Finite Group Databasebeta

← #7593108

Subgroups — #7593108

Order 512.

1373 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45121C211yesmaximal, characteristic
2#44923C211yesmaximal, characteristic
3#32355C211yesmaximal, characteristic, complemented
4#32350C211yesmaximal, characteristic, complemented
5#32348C211yesmaximal, characteristic, complemented
6#32345C211yesmaximal, characteristic, complemented
7#28810C211yesmaximal, characteristic, complemented
8#28542C211yesmaximal, characteristic, complemented
9#28538C211yesmaximal, characteristic, complemented
10#28271C211yesmaximal, characteristic, complemented
11#28009C211yesmaximal, characteristic, complemented
12#28008C211yesmaximal, characteristic, complemented
13#27690C211yesmaximal, characteristic
14#27689C211yesmaximal, characteristic
15#26351C211yesmaximal, characteristic
16#26344C211yesmaximal, characteristic
17#26342C211yesmaximal, characteristic
18#26337C211yesmaximal, characteristic
19#26073C211yesmaximal, characteristic
20#26072C211yesmaximal, characteristic
21#26055C211yesmaximal, characteristic, complemented
22#26054C211yesmaximal, characteristic, complemented
23#25071C211yesmaximal, characteristic, complemented
24#25070C211yesmaximal, characteristic, complemented
25#23036C211yesmaximal, characteristic
26#23036C211yesmaximal, characteristic
27#22728C211yesmaximal, characteristic, complemented
28C4⋊C4×Q16C211yesmaximal, characteristic, complemented
29#21604C211yesmaximal, characteristic
30#21537C211yesmaximal, characteristic
31#20803C211yesmaximal, characteristic
32C2×#499C2211yescharacteristic
33C2×#498C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×#475C2211yescharacteristic
38C2×#470C2211yescharacteristic
39C2×#446C2211yescharacteristic
40C2×C4×Q16C2211yescharacteristic
41C2×C4×Q16C2211yescharacteristic
42C2×C4×Q16C2211yescharacteristic
43C2×#428C2211yescharacteristic
44C2×#428C2211yescharacteristic
45C2×#427C2211yescharacteristic
46C22×#107C2211yescharacteristic
47C2×#405C2211yescharacteristic
48#2807—21no—
49#2806—21no—
50#2805—21no—
51#2792—21no—
52#2791—21no—
53#2790—21no—
54#2788—21no—
55#2720—21no—
56#2589—21no—
57#2588—21no—
58#2587—21no—
59#2585—21no—
60#2584—21no—
61#2581C2211yescharacteristic
62#2581C2211yescharacteristic
63#2574—21no—
64#2568C2211yescharacteristic
65#2567C2211yescharacteristic
66#2565C2211yescharacteristic
67#2565C2211yescharacteristic
68#2550C2211yescharacteristic
69#2550C2211yescharacteristic
70#2509—21no—
71#2509C2211yescharacteristic
72#2508C2211yescharacteristic
73#2507C2211yescharacteristic
74#2506C2211yescharacteristic
75#2465—21no—
76#2442C2211yescharacteristic
77#2441C2211yescharacteristic
78#2440C2211yescharacteristic
79#2439C2211yescharacteristic
80#2396C2211yescharacteristic
81#2362C2211yescharacteristic
82#2362C2211yescharacteristic
83#2360C2211yescharacteristic
84#2360C2211yescharacteristic
85#2355C2211yescharacteristic
86Q8×C4⋊C4C2211yescharacteristic
87Q8×C4⋊C4C2211yescharacteristic
88Q8×C4⋊C4C2211yescharacteristic
89#2323C2211yescharacteristic
90#2323C2211yescharacteristic
91#2317C2211yescharacteristic
92#2317C2211yescharacteristic
93#2101C2211yescharacteristic
94#2101C2211yescharacteristic
95#2100C2211yescharacteristic
96#2099C2211yescharacteristic
97#2097C2211yescharacteristic
98#2097C2211yescharacteristic
99#2097C2211yescharacteristic
100#2097C2211yescharacteristic
101#2096C2211yescharacteristic
102#2096C2211yescharacteristic
103#2095C2211yescharacteristic
104#2095C2211yescharacteristic
105#2088C2211yescharacteristic
106#2088C2211yescharacteristic
107#2087C2211yescharacteristic
108#2086C2211yescharacteristic
109#2085C2211yescharacteristic
110#2085C2211yescharacteristic
111#2084C2211yescharacteristic
112#2083C2211yescharacteristic
113#2068C2211yescharacteristic
114#2068C2211yescharacteristic
115#2068C2211yescharacteristic
116#2068C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2059C2211yescharacteristic
120#2059C2211yescharacteristic
121#2058C2211yescharacteristic
122#2057C2211yescharacteristic
123#2057C2211yescharacteristic
124#2057C2211yescharacteristic
125#1985C2211yescharacteristic
126#1971C2211yescharacteristic
127#1971C2211yescharacteristic
128#1971C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1948C2211yescharacteristic
134#1947C2211yescharacteristic
135#1947C2211yescharacteristic
136#1947C2211yescharacteristic
137#1944C2211yescharacteristic
138#1944C2211yescharacteristic
139#1944C2211yescharacteristic
140#1942C2211yescharacteristic
141#1942C2211yescharacteristic
142#1941C2211yescharacteristic
143#1941C2211yescharacteristic
144#1940C2211yescharacteristic
145#1933C2211yescharacteristic
146#1933C2211yescharacteristic
