Finite Group Databasebeta

← #6571813

Subgroups — #6571813

Order 512.

1416 conjugacy classes of subgroups.

The subgroup lattice has 1159 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36279C211yesmaximal, characteristic
2#34231C211yesmaximal, characteristic
3#30155C211yesmaximal, characteristic, complemented
4#30067C211yesmaximal, characteristic, complemented
5#29645C211yesmaximal, characteristic
6#29522C211yesmaximal, characteristic, complemented
7#29399C211yesmaximal, characteristic, complemented
8#29349C211yesmaximal, characteristic, complemented
9#29257C211yesmaximal, characteristic, complemented
10#27866C211yesmaximal, characteristic
11#27589C211yesmaximal, characteristic
12#27132C211yesmaximal, characteristic, complemented
13#27128C211yesmaximal, characteristic, complemented
14#27021C211yesmaximal, characteristic, complemented
15#27017C211yesmaximal, characteristic, complemented
16#26711C211yesmaximal, characteristic, complemented
17#26707C211yesmaximal, characteristic, complemented
18#26694C211yesmaximal, characteristic, complemented
19#26690C211yesmaximal, characteristic, complemented
20#26009C211yesmaximal, characteristic
21#26005C211yesmaximal, characteristic
22#24498C211yesmaximal, characteristic
23#24496C211yesmaximal, characteristic
24#23825C211yesmaximal, characteristic, complemented
25#23779C211yesmaximal, characteristic, complemented
26#23455C211yesmaximal, characteristic
27#22942C211yesmaximal, characteristic
28#22940C211yesmaximal, characteristic
29#22592C211yesmaximal, characteristic
30#22585C211yesmaximal, characteristic
31#22581C211yesmaximal, characteristic
32C2×#533C2211yescharacteristic
33C2×#485C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#419C2211yescharacteristic
36C2×#419C2211yescharacteristic
37#2863C2211yescharacteristic
38#2862C2211yescharacteristic
39#2855C2211yescharacteristic
40#2612—21no—
41#2605—21no—
42#2586—21no—
43#2520—21no—
44#2511C2211yescharacteristic
45#2505—21no—
46#2451C2211yescharacteristic
47#2446C2211yescharacteristic
48#2446C2211yescharacteristic
49#2440C2211yescharacteristic
50#2438—21no—
51#2434C2211yescharacteristic
52#2369C2211yescharacteristic
53#2369C2211yescharacteristic
54#2368—21no—
55#2365C2211yescharacteristic
56#2365C2211yescharacteristic
57#2362—21no—
58#2362—21no—
59#2360C2211yescharacteristic
60#2356—21no—
61#2356—21no—
62#2347C2211yescharacteristic
63#2347C2211yescharacteristic
64#2346C2211yescharacteristic
65#2346C2211yescharacteristic
66#2343—21no—
67Q8×C22⋊C4C2211yescharacteristic
68#2332—21no—
69#2332—21no—
70#2320—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×#125C2211yescharacteristic
73C4×#125C2211yescharacteristic
74C4×#125C2211yescharacteristic
75C4×#125C2211yescharacteristic
76#2295C2211yescharacteristic
77C2×#391C2211yescharacteristic
78#2283C2211yescharacteristic
79#2276—21no—
80C4×#117C2211yescharacteristic
81#2101C2211yescharacteristic
82#2100C2211yescharacteristic
83#2100C2211yescharacteristic
84#2097C2211yescharacteristic
85#2097C2211yescharacteristic
86#2097C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2086C2211yescharacteristic
91#2085C2211yescharacteristic
92#2074C2211yescharacteristic
93#2074C2211yescharacteristic
94#2074C2211yescharacteristic
95#2068C2211yescharacteristic
96#2068C2211yescharacteristic
97#2066C2211yescharacteristic
98#2066C2211yescharacteristic
99#2059C2211yescharacteristic
100#2059C2211yescharacteristic
101#2058C2211yescharacteristic
102#2058C2211yescharacteristic
103#2057C2211yescharacteristic
104#2057C2211yescharacteristic
105#2043C2211yescharacteristic
106#2043C2211yescharacteristic
107#2043C2211yescharacteristic
108#2043C2211yescharacteristic
109#2026C2211yescharacteristic
110#2026C2211yescharacteristic
111#2026C2211yescharacteristic
112#2026C2211yescharacteristic
113#2026C2211yescharacteristic
114#2026C2211yescharacteristic
115#2024C2211yescharacteristic
116#2024C2211yescharacteristic
117#2024C2211yescharacteristic
118#2024C2211yescharacteristic
