Finite Group Databasebeta

← #6936947

Subgroups — #6936947

Order 512.

1643 conjugacy classes of subgroups.

The subgroup lattice has 1401 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38034C211yesmaximal, characteristic
2#37555C211yesmaximal, characteristic, complemented
3#32781C211yesmaximal, characteristic, complemented
4#32733C211yesmaximal, characteristic, complemented
5#32661C211yesmaximal, characteristic, complemented
6#32654C211yesmaximal, characteristic, complemented
7#32624C211yesmaximal, characteristic, complemented
8#32603C211yesmaximal, characteristic, complemented
9#30580C211yesmaximal, characteristic, complemented
10#30562C211yesmaximal, characteristic, complemented
11#30424C211yesmaximal, characteristic, complemented
12#30408C211yesmaximal, characteristic, complemented
13#30370C211yesmaximal, characteristic, complemented
14#30252C211yesmaximal, characteristic, complemented
15#30120C211yesmaximal, characteristic, complemented
16#29959C211yesmaximal, characteristic, complemented
17#29912C211yesmaximal, characteristic, complemented
18#29175C211yesmaximal, characteristic, complemented
19#28320C211yesmaximal, characteristic, complemented
20#26155C211yesmaximal, characteristic, complemented
21#26151C211yesmaximal, characteristic, complemented
22#25503C211yesmaximal, characteristic, complemented
23#25135C211yesmaximal, characteristic, complemented
24#25119C211yesmaximal, characteristic, complemented
25#24795C211yesmaximal, characteristic, complemented
26#24788C211yesmaximal, characteristic, complemented
27#24452C211yesmaximal, characteristic, complemented
28#24452C211yesmaximal, characteristic, complemented
29#23935C211yesmaximal, characteristic, complemented
30#23733C211yesmaximal, characteristic, complemented
31#22472C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#533C2211yescharacteristic, complemented
34C2×#529C2211yescharacteristic
35C2×#485C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#470C2211yescharacteristic, complemented
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#468C2211yescharacteristic
41C2×#467C2211yescharacteristic, complemented
42C2×#465C2211yescharacteristic
43C2×#452C2211yescharacteristic
44C2×#452C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#450C2211yescharacteristic
47C2×#436C2211yescharacteristic, complemented
48C2×#435C2211yescharacteristic, complemented
49C2×#428C2211yescharacteristic, complemented
50C2×#428C2211yescharacteristic, complemented
51C2×#417C2211yescharacteristic
52C2×#417C2211yescharacteristic
53#2854C2211yescharacteristic
54#2822—21no—
55#2820—21no—
56#2703—21no—
57#2697—21no—
58#2681—21no—
59#2678—21no—
60#2659—21no—
61#2639—21no—
62#2637—21no—
63#2637—21no—
64#2628C2211yescharacteristic
65#2628C2211yescharacteristic, complemented
66#2625C2211yescharacteristic
67#2621C2211yescharacteristic
68#2621C2211yescharacteristic, complemented
69#2620C2211yescharacteristic
70#2592C2211yescharacteristic
71#2581C2211yescharacteristic, complemented
72#2581C2211yescharacteristic, complemented
73#2558—21no—
74#2554—21no—
75#2538C2211yescharacteristic
76#2536C2211yescharacteristic
77#2536C2211yescharacteristic
78#2498—21no—
79#2498—21no—
80#2480—21no—
81#2472—21no—
82#2417C2211yescharacteristic
83#2417C2211yescharacteristic
84#2417C2211yescharacteristic, complemented
85#2417C2211yescharacteristic, complemented
86#2415C2211yescharacteristic
87#2414C2211yescharacteristic
88#2408C2211yescharacteristic
89#2407C2211yescharacteristic
90#2354C2211yescharacteristic
91#2324C2211yescharacteristic
92#2309C2211yescharacteristic
93#2297C2211yescharacteristic
94C2×#382C2211yescharacteristic, complemented
95#2101C2211yescharacteristic, complemented
96#2101C2211yescharacteristic, complemented
97#2097C2211yescharacteristic, complemented
98#2097C2211yescharacteristic, complemented
99#2097C2211yescharacteristic, complemented
100#2097C2211yescharacteristic, complemented
101#2096C2211yescharacteristic, complemented
102#2095C2211yescharacteristic, complemented
103#2092C2211yescharacteristic
