Finite Group Databasebeta

← C2×#10594740 #11918656

Subgroups — C2×#10594740 #11918656

Order 1152.

3589 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64319C211yesmaximal, characteristic, complemented
2C2×D32×D4C211yesmaximal, characteristic, complemented
3C2×SD16×C3⋊D3C211yesmaximal, characteristic, complemented
4C2×C3×#914C212yesmaximal, complemented
5C2×#63940C211yesmaximal, characteristic, complemented
6C2×#63939C212yesmaximal, complemented
7C2×#63932C212yesmaximal, complemented
8C2×#63926C211yesmaximal, characteristic, complemented
9#10594740C2116yesmaximal, direct product factor
10C2×#63797C211yesmaximal, characteristic, complemented
11C2×#63795C212yesmaximal, complemented
12C2×#63791C211yesmaximal, characteristic, complemented
13C2×D3×AGL(1,ℤ/8)—32nomaximal
14C23×D32—21no—
15C2×Q8×C3⋊D3C2211yescharacteristic, complemented
16C2×D4×C3⋊D3C2211yescharacteristic
17C2×C3×#239C2212yescomplemented
18C2×C3×D3×D4C2212yescomplemented
19C2×#3811—21no—
20C2×D3×#67—22no—
21#64319—24no—
22#64319C2218yescomplemented
23D32×D4—24no—
24D32×D4C2218yescomplemented
25C2×#3802—21no—
26C2×#3802C2211yescharacteristic
27C2×#3802C2211yescharacteristic, complemented
28C2×D3×D12C2212yescomplemented
29C2×C4×D32—21no—
30C2×C4×D32C2211yescharacteristic
31C2×#3795—22no—
32C2×#3795C2212yescomplemented
33C2×C32×SD16C2211yescharacteristic, complemented
34C2×#3755C2211yescharacteristic, complemented
35C2×#3754C2211yescharacteristic, complemented
36SD16×C3⋊D3C2218yescomplemented
37C2×#3744C2211yescharacteristic, complemented
38C2×C8×C3⋊D3C2211yescharacteristic, complemented
39C2×C3×#215C2212yescomplemented
40C2×C3×#213C2212yescomplemented
41C3×#914C22116yescomplemented
42C2×C3×D24C2212yescomplemented
43C2×C3×ΓL(1,𝔽25)C2212yescomplemented
44#63940C2218yescomplemented
45#63939C22116yescomplemented
46#63932C22116yescomplemented
47#63926C2218yescomplemented
48C2×#3716C2212yescomplemented
49C2×#3714C2212yescomplemented
50C2×#3713C2212yescomplemented
51C2×#3711C2212yescomplemented
52C2×#3710C2211yescharacteristic, complemented
53#63797C2218yescomplemented
54#63795C22116yescomplemented
55#63791C2218yescomplemented
56C2×D3×#41—32no—
57C22×D3×D4—32no—
58C2×C3×AGL(1,ℤ/8)—32no—
59C2×#949—32no—
60C2×#932—32no—
61D3×AGL(1,ℤ/8)—332no—
62C2×#914—32no—
63C2×#914D312yescomplemented
64C2×D3×SD16—32no—
65C2×D3×SD16—32no—
66C2×D3×SD16—61no—
67C2×#911—32no—
68C2×#911—32no—
69C2×D3×D8—32no—
70C2×D3×D8—32no—
71C2×#908—32no—
72C2×D3×M16—32no—
73C23×C3⋊D3—21no—
74C23×C3×D3—22no—
75C22×D32—21no—
76C22×D32—21no—
77C22×D32—22no—
78C22×D32—28no—
79C22×D32—48no—
80C22×D32D411yescharacteristic
81C2×C32×Q8C2311yescharacteristic, complemented
82C2×C32×D4C2311yescharacteristic
83C2×#638—21no—
84Q8×C3⋊D3—22no—
85Q8×C3⋊D3C2314yescomplemented
