Finite Group Databasebeta

← #7045320

Subgroups — #7045320

Order 512.

1366 conjugacy classes of subgroups.

The subgroup lattice has 1181 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59425C211yesmaximal, characteristic
2#59321C211yesmaximal, characteristic
3#32602C211yesmaximal, characteristic, complemented
4#32557C211yesmaximal, characteristic, complemented
5#32497C211yesmaximal, characteristic, complemented
6#32434C211yesmaximal, characteristic, complemented
7#32235C211yesmaximal, characteristic, complemented
8#31964C211yesmaximal, characteristic, complemented
9#31664C211yesmaximal, characteristic, complemented
10#30834C211yesmaximal, characteristic, complemented
11#28124C211yesmaximal, characteristic
12#27699C211yesmaximal, characteristic
13#27681C211yesmaximal, characteristic
14#27570C211yesmaximal, characteristic, complemented
15#27382C211yesmaximal, characteristic, complemented
16#27268C211yesmaximal, characteristic
17#26756C211yesmaximal, characteristic, complemented
18#26333C211yesmaximal, characteristic, complemented
19#26171C211yesmaximal, characteristic, complemented
20#25998C211yesmaximal, characteristic
21#25957C211yesmaximal, characteristic
22#25333C211yesmaximal, characteristic, complemented
23#25208C211yesmaximal, characteristic
24#25082C211yesmaximal, characteristic
25#25001C211yesmaximal, characteristic, complemented
26#24687C211yesmaximal, characteristic, complemented
27C2×#2072C211yesmaximal, characteristic
28#22934C211yesmaximal, characteristic
29#22871C211yesmaximal, characteristic
30#22291C211yesmaximal, characteristic
31#22183C211yesmaximal, characteristic
32C2×#491C2211yescharacteristic
33C2×#483C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#467C2211yescharacteristic
36C2×#462C2211yescharacteristic
37C2×#451C2211yescharacteristic
38C2×C4×Q16C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41#2791—21no—
42#2791—21no—
43#2789—21no—
44#2758—21no—
45#2605—21no—
46#2588—21no—
47#2582C2211yescharacteristic
48#2581C2211yescharacteristic
49#2568C2211yescharacteristic
50#2565C2211yescharacteristic
51#2565C2211yescharacteristic
52#2552—21no—
53#2552C2211yescharacteristic
54#2514C2211yescharacteristic
55#2514C2211yescharacteristic
56#2511—21no—
57#2506C2211yescharacteristic
58#2506C2211yescharacteristic
59#2503C2211yescharacteristic
60#2502—21no—
61#2493—21no—
62#2493—21no—
63#2473—21no—
64#2473—21no—
65#2446C2211yescharacteristic
66#2446C2211yescharacteristic
67#2442C2211yescharacteristic
68#2442C2211yescharacteristic
69#2438—21no—
70#2434C2211yescharacteristic
71#2365C2211yescharacteristic
72#2360C2211yescharacteristic
73#2360C2211yescharacteristic
74#2356C2211yescharacteristic
75#2355C2211yescharacteristic
76Q8×C4⋊C4C2211yescharacteristic
77#2345—21no—
78#2344C2211yescharacteristic
79#2343—21no—
80Q8×C22⋊C4C2211yescharacteristic
81C4×C22⋊Q8C2211yescharacteristic
82C4×C22⋊Q8C2211yescharacteristic
83C4×C22⋊Q8C2211yescharacteristic
84C2×#391C2211yescharacteristic
85C2×#384C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2100C2211yescharacteristic
90#2100C2211yescharacteristic
91#2097C2211yescharacteristic
92#2095C2211yescharacteristic
93#2095C2211yescharacteristic
94#2088C2211yescharacteristic
95#2087C2211yescharacteristic
96#2085C2211yescharacteristic
97#2074C2211yescharacteristic
98#2074C2211yescharacteristic
99#2074C2211yescharacteristic
100#2072C2211yescharacteristic
101#2072C2211yescharacteristic
102#2072C2211yescharacteristic
103#2072C2211yescharacteristic
104#2072C2211yescharacteristic
105#2072C2211yescharacteristic
106#2072C2211yescharacteristic
107#2072C2211yescharacteristic
108#2068C2211yescharacteristic
109#2068C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2066C2211yescharacteristic
113#2066C2211yescharacteristic
114#2059C2211yescharacteristic
115#2056C2211yescharacteristic
116#2056C2211yescharacteristic
117#2056C2211yescharacteristic
118#2056C2211yescharacteristic
119#2043C2211yescharacteristic
120#2043C2211yescharacteristic
121#2043C2211yescharacteristic
122#2026C2211yescharacteristic
123#2026C2211yescharacteristic
124#2026C2211yescharacteristic
125#2016C2211yescharacteristic
126#1991C2211yescharacteristic
127#1989C2211yescharacteristic
128#1985C2211yescharacteristic
129#1984C2211yescharacteristic
130#1981C2211yescharacteristic
131#1969C2211yescharacteristic
132#1960C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1947C2211yescharacteristic
136#1947C2211yescharacteristic
137#1944C2211yescharacteristic
138#1940C2211yescharacteristic
139#1939C2211yescharacteristic
140#1935C2211yescharacteristic