104#2092C2211yescharacteristic
105#2092C2211yescharacteristic
106#2092C2211yescharacteristic
107#2092C2211yescharacteristic
108#2092C2211yescharacteristic
109#2085C2211yescharacteristic, complemented
110#2085C2211yescharacteristic, complemented
111#2084C2211yescharacteristic, complemented
112#2083C2211yescharacteristic, complemented
113#2077C2211yescharacteristic
114#2075C2211yescharacteristic
115#2073C2211yescharacteristic
116#2073C2211yescharacteristic
117#2068C2211yescharacteristic, complemented
118#2067C2211yescharacteristic
119#2067C2211yescharacteristic
120#2066C2211yescharacteristic, complemented
121#2065C2211yescharacteristic
122#2065C2211yescharacteristic
123#2057C2211yescharacteristic, complemented
124#2056C2211yescharacteristic, complemented
125#2056C2211yescharacteristic, complemented
126#2043C2211yescharacteristic, complemented
127#2042C2211yescharacteristic
128#2042C2211yescharacteristic
129#2036C2211yescharacteristic
130#2036C2211yescharacteristic
131#2036C2211yescharacteristic
132#2036C2211yescharacteristic, complemented
133#2036C2211yescharacteristic, complemented
134#2035C2211yescharacteristic
135#2035C2211yescharacteristic, complemented
136#2035C2211yescharacteristic, complemented
137#2034C2211yescharacteristic
138#2033C2211yescharacteristic
139#2024C2211yescharacteristic, complemented
140#2023C2211yescharacteristic
141#2023C2211yescharacteristic
142#2016C2211yescharacteristic, complemented
143#2015C2211yescharacteristic
144#2015C2211yescharacteristic
145#2013C2211yescharacteristic
146#2013C2211yescharacteristic
147#2001C2211yescharacteristic
148#2001C2211yescharacteristic
149#2000C2211yescharacteristic
150#2000C2211yescharacteristic
151#1985C2211yescharacteristic, complemented
152#1984C2211yescharacteristic, complemented
153#1973C2211yescharacteristic
154#1973C2211yescharacteristic
155#1968C2211yescharacteristic
156#1968C2211yescharacteristic
157#1944C2211yescharacteristic, complemented
158#1942C2211yescharacteristic, complemented
159#1935C2211yescharacteristic, complemented
160#1933C2211yescharacteristic, complemented
161#1928C2211yescharacteristic, complemented
162#1927C2211yescharacteristic, complemented
163#1921C2211yescharacteristic, complemented
164#1920C2211yescharacteristic, complemented
165#1895C2211yescharacteristic
166#1894C2211yescharacteristic, complemented
167#1894C2211yescharacteristic, complemented
168#1893C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1874C2211yescharacteristic
178#1874C2211yescharacteristic
179#1873C2211yescharacteristic, complemented
180#1873C2211yescharacteristic, complemented
181#1870C2211yescharacteristic
182#1870C2211yescharacteristic
183#1870C2211yescharacteristic
184#1869C2211yescharacteristic
185#1863C2211yescharacteristic, complemented
186#1863C2211yescharacteristic, complemented
187#1862C2211yescharacteristic
188#1862C2211yescharacteristic
189#1854C2211yescharacteristic
190#1854C2211yescharacteristic
191#1853C2211yescharacteristic, complemented
192#1852C2211yescharacteristic, complemented
193#1818C2211yescharacteristic, complemented
194#1817C2211yescharacteristic, complemented
195#1809C2211yescharacteristic, complemented
196#1808C2211yescharacteristic, complemented
197#1798C2211yescharacteristic
198#1786C2211yescharacteristic
199#1786C2211yescharacteristic
200#1750C2211yescharacteristic
201#1729C2211yescharacteristic, complemented
202#1728C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#546—42no—
216#546—42no—
217#533—42no—
218#533—42no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221#529—42no—
222#529—42no—
223C2×#126D411yescharacteristic
224C2×#126D411yescharacteristic
225C2×#125—21no—
226C2×#125D411yescharacteristic
227C2×#124D411yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#123—21no—
230C2×#123—21no—
231C2×#123D411yescharacteristic
232C2×#123D411yescharacteristic
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8D411yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×#121—21no—
245C2×#121D411yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#120—21no—
