Finite Group Databasebeta

← #6506398

Subgroups — #6506398

Order 512.

1620 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37286C211yesmaximal, characteristic, complemented
2#34368C211yesmaximal, characteristic, complemented
3#29169C211yesmaximal, characteristic, complemented
4#28584C211yesmaximal, characteristic, complemented
5#27863C211yesmaximal, characteristic, complemented
6#27856C211yesmaximal, characteristic, complemented
7#27571C211yesmaximal, characteristic, complemented
8#27486C211yesmaximal, characteristic, complemented
9#27438C211yesmaximal, characteristic, complemented
10#27376C211yesmaximal, characteristic, complemented
11#27301C211yesmaximal, characteristic, complemented
12#27190C211yesmaximal, characteristic, complemented
13#27147C211yesmaximal, characteristic, complemented
14#27062C211yesmaximal, characteristic, complemented
15#27003C211yesmaximal, characteristic, complemented
16#26905C211yesmaximal, characteristic, complemented
17#26863C211yesmaximal, characteristic, complemented
18#26770C211yesmaximal, characteristic, complemented
19#26709C211yesmaximal, characteristic, complemented
20#26584C211yesmaximal, characteristic, complemented
21#26382C211yesmaximal, characteristic, complemented
22#26174C211yesmaximal, characteristic, complemented
23#25502C211yesmaximal, characteristic, complemented
24#25496C211yesmaximal, characteristic, complemented
25#24848C211yesmaximal, characteristic, complemented
26#24762C211yesmaximal, characteristic, complemented
27#22199C211yesmaximal, characteristic, complemented
28#22196C211yesmaximal, characteristic, complemented
29#21541C211yesmaximal, characteristic, complemented
30#21524C211yesmaximal, characteristic, complemented
31#21026C211yesmaximal, characteristic, complemented
32C2×#532C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#469C2211yescharacteristic
35C2×#469C2211yescharacteristic
36C2×#466C2211yescharacteristic
37C2×#466C2211yescharacteristic
38C2×#459C2211yescharacteristic
39C2×#442C2211yescharacteristic
40C2×C4×D8C2211yescharacteristic
41C2×#424C2211yescharacteristic
42C2×#405C2211yescharacteristic
43#2854C2211yescharacteristic
44#2854C2211yescharacteristic
45#2781—21no—
46#2781—21no—
47#2718—21no—
48#2718—21no—
49#2705—21no—
50#2705—21no—
51#2693—21no—
52#2693—21no—
53#2629C2211yescharacteristic
54#2619C2211yescharacteristic
55#2512C2211yescharacteristic
56#2512C2211yescharacteristic
57#2509C2211yescharacteristic
58#2509C2211yescharacteristic
59#2454C2211yescharacteristic
60#2454C2211yescharacteristic
61#2445C2211yescharacteristic
62#2445C2211yescharacteristic
63#2379—21no—
64#2379—21no—
65#2369C2211yescharacteristic
66#2369C2211yescharacteristic
67#2366C2211yescharacteristic
68#2366C2211yescharacteristic
69#2354—21no—
70#2354C2211yescharacteristic
71#2354C2211yescharacteristic
72D4×C4⋊C4—21no—
73D4×C4⋊C4C2211yescharacteristic
74D4×C4⋊C4C2211yescharacteristic
75#2324—21no—
76#2324—21no—
77#2324C2211yescharacteristic
78#2324C2211yescharacteristic
79#2324C2211yescharacteristic
80#2324C2211yescharacteristic
81#2324C2211yescharacteristic
82#2324C2211yescharacteristic
83#2311—21no—
84#2311—21no—
85#2285C2211yescharacteristic
86#2285C2211yescharacteristic
87#2100C2211yescharacteristic
88#2100C2211yescharacteristic
89#2099C2211yescharacteristic
90#2094C2211yescharacteristic
91#2093C2211yescharacteristic
92#2093C2211yescharacteristic
93#2088C2211yescharacteristic
94#2087C2211yescharacteristic
95#2085C2211yescharacteristic
96#2083C2211yescharacteristic
97#2083C2211yescharacteristic
98#2073C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2065C2211yescharacteristic
105#2059C2211yescharacteristic
106#2058C2211yescharacteristic
107#2057C2211yescharacteristic
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic
110#2041C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2025C2211yescharacteristic
114#2023C2211yescharacteristic
115#2023C2211yescharacteristic
116#2011C2211yescharacteristic
117#2011C2211yescharacteristic
118#2011C2211yescharacteristic
119#1989C2211yescharacteristic
120#1982C2211yescharacteristic
121#1970C2211yescharacteristic
122#1970C2211yescharacteristic
123#1949C2211yescharacteristic
124#1947C2211yescharacteristic
125#1942C2211yescharacteristic
126#1941C2211yescharacteristic
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1926C2211yescharacteristic
132#1925C2211yescharacteristic
133#1925C2211yescharacteristic
134#1925C2211yescharacteristic
135#1925C2211yescharacteristic
136#1925C2211yescharacteristic
137#1925C2211yescharacteristic
138#1925C2211yescharacteristic
139#1925C2211yescharacteristic
140#1925C2211yescharacteristic
141#1921C2211yescharacteristic
142#1921C2211yescharacteristic
