Finite Group Databasebeta

← #6343483

Subgroups — #6343483

Order 512.

3103 conjugacy classes of subgroups.

The subgroup lattice has 925 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62815C211yesmaximal, characteristic
2#60277C211yesmaximal, characteristic, complemented
3C4⋊C4×#41C211yesmaximal, characteristic, complemented
4#17630C214yesmaximal, complemented
5#17628C214yesmaximal, complemented
6#17622C218yesmaximal, complemented
7#17575C211yesmaximal, characteristic, complemented
8#17574C211yesmaximal, characteristic, complemented
9#17563C214yesmaximal, complemented
10#17546C214yesmaximal, complemented
11C2×#1503C211yesmaximal, characteristic, complemented
12C2×#1502C211yesmaximal, characteristic, complemented
13#3512—22no—
14#3511C412yescomplemented
15#3511C412yescomplemented
16#3510—22no—
17#3509C412yescomplemented
18#3508C412yescomplemented
19#3507—21no—
20#3507C2212yes—
21#3506—21no—
22#3506C2212yes—
23#3505—22no—
24#3505C2214yes—
25#3480—22no—
26#3480C414yescomplemented
27#3475—22no—
28#3475C414yescomplemented
29#3455—22no—
30#3449—21no—
31#3444C2214yes—
32C2×#533C2211yescharacteristic
33C2×#532C2211yescharacteristic
34#3428—21no—
35C2×C4×#41—21no—
36C2×C4×#41C2211yescharacteristic
37#2989—22no—
38#2989—22no—
39#2983C2212yescomplemented
40#2975C2212yescomplemented
41#2973C2214yes—
42#2965—22no—
43#2965—22no—
44#2920C2214yescomplemented
45C2×#431C2211yescharacteristic
46C2×#431C2211yescharacteristic
47#2351C2212yescomplemented
48Q8×C4⋊C4—21no—
49#2349C2214yes—
50#2349C2212yescomplemented
51D4×C4⋊C4—22no—
52D4×C4⋊C4—21no—
53#2296—21no—
54#2296—22no—
55#2285C2211yescharacteristic
56#2285C2212yescomplemented
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2212yescomplemented
59#1520C2214yes—
60#1519C2214yes—
61#1518C2214yescomplemented
62#1517C2214yes—
63#1513C22116yescomplemented
64#1512C22116yescomplemented
65#1509C22116yescomplemented
66#1504C22116yescomplemented
67#1503C2212yescomplemented
68#1503C2212yescomplemented
69#1503C2214yescomplemented
70#1503C2214yescomplemented
71#1502C2212yes—
72#1502C2212yes—
73#1502C2214yes—
74#1502C2214yes—
75C2×#328C2214yes—
76C2×#327C2214yes—
77C22×#41—21no—
78C22×#41D411yescharacteristic
79#559—22no—
80#559—24no—
81#559—24no—
82#559C2×C414yescomplemented
83#557—22no—
84#557C2×C414yescomplemented
85#556—22no—
86#556—24no—
87#556—24no—
88#556—22no—
89#556C2×C414yescomplemented
90#556C2×C414yescomplemented
91#555—22no—
92#555C2×C414yescomplemented
93#554—22no—
94#554C2×C414yescomplemented
95#553—24no—
96#553—24no—
97#553—28no—
98#553—24no—
99#553—28no—
100#553C2×C418yescomplemented
101#552—24no—
102#552—24no—
103#552—24no—
104#552C2×C418yescomplemented
105#551—28no—
106#551—28no—
107#550—22no—
