Finite Group Databasebeta

← #7489523

Subgroups — #7489523

Order 512.

1421 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59413C211yesmaximal, characteristic
2#38984C211yesmaximal, characteristic, complemented
3#32661C211yesmaximal, characteristic
4#32656C211yesmaximal, characteristic, complemented
5#32625C211yesmaximal, characteristic, complemented
6#32598C211yesmaximal, characteristic
7#32249C211yesmaximal, characteristic, complemented
8#32234C211yesmaximal, characteristic, complemented
9#31545C211yesmaximal, characteristic, complemented
10#31531C211yesmaximal, characteristic
11#30894C211yesmaximal, characteristic
12#30880C211yesmaximal, characteristic, complemented
13#30836C211yesmaximal, characteristic, complemented
14#30806C211yesmaximal, characteristic, complemented
15#30060C211yesmaximal, characteristic, complemented
16#30046C211yesmaximal, characteristic
17#29394C211yesmaximal, characteristic, complemented
18#29375C211yesmaximal, characteristic
19#27091C211yesmaximal, characteristic
20#27070C211yesmaximal, characteristic
21#27017C211yesmaximal, characteristic, complemented
22#26999C211yesmaximal, characteristic
23#26918C211yesmaximal, characteristic
24#26894C211yesmaximal, characteristic, complemented
25#26610C211yesmaximal, characteristic
26#26599C211yesmaximal, characteristic
27#25943C211yesmaximal, characteristic, complemented
28#25929C211yesmaximal, characteristic
29#24342C211yesmaximal, characteristic
30#24336C211yesmaximal, characteristic, complemented
31#23364C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#491C2211yescharacteristic
35C2×#487C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#477C2211yescharacteristic
38C2×#462C2211yescharacteristic
39C2×#461C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×C4×Q16C2211yescharacteristic
42#2862C2211yescharacteristic
43#2767—21no—
44#2767—21no—
45#2762—21no—
46#2762—21no—
47#2704—21no—
48#2704—21no—
49#2645—21no—
50#2582C2211yescharacteristic
51#2581C2211yescharacteristic
52#2581C2211yescharacteristic
53#2568C2211yescharacteristic
54#2568C2211yescharacteristic
55#2568C2211yescharacteristic
56#2556—21no—
57#2556—21no—
58#2550C2211yescharacteristic
59#2550C2211yescharacteristic
60#2546C2211yescharacteristic
61#2538C2211yescharacteristic
62#2514C2211yescharacteristic
63#2514C2211yescharacteristic
64#2511—21no—
65#2454C2211yescharacteristic
66#2454C2211yescharacteristic
67#2451—21no—
68#2451C2211yescharacteristic
69#2451C2211yescharacteristic
70#2446C2211yescharacteristic
71#2446C2211yescharacteristic
72#2434—21no—
73#2429—21no—
74#2423—21no—
75#2367C2211yescharacteristic
76#2367C2211yescharacteristic
77#2365C2211yescharacteristic
78#2365C2211yescharacteristic
79Q8×C22⋊C4—21no—
80#2320—21no—
81C4×C4⋊Q8C2211yescharacteristic
82C4×C4⋊Q8C2211yescharacteristic
83C4×#124C2211yescharacteristic
84#2295C2211yescharacteristic
85#2101C2211yescharacteristic
86#2097C2211yescharacteristic
87#2097C2211yescharacteristic
88#2096C2211yescharacteristic
89#2096C2211yescharacteristic
90#2092C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2083C2211yescharacteristic
94#2074C2211yescharacteristic
95#2074C2211yescharacteristic
96#2072C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2066C2211yescharacteristic
100#2066C2211yescharacteristic
101#2066C2211yescharacteristic
102#2065C2211yescharacteristic
103#2059C2211yescharacteristic
104#2058C2211yescharacteristic
105#2058C2211yescharacteristic
106#2057C2211yescharacteristic
107#2057C2211yescharacteristic
108#2056C2211yescharacteristic
109#2055C2211yescharacteristic
110#2043C2211yescharacteristic
111#2043C2211yescharacteristic
112#2043C2211yescharacteristic
113#2043C2211yescharacteristic
114#2042C2211yescharacteristic
115#2026C2211yescharacteristic
116#2026C2211yescharacteristic
117#2026C2211yescharacteristic
118#2024C2211yescharacteristic
119#2024C2211yescharacteristic
120#2024C2211yescharacteristic
121#2024C2211yescharacteristic
122#2024C2211yescharacteristic
123#2024C2211yescharacteristic
124#2024C2211yescharacteristic
125#2023C2211yescharacteristic
126#2016C2211yescharacteristic
127#2016C2211yescharacteristic
128#2015C2211yescharacteristic
129#2015C2211yescharacteristic
130#2015C2211yescharacteristic
131#2013C2211yescharacteristic
132#2013C2211yescharacteristic
133#1993C2211yescharacteristic
134#1991C2211yescharacteristic
135#1989C2211yescharacteristic
136#1988C2211yescharacteristic
137#1985C2211yescharacteristic
138#1985C2211yescharacteristic
139#1984C2211yescharacteristic
140#1984C2211yescharacteristic
