Finite Group Databasebeta

← C2×#80961 #11675692

Subgroups — C2×#80961 #11675692

Order 768.

2006 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5721C211yesmaximal, characteristic, complemented
2C2×D4×Dic6C211yesmaximal, characteristic
3C2×C3×#474C211yesmaximal, characteristic
4C2×#5078C211yesmaximal, characteristic, complemented
5C2×C4×#214C211yesmaximal, characteristic
6#80961C2116yesmaximal, direct product factor
7C2×#4875C212yesmaximal, complemented
8C2×#4876C212yesmaximal, complemented
9C2×#4851C211yesmaximal, characteristic, complemented
10C2×#4831C211yesmaximal, characteristic, complemented
11C2×#4763C212yesmaximal
12C2×#4757C212yesmaximal
13C2×#3386—31nomaximal, Sylow
14C23×Dic6—21no—
15C2×C3×C4⋊Q8C2211yescharacteristic
16C2×C3×C4×D4C2211yescharacteristic
17C2×Q8×Dic3—21no—
18C2×#944—21no—
19C2×D4×Dic3C2212yes—
20C22×#214C2211yescharacteristic
21C2×#924—21no—
22#5721—24no—
23#5721C2218yescomplemented
24D4×Dic6—24no—
25D4×Dic6C2218yes—
26C2×#890C2212yes—
27C2×#889—22no—
28C2×#888C2212yes—
29C2×#887C2212yes—
30C2×#878—22no—
31C2×#869C2211yescharacteristic
32C2×C4×Dic6C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34C3×#474C2218yes—
35C2×C3×#107C2212yes—
36C2×C3×C4⋊C8C2211yescharacteristic
37C2×C3×#102C2212yes—
38C2×#832C2211yescharacteristic
39C2×#817C2212yes—
40C2×#816C2212yes—
41C2×#815C2212yes—
42C2×Dic3⋊C8C2212yes—
43#5078C2218yescomplemented
44C4×#214C2218yes—
45C2×#810C2211yescharacteristic
46C2×#808C2211yescharacteristic
47C2×#807C2212yes—
48C2×#807C2212yes—
49C2×C4×C3⋊C8C2211yescharacteristic
50#4876C22116yescomplemented
51#4875C22116yescomplemented
52#4851C2218yescomplemented
53#4831C2218yescomplemented
54#4763C22116yes—
55#4757C22116yes—
56C2×#557—31no—
57C2×D4×Q8—31no—
58#3386—316no—
59C2×#501—32no—
60C2×#500—31no—
61C2×#477—32no—
62C2×#475—31no—
63C2×#478—32no—
64C2×#474D311yescharacteristic
65C2×#446—31no—
66C2×#440—32no—
67C2×C4×SD16—31no—
68C22×C3×Q8—21no—
69C22×C3×D4C2311yescharacteristic
70C23×C3×C4—21no—
71C23×Dic3—22no—
72C22×Dic6—21no—
73C22×Dic6—22no—
74C22×Dic6—28no—
75C22×Dic6—48no—
76C22×Dic6D411yescharacteristic
77C22×Dic6C2311yescharacteristic
78C22×C3×C8C2312yes—
79C3×C4⋊Q8—22no—
80C3×C4⋊Q8C2314yes—
81C3×C4×D4—22no—
82C3×C4×D4C2314yes—
83C2×C3×C4⋊C4—21no—
84C2×C3×C4⋊C4C2312yes—
85C2×C3×C4⋊C4C2311yescharacteristic
86C2×C3×C22⋊C4—21no—
87C2×C3×C42C2311yescharacteristic
88C2×#217—22no—
89Q8×Dic3—28no—
90#944—28no—
91D4×Dic3—24no—
92D4×Dic3C2318yes—
93C2×#214Q818yescomplemented
94C2×#214C2314yes—
95C2×C4⋊Dic3—21no—
96C2×C4⋊Dic3—22no—
97C2×C4⋊Dic3D411yescharacteristic
98C2×C4⋊Dic3C2311yescharacteristic
99C2×C4⋊Dic3C2312yes—
100#924—28no—
101C2×Dic3⋊C4—21no—
102C2×Dic3⋊C4—22no—
103C2×Dic3⋊C4—22no—
104C2×Dic3⋊C4—22no—
105C2×Dic3⋊C4D412yes—
106C2×C4×Dic3—21no—
107C2×C4×Dic3—22no—
108C2×C4×Dic3C2312yes—
109C22×C3⋊C8C2311yescharacteristic
110C22×C3⋊C8C2311yescharacteristic
111#890—24no—
112#890C2318yes—
113#889—216no—
114#888—24no—
115#888C2318yes—
116#887—24no—
117#887C2318yes—
118#878—216no—
119#869—22no—
120#869C2314yes—
121C4×Dic6—22no—
122C4×Dic6D414yes—
123C4×Dic6C2314yes—
