Finite Group Databasebeta

← #6500626

Subgroups — #6500626

Order 512.

1722 conjugacy classes of subgroups.

The subgroup lattice has 1321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35253C211yesmaximal, characteristic, complemented
2#34404C211yesmaximal, characteristic
3#29253C211yesmaximal, characteristic, complemented
4#29252C211yesmaximal, characteristic, complemented
5#29247C211yesmaximal, characteristic, complemented
6#29246C211yesmaximal, characteristic, complemented
7#27690C211yesmaximal, characteristic, complemented
8#27687C211yesmaximal, characteristic, complemented
9#26420C211yesmaximal, characteristic, complemented
10#26418C211yesmaximal, characteristic, complemented
11#26414C211yesmaximal, characteristic, complemented
12#26408C211yesmaximal, characteristic, complemented
13#26348C211yesmaximal, characteristic, complemented
14#26346C211yesmaximal, characteristic, complemented
15#26342C211yesmaximal, characteristic, complemented
16#26336C211yesmaximal, characteristic, complemented
17#26003C211yesmaximal, characteristic, complemented
18#25997C211yesmaximal, characteristic, complemented
19#25995C211yesmaximal, characteristic, complemented
20#25989C211yesmaximal, characteristic, complemented
21#25961C211yesmaximal, characteristic, complemented
22#25959C211yesmaximal, characteristic, complemented
23#25956C211yesmaximal, characteristic, complemented
24#25954C211yesmaximal, characteristic, complemented
25#24311C211yesmaximal, characteristic, complemented
26#24308C211yesmaximal, characteristic, complemented
27#21940C211yesmaximal, characteristic, complemented
28#21931C211yesmaximal, characteristic, complemented
29#21763C211yesmaximal, characteristic
30#20908C211yesmaximal, characteristic
31C2×#1854C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C2×#479C2211yescharacteristic, complemented
36C2×#477C2211yescharacteristic, complemented
37C2×#478C2211yescharacteristic, complemented
38C2×#474C2211yescharacteristic, complemented
39C22×#107C2211yescharacteristic
40C22×#106C2211yescharacteristic
41C2×#416C2211yescharacteristic
42C2×#416C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic
45#2857—21no—
46#2851—21no—
47#2629—21no—
48#2628—21no—
49#2442C2211yescharacteristic
50#2442C2211yescharacteristic
51#2441C2211yescharacteristic
52#2441C2211yescharacteristic
53#2440C2211yescharacteristic
54#2440C2211yescharacteristic
55#2439C2211yescharacteristic
56#2439C2211yescharacteristic
57#2438—21no—
58#2438—21no—
59#2437—21no—
60#2437—21no—
61#2376—21no—
62#2376—21no—
63#2361C2211yescharacteristic
64#2361C2211yescharacteristic
65#2360C2211yescharacteristic
66#2360C2211yescharacteristic
67#2353—21no—
68#2349—21no—
69#2347C2211yescharacteristic
70#2346C2211yescharacteristic
71#2341C2211yescharacteristic
72#2339C2211yescharacteristic
73#2324C2211yescharacteristic
74#2324C2211yescharacteristic
75#2323C2211yescharacteristic
76#2323C2211yescharacteristic
77#2321—21no—
78#2321—21no—
79#2319—21no—
80#2318—21no—
81#2317C2211yescharacteristic
82#2317C2211yescharacteristic
83#2316C2211yescharacteristic
84#2280C2211yescharacteristic
85C2×#380C2211yescharacteristic
86C2×#380C2211yescharacteristic
87#2101C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2095C2211yescharacteristic, complemented
93#2093C2211yescharacteristic, complemented
94#2092C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2087C2211yescharacteristic, complemented
98#2087C2211yescharacteristic, complemented
99#2087C2211yescharacteristic, complemented
100#2086C2211yescharacteristic, complemented
101#2086C2211yescharacteristic, complemented
102#2086C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2068C2211yescharacteristic, complemented
106#2067C2211yescharacteristic, complemented
107#2067C2211yescharacteristic, complemented
108#2067C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2065C2211yescharacteristic, complemented
111#2059C2211yescharacteristic, complemented
112#2059C2211yescharacteristic, complemented
113#2057C2211yescharacteristic, complemented
114#2057C2211yescharacteristic, complemented
115#2026C2211yescharacteristic, complemented
116#2025C2211yescharacteristic, complemented
117#2024C2211yescharacteristic, complemented
118#2023C2211yescharacteristic, complemented
119#1989C2211yescharacteristic, complemented
120#1989C2211yescharacteristic, complemented
121#1988C2211yescharacteristic, complemented
122#1987C2211yescharacteristic, complemented
123#1949C2211yescharacteristic, complemented
124#1949C2211yescharacteristic, complemented
125#1947C2211yescharacteristic, complemented
126#1947C2211yescharacteristic, complemented
127#1921C2211yescharacteristic, complemented
128#1921C2211yescharacteristic, complemented
