Finite Group Databasebeta

← #7105465

Subgroups — #7105465

Order 512.

1561 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59318C211yesmaximal, characteristic
2#39632C211yesmaximal, characteristic, complemented
3#32250C211yesmaximal, characteristic, complemented
4#32233C211yesmaximal, characteristic, complemented
5#31954C211yesmaximal, characteristic, complemented
6#31954C211yesmaximal, characteristic, complemented
7#31763C211yesmaximal, characteristic, complemented
8#31762C211yesmaximal, characteristic, complemented
9#31408C211yesmaximal, characteristic, complemented
10#31394C211yesmaximal, characteristic, complemented
11#29157C211yesmaximal, characteristic, complemented
12#28996C211yesmaximal, characteristic, complemented
13#28988C211yesmaximal, characteristic, complemented
14#28105C211yesmaximal, characteristic, complemented
15#28095C211yesmaximal, characteristic, complemented
16#27969C211yesmaximal, characteristic, complemented
17#27721C211yesmaximal, characteristic, complemented
18#27715C211yesmaximal, characteristic, complemented
19#27576C211yesmaximal, characteristic, complemented
20#27565C211yesmaximal, characteristic, complemented
21#26221C211yesmaximal, characteristic, complemented
22#26210C211yesmaximal, characteristic, complemented
23#24939C211yesmaximal, characteristic, complemented
24#24933C211yesmaximal, characteristic, complemented
25#23964C211yesmaximal, characteristic, complemented
26#23961C211yesmaximal, characteristic, complemented
27C2×#2074C211yesmaximal, characteristic, complemented
28#23117C211yesmaximal, characteristic, complemented
29#22493C211yesmaximal, characteristic, complemented
30#22485C211yesmaximal, characteristic, complemented
31#22047C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#547C2211yescharacteristic
34C2×#448C2211yescharacteristic
35C2×#435C2211yescharacteristic
36C2×C8×D4C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39#2857C2211yescharacteristic
40#2806—21no—
41#2804—21no—
42#2788—21no—
43#2788—21no—
44#2706—21no—
45#2698—21no—
46#2646—21no—
47#2553—21no—
48#2550C2211yescharacteristic
49#2535C2211yescharacteristic
50#2511C2211yescharacteristic
51#2511C2211yescharacteristic
52#2502C2211yescharacteristic
53#2502C2211yescharacteristic
54#2492C2211yescharacteristic
55#2492C2211yescharacteristic
56#2488—21no—
57#2487C2211yescharacteristic
58#2486C2211yescharacteristic
59#2450—21no—
60#2450—21no—
61#2442C2211yescharacteristic
62#2439C2211yescharacteristic
63#2430—21no—
64#2425—21no—
65#2420C2211yescharacteristic
66#2420C2211yescharacteristic
67#2419—21no—
68#2417C2211yescharacteristic
69#2417C2211yescharacteristic
70#2409C2211yescharacteristic
71#2409C2211yescharacteristic
72#2352C2211yescharacteristic
73#2349C2211yescharacteristic
74D4×C4⋊C4C2211yescharacteristic
75D4×C4⋊C4C2211yescharacteristic
76#2339—21no—
77#2325—21no—
78C4×#121C2211yescharacteristic
79C4×#121C2211yescharacteristic
80C2×#391C2211yescharacteristic
81C2×#382C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2100C2211yescharacteristic
87#2099C2211yescharacteristic
88#2099C2211yescharacteristic
89#2093C2211yescharacteristic
90#2083C2211yescharacteristic
91#2083C2211yescharacteristic
92#2076C2211yescharacteristic
93#2076C2211yescharacteristic
94#2075C2211yescharacteristic
95#2075C2211yescharacteristic
96#2074C2211yescharacteristic
97#2074C2211yescharacteristic
98#2074C2211yescharacteristic
99#2074C2211yescharacteristic
100#2074C2211yescharacteristic
101#2074C2211yescharacteristic
102#2074C2211yescharacteristic
103#2074C2211yescharacteristic
104#2068C2211yescharacteristic
105#2068C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2057C2211yescharacteristic
109#2036C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic
113#2026C2211yescharacteristic
114#2026C2211yescharacteristic
115#2024C2211yescharacteristic
116#2024C2211yescharacteristic
117#2023C2211yescharacteristic
118#2000C2211yescharacteristic
119#2000C2211yescharacteristic
120#2000C2211yescharacteristic
121#2000C2211yescharacteristic
122#1993C2211yescharacteristic
123#1993C2211yescharacteristic
124#1992C2211yescharacteristic
125#1990C2211yescharacteristic
126#1989C2211yescharacteristic
127#1988C2211yescharacteristic
128#1973C2211yescharacteristic
129#1973C2211yescharacteristic
130#1935C2211yescharacteristic
131#1935C2211yescharacteristic
132#1935C2211yescharacteristic
133#1935C2211yescharacteristic
134#1933C2211yescharacteristic
135#1933C2211yescharacteristic
136#1928C2211yescharacteristic
137#1928C2211yescharacteristic
138#1924C2211yescharacteristic
139#1924C2211yescharacteristic
140#1921C2211yescharacteristic
141#1921C2211yescharacteristic
142#1918C2211yescharacteristic
143#1918C2211yescharacteristic
144#1918C2211yescharacteristic
145#1918C2211yescharacteristic
146#1917C2211yescharacteristic
147#1916C2211yescharacteristic
148#1895C2211yescharacteristic
149#1894C2211yescharacteristic
150#1894C2211yescharacteristic
151#1893C2211yescharacteristic
152#1893C2211yescharacteristic
153#1893C2211yescharacteristic
