Finite Group Databasebeta

← #6996830

Subgroups — #6996830

Order 512.

1747 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59148C211yesmaximal, characteristic
2#39179C211yesmaximal, characteristic, complemented
3#32611C211yesmaximal, characteristic, complemented
4#32603C211yesmaximal, characteristic, complemented
5#31647C211yesmaximal, characteristic, complemented
6#31642C211yesmaximal, characteristic, complemented
7#30888C211yesmaximal, characteristic, complemented
8#30888C211yesmaximal, characteristic, complemented
9#30885C211yesmaximal, characteristic, complemented
10#30881C211yesmaximal, characteristic, complemented
11#29158C211yesmaximal, characteristic, complemented
12#28407C211yesmaximal, characteristic, complemented
13#28403C211yesmaximal, characteristic, complemented
14#27258C211yesmaximal, characteristic, complemented
15#27256C211yesmaximal, characteristic
16#26899C211yesmaximal, characteristic, complemented
17#26893C211yesmaximal, characteristic, complemented
18#26823C211yesmaximal, characteristic, complemented
19#26817C211yesmaximal, characteristic, complemented
20#25957C211yesmaximal, characteristic, complemented
21#25950C211yesmaximal, characteristic
22#25859C211yesmaximal, characteristic
23#24360C211yesmaximal, characteristic, complemented
24#24357C211yesmaximal, characteristic
25#24195C211yesmaximal, characteristic, complemented
26#24189C211yesmaximal, characteristic, complemented
27C2×#2015C211yesmaximal, characteristic
28#23237C211yesmaximal, characteristic, complemented
29C22⋊C4×Q16C211yesmaximal, characteristic, complemented
30C22⋊C4×SD16C211yesmaximal, characteristic
31#22044C211yesmaximal, characteristic, complemented
32C23×Q16C2211yescharacteristic
33C23×SD16C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C22×#124C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#488C2211yescharacteristic
38C2×#488C2211yescharacteristic
39C2×#487C2211yescharacteristic, complemented
40C2×#479C2211yescharacteristic, complemented
41C2×#474C2211yescharacteristic
42C2×#464C2211yescharacteristic
43C2×#464C2211yescharacteristic
44C2×#462C2211yescharacteristic, complemented
45C2×#462C2211yescharacteristic, complemented
46C2×#451C2211yescharacteristic
47C2×C4×Q16C2211yescharacteristic, complemented
48C2×C4×Q16C2211yescharacteristic, complemented
49C2×C4×SD16C2211yescharacteristic
50C2×C4×SD16C2211yescharacteristic
51C22×#103C2211yescharacteristic
52C22×#102C2211yescharacteristic
53#2851C2211yescharacteristic
54#2809—21no—
55#2806—21no—
56#2799—21no—
57#2799—21no—
58#2715—21no—
59#2700—21no—
60#2646—21no—
61#2592C2211yescharacteristic
62#2582C2211yescharacteristic, complemented
63#2581C2211yescharacteristic, complemented
64#2569—21no—
65#2568C2211yescharacteristic, complemented
66#2565C2211yescharacteristic, complemented
67#2549—21no—
68#2547C2211yescharacteristic
69#2545C2211yescharacteristic
70#2545C2211yescharacteristic
71#2521—21no—
72#2480—21no—
73#2480—21no—
74#2474—21no—
75#2453C2211yescharacteristic, complemented
76#2453C2211yescharacteristic, complemented
77#2453C2211yescharacteristic, complemented
78#2451C2211yescharacteristic, complemented
79#2448C2211yescharacteristic
80#2447C2211yescharacteristic
81#2442C2211yescharacteristic
82#2440C2211yescharacteristic
83#2437—21no—
84#2435C2211yescharacteristic
85#2434C2211yescharacteristic
86#2367C2211yescharacteristic
87#2342—21no—
88Q8×C22⋊C4C2211yescharacteristic
89Q8×C22⋊C4C2211yescharacteristic
90Q8×C22⋊C4C2211yescharacteristic
91D4×C22⋊C4C2211yescharacteristic
92#2329—21no—
93C4×C22⋊Q8C2211yescharacteristic
94C4×C22⋊Q8C2211yescharacteristic
95C2×#391C2211yescharacteristic
96#2101C2211yescharacteristic, complemented
97#2097C2211yescharacteristic, complemented
98#2097C2211yescharacteristic, complemented
99#2093C2211yescharacteristic
100#2073C2211yescharacteristic