108#550C2×C414yescomplemented
109#548—24no—
110#548C2×C418yescomplemented
111#547—22no—
112#547C2×C414yescomplemented
113#546—24no—
114#546C2×C418yescomplemented
115#542—24no—
116#542—24no—
117#541—24no—
118#540—24no—
119#539—24no—
120#539—24no—
121#538—24no—
122#538—24no—
123#537—22no—
124#537—22no—
125#536—22no—
126#536—22no—
127#535—22no—
128#535—22no—
129#534—24no—
130#533—21no—
131#533—21no—
132#533—21no—
133#533—21no—
134#533C2×C412yescomplemented
135#533C2×C412yescomplemented
136#533C2×C414yescomplemented
137#533C2×C414yescomplemented
138#533C2312yes—
139#533C2312yes—
140#532—24no—
141#532—21no—
142#532—21no—
143#532—21no—
144#532—21no—
145#532C2×C414yescomplemented
146#532C2×C412yescomplemented
147#532C2×C412yescomplemented
148#532C2×C414yescomplemented
149#532C2312yes—
150#532C2312yes—
151C2×C4⋊Q8C2×C411yescharacteristic, complemented
152C2×C4⋊Q8C2×C411yescharacteristic, complemented
153C2×C4⋊Q8C2×C411yescharacteristic, complemented
154C2×#127C2×C411yescharacteristic, complemented
155#529—28no—
156#529—28no—
157#529—24no—
158#529—24no—
159#529—24no—
160#529—24no—
161#529C2×C418yescomplemented
162#529C2318yes—
163C2×#125—21no—
164C2×#124—21no—
165#525—24no—
166#525—24no—
167#525—24no—
168#525C2318yes—
169C2×C22⋊Q8—21no—
170C2×C22⋊Q8C2312yes—
171C2×#121—21no—
172C2×#121C2312yes—
173#520—22no—
174#520—22no—
175#520—22no—
176#520—22no—
177#519—22no—
178#518—22no—
179#518—24no—
180C4×#41—24no—
181C4×#41—24no—
182C4×#41—24no—
183C4×#41—48no—
184C4×#41C2×C412yes—
185C4×#41C2×C412yes—
186C4×#41C2×C412yes—
187C4×#41C2×C412yes—
188C4×#41C2×C418yescomplemented
189C4×#41D412yes—
190C4×#41D412yes—
191C4×#41D412yes—
192C4×#41D412yes—
193C2×C4×Q8—22no—
194C2×C4×Q8—21no—
195C2×C4×Q8C2×C412yescomplemented
196C2×C4×Q8D411yescharacteristic
197C2×C4×Q8C2311yescharacteristic
198C2×C4×D4—24no—
199C2×C4×D4—22no—
200C2×C4×D4—21no—
201C2×C4×D4C2×C412yescomplemented
202C2×C4×D4D412yes—
203C2×C4×D4D411yescharacteristic
204C2×C4×D4C2312yes—
205C2×C4×D4C2311yescharacteristic
206C2×#117—21no—
207C2×#117—24no—
208C2×#117—21no—
209C2×#117—22no—
210C2×#117D411yescharacteristic
211C2×#117D412yes—
212C22×C4⋊C4—21no—
213C22×C4⋊C4—22no—
214C22×C42—21no—
215C22×C42—22no—
216C22×C42C2311yescharacteristic
217C22×C42C2312yes—
218#446—24no—
219#446—24no—
220#436—24no—
221#436—24no—
222#435—28no—
223#435—28no—
224#432—24no—
225#432C2318yes—
226#431—21no—
227#431—21no—
228#431—21no—
229#431—21no—
230#431—24no—
231#431C2312yes—
232#431C2312yes—
233#431C2312yes—
234#431C2312yes—
235#423—24no—
236C2×C4⋊C8—21no—
237C2×C4⋊C8—21no—
238#407C2318yes—
239C2×C22⋊C8C2312yes—
240C2×C22⋊C8C2312yes—
241C4×M16—24no—
242C2×C4×C8—21no—
243C2×C4×C8—21no—
244#389—22no—
245#389—24no—
246#389—24no—
247#389—22no—
