Finite Group Databasebeta

← #6851651

Subgroups — #6851651

Order 512.

1284 conjugacy classes of subgroups.

The subgroup lattice has 1101 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36556C211yesmaximal, characteristic, complemented
2#34893C211yesmaximal, characteristic
3#33070C211yesmaximal, characteristic
4#32688C211yesmaximal, characteristic, complemented
5#32687C211yesmaximal, characteristic, complemented
6#32577C211yesmaximal, characteristic
7#32573C211yesmaximal, characteristic
8#32356C211yesmaximal, characteristic
9#32354C211yesmaximal, characteristic
10#32140C211yesmaximal, characteristic, complemented
11#32138C211yesmaximal, characteristic, complemented
12#30000C211yesmaximal, characteristic
13#29982C211yesmaximal, characteristic
14#29316C211yesmaximal, characteristic, complemented
15#29315C211yesmaximal, characteristic, complemented
16#29288C211yesmaximal, characteristic, complemented
17#29279C211yesmaximal, characteristic, complemented
18#29279C211yesmaximal, characteristic, complemented
19#29209C211yesmaximal, characteristic, complemented
20#28950C211yesmaximal, characteristic
21#28944C211yesmaximal, characteristic
22#27993C211yesmaximal, characteristic, complemented
23#27991C211yesmaximal, characteristic, complemented
24#27002C211yesmaximal, characteristic
25#26998C211yesmaximal, characteristic
26#26862C211yesmaximal, characteristic, complemented
27#26858C211yesmaximal, characteristic, complemented
28#22821C211yesmaximal, characteristic, complemented
29#22114C211yesmaximal, characteristic
30#22114C211yesmaximal, characteristic
31C4×#478C211yesmaximal, characteristic
32C2×#478C2211yescharacteristic
33#2864C2211yescharacteristic
34#2864C2211yescharacteristic
35#2862C2211yescharacteristic
36#2589—21no—
37#2588—21no—
38#2588—21no—
39#2587—21no—
40#2584C2211yescharacteristic
41#2580C2211yescharacteristic
42#2567C2211yescharacteristic
43#2566C2211yescharacteristic
44#2550C2211yescharacteristic
45#2546C2211yescharacteristic
46#2522—21no—
47#2520—21no—
48#2520—21no—
49#2511—21no—
50#2509C2211yescharacteristic
51#2509C2211yescharacteristic
52#2509C2211yescharacteristic
53#2508C2211yescharacteristic
54#2508C2211yescharacteristic
55#2507C2211yescharacteristic
56#2465—21no—
57#2454C2211yescharacteristic
58#2452C2211yescharacteristic
59#2446—21no—
60#2396—21no—
61#2396—21no—
62#2369C2211yescharacteristic
63#2365—21no—
64#2365C2211yescharacteristic
65#2355—21no—
66C4×C4⋊Q8C2211yescharacteristic
67C4×#125C2211yescharacteristic
68C4×#125C2211yescharacteristic
69C4×#125C2211yescharacteristic
70C4×#125C2211yescharacteristic
71C4×#125C2211yescharacteristic
72C4×C22⋊Q8—21no—
73#2296—21no—
74#2293C2211yescharacteristic
75#2293C2211yescharacteristic
76C42×Q8C2211yescharacteristic
77C42×D4C2211yescharacteristic
78#2101C2211yescharacteristic
79#2101C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2092C2211yescharacteristic
85#2092C2211yescharacteristic
86#2088C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2087C2211yescharacteristic
91#2087C2211yescharacteristic
92#2087C2211yescharacteristic
93#2086C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2084C2211yescharacteristic
97#2083C2211yescharacteristic
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic
100#2065C2211yescharacteristic
101#2065C2211yescharacteristic
102#2059C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2058C2211yescharacteristic
109#2058C2211yescharacteristic
110#2058C2211yescharacteristic
111#2058C2211yescharacteristic
112#2057C2211yescharacteristic
113#2057C2211yescharacteristic
114#2057C2211yescharacteristic
115#2057C2211yescharacteristic
116#2023C2211yescharacteristic
117#2023C2211yescharacteristic
118#1991C2211yescharacteristic
119#1991C2211yescharacteristic
120#1989C2211yescharacteristic
121#1989C2211yescharacteristic
122#1989C2211yescharacteristic
123#1988C2211yescharacteristic
124#1988C2211yescharacteristic
125#1984C2211yescharacteristic
