Finite Group Databasebeta

← #7361773

Subgroups — #7361773

Order 512.

1735 conjugacy classes of subgroups.

The subgroup lattice has 1438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45079C211yesmaximal, characteristic, complemented
2#42970C211yesmaximal, characteristic, complemented
3#31538C211yesmaximal, characteristic, complemented
4#31520C211yesmaximal, characteristic, complemented
5#31371C211yesmaximal, characteristic, complemented
6#31352C211yesmaximal, characteristic, complemented
7#31347C211yesmaximal, characteristic, complemented
8#31336C211yesmaximal, characteristic, complemented
9#31033C211yesmaximal, characteristic, complemented
10#31024C211yesmaximal, characteristic, complemented
11#30614C211yesmaximal, characteristic, complemented
12#30607C211yesmaximal, characteristic, complemented
13#30577C211yesmaximal, characteristic, complemented
14#30575C211yesmaximal, characteristic, complemented
15#30119C211yesmaximal, characteristic, complemented
16#29677C211yesmaximal, characteristic, complemented
17#29249C211yesmaximal, characteristic, complemented
18#26915C211yesmaximal, characteristic, complemented
19#26900C211yesmaximal, characteristic, complemented
20#25975C211yesmaximal, characteristic, complemented
21#25968C211yesmaximal, characteristic, complemented
22#25164C211yesmaximal, characteristic, complemented
23#25155C211yesmaximal, characteristic, complemented
24#24444C211yesmaximal, characteristic, complemented
25#24442C211yesmaximal, characteristic, complemented
26#24137C211yesmaximal, characteristic, complemented
27#24121C211yesmaximal, characteristic, complemented
28#24074C211yesmaximal, characteristic, complemented
29#23978C211yesmaximal, characteristic, complemented
30#23976C211yesmaximal, characteristic, complemented
31#23332C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#552C2211yescharacteristic, complemented
34C2×#546C2211yescharacteristic
35C2×#542C2211yescharacteristic
36C2×#481C2211yescharacteristic
37C2×#483C2211yescharacteristic, complemented
38C2×#477C2211yescharacteristic, complemented
39C2×#478C2211yescharacteristic
40C2×#470C2211yescharacteristic
41C2×#469C2211yescharacteristic
42C2×#464C2211yescharacteristic, complemented
43C2×#463C2211yescharacteristic
44C2×#452C2211yescharacteristic
45C2×#449C2211yescharacteristic
46C2×#450C2211yescharacteristic
47C2×#447C2211yescharacteristic
48C2×#440C2211yescharacteristic
49C2×C4×SD16C2211yescharacteristic, complemented
50C2×#417C2211yescharacteristic
51C2×#418C2211yescharacteristic
52#2820—21no—
53#2715—21no—
54#2706—21no—
55#2691—21no—
56#2685—21no—
57#2681—21no—
58#2676—21no—
59#2672—21no—
60#2671—21no—
61#2629—21no—
62#2620—21no—
63#2620C2211yescharacteristic, complemented
64#2609—21no—
65#2563C2211yescharacteristic
66#2553—21no—
67#2542C2211yescharacteristic
68#2539—21no—
69#2538C2211yescharacteristic
70#2537C2211yescharacteristic
71#2472—21no—
72#2454C2211yescharacteristic, complemented
73#2451C2211yescharacteristic, complemented
74#2441C2211yescharacteristic
75#2440C2211yescharacteristic, complemented
76#2437—21no—
77#2427C2211yescharacteristic, complemented
78#2426C2211yescharacteristic
79#2423C2211yescharacteristic
80#2422C2211yescharacteristic
81#2417C2211yescharacteristic
82#2416C2211yescharacteristic
83#2416C2211yescharacteristic, complemented
84#2415C2211yescharacteristic
85#2408C2211yescharacteristic
86#2407C2211yescharacteristic
87#2392C2211yescharacteristic
88#2367C2211yescharacteristic
89#2341C2211yescharacteristic
90D4×C22⋊C4C2211yescharacteristic
91#2324C2211yescharacteristic
92#2317C2211yescharacteristic, complemented
93#2100C2211yescharacteristic, complemented
94#2096C2211yescharacteristic, complemented