248#385—24no—
249#385—24no—
250#385—24no—
251#384—21no—
252#384—22no—
253#382C2314yes—
254#382C2312yes—
255#380—21no—
256#380—22no—
257#380C2312yes—
258#380C2314yes—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—22no—
261C4×C4⋊C4—21no—
262C4×C4⋊C4—22no—
263C4×C4⋊C4—21no—
264C4×C4⋊C4—22no—
265C4×C4⋊C4C2314yes—
266C4×C4⋊C4C2312yes—
267C4×C4⋊C4C2311yescharacteristic
268C4×C4⋊C4C2311yescharacteristic
269C4×C4⋊C4C2312yes—
270C2×#95C2312yes—
271C2×#95C2314yes—
272#328C2318yes—
273#328C2318yes—
274#328C23116yes—
275#327C2318yes—
276#327C2318yes—
277#327C23116yes—
278C2×#41—22no—
279C2×#41—22no—
280C2×#41—24no—
281C2×#41—24no—
282C2×#41—24no—
283C2×#41—22no—
284C2×#41—22no—
285C2×#41—44no—
286C2×#41—44no—
287C2×#41C22⋊C412yes—
288C2×#41C22⋊C412yes—
289C2×#41C22⋊C412yes—
290C2×#41C22⋊C412yes—
291C2×#41C22×C418yes—
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8C22×C412yes—
295C22×Q8C2×D411yescharacteristic
296C22×D4—22no—
297C22×D4—21no—
298C22×D4—21no—
299C22×D4C22×C412yes—
300C22×D4C2×D412yes—
301C22×D4C2×D411yescharacteristic
302C23×C4—22no—
303C23×C4—24no—
304C23×C4—22no—
305C23×C4C2×D412yes—
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D412yes—
308C23×C4C2×D411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2412yes—
311C2×M16—28no—
312C22×C8—22no—
313C22×C8—22no—
314C4⋊Q8—24no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8C22×C412yes—
322C4⋊Q8C22×C412yes—
323C4⋊Q8C22×C412yes—
324C4⋊Q8C22×C412yes—
325C4⋊Q8C22×C412yes—
326C4⋊Q8C22×C412yes—
327#127—24no—
328#127—21no—
329#127—21no—
330#127C22×C412yes—
331#127C22×C412yes—
332#126—28no—
333#126—28no—
334#126—28no—
335#126—28no—
336#126—28no—
337#126—28no—
338#125—28no—
339#125—28no—
340#125—22no—
341#125—22no—
342#125—24no—
343#125—22no—
344#125—22no—
345#125C22×C418yes—
346#124—24no—
347#124—24no—
348#124—28no—
349#124—28no—
350#124—22no—
351#124—22no—
352#124—24no—
353#124—22no—
354#124—22no—
355#124C22×C418yes—
356#123—28no—
357#123—28no—
358#123—28no—
359#123—28no—
360#123—28no—
361#123—28no—
362#123—28no—
363#123—28no—
364C22⋊Q8—24no—
365C22⋊Q8—24no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—24no—
369C22⋊Q8—24no—
370C22⋊Q8—24no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—28no—
376C22⋊Q8—28no—
377C22⋊Q8C22×C414yes—
378C22⋊Q8C22×C418yes—
379C22⋊Q8C2414yes—
380#121—24no—
381#121—24no—
382#121—28no—
383#121—28no—
384#121—22no—
385#121—22no—
386#121—24no—
387#121—24no—
388#121—24no—
389#121—22no—
390#121—22no—
391#121—22no—
392#121—22no—
393#121—28no—
394#121—28no—
395#121C22×C414yes—
396#121C22×C418yes—
397#121C2414yes—
398#120—28no—
399#120—28no—
400C4×Q8—24no—
401C4×Q8—24no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8—22no—
405C4×Q8—22no—
406C4×Q8—24no—