86D4×C3⋊D3—22no—
87D4×C3⋊D3C2314yes—
88C2×C4⋊(C3⋊D3)C2311yescharacteristic
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3C2311yescharacteristic
91C2×#634—21no—
92C2×#634C2311yescharacteristic, complemented
93C2×C3×#67—22no—
94C3×#239—24no—
95C3×#239C2318yescomplemented
96C3×D3×D4—24no—
97C3×D3×D4C2318yescomplemented
98C2×C3×D12—22no—
99C2×C3×D12C2312yes—
100C2×C3×D12C2312yescomplemented
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3C2312yes—
103#3811—28no—
104D3×#67—216no—
105C2×#626—22no—
106C2×#625—22no—
107C2×#625—21no—
108C2×#625—21no—
109C2×#624D411yescharacteristic
110C2×D3×Dic3—22no—
111C2×D3×Dic3D412yes—
112#3802—28no—
113#3802—22no—
114#3802—22no—
115#3802C2314yes—
116#3802C2314yescomplemented
117D3×D12—24no—
118D3×D12C2318yescomplemented
119C4×D32—28no—
120C4×D32D414yes—
121C4×D32C2314yes—
122#3795—24no—
123#3795—216no—
124#3795C2318yescomplemented
125C32×SD16C2314yescomplemented
126C2×C32×C8C2311yescharacteristic, complemented
127#3755C2314yescomplemented
128#3754C2314yescomplemented
129C2×C3⋊(C3⋊C8)C2311yescharacteristic, complemented
130#3744C2314yescomplemented
131C8×C3⋊D3C2314yescomplemented
132C3×#215C2318yescomplemented
133C3×#213C2318yescomplemented
134C2×C3×C3⋊C8C2312yescomplemented
135C3×D24C2318yescomplemented
136C3×ΓL(1,𝔽25)C2318yescomplemented
137#3716C2318yescomplemented
138#3714C2318yescomplemented
139#3713C2318yescomplemented
140#3711C2318yescomplemented
141#3710C2314yescomplemented
142C22×AGL(1,ℤ/8)—91noSylow
143C24×D3—62no—
144C2×C3×#41—32no—
145C22×C3×D4—32no—
146C22×#67—62no—
147D3×#41—316no—
148D3×#41—68no—
149C2×#239C2×D312yescomplemented
150C2×D3×Q8—32no—
151C2×D3×Q8—61no—
152C2×#237—32no—
153C2×#237—62no—
154C2×D3×D4—32no—
155C2×D3×D4—316no—
156C2×D3×D4—32no—
157C2×D3×D4—32no—
158C2×D3×D4—32no—
159C2×D3×D4—61no—
160C2×D3×D4—68no—
161C2×D3×D4—62no—
162C2×D3×D4—62no—
163C2×D3×D4—62no—
164C2×D3×D4C2×D312yescomplemented
165C2×#235—32no—
166C2×#235—62no—
167C22×D12—32no—
168C22×C4×D3—32no—
169C22×C4×D3—62no—
170C3×AGL(1,ℤ/8)—316no—
171C2×C3×SD16—21no—
172C2×C3×SD16—32no—
173C2×C3×SD16C2×D312yescomplemented
174C2×C3×D8—32no—
175C2×C3×D8—32no—
176C2×C3×M16—32no—
177#949—316no—
178C2×#215—32no—
179C2×#215—61no—
180C2×#215C2×D312yescomplemented
181C2×#214—32no—
182C2×#214—32no—
183C2×#214—61no—
184#932—316no—
185C2×#213—32no—
186C2×#213—32no—
187C2×#213—32no—
188C2×#213C2×D312yescomplemented
189C2×#208—32no—
190#914—316no—
191#914C2×D3116yescomplemented
192D3×SD16—316no—
193D3×SD16—316no—
194D3×SD16—68no—
195#911—316no—
196#911—316no—
197D3×D8—316no—
198D3×D8—316no—
199#908—316no—
200D3×M16—316no—
201C2×D24—32no—
202C2×D24C2×D312yescomplemented
203C2×#204—32no—
204C2×#204—32no—
205C2×#204—61no—
206C2×ΓL(1,𝔽25)—32no—
207C2×ΓL(1,𝔽25)C2×D312yescomplemented
