Finite Group Databasebeta

← #6600802

Subgroups — #6600802

Order 512.

1465 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38069C211yesmaximal, characteristic
2#34192C211yesmaximal, characteristic
3#33091C211yesmaximal, characteristic, complemented
4#33077C211yesmaximal, characteristic, complemented
5#33010C211yesmaximal, characteristic
6#29589C211yesmaximal, characteristic, complemented
7#29550C211yesmaximal, characteristic, complemented
8#29439C211yesmaximal, characteristic, complemented
9#29402C211yesmaximal, characteristic, complemented
10#27860C211yesmaximal, characteristic
11#27616C211yesmaximal, characteristic
12#27580C211yesmaximal, characteristic, complemented
13#27501C211yesmaximal, characteristic, complemented
14#27448C211yesmaximal, characteristic, complemented
15#27387C211yesmaximal, characteristic, complemented
16#27368C211yesmaximal, characteristic, complemented
17#27321C211yesmaximal, characteristic, complemented
18#27306C211yesmaximal, characteristic, complemented
19#26369C211yesmaximal, characteristic, complemented
20#25994C211yesmaximal, characteristic
21#25955C211yesmaximal, characteristic
22#24579C211yesmaximal, characteristic
23#24529C211yesmaximal, characteristic
24#22932C211yesmaximal, characteristic
25#22871C211yesmaximal, characteristic
26#22609C211yesmaximal, characteristic
27#22595C211yesmaximal, characteristic
28#22563C211yesmaximal, characteristic
29#21626C211yesmaximal, characteristic, complemented
30#21132C211yesmaximal, characteristic, complemented
31C2×#1865C211yesmaximal, characteristic
32C22×C4×Q8C2211yescharacteristic
33C2×#484C2211yescharacteristic
34C2×#475C2211yescharacteristic
35C2×#451C2211yescharacteristic
36C2×C4×Q16C2211yescharacteristic
37C22×#106C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40#2855C2211yescharacteristic
41#2774—21no—
42#2767—21no—
43#2766—21no—
44#2758—21no—
45#2647C2211yescharacteristic
46#2645C2211yescharacteristic
47#2511C2211yescharacteristic
48#2509C2211yescharacteristic
49#2508C2211yescharacteristic
50#2503—21no—
51#2503C2211yescharacteristic
52#2493—21no—
53#2484—21no—
54#2451C2211yescharacteristic
55#2440C2211yescharacteristic
56#2438—21no—
57#2360C2211yescharacteristic
58#2356—21no—
59#2356—21no—
60#2356C2211yescharacteristic
61#2356C2211yescharacteristic
62#2351C2211yescharacteristic
63#2351C2211yescharacteristic
64#2345—21no—
65#2345—21no—
66#2345C2211yescharacteristic
67#2345C2211yescharacteristic
68#2344C2211yescharacteristic
69Q8×C22⋊C4C2211yescharacteristic
70Q8×C22⋊C4C2211yescharacteristic
71#2331C2211yescharacteristic
72#2320—21no—
73#2320—21no—
74#2320C2211yescharacteristic
75#2320C2211yescharacteristic
76#2320C2211yescharacteristic
77C2×#389C2211yescharacteristic
78#2283—21no—
79#2283—21no—
80#2283C2211yescharacteristic
81#2283C2211yescharacteristic
82#2276C2211yescharacteristic
83#2276C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2097C2211yescharacteristic
89#2096C2211yescharacteristic
90#2087C2211yescharacteristic
91#2087C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2074C2211yescharacteristic
98#2074C2211yescharacteristic
99#2074C2211yescharacteristic
100#2066C2211yescharacteristic
101#2066C2211yescharacteristic
102#2066C2211yescharacteristic
103#2066C2211yescharacteristic
104#2057C2211yescharacteristic
105#2056C2211yescharacteristic
106#2056C2211yescharacteristic
107#2024C2211yescharacteristic
108#1987C2211yescharacteristic
109#1969C2211yescharacteristic
110#1949C2211yescharacteristic
111#1949C2211yescharacteristic
112#1947C2211yescharacteristic
113#1943C2211yescharacteristic
114#1941C2211yescharacteristic
115#1941C2211yescharacteristic
116#1935C2211yescharacteristic
117#1935C2211yescharacteristic
118#1935C2211yescharacteristic
119#1933C2211yescharacteristic