147#1928C2211yescharacteristic
148#1928C2211yescharacteristic
149#1927C2211yescharacteristic
150#1927C2211yescharacteristic
151#1921C2211yescharacteristic
152#1920C2211yescharacteristic
153#1919C2211yescharacteristic
154#1918C2211yescharacteristic
155#1916C2211yescharacteristic
156#1916C2211yescharacteristic
157#1892C2211yescharacteristic
158#1892C2211yescharacteristic
159#1873C2211yescharacteristic
160#1873C2211yescharacteristic
161#1872C2211yescharacteristic
162#1872C2211yescharacteristic
163#1865C2211yescharacteristic
164#1865C2211yescharacteristic
165#1863C2211yescharacteristic
166#1863C2211yescharacteristic
167#1863C2211yescharacteristic
168#1863C2211yescharacteristic
169#1863C2211yescharacteristic
170#1863C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1853C2211yescharacteristic
174#1852C2211yescharacteristic
175#1850C2211yescharacteristic
176#1850C2211yescharacteristic
177#1847C2211yescharacteristic
178#1847C2211yescharacteristic
179#1847C2211yescharacteristic
180#1847C2211yescharacteristic
181#1847C2211yescharacteristic
182#1847C2211yescharacteristic
183#1846C2211yescharacteristic
184#1846C2211yescharacteristic
185#1845C2211yescharacteristic
186#1845C2211yescharacteristic
187#1809C2211yescharacteristic
188#1805C2211yescharacteristic
189#1805C2211yescharacteristic
190#1803C2211yescharacteristic
191#1803C2211yescharacteristic
192#1798C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1770C2211yescharacteristic
197#1770C2211yescharacteristic
198C8×C4⋊C4C2211yescharacteristic
199#1763C2211yescharacteristic
200#1763C2211yescharacteristic
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#125—21no—
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×C22⋊Q8—21no—
212C2×C22⋊Q8C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
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×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227#499—42no—
228#498—42no—
229#479—42no—
230#479—42no—
231#477—42no—
232#475—42no—
233#470Q818yescomplemented
234#446—24no—
235C4×Q16—24no—
236C4×Q16—42no—
237C4×Q16—42no—
238#428—42no—
239#428—42no—
240#427—42no—
241C2×#107—42no—
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291#405—24no—
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400D411yescharacteristic
310#399—21no—
311#399D411yescharacteristic
312#398—21no—
313#398—21no—
314#398—21no—
315#398—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#398D411yescharacteristic
325#398D411yescharacteristic
326#396—21no—
327#396—21no—
328#396D411yescharacteristic
329#396D411yescharacteristic
330#395—21no—
331#395—21no—
332#395—21no—
333#395—21no—
334#395—21no—
335#395—21no—
336#395—21no—
337#395D411yescharacteristic
338#393—21no—
339#393D411yescharacteristic
340#391—21no—
341#391—21no—
342#391—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#388—21no—
389#388—21no—
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#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#384—21no—
427#384—21no—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#382—21no—
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#380—21no—
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8C2×D411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4C2411yescharacteristic
502C2×Q16—22no—
503C2×Q16—22no—
504C2×Q16C2×Q814yes—
505C2×M16—22no—
506C2×M16—22no—
507C2×M16C2×Q814yes—
508C22×C8—22no—
509C22×C8—22no—
510C22×C8—22no—
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C4⋊Q8—41no—
520C4⋊Q8—41no—
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523#125—41no—
524#125—41no—
525#125—41no—
526#125—41no—
527#125—82no—
528C22⋊Q8—22no—
529C22⋊Q8—22no—
530C22⋊Q8—82no—
531C22⋊Q8C2×Q814yes—
532C22⋊Q8C2×Q814yes—
533C4×Q8—22no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—22no—
538C4×Q8—22no—
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—82no—
548#117—22no—
549#117—22no—
550#117—41no—
551#117—41no—
552#117—41no—
553#117—41no—
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—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—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4C2×D411yescharacteristic
632C2×C22⋊C4C2×D411yescharacteristic
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C22⋊C4C2×D411yescharacteristic
635C2×C22⋊C4C2×D411yescharacteristic
636C2×C22⋊C4C2×D411yescharacteristic
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—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657#107—22no—
658#107—22no—
659#107—22no—
660#107—22no—
661#107—22no—
662#107—41no—
663#107—41no—
664#107—41no—
665#107—41no—
666#107—41no—
667#107—41no—
668#107—41no—
669#107—41no—
670#107—41no—
671#107—41no—
672#106—22no—
673#106—22no—
674#106—22no—
675#106—22no—
676#106—22no—