141#1973C2211yescharacteristic
142#1971C2211yescharacteristic
143#1969C2211yescharacteristic
144#1968C2211yescharacteristic
145#1944C2211yescharacteristic
146#1941C2211yescharacteristic
147#1935C2211yescharacteristic
148#1933C2211yescharacteristic
149#1928C2211yescharacteristic
150#1928C2211yescharacteristic
151#1928C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1927C2211yescharacteristic
156#1927C2211yescharacteristic
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic
159#1921C2211yescharacteristic
160#1921C2211yescharacteristic
161#1921C2211yescharacteristic
162#1921C2211yescharacteristic
163#1920C2211yescharacteristic
164#1919C2211yescharacteristic
165#1917C2211yescharacteristic
166#1917C2211yescharacteristic
167#1917C2211yescharacteristic
168#1917C2211yescharacteristic
169#1916C2211yescharacteristic
170#1916C2211yescharacteristic
171#1916C2211yescharacteristic
172#1916C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1878C2211yescharacteristic
180#1878C2211yescharacteristic
181#1878C2211yescharacteristic
182#1878C2211yescharacteristic
183#1877C2211yescharacteristic
184#1877C2211yescharacteristic
185#1877C2211yescharacteristic
186#1877C2211yescharacteristic
187#1877C2211yescharacteristic
188#1877C2211yescharacteristic
189#1865C2211yescharacteristic
190#1865C2211yescharacteristic
191#1863C2211yescharacteristic
192#1863C2211yescharacteristic
193#1863C2211yescharacteristic
194#1863C2211yescharacteristic
195#1862C2211yescharacteristic
196#1862C2211yescharacteristic
197#1839C2211yescharacteristic
198#1839C2211yescharacteristic
199#1805C2211yescharacteristic
200#1804C2211yescharacteristic
201#1763C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C23×Q8—21no—
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210#557—42no—
211#557—42no—
212D4×Q8—42no—
213D4×Q8—42no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8D411yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×#125—21no—
224C2×#125—21no—
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C4×Q8—21no—
233C2×C4×Q8—21no—
234C2×C4×Q8—21no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246#491—42no—
247#487—42no—
248#479—42no—
249#477—42no—
250#462—42no—
251#461—42no—
252#440—42no—
253C4×Q16—42no—
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
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×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300#401—21no—
301#401—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#399—21no—
315#399—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#395—21no—
334#395—21no—
335#395—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391D411yescharacteristic
350#391D411yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389D411yescharacteristic
377#389D411yescharacteristic
378#389D411yescharacteristic
379#389D411yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#384D411yescharacteristic
419#384C2311yescharacteristic
420#383—21no—
421#383—21no—
422#382—21no—
423#382—21no—
424#382—21no—
425#382—21no—
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#380—21no—
430#380—21no—
431#380—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448#376—21no—
449C43C2311yescharacteristic
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#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
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
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—44no—
495C22×Q8—44no—
496C22×Q8—82no—
497C22×Q8C2×D411yescharacteristic
498C22×Q8C2×D411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C2×Q16—22no—
508C2×Q16—22no—
509C2×Q16—22no—
510C2×Q16—41no—
511C2×Q16—41no—
512C2×Q16—41no—
513C2×Q16—41no—
514C2×Q16—41no—
515C2×Q16—41no—
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C4⋊Q8—22no—
534C4⋊Q8—22no—
535C4⋊Q8—22no—
536C4⋊Q8—22no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543C4⋊Q8—41no—
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547C4⋊Q8—42no—
548C4⋊Q8—44no—
549#125—22no—
550#125—22no—
551#125—41no—
552#125—41no—
553#125—44no—
554#125—44no—
555#124—22no—
556#124—22no—
557C22⋊Q8—44no—
558C22⋊Q8—44no—
559C22⋊Q8—44no—
560C22⋊Q8—82no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×Q8—41no—
576C4×Q8—41no—
577C4×Q8—44no—
578C4×Q8—44no—
579C4×Q8—82no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
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×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42C2×D411yescharacteristic
666C2×C42C2×D411yescharacteristic
667C2×C42C2×D411yescharacteristic