143#1921C2211yescharacteristic
144#1920C2211yescharacteristic
145#1920C2211yescharacteristic
146#1919C2211yescharacteristic
147#1919C2211yescharacteristic
148#1918C2211yescharacteristic
149#1918C2211yescharacteristic
150#1918C2211yescharacteristic
151#1917C2211yescharacteristic
152#1917C2211yescharacteristic
153#1917C2211yescharacteristic
154#1917C2211yescharacteristic
155#1916C2211yescharacteristic
156#1916C2211yescharacteristic
157#1916C2211yescharacteristic
158#1916C2211yescharacteristic
159#1895C2211yescharacteristic
160#1895C2211yescharacteristic
161#1895C2211yescharacteristic
162#1895C2211yescharacteristic
163#1893C2211yescharacteristic
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1808C2211yescharacteristic
190#1808C2211yescharacteristic
191#1804C2211yescharacteristic
192#1802C2211yescharacteristic
193#1776C2211yescharacteristic
194C4×#107C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1729C2211yescharacteristic
200#1729C2211yescharacteristic
201#1728C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×#41—21no—
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#532—24no—
213#532—24no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#126—21no—
218C2×#126—21no—
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×#121—21no—
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117—21no—
242C2×#117—21no—
243C2×#117—21no—
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C22×C4⋊C4—21no—
247C22×C4⋊C4—21no—
248C22×C42C2311yescharacteristic
249#478—42no—
250#469—24no—
251#469—24no—
252#466—24no—
253#466—24no—
254#459—42no—
255#442—42no—
256C4×D8—42no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269#424—42no—
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298#405—42no—
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#399—21no—
308#399—21no—
309#398—21no—
310#398—21no—
311#397—21no—
312#397—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#396—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#392—21no—
326#392—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#390—21no—
332#390—21no—
333#390—21no—
334#390—21no—
335#390—21no—
336#390—21no—
337#390—21no—
338#390—21no—
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#387—21no—
384#387—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#384D411yescharacteristic
412#384D411yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#382—21no—
417#382D411yescharacteristic
418#382D411yescharacteristic
419#382C2311yescharacteristic
420#380—21no—
421#380—21no—
422#380—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380—21no—
427#380D411yescharacteristic
428#380D411yescharacteristic
429#380D411yescharacteristic
430#380D411yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C2×#41—28no—
491C2×#41—82no—
492C2×#41—82no—
493C22×Q8—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4C2×D411yescharacteristic
515C23×C4C2×D411yescharacteristic
516C23×C4C2411yescharacteristic
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—22no—
520C2×D8—22no—
521C2×D8—22no—
522C2×D8—22no—
523C2×D8—41no—
524C2×D8—41no—
525C2×D8—41no—
526C2×D8—41no—
527C2×D8—41no—
528C2×D8—41no—
529C2×M16—22no—
530C2×M16—22no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—22no—
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—22no—
551#127—22no—
552#127—22no—
553#127—41no—
554#127—41no—
555#126—82no—
556#126—82no—
557#125—41no—
558#125—41no—
559#124—28no—
560#123—82no—
561#123—82no—
562#123—82no—
563#123—82no—
564#121—28no—
565#121—22no—
566#121—22no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121#4114yes—
572#121#4114yes—
573C4×D4—28no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—82no—
591C4×D4—82no—
592#117—41no—
593#117—41no—
594#117—41no—
595#117—41no—
596#117—82no—
597#117—82no—
598#117—82no—
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—82no—
621C2×C4⋊C4—82no—
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
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⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C42—22no—
691C2×C42—22no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42C2×D411yescharacteristic
701C2×C42C2×D411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708#107—22no—
709#107—22no—
710#107—22no—
711#107—41no—
712#107—41no—
713#107—41no—
714#107—41no—
715#107—41no—
716#106—22no—
717#106—22no—
718#106—22no—
719#106—41no—
720C4⋊C8—22no—
721C4⋊C8—22no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#97—22no—
749#97—41no—
750C4×C8—22no—
751C4×C8—41no—
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#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24C22×D411yescharacteristic
791#41—816no—
792C2×Q8—24no—
793C2×Q8—81no—