95#2094C2211yescharacteristic, complemented
96#2093C2211yescharacteristic
97#2088C2211yescharacteristic, complemented
98#2088C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2084C2211yescharacteristic, complemented
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic, complemented
103#2067C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2058C2211yescharacteristic, complemented
108#2058C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic, complemented
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic, complemented
114#2036C2211yescharacteristic, complemented
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic, complemented
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic, complemented
121#2034C2211yescharacteristic, complemented
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic, complemented
124#2026C2211yescharacteristic, complemented
125#2025C2211yescharacteristic
126#2024C2211yescharacteristic, complemented
127#2023C2211yescharacteristic
128#2023C2211yescharacteristic
129#2023C2211yescharacteristic, complemented
130#2015C2211yescharacteristic
131#2012C2211yescharacteristic
132#2012C2211yescharacteristic
133#2001C2211yescharacteristic, complemented
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic
138#2000C2211yescharacteristic, complemented
139#1999C2211yescharacteristic
140#1999C2211yescharacteristic
141#1992C2211yescharacteristic, complemented
142#1990C2211yescharacteristic, complemented
143#1972C2211yescharacteristic
144#1968C2211yescharacteristic
145#1955C2211yescharacteristic, complemented
146#1954C2211yescharacteristic
147#1935C2211yescharacteristic, complemented
148#1934C2211yescharacteristic
149#1928C2211yescharacteristic, complemented
150#1925C2211yescharacteristic, complemented
151#1924C2211yescharacteristic
152#1923C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1917C2211yescharacteristic, complemented
156#1916C2211yescharacteristic, complemented
157#1895C2211yescharacteristic
158#1894C2211yescharacteristic, complemented
159#1880C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1878C2211yescharacteristic, complemented
165#1878C2211yescharacteristic, complemented
166#1877C2211yescharacteristic
167#1875C2211yescharacteristic
168#1875C2211yescharacteristic
169#1874C2211yescharacteristic
170#1874C2211yescharacteristic
171#1873C2211yescharacteristic
172#1873C2211yescharacteristic, complemented
173#1870C2211yescharacteristic
174#1870C2211yescharacteristic
175#1870C2211yescharacteristic
176#1870C2211yescharacteristic, complemented
177#1865C2211yescharacteristic, complemented
178#1865C2211yescharacteristic, complemented
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1863C2211yescharacteristic, complemented
184#1862C2211yescharacteristic
185#1854C2211yescharacteristic
186#1854C2211yescharacteristic, complemented
187#1853C2211yescharacteristic, complemented
188#1852C2211yescharacteristic, complemented
189#1851C2211yescharacteristic
190#1851C2211yescharacteristic, complemented
191#1825C2211yescharacteristic
192#1824C2211yescharacteristic, complemented
193#1818C2211yescharacteristic, complemented
194#1809C2211yescharacteristic
195#1809C2211yescharacteristic, complemented
196#1803C2211yescharacteristic, complemented
197#1803C2211yescharacteristic, complemented
198#1802C2211yescharacteristic
199#1802C2211yescharacteristic, complemented
200#1798C2211yescharacteristic, complemented
201#1788C2211yescharacteristic
202#1786C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213#555—42no—
214#555—42no—
215#552—42no—
216#552—42no—
217#546—42no—
218#546—42no—
219#542—42no—
220#542—42no—
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×#126—21no—
