Finite Group Databasebeta

← #6625567

Subgroups — #6625567

Order 512.

2805 conjugacy classes of subgroups.

The subgroup lattice has 1403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3502C211yesmaximal, characteristic
2C2×#3390C211yesmaximal, characteristic, complemented
3C2×#3383C211yesmaximal, characteristic, complemented
4#39591C211yesmaximal, characteristic
5#32967C211yesmaximal, characteristic
6#32964C211yesmaximal, characteristic
7#32960C211yesmaximal, characteristic
8#25848C211yesmaximal, characteristic, complemented
9#25847C211yesmaximal, characteristic, complemented
10#25842C211yesmaximal, characteristic, complemented
11#25842C211yesmaximal, characteristic, complemented
12#25842C211yesmaximal, characteristic, complemented
13#25841C211yesmaximal, characteristic, complemented
14#25822C211yesmaximal, characteristic
15#25821C211yesmaximal, characteristic
16#25814C211yesmaximal, characteristic
17#24348C211yesmaximal, characteristic, complemented
18#24345C211yesmaximal, characteristic, complemented
19#24336C211yesmaximal, characteristic, complemented
20#24336C211yesmaximal, characteristic, complemented
21#24336C211yesmaximal, characteristic, complemented
22#24333C211yesmaximal, characteristic, complemented
23#24311C211yesmaximal, characteristic
24#24310C211yesmaximal, characteristic
25#24306C211yesmaximal, characteristic
26#22527C211yesmaximal, characteristic, complemented
27#22521C211yesmaximal, characteristic, complemented
28#22509C211yesmaximal, characteristic
29#21463C211yesmaximal, characteristic
30#21463C211yesmaximal, characteristic
31C4×#451C211yesmaximal, characteristic
32#3502—28no—
33#3502—28no—
34C2×Q82—21no—
35C2×Q82C2211yescharacteristic
36C2×Q82C2211yescharacteristic
37C2×#557—21no—
38C2×#557—21no—
39C2×#557—21no—
40C2×#557C2211yescharacteristic
41C2×#557C2211yescharacteristic
42C2×#557C2211yescharacteristic
43C2×#557C2211yescharacteristic
44C2×#557C2211yescharacteristic
45C2×#557C2211yescharacteristic
46C2×#557C2211yescharacteristic
47C2×#544—21no—
48C2×#544—21no—
49C2×#544C2211yescharacteristic
50C2×#544C2211yescharacteristic
51C2×#533—21no—
52C2×#533—21no—
53C2×#533C2211yescharacteristic
54C2×#533C2211yescharacteristic
55C2×#519C2211yescharacteristic
56C2×#519C2211yescharacteristic
57C22×C4×Q8C2211yescharacteristic
58#3390—28no—
59#3383—28no—
60C2×#501C2211yescharacteristic
61C2×#501C2211yescharacteristic
62C2×#500C2211yescharacteristic
63C2×#499C2211yescharacteristic
64C2×#499C2211yescharacteristic
65C2×#499C2211yescharacteristic
66C2×#479C2211yescharacteristic
67C2×#479C2211yescharacteristic
68C2×#479C2211yescharacteristic
69C2×#479C2211yescharacteristic
70C2×#479C2211yescharacteristic
71C2×#479C2211yescharacteristic
72C2×#479C2211yescharacteristic
73C2×#479C2211yescharacteristic
74C2×#477C2211yescharacteristic
75C2×#477C2211yescharacteristic
76C2×#475C2211yescharacteristic
77C2×#475C2211yescharacteristic
78C2×#451C2211yescharacteristic
79C2×#446C2211yescharacteristic
80C2×C8×Q8C2211yescharacteristic
81C2×#441C2211yescharacteristic
82C2×#441C2211yescharacteristic
83C2×C4×Q16C2211yescharacteristic
84C2×C4×Q16C2211yescharacteristic
85C2×C4×Q16C2211yescharacteristic
86C2×C4×Q16C2211yescharacteristic
87#2851C2211yescharacteristic
88#2734—21no—
89#2729—21no—
90#2720—21no—
91#2713—21no—
92#2629C2211yescharacteristic
93#2628C2211yescharacteristic
94#2584C2211yescharacteristic