250C2×#120—21no—
251C2×C4×Q8—21no—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×#117—21no—
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C22⋊C4—21no—
267C22×C42C2311yescharacteristic
268#485—42no—
269#485—42no—
270#470—42no—
271#468—42no—
272#468—42no—
273#468—42no—
274#467—42no—
275#465—42no—
276#452—42no—
277#452—42no—
278#450—42no—
279#450—42no—
280#436—42no—
281#435—42no—
282#428—42no—
283#428—42no—
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#106C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×C4⋊C8C2311yescharacteristic
299C2×C4⋊C8C2311yescharacteristic
300#417—42no—
301#417—42no—
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×#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×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×#97C2311yescharacteristic
339C2×C4×C8C2311yescharacteristic
340#400—21no—
341#400—21no—
342#400—21no—
343#400—21no—
344#400—21no—
345#399—21no—
346#399—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#398—21no—
351#398—21no—
352#398—21no—
353#398—21no—
354#398—21no—
355#398—21no—
356#398—21no—
357#398—21no—
358#397—21no—
359#397—21no—
360#397—21no—
361#397—21no—
362#397—21no—
363#397—21no—
364#397—21no—
365#397—21no—
366#396—21no—
367#396—21no—
368#396—21no—
369#396—21no—
370#396—21no—
371#396—21no—
372#396—21no—
373#396—21no—
374#395—21no—
375#395—21no—
376#395—21no—
377#395—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#393—21no—
387#393—21no—
388#393—21no—
389#392—21no—
390#392—21no—
391#392—21no—
392#391C2311yescharacteristic
393#391C2311yescharacteristic
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#390—21no—
400#390—21no—
401#390—21no—
402#390—21no—
403#390—21no—
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#389—21no—
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#387—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#385—21no—
445#385—21no—
446#384C2311yescharacteristic
447#382—21no—
448#382—21no—
449#382C2311yescharacteristic
450#382C2311yescharacteristic
451#382C2311yescharacteristic
452#382C2311yescharacteristic
453#380—21no—
454#380—21no—
455#380—21no—
456#380—21no—
457#380—21no—
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#380C2311yescharacteristic
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464#380C2311yescharacteristic
465#379—21no—
466#379—21no—
467#379—21no—
468C4×C4⋊C4—21no—
469C4×C4⋊C4C2311yescharacteristic
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C2×#95—21no—
473C2×#95—21no—
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#336C2311yescharacteristic
491#336C2311yescharacteristic
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—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8—21no—
510C22×Q8C2×D411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×D4—22no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×D411yescharacteristic
526C22×D4C2×D411yescharacteristic
527C22×D4C2×D411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4C2×D411yescharacteristic
535C23×C4C2×D411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×Q16—41no—
545C2×SD16—22no—
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×SD16—41no—
556C2×SD16—41no—
557C2×M16—22no—
558C2×M16—22no—
559C2×M16—22no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—41no—
563C2×M16—41no—
564C2×M16—41no—
565C2×M16—41no—
566C22×C8—22no—
567C22×C8—41no—
568C22×C8—41no—
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579C4⋊Q8—41no—
580C4⋊Q8—41no—
581#126—42no—
582#126—42no—
583#125—42no—
584#125—44no—
585#124—42no—
586#124—41no—
587#124—41no—
588#123—42no—
589#123—42no—
590#123—44no—
591#123—82no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—42no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—44no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606C22⋊Q8—41no—
607C22⋊Q8—41no—
608C22⋊Q8—41no—
609C22⋊Q8—41no—
610C22⋊Q8—82no—
611#121—22no—
612#121—22no—
613#121—22no—
614#121—44no—
615#121—41no—
616#121—42no—
617#121—41no—
618#121—41no—
619#120—44no—
620#120—82no—