677#106—41no—
678#106—41no—
679#106—41no—
680#106—41no—
681#106—41no—
682#106—41no—
683#106C2×Q814yes—
684C4⋊C8—22no—
685C4⋊C8—22no—
686C4⋊C8—22no—
687C4⋊C8—22no—
688C4⋊C8—22no—
689C4⋊C8—22no—
690#103—22no—
691#103—22no—
692#103—22no—
693#103—22no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#103C2×Q814yes—
703#103C2×Q814yes—
704C22⋊C8—22no—
705C22⋊C8—22no—
706#97—22no—
707#97—22no—
708#97—22no—
709#97—22no—
710C4×C8—22no—
711C4×C8—22no—
712C4×C8—22no—
713C4×C8#4114yes—
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#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770C24C22×D411yescharacteristic
771C2×Q8—22no—
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—41no—
783C2×Q8—41no—
784C2×Q8—42no—
785C2×Q8—81no—
786C2×Q8—81no—
787C2×Q8—81no—
788C2×Q8—81no—
789C2×Q8—81no—
790C2×Q8C22×Q812yes—
791C2×Q8C22×Q812yes—
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—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—81no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×Q812yes—
832C22×C42−1+412yes—
833C22×C4C2511yescharacteristic
834Q16—28no—
835M16—28no—
836C2×C8—28no—
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×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8C22×Q812yes—
856C2×C8C22×Q812yes—
857C2×C8C2×#4112yes—
858C2×C8C2×#4112yes—
859C2×C8H(5,𝔽2)12yes—
860C2×C8H(5,𝔽2)12yes—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
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—41no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—41no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
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⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4C22×Q812yes—
941C4⋊C4C22×Q812yes—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—22no—
945C22⋊C4—22no—
946C22⋊C4—22no—
947C22⋊C4—41no—
948C22⋊C4—41no—
949C22⋊C4—41no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—42no—
965C42—42no—
966C42—42no—
967C42—81no—
968C42—81no—
969C42—81no—
970C42—81no—
971C42—81no—
972C42—81no—
973C42—81no—
974C42—81no—
975C42—81no—
976C42—81no—
977C42—81no—
978C42C2×#4112yes—
979C422−1+412yes—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23D4×Q812yes—
987C23C23×D411yescharacteristic
988Q8—22no—
989Q8—22no—
990Q8—22no—
991Q8—22no—
992Q8—44no—
993Q8—41no—
994Q8—41no—
995Q8—41no—
996Q8—41no—
997Q8—162no—
998Q8—162no—
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—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
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—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—162no—
1087C2×C4—162no—
1088C2×C4#54712yes—
1089C2×C4#54712yes—
1090C2×C4D4×Q812yes—
1091C2×C4#57812yes—
1092C2×C4C23×Q811yescharacteristic
1093C2×C4C22×#4111yescharacteristic
1094C2×C4C2×H(5,𝔽2)11yescharacteristic
1095C2×C4C2×H(5,𝔽2)11yescharacteristic
1096C2×C4C2×2−1+411yescharacteristic
1097C2×C4C2×2−1+411yescharacteristic
1098C8—22no—
1099C8—22no—
1100C8—22no—
1101C8—41no—
1102C8—41no—
1103C8—41no—
1104C8—41no—
1105C8#55414yes—
1106C22—22no—
1107C22—22no—
1108C22—22no—
1109C22—41no—
1110C22—41no—
1111C22—41no—
1112C22—41no—
1113C22C2×#54711yescharacteristic
1114C22C2×D4×Q811yescharacteristic
1115C22#349811yescharacteristic
1116C22C2×#57811yescharacteristic
1117C22#358411yescharacteristic
1118C22#358511yescharacteristic
1119C22#358611yescharacteristic
1120C4—22no—
1121C4—22no—
1122C4—22no—
1123C4—22no—
1124C4—41no—
1125C4—41no—
1126C4—41no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—41no—
1135C4—41no—
1136C4—41no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4C2×#55411yescharacteristic
1150C4#349211yescharacteristic
1151C4#350311yescharacteristic
1152C4#355211yescharacteristic
1153C2—42no—
1154C2#5931411yescharacteristic
1155C2#6126611yescharacteristic
1156C2#6128611yescharacteristic
1157C2#6138411yescharacteristic
1158C2#6138611yescharacteristic
1159C2#6246011yescharacteristic
1160C2#6246111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32355C2semidirect
4. #32350C2semidirect
5. #32348C2semidirect
6. #32345C2semidirect
7. #28810C2semidirect
8. #28542C2semidirect
9. #28538C2semidirect
10. #28271C2semidirect
11. #28009C2semidirect
12. #28008C2semidirect
21. #26055C2semidirect
22. #26054C2semidirect
23. #25071C2semidirect
24. #25070C2semidirect
27. #22728C2semidirect
28. C4⋊C4×Q16C2semidirect
233. #470Q8semidirect

Maximal subgroups

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

subgroupindex
#451212
#449232
#323552
#323502
#323482
#323452
#288102
#285422
#285382
#282712
#280092
#280082
#276902
#276892
#263512
#263442
#263422
#263372
#260732
#260722
#260552
#260542
#250712
#250702
#230362
#227282
C4⋊C4×Q162
#216042
#215372
#208032