95#2584C2211yescharacteristic
96#2582C2211yescharacteristic
97#2581C2211yescharacteristic
98#2581C2211yescharacteristic
99#2567C2211yescharacteristic
100#2556—21no—
101#2506—21no—
102#2465—21no—
103#2462—21no—
104#2355C2211yescharacteristic
105#2323C2211yescharacteristic
106#2323C2211yescharacteristic
107C4×C22⋊Q8C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2058C2211yescharacteristic
115#2058C2211yescharacteristic
116#2058C2211yescharacteristic
117#2058C2211yescharacteristic
118#2058C2211yescharacteristic
119#2057C2211yescharacteristic
120#2057C2211yescharacteristic
121#2057C2211yescharacteristic
122#2057C2211yescharacteristic
123#2057C2211yescharacteristic
124#2057C2211yescharacteristic
125#2057C2211yescharacteristic
126#2026C2211yescharacteristic
127#2026C2211yescharacteristic
128#2024C2211yescharacteristic
129#2024C2211yescharacteristic
130#2024C2211yescharacteristic
131#2024C2211yescharacteristic
132#1993C2211yescharacteristic
133#1992C2211yescharacteristic
134#1991C2211yescharacteristic
135#1991C2211yescharacteristic
136#1991C2211yescharacteristic
137#1990C2211yescharacteristic
138#1989C2211yescharacteristic
139#1989C2211yescharacteristic
140#1989C2211yescharacteristic
141#1989C2211yescharacteristic
142#1988C2211yescharacteristic
143#1987C2211yescharacteristic
144#1985C2211yescharacteristic
145#1985C2211yescharacteristic
146#1984C2211yescharacteristic
147#1984C2211yescharacteristic
148#1984C2211yescharacteristic
149#1984C2211yescharacteristic
150#1878C2211yescharacteristic
151#1878C2211yescharacteristic
152#1878C2211yescharacteristic
153#1878C2211yescharacteristic
154#1878C2211yescharacteristic
155#1878C2211yescharacteristic
156#1873C2211yescharacteristic
157#1873C2211yescharacteristic
158#1872C2211yescharacteristic
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#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1853C2211yescharacteristic
184#1852C2211yescharacteristic
185#1852C2211yescharacteristic
186#1805C2211yescharacteristic
187#1805C2211yescharacteristic
188#1805C2211yescharacteristic
189#1805C2211yescharacteristic
190#1803C2211yescharacteristic
191#1803C2211yescharacteristic
192#1798C2211yescharacteristic
193#1798C2211yescharacteristic
194#1797C2211yescharacteristic
195#1787C2211yescharacteristic
196#1787C2211yescharacteristic
197#1787C2211yescharacteristic
198#1763C2211yescharacteristic
199#1763C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C4×#103C2211yescharacteristic
204#1750C2211yescharacteristic
205#1750C2211yescharacteristic
206C4×C22⋊C8C2211yescharacteristic
207C23×Q8C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210Q82—216no—
211Q82—24no—
212Q82—24no—
213Q82—24no—
214Q82—24no—
215#557—216no—
216#557—216no—
217#557—216no—
218#557—24no—
219#557—24no—
220#557—24no—
221#557—24no—
222#557—24no—
223#557—24no—
224#557—24no—
225#557—24no—
226#557—24no—
227#557—24no—
228#557—24no—
229#557—24no—
230#557D418yes—
231#557D418yes—
232#544—216no—
233#544—216no—
234#544—24no—
235#544—24no—
236#544—24no—
237#544—24no—
238#533—216no—
239#533—216no—
240#533—24no—
241#533—24no—
242#533—24no—
243#533—24no—
244C2×C4⋊Q8—21no—
245C2×C4⋊Q8—21no—
246C2×C4⋊Q8—21no—
247C2×C4⋊Q8—21no—
248C2×C4⋊Q8—21no—
249C2×C4⋊Q8—21no—
250C2×C4⋊Q8—21no—
251C2×C4⋊Q8—21no—
252C2×C4⋊Q8—21no—
253C2×C4⋊Q8—21no—
254C2×C4⋊Q8—21no—
255C2×C4⋊Q8—21no—
256C2×C4⋊Q8—21no—
257C2×C4⋊Q8—21no—
258C2×C4⋊Q8—21no—