224C2×#126—21no—
225C2×#125—21no—
226C2×#125C2311yescharacteristic
227C2×#124—21no—
228C2×#124—21no—
229C2×#124—21no—
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#123—21no—
233C2×#123—21no—
234C2×#123—21no—
235C2×#123—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×C22⋊Q8C2311yescharacteristic
245C2×#121—21no—
246C2×#121—21no—
247C2×#121—21no—
248C2×#121—21no—
249C2×#121—21no—
250C2×#121C2311yescharacteristic
251C2×#121C2311yescharacteristic
252C2×#121C2311yescharacteristic
253C2×#121C2311yescharacteristic
254C2×#121C2311yescharacteristic
255C2×#121C2311yescharacteristic
256C2×#120—21no—
257C2×#120—21no—
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C2×#117—21no—
269C2×#117—21no—
270C2×#117C2311yescharacteristic
271C2×#117C2311yescharacteristic
272C2×#117C2311yescharacteristic
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C22⋊C4—21no—
276C22×C22⋊C4—21no—
277#483—42no—
278#481—42no—
279#478—42no—
280#477—42no—
281#470—42no—
282#469—42no—
283#464—42no—
284#463—42no—
285#452—42no—
286#450—42no—
287#449—42no—
288#447—42no—
289#440—42no—
290C4×SD16—42no—
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×C4⋊C8C2311yescharacteristic
302C2×C4⋊C8C2311yescharacteristic
303C2×C4⋊C8C2311yescharacteristic
304C2×C4⋊C8C2311yescharacteristic
305#418—42no—
306#417—42no—
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×C22⋊C8C2311yescharacteristic
339C2×C22⋊C8C2311yescharacteristic
340C2×C22⋊C8C2311yescharacteristic
341C2×C22⋊C8C2311yescharacteristic
342C2×C22⋊C8C2311yescharacteristic
343C2×C22⋊C8C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×#97C2311yescharacteristic
346C2×C4×C8C2311yescharacteristic
347#399—21no—
348#399—21no—
349#399—21no—
350#399—21no—
351#399—21no—
352#398—21no—
353#398—21no—
354#398—21no—
355#398—21no—
356#398D411yescharacteristic
357#397—21no—
358#397—21no—
359#397—21no—
360#397D411yescharacteristic
361#396—21no—
362#396—21no—
363#396—21no—
364#396—21no—
365#396—21no—
366#396—21no—
367#396—21no—
368#396—21no—
369#396—21no—
370#396—21no—
371#396D411yescharacteristic
372#396D411yescharacteristic
373#395—21no—
374#395—21no—
375#394—21no—
376#394—21no—
377#394—21no—
378#394—21no—
379#394—21no—
380#394—21no—
381#394—21no—
382#394—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#394—21no—
387#394D411yescharacteristic
388#394D411yescharacteristic
389#394D411yescharacteristic
390#393—21no—
391#393—21no—
392#392—21no—
393#392—21no—
394#392D411yescharacteristic
395#391—21no—
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#390—21no—
400#390—21no—
401#390—21no—
402#390—21no—
403#390—21no—
404#390—21no—
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#389—21no—
412#389—21no—
413#389—21no—
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#387—21no—
428#387—21no—
429#387—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#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#384—21no—
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#382—21no—
451#382—21no—
452#380—21no—
453#380—21no—
454#380—21no—
455#380—21no—
456#380—21no—
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#380C2311yescharacteristic
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464#379—21no—
465#379—21no—
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
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×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×D4—22no—
514C22×D4—22no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4C2×D411yescharacteristic
528C22×D4C2×D411yescharacteristic
529C22×D4C2×D411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C23×C4C2411yescharacteristic
543C2×Q16—22no—
544C2×Q16—41no—
