Finite Group Databasebeta

← #7572513

Subgroups — #7572513

Order 512.

1322 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59668C211yesmaximal, characteristic, complemented
2#36479C211yesmaximal, characteristic
3#31890C211yesmaximal, characteristic
4#31870C211yesmaximal, characteristic
5#30970C211yesmaximal, characteristic
6#30954C211yesmaximal, characteristic
7#29317C211yesmaximal, characteristic, complemented
8#29182C211yesmaximal, characteristic, complemented
9#28968C211yesmaximal, characteristic
10#28957C211yesmaximal, characteristic
11#28819C211yesmaximal, characteristic, complemented
12#28802C211yesmaximal, characteristic, complemented
13#27019C211yesmaximal, characteristic
14#27018C211yesmaximal, characteristic
15#26882C211yesmaximal, characteristic, complemented
16#26882C211yesmaximal, characteristic, complemented
17#26875C211yesmaximal, characteristic, complemented
18#26862C211yesmaximal, characteristic, complemented
19#26458C211yesmaximal, characteristic, complemented
20#26454C211yesmaximal, characteristic, complemented
21#26453C211yesmaximal, characteristic, complemented
22#26446C211yesmaximal, characteristic, complemented
23#26102C211yesmaximal, characteristic
24#26036C211yesmaximal, characteristic
25#23256C211yesmaximal, characteristic, complemented
26#23167C211yesmaximal, characteristic, complemented
27#23163C211yesmaximal, characteristic, complemented
28#23079C211yesmaximal, characteristic
29#23079C211yesmaximal, characteristic
30#21614C211yesmaximal, characteristic
31#21613C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#498C2211yescharacteristic
34C2×#476C2211yescharacteristic
35C2×#474C2211yescharacteristic
36#2864C2211yescharacteristic
37#2855—21no—
38#2806—21no—
39#2806—21no—
40#2608—21no—
41#2607—21no—
42#2584—21no—
43#2574—21no—
44#2556—21no—
45#2552C2211yescharacteristic
46#2551C2211yescharacteristic
47#2551C2211yescharacteristic
48#2551C2211yescharacteristic
49#2550—21no—
50#2550C2211yescharacteristic
51#2550C2211yescharacteristic
52#2546—21no—
53#2522—21no—
54#2507C2211yescharacteristic
55#2507C2211yescharacteristic
56#2507C2211yescharacteristic
57#2507C2211yescharacteristic
58#2465—21no—
59#2454C2211yescharacteristic
60#2454C2211yescharacteristic
61#2452C2211yescharacteristic
62#2452C2211yescharacteristic
63#2451—21no—
64#2451—21no—
65#2370—21no—
66#2370C2211yescharacteristic
67#2370C2211yescharacteristic
68#2369C2211yescharacteristic
69#2369C2211yescharacteristic
70#2369C2211yescharacteristic
71#2369C2211yescharacteristic
72#2369C2211yescharacteristic
73#2365C2211yescharacteristic
74#2357C2211yescharacteristic
75#2357C2211yescharacteristic
76C4×C4⋊Q8C2211yescharacteristic
77C4×C4⋊Q8C2211yescharacteristic
78C4×#125C2211yescharacteristic
79C4×C22⋊Q8—21no—
80C42×D4C2211yescharacteristic
81#2094C2211yescharacteristic
82#2093C2211yescharacteristic
83#2088C2211yescharacteristic
84#2088C2211yescharacteristic
85#2088C2211yescharacteristic
86#2088C2211yescharacteristic
87#2087C2211yescharacteristic
88#2087C2211yescharacteristic
89#2087C2211yescharacteristic
90#2086C2211yescharacteristic
91#2084C2211yescharacteristic
92#2084C2211yescharacteristic
93#2084C2211yescharacteristic
94#2083C2211yescharacteristic
95#2067C2211yescharacteristic
96#2067C2211yescharacteristic
97#2065C2211yescharacteristic
98#2065C2211yescharacteristic
99#2059C2211yescharacteristic
100#2059C2211yescharacteristic
101#2059C2211yescharacteristic
102#2059C2211yescharacteristic
103#2058C2211yescharacteristic
104#2058C2211yescharacteristic
105#2058C2211yescharacteristic
106#2058C2211yescharacteristic
107#2057C2211yescharacteristic
108#2057C2211yescharacteristic
109#2057C2211yescharacteristic
110#2057C2211yescharacteristic
