Finite Group Databasebeta

← #6948561

Subgroups — #6948561

Order 512.

1488 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38920C211yesmaximal, characteristic
2#38048C211yesmaximal, characteristic, complemented
3#32754C211yesmaximal, characteristic, complemented
4#32740C211yesmaximal, characteristic, complemented
5#32688C211yesmaximal, characteristic, complemented
6#32591C211yesmaximal, characteristic, complemented
7#32585C211yesmaximal, characteristic, complemented
8#32546C211yesmaximal, characteristic, complemented
9#32465C211yesmaximal, characteristic, complemented
10#31783C211yesmaximal, characteristic, complemented
11#31775C211yesmaximal, characteristic, complemented
12#31735C211yesmaximal, characteristic, complemented
13#30035C211yesmaximal, characteristic, complemented
14#30017C211yesmaximal, characteristic, complemented
15#29979C211yesmaximal, characteristic, complemented
16#29971C211yesmaximal, characteristic, complemented
17#29787C211yesmaximal, characteristic, complemented
18#29251C211yesmaximal, characteristic, complemented
19#29239C211yesmaximal, characteristic, complemented
20#26209C211yesmaximal, characteristic, complemented
21#26207C211yesmaximal, characteristic, complemented
22#25555C211yesmaximal, characteristic, complemented
23#25547C211yesmaximal, characteristic, complemented
24#24964C211yesmaximal, characteristic, complemented
25#24960C211yesmaximal, characteristic, complemented
26#24618C211yesmaximal, characteristic, complemented
27#24614C211yesmaximal, characteristic, complemented
28#24095C211yesmaximal, characteristic, complemented
29#24089C211yesmaximal, characteristic, complemented
30#23668C211yesmaximal, characteristic, complemented
31#21855C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#547C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×#484C2211yescharacteristic
36C2×#481C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#433C2211yescharacteristic
39C22×#106C2211yescharacteristic
40C2×#424C2211yescharacteristic
41#2857C2211yescharacteristic
42#2855C2211yescharacteristic
43#2724—21no—
44#2718—21no—
45#2718—21no—
46#2718—21no—
47#2706—21no—
48#2706—21no—
49#2701—21no—
50#2698—21no—
51#2629C2211yescharacteristic
52#2625C2211yescharacteristic
53#2624C2211yescharacteristic
54#2624C2211yescharacteristic
55#2584C2211yescharacteristic
56#2582C2211yescharacteristic
57#2546C2211yescharacteristic
58#2542—21no—
59#2538C2211yescharacteristic
60#2519—21no—
61#2506—21no—
62#2489—21no—
63#2487C2211yescharacteristic
64#2487C2211yescharacteristic
65#2487C2211yescharacteristic
66#2485C2211yescharacteristic
67#2478—21no—
68#2474—21no—
69#2432—21no—
70#2415C2211yescharacteristic
71#2415C2211yescharacteristic
72#2414C2211yescharacteristic
73#2414C2211yescharacteristic
74#2407—21no—
75#2354C2211yescharacteristic
76#2354C2211yescharacteristic
77#2323C2211yescharacteristic
78#2317C2211yescharacteristic
79#2317C2211yescharacteristic
80#2317C2211yescharacteristic
81C4×#121C2211yescharacteristic
82#2296C2211yescharacteristic
83#2100C2211yescharacteristic
84#2099C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2087C2211yescharacteristic
98#2087C2211yescharacteristic
99#2086C2211yescharacteristic
100#2086C2211yescharacteristic
101#2084C2211yescharacteristic
102#2083C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2077C2211yescharacteristic
106#2076C2211yescharacteristic
107#2075C2211yescharacteristic
108#2075C2211yescharacteristic
109#2072C2211yescharacteristic
110#2071C2211yescharacteristic
111#2068C2211yescharacteristic
112#2068C2211yescharacteristic
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic
115#2066C2211yescharacteristic
116#2066C2211yescharacteristic
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic
119#2059C2211yescharacteristic
120#2059C2211yescharacteristic
121#2059C2211yescharacteristic
122#2058C2211yescharacteristic
123#2058C2211yescharacteristic
124#2057C2211yescharacteristic
125#2055C2211yescharacteristic
126#2055C2211yescharacteristic
127#2035C2211yescharacteristic
128#2035C2211yescharacteristic
129#2035C2211yescharacteristic
130#2035C2211yescharacteristic
131#2034C2211yescharacteristic
132#2034C2211yescharacteristic
133#2033C2211yescharacteristic
134#2033C2211yescharacteristic
135#2025C2211yescharacteristic
136#2024C2211yescharacteristic
137#2000C2211yescharacteristic
138#2000C2211yescharacteristic
139#1985C2211yescharacteristic
140#1984C2211yescharacteristic
141#1955C2211yescharacteristic
142#1954C2211yescharacteristic
143#1944C2211yescharacteristic
144#1943C2211yescharacteristic
145#1942C2211yescharacteristic
