristic, complemented
144#1987C2211yescharacteristic, complemented
145#1983C2211yescharacteristic
146#1981C2211yescharacteristic, complemented
147#1973C2211yescharacteristic
148#1971C2211yescharacteristic, complemented
149#1971C2211yescharacteristic, complemented
150#1959C2211yescharacteristic
151#1955C2211yescharacteristic
152#1940C2211yescharacteristic, complemented
153#1940C2211yescharacteristic, complemented
154#1936C2211yescharacteristic
155#1935C2211yescharacteristic, complemented
156#1935C2211yescharacteristic, complemented
157#1928C2211yescharacteristic, complemented
158#1927C2211yescharacteristic, complemented
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1925C2211yescharacteristic
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic
164#1924C2211yescharacteristic, complemented
165#1924C2211yescharacteristic, complemented
166#1918C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1917C2211yescharacteristic, complemented
169#1895C2211yescharacteristic
170#1894C2211yescharacteristic, complemented
171#1894C2211yescharacteristic, complemented
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1878C2211yescharacteristic, complemented
176#1878C2211yescharacteristic, complemented
177#1878C2211yescharacteristic, complemented
178#1878C2211yescharacteristic, complemented
179#1878C2211yescharacteristic, complemented
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic
182#1872C2211yescharacteristic
183#1872C2211yescharacteristic
184#1870C2211yescharacteristic
185#1865C2211yescharacteristic, complemented
186#1863C2211yescharacteristic, complemented
187#1863C2211yescharacteristic, complemented
188#1863C2211yescharacteristic, complemented
189#1851C2211yescharacteristic, complemented
190#1851C2211yescharacteristic, complemented
191#1823C2211yescharacteristic
192#1803C2211yescharacteristic, complemented
193#1803C2211yescharacteristic, complemented
194#1802C2211yescharacteristic
195#1797C2211yescharacteristic
196#1797C2211yescharacteristic
197#1788C2211yescharacteristic
198#1788C2211yescharacteristic
199#1787C2211yescharacteristic, complemented
200#1786C2211yescharacteristic
201#1763C2211yescharacteristic, complemented
202#1763C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×#137—42no—
207C2×#137—42no—
208C2×#137—42no—
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×Q16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×M16C2311yescharacteristic
222#546—42no—
223#546—42no—
224#533—42no—
225#533—42no—
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×#125—21no—
232C2×#124—21no—
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#123—21no—
237C2×#123D411yescharacteristic
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2311yescharacteristic
247C2×#121—21no—
248C2×#121C2311yescharacteristic
249C2×#120—21no—
250C2×C4×Q8—21no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×#117—21no—
260C22×C4⋊C4C2311yescharacteristic
261C22×C22⋊C4—21no—
262C22×C22⋊C4—21no—
263C22×C22⋊C4—21no—
264C22×C42C2311yescharacteristic
265#497—42no—
266#489—42no—
267#483—42no—
268#477—42no—
269#464—42no—
270#464—42no—
271#462—42no—
272#462—42no—
273#462—42no—
274#462—42no—
275#452—42no—
276#451—42no—
277#450—42no—
278#450—42no—
279#450—42no—
280#448—42no—
281#440—42no—
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×#97C2311yescharacteristic
335#400—21no—
336#400—21no—
337#400—21no—
338#400—21no—
339#400—21no—
340#400—21no—
341#399—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#397—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#395—21no—
356#395—21no—
357#395—21no—
358#395—21no—
359#395—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#393—21no—
367#393—21no—
368#393—21no—
369#393—21no—
370#393—21no—
371#391—21no—
372#391—21no—
373#391—21no—
374#391—21no—
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#390—21no—
386#390—21no—
387#390—21no—
388#390—21no—
389#390—21no—
390#390—21no—
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#389—21no—
398#389—21no—
399#389—21no—
400#389—21no—
401#389—21no—
402#389—21no—
403#389—21no—
404#389—21no—
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
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#388D411yescharacteristic
422#388D411yescharacteristic
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387D411yescharacteristic
433#387D411yescharacteristic
434#386—21no—
435#386—21no—
436#386D411yescharacteristic
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385D411yescharacteristic
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#381D411yescharacteristic
450#380—21no—
451#380—21no—
452#380—21no—
453#380—21no—
454#380—21no—
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#379—21no—
460#379—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4—21no—