126#1984C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1948C2211yescharacteristic
137#1947C2211yescharacteristic
138#1942C2211yescharacteristic
139#1942C2211yescharacteristic
140#1942C2211yescharacteristic
141#1942C2211yescharacteristic
142#1942C2211yescharacteristic
143#1942C2211yescharacteristic
144#1941C2211yescharacteristic
145#1941C2211yescharacteristic
146#1941C2211yescharacteristic
147#1941C2211yescharacteristic
148#1941C2211yescharacteristic
149#1941C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic
158#1921C2211yescharacteristic
159#1921C2211yescharacteristic
160#1921C2211yescharacteristic
161#1921C2211yescharacteristic
162#1921C2211yescharacteristic
163#1921C2211yescharacteristic
164#1920C2211yescharacteristic
165#1920C2211yescharacteristic
166#1920C2211yescharacteristic
167#1920C2211yescharacteristic
168#1920C2211yescharacteristic
169#1919C2211yescharacteristic
170#1919C2211yescharacteristic
171#1919C2211yescharacteristic
172#1919C2211yescharacteristic
173#1918C2211yescharacteristic
174#1918C2211yescharacteristic
175#1918C2211yescharacteristic
176#1916C2211yescharacteristic
177#1916C2211yescharacteristic
178#1916C2211yescharacteristic
179#1916C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1846C2211yescharacteristic
187#1846C2211yescharacteristic
188#1842C2211yescharacteristic
189#1831C2211yescharacteristic
190#1831C2211yescharacteristic
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic
194C4×#107C2211yescharacteristic
195C4×#106C2211yescharacteristic
196C8×C4⋊C4C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic
198C4×C4⋊C8C2211yescharacteristic
199C4×C4⋊C8C2211yescharacteristic
200C4×C4⋊C8C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C2×C4⋊Q8—21no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#125C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×C22⋊Q8—21no—
211C2×C4×Q8—21no—
212C2×C4×Q8—21no—
213C2×C4×Q8D411yescharacteristic
214C2×C4×Q8D411yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×D4C2311yescharacteristic
217C2×C4×D4C2311yescharacteristic
218C2×C4×D4C2311yescharacteristic
219C2×#117—21no—
220C2×#117—21no—
221C22×C42—21no—
222#478Q818yescomplemented
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×#102C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×C4×C8C2311yescharacteristic
260C2×C4×C8C2311yescharacteristic
261C2×C4×C8C2311yescharacteristic
262C2×C4×C8C2311yescharacteristic
263C2×C4×C8C2311yescharacteristic
264C2×C4×C8C2311yescharacteristic
265#400—21no—
266#400—21no—
267#400—21no—
268#400—21no—
269#400—21no—
270#400—21no—
271#400—21no—
272#400—21no—
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#396—21no—
284#396—21no—
285#396—21no—
286#396—21no—
287#395—21no—
288#395—21no—
289#395—21no—
290#395—21no—
291#393—21no—
292#393—21no—
293#391—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#390C2311yescharacteristic
305#390C2311yescharacteristic
306#390C2311yescharacteristic
307#390C2311yescharacteristic
308#389—21no—
309#389—21no—
310#389—21no—
311#389—21no—
312#389—21no—
313#389—21no—
314#389—21no—
315#389—21no—
316#389—21no—
317#389C2311yescharacteristic
318#389C2311yescharacteristic
319#389C2311yescharacteristic
320#389C2311yescharacteristic
321#389C2311yescharacteristic
322#389C2311yescharacteristic
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#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#388—21no—
342#388—21no—
343#388—21no—
344#388—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#385—21no—
377#384—21no—
378#384C2311yescharacteristic
379#382—21no—
380#382—21no—
381#382C2311yescharacteristic
382#382C2311yescharacteristic
383#382C2311yescharacteristic
384#382C2311yescharacteristic
385#382C2311yescharacteristic
386#382C2311yescharacteristic
387#382C2311yescharacteristic
388#380—21no—
389C4×C4⋊C4—21no—
390C4×C4⋊C4—21no—
391C4×C4⋊C4—21no—
392C4×C4⋊C4—21no—
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⋊C4D411yescharacteristic
402C4×C4⋊C4D411yescharacteristic