407C4×Q8—24no—
408C4×Q8—24no—
409C4×Q8—22no—
410C4×Q8—22no—
411C4×Q8—48no—
412C4×Q8C22⋊C412yes—
413C4×Q8C22⋊C412yes—
414C4×Q8C22⋊C412yes—
415C4×Q8C22⋊C412yes—
416C4×Q8C22×C414yes—
417C4×Q8C22×C414yes—
418C4×Q8C22×C418yes—
419C4×Q8C22×C412yes—
420C4×Q8C22×C412yes—
421C4×Q8C2×D412yes—
422C4×Q8C2×D412yes—
423C4×D4—28no—
424C4×D4—28no—
425C4×D4—28no—
426C4×D4—28no—
427C4×D4—28no—
428C4×D4—28no—
429C4×D4—24no—
430C4×D4—24no—
431C4×D4—28no—
432C4×D4—28no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—24no—
438C4×D4—24no—
439C4×D4—24no—
440C4×D4—22no—
441C4×D4—22no—
442C4×D4—416no—
443C4×D4—48no—
444C4×D4C22⋊C414yes—
445C4×D4C22⋊C412yes—
446C4×D4C22⋊C414yes—
447C4×D4C22⋊C412yes—
448C4×D4C22⋊C414yes—
449C4×D4C22⋊C414yes—
450C4×D4C22⋊C412yes—
451C4×D4C22⋊C412yes—
452C4×D4C22×C414yes—
453C4×D4C22×C414yes—
454C4×D4C22×C418yes—
455C4×D4C22×C414yes—
456C4×D4C22×C412yes—
457C4×D4C22×C414yes—
458C4×D4C22×C412yes—
459C4×D4C2×D414yes—
460C4×D4C2×D414yes—
461C4×D4C2×D412yes—
462C4×D4C2×D412yes—
463#117—22no—
464#117—22no—
465#117—24no—
466#117—22no—
467#117—22no—
468#117—24no—
469#117—24no—
470#117—28no—
471#117—28no—
472#117—28no—
473#117—28no—
474#117—48no—
475#117—44no—
476#117C22⋊C412yes—
477#117C22⋊C412yes—
478#117C22⋊C412yes—
479#117C22⋊C412yes—
480#117C22⋊C414yes—
481#117C22⋊C414yes—
482#117C22⋊C414yes—
483#117C22⋊C414yes—
484#117C22×C418yes—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—44no—
503C2×C4⋊C4—48no—
504C2×C4⋊C4C22×C412yes—
505C2×C4⋊C4C22×C412yes—
506C2×C4⋊C4C2×D411yescharacteristic
507C2×C4⋊C4C2×D412yes—
508C2×C4⋊C4C2×D411yescharacteristic
509C2×C4⋊C4C2×D412yes—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—28no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4C2×D412yes—
517C2×C22⋊C4C2×D412yes—
518C2×C22⋊C4C2×D412yes—
519C2×C42—22no—
520C2×C42—28no—
521C2×C42—22no—
522C2×C42—21no—
523C2×C42—24no—
524C2×C42—22no—
525C2×C42—21no—
526C2×C42—48no—
527C2×C42—44no—
528C2×C42C22×C411yescharacteristic
529C2×C42C22×C411yescharacteristic
530C2×C42C22×C414yes—
531C2×C42C22×C411yescharacteristic
532C2×C42C22×C411yescharacteristic
533C2×C42C22×C414yes—
534C2×C42C2×D412yes—
535C2×C42C2×D411yescharacteristic
536C2×C42C2×D412yes—
537C2×C42C2×D411yescharacteristic
538C2×C42C2×D411yescharacteristic
539C2×C42C2×D411yescharacteristic
540C2×C42C2×D414yes—
541C2×C42C2×D411yescharacteristic
542C2×C42C2×D411yescharacteristic
543C2×C42C2×D414yes—
544C2×C42C2412yes—
545C2×C42C2411yescharacteristic
546C2×C42C2411yescharacteristic
547C4⋊C8—22no—
548C4⋊C8—22no—
549C4⋊C8—22no—
550C4⋊C8—22no—
551C4⋊C8—28no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554C22⋊C8—28no—
555C22⋊C8C2414yes—
556C22⋊C8C2414yes—
557#97—28no—
558C4×C8—22no—
559C4×C8—22no—
