Finite Group Databasebeta

← #7327235

Subgroups — #7327235

Order 512.

1615 conjugacy classes of subgroups.

The subgroup lattice has 1412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53015C211yesmaximal, characteristic
2#45237C211yesmaximal, characteristic, complemented
3#32117C211yesmaximal, characteristic, complemented
4#32048C211yesmaximal, characteristic, complemented
5#32048C211yesmaximal, characteristic, complemented
6#31741C211yesmaximal, characteristic, complemented
7#31347C211yesmaximal, characteristic, complemented
8#31329C211yesmaximal, characteristic, complemented
9#31272C211yesmaximal, characteristic, complemented
10#31058C211yesmaximal, characteristic, complemented
11#31044C211yesmaximal, characteristic, complemented
12#30794C211yesmaximal, characteristic, complemented
13#30664C211yesmaximal, characteristic, complemented
14#30404C211yesmaximal, characteristic, complemented
15#29899C211yesmaximal, characteristic, complemented
16#29603C211yesmaximal, characteristic, complemented
17#29005C211yesmaximal, characteristic, complemented
18#27796C211yesmaximal, characteristic, complemented
19#27239C211yesmaximal, characteristic, complemented
20#27226C211yesmaximal, characteristic, complemented
21#26793C211yesmaximal, characteristic, complemented
22#26733C211yesmaximal, characteristic, complemented
23#26297C211yesmaximal, characteristic, complemented
24#25715C211yesmaximal, characteristic, complemented
25#25349C211yesmaximal, characteristic, complemented
26#25136C211yesmaximal, characteristic, complemented
27#24886C211yesmaximal, characteristic, complemented
28#24567C211yesmaximal, characteristic, complemented
29#24396C211yesmaximal, characteristic, complemented
30#23982C211yesmaximal, characteristic, complemented
31#22039C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#536C2211yescharacteristic, complemented
34C2×#501C2211yescharacteristic, complemented
35C2×#482C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#477C2211yescharacteristic, complemented
38C2×#475C2211yescharacteristic, complemented
39C2×#468C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#448C2211yescharacteristic
42C2×#448C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#436C2211yescharacteristic
46C2×#418C2211yescharacteristic
47C2×#408C2211yescharacteristic, complemented
48#2840—21no—
49#2819—21no—
50#2819—21no—
51#2819—21no—
52#2785—21no—
53#2716—21no—
54#2710—21no—
55#2706—21no—
56#2694—21no—
57#2670—21no—
58#2670—21no—
59#2670—21no—
60#2615C2211yescharacteristic
61#2615C2211yescharacteristic
62#2563C2211yescharacteristic
63#2563C2211yescharacteristic
64#2563C2211yescharacteristic
65#2554—21no—
66#2550—21no—
67#2538C2211yescharacteristic
68#2502C2211yescharacteristic, complemented
69#2491C2211yescharacteristic
70#2491C2211yescharacteristic
71#2491C2211yescharacteristic
72#2491C2211yescharacteristic
73#2491C2211yescharacteristic
74#2491C2211yescharacteristic
75#2489C2211yescharacteristic, complemented
76#2474—21no—
77#2470—21no—
78#2441C2211yescharacteristic, complemented
79#2423C2211yescharacteristic, complemented
80#2415C2211yescharacteristic
81#2415C2211yescharacteristic
82#2409C2211yescharacteristic
83#2408C2211yescharacteristic
84#2408C2211yescharacteristic
85#2408C2211yescharacteristic
86#2388C2211yescharacteristic
87#2362C2211yescharacteristic, complemented
88#2354C2211yescharacteristic
89Q8×C22⋊C4C2211yescharacteristic, complemented
90#2311C2211yescharacteristic, complemented
91#2094C2211yescharacteristic
92#2094C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic, complemented
95#2077C2211yescharacteristic, complemented
96#2077C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2075C2211yescharacteristic
99#2075C2211yescharacteristic, complemented
100#2075C2211yescharacteristic, complemented
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic
103#2067C2211yescharacteristic
104#2065C2211yescharacteristic
105#2058C2211yescharacteristic, complemented
106#2058C2211yescharacteristic, complemented
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2036C2211yescharacteristic, complemented
112#2036C2211yescharacteristic, complemented
113#2036C2211yescharacteristic, complemented
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic, complemented
119#2035C2211yescharacteristic, complemented
120#2035C2211yescharacteristic, complemented
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2033C2211yescharacteristic
127#2025C2211yescharacteristic
128#2025C2211yescharacteristic
129#2024C2211yescharacteristic, complemented
130#2024C2211yescharacteristic, complemented
131#2024C2211yescharacteristic, complemented
132#2024C2211yescharacteristic, complemented
133#2000C2211yescharacteristic
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic
138#2000C2211yescharacteristic