141#1935C2211yescharacteristic
142#1935C2211yescharacteristic
143#1933C2211yescharacteristic
144#1933C2211yescharacteristic
145#1933C2211yescharacteristic
146#1928C2211yescharacteristic
147#1928C2211yescharacteristic
148#1928C2211yescharacteristic
149#1927C2211yescharacteristic
150#1927C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1921C2211yescharacteristic
155#1920C2211yescharacteristic
156#1919C2211yescharacteristic
157#1919C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1917C2211yescharacteristic
161#1917C2211yescharacteristic
162#1916C2211yescharacteristic
163#1916C2211yescharacteristic
164#1892C2211yescharacteristic
165#1892C2211yescharacteristic
166#1878C2211yescharacteristic
167#1878C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic
176#1865C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1863C2211yescharacteristic
180#1863C2211yescharacteristic
181#1863C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1850C2211yescharacteristic
185#1850C2211yescharacteristic
186#1835C2211yescharacteristic
187#1823C2211yescharacteristic
188#1807C2211yescharacteristic
189#1805C2211yescharacteristic
190#1805C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1797C2211yescharacteristic
194#1787C2211yescharacteristic
195#1776C2211yescharacteristic
196#1763C2211yescharacteristic
197C4×#103C2211yescharacteristic
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#125—21no—
212C2×#125—21no—
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×C22⋊Q8D411yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×#117—21no—
226C22×C4⋊C4—21no—
227C22×C4⋊C4—21no—
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C42C2311yescharacteristic
232#491—42no—
233#483—24no—
234#479—42no—
235#467—24no—
236#462—42no—
237#451—24no—
238C4×Q16—42no—
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×#103—42no—
255C2×#103—42no—
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288#401—21no—
289#401—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#398—21no—
304#398—21no—
305#398—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#398—21no—
317#395—21no—
318#395—21no—
319#395—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391D411yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389D411yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—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#387D411yescharacteristic
387#387D411yescharacteristic
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385D411yescharacteristic
397#385D411yescharacteristic
398#384—21no—
399#384—21no—
400#384—21no—
401#384—21no—
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#383—21no—
407#383—21no—
408#383—21no—
409#382—21no—
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#381—21no—
415#381—21no—
416#381—21no—
417#380—21no—
418#380—21no—
419#380—21no—
420#380D411yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4C2311yescharacteristic
443C4×C22⋊C4C2311yescharacteristic
444#376—21no—
445C2×#95—21no—
446C2×#95—21no—
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
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#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
487C22×Q8—21no—
488C22×Q8—22no—
489C22×Q8—22no—
490C22×Q8—22no—
491C22×Q8—41no—
492C22×Q8—41no—
493C22×Q8—41no—
494C22×Q8C2×D411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C2×D411yescharacteristic
504C23×C4C2×D411yescharacteristic
505C23×C4C2411yescharacteristic
506C2×Q16—22no—
507C2×Q16—22no—
508C2×Q16—22no—
509C2×Q16—22no—
510C2×Q16—41no—
511C2×Q16—41no—
512C2×Q16—41no—
513C2×Q16—41no—
514C2×Q16—41no—
515C22×C8—22no—
516C22×C8—22no—
517C22×C8—41no—
518C22×C8—41no—
519C22×C8—41no—
520C22×C8—41no—
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C4⋊Q8—22no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533#125—41no—
534#125—41no—
535#125—41no—
536#125—41no—
537#125—82no—
538#125—82no—
539C22⋊Q8—22no—
540C22⋊Q8—22no—
541C22⋊Q8—22no—
542C22⋊Q8—42no—
543C22⋊Q8#4114yes—
544C4×Q8—22no—
545C4×Q8—41no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×Q8—41no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×Q8—41no—
557C4×Q8—41no—
558#117—44no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
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—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
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—41no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—44no—
603C2×C4⋊C4—82no—
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C22⋊C4C2×D411yescharacteristic
631C2×C22⋊C4C2×D411yescharacteristic