208C2×D3×C8—32no—
209C2×D3×C8—32no—
210C2×D3×C8—61no—
211C23×C32—21no—
212C22×C3⋊D3—21no—
213C22×C3⋊D3—24no—
214C22×C3⋊D3—44no—
215C22×C3⋊D3C2×D411yescharacteristic
216C22×C3×D3—22no—
217C22×C3×D3—22no—
218C22×C3×D3—28no—
219C22×C3×D3—48no—
220C22×C3×D3C2×D412yes—
221C2×D32—24no—
222C2×D32—24no—
223C2×D32—24no—
224C2×D32—28no—
225C2×D32—432no—
226C2×D32—48no—
227C2×D32—44no—
228C2×D32—44no—
229C2×D32C2×D414yes—
230C32×Q8—21no—
231C32×Q8C2412yescomplemented
232C32×D4—21no—
233C32×D4C2412yes—
234C2×C32×C4—21no—
235C2×C32×C4C2411yescharacteristic
236#638—24no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3C2×D411yescharacteristic
239C4⋊(C3⋊D3)—21no—
240C4⋊(C3⋊D3)C2412yes—
241C4×C3⋊D3—24no—
242C4×C3⋊D3C2×D412yes—
243C4×C3⋊D3C2412yes—
244#634—21no—
245#634—24no—
246#634C2412yescomplemented
247C3×#67—28no—
248C2×C3×Dic3C2×D412yes—
249C3×D12—28no—
250C3×D12—22no—
251C3×D12—22no—
252C3×D12C2414yes—
253C3×D12C2414yescomplemented
254C3×C4×D3—28no—
255C3×C4×D3C2×D414yes—
256C3×C4×D3C2414yes—
257#626—28no—
258#625—28no—
259#625—24no—
260#625—24no—
261#624C2×D414yes—
262D3×Dic3—28no—
263D3×Dic3C2×D418yes—
264C32×C8C2412yescomplemented
265C3⋊(C3⋊C8)C2412yescomplemented
266C3×C3⋊C8C2414yescomplemented
267C22×#41—91no—
268C23×D4—91no—
269C2×AGL(1,ℤ/8)—32no—
270C2×AGL(1,ℤ/8)—92no—
271C2×AGL(1,ℤ/8)—92no—
272C2×AGL(1,ℤ/8)—92no—
273C2×AGL(1,ℤ/8)—916no—
274C22×SD16—91no—
275C22×SD16—91no—
276C22×D8—91no—
277C22×D8—91no—
278C22×M16—91no—
279C24×C3—62no—
280C23×D3—22no—
281C23×D3—32no—
282C23×D3—62no—
283C23×D3—62no—
284C23×D3—616no—
285C23×D3—62no—
286C23×D3—62no—
287C23×D3—62no—
288C23×D3—121no—
289C23×D3—1216no—
290C3×#41—38no—
291C3×#41—64no—
292C2×C3×Q8—21no—
293C2×C3×Q8C22×D312yescomplemented
294C2×C3×D4—21no—
295C2×C3×D4—38no—
296C2×C3×D4—32no—
297C2×C3×D4—32no—
298C2×C3×D4—62no—
299C2×C3×D4—64no—
300C2×C3×D4—62no—
301C2×C3×D4C22×D312yes—
302C22×C3×C4—32no—
303C22×C3×C4—62no—
304C2×#67—22no—
305C2×#67—616no—
306C2×#67—62no—
307C2×#67—62no—
308C2×#67—62no—
309C2×#67—62no—
310C2×#67—62no—
311C2×#67—62no—
312C2×#67—121no—
313C22×Dic3—32no—
314C22×Dic3—62no—
315#239—24no—
316#239C22×D318yescomplemented
317D3×Q8—38no—
318D3×Q8—64no—
319D3×Q8—64no—
320D3×Q8—122no—
321#237—38no—
322#237—616no—
323#237—64no—
324D3×D4—24no—
325D3×D4—38no—
326D3×D4—38no—
327D3×D4—38no—
328D3×D4—38no—
329D3×D4—64no—
330D3×D4—64no—
331D3×D4—64no—
332D3×D4—616no—
333D3×D4—64no—
334D3×D4—616no—
335D3×D4—616no—
336D3×D4—64no—
337D3×D4—122no—
338D3×D4C22×D318yescomplemented
339#235—38no—
340#235—616no—
341#235—64no—
342C2×D12—22no—
343C2×D12—32no—
344C2×D12—38no—
345C2×D12—61no—
346C2×D12—64no—
347C2×D12—62no—
348C2×D12C22×D312yes—
349C2×D12C22×D312yescomplemented
350C2×C4×D3—22no—
351C2×C4×D3—32no—
352C2×C4×D3—32no—
