Finite Group Databasebeta

← C2×#79634 #11675674

Subgroups — C2×#79634 #11675674

Order 768.

1854 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic6C211yesmaximal, characteristic, complemented
2C2×#5543C211yesmaximal, characteristic
3C2×C3×C4×SD16C211yesmaximal, characteristic
4C2×#5164C212yesmaximal
5C2×#5021C211yesmaximal, characteristic, complemented
6C2×#5008C211yesmaximal, characteristic
7#79634C2116yesmaximal, direct product factor
8C2×#4856C212yesmaximal, complemented
9C2×#4796C212yesmaximal, complemented
10C2×#4759C212yesmaximal
11C2×#4679C211yesmaximal, characteristic, complemented
12C2×#4682C211yesmaximal, characteristic, complemented
13C2×#3385—31nomaximal, Sylow
14C22×C3×SD16C2211yescharacteristic
15C2×C3×C4×Q8C2211yescharacteristic
16C2×C3×C4×D4C2211yescharacteristic
17C2×Q8×Dic3C2212yes—
18C2×D4×Dic3C2212yes—
19C22×C4⋊Dic3—21no—
20C2×#924—21no—
21Q8×Dic6—24no—
22Q8×Dic6C2218yescomplemented
23#5543—24no—
24#5543C2218yes—
25C2×#890C2212yes—
26C2×#888—22no—
27C2×#888C2212yes—
28C2×#878—22no—
29C2×#869—21no—
30C2×#869C2211yescharacteristic
31C2×#869C2211yescharacteristic
32C2×C4×Dic6—21no—
33C2×C4×Dic6C2211yescharacteristic
34C3×C4×SD16C2218yes—
35C2×C3×#106C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×C4×C8C2211yescharacteristic
39C2×#835C2212yes—
40C2×#832C2212yes—
41#5164C22116yes—
42C2×#818C2212yes—
43C2×#818C2212yes—
44C2×#815C2212yes—
45C2×Dic3⋊C8C2212yes—
46#5021C2218yescomplemented
47#5008C2218yes—
48C2×#808C2212yes—
49C2×#807C2212yes—
50C2×C4⋊(C3⋊C8)C2211yescharacteristic
51#4856C22116yescomplemented
52#4796C22116yescomplemented
53#4759C22116yes—
54#4682C2218yescomplemented
55#4679C2218yescomplemented
56C2×Q82—31no—
57C2×#554—31no—
58#3385—316no—
59C2×#501—32no—
60C2×#500—31no—
61C2×#479—32no—
62C2×#477—31no—
63C2×#476—31no—
64C2×#474—32no—
65C2×#446—31no—
66C2×#440—32no—
67C2×C4×SD16D311yescharacteristic
68C22×C3×Q8C2311yescharacteristic
69C22×C3×D4C2311yescharacteristic
70C23×C3×C4—21no—
71C23×Dic3—22no—
72C22×Dic6—21no—
73C22×Dic6—21no—
74C22×Dic6—22no—
75C22×Dic6D411yescharacteristic
76C2×C3×SD16Q818yescomplemented
77C2×C3×SD16C2314yes—
78C22×C3×C8C2311yescharacteristic
79C22×C3×C8C2311yescharacteristic
80C3×C4×Q8—22no—
81C3×C4×Q8C2314yes—
82C3×C4×D4—22no—
83C3×C4×D4C2314yes—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4C2311yescharacteristic
86C2×C3×C4⋊C4C2311yescharacteristic
87C2×C3×C22⋊C4—21no—
88C2×C3×C42—21no—
89C2×C3×C42C2311yescharacteristic
90C2×#217—22no—
91Q8×Dic3—24no—
92Q8×Dic3C2318yes—
93D4×Dic3—24no—
94D4×Dic3C2318yes—
95C2×C4⋊Dic3—21no—
96C2×C4⋊Dic3—21no—
97C2×C4⋊Dic3—22no—
98C2×C4⋊Dic3—22no—
99C2×C4⋊Dic3—28no—
100C2×C4⋊Dic3D411yescharacteristic
101C2×C4⋊Dic3C2312yes—
102C2×C4⋊Dic3C2312yes—
103#924—28no—
104C2×Dic3⋊C4—22no—
105C2×Dic3⋊C4—22no—
106C2×Dic3⋊C4D412yes—
107C2×C4×Dic3—22no—