259C2×C4⋊Q8D411yescharacteristic
260C2×C4⋊Q8D411yescharacteristic
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×#125—21no—
269C2×#125—21no—
270C2×#125—21no—
271C2×#125—21no—
272C2×#125—21no—
273C2×#125—21no—
274C2×#125—21no—
275C2×#125—21no—
276C2×#125—21no—
277C2×#125—21no—
278C2×#125—21no—
279C2×#125—21no—
280C2×#125—21no—
281C2×#125—21no—
282C2×#125—21no—
283C2×#125—21no—
284C2×#125D411yescharacteristic
285C2×#125D411yescharacteristic
286C2×#125C2311yescharacteristic
287C2×#125C2311yescharacteristic
288C2×#125C2311yescharacteristic
289C2×#125C2311yescharacteristic
290C2×#125C2311yescharacteristic
291C2×#125C2311yescharacteristic
292C2×#125C2311yescharacteristic
293C2×#125C2311yescharacteristic
294C2×C22⋊Q8—21no—
295C2×C22⋊Q8—21no—
296C2×C22⋊Q8—21no—
297C2×C22⋊Q8—21no—
298C2×C22⋊Q8—21no—
299C2×C22⋊Q8—21no—
300C2×C22⋊Q8D411yescharacteristic
301C2×C22⋊Q8D411yescharacteristic
302C2×C22⋊Q8D411yescharacteristic
303C2×C22⋊Q8D411yescharacteristic
304C2×C22⋊Q8C2311yescharacteristic
305#519—24no—
306#519—24no—
307#519—24no—
308#519—24no—
309C2×C4×Q8—21no—
310C2×C4×Q8—21no—
311C2×C4×Q8—24no—
312C2×C4×Q8—24no—
313C2×C4×Q8—21no—
314C2×C4×Q8—21no—
315C2×C4×Q8—21no—
316C2×C4×Q8—21no—
317C2×C4×Q8—21no—
318C2×C4×Q8—21no—
319C2×C4×Q8—21no—
320C2×C4×Q8—21no—
321C2×C4×Q8—21no—
322C2×C4×Q8—21no—
323C2×C4×Q8—21no—
324C2×C4×Q8—21no—
325C2×C4×Q8—21no—
326C2×C4×Q8—21no—
327C2×C4×Q8—21no—
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2311yescharacteristic
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2311yescharacteristic
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2311yescharacteristic
341C2×C4×Q8C2311yescharacteristic
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2311yescharacteristic
347C2×#117—21no—
348C2×#117—21no—
349C2×#117—21no—
350C2×#117—21no—
351C2×#117C2311yescharacteristic
352C2×#117C2311yescharacteristic
353C2×#117C2311yescharacteristic
354C2×#117C2311yescharacteristic
355C22×C4⋊C4—21no—
356C22×C4⋊C4C2311yescharacteristic
357C22×C42—21no—
358C22×C42C2311yescharacteristic
359#501—24no—
360#501—24no—
361#500—24no—
362#499—24no—
363#499—24no—
364#499—24no—
365#479—24no—
366#479—24no—
367#479—24no—
368#479—24no—
369#479—24no—
370#479—24no—
371#479—24no—
372#479—24no—
373#477—24no—
374#477—24no—
375#475—24no—
376#475—24no—
377#451Q818yescomplemented
378#446—24no—
379C8×Q8—24no—
380#441—24no—
381#441—24no—
382C4×Q16—24no—
383C4×Q16—24no—
384C4×Q16—24no—
385C4×Q16—24no—
386C2×#107C2311yescharacteristic
387C2×#107C2311yescharacteristic
388C2×#107C2311yescharacteristic
389C2×#107C2311yescharacteristic
390C2×#107C2311yescharacteristic
391C2×#107C2311yescharacteristic
392C2×#107C2311yescharacteristic
393C2×#107C2311yescharacteristic
394C2×#107C2311yescharacteristic
395C2×#107C2311yescharacteristic
396C2×#106C2311yescharacteristic
397C2×#106C2311yescharacteristic
398C2×#106C2311yescharacteristic
399C2×#106C2311yescharacteristic
400C2×#106C2311yescharacteristic
401C2×#106C2311yescharacteristic
402C2×#106C2311yescharacteristic
403C2×#106C2311yescharacteristic
404C2×C4⋊C8C2311yescharacteristic
405C2×C4⋊C8C2311yescharacteristic
406C2×C4⋊C8C2311yescharacteristic
407C2×C4⋊C8C2311yescharacteristic
408C2×C4⋊C8C2311yescharacteristic
409C2×C4⋊C8C2311yescharacteristic
410C2×#103C2311yescharacteristic
411C2×#103C2311yescharacteristic
412C2×#103C2311yescharacteristic
413C2×#103C2311yescharacteristic