139#1990C2211yescharacteristic, complemented
140#1990C2211yescharacteristic, complemented
141#1989C2211yescharacteristic, complemented
142#1987C2211yescharacteristic, complemented
143#1973C2211yescharacteristic
144#1968C2211yescharacteristic
145#1968C2211yescharacteristic
146#1968C2211yescharacteristic
147#1955C2211yescharacteristic
148#1954C2211yescharacteristic
149#1948C2211yescharacteristic, complemented
150#1948C2211yescharacteristic, complemented
151#1936C2211yescharacteristic
152#1934C2211yescharacteristic
153#1928C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1927C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1924C2211yescharacteristic, complemented
160#1923C2211yescharacteristic, complemented
161#1923C2211yescharacteristic, complemented
162#1923C2211yescharacteristic, complemented
163#1919C2211yescharacteristic, complemented
164#1918C2211yescharacteristic, complemented
165#1895C2211yescharacteristic
166#1894C2211yescharacteristic
167#1894C2211yescharacteristic
168#1894C2211yescharacteristic, complemented
169#1893C2211yescharacteristic
170#1892C2211yescharacteristic, complemented
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1875C2211yescharacteristic
176#1875C2211yescharacteristic
177#1874C2211yescharacteristic
178#1874C2211yescharacteristic
179#1870C2211yescharacteristic
180#1870C2211yescharacteristic
181#1869C2211yescharacteristic
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic, complemented
185#1854C2211yescharacteristic, complemented
186#1853C2211yescharacteristic, complemented
187#1853C2211yescharacteristic, complemented
188#1850C2211yescharacteristic, complemented
189#1825C2211yescharacteristic
190#1825C2211yescharacteristic, complemented
191#1825C2211yescharacteristic, complemented
192#1809C2211yescharacteristic
193#1809C2211yescharacteristic, complemented
194#1807C2211yescharacteristic, complemented
195#1787C2211yescharacteristic, complemented
196#1787C2211yescharacteristic, complemented
197#1786C2211yescharacteristic
198#1780C2211yescharacteristic, complemented
199C4×#107C2211yescharacteristic, complemented
200#1763C2211yescharacteristic, complemented
201C4×#103C2211yescharacteristic, complemented
202#1753C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#552—42no—
214#552—42no—
215#536—42no—
216#536—42no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#126—21no—
222C2×#125—21no—
223C2×#125C2311yescharacteristic
224C2×#124—21no—
225C2×#124—21no—
226C2×#124—21no—
227C2×#124—21no—
228C2×#124—21no—
229C2×#124—21no—
230C2×#124—21no—
231C2×#123—21no—
232C2×#123—21no—
233C2×#123—21no—
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#120—21no—
247C2×#120—21no—
248C2×#120—21no—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×#117—21no—
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259#501—42no—
260#482—42no—
261#482—42no—
262#477—42no—
263#475—42no—
264#468—42no—
265#465—42no—
266#450—42no—
267#450—42no—
268#448—42no—
269#448—42no—
270#436—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286#418—42no—
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311#408—42no—
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328#400—21no—
329#399—21no—
330#399—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#395—21no—
341#395D411yescharacteristic
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394D411yescharacteristic
354#394D411yescharacteristic
355#394D411yescharacteristic
356#393—21no—
357#393—21no—
358#393—21no—
359#393—21no—
360#393—21no—
361#393—21no—
362#393—21no—
363#393—21no—
364#393—21no—
365#393—21no—
366#393—21no—
367#393—21no—
368#393—21no—
369#393—21no—
370#393—21no—
371#393D411yescharacteristic
372#392—21no—
373#392—21no—
374#392—21no—
375#392—21no—
376#392—21no—
377#392—21no—
378#392—21no—
379#392—21no—
380#392—21no—
381#392D411yescharacteristic
382#392D411yescharacteristic
383#392D411yescharacteristic
384#391—21no—
385#391—21no—
386#391—21no—
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#390—21no—
392#390—21no—
393#390—21no—
394#390—21no—
395#390—21no—
396#390—21no—
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#389—21no—
404#389—21no—
405#389—21no—
406#389—21no—
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#382—21no—
435#382—21no—
436#382—21no—
437#382—21no—
438#380—21no—
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#379—21no—
454#379—21no—
455#379—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4—21no—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
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#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8—21no—
506C22×Q8—21no—
507C22×Q8—22no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8—41no—
512C22×Q8—41no—
513C22×Q8C2×D411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