146#1941C2211yescharacteristic
147#1936C2211yescharacteristic
148#1935C2211yescharacteristic
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic
151#1928C2211yescharacteristic
152#1926C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1919C2211yescharacteristic
159#1893C2211yescharacteristic
160#1892C2211yescharacteristic
161#1880C2211yescharacteristic
162#1877C2211yescharacteristic
163#1875C2211yescharacteristic
164#1875C2211yescharacteristic
165#1875C2211yescharacteristic
166#1873C2211yescharacteristic
167#1873C2211yescharacteristic
168#1872C2211yescharacteristic
169#1870C2211yescharacteristic
170#1870C2211yescharacteristic
171#1869C2211yescharacteristic
172#1869C2211yescharacteristic
173#1865C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic
178#1862C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1854C2211yescharacteristic
186#1853C2211yescharacteristic
187#1853C2211yescharacteristic
188#1852C2211yescharacteristic
189#1825C2211yescharacteristic
190#1825C2211yescharacteristic
191#1825C2211yescharacteristic
192#1825C2211yescharacteristic
193#1823C2211yescharacteristic
194#1823C2211yescharacteristic
195#1809C2211yescharacteristic
196#1798C2211yescharacteristic
197#1798C2211yescharacteristic
198#1797C2211yescharacteristic
199#1797C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202#1735C2211yescharacteristic
203C22×#41—21no—
204C22×SD16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207#552—42no—
208#552—42no—
209#547—42no—
210#547—42no—
211C2×C4⋊Q8—21no—
212C2×C4⋊Q8C2311yescharacteristic
213#529—42no—
214#529—42no—
215C2×#126—21no—
216C2×#126D411yescharacteristic
217C2×#126D411yescharacteristic
218C2×#125—21no—
219C2×#125D411yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#124D411yescharacteristic
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×#123D411yescharacteristic
226C2×#123D411yescharacteristic
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8D411yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121D411yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C42C2311yescharacteristic
257#484—42no—
258#481—42no—
259#468—42no—
260#433—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#106—42no—
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277#424—42no—
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#399—21no—
315#399—21no—
316#399—21no—
317#399—21no—
318#399—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#395—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#392—21no—
349#392—21no—
350#391—21no—
351#391—21no—
352#391—21no—
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#390—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#384—21no—
421#384—21no—
422#384—21no—
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#382—21no—
426#382—21no—
427#382—21no—
428#381—21no—
429#380—21no—
430#380—21no—
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C22⋊C4—21no—
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
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#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C2×#41—44no—
491C2×#41—82no—
492C2×#41—82no—
493C22×Q8—21no—
494C22×Q8C2×D411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C2×D411yescharacteristic
500C22×D4C2×D411yescharacteristic
501C22×D4C2×D411yescharacteristic
502C22×D4C2411yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C2×D411yescharacteristic
508C23×C4C2×D411yescharacteristic
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C2×SD16—41no—
513C2×SD16—41no—
514C2×SD16—41no—
515C2×M16—22no—
516C2×M16—41no—
517C2×M16—41no—
518C22×C8—22no—
519C22×C8—41no—
520C22×C8—41no—
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531C4⋊Q8—82no—
532#126—42no—
533#126—42no—
534#126—44no—
535#125—41no—
536#125—41no—
537#125—42no—
538#125—44no—
539#124—42no—
540#123—42no—
541#123—42no—
542#123—44no—
543#123—44no—
544#123—44no—
545C22⋊Q8—22no—
546C22⋊Q8—22no—
547C22⋊Q8—22no—
548C22⋊Q8—42no—
549C22⋊Q8—41no—
550C22⋊Q8—41no—
551C22⋊Q8—41no—
552C22⋊Q8—44no—
553C22⋊Q8—82no—
554C22⋊Q8—82no—
555#121—22no—
556#121—22no—
557#121—22no—
558#121—42no—
559#121—41no—
560#121—41no—
561#121—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—82no—
575#117—22no—
576#117—22no—
577#117—22no—
578#117—22no—
579#117—22no—
580#117—22no—
581#117—41no—
582#117—41no—
583#117—44no—
584#117—41no—
585#117—41no—
586#117—41no—
587#117—41no—
588#117—41no—
589#117—41no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—41no—
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—41no—
699C2×C42—41no—
700C2×C42C2×D411yescharacteristic