129#1921C2211yescharacteristic, complemented
130#1920C2211yescharacteristic, complemented
131#1919C2211yescharacteristic, complemented
132#1918C2211yescharacteristic, complemented
133#1918C2211yescharacteristic, complemented
134#1918C2211yescharacteristic, complemented
135#1893C2211yescharacteristic
136#1893C2211yescharacteristic
137#1892C2211yescharacteristic
138#1892C2211yescharacteristic
139#1875C2211yescharacteristic
140#1875C2211yescharacteristic
141#1874C2211yescharacteristic
142#1874C2211yescharacteristic
143#1874C2211yescharacteristic
144#1874C2211yescharacteristic
145#1873C2211yescharacteristic
146#1873C2211yescharacteristic
147#1872C2211yescharacteristic
148#1872C2211yescharacteristic
149#1872C2211yescharacteristic
150#1872C2211yescharacteristic
151#1865C2211yescharacteristic, complemented
152#1864C2211yescharacteristic, complemented
153#1863C2211yescharacteristic, complemented
154#1863C2211yescharacteristic, complemented
155#1863C2211yescharacteristic, complemented
156#1862C2211yescharacteristic, complemented
157#1862C2211yescharacteristic, complemented
158#1862C2211yescharacteristic, complemented
159#1854C2211yescharacteristic
160#1854C2211yescharacteristic
161#1854C2211yescharacteristic
162#1854C2211yescharacteristic
163#1854C2211yescharacteristic
164#1854C2211yescharacteristic
165#1854C2211yescharacteristic
166#1854C2211yescharacteristic
167#1852C2211yescharacteristic
168#1852C2211yescharacteristic
169#1852C2211yescharacteristic
170#1852C2211yescharacteristic
171#1852C2211yescharacteristic
172#1852C2211yescharacteristic
173#1852C2211yescharacteristic
174#1852C2211yescharacteristic
175#1850C2211yescharacteristic
176#1850C2211yescharacteristic
177#1850C2211yescharacteristic
178#1850C2211yescharacteristic
179#1850C2211yescharacteristic
180#1850C2211yescharacteristic
181#1850C2211yescharacteristic
182#1850C2211yescharacteristic
183#1825C2211yescharacteristic
184#1825C2211yescharacteristic
185#1808C2211yescharacteristic
186#1808C2211yescharacteristic
187#1808C2211yescharacteristic
188#1808C2211yescharacteristic
189#1805C2211yescharacteristic, complemented
190#1804C2211yescharacteristic, complemented
191#1803C2211yescharacteristic, complemented
192#1802C2211yescharacteristic, complemented
193#1798C2211yescharacteristic
194#1798C2211yescharacteristic
195#1798C2211yescharacteristic
196#1798C2211yescharacteristic
197#1788C2211yescharacteristic
198#1788C2211yescharacteristic
199#1735C2211yescharacteristic
200#1735C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#544—42no—
210#544—42no—
211C2×C4⋊Q8—21no—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#125—21no—
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217#525—24no—
218#525Q818yescomplemented
219C2×#123—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#120—21no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117—21no—
238C2×#117—21no—
239C2×#117—42no—
240C2×#117—42no—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257C22×C42—21no—
258#479—42no—
259#478—42no—
260#477—42no—
261#474—42no—
262C2×#107—42no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106—42no—
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288#416—42no—
289#416—42no—
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×C22⋊C8—24no—
307C2×C22⋊C8—24no—
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316#400—21no—
317#400—21no—
318#399—21no—
319#399—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#395—21no—
329#395—21no—
330#393—21no—
331#393—21no—
332#391—21no—
333#391—21no—
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#390—21no—
337#390—21no—
338#390—21no—
339#390—21no—
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#389—21no—
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
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#388—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#386—21no—
385#386—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#384—21no—
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#383—21no—
408#382—21no—
409#382—21no—
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#381—21no—
413#381D411yescharacteristic
414#381D411yescharacteristic
415#380—21no—
416#380—21no—
417#380—21no—
418#380—21no—
419#380—21no—
420#380—21no—
421#380—21no—
422#380—21no—
423#380—21no—
424#380D411yescharacteristic
425#380D411yescharacteristic
426#380D411yescharacteristic
427#380D411yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#379D411yescharacteristic
437#379D411yescharacteristic
438C4×C4⋊C4—21no—
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
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450#376—21no—
451C2×#95—21no—
452C2×#95—21no—
453C2×#95—21no—