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×D4—41no—
528C22×D4—41no—
529C22×D4C2×D411yescharacteristic
530C22×D4C2×D411yescharacteristic
531C22×D4C2×D411yescharacteristic
532C22×D4C2×D411yescharacteristic
533C22×D4C2×D411yescharacteristic
534C22×D4C2×D411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2411yescharacteristic
537C23×C4—21no—
538C23×C4—21no—
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C23×C4C2411yescharacteristic
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×M16—22no—
556C2×M16—41no—
557C2×M16—41no—
558C2×M16—41no—
559C2×M16—41no—
560C2×M16—41no—
561C22×C8—41no—
562C22×C8—41no—
563C22×C8—41no—
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C4⋊Q8—41no—
573C4⋊Q8—41no—
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577C4⋊Q8—41no—
578C4⋊Q8—44no—
579#126—44no—
580#125—22no—
581#125—41no—
582#125—44no—
583#124—44no—
584#124—82no—
585#124—82no—
586#124—82no—
587#124—82no—
588#124—82no—
589#124—82no—
590#123—44no—
591#123—44no—
592#123—44no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605#121—41no—
606#121—41no—
607#121—41no—
608#121—41no—
609#121—41no—
610#121—41no—
611#121—41no—
612#121—41no—
613#121—41no—
614#121—41no—
615#121—41no—
616#121—41no—
617#120—82no—
618#120—82no—
619#120—82no—
620C4×Q8—22no—
621C4×Q8—41no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630#117—22no—
631#117—22no—
632#117—44no—
633#117—41no—
634#117—41no—
635#117—41no—
636#117—41no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
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—41no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739#107—22no—
740#107—22no—
741#107—22no—
742#107—41no—
743#106—41no—
744#106—41no—
745#106—41no—
746#106—41no—
747#106—41no—
748#106—41no—
749#106—41no—
750#106—41no—
751C4⋊C8—22no—
752C4⋊C8—41no—
753C4⋊C8—41no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—41no—
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#102—22no—
767#102—22no—
768#102—22no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778C22⋊C8—22no—
779C22⋊C8—22no—
780C22⋊C8—22no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785C22⋊C8—41no—
786C22⋊C8—41no—
787C22⋊C8—41no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791#97—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#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828C24—21no—
829C24—21no—
830C24—42no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24—81no—
836C24—81no—
837C24C22×D411yescharacteristic
838C24C22×D411yescharacteristic
839C24C22×D411yescharacteristic
840C24C22×D411yescharacteristic
841#41—82no—
842#41—82no—
843#41—82no—
844#41—82no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—41no—
857C2×Q8—41no—
858C2×Q8—41no—
859C2×Q8—42no—
860C2×Q8—42no—
861C2×Q8—81no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8—81no—
865C2×Q8—81no—
866C2×Q8—81no—
867C2×Q8—81no—
868C2×Q8—81no—
869C2×Q8—81no—
870C2×Q8—81no—
871C2×Q8—82no—
872C2×Q8—82no—
873C2×Q8—82no—
874C2×Q8—82no—
875C2×Q8H(5,𝔽2)12yes—
876C2×D4—22no—
877C2×D4—22no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—41no—
891C2×D4—41no—
892C2×D4—41no—
893C2×D4—41no—
894C2×D4—41no—
895C2×D4—41no—
896C2×D4—41no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—41no—
900C2×D4—41no—
901C2×D4—41no—
902C2×D4—41no—
903C2×D4—41no—
904C2×D4—41no—
905C2×D4—41no—
906C2×D4—44no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—82no—
911C2×D4—82no—
912C2×D4—82no—
913C2×D4—81no—
914C2×D4—81no—
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×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
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—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—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
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×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C2511yescharacteristic
986SD16—82no—
987SD16—82no—
988SD16—82no—
989SD16—82no—
990M16—82no—
991M16—82no—
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—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—82no—
1016C2×C8H(5,𝔽2)12yes—
1017C4⋊C4—24no—
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—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—41no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
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⋊C4H(5,𝔽2)12yes—
1064C22⋊C4—24no—
1065C22⋊C4—22no—
1066C22⋊C4—22no—
1067C22⋊C4—22no—
1068C22⋊C4—22no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
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—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—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—42no—
1124C42—42no—
1125C42—42no—
1126C42—42no—
1127C42—42no—
1128C42—42no—
1129C42—42no—
1130C42—81no—
1131C42—81no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