414C2×#103C2311yescharacteristic
415C2×#103C2311yescharacteristic
416C2×#103C2311yescharacteristic
417C2×#103C2311yescharacteristic
418C2×#103C2311yescharacteristic
419C2×#103C2311yescharacteristic
420C2×#103C2311yescharacteristic
421C2×#103C2311yescharacteristic
422C2×#103C2311yescharacteristic
423C2×#103C2311yescharacteristic
424C2×#103C2311yescharacteristic
425C2×#103C2311yescharacteristic
426C2×#103C2311yescharacteristic
427C2×#103C2311yescharacteristic
428C2×#103C2311yescharacteristic
429C2×#103C2311yescharacteristic
430C2×C22⋊C8C2311yescharacteristic
431C2×C22⋊C8C2311yescharacteristic
432C2×C22⋊C8C2311yescharacteristic
433C2×C22⋊C8C2311yescharacteristic
434C2×#97C2311yescharacteristic
435C2×#97C2311yescharacteristic
436C2×C4×C8C2311yescharacteristic
437C2×C4×C8C2311yescharacteristic
438C2×C4×C8C2311yescharacteristic
439C2×C4×C8C2311yescharacteristic
440#400—21no—
441#400—21no—
442#400—21no—
443#399—21no—
444#398—21no—
445#398—21no—
446#398—21no—
447#398—21no—
448#398—21no—
449#398—21no—
450#396—21no—
451#396—21no—
452#395—21no—
453#395—21no—
454#395—21no—
455#395—21no—
456#395—21no—
457#395—21no—
458#395—21no—
459#393—21no—
460#391—21no—
461#391—21no—
462#391—21no—
463#391C2311yescharacteristic
464#391C2311yescharacteristic
465#391C2311yescharacteristic
466#389—21no—
467#389—21no—
468#389—21no—
469#389—21no—
470#389—21no—
471#389—21no—
472#389—21no—
473#389C2311yescharacteristic
474#389C2311yescharacteristic
475#389C2311yescharacteristic
476#389C2311yescharacteristic
477#389C2311yescharacteristic
478#389C2311yescharacteristic
479#389C2311yescharacteristic
480#389C2311yescharacteristic
481#389C2311yescharacteristic
482#388—21no—
483#388—21no—
484#388—21no—
485#388—21no—
486#387—21no—
487#387—21no—
488#387—21no—
489#387—21no—
490#387—21no—
491#387—21no—
492#387—21no—
493#387—21no—
494#387—21no—
495#387—21no—
496#387—21no—
497#385—21no—
498#385—21no—
499#385—21no—
500#384—21no—
501#384C2311yescharacteristic
502#382C2311yescharacteristic
503#382C2311yescharacteristic
504#380C2311yescharacteristic
505#380C2311yescharacteristic
506#380C2311yescharacteristic
507C4×C4⋊C4—21no—
508C4×C4⋊C4—21no—
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2311yescharacteristic
512C4×C22⋊C4—21no—
513#340C2311yescharacteristic
514#340C2311yescharacteristic
515#340C2311yescharacteristic
516#340C2311yescharacteristic
517#340C2311yescharacteristic
518#340C2311yescharacteristic
519#340C2311yescharacteristic
520#340C2311yescharacteristic
521#340C2311yescharacteristic
522#340C2311yescharacteristic
523#340C2311yescharacteristic
524#340C2311yescharacteristic
525#340C2311yescharacteristic
526#340C2311yescharacteristic
527#340C2311yescharacteristic
528#340C2311yescharacteristic
529#340C2311yescharacteristic
530#340C2311yescharacteristic
531#340C2311yescharacteristic
532#340C2311yescharacteristic
533#340C2311yescharacteristic
534#340C2311yescharacteristic
535#340C2311yescharacteristic
536#340C2311yescharacteristic
537#336C2311yescharacteristic
538#336C2311yescharacteristic
539#336C2311yescharacteristic
540#336C2311yescharacteristic
541#336C2311yescharacteristic
542#336C2311yescharacteristic
543#336C2311yescharacteristic
544#336C2311yescharacteristic
545#336C2311yescharacteristic
546#336C2311yescharacteristic
547#336C2311yescharacteristic
548#336C2311yescharacteristic
549C22×Q8—22no—
550C22×Q8—22no—
551C22×Q8—22no—