353C2×C4×D3—32no—
354C2×C4×D3—38no—
355C2×C4×D3—38no—
356C2×C4×D3—61no—
357C2×C4×D3—616no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×C4×D3—121no—
361C2×C4×D3C22×D312yes—
362C2×Dic6—32no—
363C2×Dic6—61no—
364C2×Dic6—62no—
365C2×Dic6—121no—
366C3×SD16—24no—
367C3×SD16—38no—
368C3×SD16C22×D318yescomplemented
369C3×D8—38no—
370C3×D8—38no—
371C3×M16—38no—
372C2×C3×C8—21no—
373C2×C3×C8—32no—
374C2×C3×C8C22×D312yescomplemented
375#215—38no—
376#215—64no—
377#215C22×D318yescomplemented
378#214—38no—
379#214—38no—
380#214—64no—
381#213—38no—
382#213—38no—
383#213—38no—
384#213C22×D318yescomplemented
385#208—38no—
386C2×C3⋊C8—32no—
387C2×C3⋊C8—61no—
388C2×C3⋊C8C22×D312yescomplemented
389D24—38no—
390D24C22×D318yescomplemented
391#204—38no—
392#204—38no—
393#204—64no—
394ΓL(1,𝔽25)—38no—
395ΓL(1,𝔽25)C22×D318yescomplemented
396D3×C8—38no—
397D3×C8—38no—
398D3×C8—64no—
399C22×C32—22no—
400C22×C32—42no—
401C22×C32C22×D411yescharacteristic
402C2×C3⋊D3—22no—
403C2×C3⋊D3—42no—
404C2×C3⋊D3—48no—
405C2×C3⋊D3AGL(1,ℤ/8)14yescomplemented
406C2×C3⋊D3C22×D412yes—
407C2×C3×D3—24no—
408C2×C3×D3—24no—
409C2×C3×D3—24no—
410C2×C3×D3—416no—
411C2×C3×D3—44no—
412C2×C3×D3—44no—
413C2×C3×D3C22×D414yes—
414D32—28no—
415D32—416no—
416D32—48no—
417D32—48no—
418C32×C4—22no—
419C32×C4C22×D411yescharacteristic
420C32×C4C2511yescharacteristic
421C3⋊Dic3—22no—
422C3⋊Dic3C22×D412yes—
423C3×Dic3C22×D414yes—
424C25—181no—
425C2×#41—32no—
426C2×#41—92no—
427C2×#41—98no—
428C2×#41—182no—
429C2×#41—184no—
430C22×Q8—91no—
431C22×D4—32no—
432C22×D4—92no—
433C22×D4—91no—
434C22×D4—91no—
435C22×D4—98no—
436C22×D4—91no—
437C22×D4—181no—
438C22×D4—184no—
439C22×D4—182no—
440C22×D4—181no—
441C23×C4—91no—
442C23×C4—181no—
443AGL(1,ℤ/8)—316no—
444AGL(1,ℤ/8)—916no—
445AGL(1,ℤ/8)—916no—
446AGL(1,ℤ/8)—916no—
447C2×SD16—32no—
448C2×SD16—92no—
449C2×SD16—98no—
450C2×SD16—91no—
451C2×SD16—91no—
452C2×SD16—98no—
453C2×SD16—91no—
454C2×SD16D3211yescharacteristic, complemented
455C2×D8—32no—
456C2×D8—32no—
457C2×D8—92no—
458C2×D8—98no—
459C2×D8—98no—
460C2×D8—92no—
461C2×M16—32no—
462C2×M16—92no—
463C2×M16—98no—
464C22×C8—91no—
465C22×C8—91no—
466C23×C3—22no—
467C23×C3—32no—
468C23×C3—41no—
469C23×C3—68no—
470C23×C3—62no—
471C23×C3—62no—
472C23×C3—128no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—28no—
476C22×D3—32no—
477C22×D3—38no—
478C22×D3—48no—
479C22×D3—61no—
480C22×D3—68no—
481C22×D3—68no—
482C22×D3—68no—
483C22×D3—68no—
484C22×D3—68no—
485C22×D3—62no—
486C22×D3—68no—
487C22×D3—124no—
488C22×D3—121no—
489C22×D3—128no—
490C22×D3—128no—
491C22×D3—128no—
492C22×D3—128no—
493C22×D3—1264no—
494C22×D3—128no—
495C22×D3—244no—
496C22×D3D3×D412yes—
497C3×Q8—22no—
498C3×Q8—22no—
499C3×Q8—41no—
500C3×Q8C23×D314yescomplemented