120#1928C2211yescharacteristic
121#1928C2211yescharacteristic
122#1928C2211yescharacteristic
123#1928C2211yescharacteristic
124#1927C2211yescharacteristic
125#1927C2211yescharacteristic
126#1927C2211yescharacteristic
127#1927C2211yescharacteristic
128#1921C2211yescharacteristic
129#1921C2211yescharacteristic
130#1921C2211yescharacteristic
131#1921C2211yescharacteristic
132#1920C2211yescharacteristic
133#1920C2211yescharacteristic
134#1920C2211yescharacteristic
135#1920C2211yescharacteristic
136#1919C2211yescharacteristic
137#1919C2211yescharacteristic
138#1919C2211yescharacteristic
139#1918C2211yescharacteristic
140#1918C2211yescharacteristic
141#1918C2211yescharacteristic
142#1917C2211yescharacteristic
143#1917C2211yescharacteristic
144#1916C2211yescharacteristic
145#1916C2211yescharacteristic
146#1892C2211yescharacteristic
147#1892C2211yescharacteristic
148#1878C2211yescharacteristic
149#1878C2211yescharacteristic
150#1878C2211yescharacteristic
151#1878C2211yescharacteristic
152#1878C2211yescharacteristic
153#1878C2211yescharacteristic
154#1878C2211yescharacteristic
155#1878C2211yescharacteristic
156#1865C2211yescharacteristic
157#1865C2211yescharacteristic
158#1865C2211yescharacteristic
159#1865C2211yescharacteristic
160#1865C2211yescharacteristic
161#1865C2211yescharacteristic
162#1865C2211yescharacteristic
163#1865C2211yescharacteristic
164#1865C2211yescharacteristic
165#1865C2211yescharacteristic
166#1865C2211yescharacteristic
167#1863C2211yescharacteristic
168#1863C2211yescharacteristic
169#1863C2211yescharacteristic
170#1863C2211yescharacteristic
171#1863C2211yescharacteristic
172#1863C2211yescharacteristic
173#1863C2211yescharacteristic
174#1853C2211yescharacteristic
175#1852C2211yescharacteristic
176#1850C2211yescharacteristic
177#1850C2211yescharacteristic
178#1840C2211yescharacteristic
179#1832C2211yescharacteristic
180#1824C2211yescharacteristic
181#1823C2211yescharacteristic
182#1823C2211yescharacteristic
183#1817C2211yescharacteristic
184#1808C2211yescharacteristic
185#1807C2211yescharacteristic
186#1805C2211yescharacteristic
187#1805C2211yescharacteristic
188#1803C2211yescharacteristic
189#1787C2211yescharacteristic
190#1776C2211yescharacteristic
191C4×#106C2211yescharacteristic
192C4×#106C2211yescharacteristic
193#1768C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197C4×#103C2211yescharacteristic
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1746C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C22⋊Q8—21no—
210C2×C22⋊Q8C2311yescharacteristic
211C2×C4×Q8—24no—
212C2×C4×Q8—24no—
213C2×C4×Q8—21no—
214C2×C4×Q8—21no—
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×#117—21no—
225C22×C4⋊C4—21no—
226C22×C4⋊C4—21no—
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C42—21no—
231C22×C42C2311yescharacteristic
232#484—24no—
233#475—24no—
234#451—24no—
235C4×Q16—24no—
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106—24no—
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×#103—24no—
256C2×#103—24no—
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×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283#401—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#395—21no—
302#395—21no—
303#391—21no—
304#391—21no—
305#391—21no—
306#391—21no—
307#391—21no—
308#391—21no—
309#391—21no—
310#391C2311yescharacteristic
311#391C2311yescharacteristic
312#391C2311yescharacteristic
313#391C2311yescharacteristic
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#389—21no—
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#387—21no—
343#387—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#385—21no—
369#385—21no—
370#385—21no—
371#384C2311yescharacteristic
372#383—21no—
373#383—21no—
374#383—21no—
375#383—21no—
376#383—21no—