560C4×C8—22no—
561C4×C8—22no—
562#95—24no—
563#95—22no—
564#95—24no—
565#95—22no—
566#95C2412yes—
567#95C2412yes—
568#95C2414yes—
569C24—22no—
570C24C22×D412yes—
571C24C22×D411yescharacteristic
572#41—28no—
573#41—28no—
574#41—28no—
575#41—28no—
576#41—44no—
577#41—44no—
578#41—44no—
579#41—44no—
580#41—48no—
581#41—48no—
582#41—88no—
583#41—88no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—44no—
592C2×Q8—82no—
593C2×Q8—82no—
594C2×Q8C2×C22⋊C412yes—
595C2×Q8C2×C22⋊C412yes—
596C2×Q8C23×C414yes—
597C2×D4—24no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—24no—
601C2×D4—28no—
602C2×D4—28no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—44no—
611C2×D4—44no—
612C2×D4—44no—
613C2×D4—82no—
614C2×D4—82no—
615C2×D4C2×C22⋊C414yes—
616C2×D4C2×C22⋊C414yes—
617C2×D4C2×C22⋊C412yes—
618C2×D4C2×C22⋊C412yes—
619C2×D4C23×C414yes—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—28no—
629C22×C4—28no—
630C22×C4—24no—
631C22×C4—22no—
632C22×C4—42no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—44no—
639C22×C4—81no—
640C22×C4—82no—
641C22×C4—82no—
642C22×C4—84no—
643C22×C4C2×C22⋊C411yescharacteristic
644C22×C4C2×C22⋊C411yescharacteristic
645C22×C4C2×C22⋊C414yes—
646C22×C4C2×C22⋊C414yes—
647C22×C4C2×C22⋊C414yes—
648C22×C4C2×C22⋊C411yescharacteristic
649C22×C4C2×C22⋊C411yescharacteristic
650C22×C4C2×C22⋊C414yes—
651C22×C4C2×C22⋊C411yescharacteristic
652C22×C4C2×C22⋊C411yescharacteristic
653C22×C4C2×C22⋊C411yescharacteristic
654C22×C4C2×C22⋊C411yescharacteristic
655C22×C4AGL(1,ℤ/8)14yes—
656C22×C4#13714yes—
657C22×C4C23×C411yescharacteristic
658C22×C4C23×C411yescharacteristic
659C22×C4C23×C414yes—
660C22×C4C22×D412yes—
661C22×C4C22×D411yescharacteristic
662C22×C4C22×D412yes—
663C22×C4C22×D411yescharacteristic
664C22×C4C22×D412yes—
665C22×C4C22×D411yescharacteristic
666C22×C4C22×D411yescharacteristic
667C22×C4C22×D411yescharacteristic
668C22×C4C22×D414yes—
669C22×C4C22×D411yescharacteristic
670C22×C4C22×D411yescharacteristic
671C22×C4C2511yescharacteristic
672M16—88no—
673C2×C8—24no—
674C2×C8—24no—
675C2×C8—82no—
676C2×C8—82no—
677C4⋊C4—24no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—28no—
685C4⋊C4—28no—
686C4⋊C4—24no—
687C4⋊C4—22no—
688C4⋊C4—24no—
689C4⋊C4—22no—
690C4⋊C4—24no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—28no—
694C4⋊C4—28no—
695C4⋊C4—24no—
696C4⋊C4—42no—
697C4⋊C4—44no—
698C4⋊C4—48no—
699C4⋊C4—44no—
700C4⋊C4—48no—
701C4⋊C4—44no—
702C4⋊C4—84no—
703C4⋊C4—82no—
704C4⋊C4C2×C22⋊C412yes—
705C4⋊C4C2×C22⋊C412yes—
706C4⋊C4C2×C22⋊C412yes—
707C4⋊C4C2×C22⋊C412yes—
708C4⋊C4C2×C22⋊C414yes—
709C4⋊C4C2×C22⋊C414yes—
710C4⋊C4C2×C22⋊C414yes—
711C4⋊C4C2×C22⋊C414yes—
712C4⋊C4C23×C414yes—
713C4⋊C4C23×C414yes—
714C22⋊C4—24no—
715C22⋊C4—28no—