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#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C25C2×D411yescharacteristic
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41C2×Q814yes—
501C22×Q8—21no—
502C22×Q8—21no—
503C22×Q8C2411yescharacteristic
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
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—41no—
518C23×C4—41no—
519C23×C4—41no—
520C23×C4—41no—
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2×D411yescharacteristic
524C23×C4C2×Q814yes—
525C23×C4#4114yes—
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C22×C8—22no—
530C22×C8—22no—
531C22×C8—22no—
532C22×C8—22no—
533C22×C8—41no—
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—22no—
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553C4⋊Q8—44no—
554#125—22no—
555#125—22no—
556#125—41no—
557#125—41no—
558#125—44no—
559#123—28no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—44no—
563C22⋊Q8—44no—
564C22⋊Q8—82no—
565C22⋊Q8—82no—
566C22⋊Q8C2×Q814yes—
567C22⋊Q8C2×Q814yes—
568#121—22no—
569#121—22no—
570#121C2×Q814yes—
571#121C2×Q814yes—
572#120—28no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×Q8—41no—
576C4×Q8—41no—
577C4×D4—28no—
578C4×D4—28no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—82no—
584C4×D4—82no—
585#117—22no—
586#117—22no—
587#117—22no—
588#117—22no—
589#117—22no—
590#117—41no—
591#117—41no—
592#117—41no—
593#117—41no—
594#117—44no—
595#117—44no—
596#117—41no—
597#117—41no—
598#117—41no—
599#117—41no—
600#117C2×Q814yes—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
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—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
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⋊C4—44no—
687C2×C22⋊C4—82no—
688C2×C22⋊C4—82no—
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—44no—
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#107—22no—
718#107—22no—
719#107—41no—
720#107—41no—
721#107—41no—
722#107—41no—
723#107—41no—
724#107—41no—
725#107—41no—
726#107—41no—
727#107—41no—
728#107—41no—
729#106—22no—
730#106—22no—
731#106—41no—
732#106—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741#103—22no—
742#103—22no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#102—22no—
750#102—22no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757C22⋊C8—22no—
758C22⋊C8—22no—
759C22⋊C8—22no—
760C22⋊C8—22no—
761C22⋊C8—22no—
762C22⋊C8—22no—
763C22⋊C8—22no—
764C22⋊C8—22no—
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—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805C24—22no—
806C24—22no—
807C24—21no—
808C24—41no—
809C24—41no—
810C24—41no—
811C24—41no—
812C24C22⋊Q814yes—
813C24C22×D411yescharacteristic
814C24C22×D411yescharacteristic
815C24C22×D411yescharacteristic
816#41—44no—
817#41—44no—
818#41—82no—
819#41—82no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—42no—
826C2×Q8—42no—
827C2×Q8—81no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8C22×Q812yes—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—24no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4C22×Q812yes—
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—24no—
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—21no—
874C22×C4—21no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
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×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4C22⋊Q814yes—
912C22×C4C22⋊Q814yes—
913C22×C4C22⋊Q814yes—
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×Q812yes—
926C22×C4C22×Q812yes—
927C22×C4C22×Q812yes—
928C22×C4C2×#4112yes—
929C22×C4C2×#4112yes—
930C22×C4C2×#4112yes—
931C22×C4C2511yescharacteristic
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—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—44no—
957C2×C8—44no—
958C2×C8—82no—
959C2×C8—82no—
960C4⋊C4—24no—
961C4⋊C4—24no—
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—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
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⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4C22×Q812yes—
1021C4⋊C4C22×Q812yes—
1022C4⋊C4H(5,𝔽2)12yes—
1023C4⋊C4H(5,𝔽2)12yes—
1024C22⋊C4—24no—
1025C22⋊C4—24no—
1026C22⋊C4—24no—
1027C22⋊C4—24no—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—24no—
1033C22⋊C4—24no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C42—24no—
1060C42—24no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—42no—
1070C42—42no—
1071C42—42no—
1072C42—81no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—28no—
1095C23—22no—
1096C23—44no—
1097C23—44no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—82no—
1105C23—82no—
1106C23—82no—
1107C23—82no—
1108C23C2×C22⋊Q812yes—
