Finite Group Databasebeta

← #6551945

Subgroups — #6551945

Order 512.

1373 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39177C211yesmaximal, characteristic, complemented
2#34481C211yesmaximal, characteristic
3#30004C211yesmaximal, characteristic, complemented
4#30004C211yesmaximal, characteristic, complemented
5#30000C211yesmaximal, characteristic
6#29203C211yesmaximal, characteristic
7#29199C211yesmaximal, characteristic
8#29196C211yesmaximal, characteristic, complemented
9#28293C211yesmaximal, characteristic
10#28288C211yesmaximal, characteristic
11#28287C211yesmaximal, characteristic, complemented
12#26543C211yesmaximal, characteristic
13#26540C211yesmaximal, characteristic, complemented
14#26535C211yesmaximal, characteristic
15#26479C211yesmaximal, characteristic
16#26474C211yesmaximal, characteristic, complemented
17#26471C211yesmaximal, characteristic
18#26120C211yesmaximal, characteristic, complemented
19#26118C211yesmaximal, characteristic
20#26113C211yesmaximal, characteristic, complemented
21#26055C211yesmaximal, characteristic, complemented
22#26052C211yesmaximal, characteristic
23#26043C211yesmaximal, characteristic, complemented
24#23792C211yesmaximal, characteristic, complemented
25#23788C211yesmaximal, characteristic, complemented
26#23784C211yesmaximal, characteristic
27#22743C211yesmaximal, characteristic, complemented
28#22729C211yesmaximal, characteristic, complemented
29#22723C211yesmaximal, characteristic, complemented
30#22548C211yesmaximal, characteristic
31#22548C211yesmaximal, characteristic
32C2×#556C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#474C2211yescharacteristic
39C2×#446C2211yescharacteristic
40C2×#446C2211yescharacteristic
41#2864C2211yescharacteristic
42#2809—21no—
43#2799—21no—
44#2791—21no—
45#2774—21no—
46#2647C2211yescharacteristic
47#2647C2211yescharacteristic
48#2590—21no—
49#2585—21no—
50#2571C2211yescharacteristic
51#2570C2211yescharacteristic
52#2570C2211yescharacteristic
53#2552C2211yescharacteristic
54#2550C2211yescharacteristic
55#2550C2211yescharacteristic
56#2520—21no—
57#2511—21no—
58#2383—21no—
59#2383—21no—
60#2367C2211yescharacteristic
61#2367C2211yescharacteristic
62#2365C2211yescharacteristic
63#2360—21no—
64#2355C2211yescharacteristic
65#2355C2211yescharacteristic
66Q8×C4⋊C4C2211yescharacteristic
67Q8×C4⋊C4C2211yescharacteristic
68Q8×C4⋊C4C2211yescharacteristic
69D4×C4⋊C4C2211yescharacteristic
70#2347—21no—
71#2334—21no—
72#2334—21no—
73#2331C2211yescharacteristic
74#2330C2211yescharacteristic
75#2326C2211yescharacteristic
76#2326C2211yescharacteristic
77#2323—21no—
78#2320C2211yescharacteristic
79#2320C2211yescharacteristic
80#2317—21no—
81C4×C4⋊Q8C2211yescharacteristic
82C4×#125C2211yescharacteristic
83#2295C2211yescharacteristic
84#2293C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2099C2211yescharacteristic
88#2097C2211yescharacteristic
89#2095C2211yescharacteristic
90#2092C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2087C2211yescharacteristic
98#2087C2211yescharacteristic
99#2086C2211yescharacteristic
100#2086C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2068C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2066C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2066C2211yescharacteristic
113#2066C2211yescharacteristic
114#2066C2211yescharacteristic
115#2066C2211yescharacteristic
116#2065C2211yescharacteristic
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic
119#2059C2211yescharacteristic
120#2059C2211yescharacteristic
121#2057C2211yescharacteristic
122#2026C2211yescharacteristic
123#2025C2211yescharacteristic
124#2024C2211yescharacteristic
125#1983C2211yescharacteristic
126#1983C2211yescharacteristic
127#1983C2211yescharacteristic
128#1983C2211yescharacteristic
129#1981C2211yescharacteristic
130#1981C2211yescharacteristic
131#1960C2211yescharacteristic
132#1960C2211yescharacteristic
133#1959C2211yescharacteristic
134#1959C2211yescharacteristic
135#1958C2211yescharacteristic
136#1958C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1949C2211yescharacteristic
141#1948C2211yescharacteristic
142#1948C2211yescharacteristic
143#1948C2211yescharacteristic
144#1948C2211yescharacteristic
145#1947C2211yescharacteristic
146#1947C2211yescharacteristic
147#1947C2211yescharacteristic
148#1947C2211yescharacteristic
149#1940C2211yescharacteristic
150#1940C2211yescharacteristic
151#1940C2211yescharacteristic
152#1940C2211yescharacteristic
153#1939C2211yescharacteristic