403C4×C4⋊C4D411yescharacteristic
404C4×C4⋊C4D411yescharacteristic
405C4×C4⋊C4D411yescharacteristic
406C4×C4⋊C4D411yescharacteristic
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×C22⋊C4—21no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C43C2311yescharacteristic
427C43C2311yescharacteristic
428C43C2311yescharacteristic
429#340C2311yescharacteristic
430#340C2311yescharacteristic
431#340C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
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#336C2311yescharacteristic
466#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479C22×Q8—21no—
480C22×Q8—21no—
481C22×Q8—21no—
482C22×Q8C2×D411yescharacteristic
483C22×D4C2411yescharacteristic
484C23×C4—21no—
485C23×C4—21no—
486C23×C4—21no—
487C22×C8C2411yescharacteristic
488C22×C8C2411yescharacteristic
489C22×C8C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C4⋊Q8—22no—
496C4⋊Q8—41no—
497C4⋊Q8—41no—
498C4⋊Q8—41no—
499C4⋊Q8—41no—
500C4⋊Q8—41no—
501C4⋊Q8—44no—
502#125—22no—
503#125—22no—
504#125—41no—
505#125—41no—
506#125—41no—
507#125C2×Q814yes—
508C22⋊Q8—44no—
509C4×Q8—24no—
510C4×Q8—41no—
511C4×Q8—41no—
512C4×Q8—42no—
513C4×Q8—44no—
514C4×Q8—82no—
515C4×D4—22no—
516C4×D4—22no—
517C4×D4—41no—
518C4×D4—41no—
519C4×D4—41no—
520C4×D4C2×Q814yes—
521#117—44no—
522#117—82no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
559C2×C4⋊C4C2×D411yescharacteristic
560C2×C4⋊C4C2×D411yescharacteristic
561C2×C4⋊C4C2×D411yescharacteristic
562C2×C4⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C42—21no—
594C2×C42—21no—
595C2×C42—21no—
596C2×C42—21no—
597C2×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—82no—
605C2×C42C2×D411yescharacteristic
606C2×C42C2×D411yescharacteristic
607C2×C42C2×D411yescharacteristic
608C2×C42C2×D411yescharacteristic
609C2×C42C2×D411yescharacteristic
610C2×C42C2×D411yescharacteristic
611C2×C42C2×D411yescharacteristic
612C2×C42C2×D411yescharacteristic
613C2×C42C2×D411yescharacteristic
614C2×C42C2×D411yescharacteristic
615C2×C42C2×D411yescharacteristic
616C2×C42C2×D411yescharacteristic
617C2×C42C2411yescharacteristic
618C2×C42C2411yescharacteristic
619C2×C42C2411yescharacteristic
620C2×C42C2411yescharacteristic
621C2×C42C2411yescharacteristic
622C2×C42C2411yescharacteristic
623C2×C42C2411yescharacteristic
624#107—22no—
625#107—41no—
626#107—41no—
627#107—41no—
628#107—41no—
629#107—41no—
630#107—41no—
631#107—41no—
632#107—41no—
633#107C2×Q814yes—
634#106—22no—
635#106—41no—
636#106—41no—
637#106—41no—
638#106—41no—
639#106—41no—
640#106—41no—
641#106—41no—
642#106—41no—
643#106C2×Q814yes—
644C4⋊C8—22no—
645C4⋊C8—22no—
646C4⋊C8—22no—
647C4⋊C8—41no—
648C4⋊C8—41no—
649C4⋊C8—41no—
650C4⋊C8—41no—
651C4⋊C8C2×Q814yes—
652#102—41no—
653#102—41no—
654#102—41no—
655#102—41no—
656#102—41no—
657#102—41no—
658#102C2×Q814yes—
659#102C2×Q814yes—
660C4×C8—41no—
661C4×C8—41no—
662C4×C8—41no—
663C4×C8—41no—
664C4×C8—41no—
665C4×C8—41no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
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#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721C24—21no—
722C2×Q8—22no—
723C2×Q8—22no—
724C2×Q8—41no—
725C2×Q8—42no—
726C2×Q8—42no—
727C2×Q8—42no—
728C2×Q8—42no—
729C2×Q8—42no—
730C2×Q8—42no—
731C2×Q8—81no—
732C2×Q8—81no—
733C2×Q8—81no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4C22×Q812yes—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—24no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—81no—
762C22×C4—81no—
763C22×C4—81no—
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C22×D411yescharacteristic
767C22×C4C22×D411yescharacteristic
768C22×C4C22×D411yescharacteristic
769C22×C4C22×D411yescharacteristic
770C22×C4C22×D411yescharacteristic
771C22×C4C22×D411yescharacteristic
772C22×C4C22×D411yescharacteristic
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D411yescharacteristic
775C22×C4C22×D411yescharacteristic
776C22×C4C22×D411yescharacteristic
777C22×C4C22×D411yescharacteristic