108C2×C4×Dic3C2312yes—
109C22×C3⋊C8C2312yes—
110#890—24no—
111#890C2318yes—
112#888—216no—
113#888—24no—
114#888C2318yes—
115#878—216no—
116#869—22no—
117#869—22no—
118#869—28no—
119#869C2314yes—
120#869C2314yes—
121C4×Dic6—28no—
122C4×Dic6D414yes—
123C4×Dic6C2314yes—
124C3×#106C2314yes—
125C3×#103C2314yes—
126C3×#102C2314yes—
127C3×C4×C8C2314yes—
128#835C2318yes—
129#832C2318yes—
130#818C2318yes—
131#818C2318yes—
132#815C2318yes—
133Dic3⋊C8C2318yes—
134#808C2318yes—
135#807C2318yes—
136C4⋊(C3⋊C8)C2314yes—
137C22×SD16C2×D311yescharacteristic
138Q82—38no—
139Q82—64no—
140#554—38no—
141#554—64no—
142C2×C4⋊Q8—32no—
143C2×C4⋊Q8—31no—
144C2×C4⋊Q8—31no—
145C2×C4⋊Q8—61no—
146C2×C4⋊Q8—62no—
147C2×#125—32no—
148C2×C22⋊Q8—62no—
149C2×C22⋊Q8—61no—
150C2×C4×Q8—31no—
151C2×C4×Q8—32no—
152C2×C4×Q8—61no—
153C2×C4×Q8C2×D311yescharacteristic
154C2×C4×D4—32no—
155C2×C4×D4C2×D311yescharacteristic
156C22×C4⋊C4—61no—
157#501—316no—
158#500—38no—
159#479—316no—
160#477—38no—
161#476—38no—
162#474—316no—
163#446—38no—
164#440—316no—
165C4×SD16C2×D318yes—
166C2×#107—32no—
167C2×#107—32no—
168C2×#107—32no—
169C2×#106—32no—
170C2×#106C2×D311yescharacteristic
171C2×C4⋊C8—32no—
172C2×C4⋊C8—31no—
173C2×#103—32no—
174C2×#103C2×D311yescharacteristic
175C2×#102—32no—
176C2×#102C2×D311yescharacteristic
177C2×#97—32no—
178C2×C4×C8C2×D311yescharacteristic
179C24×C3—21no—
180C2×C3×Q8—21no—
181C2×C3×Q8—22no—
182C2×C3×Q8C2×Q814yes—
183C2×C3×Q8C2412yes—
184C2×C3×D4—21no—
185C2×C3×D4—22no—
186C2×C3×D4C2×Q814yes—
187C2×C3×D4C2412yes—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—24no—
192C22×C3×C4—44no—
193C22×C3×C4C2×D411yescharacteristic
194C22×C3×C4C2×D411yescharacteristic
195C22×C3×C4C2411yescharacteristic
196C22×Dic3—22no—
197C22×Dic3—22no—
198C22×Dic3—28no—
199C22×Dic3—84no—
200C22×Dic3C2×D412yes—
201C22×Dic3C2×D412yes—
202C2×Dic6—24no—
203C2×Dic6—24no—
204C2×Dic6—24no—
205C2×Dic6—28no—
206C2×Dic6—84no—
207C2×Dic6—82no—
208C2×Dic6—82no—
209C2×Dic6C2×D414yes—
210C3×SD16C2×Q8116yescomplemented
211C2×C3×C8—22no—
212C2×C3×C8C2×Q814yes—
213C2×C3×C8C2412yes—
214C2×C3×C8C2412yes—
215C3×C4⋊C4—24no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4C2412yes—
219C3×C4⋊C4C2412yes—
220C3×C22⋊C4—24no—
221C3×C42—24no—
222C3×C42C2×D412yes—
223C3×C42C2412yes—
224#217—28no—
225C4⋊Dic3—24no—
226C4⋊Dic3—22no—
227C4⋊Dic3—22no—
228C4⋊Dic3—24no—
229C4⋊Dic3—28no—
230C4⋊Dic3—28no—
231C4⋊Dic3C2×D414yes—
232C4⋊Dic3C2414yes—
233C4⋊Dic3C2414yes—
234Dic3⋊C4—28no—
235Dic3⋊C4—28no—
236Dic3⋊C4C2×D418yes—
237C4×Dic3—28no—
238C4×Dic3C2×D414yes—
239C4×Dic3C2414yes—
240C2×C3⋊C8—24no—
241C2×C3⋊C8C2414yes—
242C22×Q8—31no—
243C22×Q8—62no—
244C22×Q8—61no—
245C22×Q8—61no—
246C22×Q8C22×D311yescharacteristic
247C22×D4C22×D311yescharacteristic
248C23×C4—21no—
249C23×C4—62no—
250C2×SD16Dic618yescomplemented
251C2×SD16C22×D314yes—