716C22⋊C4—28no—
717C22⋊C4—24no—
718C22⋊C4—28no—
719C22⋊C4—28no—
720C22⋊C4—24no—
721C22⋊C4—24no—
722C22⋊C4—24no—
723C22⋊C4—28no—
724C22⋊C4—28no—
725C22⋊C4—24no—
726C22⋊C4—48no—
727C22⋊C4—44no—
728C22⋊C4C2×C22⋊C414yes—
729C22⋊C4C2×C22⋊C414yes—
730C22⋊C4C2×C22⋊C414yes—
731C22⋊C4C2×C22⋊C414yes—
732C22⋊C4C2×C22⋊C414yes—
733C22⋊C4C2×C22⋊C414yes—
734C42—28no—
735C42—28no—
736C42—24no—
737C42—24no—
738C42—48no—
739C42—42no—
740C42—44no—
741C42—42no—
742C42—44no—
743C42C2×C22⋊C414yes—
744C42C2×C22⋊C414yes—
745C42C2×C22⋊C411yescharacteristic
746C42C2×C22⋊C411yescharacteristic
747C42C2×C22⋊C411yescharacteristic
748C42C2×C22⋊C411yescharacteristic
749C42C2×C22⋊C414yes—
750C42C2×C22⋊C411yescharacteristic
751C42C2×C22⋊C411yescharacteristic
752C42C2×C22⋊C414yes—
753C42C2×C22⋊C411yescharacteristic
754C42C2×C22⋊C411yescharacteristic
755C42C23×C411yescharacteristic
756C42C23×C411yescharacteristic
757C42C23×C414yes—
758C42C23×C411yescharacteristic
759C42C23×C411yescharacteristic
760C42C22×D411yescharacteristic
761C42C22×D411yescharacteristic
762C42C22×D414yes—
763C42C22×D411yescharacteristic
764C42C22×D411yescharacteristic
765C23—22no—
766C23—22no—
767C23—24no—
768C23—41no—
769C23—42no—
770C23—41no—
771C23—42no—
772C23—44no—
773C23—82no—
774C23—82no—
775C23C22×C22⋊C414yes—
776C23C22×C22⋊C411yescharacteristic
777C23C22×C22⋊C411yescharacteristic
778C23C2×AGL(1,ℤ/8)12yes—
779C23C2×#13712yes—
780C23C23×D411yescharacteristic
781Q8—24no—
782Q8—24no—
783Q8—44no—
784Q8—44no—
785Q8—44no—
786Q8—44no—
787Q8—82no—
788Q8—82no—
789D4—28no—
790D4—28no—
791D4—24no—
792D4—24no—
793D4—44no—
794D4—48no—
795D4—44no—
796D4—44no—
797D4—44no—
798D4—44no—
799D4—44no—
800D4—82no—
801D4—82no—
802D4—88no—
803D4—88no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—28no—
807C2×C4—28no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—28no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—44no—
830C2×C4—42no—
831C2×C4—44no—
832C2×C4—42no—
833C2×C4—48no—
834C2×C4—48no—
835C2×C4—44no—
836C2×C4—42no—
837C2×C4—44no—
838C2×C4—42no—
839C2×C4—44no—
840C2×C4—42no—
841C2×C4—88no—
842C2×C4—88no—
843C2×C4—82no—
844C2×C4—82no—
845C2×C4—88no—
846C2×C4—816no—
847C2×C4#41714yes—
848C2×C4#41714yes—
849C2×C4#41714yes—
850C2×C4#41714yes—
851C2×C4C22×C22⋊C414yes—
852C2×C4C22×C22⋊C414yes—
853C2×C4C22×C22⋊C411yescharacteristic
854C2×C4C22×C22⋊C411yescharacteristic
855C2×C4C22×C22⋊C411yescharacteristic
856C2×C4C22×C22⋊C411yescharacteristic
857C2×C4C22×C22⋊C414yes—
858C2×C4C22×C22⋊C411yescharacteristic
859C2×C4C22×C22⋊C411yescharacteristic
860C2×C4C22×C22⋊C411yescharacteristic
861C2×C4C22×C22⋊C411yescharacteristic
862C2×C4C22×C22⋊C411yescharacteristic
863C2×C4C22×C22⋊C411yescharacteristic
864C2×C4C2×AGL(1,ℤ/8)12yes—