101#2072C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2066C2211yescharacteristic, complemented
106#2059C2211yescharacteristic, complemented
107#2056C2211yescharacteristic, complemented
108#2056C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2043C2211yescharacteristic, complemented
112#2043C2211yescharacteristic, complemented
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2026C2211yescharacteristic, complemented
120#2026C2211yescharacteristic, complemented
121#2025C2211yescharacteristic
122#2024C2211yescharacteristic, complemented
123#2023C2211yescharacteristic
124#2016C2211yescharacteristic, complemented
125#2016C2211yescharacteristic, complemented
126#2015C2211yescharacteristic
127#2015C2211yescharacteristic
128#2015C2211yescharacteristic
129#2015C2211yescharacteristic
130#2015C2211yescharacteristic
131#2015C2211yescharacteristic
132#2015C2211yescharacteristic
133#2015C2211yescharacteristic
134#2015C2211yescharacteristic
135#2015C2211yescharacteristic
136#1984C2211yescharacteristic, complemented
137#1984C2211yescharacteristic, complemented
138#1969C2211yescharacteristic, complemented
139#1969C2211yescharacteristic, complemented
140#1969C2211yescharacteristic, complemented
141#1969C2211yescharacteristic, complemented
142#1968C2211yescharacteristic
143#1968C2211yescharacteristic
144#1958C2211yescharacteristic
145#1958C2211yescharacteristic
146#1958C2211yescharacteristic
147#1956C2211yescharacteristic, complemented
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1933C2211yescharacteristic, complemented
153#1933C2211yescharacteristic, complemented
154#1928C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1920C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1916C2211yescharacteristic, complemented
159#1916C2211yescharacteristic, complemented
160#1916C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1892C2211yescharacteristic
163#1892C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1878C2211yescharacteristic, complemented
169#1878C2211yescharacteristic, complemented
170#1878C2211yescharacteristic, complemented
171#1878C2211yescharacteristic, complemented
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1872C2211yescharacteristic
179#1865C2211yescharacteristic, complemented
180#1865C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1852C2211yescharacteristic
186#1850C2211yescharacteristic
187#1850C2211yescharacteristic
188#1808C2211yescharacteristic
189#1807C2211yescharacteristic
190#1805C2211yescharacteristic, complemented
191#1802C2211yescharacteristic
192#1787C2211yescharacteristic
193#1787C2211yescharacteristic
194#1787C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic, complemented
198C8×C4⋊C4C2211yescharacteristic, complemented
199C8×C22⋊C4C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201C4×C22⋊C8C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×Q16—24no—
207C22×Q16—42no—
208C22×Q16—42no—
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×Q16C2311yescharacteristic
215C22×SD16—24no—
216C22×SD16—42no—
217C22×SD16—42no—
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C23×C8C2311yescharacteristic
223C23×C8C2311yescharacteristic
224#556—42no—
225#556—42no—
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×#126—21no—
230C2×#126—21no—
231C2×#125C2311yescharacteristic
232C2×#125C2311yescharacteristic
233C2×#124—21no—
234C2×#124—21no—
235C2×#124—42no—
236C2×#124—42no—
237C2×#124C2311yescharacteristic
238C2×#124C2311yescharacteristic
239C2×#124C2311yescharacteristic
240C2×#124C2311yescharacteristic
241C2×#124C2311yescharacteristic
242C2×#124C2311yescharacteristic
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8D411yescharacteristic
246C2×C22⋊Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×#117—21no—
258C22×C4⋊C4C2311yescharacteristic
259C22×C22⋊C4—21no—
260C22×C22⋊C4—21no—
261C22×C22⋊C4—21no—