377#383—21no—
378#383D411yescharacteristic
379#383D411yescharacteristic
380#382—21no—
381#382—21no—
382#382—21no—
383#382—21no—
384#382—21no—
385#382—21no—
386#382D411yescharacteristic
387#382D411yescharacteristic
388#382C2311yescharacteristic
389#382C2311yescharacteristic
390#382C2311yescharacteristic
391#382C2311yescharacteristic
392#381—21no—
393#381—21no—
394#381—21no—
395#381—21no—
396#381—21no—
397#381D411yescharacteristic
398#381D411yescharacteristic
399#380—21no—
400#380—21no—
401#380—21no—
402#380—21no—
403#380D411yescharacteristic
404#380D411yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4C2311yescharacteristic
434C4×C22⋊C4C2311yescharacteristic
435#376—21no—
436#376—21no—
437#376—21no—
438#376—21no—
439#376—21no—
440#376C2311yescharacteristic
441#376C2311yescharacteristic
442C2×#95—21no—
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#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
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
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—22no—
490C22×Q8—22no—
491C22×Q8—22no—
492C22×Q8—41no—
493C22×Q8—41no—
494C22×Q8#4114yes—
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×Q8C2411yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2×D411yescharacteristic
503C23×C4C2×D411yescharacteristic
504C23×C4C2411yescharacteristic
505C2×Q16—22no—
506C2×Q16—22no—
507C2×Q16—22no—
508C2×Q16—22no—
509C2×Q16—41no—
510C2×Q16—41no—
511C22×C8—22no—
512C22×C8—22no—
513C22×C8—22no—
514C22×C8—41no—
515C22×C8—41no—
516C22×C8—41no—
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C4⋊Q8—22no—
526C4⋊Q8—41no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529C22⋊Q8—82no—
530C4×Q8—28no—
531C4×Q8—28no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—41no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—41no—
550#117—82no—
551C2×C4⋊C4—28no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
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—41no—
588C2×C4⋊C4—82no—
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4#4114yes—
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4C2×D411yescharacteristic
612C2×C22⋊C4C2×D411yescharacteristic
613C2×C22⋊C4C2×D411yescharacteristic
614C2×C22⋊C4C2×D411yescharacteristic
615C2×C42—28no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—22no—
621C2×C42—22no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42C2×D411yescharacteristic
637C2×C42C2×D411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644#107—22no—
645#107—22no—
646#107—22no—
647#107—41no—
648#107—41no—
649#107—41no—
650#106—22no—
651#106—22no—
652#106—22no—
653#106—22no—
654#106—22no—
655#106—22no—
656#106—41no—
657#106—41no—
658C4⋊C8—22no—
659C4⋊C8—41no—
660C4⋊C8—41no—
661C4⋊C8—41no—
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—22no—
676#103—41no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#103#4114yes—
682C22⋊C8—22no—
683C22⋊C8—22no—
684#97—41no—
685#97—41no—
686C4×C8—22no—
687C4×C8—41no—
688#95—21no—
689#95—21no—
690#95—21no—
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#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757C24C22×D411yescharacteristic
758C2×Q8—24no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—28no—
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—21no—
773C2×Q8—21no—
774C2×Q8—42no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×Q8—44no—
778C2×Q8—44no—
779C2×Q8—44no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8C2×#4112yes—
783C2×Q8C2×#4112yes—
784C2×Q8C2×#4112yes—
785C2×Q82−1+412yes—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—24no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—24no—
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—41no—
813C22×C4—41no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4—81no—