119#2024C2211yescharacteristic
120#2024C2211yescharacteristic
121#1988C2211yescharacteristic
122#1988C2211yescharacteristic
123#1981C2211yescharacteristic
124#1981C2211yescharacteristic
125#1981C2211yescharacteristic
126#1981C2211yescharacteristic
127#1948C2211yescharacteristic
128#1947C2211yescharacteristic
129#1944C2211yescharacteristic
130#1943C2211yescharacteristic
131#1935C2211yescharacteristic
132#1935C2211yescharacteristic
133#1933C2211yescharacteristic
134#1933C2211yescharacteristic
135#1933C2211yescharacteristic
136#1933C2211yescharacteristic
137#1928C2211yescharacteristic
138#1928C2211yescharacteristic
139#1928C2211yescharacteristic
140#1928C2211yescharacteristic
141#1928C2211yescharacteristic
142#1928C2211yescharacteristic
143#1928C2211yescharacteristic
144#1928C2211yescharacteristic
145#1927C2211yescharacteristic
146#1927C2211yescharacteristic
147#1927C2211yescharacteristic
148#1927C2211yescharacteristic
149#1927C2211yescharacteristic
150#1927C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1919C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1917C2211yescharacteristic
164#1917C2211yescharacteristic
165#1916C2211yescharacteristic
166#1916C2211yescharacteristic
167#1894C2211yescharacteristic
168#1894C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1863C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1853C2211yescharacteristic
176#1852C2211yescharacteristic
177#1851C2211yescharacteristic
178#1851C2211yescharacteristic
179#1839C2211yescharacteristic
180#1831C2211yescharacteristic
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic
183#1817C2211yescharacteristic
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic
186#1787C2211yescharacteristic
187#1787C2211yescharacteristic
188C4×#107C2211yescharacteristic
189C4×#106C2211yescharacteristic
190C4×C4⋊C8C2211yescharacteristic
191#1763C2211yescharacteristic
192#1763C2211yescharacteristic
193#1763C2211yescharacteristic
194#1763C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#103C2211yescharacteristic
197#1753C2211yescharacteristic
198#1753C2211yescharacteristic
199#1745C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202#1728C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206#533—24no—
207#533—24no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8C2311yescharacteristic
219C2×C4×Q8—21no—
220C2×C4×Q8—21no—
221C2×C4×Q8—21no—
222C2×C4×Q8—21no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×#117D411yescharacteristic
227C2×#117D411yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C42C2311yescharacteristic
232#485—24no—
233#485—24no—
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250#419—24no—
251#419—24no—
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#395—21no—
291#395—21no—
292#395—21no—
293#395—21no—
294#391—21no—
295#391—21no—
296#391—21no—
297#391—21no—
298#391—21no—
299#391—21no—
300#391—21no—
301#391—21no—
302#391—21no—
303#391—21no—
304#391—21no—
305#391—21no—
306#391—21no—
307#391C2311yescharacteristic
308#391C2311yescharacteristic
309#391C2311yescharacteristic
310#391C2311yescharacteristic
311#391C2311yescharacteristic
312#391C2311yescharacteristic
313#391C2311yescharacteristic
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#389—21no—
319#389—21no—
320#389—21no—
321#389—21no—
322#389—21no—
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#388—21no—
337#388—21no—
338#388—21no—
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
343#388—21no—
344#387—21no—
345#387—21no—
346#387—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
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#385—21no—
372#385—21no—
373#385—21no—
374#385—21no—
375#385—21no—
376#384C2311yescharacteristic
377#383—21no—
378#383—21no—
379#383—21no—
380#383—21no—
381#382—21no—
382#382—21no—
383#382—21no—
384#382—21no—
385#382C2311yescharacteristic
386#382C2311yescharacteristic
387#381—21no—
388#381—21no—
389#380—21no—
390#380C2311yescharacteristic