501C3×D4—22no—
502C3×D4—22no—
503C3×D4—34no—
504C3×D4—34no—
505C3×D4—41no—
506C3×D4—68no—
507C3×D4—68no—
508C3×D4—62no—
509C3×D4—62no—
510C3×D4C23×D314yes—
511C2×C3×C4—22no—
512C2×C3×C4—21no—
513C2×C3×C4—32no—
514C2×C3×C4—34no—
515C2×C3×C4—34no—
516C2×C3×C4—41no—
517C2×C3×C4—68no—
518C2×C3×C4C23×D312yes—
519#67—28no—
520#67—68no—
521#67—68no—
522#67—68no—
523#67—68no—
524#67—68no—
525#67—68no—
526#67—124no—
527C2×Dic3—32no—
528C2×Dic3—38no—
529C2×Dic3—61no—
530C2×Dic3—62no—
531C2×Dic3—68no—
532C2×Dic3—121no—
533C2×Dic3D3×D412yes—
534D12—28no—
535D12—22no—
536D12—22no—
537D12—34no—
538D12—62no—
539D12—68no—
540D12—62no—
541D12—121no—
542D12C23×D314yes—
543D12C23×D314yescomplemented
544C4×D3—28no—
545C4×D3—38no—
546C4×D3—34no—
547C4×D3—34no—
548C4×D3—38no—
549C4×D3—62no—
550C4×D3—62no—
551C4×D3—68no—
552C4×D3—68no—
553C4×D3—124no—
554C4×D3D3×D414yes—
555C4×D3C23×D314yes—
556Dic6—34no—
557Dic6—62no—
558Dic6—68no—
559Dic6—62no—
560Dic6—124no—
561Dic6—121no—
562C3×C8—22no—
563C3×C8—34no—
564C3×C8C23×D314yescomplemented
565C3⋊C8—34no—
566C3⋊C8—62no—
567C3⋊C8C23×D314yescomplemented
568C2×C32—42no—
569C2×C32C2×AGL(1,ℤ/8)12yescomplemented
570C2×C32C23×D411yescharacteristic
571C3⋊D3—42no—
572C3⋊D3C2×AGL(1,ℤ/8)14yescomplemented
573C3×D3—24no—
574C3×D3—44no—
575C3×D3—44no—
576C24—62no—
577C24—91no—
578C24—181no—
579C24—182no—
580C24—181no—
581C24—188no—
582C24—181no—
583C24—368no—
584#41—38no—
585#41—64no—
586#41—98no—
587#41—184no—
588#41—1816no—
589C2×Q8—94no—
590C2×Q8—91no—
591C2×Q8—181no—
592C2×Q8—182no—
593C2×Q8C2×D3211yescharacteristic, complemented
594C2×D4—38no—
595C2×D4—32no—
596C2×D4—32no—
597C2×D4—62no—
598C2×D4—64no—
599C2×D4—62no—
600C2×D4—98no—
601C2×D4—94no—
602C2×D4—94no—
603C2×D4—94no—
604C2×D4—91no—
605C2×D4—184no—
606C2×D4—182no—
607C2×D4—182no—
608C2×D4—188no—
609C2×D4—182no—
610C2×D4—182no—
611C2×D4—1816no—
612C2×D4—181no—
613C2×D4—181no—
614C2×D4—181no—
615C2×D4—188no—
616C2×D4—182no—
617C2×D4C2×D3211yescharacteristic
618C22×C4—32no—
619C22×C4—62no—
620C22×C4—94no—
621C22×C4—91no—
622C22×C4—94no—
623C22×C4—92no—
624C22×C4—91no—
625C22×C4—181no—
626C22×C4—182no—
627C22×C4—188no—
628SD16—38no—
629SD16—98no—
630SD16—94no—
631SD16—94no—
632SD16—94no—
633SD16C2×D3214yescomplemented
634D8—38no—
635D8—38no—
636D8—98no—
637D8—98no—
638M16—38no—
639M16—98no—
640C2×C8—32no—
641C2×C8—94no—
642C2×C8—91no—
643C2×C8—94no—
644C2×C8C2×D3211yescharacteristic, complemented
645C22×C3—24no—
646C22×C3—21no—
647C22×C3—34no—
648C22×C3—42no—
649C22×C3—44no—
650C22×C3—64no—
651C22×C3—64no—
652C22×C3—64no—
653C22×C3—82no—
654C22×C3—1216no—
655C22×C3—124no—
656C22×C3—124no—
657C22×C3C2×D3×D412yes—
658C2×D3—24no—
659C2×D3—24no—
660C2×D3—24no—
661C2×D3—34no—
662C2×D3—38no—
663C2×D3—416no—
664C2×D3—44no—