1109C23C2×C22⋊Q812yes—
1110C23C2×C22⋊Q812yes—
1111C23#57612yes—
1112C23#57812yes—
1113C23C23×D411yescharacteristic
1114Q8—22no—
1115Q8—22no—
1116Q8—41no—
1117Q8—41no—
1118Q8—162no—
1119Q8—162no—
1120D4—22no—
1121D4—22no—
1122D4—48no—
1123D4—41no—
1124D4—41no—
1125D4—84no—
1126D4—84no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
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—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—44no—
1175C2×C4—44no—
1176C2×C4—44no—
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—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—84no—
1218C2×C4—84no—
1219C2×C4—84no—
1220C2×C4—162no—
1221C2×C4—162no—
1222C2×C4—162no—
1223C2×C4—162no—
1224C2×C4—162no—
1225C2×C4—162no—
1226C2×C4C2×C22⋊Q812yes—
1227C2×C4C2×C22⋊Q812yes—
1228C2×C4C2×C22⋊Q812yes—
1229C2×C4C23×Q811yescharacteristic
1230C2×C4C22×#4111yescharacteristic
1231C2×C4C2×H(5,𝔽2)11yescharacteristic
1232C2×C4C2×H(5,𝔽2)11yescharacteristic
1233C2×C4#58511yescharacteristic
1234C2×C4#58511yescharacteristic
1235C8—41no—
1236C8—41no—
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C8—41no—
1243C22—22no—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—22no—
1251C22—22no—
1252C22—22no—
1253C22—22no—
1254C22—22no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—88no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22#308314yes—
1272C22C22×C22⋊Q811yescharacteristic
1273C22#348411yescharacteristic
1274C22#348511yescharacteristic
1275C22C2×#57611yescharacteristic
1276C22C2×#57811yescharacteristic
1277C22#358411yescharacteristic
1278C22#358411yescharacteristic
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—42no—
1292C4—41no—
1293C4—41no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4#350111yescharacteristic
1306C4#350111yescharacteristic
1307C4#350511yescharacteristic
1308C4#350511yescharacteristic
1309C2—24no—
1310C2—42no—
1311C2—42no—
1312C2—82no—
1313C2#3534911yescharacteristic
1314C2C2×#308311yescharacteristic
1315C2#6048911yescharacteristic
1316C2#6163911yescharacteristic
1317C2#6164211yescharacteristic
1318C2#6177111yescharacteristic
1319C2#6177211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35253C2semidirect
3. #29253C2semidirect
4. #29252C2semidirect
5. #29247C2semidirect
6. #29246C2semidirect
7. #27690C2semidirect
8. #27687C2semidirect
9. #26420C2semidirect
10. #26418C2semidirect
11. #26414C2semidirect
12. #26408C2semidirect
13. #26348C2semidirect
14. #26346C2semidirect
15. #26342C2semidirect
16. #26336C2semidirect
17. #26003C2semidirect
18. #25997C2semidirect
19. #25995C2semidirect
20. #25989C2semidirect
21. #25961C2semidirect
22. #25959C2semidirect
23. #25956C2semidirect
24. #25954C2semidirect
25. #24311C2semidirect
26. #24308C2semidirect
27. #21940C2semidirect
28. #21931C2semidirect
31. C2×#1854C2semidirect
35. C2×#479C22semidirect
36. C2×#477C22semidirect
37. C2×#478C22semidirect
38. C2×#474C22semidirect
87. #2101C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2099C22semidirect
91. #2097C22semidirect
92. #2095C22semidirect
93. #2093C22semidirect
94. #2092C22semidirect
95. #2088C22semidirect
96. #2088C22semidirect
97. #2087C22semidirect
98. #2087C22semidirect
99. #2087C22semidirect
100. #2086C22semidirect
101. #2086C22semidirect
102. #2086C22semidirect
103. #2068C22semidirect
104. #2068C22semidirect
105. #2068C22semidirect
106. #2067C22semidirect
107. #2067C22semidirect
108. #2067C22semidirect
109. #2066C22semidirect
110. #2065C22semidirect
111. #2059C22semidirect
112. #2059C22semidirect
113. #2057C22semidirect
114. #2057C22semidirect
115. #2026C22semidirect
116. #2025C22semidirect
117. #2024C22semidirect
118. #2023C22semidirect
119. #1989C22semidirect
120. #1989C22semidirect
121. #1988C22semidirect
122. #1987C22semidirect
123. #1949C22semidirect
124. #1949C22semidirect
125. #1947C22semidirect
126. #1947C22semidirect
127. #1921C22semidirect
128. #1921C22semidirect
129. #1921C22semidirect
130. #1920C22semidirect
131. #1919C22semidirect
132. #1918C22semidirect
133. #1918C22semidirect
134. #1918C22semidirect
151. #1865C22semidirect
152. #1864C22semidirect
153. #1863C22semidirect
154. #1863C22semidirect
155. #1863C22semidirect
156. #1862C22semidirect
157. #1862C22semidirect
158. #1862C22semidirect
189. #1805C22semidirect
190. #1804C22semidirect
191. #1803C22semidirect
192. #1802C22semidirect
218. #525Q8semidirect

Maximal subgroups

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

subgroupindex
#352532
#344042
#292532
#292522
#292472
#292462
#276902
#276872
#264202
#264182
#264142
#264082
#263482
#263462
#263422
#263362
#260032
#259972
#259952
#259892
#259612
#259592
#259562
#259542
#243112
#243082
#219402
#219312
#217632
#209082
C2×#18542