252C22×C8—32no—
253C22×C8C22×D311yescharacteristic
254C22×C8C22×D311yescharacteristic
255C4⋊Q8—38no—
256C4⋊Q8—34no—
257C4⋊Q8—34no—
258C4⋊Q8—68no—
259C4⋊Q8—64no—
260C4⋊Q8—616no—
261C4⋊Q8—62no—
262C4⋊Q8—62no—
263#125—38no—
264#125—64no—
265C22⋊Q8—616no—
266C22⋊Q8—68no—
267C4×Q8—22no—
268C4×Q8—34no—
269C4×Q8—34no—
270C4×Q8—38no—
271C4×Q8—68no—
272C4×Q8—64no—
273C4×Q8C22×D314yes—
274C4×D4—22no—
275C4×D4—38no—
276C4×D4—64no—
277C4×D4C22×D314yes—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—31no—
280C2×C4⋊C4—32no—
281C2×C4⋊C4—32no—
282C2×C4⋊C4—32no—
283C2×C4⋊C4—68no—
284C2×C4⋊C4—62no—
285C2×C4⋊C4—62no—
286C2×C4⋊C4—62no—
287C2×C4⋊C4—62no—
288C2×C4⋊C4—61no—
289C2×C4⋊C4—61no—
290C2×C4⋊C4C22×D311yescharacteristic
291C2×C4⋊C4C22×D311yescharacteristic
292C2×C22⋊C4—21no—
293C2×C22⋊C4—62no—
294C2×C42—21no—
295C2×C42—32no—
296C2×C42—62no—
297C2×C42C22×D311yescharacteristic
298#107—38no—
299#107—38no—
300#107—38no—
301#106—38no—
302#106C22×D314yes—
303C4⋊C8—38no—
304C4⋊C8—34no—
305#103—38no—
306#103C22×D314yes—
307#102—38no—
308#102C22×D314yes—
309#97—38no—
310C4×C8C22×D314yes—
311C23×C3—24no—
312C23×C3—22no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3C22×D411yescharacteristic
316C3×Q8—24no—
317C3×Q8—22no—
318C3×Q8C22×Q814yes—
319C3×D4—24no—
320C3×D4—22no—
321C3×D4C22×Q814yes—
322C2×C3×C4—24no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—42no—
328C2×C3×C4—42no—
329C2×C3×C4—48no—
330C2×C3×C4#13714yes—
331C2×C3×C4C22×D412yes—
332C2×C3×C4C22×D411yescharacteristic
333C2×C3×C4C22×D412yes—
334C2×C3×C4C22×Q812yes—
335C2×C3×C42−1+412yes—
336C2×C3×C4C2511yescharacteristic
337C2×Dic3—24no—
338C2×Dic3—24no—
339C2×Dic3—24no—
340C2×Dic3—24no—
341C2×Dic3—44no—
342C2×Dic3—44no—
343C2×Dic3—88no—
344C2×Dic3C22×D414yes—
345C2×Dic3C22×D414yes—
346Dic6—28no—
347Dic6—88no—
348Dic6—84no—
349Dic6—84no—
350C3×C8—22no—
351C3×C8C22×Q814yes—
352C3⋊C8—24no—
353C24—21no—
354C2×Q8—21no—
355C2×Q8—22no—
356C2×Q8—34no—
357C2×Q8—68no—
358C2×Q8—64no—
359C2×Q8—64no—
360C2×Q8—64no—
361C2×Q8—242no—
362C2×Q8—242no—
363C2×Q8—244no—
364C2×Q8C2×Dic614yes—
365C2×Q8C23×D312yes—
366C2×D4—21no—
367C2×D4—22no—
368C2×D4C2×Dic614yes—
369C2×D4C23×D312yes—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—24no—
374C22×C4—32no—
375C22×C4—32no—
376C22×C4—44no—
377C22×C4—68no—
378C22×C4—62no—
379C22×C4—62no—
380C22×C4—244no—
381C22×C4D3×D411yescharacteristic
382C22×C4D3×D411yescharacteristic
383C22×C4C23×D311yescharacteristic
384SD16C2×Dic6116yescomplemented
385C2×C8—22no—
386C2×C8—34no—
387C2×C8—64no—
388C2×C8C2×Dic614yes—
389C2×C8C23×D312yes—
390C2×C8C23×D312yes—
391C4⋊C4—24no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—34no—
395C4⋊C4—38no—
396C4⋊C4—34no—
397C4⋊C4—34no—
398C4⋊C4—68no—
399C4⋊C4—68no—
400C4⋊C4—68no—
401C4⋊C4—68no—
402C4⋊C4—62no—
403C4⋊C4—62no—
404C4⋊C4—64no—
405C4⋊C4—64no—