111#2023C2211yescharacteristic
112#2023C2211yescharacteristic
113#1993C2211yescharacteristic
114#1993C2211yescharacteristic
115#1992C2211yescharacteristic
116#1990C2211yescharacteristic
117#1989C2211yescharacteristic
118#1989C2211yescharacteristic
119#1988C2211yescharacteristic
120#1988C2211yescharacteristic
121#1988C2211yescharacteristic
122#1987C2211yescharacteristic
123#1987C2211yescharacteristic
124#1987C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1948C2211yescharacteristic
130#1948C2211yescharacteristic
131#1947C2211yescharacteristic
132#1947C2211yescharacteristic
133#1944C2211yescharacteristic
134#1944C2211yescharacteristic
135#1944C2211yescharacteristic
136#1943C2211yescharacteristic
137#1943C2211yescharacteristic
138#1943C2211yescharacteristic
139#1942C2211yescharacteristic
140#1941C2211yescharacteristic
141#1940C2211yescharacteristic
142#1940C2211yescharacteristic
143#1940C2211yescharacteristic
144#1939C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1921C2211yescharacteristic
159#1921C2211yescharacteristic
160#1920C2211yescharacteristic
161#1920C2211yescharacteristic
162#1920C2211yescharacteristic
163#1919C2211yescharacteristic
164#1919C2211yescharacteristic
165#1919C2211yescharacteristic
166#1919C2211yescharacteristic
167#1919C2211yescharacteristic
168#1918C2211yescharacteristic
169#1918C2211yescharacteristic
170#1918C2211yescharacteristic
171#1918C2211yescharacteristic
172#1918C2211yescharacteristic
173#1917C2211yescharacteristic
174#1917C2211yescharacteristic
175#1917C2211yescharacteristic
176#1916C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1847C2211yescharacteristic
182#1836C2211yescharacteristic
183#1802C2211yescharacteristic
184#1802C2211yescharacteristic
185#1776C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191C4×#107C2211yescharacteristic
192C4×#107C2211yescharacteristic
193#1771C2211yescharacteristic
194#1771C2211yescharacteristic
195#1771C2211yescharacteristic
196#1770C2211yescharacteristic
197#1767C2211yescharacteristic
198#1767C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201#1762C2211yescharacteristic
202#1762C2211yescharacteristic
203C2×C4⋊Q8—21no—
204C2×C4⋊Q8—21no—
205C2×C4⋊Q8—21no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#125—21no—
213C2×#125D411yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C4×Q8—21no—
219C2×C4×Q8—21no—
220C2×C4×Q8—21no—
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C22×C42—21no—
225#501—24no—
226#498—24no—
227#476—24no—
228#474Q818yescomplemented
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#97C2311yescharacteristic
266C2×#97C2311yescharacteristic
267C2×#97C2311yescharacteristic
268C2×#97C2311yescharacteristic
269C2×#97C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×C4×C8C2311yescharacteristic
272C2×C4×C8C2311yescharacteristic
273#399—21no—
274#399—21no—
275#398—21no—
276#398—21no—
277#398—21no—
278#398—21no—
279#398—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#396—21no—
288#396—21no—
289#396—21no—
290#396—21no—
291#395—21no—
292#395—21no—
293#395—21no—
294#395—21no—
295#395—21no—
296#395—21no—
297#395—21no—
298#395—21no—
299#393—21no—
300#393—21no—
301#391—21no—
302#391—21no—
303#391—21no—
304#391—21no—
305#391—21no—
306#391—21no—
307#391—21no—
308#391—21no—
309#391—21no—
310#391—21no—
311#391—21no—
312#391—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#390C2311yescharacteristic
317#390C2311yescharacteristic
318#390C2311yescharacteristic
319#390C2311yescharacteristic
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389D411yescharacteristic
340#389D411yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#388—21no—
362#388—21no—
363#388—21no—