621C4×Q8—41no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×Q8—41no—
625C4×Q8—41no—
626C4×Q8—41no—
627C4×Q8—44no—
628C4×D4—22no—
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—41no—
635C4×D4—41no—
636#117—41no—
637#117—41no—
638#117—41no—
639#117—41no—
640#117—44no—
641#117—41no—
642#117—41no—
643#117—41no—
644#117—41no—
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⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—44no—
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×C22⋊C4C2×D411yescharacteristic
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C42—22no—
741C2×C42—22no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42C2×D411yescharacteristic
748C2×C42C2×D411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753#107—22no—
754#107—22no—
755#107—41no—
756#107—41no—
757#107—41no—
758#107—41no—
759#107—41no—
760#107—41no—
761#106—22no—
762#106—22no—
763#106—41no—
764#106—41no—
765#106—41no—
766#106—41no—
767C4⋊C8—41no—
768C4⋊C8—41no—
769#103—22no—
770#103—22no—
771#103—22no—
772#103—22no—
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#102—22no—
786#102—22no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795#102—41no—
796#102—41no—
797C22⋊C8—22no—
798C22⋊C8—22no—
799C22⋊C8—22no—
800C22⋊C8—22no—
801C22⋊C8—41no—
802C22⋊C8—41no—
803C22⋊C8—41no—
804C22⋊C8—41no—
805#97—41no—
806C4×C8—41no—
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#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—
844C24—21no—
845C24—21no—
846C24—42no—
847C24—42no—
848C24—81no—
849C24—81no—
850C24—81no—
851C24—81no—
852C24—81no—
853C24C22×D411yescharacteristic
854C24C22×D411yescharacteristic
855C24C22×D411yescharacteristic
856#41—44no—
857#41—44no—
858#41—82no—
859#41—82no—
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—41no—
879C2×Q8—41no—
880C2×Q8—41no—
881C2×Q8—42no—
882C2×Q8—81no—
883C2×Q8—81no—
884C2×D4—22no—
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—41no—
898C2×D4—41no—
899C2×D4—41no—
900C2×D4—41no—
901C2×D4—41no—
902C2×D4—41no—
903C2×D4—41no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—81no—
911C2×D4—82no—
912C2×D4—82no—
913C2×D4—82no—
914C2×D4—82no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D42−1+412yes—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
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—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—41no—
957C22×C4—41no—
958C22×C4—41no—
959C22×C4—41no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4H(5,𝔽2)12yes—
984C22×C4H(5,𝔽2)12yes—
985C22×C4C2511yescharacteristic
986Q16—82no—
987Q16—82no—
988SD16—82no—
989SD16—82no—
990SD16—82no—
991SD16—82no—
992M16—44no—
993M16—44no—
994M16—82no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—82no—
1018C2×C8H(5,𝔽2)12yes—
1019C2×C8H(5,𝔽2)12yes—
1020C4⋊C4—22no—
1021C4⋊C4—22no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—41no—
1045C4⋊C4—41no—
1046C4⋊C4—41no—
1047C4⋊C4—41no—
1048C4⋊C4—41no—
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—81no—
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—
1076C22⋊C4—22no—
1077C22⋊C4—22no—
1078C22⋊C4—22no—
1079C22⋊C4—22no—
1080C22⋊C4—41no—
1081C22⋊C4—41no—
1082C22⋊C4—41no—
1083C22⋊C4—41no—
1084C22⋊C4—41no—
1085C22⋊C4—41no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C42—22no—
1122C42—22no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—42no—
1132C42—42no—
1133C42—81no—
1134C42—81no—
1135C42—81no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
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—21no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—84no—
1171C23—84no—
1172C23—162no—
1173C23—162no—
1174C23—162no—
1175C23—162no—
1176C23—162no—
1177C23#53412yes—
1178C23C23×D411yescharacteristic
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—82no—
1192Q8—84no—
1193D4—22no—
1194D4—22no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—82no—
1202D4—82no—
1203D4—82no—
1204D4—84no—
1205D4—84no—
1206D4—162no—
1207D4—162no—
1208D4—162no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—44no—