262C22×C42C2311yescharacteristic
263#488—42no—
264#488—42no—
265#488—42no—
266#487—42no—
267#479—42no—
268#474—42no—
269#464—42no—
270#464—42no—
271#462—42no—
272#462—42no—
273#451—24no—
274C4×Q16—42no—
275C4×Q16—42no—
276C4×SD16—42no—
277C4×SD16—42no—
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×#103—42no—
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#102—42no—
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333C2×C4×C8C2311yescharacteristic
334#400—21no—
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#398—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#398—21no—
351#398—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#397—21no—
357#397—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#396—21no—
362#395—21no—
363#395—21no—
364#395—21no—
365#395—21no—
366#395—21no—
367#394—21no—
368#394—21no—
369#393—21no—
370#391—21no—
371#391—21no—
372#391—21no—
373#391—21no—
374#391—21no—
375#391—21no—
376#391—21no—
377#391—21no—
378#391—21no—
379#391—21no—
380#391—21no—
381#391—21no—
382#391D411yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#391C2311yescharacteristic
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#389—21no—
401#389—21no—
402#389—21no—
403#389—21no—
404#389D411yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
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#387—21no—
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#387—21no—
433#387D411yescharacteristic
434#387D411yescharacteristic
435#386—21no—
436#386—21no—
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#385D411yescharacteristic
448#384C2311yescharacteristic
449#382C2311yescharacteristic
450#382C2311yescharacteristic
451#381—21no—
452#380—21no—
453#380—21no—
454#380—21no—
455#380—21no—
456#380—21no—
457#380—21no—
458#380D411yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#380C2311yescharacteristic
462#379—21no—
463#379—21no—
464#379—21no—
465C4×C4⋊C4—21no—
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4—21no—
473C4×C22⋊C4—21no—
474C4×C22⋊C4—21no—
475C4×C22⋊C4C2311yescharacteristic
476C4×C22⋊C4C2311yescharacteristic
477C2×#95—21no—
478C2×#95—21no—
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502#336C2311yescharacteristic
503#336C2311yescharacteristic
504#336C2311yescharacteristic
505C25—21no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8—21no—
509C22×Q8—22no—
510C22×Q8—22no—
511C22×Q8—22no—
512C22×Q8—22no—
513C22×Q8—41no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8—41no—
517C22×Q8—41no—
518C22×Q8—41no—
519C22×Q8—41no—
520C22×Q8C2×D411yescharacteristic
521C22×Q8#4114yes—
522C22×Q8C2411yescharacteristic
523C22×Q8C2411yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×D4—22no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—22no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4—41no—
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4C2×D411yescharacteristic
542C23×C4C2×D411yescharacteristic
543C23×C4C2411yescharacteristic
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—22no—
553C2×Q16—22no—
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×Q16—416no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—416no—
576C22×C8—22no—
577C22×C8—22no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8—41no—
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C4⋊Q8—22no—
591C4⋊Q8—41no—
592C4⋊Q8—41no—
593C4⋊Q8—41no—
594C4⋊Q8—41no—
595C4⋊Q8—41no—
596#126—44no—
597#126—44no—
598#125—41no—
599#125—41no—
600#125—41no—
601#125—41no—
602#124—22no—
603#124—22no—
604#124—22no—
605#124—22no—
606#124—22no—
607#124—41no—
608#124—41no—
609#124—41no—
610#124—41no—
611#124—41no—
612#124—41no—
613#124—41no—
614#124—44no—
615#124—44no—
616C22⋊Q8—24no—
617C22⋊Q8—22no—
618C22⋊Q8—22no—
619C22⋊Q8—44no—
620C22⋊Q8—44no—
621C4×Q8—22no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×Q8—41no—
625C4×Q8—41no—