545C2×Q16—41no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×M16—41no—
562C2×M16—41no—
563C2×M16—41no—
564C2×M16—41no—
565C2×M16—41no—
566C2×M16—41no—
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C4⋊Q8—22no—
576C4⋊Q8—41no—
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579#126—44no—
580#126—44no—
581#125—22no—
582#125—41no—
583#125—44no—
584#124—22no—
585#124—22no—
586#124—44no—
587#124—41no—
588#124—41no—
589#124—44no—
590#124—44no—
591#123—44no—
592#123—44no—
593#123—44no—
594#123—82no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—44no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606C22⋊Q8—82no—
607C22⋊Q8—82no—
608C22⋊Q8—82no—
609#121—22no—
610#121—22no—
611#121—22no—
612#121—22no—
613#121—44no—
614#121—44no—
615#121—41no—
616#121—41no—
617#121—41no—
618#121—41no—
619#121—41no—
620#121—41no—
621#121—41no—
622#121—41no—
623#121—82no—
624#121—82no—
625#121—82no—
626#120—44no—
627#120—82no—
628C4×Q8—22no—
629C4×Q8—22no—
630C4×Q8—41no—
631C4×Q8—41no—
632C4×Q8—41no—
633C4×Q8—41no—
634C4×D4—22no—
635C4×D4—22no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—41no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—41no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—41no—
648#117—22no—
649#117—22no—
650#117—22no—
651#117—41no—
652#117—41no—
653#117—44no—
654#117—44no—
655#117—41no—
656C2×C4⋊C4—22no—
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—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—41no—
685C2×C4⋊C4—41no—
686C2×C4⋊C4—41no—
687C2×C4⋊C4C2×D411yescharacteristic
688C2×C4⋊C4C2×D411yescharacteristic
689C2×C4⋊C4C2×D411yescharacteristic
690C2×C4⋊C4C2×D411yescharacteristic
691C2×C4⋊C4C2×D411yescharacteristic
692C2×C4⋊C4C2×D411yescharacteristic
693C2×C4⋊C4C2×D411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—44no—
746C2×C22⋊C4—82no—
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C22⋊C4C2×D411yescharacteristic
749C2×C22⋊C4C2×D411yescharacteristic
750C2×C22⋊C4C2×D411yescharacteristic
751C2×C22⋊C4C2×D411yescharacteristic
752C2×C22⋊C4C2×D411yescharacteristic
753C2×C22⋊C4C2×D411yescharacteristic
754C2×C22⋊C4C2×D411yescharacteristic
755C2×C22⋊C4C2×D411yescharacteristic
756C2×C22⋊C4C2×D411yescharacteristic
757C2×C22⋊C4C2×D411yescharacteristic
758C2×C22⋊C4C2×D411yescharacteristic
759C2×C42—21no—
760C2×C42—21no—
761C2×C42—21no—
762C2×C42—21no—
763C2×C42—21no—
764C2×C42—21no—
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769#107—22no—
770#107—41no—
771#107—41no—
772#106—22no—
773#106—41no—
774#106—41no—
775#106—41no—
776#106—41no—
777#106—41no—
778#106—41no—
779C4⋊C8—41no—
780C4⋊C8—41no—
781C4⋊C8—41no—
782C4⋊C8—41no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—41no—
788#103—41no—
789#103—41no—
790#103—41no—
791#103—41no—
792#103—41no—
793#103—41no—
794#102—22no—
795#102—22no—
796#102—22no—
797#102—22no—
798#102—22no—
799#102—22no—
800#102—41no—
801#102—41no—
802#102—41no—
803#102—41no—
804#102—41no—
805#102—41no—
806#102—41no—
807#102—41no—
808#102—41no—
809#102—41no—
810#102—41no—
811C22⋊C8—41no—
812C22⋊C8—41no—
813C22⋊C8—41no—
814C22⋊C8—41no—
815C22⋊C8—41no—
816C22⋊C8—41no—
817C22⋊C8—41no—
818C22⋊C8—41no—
819C22⋊C8—41no—
820C22⋊C8—41no—
821#97—41no—
822C4×C8—41no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850C24—21no—
851C24—21no—
852C24—21no—
853C24—42no—
854C24—42no—
855C24—42no—
856C24—81no—
857C24—81no—
858C24—81no—
859C24—81no—
860C24C22×D411yescharacteristic
861C24C22×D411yescharacteristic
862C24C22×D411yescharacteristic
863#41—44no—
864#41—82no—
865#41—82no—
866#41—82no—
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—42no—
879C2×Q8—42no—
880C2×Q8—81no—
881C2×Q8—81no—
882C2×Q8—81no—
883C2×Q8—81no—
884C2×Q8H(5,𝔽2)12yes—