364#388—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#387D411yescharacteristic
380#387D411yescharacteristic
381#387D411yescharacteristic
382#387D411yescharacteristic
383#385—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#384C2311yescharacteristic
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#382D411yescharacteristic
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#381—21no—
395#381—21no—
396#380—21no—
397#380—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⋊C4C2311yescharacteristic
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C43C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
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#340C2311yescharacteristic
469#340C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482C22×Q8—21no—
483C22×Q8—21no—
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8—21no—
488C22×D4C2411yescharacteristic
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—21no—
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C4⋊Q8—22no—
501C4⋊Q8—22no—
502C4⋊Q8—22no—
503C4⋊Q8—22no—
504C4⋊Q8—22no—
505C4⋊Q8—22no—
506C4⋊Q8—41no—
507C4⋊Q8—41no—
508C4⋊Q8—41no—
509C4⋊Q8—41no—
510C4⋊Q8—41no—
511C4⋊Q8—82no—
512C4⋊Q8—82no—
513C4⋊Q8—82no—
514C4⋊Q8C2×Q814yes—
515#125—24no—
516#125—22no—
517#125—22no—
518#125—41no—
519#125—41no—
520#125—82no—
521C22⋊Q8—44no—
522C22⋊Q8—82no—
523C4×Q8—82no—
524C4×Q8—82no—
525C4×Q8—82no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—41no—
530C4×D4—41no—
531C4×D4C2×Q814yes—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
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⋊C4—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
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—82no—
624C2×C42C2×D411yescharacteristic
625C2×C42C2×D411yescharacteristic
626C2×C42C2×D411yescharacteristic
627C2×C42C2×D411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635#107—22no—
636#107—22no—
637#107—22no—
638#107—22no—
639#107—41no—
640#107—41no—
641#107—41no—
642#107—41no—
643#107C2×Q814yes—
644#107C2×Q814yes—
645#106—22no—
646#106—22no—
647#106—22no—
648#106—22no—
649#106—22no—
650#106—41no—
651#106—41no—
652#106—41no—
653#106—41no—
654#106#4114yes—
655C4⋊C8—22no—
656C4⋊C8—22no—
657C4⋊C8—41no—
658C4⋊C8—41no—
659C4⋊C8—41no—
660C4⋊C8—41no—
661C4⋊C8—41no—
662C4⋊C8C2×Q814yes—
663#102—22no—
664#102—22no—
665#102—41no—
666#102—41no—
667#102—41no—
668#102—41no—
669#102C2×Q814yes—
670#102C2×Q814yes—
671#97—22no—
672#97—22no—
673#97—22no—
674#97—41no—
675#97—41no—
676#97—41no—
677C4×C8—22no—
678C4×C8—41no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
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#95C2×D411yescharacteristic
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730C24—21no—
731C2×Q8—24no—
732C2×Q8—42no—
733C2×Q8—42no—
734C2×Q8—42no—
735C2×Q8—42no—
736C2×Q8—42no—
737C2×Q8—42no—
738C2×Q8—42no—
739C2×Q8—81no—
740C2×Q8—81no—
741C2×Q8—81no—
742C2×Q8—81no—
743C2×Q8—81no—
744C2×Q8—81no—
745C2×Q8—81no—
746C2×Q8—81no—
747C2×Q8—81no—
748C2×Q8—81no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4C22×Q812yes—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—24no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—81no—
776C22×C4—81no—
777C22×C4—81no—
778C22×C4—81no—
779C22×C4C22×D411yescharacteristic
780C22×C4C22×D411yescharacteristic
781C22×C4C22×D411yescharacteristic
782C22×C4C22×D411yescharacteristic
783C22×C4C22×D411yescharacteristic
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D411yescharacteristic
788C22×C4C22×D411yescharacteristic
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C2511yescharacteristic
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8C22×Q812yes—
816C2×C8C22×Q812yes—
817C2×C8C2×#4112yes—
818C4⋊C4—24no—
819C4⋊C4—22no—