865C2×C4C2×AGL(1,ℤ/8)12yes—
866C2×C4C2×#13712yes—
867C2×C4C2×#13712yes—
868C2×C4C24×C411yescharacteristic
869C2×C4C23×D411yescharacteristic
870C8—44no—
871C8—44no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—21no—
877C22—21no—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—42no—
882C22—42no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—164no—
889C22C2×#41712yes—
890C22C2×#41712yes—
891C22C23×C22⋊C411yescharacteristic
892C22C22×AGL(1,ℤ/8)11yescharacteristic
893C22C22×#13711yescharacteristic
894C4—21no—
895C4—21no—
896C4—24no—
897C4—21no—
898C4—21no—
899C4—24no—
900C4—21no—
901C4—24no—
902C4—21no—
903C4—21no—
904C4—44no—
905C4—44no—
906C4—44no—
907C4—44no—
908C4—84no—
909C4—82no—
910C4C2×#41712yes—
911C4C2×#41712yes—
912C4C2×#41712yes—
913C4C2×#41712yes—
914C4#290112yes—
915C2—21no—
916C2—21no—
917C2—22no—
918C2—22no—
919C2—44no—
920C2—84no—
921C2#6007011yescharacteristic
922C2C22×#41711yescharacteristic
923C2C2×#290111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C23×C22⋊C4
prime radical#62815C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60277C2semidirect
3. C4⋊C4×#41C2semidirect
4. #17630C2semidirect
5. #17628C2semidirect
6. #17622C2semidirect
7. #17575C2semidirect
8. #17574C2semidirect
9. #17563C2semidirect
10. #17546C2semidirect
11. C2×#1503C2semidirect
12. C2×#1502C2semidirect
14. #3511C4semidirect
15. #3511C4semidirect
17. #3509C4semidirect
18. #3508C4semidirect
26. #3480C4semidirect
28. #3475C4semidirect
39. #2983C22semidirect
40. #2975C22semidirect
44. #2920C22semidirect
47. #2351C22semidirect
50. #2349C22semidirect
56. #2285C22semidirect
58. C2×C4×C4⋊C4C22semidirect
61. #1518C22semidirect
63. #1513C22semidirect
64. #1512C22semidirect
65. #1509C22semidirect
66. #1504C22semidirect
67. #1503C22semidirect
68. #1503C22semidirect
69. #1503C22semidirect
70. #1503C22semidirect
82. #559C2×C4semidirect
84. #557C2×C4semidirect
89. #556C2×C4semidirect
90. #556C2×C4semidirect
92. #555C2×C4semidirect
94. #554C2×C4semidirect
100. #553C2×C4semidirect
104. #552C2×C4semidirect
108. #550C2×C4semidirect
110. #548C2×C4semidirect
112. #547C2×C4semidirect
114. #546C2×C4semidirect
134. #533C2×C4semidirect
135. #533C2×C4semidirect
136. #533C2×C4semidirect
137. #533C2×C4semidirect
145. #532C2×C4semidirect
146. #532C2×C4semidirect
147. #532C2×C4semidirect
148. #532C2×C4semidirect
151. C2×C4⋊Q8C2×C4semidirect
152. C2×C4⋊Q8C2×C4semidirect
153. C2×C4⋊Q8C2×C4semidirect
154. C2×#127C2×C4semidirect
161. #529C2×C4semidirect
188. C4×#41C2×C4semidirect
195. C2×C4×Q8C2×C4semidirect
201. C2×C4×D4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#628152
#602772
C4⋊C4×#412
#176302
#176282
#176222
#175752
#175742
#175632
#175462
C2×#15032
C2×#15022