778C22×C4C2511yescharacteristic
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8C22×Q812yes—
802C2×C8C22×Q812yes—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
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—41no—
835C4⋊C4—41no—
836C4⋊C4—41no—
837C4⋊C4—41no—
838C4⋊C4—41no—
839C4⋊C4—42no—
840C4⋊C4—42no—
841C4⋊C4—42no—
842C4⋊C4—42no—
843C4⋊C4—42no—
844C4⋊C4—42no—
845C4⋊C4—42no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—42no—
849C4⋊C4—42no—
850C4⋊C4—42no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—81no—
857C4⋊C4—81no—
858C4⋊C4—81no—
859C4⋊C4—81no—
860C4⋊C4—81no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4#13514yes—
873C4⋊C4C22×Q812yes—
874C4⋊C4C22×Q812yes—
875C4⋊C4C22×Q812yes—
876C4⋊C42−1+412yes—
877C22⋊C4—24no—
878C22⋊C4—42no—
879C22⋊C4—42no—
880C22⋊C4—42no—
881C22⋊C4—42no—
882C22⋊C4—42no—
883C22⋊C4—42no—
884C22⋊C4—81no—
885C22⋊C4—81no—
886C22⋊C4—81no—
887C22⋊C4—81no—
888C42—22no—
889C42—22no—
890C42—22no—
891C42—22no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—21no—
898C42—21no—
899C42—21no—
900C42—21no—
901C42—21no—
902C42—21no—
903C42—21no—
904C42—41no—
905C42—41no—
906C42—41no—
907C42—41no—
908C42—41no—
909C42—41no—
910C42—41no—
911C42—41no—
912C42—42no—
913C42—42no—
914C42—42no—
915C42—42no—
916C42—42no—
917C42—42no—
918C42—42no—
919C42—81no—
920C42—81no—
921C42—81no—
922C42—81no—
923C42C22×Q812yes—
924C422−1+412yes—
925C23—22no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23C23×D411yescharacteristic
933Q8—44no—
934Q8—84no—
935Q8—84no—
936Q8—162no—
937D4—22no—
938D4—22no—
939D4—41no—
940D4—41no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—48no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
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—84no—
1024C2×C4—84no—
1025C2×C4D4×Q812yes—
1026C2×C4D4×Q812yes—
1027C2×C4C2×#13512yes—
1028C2×C4C2×#13512yes—
1029C2×C4C2×#13512yes—
1030C2×C4#57512yes—
1031C2×C4C23×Q811yescharacteristic
1032C2×C4C2×2−1+411yescharacteristic
1033C2×C4C2×2−1+411yescharacteristic
1034C2×C4#58511yescharacteristic
1035C2×C4#58511yescharacteristic
1036C2×C4#58511yescharacteristic
1037C8—22no—
1038C8—22no—
1039C8—41no—
1040C8—41no—
1041C8—41no—
1042C8—41no—
1043C8—41no—
1044C8—41no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22#344911yescharacteristic
1053C22C2×D4×Q811yescharacteristic
1054C22#348911yescharacteristic
1055C22C22×#13511yescharacteristic
1056C22C2×#57511yescharacteristic
1057C22#358411yescharacteristic
1058C22#358511yescharacteristic
1059C4—22no—
1060C4—22no—
1061C4—22no—
1062C4—22no—
1063C4—22no—
1064C4—22no—
1065C4—41no—
1066C4—41no—
1067C4—41no—
1068C4—41no—
1069C4—41no—
1070C4—42no—
1071C4—42no—
1072C4—42no—
1073C4—42no—
1074C4—41no—
1075C4—41no—
1076C4—41no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4—81no—
1086C4—81no—
1087C4—81no—
1088C4#350211yescharacteristic
1089C4#350411yescharacteristic
1090C4#355511yescharacteristic
1091C4#355711yescharacteristic
1092C2—82no—
1093C2#3959111yescharacteristic
1094C2#6094211yescharacteristic
1095C2#6099811yescharacteristic
1096C2Q8×#13511yescharacteristic
1097C2#6136711yescharacteristic
1098C2#6210311yescharacteristic
1099C2#6214211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36556C2semidirect
4. #32688C2semidirect
5. #32687C2semidirect
10. #32140C2semidirect
11. #32138C2semidirect
14. #29316C2semidirect
15. #29315C2semidirect
16. #29288C2semidirect
17. #29279C2semidirect
18. #29279C2semidirect
19. #29209C2semidirect
22. #27993C2semidirect
23. #27991C2semidirect
26. #26862C2semidirect
27. #26858C2semidirect
28. #22821C2semidirect
222. #478Q8semidirect

Maximal subgroups

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

subgroupindex
#365562
#348932
#330702
#326882
#326872
#325772
#325732
#323562
#323542
#321402
#321382
#300002
#299822
#293162
#293152
#292882
#292792
#292092
#289502
#289442
#279932
#279912
#270022
#269982
#268622
#268582
#228212
#221142
C4×#4782