820C4⋊C4—22no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—41no—
849C4⋊C4—41no—
850C4⋊C4—41no—
851C4⋊C4—41no—
852C4⋊C4—41no—
853C4⋊C4—41no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—42no—
860C4⋊C4—42no—
861C4⋊C4—42no—
862C4⋊C4—42no—
863C4⋊C4—42no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—42no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4#13714yes—
892C4⋊C4C22×Q812yes—
893C4⋊C4C22×Q812yes—
894C4⋊C4C22×Q812yes—
895C4⋊C4C2×#4112yes—
896C4⋊C4C2×#4112yes—
897C4⋊C42−1+412yes—
898C22⋊C4—24no—
899C22⋊C4—42no—
900C22⋊C4—42no—
901C22⋊C4—42no—
902C22⋊C4—42no—
903C22⋊C4—81no—
904C22⋊C4—81no—
905C22⋊C4—81no—
906C22⋊C4—81no—
907C22⋊C4—81no—
908C22⋊C4—81no—
909C42—22no—
910C42—21no—
911C42—21no—
912C42—21no—
913C42—21no—
914C42—21no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—41no—
923C42—41no—
924C42—41no—
925C42—42no—
926C42—42no—
927C42—42no—
928C42—81no—
929C42—81no—
930C42—81no—
931C42—81no—
932C42—81no—
933C42—81no—
934C42—81no—
935C42—81no—
936C42—81no—
937C42—81no—
938C42—81no—
939C42—81no—
940C42C22×Q812yes—
941C422−1+412yes—
942C23—22no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23C23×D411yescharacteristic
950Q8—84no—
951Q8—84no—
952Q8—84no—
953Q8—162no—
954Q8—162no—
955Q8—162no—
956D4—22no—
957D4—22no—
958D4—41no—
959D4—41no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—22no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—84no—
1043C2×C4—84no—
1044C2×C4—84no—
1045C2×C4D4×Q812yes—
1046C2×C4D4×Q812yes—
1047C2×C4C2×#13712yes—
1048C2×C4C2×#13712yes—
1049C2×C4C2×#13712yes—
1050C2×C4C23×Q811yescharacteristic
1051C2×C4C22×#4111yescharacteristic
1052C2×C4C2×2−1+411yescharacteristic
1053C2×C4C2×2−1+411yescharacteristic
1054C2×C4#58511yescharacteristic
1055C2×C4#58511yescharacteristic
1056C8—22no—
1057C8—22no—
1058C8—22no—
1059C8—41no—
1060C8—41no—
1061C8—41no—
1062C8—41no—
1063C8—41no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—81no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22C2×D4×Q811yescharacteristic
1072C22D4×#4111yescharacteristic
1073C22#348911yescharacteristic
1074C22C22×#13711yescharacteristic
1075C22#358511yescharacteristic
1076C22#358511yescharacteristic
1077C22#358511yescharacteristic
1078C4—22no—
1079C4—22no—
1080C4—22no—
1081C4—22no—
1082C4—22no—
1083C4—41no—
1084C4—42no—
1085C4—41no—
1086C4—41no—
1087C4—41no—
1088C4—42no—
1089C4—41no—
1090C4—41no—
1091C4—41no—
1092C4—42no—
1093C4—41no—
1094C4—41no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—81no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4Q8×#4111yescharacteristic
1108C4#350211yescharacteristic
1109C4#350911yescharacteristic
1110C4#356511yescharacteristic
1111C2—82no—
1112C2#5915211yescharacteristic
1113C2Q8×#13711yescharacteristic
1114C2#6137811yescharacteristic
1115C2#6145311yescharacteristic
1116C2#6150411yescharacteristic
1117C2#6211211yescharacteristic
1118C2#6223111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#125 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59668C2semidirect
7. #29317C2semidirect
8. #29182C2semidirect
11. #28819C2semidirect
12. #28802C2semidirect
15. #26882C2semidirect
16. #26882C2semidirect
17. #26875C2semidirect
18. #26862C2semidirect
19. #26458C2semidirect
20. #26454C2semidirect
21. #26453C2semidirect
22. #26446C2semidirect
25. #23256C2semidirect
26. #23167C2semidirect
27. #23163C2semidirect
228. #474Q8semidirect

Maximal subgroups

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

subgroupindex
#596682
#364792
#318902
#318702
#309702
#309542
#293172
#291822
#289682
#289572
#288192
#288022
#270192
#270182
#268822
#268752
#268622
#264582
#264542
#264532
#264462
#261022
#260362
#232562
#231672
#231632
#230792
#216142
#216132