473C4×C22⋊C4C2311yescharacteristic
474C4×C22⋊C4C2311yescharacteristic
475C4×C22⋊C4C2311yescharacteristic
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—21no—
511C22×Q8—21no—
512C22×Q8—22no—
513C22×Q8—41no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8—41no—
517C22×Q8—41no—
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×Q8C2411yescharacteristic
523C22×D4—22no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×D411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4C2×D411yescharacteristic
540C23×C4C2×D411yescharacteristic
541C23×C4C2411yescharacteristic
542C23×C4C2411yescharacteristic
543#137—416no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×Q16—41no—
561C2×Q16—41no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×M16—41no—
581C2×M16—41no—
582C2×M16—41no—
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C4⋊Q8—22no—
592C4⋊Q8—22no—
593C4⋊Q8—22no—
594C4⋊Q8—41no—
595C4⋊Q8—41no—
596C4⋊Q8—41no—
597C4⋊Q8—41no—
598C4⋊Q8—41no—
599C4⋊Q8—41no—
600C4⋊Q8—41no—
601#125—44no—
602#124—22no—
603#124—22no—
604#124—41no—
605#124—41no—
606#124—41no—
607#124—41no—
608#124—82no—
609#123—24no—
610#123—44no—
611C22⋊Q8—22no—
612C22⋊Q8—22no—
613C22⋊Q8—22no—
614C22⋊Q8—44no—
615C22⋊Q8—41no—
616C22⋊Q8—41no—
617C22⋊Q8—41no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8—41no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626C22⋊Q8—82no—
627#121—22no—
628#121—41no—
629#121—44no—
630#120—44no—
631C4×Q8—22no—
632C4×Q8—22no—
633C4×Q8—41no—
634C4×Q8—41no—
635C4×Q8—41no—
636C4×Q8—41no—
637C4×Q8—41no—
638C4×Q8—41no—
639C4×Q8—41no—
640C4×Q8—41no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×Q8—44no—
644C4×D4—22no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—41no—
648#117—44no—
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—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—41no—
680C2×C4⋊C4—41no—
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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—44no—
727C2×C22⋊C4—44no—
728C2×C22⋊C4—82no—
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—41no—
747C2×C42—41no—
748C2×C42C2×D411yescharacteristic
749C2×C42C2×D411yescharacteristic
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—22no—
771#103—22no—
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#103—41no—
781#103—41no—
782#103—41no—
783#103—41no—
784#103—41no—
785#103—41no—
786#103—41no—
787#103—41no—
788#102—22no—
789#102—22no—
790#102—22no—
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—
805#97—41no—
806#97—41no—
807#97—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#95—21no—
838#95—21no—
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849C24—21no—
850C24—21no—
851C24—42no—
852C24—42no—
853C24—42no—
854C24—42no—
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—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—42no—
893C2×Q8—42no—
894C2×Q8—42no—
895C2×Q8—44no—
896C2×Q8—81no—
897C2×Q8—81no—
898C2×Q8—81no—
899C2×Q8—81no—
900C2×Q8—81no—
901C2×Q8—81no—
902C2×Q8—82no—
903C2×Q8—82no—
904C2×Q8—82no—
905C2×Q8H(5,𝔽2)12yes—
906C2×Q8H(5,𝔽2)12yes—
907C2×D4—22no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—41no—
920C2×D4—41no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—81no—
927C2×D4—82no—
928C2×D4—82no—
929C2×D4—82no—
930C2×D4—82no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4H(5,𝔽2)12yes—
935C22×C4—21no—
936C22×C4—21no—
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—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—41no—
962C22×C4—41no—
963C22×C4—41no—
964C22×C4—41no—
965C22×C4—41no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4#13714yescomplemented
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C2511yescharacteristic
992Q16—44no—
993Q16—44no—
994Q16—82no—
995Q16—82no—
996Q16—82no—
997Q16—82no—
998SD16—44no—
999SD16—44no—
1000SD16—44no—
1001SD16—82no—
1002SD16—82no—
1003SD16—82no—
1004M16—44no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—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—
1029C4⋊C4—24no—
1030C4⋊C4—22no—
1031C4⋊C4—22no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—41no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊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—22no—
1084C22⋊C4—22no—
1085C22⋊C4—22no—
1086C22⋊C4—41no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—41no—
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—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
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—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—41no—
1132C42—41no—
1133C42—42no—
1134C42—42no—
1135C42—81no—
1136C42—81no—
1137C42—81no—
1138C42—81no—
1139C42—81no—
1140C42—81no—