552C22×Q8—22no—
553C22×Q8—21no—
554C22×Q8—21no—
555C22×Q8—21no—
556C22×Q8—21no—
557C22×Q8—21no—
558C22×Q8—21no—
559C22×Q8—21no—
560C22×Q8—21no—
561C22×Q8—22no—
562C22×Q8C2×D411yescharacteristic
563C22×Q8C2×D411yescharacteristic
564C22×Q8C2×D411yescharacteristic
565C22×Q8C2×D411yescharacteristic
566C22×Q8C2×Q814yes—
567C22×Q8C2411yescharacteristic
568C22×Q8C2411yescharacteristic
569C22×Q8C2411yescharacteristic
570C23×C4—21no—
571C23×C4—21no—
572C23×C4C2×D411yescharacteristic
573C23×C4C2×D411yescharacteristic
574C23×C4C2411yescharacteristic
575C2×Q16—22no—
576C2×Q16—22no—
577C2×Q16—22no—
578C2×Q16—22no—
579C2×Q16C2×Q814yes—
580C2×Q16C2×Q814yes—
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C4⋊Q8—28no—
590C4⋊Q8—28no—
591C4⋊Q8—28no—
592C4⋊Q8—28no—
593C4⋊Q8—28no—
594C4⋊Q8—28no—
595C4⋊Q8—28no—
596C4⋊Q8—28no—
597C4⋊Q8—28no—
598C4⋊Q8—28no—
599C4⋊Q8—28no—
600C4⋊Q8—28no—
601C4⋊Q8—28no—
602C4⋊Q8—28no—
603C4⋊Q8—24no—
604C4⋊Q8—24no—
605C4⋊Q8—22no—
606C4⋊Q8—22no—
607C4⋊Q8—22no—
608C4⋊Q8—22no—
609C4⋊Q8—22no—
610C4⋊Q8—22no—
611C4⋊Q8—22no—
612C4⋊Q8—22no—
613C4⋊Q8—22no—
614C4⋊Q8—22no—
615C4⋊Q8—22no—
616C4⋊Q8—22no—
617C4⋊Q8—44no—
618C4⋊Q8C2×D414yes—
619C4⋊Q8C2×D414yes—
620#125—28no—
621#125—28no—
622#125—28no—
623#125—28no—
624#125—28no—
625#125—28no—
626#125—28no—
627#125—28no—
628#125—28no—
629#125—28no—
630#125—28no—
631#125—28no—
632#125—28no—
633#125—28no—
634#125—24no—
635#125—24no—
636#125—22no—
637#125—22no—
638#125—22no—
639#125—22no—
640#125—22no—
641#125—22no—
642#125—22no—
643#125—22no—
644#125—22no—
645#125—22no—
646#125—22no—
647#125—22no—
648#125—44no—
649#125—44no—
650#125C2×D414yes—
651#125C2×D414yes—
652#125C2×D414yes—
653#125C2×D414yes—
654C22⋊Q8—28no—
655C22⋊Q8—28no—
656C22⋊Q8—28no—
657C22⋊Q8—28no—
658C22⋊Q8—28no—
659C22⋊Q8—28no—
660C22⋊Q8—24no—
661C22⋊Q8—22no—
662C22⋊Q8—24no—
663C22⋊Q8—24no—
664C22⋊Q8—24no—
665C22⋊Q8C2×Q814yes—
666C4×Q8—28no—
667C4×Q8—28no—
668C4×Q8—28no—
669C4×Q8—28no—
670C4×Q8—28no—
671C4×Q8—28no—
672C4×Q8—28no—
673C4×Q8—28no—
674C4×Q8—28no—
675C4×Q8—28no—
676C4×Q8—28no—
677C4×Q8—28no—
678C4×Q8—28no—
679C4×Q8—28no—
680C4×Q8—22no—
681C4×Q8—22no—
682C4×Q8—22no—
683C4×Q8—22no—
684C4×Q8—22no—
685C4×Q8—22no—
686C4×Q8—28no—
687C4×Q8—28no—
688C4×Q8—22no—
689C4×Q8—22no—
690C4×Q8—22no—
691C4×Q8—22no—
692C4×Q8—22no—
693C4×Q8—22no—
694C4×Q8—22no—
695C4×Q8—22no—
696C4×Q8—22no—
697C4×Q8—22no—
698C4×Q8—22no—
699C4×Q8—22no—
700C4×Q8—22no—
701C4×Q8—22no—
702C4×Q8—22no—
703C4×Q8—22no—
704C4×Q8—22no—
705C4×Q8—22no—
706C4×Q8—22no—
707C4×Q8—22no—
708C4×Q8—22no—
709C4×Q8—22no—
710C4×Q8—22no—
711C4×Q8—22no—
712C4×Q8—44no—
713C4×Q8C2×D414yes—
714C4×Q8C2×D414yes—
715C4×Q8C2×D414yes—
716C4×Q8C2×D414yes—
717C4×Q8C2×D414yes—
718C4×Q8C2×D414yes—
719C4×Q8C2×D414yes—
720C4×Q8C2×D414yes—
721#117—28no—
722#117—28no—
723#117—28no—
724#117—28no—
725#117—22no—
726#117—22no—
727#117—22no—
728#117—22no—
729#117—22no—
730#117—22no—
731#117—22no—
732#117—22no—
733C2×C4⋊C4—28no—
734C2×C4⋊C4—21no—
735C2×C4⋊C4—21no—
736C2×C4⋊C4—21no—
737C2×C4⋊C4—21no—
738C2×C4⋊C4—21no—
739C2×C4⋊C4—21no—
740C2×C4⋊C4—21no—
741C2×C4⋊C4—21no—
742C2×C4⋊C4—21no—
743C2×C4⋊C4—21no—
744C2×C4⋊C4—21no—
745C2×C4⋊C4—21no—
746C2×C4⋊C4—21no—
747C2×C4⋊C4—21no—
748C2×C4⋊C4—21no—
749C2×C4⋊C4—21no—
750C2×C4⋊C4—21no—
751C2×C4⋊C4—21no—
752C2×C4⋊C4—21no—
753C2×C4⋊C4—21no—
754C2×C4⋊C4—21no—
755C2×C4⋊C4—21no—
756C2×C4⋊C4—21no—
757C2×C4⋊C4—21no—
758C2×C4⋊C4—21no—