668C2×C42C2×D411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676#107—22no—
677#107—22no—
678#107—41no—
679#107—41no—
680#107—41no—
681#106—41no—
682#106—41no—
683#106—41no—
684#106—41no—
685#106—41no—
686C4⋊C8—41no—
687C4⋊C8—41no—
688C4⋊C8—41no—
689C4⋊C8—41no—
690#103—22no—
691#103—22no—
692#103—22no—
693#103—22no—
694#103—22no—
695#103—22no—
696#103—22no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#103—41no—
703#103—41no—
704#103—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#102—22no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#97—41no—
719#97—41no—
720C4×C8—41no—
721C4×C8—41no—
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#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781C24—21no—
782C2×Q8—24no—
783C2×Q8—22no—
784C2×Q8—22no—
785C2×Q8—22no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—41no—
810C2×Q8—41no—
811C2×Q8—41no—
812C2×Q8—42no—
813C2×Q8—42no—
814C2×Q8—42no—
815C2×Q8—42no—
816C2×Q8—42no—
817C2×Q8—42no—
818C2×Q8—42no—
819C2×Q8—42no—
820C2×Q8—42no—
821C2×Q8—81no—
822C2×Q8—81no—
823C2×Q8—816no—
824C2×Q82−1+412yes—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D42−1+412yes—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C2511yescharacteristic
870Q16—44no—
871Q16—82no—
872Q16—82no—
873SD16—44no—
874SD16—82no—
875SD16—82no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C4⋊C4—24no—
901C4⋊C4—22no—
902C4⋊C4—22no—
903C4⋊C4—22no—
904C4⋊C4—22no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—41no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—41no—
934C4⋊C4—41no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4H(5,𝔽2)12yes—
967C4⋊C4H(5,𝔽2)12yes—
968C22⋊C4—24no—
969C22⋊C4—24no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C42—22no—
980C42—22no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—41no—
996C42—41no—
997C42—42no—
998C42—42no—
999C42—42no—
1000C42—42no—
1001C42—42no—
1002C42—42no—
1003C42—42no—
1004C42—81no—
1005C42—81no—
1006C42—81no—
1007C42—81no—
1008C23—22no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23C23×D411yescharacteristic
1016Q8—22no—
1017Q8—22no—
1018Q8—44no—
1019Q8—48no—
1020Q8—41no—
1021Q8—41no—
1022Q8—41no—
1023Q8—41no—
1024Q8—41no—
1025Q8—41no—
1026Q8—41no—
1027Q8—41no—
1028Q8—41no—
1029Q8—41no—
1030Q8—41no—
1031Q8—41no—
1032Q8—41no—
1033Q8—41no—
1034Q8—82no—
1035Q8—84no—
1036Q8—84no—
1037Q8—84no—
1038D4—22no—
1039D4—22no—
1040D4—41no—
1041D4—41no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—84no—
1127C2×C4—84no—
1128C2×C4—84no—
1129C2×C4#57512yes—
1130C2×C4#57712yes—
1131C2×C4#57812yes—
1132C2×C4C2×H(5,𝔽2)11yescharacteristic
1133C2×C4C2×H(5,𝔽2)11yescharacteristic
1134C2×C4C2×2−1+411yescharacteristic
1135C2×C4C2×2−1+411yescharacteristic
1136C2×C4#58511yescharacteristic
1137C2×C4#58511yescharacteristic
1138C8—41no—
1139C8—41no—
1140C8—41no—
1141C8—41no—
1142C8—41no—
1143C8—41no—
1144C8—41no—
1145C8—41no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22#348411yescharacteristic
1154C22#348611yescharacteristic
1155C22#348711yescharacteristic
1156C22C2×#57511yescharacteristic
1157C22C2×#57711yescharacteristic
1158C22C2×#57811yescharacteristic
1159C22#358611yescharacteristic
1160C4—22no—
1161C4—22no—
1162C4—22no—
1163C4—42no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—42no—
1169C4—42no—
1170C4—41no—
1171C4—41no—
1172C4—41no—
1173C4—41no—
1174C4—41no—
1175C4—41no—
1176C4—41no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4—81no—
1189C4#354111yescharacteristic
1190C4#354111yescharacteristic
1191C4#356111yescharacteristic
1192C4#356111yescharacteristic
1193C2—82no—
1194C2#5201111yescharacteristic
1195C2#6160111yescharacteristic
1196C2#6168311yescharacteristic
1197C2#6183411yescharacteristic
1198C2#6186911yescharacteristic
1199C2#6190511yescharacteristic
1200C2#6192311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #38984C2semidirect
4. #32656C2semidirect
5. #32625C2semidirect
7. #32249C2semidirect
8. #32234C2semidirect
9. #31545C2semidirect
12. #30880C2semidirect
13. #30836C2semidirect
14. #30806C2semidirect
15. #30060C2semidirect
17. #29394C2semidirect
21. #27017C2semidirect
24. #26894C2semidirect
27. #25943C2semidirect
30. #24336C2semidirect
31. #23364C2semidirect

Maximal subgroups

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

subgroupindex
#594132
#389842
#326612
#326562
#326252
#325982
#322492
#322342
#315452
#315312
#308942
#308802
#308362
#308062
#300602
#300462
#293942
#293752
#270912
#270702
#270172
#269992
#269182
#268942
#266102
#265992
#259432
#259292
#243422
#243362
#233642