406C4⋊C4C23×D312yes—
407C4⋊C4C23×D312yes—
408C22⋊C4—24no—
409C22⋊C4—68no—
410C42—24no—
411C42—34no—
412C42—34no—
413C42—68no—
414C42D3×D412yes—
415C42C23×D312yes—
416C22×C3—24no—
417C22×C3—48no—
418C22×C3—42no—
419C22×C3—42no—
420C22×C3D4×Q812yes—
421C22×C3C2×#13712yes—
422C22×C3#57612yes—
423C22×C3C23×D411yescharacteristic
424C3×C4—24no—
425C3×C4—22no—
426C3×C4—42no—
427C3×C4—42no—
428C3×C4D4×Q812yes—
429C3×C4C2×#13714yes—
430C3×C4C23×Q811yescharacteristic
431C3×C4C2×2−1+411yescharacteristic
432Dic3—24no—
433Dic3—24no—
434Dic3—44no—
435Dic3—44no—
436C23—22no—
437C23—24no—
438C23—42no—
439C23—42no—
440C23C2×D3×D411yescharacteristic
441Q8—22no—
442Q8—24no—
443Q8—68no—
444Q8—244no—
445Q8—244no—
446Q8—248no—
447Q8C22×Dic614yes—
448D4—22no—
449D4—24no—
450D4C22×Dic614yes—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—34no—
457C2×C4—34no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—48no—
461C2×C4—64no—
462C2×C4—64no—
463C2×C4—64no—
464C2×C4—64no—
465C2×C4—124no—
466C2×C4—124no—
467C2×C4—248no—
468C2×C4#91514yes—
469C2×C4C22×Dic612yes—
470C2×C4C2×D3×D412yes—
471C2×C4C2×D3×D412yes—
472C2×C4C2×D3×D411yescharacteristic
473C2×C4#101012yes—
474C2×C4C24×D311yescharacteristic
475C8—22no—
476C8—64no—
477C8C22×Dic614yes—
478C2×C3—44no—
479C2×C3#338514yescomplemented
480C2×C3C2×D4×Q811yescharacteristic
481C2×C3C22×#13711yescharacteristic
482C2×C3C2×#57611yescharacteristic
483C22—24no—
484C22—48no—
485C22—42no—
486C22—42no—
487C22D4×Dic612yes—
488C22C2×#91512yes—
489C22#576912yes—
490C22C22×D3×D411yescharacteristic
491C4—22no—
492C4—24no—
493C4—42no—
494C4—42no—
495C4—64no—
496C4—64no—
497C4—124no—
498C4—124no—
499C4D4×Dic612yes—
500C4C2×#91514yes—
501C4C23×Dic611yescharacteristic
502C4C2×#101011yescharacteristic
503C3C2×#338511yescharacteristic, complemented, Sylow
504C2—44no—
505C2#7963414yesdirect product factor
506C2C2×D4×Dic611yescharacteristic
507C2C22×#91511yescharacteristic
508C2C2×#576911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×C4×SD16C2
socleC23×C3C22×D4
prime radicalC22×C3×D4C23
hypercenterC2×C4×SD16D3
hypocenterC3C2×#3385
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic6C2semidirect
5. C2×#5021C2semidirect
7. #79634C2direct (N × H)
8. C2×#4856C2semidirect
9. C2×#4796C2semidirect
11. C2×#4679C2semidirect
12. C2×#4682C2semidirect
22. Q8×Dic6C22semidirect
46. #5021C22semidirect
51. #4856C22semidirect
52. #4796C22semidirect
54. #4682C22semidirect
55. #4679C22semidirect
76. C2×C3×SD16Q8semidirect
210. C3×SD16C2×Q8semidirect
250. C2×SD16Dic6semidirect
384. SD16C2×Dic6semidirect
479. C2×C3#3385semidirect
503. C3C2×#3385semidirect
505. C2#79634direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic62
C2×#55432
C2×C3×C4×SD162
C2×#51642
C2×#50212
C2×#50082
#796342
C2×#48562
C2×#47962
C2×#47592
C2×#46792
C2×#46822
C2×#33853