701C2×C42C2×D411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706#107—22no—
707#107—41no—
708#107—41no—
709#107—41no—
710#107—41no—
711#107—41no—
712#106—22no—
713#106—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718#106—41no—
719#106—41no—
720#106—41no—
721C4⋊C8—41no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724C4⋊C8—41no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727#103—22no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#102—22no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741C22⋊C8—22no—
742C22⋊C8—22no—
743C22⋊C8—41no—
744C22⋊C8—41no—
745C22⋊C8—41no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751#97—41no—
752C4×C8—41no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789C24—21no—
790C24C22×D411yescharacteristic
791C24C22×D411yescharacteristic
792C24C22×D411yescharacteristic
793#41—816no—
794C2×Q8—22no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—41no—
802C2×Q8—41no—
803C2×Q8—42no—
804C2×Q8—42no—
805C2×Q8—42no—
806C2×D4—22no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—41no—
816C2×D4—41no—
817C2×D4—41no—
818C2×D4—41no—
819C2×D4—41no—
820C2×D4—41no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—81no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—81no—
829C2×D4—81no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—41no—
863C22×C4—41no—
864C22×C4—41no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4H(5,𝔽2)12yes—
891C22×C4H(5,𝔽2)12yes—
892C22×C4C2511yescharacteristic
893SD16—82no—
894M16—82no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—44no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C42−1+412yes—
989C4⋊C42−1+412yes—
990C22⋊C4—22no—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—41no—
1037C42—41no—
1038C42—42no—
1039C42—42no—
1040C42—42no—
1041C42—42no—
1042C42—42no—
1043C42—42no—
1044C42—42no—
1045C42—81no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23#53412yes—
1074C23C23×D411yescharacteristic
1075Q8—41no—
1076Q8—41no—
1077Q8—41no—
1078Q8—41no—
1079Q8—82no—
1080Q8—84no—
1081D4—44no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—82no—
1087D4—82no—
1088D4—84no—
1089D4—84no—
1090D4—84no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—82no—
1180C2×C4—84no—
1181C2×C4—82no—
1182C2×C4—84no—
1183C2×C4—84no—
1184C2×C4—84no—
1185C2×C4#53412yes—
1186C2×C4#57712yes—
1187C2×C4C2×H(5,𝔽2)11yescharacteristic
1188C2×C4C2×H(5,𝔽2)11yescharacteristic
1189C2×C4C2×2−1+411yescharacteristic
1190C2×C4C2×2−1+411yescharacteristic
1191C2×C4#58511yescharacteristic
1192C2×C4#58511yescharacteristic
1193C8—41no—
1194C8—41no—
1195C8—41no—
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C8—41no—
1200C8—41no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22C2×#53411yescharacteristic
1230C22#348911yescharacteristic
1231C22#348911yescharacteristic
1232C22C2×#57711yescharacteristic
1233C22#358411yescharacteristic
1234C22#358511yescharacteristic
1235C22#358611yescharacteristic
1236C4—22no—
1237C4—22no—
1238C4—42no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—42no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4#353311yescharacteristic
1263C4#354411yescharacteristic
1264C4#355911yescharacteristic
1265C4#355911yescharacteristic
1266C2—42no—
1267C2—81no—
1268C2—81no—
1269C2—161no—
1270C2#4216611yescharacteristic
1271C2#6075711yescharacteristic
1272C2#6076111yescharacteristic
1273C2#6217311yescharacteristic
1274C2#6218211yescharacteristic
1275C2#6222111yescharacteristic
1276C2#6222411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#38920C2
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. #38048C2semidirect
3. #32754C2semidirect
4. #32740C2semidirect
5. #32688C2semidirect
6. #32591C2semidirect
7. #32585C2semidirect
8. #32546C2semidirect
9. #32465C2semidirect
10. #31783C2semidirect
11. #31775C2semidirect
12. #31735C2semidirect
13. #30035C2semidirect
14. #30017C2semidirect
15. #29979C2semidirect
16. #29971C2semidirect
17. #29787C2semidirect
18. #29251C2semidirect
19. #29239C2semidirect
20. #26209C2semidirect
21. #26207C2semidirect
22. #25555C2semidirect
23. #25547C2semidirect
24. #24964C2semidirect
25. #24960C2semidirect
26. #24618C2semidirect
27. #24614C2semidirect
28. #24095C2semidirect
29. #24089C2semidirect
30. #23668C2semidirect
31. #21855C2semidirect

Maximal subgroups

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

subgroupindex
#389202
#380482
#327542
#327402
#326882
#325912
#325852
#325462
#324652
#317832
#317752
#317352
#300352
#300172
#299792
#299712
#297872
#292512
#292392
#262092
#262072
#255552
#255472
#249642
#249602
#246182
#246142
#240952
#240892
#236682
#218552