Finite Group Databasebeta

← #6562107

Subgroups — #6562107

Order 512.

1618 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38054C211yesmaximal, characteristic, complemented
2#34384C211yesmaximal, characteristic, complemented
3#30163C211yesmaximal, characteristic, complemented
4#30055C211yesmaximal, characteristic, complemented
5#29908C211yesmaximal, characteristic, complemented
6#29510C211yesmaximal, characteristic, complemented
7#29406C211yesmaximal, characteristic, complemented
8#29363C211yesmaximal, characteristic, complemented
9#28172C211yesmaximal, characteristic, complemented
10#27567C211yesmaximal, characteristic, complemented
11#27550C211yesmaximal, characteristic, complemented
12#27439C211yesmaximal, characteristic, complemented
13#27422C211yesmaximal, characteristic, complemented
14#27208C211yesmaximal, characteristic, complemented
15#27193C211yesmaximal, characteristic, complemented
16#26412C211yesmaximal, characteristic, complemented
17#26410C211yesmaximal, characteristic, complemented
18#26180C211yesmaximal, characteristic, complemented
19#26161C211yesmaximal, characteristic, complemented
20#25499C211yesmaximal, characteristic, complemented
21#25088C211yesmaximal, characteristic
22#25084C211yesmaximal, characteristic, complemented
23#23936C211yesmaximal, characteristic
24#23832C211yesmaximal, characteristic, complemented
25#23693C211yesmaximal, characteristic, complemented
26C2×#2071C211yesmaximal, characteristic, complemented
27#23133C211yesmaximal, characteristic, complemented
28#23126C211yesmaximal, characteristic, complemented
29#22874C211yesmaximal, characteristic, complemented
30#22858C211yesmaximal, characteristic
31#22595C211yesmaximal, characteristic, complemented
32C2×#529C2211yescharacteristic
33C2×#467C2211yescharacteristic
34C2×#465C2211yescharacteristic
35C2×#464C2211yescharacteristic
36C2×#463C2211yescharacteristic
37C2×#450C2211yescharacteristic
38C2×#447C2211yescharacteristic
39C2×#442C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×#102C2211yescharacteristic
43#2855C2211yescharacteristic
44#2761—21no—
45#2757—21no—
46#2737—21no—
47#2723—21no—
48#2644C2211yescharacteristic
49#2640C2211yescharacteristic
50#2561—21no—
51#2512C2211yescharacteristic
52#2483—21no—
53#2480—21no—
54#2452C2211yescharacteristic
55#2448C2211yescharacteristic
56#2447C2211yescharacteristic
57#2440C2211yescharacteristic
58#2437—21no—
59#2435C2211yescharacteristic
60#2383—21no—
61#2383—21no—
62#2361C2211yescharacteristic
63#2361C2211yescharacteristic
64#2360C2211yescharacteristic
65#2360C2211yescharacteristic
66#2360C2211yescharacteristic
67#2355C2211yescharacteristic, complemented
68#2354C2211yescharacteristic, complemented
69#2352—21no—
70Q8×C4⋊C4C2211yescharacteristic, complemented
71D4×C4⋊C4—21no—
72D4×C4⋊C4C2211yescharacteristic, complemented
73D4×C22⋊C4C2211yescharacteristic
74#2330C2211yescharacteristic, complemented
75#2330C2211yescharacteristic, complemented
76#2326C2211yescharacteristic
77#2326C2211yescharacteristic, complemented
78#2326C2211yescharacteristic, complemented
79#2322—21no—
80#2322—21no—
81#2319C2211yescharacteristic
82#2317—21no—
83#2314—21no—
84C2×#390C2211yescharacteristic
85C2×#384C2211yescharacteristic
86#2283C2211yescharacteristic
87#2100C2211yescharacteristic, complemented
88#2099C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2096C2211yescharacteristic, complemented
92#2096C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2084C2211yescharacteristic, complemented
97#2072C2211yescharacteristic, complemented
98#2072C2211yescharacteristic, complemented
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic
106#2071C2211yescharacteristic
107#2067C2211yescharacteristic
108#2066C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic, complemented
111#2059C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2054C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic, complemented
117#2026C2211yescharacteristic, complemented
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic
120#2024C2211yescharacteristic, complemented
121#2023C2211yescharacteristic, complemented
122#2015C2211yescharacteristic
123#2015C2211yescharacteristic, complemented
124#2012C2211yescharacteristic
125#2012C2211yescharacteristic
126#2012C2211yescharacteristic
127#1988C2211yescharacteristic, complemented
128#1987C2211yescharacteristic, complemented
129#1983C2211yescharacteristic