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—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—84no—
1175C23—162no—
1176C23—162no—
1177C23—162no—
1178C23—162no—
1179C23—162no—
1180C23—162no—
1181C23C23×D411yescharacteristic
1182Q8—22no—
1183Q8—22no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—82no—
1191Q8—84no—
1192Q8—162no—
1193Q8—162no—
1194Q8—162no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—82no—
1204D4—82no—
1205D4—82no—
1206D4—82no—
1207D4—82no—
1208D4—82no—
1209D4—84no—
1210D4—162no—
1211D4—162no—
1212D4—162no—
1213D4—162no—
1214D4—162no—
1215D4—162no—
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—22no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—22no—
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—21no—
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—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—84no—
1303C2×C4—84no—
1304C2×C4#57712yes—
1305C2×C4#57712yes—
1306C2×C4C2×H(5,𝔽2)11yescharacteristic
1307C2×C4C2×H(5,𝔽2)11yescharacteristic
1308C2×C4C2×H(5,𝔽2)11yescharacteristic
1309C2×C4#58511yescharacteristic
1310C2×C4#58511yescharacteristic
1311C2×C4#58511yescharacteristic
1312C8—22no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—168no—
1363C22#348411yescharacteristic
1364C22#348511yescharacteristic
1365C22#349611yescharacteristic
1366C22C2×#57711yescharacteristic
1367C22C2×#57711yescharacteristic
1368C22#358511yescharacteristic
1369C22#358611yescharacteristic
1370C4—22no—
1371C4—22no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—42no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—41no—
1381C4—42no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4#354011yescharacteristic
1395C4#354511yescharacteristic
1396C4#355811yescharacteristic
1397C4#355811yescharacteristic
1398C2—81no—
1399C2—81no—
1400C2—81no—
1401C2—81no—
1402C2—161no—
1403C2—161no—
1404C2#4793311yescharacteristic
1405C2#6165011yescharacteristic
1406C2#6166411yescharacteristic
1407C2#6175511yescharacteristic
1408C2#6180511yescharacteristic
1409C2#6232111yescharacteristic
1410C2#6234611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#53015C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2388 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #45237C2semidirect
3. #32117C2semidirect
4. #32048C2semidirect
5. #32048C2semidirect
6. #31741C2semidirect
7. #31347C2semidirect
8. #31329C2semidirect
9. #31272C2semidirect
10. #31058C2semidirect
11. #31044C2semidirect
12. #30794C2semidirect
13. #30664C2semidirect
14. #30404C2semidirect
15. #29899C2semidirect
16. #29603C2semidirect
17. #29005C2semidirect
18. #27796C2semidirect
19. #27239C2semidirect
20. #27226C2semidirect
21. #26793C2semidirect
22. #26733C2semidirect
23. #26297C2semidirect
24. #25715C2semidirect
25. #25349C2semidirect
26. #25136C2semidirect
27. #24886C2semidirect
28. #24567C2semidirect
29. #24396C2semidirect
30. #23982C2semidirect
31. #22039C2semidirect
33. C2×#536C22semidirect
34. C2×#501C22semidirect
37. C2×#477C22semidirect
38. C2×#475C22semidirect
47. C2×#408C22semidirect
68. #2502C22semidirect
75. #2489C22semidirect
78. #2441C22semidirect
79. #2423C22semidirect
87. #2362C22semidirect
89. Q8×C22⋊C4C22semidirect
90. #2311C22semidirect
94. #2077C22semidirect
95. #2077C22semidirect
96. #2077C22semidirect
97. #2077C22semidirect
99. #2075C22semidirect
100. #2075C22semidirect
105. #2058C22semidirect
106. #2058C22semidirect
111. #2036C22semidirect
112. #2036C22semidirect
113. #2036C22semidirect
118. #2035C22semidirect
119. #2035C22semidirect
120. #2035C22semidirect
129. #2024C22semidirect
130. #2024C22semidirect
131. #2024C22semidirect
132. #2024C22semidirect
139. #1990C22semidirect
140. #1990C22semidirect
141. #1989C22semidirect
142. #1987C22semidirect
149. #1948C22semidirect
150. #1948C22semidirect
153. #1928C22semidirect
154. #1927C22semidirect
155. #1927C22semidirect
156. #1927C22semidirect
159. #1924C22semidirect
160. #1923C22semidirect
161. #1923C22semidirect
162. #1923C22semidirect
163. #1919C22semidirect
164. #1918C22semidirect
168. #1894C22semidirect
170. #1892C22semidirect
184. #1854C22semidirect
185. #1854C22semidirect
186. #1853C22semidirect
187. #1853C22semidirect
188. #1850C22semidirect
190. #1825C22semidirect
191. #1825C22semidirect
193. #1809C22semidirect
194. #1807C22semidirect
195. #1787C22semidirect
196. #1787C22semidirect
198. #1780C22semidirect
199. C4×#107C22semidirect
200. #1763C22semidirect
201. C4×#103C22semidirect
202. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#530152
#452372
#321172
#320482
#317412
#313472
#313292
#312722
#310582
#310442
#307942
#306642
#304042
#298992
#296032
#290052
#277962
#272392
#272262
#267932
#267332
#262972
#257152
#253492
#251362
#248862
#245672
#243962
#239822
#220392