665C2×D3—44no—
666C2×D3—62no—
667C2×D3—64no—
668C2×D3—616no—
669C2×D3—64no—
670C2×D3—122no—
671C2×D3—1216no—
672C2×D3—1216no—
673C2×D3—1216no—
674C2×D3—1216no—
675C2×D3—1216no—
676C2×D3—124no—
677C2×D3—248no—
678C2×D3—242no—
679C2×D3C2×D3×D414yes—
680C3×C4—24no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—34no—
684C3×C4—42no—
685C3×C4C2×D3×D412yes—
686C3×C4C24×D312yes—
687Dic3—34no—
688Dic3—62no—
689Dic3—64no—
690Dic3—122no—
691Dic3C2×D3×D414yes—
692C32C22×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
693C23—21no—
694C23—32no—
695C23—68no—
696C23—62no—
697C23—62no—
698C23—94no—
699C23—91no—
700C23—128no—
701C23—184no—
702C23—188no—
703C23—184no—
704C23—184no—
705C23—184no—
706C23—181no—
707C23—364no—
708C23—368no—
709C23—364no—
710C23—364no—
711C23—3632no—
712Q8—21no—
713Q8—92no—
714Q8—184no—
715Q8—181no—
716Q8C22×D3212yescomplemented
717D4—21no—
718D4—34no—
719D4—34no—
720D4—68no—
721D4—68no—
722D4—62no—
723D4—62no—
724D4—92no—
725D4—188no—
726D4—184no—
727D4—184no—
728D4—184no—
729D4—188no—
730D4—181no—
731D4C22×D3212yes—
732C2×C4—21no—
733C2×C4—32no—
734C2×C4—34no—
735C2×C4—34no—
736C2×C4—68no—
737C2×C4—94no—
738C2×C4—98no—
739C2×C4—91no—
740C2×C4—92no—
741C2×C4—92no—
742C2×C4—184no—
743C2×C4—188no—
744C2×C4—181no—
745C2×C4C22×D3211yescharacteristic
746C8—34no—
747C8—92no—
748C8C22×D3212yescomplemented
749C2×C3—21no—
750C2×C3—22no—
751C2×C3—44no—
752C2×C3—64no—
753C2×C3—82no—
754C2×C3—124no—
755C2×C3—124no—
756C2×C3D3×AGL(1,ℤ/8)14yescomplemented
757C2×C3C22×D3×D412yes—
758D3—24no—
759D3—38no—
760D3—44no—
761D3—44no—
762D3—64no—
763D3—124no—
764D3—242no—
765C22—22no—
766C22—34no—
767C22—42no—
768C22—64no—
769C22—64no—
770C22—64no—
771C22—92no—
772C22—94no—
773C22—1216no—
774C22—124no—
775C22—124no—
776C22—188no—
777C22—182no—
778C22—368no—
779C22—3616no—
780C22—368no—
781C22—368no—
782C22—362no—
783C22D32×D411yescharacteristic
784C4—22no—
785C4—34no—
786C4—92no—
787C4—182no—
788C4D32×D411yescharacteristic
789C4C23×D3211yescharacteristic
790C3—21no—
791C3C2×D3×AGL(1,ℤ/8)12yescomplemented
792C2—42no—
793C2—64no—
794C2—94no—
795C2—124no—
796C2—124no—
797C2—362no—
798C2#1059474012yesdirect product factor
799C2C2×D32×D411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32C22×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#64319C2semidirect
2. C2×D32×D4C2semidirect
3. C2×SD16×C3⋊D3C2semidirect
4. C2×C3×#914C2semidirect
5. C2×#63940C2semidirect
6. C2×#63939C2semidirect
7. C2×#63932C2semidirect
8. C2×#63926C2semidirect
9. #10594740C2direct (N × H)
10. C2×#63797C2semidirect
11. C2×#63795C2semidirect
12. C2×#63791C2semidirect
15. C2×Q8×C3⋊D3C22semidirect
17. C2×C3×#239C22semidirect
18. C2×C3×D3×D4C22semidirect
22. #64319C22semidirect
24. D32×D4C22semidirect