154#1939C2211yescharacteristic
155#1865C2211yescharacteristic
156#1865C2211yescharacteristic
157#1865C2211yescharacteristic
158#1865C2211yescharacteristic
159#1865C2211yescharacteristic
160#1864C2211yescharacteristic
161#1864C2211yescharacteristic
162#1864C2211yescharacteristic
163#1863C2211yescharacteristic
164#1863C2211yescharacteristic
165#1863C2211yescharacteristic
166#1862C2211yescharacteristic
167#1847C2211yescharacteristic
168#1847C2211yescharacteristic
169#1844C2211yescharacteristic
170#1843C2211yescharacteristic
171#1843C2211yescharacteristic
172#1842C2211yescharacteristic
173#1836C2211yescharacteristic
174#1836C2211yescharacteristic
175#1834C2211yescharacteristic
176#1805C2211yescharacteristic
177#1805C2211yescharacteristic
178#1805C2211yescharacteristic
179#1805C2211yescharacteristic
180#1805C2211yescharacteristic
181#1804C2211yescharacteristic
182#1804C2211yescharacteristic
183#1804C2211yescharacteristic
184#1803C2211yescharacteristic
185#1803C2211yescharacteristic
186#1803C2211yescharacteristic
187#1802C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192C4×#107C2211yescharacteristic
193C4×#107C2211yescharacteristic
194#1768C2211yescharacteristic
195#1768C2211yescharacteristic
196#1767C2211yescharacteristic
197#1763C2211yescharacteristic
198#1763C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×#103C2211yescharacteristic
203#556—24no—
204#556Q818yescomplemented
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#126—21no—
208C2×#126—21no—
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#124C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×C22⋊Q8—21no—
214C2×C4×Q8—21no—
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×#117—21no—
226C2×#117—21no—
227C22×C4⋊C4—21no—
228#479—42no—
229#479—42no—
230#479—42no—
231#478—42no—
232#477—42no—
233#474—42no—
234#446—24no—
235#446—24no—
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#395—21no—
317#395—21no—
318#391—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391D411yescharacteristic
325#391D411yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389D411yescharacteristic
349#389D411yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
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#387—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#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387D411yescharacteristic
399#387D411yescharacteristic
400#387D411yescharacteristic
401#387D411yescharacteristic
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#384—21no—
411#384—21no—
412#384—21no—
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#383—21no—
420#383—21no—
421#382—21no—
422#382—21no—
423#382—21no—
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#380—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
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
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455#376C2311yescharacteristic
456#376C2311yescharacteristic
457C43C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488C22×Q8—21no—
489C22×Q8C2×D411yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×Q8C2411yescharacteristic
492C22×D4C2411yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C4⋊Q8—22no—
505C4⋊Q8—22no—
506C4⋊Q8—41no—
507C4⋊Q8C2×Q814yes—
508#126—28no—
509#126—28no—
510#125—22no—
511#125—22no—
512#125—41no—
513#125—41no—
514#124—22no—
515#124—22no—
516#124C2×Q814yes—
517#124C2×Q814yes—
518C22⋊Q8—28no—
519C4×Q8—22no—
520C4×Q8—22no—
521C4×Q8—41no—
522C4×Q8—41no—
523C4×Q8—41no—
524C4×Q8—41no—
525C4×Q8—41no—
526C4×Q8—41no—
527C4×Q8—41no—
528C4×Q8—41no—
529C4×Q8—82no—
530C4×Q8C2×Q814yes—
531C4×Q8C2×Q814yes—
532C4×Q8C2×Q814yes—
533C4×Q8#4114yes—
534C4×D4—22no—
535C4×D4—41no—
536C4×D4—41no—
537C4×D4—41no—
538C4×D4—41no—
539C4×D4C2×Q814yes—
540#117—28no—
541#117—82no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—82no—
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42C2×D411yescharacteristic
631C2×C42C2×D411yescharacteristic
632C2×C42C2×D411yescharacteristic
633C2×C42C2×D411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641#107—22no—
642#107—22no—
643#107—22no—
644#107—22no—
645#107—41no—
646#107—41no—
647#107—41no—
648#107—41no—
649#106—41no—
650#106—41no—
651#106—41no—
652#106—41no—
653#106—41no—
654#106—41no—
655#106—41no—
656#106—41no—
657C4⋊C8—22no—
658C4⋊C8—22no—
659C4⋊C8—22no—
660C4⋊C8—22no—
661C4⋊C8—22no—
662C4⋊C8—22no—
663C4⋊C8—22no—
664C4⋊C8—41no—
665C4⋊C8—41no—
666C4⋊C8—41no—
667C4⋊C8—41no—
668C4⋊C8—41no—
669C4⋊C8—41no—