885C2×D4—22no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—41no—
903C2×D4—41no—
904C2×D4—41no—
905C2×D4—41no—
906C2×D4—41no—
907C2×D4—41no—
908C2×D4—41no—
909C2×D4—41no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—44no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—81no—
922C2×D4—82no—
923C2×D4—82no—
924C2×D4—82no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4H(5,𝔽2)12yes—
939C2×D42−1+412yes—
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—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—42no—
978C22×C4—42no—
979C22×C4—42no—
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×C4C2511yescharacteristic
1004Q16—82no—
1005SD16—44no—
1006SD16—44no—
1007SD16—82no—
1008D8—82no—
1009D8—82no—
1010M16—82no—
1011M16—82no—
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—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C4⋊C4—22no—
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—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C4⋊C4—81no—
1090C4⋊C4H(5,𝔽2)12yes—
1091C4⋊C4H(5,𝔽2)12yes—
1092C22⋊C4—24no—
1093C22⋊C4—24no—
1094C22⋊C4—24no—
1095C22⋊C4—22no—
1096C22⋊C4—41no—
1097C22⋊C4—41no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
1106C22⋊C4—41no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—42no—
1122C22⋊C4—42no—
1123C22⋊C4—42no—
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—
1136C22⋊C4—81no—
1137C22⋊C4—81no—
1138C22⋊C4—81no—
1139C22⋊C4—81no—
1140C22⋊C4—81no—
1141C22⋊C4—81no—
1142C22⋊C4—81no—
1143C22⋊C4—81no—
1144C42—24no—
1145C42—21no—
1146C42—21no—
1147C42—21no—
1148C42—21no—
1149C42—21no—
1150C42—21no—
1151C42—21no—
1152C42—21no—
1153C42—42no—
1154C42—42no—
1155C42—42no—
1156C42—81no—
1157C42—81no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—22no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—22no—
1175C23—21no—
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
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—41no—
1195C23—41no—
1196C23—41no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—84no—
1201C23—84no—
1202C23—84no—
1203C23—162no—
1204C23—162no—
1205C23—162no—
1206C23—162no—
1207C23C23×D411yescharacteristic
1208Q8—22no—
1209Q8—22no—
1210Q8—41no—
1211Q8—41no—
1212Q8—41no—
1213Q8—41no—
1214Q8—41no—
1215Q8—41no—
1216Q8—162no—
1217Q8—162no—
1218D4—22no—
1219D4—22no—
1220D4—22no—
1221D4—22no—
1222D4—41no—
1223D4—41no—
1224D4—41no—
1225D4—41no—
1226D4—41no—
1227D4—41no—
1228D4—41no—
1229D4—41no—
1230D4—82no—
1231D4—82no—
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—22no—
1258C2×C4—22no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—22no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
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—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—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—84no—
1325C2×C4—84no—
1326C2×C4—84no—
1327C2×C4—162no—
1328C2×C4—162no—
1329C2×C4—162no—
1330C2×C4—162no—
1331C2×C4#57712yes—
1332C2×C4C2×H(5,𝔽2)11yescharacteristic
1333C2×C4C2×H(5,𝔽2)11yescharacteristic
1334C2×C4C2×H(5,𝔽2)11yescharacteristic
1335C2×C4C2×H(5,𝔽2)11yescharacteristic
1336C2×C4C2×2−1+411yescharacteristic
1337C2×C4#58511yescharacteristic
1338C8—41no—
1339C8—41no—
1340C8—41no—
1341C8—41no—
1342C8—41no—
1343C8—41no—
1344C8—41no—
1345C8—41no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—42no—
1350C22—41no—
1351C22—41no—
1352C22—41no—
1353C22—42no—
1354C22—42no—
1355C22—41no—
1356C22—41no—
1357C22—41no—
1358C22—41no—
1359C22—41no—
1360C22—41no—
1361C22—41no—
1362C22—41no—
1363C22—41no—
1364C22—42no—
1365C22—41no—
1366C22—42no—
1367C22—41no—
1368C22—41no—
1369C22—42no—
1370C22—41no—
1371C22—41no—
1372C22—41no—