27. C2×#3802C22semidirect
28. C2×D3×D12C22semidirect
32. C2×#3795C22semidirect
33. C2×C32×SD16C22semidirect
34. C2×#3755C22semidirect
35. C2×#3754C22semidirect
36. SD16×C3⋊D3C22semidirect
37. C2×#3744C22semidirect
38. C2×C8×C3⋊D3C22semidirect
39. C2×C3×#215C22semidirect
40. C2×C3×#213C22semidirect
41. C3×#914C22semidirect
42. C2×C3×D24C22semidirect
43. C2×C3×ΓL(1,𝔽25)C22semidirect
44. #63940C22semidirect
45. #63939C22semidirect
46. #63932C22semidirect
47. #63926C22semidirect
48. C2×#3716C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3711C22semidirect
52. C2×#3710C22semidirect
53. #63797C22semidirect
54. #63795C22semidirect
55. #63791C22semidirect
63. C2×#914D3semidirect
81. C2×C32×Q8C23semidirect
85. Q8×C3⋊D3C23semidirect
92. C2×#634C23semidirect
95. C3×#239C23semidirect
97. C3×D3×D4C23semidirect
100. C2×C3×D12C23semidirect
116. #3802C23semidirect
118. D3×D12C23semidirect
124. #3795C23semidirect
125. C32×SD16C23semidirect
126. C2×C32×C8C23semidirect
127. #3755C23semidirect
128. #3754C23semidirect
129. C2×C3⋊(C3⋊C8)C23semidirect
130. #3744C23semidirect
131. C8×C3⋊D3C23semidirect
132. C3×#215C23semidirect
133. C3×#213C23semidirect
134. C2×C3×C3⋊C8C23semidirect
135. C3×D24C23semidirect
136. C3×ΓL(1,𝔽25)C23semidirect
137. #3716C23semidirect
138. #3714C23semidirect
139. #3713C23semidirect
140. #3711C23semidirect
141. #3710C23semidirect
149. C2×#239C2×D3semidirect
164. C2×D3×D4C2×D3semidirect
173. C2×C3×SD16C2×D3semidirect
180. C2×#215C2×D3semidirect
188. C2×#213C2×D3semidirect
191. #914C2×D3semidirect
202. C2×D24C2×D3semidirect
207. C2×ΓL(1,𝔽25)C2×D3semidirect
231. C32×Q8C24semidirect
246. #634C24semidirect
253. C3×D12C24semidirect
264. C32×C8C24semidirect
265. C3⋊(C3⋊C8)C24semidirect
266. C3×C3⋊C8C24semidirect
293. C2×C3×Q8C22×D3semidirect
316. #239C22×D3semidirect
338. D3×D4C22×D3semidirect
349. C2×D12C22×D3semidirect
368. C3×SD16C22×D3semidirect
374. C2×C3×C8C22×D3semidirect
377. #215C22×D3semidirect
384. #213C22×D3semidirect
388. C2×C3⋊C8C22×D3semidirect
390. D24C22×D3semidirect
395. ΓL(1,𝔽25)C22×D3semidirect
405. C2×C3⋊D3AGL(1,ℤ/8)semidirect
454. C2×SD16D32semidirect
500. C3×Q8C23×D3semidirect
543. D12C23×D3semidirect
564. C3×C8C23×D3semidirect
567. C3⋊C8C23×D3semidirect
569. C2×C32C2×AGL(1,ℤ/8)semidirect
572. C3⋊D3C2×AGL(1,ℤ/8)semidirect
593. C2×Q8C2×D32semidirect
633. SD16C2×D32semidirect
644. C2×C8C2×D32semidirect
692. C32C22×AGL(1,ℤ/8)semidirect
716. Q8C22×D32semidirect
748. C8C22×D32semidirect
756. C2×C3D3×AGL(1,ℤ/8)semidirect
791. C3C2×D3×AGL(1,ℤ/8)semidirect
798. C2#10594740direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643192
C2×D32×D42
C2×SD16×C3⋊D32
C2×C3×#9142
C2×#639402
C2×#639392
C2×#639322
C2×#639262
#105947402
C2×#637972
C2×#637952
C2×#637912
C2×D3×AGL(1,ℤ/8)3