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—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—84no—
1297C2×C4—82no—
1298C2×C4—162no—
1299C2×C4—162no—
1300C2×C4—162no—
1301C2×C4#53412yes—
1302C2×C4C2×H(5,𝔽2)11yescharacteristic
1303C2×C4C2×H(5,𝔽2)11yescharacteristic
1304C2×C4C2×H(5,𝔽2)11yescharacteristic
1305C2×C4C2×H(5,𝔽2)11yescharacteristic
1306C2×C4C2×2−1+411yescharacteristic
1307C2×C4#58511yescharacteristic
1308C8—22no—
1309C8—22no—
1310C8—41no—
1311C8—41no—
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C22—22no—
1317C22—22no—
1318C22—22no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—42no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—42no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—42no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—168no—
1352C22C2×#53411yescharacteristic
1353C22#348911yescharacteristic
1354C22#349811yescharacteristic
1355C22#358411yescharacteristic
1356C22#358511yescharacteristic
1357C22#358611yescharacteristic
1358C22#358611yescharacteristic
1359C4—22no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4#353411yescharacteristic
1385C4#353411yescharacteristic
1386C4#353611yescharacteristic
1387C4#353611yescharacteristic
1388C2—42no—
1389C2—81no—
1390C2—81no—
1391C2—82no—
1392C2—161no—
1393C2#4195211yescharacteristic
1394C2#6075411yescharacteristic
1395C2#6076711yescharacteristic
1396C2#6219611yescharacteristic
1397C2#6223611yescharacteristic
1398C2#6244611yescharacteristic
1399C2#6246711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#38034C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #37555C2semidirect
3. #32781C2semidirect
4. #32733C2semidirect
5. #32661C2semidirect
6. #32654C2semidirect
7. #32624C2semidirect
8. #32603C2semidirect
9. #30580C2semidirect
10. #30562C2semidirect
11. #30424C2semidirect
12. #30408C2semidirect
13. #30370C2semidirect
14. #30252C2semidirect
15. #30120C2semidirect
16. #29959C2semidirect
17. #29912C2semidirect
18. #29175C2semidirect
19. #28320C2semidirect
20. #26155C2semidirect
21. #26151C2semidirect
22. #25503C2semidirect
23. #25135C2semidirect
24. #25119C2semidirect
25. #24795C2semidirect
26. #24788C2semidirect
27. #24452C2semidirect
28. #24452C2semidirect
29. #23935C2semidirect
30. #23733C2semidirect
31. #22472C2semidirect
33. C2×#533C22semidirect
37. C2×#470C22semidirect
41. C2×#467C22semidirect
47. C2×#436C22semidirect
48. C2×#435C22semidirect
49. C2×#428C22semidirect
50. C2×#428C22semidirect
65. #2628C22semidirect
68. #2621C22semidirect
71. #2581C22semidirect
72. #2581C22semidirect
84. #2417C22semidirect
85. #2417C22semidirect
94. C2×#382C22semidirect
95. #2101C22semidirect
96. #2101C22semidirect
97. #2097C22semidirect
98. #2097C22semidirect
99. #2097C22semidirect
100. #2097C22semidirect
101. #2096C22semidirect
102. #2095C22semidirect
109. #2085C22semidirect
110. #2085C22semidirect
111. #2084C22semidirect
112. #2083C22semidirect
117. #2068C22semidirect
120. #2066C22semidirect
123. #2057C22semidirect
124. #2056C22semidirect
125. #2056C22semidirect
126. #2043C22semidirect
132. #2036C22semidirect
133. #2036C22semidirect
135. #2035C22semidirect
136. #2035C22semidirect
139. #2024C22semidirect
142. #2016C22semidirect
151. #1985C22semidirect
152. #1984C22semidirect
157. #1944C22semidirect
158. #1942C22semidirect
159. #1935C22semidirect
160. #1933C22semidirect
161. #1928C22semidirect
162. #1927C22semidirect
163. #1921C22semidirect
164. #1920C22semidirect
166. #1894C22semidirect
167. #1894C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
179. #1873C22semidirect
180. #1873C22semidirect
185. #1863C22semidirect
186. #1863C22semidirect
191. #1853C22semidirect
192. #1852C22semidirect
193. #1818C22semidirect
194. #1817C22semidirect
195. #1809C22semidirect
196. #1808C22semidirect
201. #1729C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#380342
#375552
#327812
#327332
#326612
#326542
#326242
#326032
#305802
#305622
#304242
#304082
#303702
#302522
#301202
#299592
#299122
#291752
#283202
#261552
#261512
#255032
#251352
#251192
#247952
#247882
#244522
#239352
#237332
#224722