794C2×Q8—81no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
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—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4C2×#4112yes—
842C2×D4C2×#4112yes—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—22no—
854C22×C4—22no—
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—41no—
866C22×C4—41no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C2×#4112yes—
903C22×C4C2×#4112yes—
904C22×C4C2511yescharacteristic
905D8—44no—
906D8—44no—
907D8—82no—
908D8—82no—
909M16—44no—
910M16—82no—
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—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
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—44no—
934C2×C8—82no—
935C2×C8H(5,𝔽2)12yes—
936C2×C82−1+412yes—
937C4⋊C4—24no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
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—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
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—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
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⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4C2×#4112yes—
993C4⋊C4C2×#4112yes—
994C22⋊C4—24no—
995C22⋊C4—24no—
996C22⋊C4—24no—
997C22⋊C4—24no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
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—
1028C22⋊C4—81no—
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—
1038C42—22no—
1039C42—22no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—42no—
1053C42—42no—
1054C42—81no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—22no—
1067C23—22no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23#52512yes—
1095C23C23×D411yescharacteristic
1096Q8—84no—
1097D4—22no—
1098D4—22no—
1099D4—22no—
1100D4—22no—
1101D4—48no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—84no—
1115D4—84no—
1116D4—84no—
1117D4—162no—
1118D4—162no—
1119D4—162no—
1120D4—162no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
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—21no—
1142C2×C4—21no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—44no—
1164C2×C4—44no—
1165C2×C4—48no—
1166C2×C4—48no—
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—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—162no—
1202C2×C4—162no—
1203C2×C4—162no—
1204C2×C4—162no—
1205C2×C4—162no—
1206C2×C4—162no—
1207C2×C4#52512yes—
1208C2×C4#57612yes—
1209C2×C4#57612yes—
1210C2×C4C22×#4111yescharacteristic
1211C2×C4C22×#4111yescharacteristic
1212C2×C4C2×H(5,𝔽2)11yescharacteristic
1213C2×C4C2×2−1+411yescharacteristic
1214C2×C4#58511yescharacteristic
1215C2×C4#58511yescharacteristic
1216C8—22no—
1217C8—22no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C8—41no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22C2×#52511yescharacteristic
1260C22#349611yescharacteristic
1261C22#349711yescharacteristic
1262C22C2×#57611yescharacteristic
1263C22C2×#57611yescharacteristic
1264C22#358511yescharacteristic
1265C22#358611yescharacteristic
1266C4—22no—
1267C4—22no—
1268C4—22no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—42no—
1279C4—42no—
1280C4—41no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4#351311yescharacteristic
1292C4#351511yescharacteristic
1293C4#352011yescharacteristic
1294C4#352111yescharacteristic
1295C2—42no—
1296C2—82no—
1297C2—82no—
1298C2—161no—
1299C2—161no—
1300C2#3536611yescharacteristic
1301C2#6057811yescharacteristic
1302C2#6058411yescharacteristic
1303C2#6234911yescharacteristic
1304C2#6235311yescharacteristic
1305C2#6237311yescharacteristic
1306C2#6238911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37286C2semidirect
2. #34368C2semidirect
3. #29169C2semidirect
4. #28584C2semidirect
5. #27863C2semidirect
6. #27856C2semidirect
7. #27571C2semidirect
8. #27486C2semidirect
9. #27438C2semidirect
10. #27376C2semidirect
11. #27301C2semidirect
12. #27190C2semidirect
13. #27147C2semidirect
14. #27062C2semidirect
15. #27003C2semidirect
16. #26905C2semidirect
17. #26863C2semidirect
18. #26770C2semidirect
19. #26709C2semidirect
20. #26584C2semidirect
21. #26382C2semidirect
22. #26174C2semidirect
23. #25502C2semidirect
24. #25496C2semidirect
25. #24848C2semidirect
26. #24762C2semidirect
27. #22199C2semidirect
28. #22196C2semidirect
29. #21541C2semidirect
30. #21524C2semidirect
31. #21026C2semidirect

Maximal subgroups

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

subgroupindex
#372862
#343682
#291692
#285842
#278632
#278562
#275712
#274862
#274382
#273762
#273012
#271902
#271472
#270622
#270032
#269052
#268632
#267702
#267092
#265842
#263822
#261742
#255022
#254962
#248482
#247622
#221992
#221962
#215412
#215242
#210262