124C4×Dic6C2314yes—
125C3×#107C2318yes—
126C3×C4⋊C8C2314yes—
127C3×#102C2318yes—
128#832C2314yes—
129#817C2318yes—
130#816C2318yes—
131#815C2318yes—
132Dic3⋊C8C2318yes—
133#810C2314yes—
134#808C2314yes—
135#807C2318yes—
136#807C2318yes—
137C4×C3⋊C8C2314yes—
138C23×Q8—61no—
139C22×SD16—31no—
140#557—38no—
141#557—64no—
142D4×Q8—38no—
143D4×Q8—64no—
144C2×C4⋊Q8—32no—
145C2×C4⋊Q8—31no—
146C2×C4⋊Q8—61no—
147C2×C4⋊Q8C2×D311yescharacteristic
148C2×#125—32no—
149C2×#125—62no—
150C2×C22⋊Q8—62no—
151C2×C22⋊Q8—61no—
152C2×C4×Q8—31no—
153C2×C4×Q8—32no—
154C2×C4×Q8—31no—
155C2×C4×Q8—61no—
156C2×C4×D4—32no—
157C2×C4×D4C2×D311yescharacteristic
158#501—316no—
159#500—38no—
160#478—316no—
161#477—316no—
162#475—38no—
163#474C2×D318yes—
164#446—38no—
165#440—316no—
166C4×SD16—38no—
167C2×#107—32no—
168C2×#107—32no—
169C2×#107C2×D312yes—
170C2×#106—32no—
171C2×#106—31no—
172C2×C4⋊C8—32no—
173C2×C4⋊C8C2×D311yescharacteristic
174C2×#103—32no—
175C2×#103—31no—
176C2×#102—31no—
177C2×#102C2×D312yes—
178C2×#97—32no—
179C2×C4×C8—31no—
180C24×C3—21no—
181C2×C3×Q8—24no—
182C2×C3×Q8—44no—
183C2×C3×D4—21no—
184C2×C3×D4—22no—
185C2×C3×D4C2×Q814yes—
186C2×C3×D4C2412yes—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—24no—
190C22×C3×C4—44no—
191C22×C3×C4C2×D411yescharacteristic
192C22×C3×C4C2×D411yescharacteristic
193C22×C3×C4C2411yescharacteristic
194C22×Dic3—21no—
195C22×Dic3—21no—
196C22×Dic3—22no—
197C22×Dic3—28no—
198C22×Dic3—48no—
199C22×Dic3C2×D412yes—
200C22×Dic3C2×D412yes—
201C2×Dic6—24no—
202C2×Dic6—21no—
203C2×Dic6—22no—
204C2×Dic6—24no—
205C2×Dic6—28no—
206C2×Dic6—432no—
207C2×Dic6—48no—
208C2×Dic6—44no—
209C2×Dic6C2×D414yes—
210C2×Dic6C2×Q814yescomplemented
211C2×Dic6C2412yes—
212C2×C3×C8—24no—
213C2×C3×C8C2414yes—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—24no—
217C3×C4⋊C4C2414yes—
218C3×C4⋊C4C2412yes—
219C3×C22⋊C4—24no—
220C3×C42C2×D412yes—
221C3×C42C2412yes—
222#217—28no—
223#214C2×Q8116yescomplemented
224C4⋊Dic3—21no—
225C4⋊Dic3—22no—
226C4⋊Dic3—24no—
227C4⋊Dic3—28no—
228C4⋊Dic3C2×D414yes—
229C4⋊Dic3C2414yes—
230C4⋊Dic3C2412yes—
231Dic3⋊C4—24no—
232Dic3⋊C4—28no—
233Dic3⋊C4—28no—
234Dic3⋊C4—28no—
235Dic3⋊C4C2×D418yes—
236C4×Dic3—24no—
237C4×Dic3—28no—
238C4×Dic3C2×D414yes—
239C4×Dic3C2414yes—
240C2×C3⋊C8—22no—
241C2×C3⋊C8C2×Q814yescomplemented
242C2×C3⋊C8C2412yes—
243C2×C3⋊C8C2412yes—
244C22×Q8—21no—
245C22×Q8—31no—
246C22×Q8—31no—
247C22×Q8—62no—
248C22×Q8—68no—
249C22×Q8—61no—
250C22×Q8—128no—
251C22×D4C22×D311yescharacteristic
252C23×C4—21no—
253C23×C4—62no—
254C2×SD16—38no—
255C2×SD16—34no—
256C22×C8—31no—
257C22×C8—31no—
258C22×C8C22×D312yes—
259C4⋊Q8—22no—
260C4⋊Q8—38no—
261C4⋊Q8—34no—
262C4⋊Q8—64no—
263C4⋊Q8—68no—
264C4⋊Q8—62no—
265C4⋊Q8C22×D314yes—
266#125—38no—
267#125—64no—
268#125—616no—
269C22⋊Q8—616no—
270C22⋊Q8—68no—
271C4×Q8—34no—
272C4×Q8—34no—
273C4×Q8—38no—
274C4×Q8—34no—
275C4×Q8—64no—
276C4×Q8—68no—
277C4×Q8—62no—
278C4×D4—22no—
279C4×D4—38no—
280C4×D4—64no—
281C4×D4C22×D314yes—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—31no—
284C2×C4⋊C4—32no—