759C2×C4⋊C4—21no—
760C2×C4⋊C4—21no—
761C2×C4⋊C4—21no—
762C2×C4⋊C4—21no—
763C2×C4⋊C4—21no—
764C2×C4⋊C4—21no—
765C2×C4⋊C4—21no—
766C2×C4⋊C4—22no—
767C2×C4⋊C4—22no—
768C2×C4⋊C4—21no—
769C2×C4⋊C4—21no—
770C2×C4⋊C4—21no—
771C2×C4⋊C4—21no—
772C2×C4⋊C4—21no—
773C2×C4⋊C4—21no—
774C2×C4⋊C4—21no—
775C2×C4⋊C4—21no—
776C2×C4⋊C4—21no—
777C2×C4⋊C4—21no—
778C2×C4⋊C4—21no—
779C2×C4⋊C4—21no—
780C2×C4⋊C4—21no—
781C2×C4⋊C4—21no—
782C2×C4⋊C4—21no—
783C2×C4⋊C4—21no—
784C2×C4⋊C4—21no—
785C2×C4⋊C4—21no—
786C2×C4⋊C4—21no—
787C2×C4⋊C4C2×D411yescharacteristic
788C2×C4⋊C4C2×D411yescharacteristic
789C2×C4⋊C4C2×D411yescharacteristic
790C2×C4⋊C4C2×D411yescharacteristic
791C2×C4⋊C4C2×D411yescharacteristic
792C2×C4⋊C4C2×D411yescharacteristic
793C2×C4⋊C4C2×D411yescharacteristic
794C2×C4⋊C4C2×D411yescharacteristic
795C2×C4⋊C4C2×D411yescharacteristic
796C2×C4⋊C4C2×D411yescharacteristic
797C2×C4⋊C4C2×D411yescharacteristic
798C2×C4⋊C4C2×D411yescharacteristic
799C2×C4⋊C4C2×D411yescharacteristic
800C2×C4⋊C4C2×D411yescharacteristic
801C2×C4⋊C4C2×D411yescharacteristic
802C2×C4⋊C4C2×D411yescharacteristic
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2411yescharacteristic
816C2×C22⋊C4—21no—
817C2×C22⋊C4—21no—
818C2×C22⋊C4—21no—
819C2×C22⋊C4—21no—
820C2×C22⋊C4—21no—
821C2×C22⋊C4—21no—
822C2×C22⋊C4C2×D411yescharacteristic
823C2×C22⋊C4C2×D411yescharacteristic
824C2×C22⋊C4C2×D411yescharacteristic
825C2×C22⋊C4C2×D411yescharacteristic
826C2×C42—28no—
827C2×C42—21no—
828C2×C42—21no—
829C2×C42—21no—
830C2×C42—21no—
831C2×C42—21no—
832C2×C42—21no—
833C2×C42—21no—
834C2×C42—21no—
835C2×C42—21no—
836C2×C42—21no—
837C2×C42—21no—
838C2×C42—21no—
839C2×C42—21no—
840C2×C42—21no—
841C2×C42—22no—
842C2×C42—22no—
843C2×C42—21no—
844C2×C42—21no—
845C2×C42—21no—
846C2×C42—21no—
847C2×C42—21no—
848C2×C42—21no—
849C2×C42C2×D411yescharacteristic
850C2×C42C2×D411yescharacteristic
851C2×C42C2411yescharacteristic
852C2×C42C2411yescharacteristic
853C2×C42C2411yescharacteristic
854C2×C42C2411yescharacteristic
855C2×C42C2411yescharacteristic
856C2×C42C2411yescharacteristic
857#107—22no—
858#107—22no—
859#107—22no—
860#107—22no—
861#107—22no—
862#107—22no—
863#107—22no—
864#107—22no—
865#107—22no—
866#107—22no—
867#106—22no—
868#106—22no—
869#106—22no—
870#106—22no—
871#106—22no—
872#106—22no—
873#106—22no—
874#106—22no—
875C4⋊C8—22no—
876C4⋊C8—22no—
877C4⋊C8—22no—
878C4⋊C8—22no—
879C4⋊C8—22no—
880C4⋊C8—22no—
881#103—22no—
882#103—22no—
883#103—22no—
884#103—22no—
885#103—22no—
886#103—22no—
887#103—22no—
888#103—22no—
889#103—22no—
890#103—22no—
891#103—22no—
892#103—22no—
893#103—22no—
894#103—22no—
895#103—22no—
896#103—22no—
897#103—22no—
898#103—22no—
899#103C2×Q814yes—
900#103C2×Q814yes—
901C22⋊C8—22no—
902C22⋊C8—22no—
903C22⋊C8—22no—
904C22⋊C8C2×Q814yes—
905#97—22no—
906#97—22no—
907C4×C8—22no—
908C4×C8—22no—
909C4×C8—22no—
910C4×C8—22no—
911#95—21no—
912#95—21no—
913#95—21no—
914#95—21no—
915#95—21no—
916#95—21no—
917#95—21no—
918#95—21no—
919#95—21no—
920#95—21no—
921#95—21no—
922#95—21no—
923#95—21no—
924#95—21no—
925#95—21no—
926#95—21no—
927#95—21no—
928#95—21no—
929#95—21no—
930#95—21no—
931#95—21no—
932#95—21no—
933#95—21no—
934#95—21no—
935#95—21no—
936C24C22×D411yescharacteristic
937C2×Q8—24no—
938C2×Q8—28no—
939C2×Q8—28no—
940C2×Q8—24no—
941C2×Q8—28no—
942C2×Q8—28no—
943C2×Q8—24no—
944C2×Q8—24no—
945C2×Q8—24no—
946C2×Q8—24no—
947C2×Q8—22no—
948C2×Q8—22no—