130#1983C2211yescharacteristic
131#1972C2211yescharacteristic
132#1968C2211yescharacteristic
133#1936C2211yescharacteristic
134#1935C2211yescharacteristic, complemented
135#1935C2211yescharacteristic, complemented
136#1934C2211yescharacteristic
137#1934C2211yescharacteristic, complemented
138#1933C2211yescharacteristic, complemented
139#1926C2211yescharacteristic
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1925C2211yescharacteristic
143#1920C2211yescharacteristic, complemented
144#1920C2211yescharacteristic, complemented
145#1919C2211yescharacteristic, complemented
146#1919C2211yescharacteristic, complemented
147#1918C2211yescharacteristic, complemented
148#1918C2211yescharacteristic, complemented
149#1917C2211yescharacteristic, complemented
150#1917C2211yescharacteristic, complemented
151#1916C2211yescharacteristic, complemented
152#1916C2211yescharacteristic, complemented
153#1893C2211yescharacteristic
154#1892C2211yescharacteristic
155#1880C2211yescharacteristic
156#1880C2211yescharacteristic
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic, complemented
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1878C2211yescharacteristic, complemented
166#1878C2211yescharacteristic, complemented
167#1878C2211yescharacteristic, complemented
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic, complemented
170#1877C2211yescharacteristic, complemented
171#1874C2211yescharacteristic
172#1872C2211yescharacteristic
173#1872C2211yescharacteristic
174#1872C2211yescharacteristic
175#1865C2211yescharacteristic, complemented
176#1865C2211yescharacteristic, complemented
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic, complemented
180#1862C2211yescharacteristic, complemented
181#1853C2211yescharacteristic
182#1853C2211yescharacteristic
183#1850C2211yescharacteristic
184#1850C2211yescharacteristic
185#1840C2211yescharacteristic, complemented
186#1832C2211yescharacteristic, complemented
187#1817C2211yescharacteristic
188#1803C2211yescharacteristic, complemented
189#1802C2211yescharacteristic, complemented
190#1768C2211yescharacteristic, complemented
191#1763C2211yescharacteristic, complemented
192#1763C2211yescharacteristic, complemented
193#1762C2211yescharacteristic
194C4×#103C2211yescharacteristic, complemented
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic, complemented
197#1752C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199#1746C2211yescharacteristic, complemented
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213#529—24no—
214#529—24no—
215C2×#126—21no—
216C2×#126—21no—
217C2×#125C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#123—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×#117—21no—
240C2×#117—21no—
241C22×C4⋊C4—21no—
242C22×C4⋊C4—21no—
243C22×C4⋊C4—21no—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C42C2311yescharacteristic
251#467—24no—
252#465—24no—
253#464—42no—
254#463—42no—
255#450—24no—
256#447—24no—
257#442—42no—
258C4×SD16—42no—
259C2×#107C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#102—42no—
281C2×#102—42no—
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
298C2×#102C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305#399—21no—
306#398—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#396—21no—
317#396—21no—
318#396—21no—
319#395—21no—
320#394—21no—
321#394—21no—
322#393—21no—
323#393—21no—
324#393—21no—
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#390—21no—
331#390—21no—
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
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#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—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#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#384—21no—
408#384—21no—
409#384—21no—
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#383D411yescharacteristic
416#383D411yescharacteristic
417#382—21no—
418#382D411yescharacteristic
419#382D411yescharacteristic
420#381—21no—
421#381—21no—
422#381—21no—
423#381D411yescharacteristic
424#381D411yescharacteristic
425#380—21no—
426#380—21no—
427#380—21no—
428#380D411yescharacteristic
429#380D411yescharacteristic
430#380C2311yescharacteristic
431#379—21no—
432#379—21no—
433#379—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4C2311yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
448#376C2311yescharacteristic
449#376C2311yescharacteristic