1141C42—81no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—22no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
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—84no—
1170C23—84no—
1171C23—84no—
1172C23—84no—
1173C23—162no—
1174C23—162no—
1175C23—162no—
1176C23C2×#13712yes—
1177C23C23×D411yescharacteristic
1178Q8—22no—
1179Q8—22no—
1180Q8—22no—
1181Q8—22no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—84no—
1199Q8—84no—
1200Q8—162no—
1201D4—22no—
1202D4—22no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—82no—
1210D4—84no—
1211D4—84no—
1212D4—162no—
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—22no—
1236C2×C4—22no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—44no—
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—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—82no—
1299C2×C4—84no—
1300C2×C4—84no—
1301C2×C4—162no—
1302C2×C4—162no—
1303C2×C4C2×#13712yes—
1304C2×C4C2×#13712yes—
1305C2×C4C2×H(5,𝔽2)11yescharacteristic
1306C2×C4C2×H(5,𝔽2)11yescharacteristic
1307C2×C4C2×H(5,𝔽2)11yescharacteristic
1308C2×C4C2×H(5,𝔽2)11yescharacteristic
1309C2×C4#58511yescharacteristic
1310C2×C4#58511yescharacteristic
1311C8—41no—
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—42no—
1328C22—41no—
1329C22—41no—
1330C22—42no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—42no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—168no—
1348C22#348411yescharacteristic
1349C22#348811yescharacteristic
1350C22#348811yescharacteristic
1351C22C22×#13711yescharacteristic
1352C22#358511yescharacteristic
1353C22#358611yescharacteristic
1354C22#358611yescharacteristic
1355C4—22no—
1356C4—22no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—42no—
1366C4—41no—
1367C4—41no—
1368C4—42no—
1369C4—42no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4#353211yescharacteristic
1382C4#354211yescharacteristic
1383C4#355811yescharacteristic
1384C4#356011yescharacteristic
1385C2—42no—
1386C2—81no—
1387C2—82no—
1388C2—161no—
1389C2#4784411yescharacteristic
1390C2#6157311yescharacteristic
1391C2#6165411yescharacteristic
1392C2#6196011yescharacteristic
1393C2#6196511yescharacteristic
1394C2#6207611yescharacteristic
1395C2#6209111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39659C2semidirect
3. #32190C2semidirect
4. #32126C2semidirect
5. #31822C2semidirect
6. #31652C2semidirect
7. #31504C2semidirect
8. #31398C2semidirect
9. #31226C2semidirect
10. #31035C2semidirect
11. #30543C2semidirect
12. #30537C2semidirect
13. #30465C2semidirect
14. #30464C2semidirect
15. #29714C2semidirect
16. #29664C2semidirect
17. #28120C2semidirect
18. #27548C2semidirect
19. #27239C2semidirect
20. #26949C2semidirect
21. #26919C2semidirect
22. #26743C2semidirect
23. #26610C2semidirect
24. #25379C2semidirect
25. #25336C2semidirect
26. #24374C2semidirect
27. #24369C2semidirect
29. #24155C2semidirect
31. #23324C2semidirect
38. C2×#477C22semidirect
41. C2×#462C22semidirect
42. C2×#462C22semidirect
43. C2×#462C22semidirect
44. C2×#462C22semidirect
46. C2×#451C22semidirect
62. #2567C22semidirect
65. #2511C22semidirect
66. #2497C22semidirect
68. #2492C22semidirect
74. #2446C22semidirect
77. #2434C22semidirect
86. #2365C22semidirect
90. Q8×C22⋊C4C22semidirect
95. #2099C22semidirect
96. #2088C22semidirect
97. #2077C22semidirect
98. #2075C22semidirect
99. #2072C22semidirect
102. #2066C22semidirect
105. #2056C22semidirect
106. #2056C22semidirect
115. #2043C22semidirect
119. #2035C22semidirect
121. #2024C22semidirect
122. #2024C22semidirect
123. #2024C22semidirect
125. #2016C22semidirect
126. #2016C22semidirect
141. #2001C22semidirect
143. #1988C22semidirect
144. #1987C22semidirect
146. #1981C22semidirect
148. #1971C22semidirect
149. #1971C22semidirect
152. #1940C22semidirect
153. #1940C22semidirect
155. #1935C22semidirect
156. #1935C22semidirect
157. #1928C22semidirect
158. #1927C22semidirect
164. #1924C22semidirect
165. #1924C22semidirect
166. #1918C22semidirect
167. #1917C22semidirect
168. #1917C22semidirect
170. #1894C22semidirect
171. #1894C22semidirect
175. #1878C22semidirect
176. #1878C22semidirect
177. #1878C22semidirect
178. #1878C22semidirect
179. #1878C22semidirect
185. #1865C22semidirect
186. #1863C22semidirect
187. #1863C22semidirect
188. #1863C22semidirect
189. #1851C22semidirect
190. #1851C22semidirect
192. #1803C22semidirect
193. #1803C22semidirect
199. #1787C22semidirect
201. #1763C22semidirect
202. #1763C22semidirect
978. C22×C4#137semidirect

Maximal subgroups

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

subgroupindex
#590942
#396592
#321902
#321262
#318222
#316522
#315042
#313982
#312262
#310352
#305432
#305372
#304652
#304642
#297142
#296642
#281202
#275482
#272392
#269492
#269192
#267432
#266102
#253792
#253362
#243742
#243692
#242592
#241552
#238622
#233242