154#1892C2211yescharacteristic
155#1892C2211yescharacteristic
156#1877C2211yescharacteristic
157#1877C2211yescharacteristic
158#1877C2211yescharacteristic
159#1877C2211yescharacteristic
160#1877C2211yescharacteristic
161#1877C2211yescharacteristic
162#1874C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1873C2211yescharacteristic
166#1873C2211yescharacteristic
167#1872C2211yescharacteristic
168#1872C2211yescharacteristic
169#1870C2211yescharacteristic
170#1869C2211yescharacteristic
171#1869C2211yescharacteristic
172#1869C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1852C2211yescharacteristic
176#1852C2211yescharacteristic
177#1852C2211yescharacteristic
178#1836C2211yescharacteristic
179#1836C2211yescharacteristic
180#1825C2211yescharacteristic
181#1824C2211yescharacteristic
182#1824C2211yescharacteristic
183#1824C2211yescharacteristic
184#1823C2211yescharacteristic
185#1823C2211yescharacteristic
186#1823C2211yescharacteristic
187#1823C2211yescharacteristic
188#1808C2211yescharacteristic
189#1808C2211yescharacteristic
190#1802C2211yescharacteristic
191#1802C2211yescharacteristic
192#1787C2211yescharacteristic
193#1762C2211yescharacteristic
194C4×#102C2211yescharacteristic
195#1753C2211yescharacteristic
196#1752C2211yescharacteristic
197#1749C2211yescharacteristic
198#1736C2211yescharacteristic
199C2×#340C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×#41—21no—
204C23×Q8C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#553—24no—
212#553—42no—
213#547—24no—
214#547—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#126—21no—
218C2×#125C2311yescharacteristic
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121—21no—
230C2×#121D411yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C42C2311yescharacteristic
252#448—24no—
253#435—42no—
254C8×D4—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×#103—42no—
264C2×#103—42no—
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#399—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#395—21no—
323#395—21no—
324#395—21no—
325#394—21no—
326#394—21no—
327#393—21no—
328#393—21no—
329#393—21no—
330#393—21no—
331#393—21no—
332#392—21no—
333#391—21no—
334#391—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#390D411yescharacteristic
349#390C2311yescharacteristic
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389D411yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388D411yescharacteristic
367#388D411yescharacteristic
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#386—21no—
375#386—21no—
376#386—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#386D411yescharacteristic
386#386D411yescharacteristic
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#382—21no—
405#382—21no—
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#381—21no—
411#381—21no—
412#381—21no—
413#380—21no—
414#380—21no—
415#380—21no—
416#380—21no—
417#380—21no—
418#380D411yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4C2311yescharacteristic
435C4×C22⋊C4C2311yescharacteristic
436C2×#95—21no—
437C2×#95—21no—
438C2×#95—21no—
439C2×#95—21no—
440C2×#95—21no—
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
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#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C2×#41—44no—
488C2×#41—44no—
489C2×#41—82no—
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—22no—
494C22×Q8—22no—
495C22×Q8—41no—
496C22×Q8—41no—
497C22×Q8—41no—
498C22×Q8—41no—
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4C2×D411yescharacteristic
505C22×D4C2×D411yescharacteristic
506C22×D4C2×D411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2×D411yescharacteristic
519C23×C4C2×D411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×M16—41no—
530C2×M16—41no—
531C2×M16—41no—
532C22×C8—22no—
533C22×C8—22no—
534C22×C8—41no—
535C22×C8—41no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8—41no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C4⋊Q8—22no—
550C4⋊Q8—41no—
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553#126—44no—
554#125—22no—
555#125—41no—
556#123—44no—
557#123—44no—
558#123—44no—
559#123—82no—
560C22⋊Q8—44no—
561C22⋊Q8—41no—
562C22⋊Q8—41no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—82no—
570#121—24no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—41no—
575#121—41no—
576#121—44no—
577#121#4114yes—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—44no—
591C4×D4—82no—
592C4×D4—82no—
593C4×D4—82no—
594#117—22no—
595#117—41no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
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—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—41no—
690C2×C42—41no—
691C2×C42C2×D411yescharacteristic
692C2×C42C2×D411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697#107—41no—
698#107—41no—
699#107—41no—
700#107—41no—
701#107—41no—
702#107—41no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705#103—22no—
706#103—22no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725C22⋊C8—22no—