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×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C2×#4112yes—
838C22×C4C2×#4112yes—
839C22×C4C2511yescharacteristic
840Q16—44no—
841Q16—82no—
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—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—44no—
866C2×C8—82no—
867C2×C8C2×#4112yes—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
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—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
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⋊C4C2×#4112yes—
927C4⋊C4C2×#4112yes—
928C4⋊C4C2×#4112yes—
929C22⋊C4—22no—
930C22⋊C4—22no—
931C22⋊C4—22no—
932C22⋊C4—22no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C42—24no—
938C42—24no—
939C42—24no—
940C42—24no—
941C42—22no—
942C42—22no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—42no—
956C42—42no—
957C42—42no—
958C42—42no—
959C42—42no—
960C42—81no—
961C42—81no—
962C42—81no—
963C42—81no—
964C42—81no—
965C42—81no—
966C42—81no—
967C42—81no—
968C42—81no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23#52512yes—
974C23#57712yes—
975C23#57812yes—
976C23C23×D411yescharacteristic
977Q8—22no—
978Q8—22no—
979Q8—22no—
980Q8—22no—
981Q8—22no—
982Q8—48no—
983Q8—41no—
984Q8—41no—
985Q8—41no—
986Q8—41no—
987Q8—41no—
988Q8—41no—
989Q8—162no—
990Q8#55214yes—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
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—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—48no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—44no—
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—82no—
1084C2×C4—84no—
1085C2×C4—84no—
1086C2×C4—84no—
1087C2×C4#52512yes—
1088C2×C4C22×#4111yescharacteristic
1089C2×C4C22×#4111yescharacteristic
1090C2×C4C22×#4111yescharacteristic
1091C2×C4C2×2−1+411yescharacteristic
1092C2×C4#58511yescharacteristic
1093C2×C4#58511yescharacteristic
1094C8—22no—
1095C8—41no—
1096C8—41no—
1097C8—41no—
1098C8—41no—
1099C8—41no—
1100C8—41no—
1101C8—41no—
1102C22—22no—
1103C22—22no—
1104C22—22no—
1105C22—22no—
1106C22—22no—
1107C22—22no—
1108C22#312114yes—
1109C22C2×#52511yescharacteristic
1110C22D4×#4111yescharacteristic
1111C22#348911yescharacteristic
1112C22C2×#57711yescharacteristic
1113C22C2×#57811yescharacteristic
1114C22#358411yescharacteristic
1115C22#358611yescharacteristic
1116C4—22no—
1117C4—24no—
1118C4—41no—
1119C4—41no—
1120C4—41no—
1121C4—41no—
1122C4—42no—
1123C4—41no—
1124C4—41no—
1125C4—42no—
1126C4—41no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—42no—
1131C4—42no—
1132C4—41no—
1133C4—41no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4C2×#55211yescharacteristic
1146C4#347511yescharacteristic
1147C4#349111yescharacteristic
1148C4#349511yescharacteristic
1149C2—24no—
1150C2#3622311yescharacteristic
1151C2C2×#312111yescharacteristic
1152C2#6058111yescharacteristic
1153C2#6147211yescharacteristic
1154C2#6152511yescharacteristic
1155C2#6215711yescharacteristic
1156C2#6221411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33091C2semidirect
4. #33077C2semidirect
6. #29589C2semidirect
7. #29550C2semidirect
8. #29439C2semidirect
9. #29402C2semidirect
12. #27580C2semidirect
13. #27501C2semidirect
14. #27448C2semidirect
15. #27387C2semidirect
16. #27368C2semidirect
17. #27321C2semidirect
18. #27306C2semidirect
19. #26369C2semidirect
29. #21626C2semidirect
30. #21132C2semidirect

Maximal subgroups

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

subgroupindex
#380692
#341922
#330912
#330772
#330102
#295892
#295502
#294392
#294022
#278602
#276162
#275802
#275012
#274482
#273872
#273682
#273212
#273062
#263692
#259942
#259552
#245792
#245292
#229322
#228712
#226092
#225952
#225632
#216262
#211322
C2×#18652