632C2×C22⋊C4C2×D411yescharacteristic
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—41no—
646C2×C42—41no—
647C2×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655#107—22no—
656#107—41no—
657#107—41no—
658#107—41no—
659#107—41no—
660#106—22no—
661#106—22no—
662#106—41no—
663#106—41no—
664C4⋊C8—41no—
665C4⋊C8—41no—
666C4⋊C8—41no—
667C4⋊C8—41no—
668C4⋊C8—41no—
669C4⋊C8—41no—
670#103—22no—
671#103—22no—
672#103—22no—
673#103—22no—
674#103—22no—
675#103—22no—
676#103—22no—
677#103—22no—
678#103—22no—
679#103—22no—
680#103—22no—
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#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696C22⋊C8—22no—
697C22⋊C8—22no—
698#97—41no—
699#97—41no—
700C4×C8—41no—
701C4×C8—41no—
702#95—21no—
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#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#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766C24C22×D411yescharacteristic
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—41no—
791C2×Q8—41no—
792C2×Q8—42no—
793C2×Q8—44no—
794C2×Q8—44no—
795C2×Q8—42no—
796C2×Q8—81no—
797C2×Q8—82no—
798C2×Q8—82no—
799C2×Q8C2×#4112yes—
800C2×Q8H(5,𝔽2)12yes—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C2×#4112yes—
853C22×C42−1+412yes—
854C22×C4C2511yescharacteristic
855Q16—44no—
856Q16—82no—
857Q16—82no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—82no—
883C2×C8—82no—
884C4⋊C4—24no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4C2×#4112yes—
954C22⋊C4—24no—
955C22⋊C4—22no—
956C22⋊C4—22no—
957C22⋊C4—22no—
958C22⋊C4—22no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—41no—
975C42—41no—
976C42—42no—
977C42—42no—
978C42—42no—
979C42—42no—
980C42—42no—
981C42—42no—
982C42—81no—
983C42—81no—
984C42—81no—
985C42—81no—
986C42—81no—
987C42—81no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23#54812yes—
993C23#57512yes—
994C23#57812yes—
995C23C23×D411yescharacteristic
996Q8—22no—
997Q8—22no—
998Q8—22no—
999Q8—22no—
1000Q8—41no—
1001Q8—41no—
1002Q8—41no—
1003Q8—41no—
1004Q8—41no—
1005Q8—41no—
1006Q8—41no—
1007Q8—41no—
1008Q8—41no—
1009Q8—41no—
1010Q8—41no—
1011Q8—41no—
1012Q8—82no—
1013Q8—84no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
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—44no—
1058C2×C4—44no—
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—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
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—84no—
1105C2×C4—84no—
1106C2×C4—162no—
1107C2×C4—162no—
1108C2×C4#54812yes—
1109C2×C4#57712yes—
1110C2×C4#57812yes—
1111C2×C4C22×#4111yescharacteristic
1112C2×C4C2×H(5,𝔽2)11yescharacteristic
1113C2×C4C2×2−1+411yescharacteristic
1114C2×C4#58511yescharacteristic
1115C2×C4#58511yescharacteristic
1116C2×C4#58511yescharacteristic
1117C8—41no—
1118C8—41no—
1119C8—41no—
1120C8—41no—
1121C8—41no—
1122C8—41no—
1123C8—41no—
1124C8—41no—
1125C22—22no—
1126C22—22no—
1127C22—22no—
1128C22—22no—
1129C22—22no—
1130C22—22no—
1131C22#337714yes—
1132C22C2×#54811yescharacteristic
1133C22#348511yescharacteristic
1134C22#348811yescharacteristic
1135C22C2×#57511yescharacteristic
1136C22C2×#57711yescharacteristic
1137C22C2×#57811yescharacteristic
1138C22C2×#57811yescharacteristic
1139C4—22no—
1140C4—22no—
1141C4—22no—
1142C4—42no—
1143C4—42no—
1144C4—41no—
1145C4—41no—
1146C4—41no—
1147C4—41no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—42no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4#351311yescharacteristic
1169C4#352111yescharacteristic
1170C4#353511yescharacteristic
1171C4#356411yescharacteristic
1172C2—24no—
1173C2#4353311yescharacteristic
1174C2C2×#337711yescharacteristic
1175C2#6133011yescharacteristic
1176C2#6173811yescharacteristic
1177C2#6176711yescharacteristic
1178C2#6198111yescharacteristic
1179C2#6205611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32602C2semidirect
4. #32557C2semidirect
5. #32497C2semidirect
6. #32434C2semidirect
7. #32235C2semidirect
8. #31964C2semidirect
9. #31664C2semidirect
10. #30834C2semidirect
14. #27570C2semidirect
15. #27382C2semidirect
17. #26756C2semidirect
18. #26333C2semidirect
19. #26171C2semidirect
22. #25333C2semidirect
25. #25001C2semidirect
26. #24687C2semidirect

Maximal subgroups

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

subgroupindex
#594252
#593212
#326022
#325572
#324972
#324342
#322352
#319642
#316642
#308342
#281242
#276992
#276812
#275702
#273822
#272682
#267562
#263332
#261712
#259982
#259572
#253332
#252082
#250822
#250012
#246872
C2×#20722
#229342
#228712
#222912
#221832