726C22⋊C8—22no—
727C22⋊C8—41no—
728C22⋊C8—41no—
729C22⋊C8—41no—
730C22⋊C8—41no—
731C22⋊C8—41no—
732C22⋊C8—41no—
733#97—41no—
734#97—41no—
735#97—41no—
736C4×C8—41no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
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#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786C24—21no—
787C24C22×D411yescharacteristic
788C24C22×D411yescharacteristic
789C24C22×D411yescharacteristic
790#41—816no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—42no—
804C2×Q8—42no—
805C2×Q8—44no—
806C2×Q8—44no—
807C2×Q8—42no—
808C2×Q8—42no—
809C2×Q8—81no—
810C2×Q8—81no—
811C2×Q8—81no—
812C2×Q8—81no—
813C2×Q8—81no—
814C2×Q8—82no—
815C2×Q8—82no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—24no—
820C2×D4—22no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—41no—
829C2×D4—41no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4#13714yes—
839C2×D4C2×#4112yes—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—21no—
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—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C2×#4112yes—
919C22×C4H(5,𝔽2)12yes—
920C22×C4C2511yescharacteristic
921SD16—82no—
922SD16—82no—
923M16—82no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—82no—
949C2×C8—82no—
950C2×C8—82no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4C2×#4112yes—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—24no—
1013C22⋊C4—22no—
1014C22⋊C4—22no—
1015C22⋊C4—22no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4—41no—
1019C22⋊C4—41no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—41no—
1050C42—41no—
1051C42—42no—
1052C42—81no—
1053C42—81no—
1054C42—81no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—22no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23#54612yes—
1080C23C2×#13712yes—
1081C23C2×#13712yes—
1082C23#57612yes—
1083C23C23×D411yescharacteristic
1084Q8—41no—
1085Q8—41no—
1086Q8—41no—
1087Q8—41no—
1088Q8—41no—
1089Q8—41no—
1090Q8—41no—
1091Q8—41no—
1092Q8—84no—
1093Q8—84no—
1094Q8—162no—
1095D4—28no—
1096D4—22no—
1097D4—22no—
1098D4—44no—
1099D4—48no—
1100D4—41no—
1101D4—41no—
1102D4—82no—
1103D4—84no—
1104D4—162no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—22no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
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—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—84no—
1194C2×C4—82no—
1195C2×C4—82no—
1196C2×C4—84no—
1197C2×C4—84no—
1198C2×C4—84no—
1199C2×C4—162no—
1200C2×C4—162no—
1201C2×C4—162no—
1202C2×C4—162no—
1203C2×C4—162no—
1204C2×C4—162no—
1205C2×C4#54612yes—
1206C2×C4C2×#13712yes—
1207C2×C4C22×#4111yescharacteristic
1208C2×C4C2×H(5,𝔽2)11yescharacteristic
1209C2×C4#58511yescharacteristic
1210C2×C4#58511yescharacteristic
1211C2×C4#58511yescharacteristic
1212C2×C4#58511yescharacteristic
1213C8—41no—
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—22no—
1228C22—22no—
1229C22—22no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—42no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—42no—
1242C22—42no—
1243C22—41no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22#331414yes—
1249C22C2×#54611yescharacteristic
1250C22#348511yescharacteristic
1251C22#350011yescharacteristic
1252C22C22×#13711yescharacteristic
1253C22C2×#57611yescharacteristic
1254C22#358411yescharacteristic
1255C22#358611yescharacteristic
1256C4—22no—
1257C4—22no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—42no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4#352111yescharacteristic
1283C4#352111yescharacteristic
1284C4#353311yescharacteristic
1285C4#353311yescharacteristic
1286C2—24no—
1287C2—42no—
1288C2—81no—
1289C2—82no—
1290C2#4445011yescharacteristic
1291C2C2×#331411yescharacteristic
1292C2#6120711yescharacteristic
1293C2#6174211yescharacteristic
1294C2#6175911yescharacteristic
1295C2#6255811yescharacteristic
1296C2#6257711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59318C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39632C2semidirect
3. #32250C2semidirect
4. #32233C2semidirect
5. #31954C2semidirect
6. #31954C2semidirect
7. #31763C2semidirect
8. #31762C2semidirect
9. #31408C2semidirect
10. #31394C2semidirect
11. #29157C2semidirect
12. #28996C2semidirect
13. #28988C2semidirect
14. #28105C2semidirect
15. #28095C2semidirect
16. #27969C2semidirect
17. #27721C2semidirect
18. #27715C2semidirect
19. #27576C2semidirect
20. #27565C2semidirect
21. #26221C2semidirect
22. #26210C2semidirect
23. #24939C2semidirect
24. #24933C2semidirect
25. #23964C2semidirect
26. #23961C2semidirect
27. C2×#2074C2semidirect
28. #23117C2semidirect
29. #22493C2semidirect
30. #22485C2semidirect
31. #22047C2semidirect

Maximal subgroups

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

subgroupindex
#593182
#396322
#322502
#322332
#319542
#317632
#317622
#314082
#313942
#291572
#289962
#289882
#281052
#280952
#279692
#277212
#277152
#275762
#275652
#262212
#262102
#249392
#249332
#239642
#239612
C2×#20742
#231172
#224932
#224852
#220472