949C2×Q8—22no—
950C2×Q8—24no—
951C2×Q8—24no—
952C2×Q8—24no—
953C2×Q8—22no—
954C2×Q8—22no—
955C2×Q8—21no—
956C2×Q8—21no—
957C2×Q8—21no—
958C2×Q8—21no—
959C2×Q8—21no—
960C2×Q8—21no—
961C2×Q8—21no—
962C2×Q8—21no—
963C2×Q8—21no—
964C2×Q8—21no—
965C2×Q8—21no—
966C2×Q8—41no—
967C2×Q8—41no—
968C2×Q8—41no—
969C2×Q8—41no—
970C2×Q8—41no—
971C2×Q8—41no—
972C2×Q8—42no—
973C2×Q8—42no—
974C2×Q8—42no—
975C2×Q8—81no—
976C2×Q8—81no—
977C2×Q8—81no—
978C2×Q8—81no—
979C2×Q8—81no—
980C2×Q8—81no—
981C2×Q8—81no—
982C2×Q8—81no—
983C2×Q8—81no—
984C2×Q8—81no—
985C2×Q8—81no—
986C2×Q8—81no—
987C2×Q8#12014yes—
988C2×Q8C22×D412yes—
989C2×Q8C22×D412yes—
990C2×Q8C22×Q812yes—
991C2×Q8C22×Q812yes—
992C2×Q8C22×Q812yes—
993C2×Q82−1+412yes—
994C2×Q82−1+412yes—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—21no—
1006C22×C4—21no—
1007C22×C4—21no—
1008C22×C4—21no—
1009C22×C4—21no—
1010C22×C4—21no—
1011C22×C4—21no—
1012C22×C4—24no—
1013C22×C4—22no—
1014C22×C4—22no—
1015C22×C4—22no—
1016C22×C4—21no—
1017C22×C4—21no—
1018C22×C4—21no—
1019C22×C4—21no—
1020C22×C4—21no—
1021C22×C4—21no—
1022C22×C4—41no—
1023C22×C4—41no—
1024C22×C4—41no—
1025C22×C4—81no—
1026C22×C4—81no—
1027C22×C4C22×D411yescharacteristic
1028C22×C4C22×D411yescharacteristic
1029C22×C4C22×D411yescharacteristic
1030C22×C4C22×D411yescharacteristic
1031C22×C4C22×D411yescharacteristic
1032C22×C4C22×D411yescharacteristic
1033C22×C4C22×D411yescharacteristic
1034C22×C4C22×D411yescharacteristic
1035C22×C4C22×D411yescharacteristic
1036C22×C4C22×D411yescharacteristic
1037C22×C4C22×D411yescharacteristic
1038C22×C4C22×D411yescharacteristic
1039C22×C4C22×D411yescharacteristic
1040C22×C4C22×Q812yes—
1041C22×C42−1+412yes—
1042C22×C4C2511yescharacteristic
1043Q16—28no—
1044Q16—28no—
1045C2×C8—21no—
1046C2×C8—21no—
1047C2×C8—21no—
1048C2×C8—21no—
1049C2×C8—21no—
1050C2×C8—21no—
1051C2×C8—21no—
1052C2×C8—21no—
1053C2×C8—21no—
1054C2×C8—21no—
1055C2×C8—21no—
1056C2×C8—21no—
1057C2×C8—21no—
1058C2×C8—21no—
1059C2×C8—21no—
1060C2×C8—21no—
1061C2×C8—21no—
1062C2×C8—21no—
1063C2×C8—21no—
1064C2×C8—21no—
1065C2×C8—21no—
1066C2×C8—21no—
1067C2×C8C22×Q812yes—
1068C2×C8C22×Q812yes—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—22no—
1101C4⋊C4—22no—
1102C4⋊C4—22no—
1103C4⋊C4—22no—
1104C4⋊C4—22no—
1105C4⋊C4—22no—
1106C4⋊C4—22no—
1107C4⋊C4—22no—
1108C4⋊C4—22no—
1109C4⋊C4—22no—
1110C4⋊C4—22no—
1111C4⋊C4—22no—
1112C4⋊C4—22no—
1113C4⋊C4—24no—
1114C4⋊C4—21no—
1115C4⋊C4—21no—
1116C4⋊C4—21no—
1117C4⋊C4—21no—
1118C4⋊C4—21no—
1119C4⋊C4—21no—
1120C4⋊C4—21no—
1121C4⋊C4—21no—
1122C4⋊C4—21no—
1123C4⋊C4—21no—
1124C4⋊C4—21no—
1125C4⋊C4—21no—
1126C4⋊C4—21no—
1127C4⋊C4—21no—
1128C4⋊C4—21no—
1129C4⋊C4—21no—
1130C4⋊C4—21no—
1131C4⋊C4—21no—
1132C4⋊C4—21no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—81no—
1143C4⋊C4—81no—
1144C4⋊C4—81no—
1145C4⋊C4—81no—
1146C4⋊C4—81no—
1147C4⋊C4—81no—
1148C4⋊C4—81no—
1149C4⋊C4—81no—
1150C4⋊C4—81no—
1151C4⋊C4—81no—
1152C4⋊C4#12014yes—
1153C4⋊C4#12014yes—
1154C4⋊C4#12014yes—
1155C4⋊C4C22×D412yes—
1156C4⋊C4C22×D412yes—
1157C4⋊C4C22×D412yes—
1158C4⋊C4C22×D412yes—
1159C4⋊C4C22×D412yes—
1160C4⋊C4C22×D412yes—
1161C4⋊C4C22×Q812yes—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—22no—
1166C22⋊C4—22no—
1167C22⋊C4—22no—
1168C22⋊C4—22no—
1169C22⋊C4—81no—
1170C22⋊C4—81no—
1171C22⋊C4—81no—
1172C42—24no—
1173C42—24no—
1174C42—24no—
1175C42—24no—
1176C42—24no—
1177C42—24no—