626C4×Q8—41no—
627C4×Q8—41no—
628C4×Q8—41no—
629C4×Q8—41no—
630C4×Q8—41no—
631C4×Q8—41no—
632C4×Q8—41no—
633C4×Q8—41no—
634C4×Q8—41no—
635C4×Q8—41no—
636C4×Q8—41no—
637C4×D4—22no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—41no—
641#117—44no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—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—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
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—44no—
716C2×C22⋊C4—44no—
717C2×C22⋊C4—44no—
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—41no—
731C2×C42—41no—
732C2×C42C2×D411yescharacteristic
733C2×C42C2×D411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740#107—22no—
741#107—41no—
742#107—41no—
743#107—41no—
744#106—22no—
745#106—41no—
746C4⋊C8—22no—
747C4⋊C8—22no—
748C4⋊C8—41no—
749C4⋊C8—41no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786C22⋊C8—22no—
787C22⋊C8—22no—
788C4×C8—22no—
789C4×C8—22no—
790C4×C8—41no—
791C4×C8—41no—
792C4×C8—41no—
793C4×C8—41no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#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#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845C24—21no—
846C24—21no—
847C24—42no—
848C24—42no—
849C24—42no—
850C24—42no—
851C24—81no—
852C24—81no—
853C24—81no—
854C24C22×D411yescharacteristic
855C2×Q8—24no—
856C2×Q8—22no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
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—41no—
885C2×Q8—41no—
886C2×Q8—42no—
887C2×Q8—44no—
888C2×Q8—44no—
889C2×Q8—44no—
890C2×Q8—44no—
891C2×Q8—42no—
892C2×Q8—42no—
893C2×Q8—81no—
894C2×Q8—81no—
895C2×Q8—81no—
896C2×Q8—81no—
897C2×Q8—81no—
898C2×Q8—82no—
899C2×Q8—82no—
900C2×Q8—82no—
901C2×Q8—82no—
902C2×Q8C2×#4112yes—
903C2×Q8C2×#4112yes—
904C2×Q8H(5,𝔽2)12yes—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
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—44no—
917C2×D4—44no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—82no—
921C2×D4—82no—
922C2×D4—81no—
923C2×D4H(5,𝔽2)12yes—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—24no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—21no—
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—41no—
946C22×C4—41no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
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×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C2×#4112yes—
977C22×C42−1+412yes—
978C22×C4C2511yescharacteristic
979Q16—28no—
980Q16—44no—
981Q16—44no—
982Q16—44no—
983Q16—82no—
984Q16—82no—
985SD16—28no—
986SD16—44no—
987SD16—44no—
988SD16—44no—
989C2×C8—21no—
990C2×C8—21no—
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—44no—
1012C2×C8—44no—
1013C2×C8H(5,𝔽2)12yes—
1014C2×C8H(5,𝔽2)12yes—
1015C4⋊C4—22no—
1016C4⋊C4—22no—
1017C4⋊C4—22no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
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—41no—
1037C4⋊C4—41no—
1038C4⋊C4—41no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—22no—
1072C22⋊C4—22no—
1073C22⋊C4—22no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
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—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4#13514yes—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—41no—
1112C42—41no—
1113C42—42no—
1114C42—42no—
1115C42—81no—
1116C42—81no—
1117C42—81no—
1118C42—81no—
1119C42—81no—
1120C42—81no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—22no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—84no—
1140C23—84no—
1141C23—84no—
1142C23—84no—
1143C23—162no—
1144C23—162no—
1145C23—162no—
1146C23#54812yes—
1147C23C2×#13512yes—
1148C23#57812yes—
1149C23C23×D411yescharacteristic
1150Q8—22no—
1151Q8—22no—
1152Q8—22no—
1153Q8—22no—
1154Q8—22no—
1155Q8—22no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—82no—
1171Q8—84no—
1172Q8—84no—
1173Q8—162no—