391#380C2311yescharacteristic
392#380C2311yescharacteristic
393C4×C4⋊C4—21no—
394C4×C4⋊C4—21no—
395C4×C4⋊C4—21no—
396C4×C4⋊C4—21no—
397C4×C4⋊C4—21no—
398C4×C4⋊C4—21no—
399C4×C4⋊C4—21no—
400C4×C4⋊C4—21no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4D411yescharacteristic
409C4×C4⋊C4D411yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4D411yescharacteristic
427C4×C22⋊C4D411yescharacteristic
428C4×C22⋊C4C2311yescharacteristic
429C4×C22⋊C4C2311yescharacteristic
430#376—21no—
431#376—21no—
432#376—21no—
433#376—21no—
434#376D411yescharacteristic
435#376D411yescharacteristic
436C2×#95—21no—
437C2×#95—21no—
438C43C2311yescharacteristic
439C43C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
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#336C2311yescharacteristic
469#336C2311yescharacteristic
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
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8—21no—
488C22×Q8—22no—
489C22×Q8—22no—
490C22×Q8—22no—
491C22×Q8—41no—
492C22×Q8—41no—
493C22×Q8—41no—
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C23×C4—21no—
498C23×C4—21no—
499C23×C4C2×D411yescharacteristic
500C23×C4C2×D411yescharacteristic
501C23×C4C2411yescharacteristic
502C2×M16—22no—
503C2×M16—22no—
504C2×M16—41no—
505C2×M16—41no—
506C2×M16—41no—
507C2×M16—41no—
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C4⋊Q8—22no—
517C4⋊Q8—22no—
518C4⋊Q8—22no—
519C4⋊Q8—22no—
520C4⋊Q8—22no—
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526#125—22no—
527#125—22no—
528#125—22no—
529#125—22no—
530C22⋊Q8—28no—
531C22⋊Q8—28no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534C22⋊Q8—44no—
535C4×Q8—28no—
536C4×Q8—28no—
537C4×Q8—22no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—44no—
544C4×Q8—44no—
545#117—22no—
546#117—22no—
547#117—24no—
548#117—42no—
549#117#4114yes—
550#117#4114yes—
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—21no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4C2×D411yescharacteristic
608C2×C22⋊C4C2×D411yescharacteristic
609C2×C22⋊C4C2×D411yescharacteristic
610C2×C22⋊C4C2×D411yescharacteristic
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—22no—
614C2×C42—22no—
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×C42C2×D411yescharacteristic
630C2×C42C2×D411yescharacteristic
631C2×C42C2×D411yescharacteristic
632C2×C42C2×D411yescharacteristic
633C2×C42C2×D411yescharacteristic
634C2×C42C2×D411yescharacteristic
635C2×C42C2×D411yescharacteristic
636C2×C42C2×D411yescharacteristic
637C2×C42C2×D411yescharacteristic
638C2×C42C2×D411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645#107—22no—
646#107—22no—
647#107—41no—
648#107—41no—
649#107—41no—
650#107—41no—
651#106—22no—
652#106—22no—
653#106—41no—
654#106—41no—
655#106—41no—
656#106—41no—
657C4⋊C8—41no—
658C4⋊C8—41no—
659C4⋊C8—41no—
660C4⋊C8—41no—
661#103—22no—
662#103—22no—
663#103—22no—
664#103—22no—
665#103—22no—
666#103—22no—
667#103—22no—
668#103—22no—
669#103—22no—
670#103—22no—
671#103—22no—
672#103—22no—
673#103—22no—
674#103—22no—
675#103—41no—
676#103—41no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#103—41no—
685C22⋊C8—22no—
686C22⋊C8—22no—
687#97—41no—
688#97—41no—
689C4×C8—41no—
690C4×C8—41no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
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#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752C24C22×D411yescharacteristic
753C2×Q8—24no—
754C2×Q8—24no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—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—21no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—44no—
775C2×Q8—44no—
776C2×Q8—42no—
777C2×Q8—42no—
778C2×Q8—42no—
779C2×Q8—81no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×Q8—81no—
784C2×Q8—82no—
785C2×Q8—82no—
786C2×Q82−1+412yes—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
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—41no—
811C22×C4—41no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4—81no—