1178C42—24no—
1179C42—24no—
1180C42—24no—
1181C42—24no—
1182C42—22no—
1183C42—22no—
1184C42—24no—
1185C42—24no—
1186C42—24no—
1187C42—24no—
1188C42—21no—
1189C42—21no—
1190C42—21no—
1191C42—21no—
1192C42—21no—
1193C42—21no—
1194C42—42no—
1195C42—42no—
1196C42—42no—
1197C42—81no—
1198C42—81no—
1199C42—81no—
1200C42C22×D412yes—
1201C42C22×D412yes—
1202C42C22×D412yes—
1203C42C22×D412yes—
1204C42C22×D412yes—
1205C42C22×D412yes—
1206C23—21no—
1207C23—21no—
1208C23—21no—
1209C23—21no—
1210C23—21no—
1211C23—21no—
1212C23D4×Q812yes—
1213C23C23×D411yescharacteristic
1214Q8—216no—
1215Q8—22no—
1216Q8—22no—
1217Q8—22no—
1218Q8—22no—
1219Q8—22no—
1220Q8—22no—
1221Q8—22no—
1222Q8—22no—
1223Q8—44no—
1224Q8—44no—
1225Q8—44no—
1226Q8—48no—
1227Q8—41no—
1228Q8—41no—
1229Q8—82no—
1230Q8—84no—
1231Q8—84no—
1232Q8—84no—
1233Q8—84no—
1234Q8—84no—
1235Q8—84no—
1236Q8D4×Q814yes—
1237Q8D4×Q814yes—
1238C2×C4—216no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—21no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—44no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—82no—
1324C2×C4—84no—
1325C2×C4C2×#12012yes—
1326C2×C4C2×#12012yes—
1327C2×C4C2×#12012yes—
1328C2×C4C2×#12012yes—
1329C2×C4C2×#12012yes—
1330C2×C4C2×#12012yes—
1331C2×C4D4×Q812yes—
1332C2×C4#57812yes—
1333C2×C4C23×D411yescharacteristic
1334C2×C4C23×D411yescharacteristic
1335C2×C4C23×Q811yescharacteristic
1336C2×C4C2×2−1+411yescharacteristic
1337C2×C4C2×2−1+411yescharacteristic
1338C2×C4C2×2−1+411yescharacteristic
1339C8—22no—
1340C8—22no—
1341C8—41no—
1342C8—41no—
1343C8—41no—
1344C8—41no—
1345C8—41no—
1346C8—41no—
1347C22—22no—
1348C22—22no—
1349C22—22no—
1350C22—41no—
1351C22—41no—
1352C22—41no—
1353C22—41no—
1354C22C22×#12011yescharacteristic
1355C22C2×D4×Q811yescharacteristic
1356C22#348611yescharacteristic
1357C22C2×#57811yescharacteristic
1358C22#358411yescharacteristic
1359C22#358411yescharacteristic
1360C22#358611yescharacteristic
1361C4—24no—
1362C4—24no—
1363C4—22no—
1364C4—22no—
1365C4—22no—
1366C4—22no—
1367C4—22no—
1368C4—22no—
1369C4—22no—
1370C4—22no—
1371C4—42no—
1372C4—42no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—42no—
1377C4—42no—
1378C4—42no—
1379C4—42no—
1380C4—41no—
1381C4—41no—
1382C4—42no—
1383C4—42no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4C2×D4×Q811yescharacteristic
1391C4C2×D4×Q811yescharacteristic
1392C4#348611yescharacteristic
1393C4#348611yescharacteristic
1394C2—42no—
1395C2Q8×#12011yescharacteristic
1396C2#6036611yescharacteristic
1397C2#6037511yescharacteristic
1398C2#6137211yescharacteristic
1399C2#6138611yescharacteristic
1400C2#6185611yescharacteristic
1401C2#6186611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#533 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3390C2semidirect
3. C2×#3383C2semidirect
8. #25848C2semidirect
9. #25847C2semidirect
10. #25842C2semidirect
11. #25842C2semidirect
12. #25842C2semidirect
13. #25841C2semidirect
17. #24348C2semidirect
18. #24345C2semidirect
19. #24336C2semidirect
20. #24336C2semidirect
21. #24336C2semidirect
22. #24333C2semidirect
26. #22527C2semidirect
27. #22521C2semidirect
377. #451Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#35022
C2×#33902
C2×#33832
#395912
#329672
#329642
#329602
#258482
#258472
#258422
#258412
#258222
#258212
#258142
#243482
#243452
#243362
#243332
#243112
#243102
#243062
#225272
#225212
#225092
#214632
C4×#4512