1174D4—22no—
1175D4—22no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—84no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—22no—
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—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—84no—
1266C2×C4—82no—
1267C2×C4—82no—
1268C2×C4—84no—
1269C2×C4—84no—
1270C2×C4—162no—
1271C2×C4—162no—
1272C2×C4#54812yes—
1273C2×C4C2×#13512yes—
1274C2×C4C2×#13512yes—
1275C2×C4C22×#4111yescharacteristic
1276C2×C4C2×H(5,𝔽2)11yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4C2×H(5,𝔽2)11yescharacteristic
1280C2×C4C2×2−1+411yescharacteristic
1281C8—22no—
1282C8—22no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—168no—
1310C22#336414yes—
1311C22C2×#54811yescharacteristic
1312C22#348411yescharacteristic
1313C22#349811yescharacteristic
1314C22C22×#13511yescharacteristic
1315C22C2×#57811yescharacteristic
1316C22#358411yescharacteristic
1317C22#358611yescharacteristic
1318C4—22no—
1319C4—22no—
1320C4—22no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—41no—
1333C4—41no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4#349011yescharacteristic
1346C4#349011yescharacteristic
1347C4#353611yescharacteristic
1348C4#353611yescharacteristic
1349C2—24no—
1350C2—82no—
1351C2—161no—
1352C2#4300211yescharacteristic
1353C2C2×#336411yescharacteristic
1354C2#6134411yescharacteristic
1355C2#6156811yescharacteristic
1356C2#6164211yescharacteristic
1357C2#6241911yescharacteristic
1358C2#6246011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39179C2semidirect
3. #32611C2semidirect
4. #32603C2semidirect
5. #31647C2semidirect
6. #31642C2semidirect
7. #30888C2semidirect
8. #30888C2semidirect
9. #30885C2semidirect
10. #30881C2semidirect
11. #29158C2semidirect
12. #28407C2semidirect
13. #28403C2semidirect
14. #27258C2semidirect
16. #26899C2semidirect
17. #26893C2semidirect
18. #26823C2semidirect
19. #26817C2semidirect
20. #25957C2semidirect
23. #24360C2semidirect
25. #24195C2semidirect
26. #24189C2semidirect
28. #23237C2semidirect
29. C22⋊C4×Q16C2semidirect
31. #22044C2semidirect
39. C2×#487C22semidirect
40. C2×#479C22semidirect
44. C2×#462C22semidirect
45. C2×#462C22semidirect
47. C2×C4×Q16C22semidirect
48. C2×C4×Q16C22semidirect
62. #2582C22semidirect
63. #2581C22semidirect
65. #2568C22semidirect
66. #2565C22semidirect
75. #2453C22semidirect
76. #2453C22semidirect
77. #2453C22semidirect
78. #2451C22semidirect
96. #2101C22semidirect
97. #2097C22semidirect
98. #2097C22semidirect
101. #2072C22semidirect
102. #2068C22semidirect
105. #2066C22semidirect
106. #2059C22semidirect
107. #2056C22semidirect
108. #2056C22semidirect
111. #2043C22semidirect
112. #2043C22semidirect
119. #2026C22semidirect
120. #2026C22semidirect
122. #2024C22semidirect
124. #2016C22semidirect
125. #2016C22semidirect
136. #1984C22semidirect
137. #1984C22semidirect
138. #1969C22semidirect
139. #1969C22semidirect
140. #1969C22semidirect
141. #1969C22semidirect
147. #1956C22semidirect
150. #1933C22semidirect
151. #1933C22semidirect
152. #1933C22semidirect
153. #1933C22semidirect
154. #1928C22semidirect
155. #1928C22semidirect
156. #1920C22semidirect
157. #1918C22semidirect
158. #1916C22semidirect
159. #1916C22semidirect
160. #1916C22semidirect
161. #1916C22semidirect
168. #1878C22semidirect
169. #1878C22semidirect
170. #1878C22semidirect
171. #1878C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
179. #1865C22semidirect
180. #1865C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
190. #1805C22semidirect
197. C8×C4⋊C4C22semidirect
198. C8×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#591482
#391792
#326112
#326032
#316472
#316422
#308882
#308852
#308812
#291582
#284072
#284032
#272582
#272562
#268992
#268932
#268232
#268172
#259572
#259502
#258592
#243602
#243572
#241952
#241892
C2×#20152
#232372
C22⋊C4×Q162
C22⋊C4×SD162
#220442