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
490C25—21no—
491C22×Q8—21no—
492C22×Q8C2411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4C2×D411yescharacteristic
514C23×C4C2×D411yescharacteristic
515C23×C4C2411yescharacteristic
516C2×Q16—22no—
517C2×Q16—41no—
518C2×Q16—41no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—41no—
532C2×D8—41no—
533C2×D8—41no—
534C22×C8—22no—
535C22×C8—22no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8—41no—
539C22×C8—41no—
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C4⋊Q8—41no—
549C4⋊Q8—41no—
550#126—28no—
551#126—82no—
552#125—22no—
553#125—22no—
554#124—22no—
555#124—22no—
556#124—22no—
557#124—41no—
558#124—41no—
559#124—41no—
560#123—28no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—82no—
565C22⋊Q8—82no—
566C22⋊Q8#4114yes—
567#121—22no—
568#121#4114yes—
569C4×Q8—22no—
570C4×Q8—22no—
571C4×Q8—41no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×Q8—41no—
576C4×Q8—41no—
577C4×D4—28no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—82no—
589C4×D4—82no—
590#117—28no—
591#117—82no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
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—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—41no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—82no—
630C2×C4⋊C4—82no—
631C2×C4⋊C4—82no—
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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—82no—
683C2×C22⋊C4—82no—
684C2×C22⋊C4—82no—
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C42—21no—
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#106—22no—
710#106—41no—
711#106—41no—
712#106—41no—
713#106—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718#103—22no—
719#103—22no—
720#103—22no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746C22⋊C8—22no—
747C22⋊C8—22no—
748#97—41no—
749#97—41no—
750C4×C8—41no—
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#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793C24—21no—
794C24—21no—
795C24—21no—
796C24—42no—
797C24—42no—
798C24—42no—
799C24—42no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24C22×D411yescharacteristic
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—81no—
816C2×Q8—81no—
817C2×Q8—81no—
818C2×Q8C2×#4112yes—
819C2×D4—24no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—44no—
837C2×D4—44no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—82no—
843C2×D4—82no—
844C2×D4—81no—
845C2×D4C2×#4112yes—
846C2×D4H(5,𝔽2)12yes—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—24no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—22no—
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—41no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
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×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
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×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C2×#4112yes—
908C22×C4C2×#4112yes—
909C22×C4C2511yescharacteristic
910Q16—82no—
911SD16—44no—
912SD16—82no—
913SD16—82no—
914D8—44no—
915D8—82no—
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—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—82no—
941C2×C8—82no—
942C4⋊C4—24no—
943C4⋊C4—24no—
944C4⋊C4—24no—
945C4⋊C4—24no—
946C4⋊C4—22no—
947C4⋊C4—22no—
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—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
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⋊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⋊C4C2×#4112yes—
998C4⋊C4C2×#4112yes—
999C22⋊C4—24no—
1000C22⋊C4—24no—
1001C22⋊C4—24no—
1002C22⋊C4—24no—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—24no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
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—24no—
1039C42—22no—
1040C42—22no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—81no—
1054C42—81no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C42—81no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—22no—
1066C23—22no—
1067C23—41no—
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—84no—
1087C23—84no—
1088C23—84no—
1089C23—84no—
1090C23—162no—
1091C23—162no—
1092C23—162no—
1093C23#52512yes—
1094C23#57712yes—
1095C23#57712yes—
1096C23C23×D411yescharacteristic
1097Q8—22no—
1098Q8—22no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—162no—
1106D4—22no—
1107D4—22no—
1108D4—22no—