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×D411yescharacteristic
832C22×C4C2×#4112yes—
833C22×C4C2×#4112yes—
834C22×C4C2511yescharacteristic
835M16—82no—
836M16—82no—
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×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—21no—
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—41no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
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⋊C4#13714yes—
918C4⋊C4C2×#4112yes—
919C4⋊C4C2×#4112yes—
920C4⋊C4C2×#4112yes—
921C4⋊C4C2×#4112yes—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—22no—
925C22⋊C4—22no—
926C22⋊C4—22no—
927C22⋊C4—41no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C42—22no—
933C42—22no—
934C42—24no—
935C42—24no—
936C42—22no—
937C42—22no—
938C42—22no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—41no—
952C42—41no—
953C42—41no—
954C42—41no—
955C42—41no—
956C42—42no—
957C42—42no—
958C42—42no—
959C42—42no—
960C42—42no—
961C42—42no—
962C42—42no—
963C42—81no—
964C42—81no—
965C42—81no—
966C42—81no—
967C42—81no—
968C42—81no—
969C42—81no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23#52512yes—
977C23C23×D411yescharacteristic
978Q8—22no—
979Q8—22no—
980Q8—48no—
981Q8—41no—
982Q8—41no—
983Q8—41no—
984Q8—41no—
985Q8—41no—
986Q8—41no—
987Q8—41no—
988Q8—41no—
989Q8—41no—
990Q8—41no—
991Q8—84no—
992Q8—84no—
993Q8—162no—
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—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
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—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
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—21no—
1037C2×C4—44no—
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—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—82no—
1082C2×C4—84no—
1083C2×C4—162no—
1084C2×C4#52512yes—
1085C2×C4C2×#13712yes—
1086C2×C4C2×#13712yes—
1087C2×C4C2×#13712yes—
1088C2×C4#57512yes—
1089C2×C4C22×#4111yescharacteristic
1090C2×C4C22×#4111yescharacteristic
1091C2×C4C2×2−1+411yescharacteristic
1092C2×C4#58511yescharacteristic
1093C2×C4#58511yescharacteristic
1094C2×C4#58511yescharacteristic
1095C8—41no—
1096C8—41no—
1097C8—41no—
1098C8—41no—
1099C8—41no—
1100C8—41no—
1101C8—41no—
1102C8—41no—
1103C22—22no—
1104C22—22no—
1105C22—22no—
1106C22—41no—
1107C22—41no—
1108C22—41no—
1109C22—41no—
1110C22C2×#52511yescharacteristic
1111C22#348911yescharacteristic
1112C22#350011yescharacteristic
1113C22C22×#13711yescharacteristic
1114C22C2×#57511yescharacteristic
1115C22#358411yescharacteristic
1116C22#358611yescharacteristic
1117C4—22no—
1118C4—22no—
1119C4—22no—
1120C4—22no—
1121C4—22no—
1122C4—41no—
1123C4—41no—
1124C4—41no—
1125C4—41no—
1126C4—42no—
1127C4—42no—
1128C4—41no—
1129C4—41no—
1130C4—42no—
1131C4—42no—
1132C4—41no—
1133C4—41no—
1134C4—42no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4#349511yescharacteristic
1147C4#349511yescharacteristic
1148C4#351011yescharacteristic
1149C4#351011yescharacteristic
1150C2—42no—
1151C2#3607911yescharacteristic
1152C2#6056211yescharacteristic
1153C2#6058611yescharacteristic
1154C2#6212411yescharacteristic
1155C2#6213911yescharacteristic
1156C2#6254711yescharacteristic
1157C2#6258911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #30155C2semidirect
4. #30067C2semidirect
6. #29522C2semidirect
7. #29399C2semidirect
8. #29349C2semidirect
9. #29257C2semidirect
12. #27132C2semidirect
13. #27128C2semidirect
14. #27021C2semidirect
15. #27017C2semidirect
16. #26711C2semidirect
17. #26707C2semidirect
18. #26694C2semidirect
19. #26690C2semidirect
24. #23825C2semidirect
25. #23779C2semidirect

Maximal subgroups

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

subgroupindex
#362792
#342312
#301552
#300672
#296452
#295222
#293992
#293492
#292572
#278662
#275892
#271322
#271282
#270212
#270172
#267112
#267072
#266942
#266902
#260092
#260052
#244982
#244962
#238252
#237792
#234552
#229422
#229402
#225922
#225852
#225812