670C4⋊C8—41no—
671C4⋊C8—41no—
672C4⋊C8—41no—
673#103—22no—
674#103—22no—
675#103—22no—
676#103—22no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#102—22no—
690#102—22no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#97—22no—
698#97—22no—
699#97—22no—
700#97—22no—
701C4×C8—22no—
702C4×C8—22no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760C24—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—41no—
772C2×Q8—41no—
773C2×Q8—42no—
774C2×Q8—81no—
775C2×Q8—81no—
776C2×Q8C22⋊Q814yes—
777C2×Q8C22×Q812yes—
778C2×Q8C22×Q812yes—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4C22×Q812yes—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—24no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—81no—
804C22×C4—81no—
805C22×C4—81no—
806C22×C4—81no—
807C22×C4—81no—
808C22×C4—81no—
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C2511yescharacteristic
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C82−1+412yes—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—41no—
877C4⋊C4—41no—
878C4⋊C4—41no—
879C4⋊C4—41no—
880C4⋊C4—41no—
881C4⋊C4—41no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4C22⋊Q814yes—
918C4⋊C4C22⋊Q814yes—
919C4⋊C4C22⋊Q814yes—
920C4⋊C4C22×Q812yes—
921C4⋊C4H(5,𝔽2)12yes—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—24no—
926C22⋊C4—24no—
927C22⋊C4—42no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C42—24no—
934C42—24no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—41no—
944C42—41no—
945C42—41no—
946C42—41no—
947C42—42no—
948C42—81no—
949C42—81no—
950C42—81no—
951C42—81no—
952C42—81no—
953C42—81no—
954C42—81no—
955C42—81no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42—81no—
960C42C22×Q812yes—
961C42C22×Q812yes—
962C42C22×Q812yes—
963C42C2×#4112yes—
964C42C2×#4112yes—
965C42C2×#4112yes—
966C23—22no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23C23×D411yescharacteristic
974Q8—22no—
975Q8—22no—
976Q8—22no—
977Q8—22no—
978Q8—44no—
979Q8—41no—
980Q8—41no—
981Q8—41no—
982Q8—41no—
983Q8—162no—
984D4—22no—
985D4—22no—
986D4—41no—
987D4—41no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—48no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—162no—
1071C2×C4—162no—
1072C2×C4C2×C22⋊Q812yes—
1073C2×C4C2×C22⋊Q812yes—
1074C2×C4C2×C22⋊Q812yes—
1075C2×C4C2×C22⋊Q812yes—
1076C2×C4C2×C22⋊Q812yes—
1077C2×C4C2×C22⋊Q812yes—
1078C2×C4C23×Q811yescharacteristic
1079C2×C4C22×#4111yescharacteristic
1080C2×C4C2×H(5,𝔽2)11yescharacteristic
1081C2×C4C2×2−1+411yescharacteristic
1082C2×C4#58511yescharacteristic
1083C2×C4#58511yescharacteristic
1084C8—22no—
1085C8—41no—
1086C8—41no—
1087C8—41no—
1088C8—41no—
1089C8—41no—
1090C8—41no—
1091C8—41no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—81no—
1096C22—81no—
1097C22—81no—
1098C22—81no—
1099C22C22×C22⋊Q811yescharacteristic
1100C22#348811yescharacteristic
1101C22#349711yescharacteristic
1102C22#358411yescharacteristic
1103C22#358511yescharacteristic
1104C22#358611yescharacteristic
1105C22#358611yescharacteristic
1106C4—22no—
1107C4—22no—
1108C4—22no—
1109C4—22no—
1110C4—22no—
1111C4—22no—
1112C4—41no—
1113C4—41no—
1114C4—41no—
1115C4—42no—
1116C4—42no—
1117C4—41no—
1118C4—41no—
1119C4—41no—
1120C4—41no—
1121C4—41no—
1122C4—42no—
1123C4—42no—
1124C4—81no—
1125C4—81no—
1126C4—81no—
1127C4—81no—
1128C4—81no—
1129C4—81no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C4—81no—
1135C4#350311yescharacteristic
1136C4#350411yescharacteristic
1137C4#351611yescharacteristic
1138C4#351711yescharacteristic
1139C2—82no—
1140C2#3581611yescharacteristic
1141C2#6049211yescharacteristic
1142C2#6049911yescharacteristic
1143C2#6202411yescharacteristic
1144C2#6208211yescharacteristic
1145C2#6238911yescharacteristic
1146C2#6241211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39177C2semidirect
3. #30004C2semidirect
4. #30004C2semidirect
8. #29196C2semidirect
11. #28287C2semidirect
13. #26540C2semidirect
16. #26474C2semidirect
18. #26120C2semidirect
20. #26113C2semidirect
21. #26055C2semidirect
23. #26043C2semidirect
24. #23792C2semidirect
25. #23788C2semidirect
27. #22743C2semidirect
28. #22729C2semidirect
29. #22723C2semidirect
204. #556Q8semidirect

Maximal subgroups

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

subgroupindex
#391772
#344812
#300042
#300002
#292032
#291992
#291962
#282932
#282882
#282872
#265432
#265402
#265352
#264792
#264742
#264712
#261202
#261182
#261132
#260552
#260522
#260432
#237922
#237882
#237842
#227432
#227292
#227232
#225482