1373C22—81no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—81no—
1385C22—81no—
1386C22—81no—
1387C22—81no—
1388C22—168no—
1389C22#348411yescharacteristic
1390C22#348411yescharacteristic
1391C22#348911yescharacteristic
1392C22C2×#57711yescharacteristic
1393C22#358511yescharacteristic
1394C22#358511yescharacteristic
1395C22#358611yescharacteristic
1396C4—22no—
1397C4—41no—
1398C4—41no—
1399C4—41no—
1400C4—42no—
1401C4—41no—
1402C4—42no—
1403C4—41no—
1404C4—41no—
1405C4—42no—
1406C4—41no—
1407C4—41no—
1408C4—41no—
1409C4—41no—
1410C4—81no—
1411C4—81no—
1412C4—81no—
1413C4—81no—
1414C4—81no—
1415C4—81no—
1416C4—81no—
1417C4—81no—
1418C4—81no—
1419C4—81no—
1420C4#353611yescharacteristic
1421C4#353611yescharacteristic
1422C4#354211yescharacteristic
1423C4#354211yescharacteristic
1424C2—81no—
1425C2—81no—
1426C2—81no—
1427C2—82no—
1428C2—82no—
1429C2—161no—
1430C2#4954611yescharacteristic
1431C2#6162011yescharacteristic
1432C2#6165311yescharacteristic
1433C2#6165611yescharacteristic
1434C2#6168911yescharacteristic
1435C2#6217911yescharacteristic
1436C2#6222411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45079C2semidirect
2. #42970C2semidirect
3. #31538C2semidirect
4. #31520C2semidirect
5. #31371C2semidirect
6. #31352C2semidirect
7. #31347C2semidirect
8. #31336C2semidirect
9. #31033C2semidirect
10. #31024C2semidirect
11. #30614C2semidirect
12. #30607C2semidirect
13. #30577C2semidirect
14. #30575C2semidirect
15. #30119C2semidirect
16. #29677C2semidirect
17. #29249C2semidirect
18. #26915C2semidirect
19. #26900C2semidirect
20. #25975C2semidirect
21. #25968C2semidirect
22. #25164C2semidirect
23. #25155C2semidirect
24. #24444C2semidirect
25. #24442C2semidirect
26. #24137C2semidirect
27. #24121C2semidirect
28. #24074C2semidirect
29. #23978C2semidirect
30. #23976C2semidirect
31. #23332C2semidirect
33. C2×#552C22semidirect
37. C2×#483C22semidirect
38. C2×#477C22semidirect
42. C2×#464C22semidirect
49. C2×C4×SD16C22semidirect
63. #2620C22semidirect
72. #2454C22semidirect
73. #2451C22semidirect
75. #2440C22semidirect
77. #2427C22semidirect
83. #2416C22semidirect
92. #2317C22semidirect
93. #2100C22semidirect
94. #2096C22semidirect
95. #2094C22semidirect
97. #2088C22semidirect
98. #2088C22semidirect
99. #2084C22semidirect
100. #2084C22semidirect
102. #2077C22semidirect
107. #2058C22semidirect
108. #2058C22semidirect
110. #2055C22semidirect
113. #2042C22semidirect
114. #2036C22semidirect
118. #2035C22semidirect
120. #2034C22semidirect
121. #2034C22semidirect
123. #2033C22semidirect
124. #2026C22semidirect
126. #2024C22semidirect
129. #2023C22semidirect
133. #2001C22semidirect
138. #2000C22semidirect
141. #1992C22semidirect
142. #1990C22semidirect
145. #1955C22semidirect
147. #1935C22semidirect
149. #1928C22semidirect
150. #1925C22semidirect
152. #1923C22semidirect
153. #1919C22semidirect
154. #1918C22semidirect
155. #1917C22semidirect
156. #1916C22semidirect
158. #1894C22semidirect
164. #1878C22semidirect
165. #1878C22semidirect
172. #1873C22semidirect
176. #1870C22semidirect
177. #1865C22semidirect
178. #1865C22semidirect
183. #1863C22semidirect
186. #1854C22semidirect
187. #1853C22semidirect
188. #1852C22semidirect
190. #1851C22semidirect
192. #1824C22semidirect
193. #1818C22semidirect
195. #1809C22semidirect
196. #1803C22semidirect
197. #1803C22semidirect
199. #1802C22semidirect
200. #1798C22semidirect

Maximal subgroups

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

subgroupindex
#450792
#429702
#315382
#315202
#313712
#313522
#313472
#313362
#310332
#310242
#306142
#306072
#305772
#305752
#301192
#296772
#292492
#269152
#269002
#259752
#259682
#251642
#251552
#244442
#244422
#241372
#241212
#240742
#239782
#239762
#233322