1109D4—22no—
1110D4—48no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—84no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
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—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
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—21no—
1164C2×C4—44no—
1165C2×C4—48no—
1166C2×C4—41no—
1167C2×C4—44no—
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—41no—
1202C2×C4—41no—
1203C2×C4—162no—
1204C2×C4—162no—
1205C2×C4—162no—
1206C2×C4—162no—
1207C2×C4—162no—
1208C2×C4—162no—
1209C2×C4—162no—
1210C2×C4#52512yes—
1211C2×C4#57612yes—
1212C2×C4C22×#4111yescharacteristic
1213C2×C4C22×#4111yescharacteristic
1214C2×C4C2×H(5,𝔽2)11yescharacteristic
1215C2×C4#58511yescharacteristic
1216C2×C4#58511yescharacteristic
1217C2×C4#58511yescharacteristic
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C22—22no—
1227C22—22no—
1228C22—22no—
1229C22—22no—
1230C22—22no—
1231C22—22no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
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—168no—
1254C22#312514yes—
1255C22C2×#52511yescharacteristic
1256C22#348811yescharacteristic
1257C22#350011yescharacteristic
1258C22C2×#57611yescharacteristic
1259C22C2×#57711yescharacteristic
1260C22C2×#57711yescharacteristic
1261C22#358611yescharacteristic
1262C4—22no—
1263C4—22no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—42no—
1273C4—42no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—42no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4#351311yescharacteristic
1289C4#351311yescharacteristic
1290C4#352111yescharacteristic
1291C4#352111yescharacteristic
1292C2—24no—
1293C2—82no—
1294C2—82no—
1295C2—161no—
1296C2#3597911yescharacteristic
1297C2C2×#312511yescharacteristic
1298C2#6058411yescharacteristic
1299C2#6200811yescharacteristic
1300C2#6205311yescharacteristic
1301C2#6255011yescharacteristic
1302C2#6260311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38054C2semidirect
2. #34384C2semidirect
3. #30163C2semidirect
4. #30055C2semidirect
5. #29908C2semidirect
6. #29510C2semidirect
7. #29406C2semidirect
8. #29363C2semidirect
9. #28172C2semidirect
10. #27567C2semidirect
11. #27550C2semidirect
12. #27439C2semidirect
13. #27422C2semidirect
14. #27208C2semidirect
15. #27193C2semidirect
16. #26412C2semidirect
17. #26410C2semidirect
18. #26180C2semidirect
19. #26161C2semidirect
20. #25499C2semidirect
22. #25084C2semidirect
24. #23832C2semidirect
25. #23693C2semidirect
26. C2×#2071C2semidirect
27. #23133C2semidirect
28. #23126C2semidirect
29. #22874C2semidirect
31. #22595C2semidirect
67. #2355C22semidirect
68. #2354C22semidirect
70. Q8×C4⋊C4C22semidirect
72. D4×C4⋊C4C22semidirect
74. #2330C22semidirect
75. #2330C22semidirect
77. #2326C22semidirect
78. #2326C22semidirect
87. #2100C22semidirect
88. #2099C22semidirect
89. #2099C22semidirect
90. #2099C22semidirect
91. #2096C22semidirect
92. #2096C22semidirect
93. #2088C22semidirect
94. #2088C22semidirect
95. #2084C22semidirect
96. #2084C22semidirect
97. #2072C22semidirect
98. #2072C22semidirect
108. #2066C22semidirect
110. #2065C22semidirect
111. #2059C22semidirect
116. #2042C22semidirect
117. #2026C22semidirect
120. #2024C22semidirect
121. #2023C22semidirect
123. #2015C22semidirect
127. #1988C22semidirect
128. #1987C22semidirect
134. #1935C22semidirect
135. #1935C22semidirect
137. #1934C22semidirect
138. #1933C22semidirect
143. #1920C22semidirect
144. #1920C22semidirect
145. #1919C22semidirect
146. #1919C22semidirect
147. #1918C22semidirect
148. #1918C22semidirect
149. #1917C22semidirect
150. #1917C22semidirect
151. #1916C22semidirect
152. #1916C22semidirect
159. #1880C22semidirect
165. #1878C22semidirect
166. #1878C22semidirect
167. #1878C22semidirect
169. #1877C22semidirect
170. #1877C22semidirect
175. #1865C22semidirect
176. #1865C22semidirect
179. #1864C22semidirect
180. #1862C22semidirect
185. #1840C22semidirect
186. #1832C22semidirect
188. #1803C22semidirect
189. #1802C22semidirect
190. #1768C22semidirect
191. #1763C22semidirect
192. #1763C22semidirect
194. C4×#103C22semidirect
196. C4×#102C22semidirect
199. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#380542
#343842
#301632
#300552
#299082
#295102
#294062
#293632
#281722
#275672
#275502
#274392
#274222
#272082
#271932
#264122
#264102
#261802
#261612
#254992
#250882
#250842
#239362
#238322
#236932
C2×#20712
#231332
#231262
#228742
#228582
#225952