285C2×C4⋊C4—32no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—62no—
288C2×C4⋊C4—62no—
289C2×C4⋊C4—62no—
290C2×C4⋊C4—62no—
291C2×C4⋊C4—61no—
292C2×C4⋊C4—61no—
293C2×C4⋊C4C22×D311yescharacteristic
294C2×C4⋊C4C22×D312yes—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—62no—
297C2×C42—32no—
298C2×C42—62no—
299C2×C42—61no—
300C2×C42C22×D311yescharacteristic
301#107—38no—
302#107—38no—
303#107C22×D318yes—
304#106—38no—
305#106—34no—
306C4⋊C8—38no—
307C4⋊C8C22×D314yes—
308#103—38no—
309#103—34no—
310#102—34no—
311#102C22×D318yes—
312#97—38no—
313C4×C8—34no—
314C23×C3—24no—
315C23×C3—22no—
316C23×C3—42no—
317C23×C3—42no—
318C23×C3C22×D411yescharacteristic
319C3×Q8—48no—
320C3×D4—24no—
321C3×D4—22no—
322C3×D4C22×Q814yes—
323C2×C3×C4—22no—
324C2×C3×C4—24no—
325C2×C3×C4—22no—
326C2×C3×C4—42no—
327C2×C3×C4—44no—
328C2×C3×C4—48no—
329C2×C3×C4AGL(1,ℤ/8)14yes—
330C2×C3×C4C22×D412yes—
331C2×C3×C4C22×D411yescharacteristic
332C2×C3×C4C22×D412yes—
333C2×C3×C4C22×Q812yes—
334C2×C3×C42−1+412yes—
335C2×C3×C4C2511yescharacteristic
336C2×Dic3—24no—
337C2×Dic3—24no—
338C2×Dic3—24no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—24no—
342C2×Dic3—416no—
343C2×Dic3—44no—
344C2×Dic3—42no—
345C2×Dic3C22×D414yes—
346C2×Dic3C22×D414yes—
347Dic6—24no—
348Dic6—28no—
349Dic6—22no—
350Dic6—416no—
351Dic6—48no—
352Dic6C22×Q814yescomplemented
353C3×C8—24no—
354C3⋊C8—22no—
355C3⋊C8C22×Q814yescomplemented
356C24—21no—
357C2×Q8—24no—
358C2×Q8—34no—
359C2×Q8—34no—
360C2×Q8—32no—
361C2×Q8—44no—
362C2×Q8—68no—
363C2×Q8—64no—
364C2×Q8—61no—
365C2×Q8—64no—
366C2×Q8—62no—
367C2×Q8—128no—
368C2×Q8—1232no—
369C2×Q8—124no—
370C2×D4—21no—
371C2×D4—22no—
372C2×D4D3×Q814yes—
373C2×D4C23×D312yes—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—24no—
377C22×C4—32no—
378C22×C4—32no—
379C22×C4—44no—
380C22×C4—68no—
381C22×C4—61no—
382C22×C4—61no—
383C22×C4—62no—
384C22×C4—128no—
385C22×C4D3×D411yescharacteristic
386C22×C4D3×D411yescharacteristic
387C22×C4C23×D311yescharacteristic
388SD16—316no—
389C2×C8—24no—
390C2×C8—34no—
391C2×C8—32no—
392C2×C8—32no—
393C2×C8—62no—
394C2×C8C23×D314yes—
395C4⋊C4—24no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—34no—
399C4⋊C4—38no—
400C4⋊C4—32no—
401C4⋊C4—34no—
402C4⋊C4—68no—
403C4⋊C4—68no—
404C4⋊C4—68no—
405C4⋊C4—68no—
406C4⋊C4—62no—
407C4⋊C4—61no—
408C4⋊C4—64no—
409C4⋊C4—64no—
410C4⋊C4C23×D314yes—
411C4⋊C4C23×D312yes—
412C22⋊C4—24no—
413C22⋊C4—68no—
414C42—34no—
415C42—34no—
416C42—68no—
417C42—64no—
418C42D3×D412yes—
419C42C23×D312yes—
420C22×C3—24no—
421C22×C3—48no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3D4×Q812yes—
425C22×C3C2×AGL(1,ℤ/8)12yes—
426C22×C3#57812yes—
427C22×C3C23×D411yescharacteristic
428C3×C4—22no—
429C3×C4—42no—
430C3×C4—44no—
431C3×C4D4×Q812yes—
432C3×C4C2×AGL(1,ℤ/8)14yes—
433C3×C4C23×Q811yescharacteristic
434C3×C4C2×2−1+411yescharacteristic
435Dic3—24no—
436Dic3—24no—
437Dic3—24no—
438Dic3—44no—
439Dic3—42no—
440C23—24no—
441C23—22no—
442C23—42no—
443C23—42no—
444C23C2×D3×D411yescharacteristic
445Q8—34no—
446Q8—48no—
447Q8—64no—
448Q8—62no—
449Q8—68no—
450Q8—1216no—
451Q8—128no—
452D4—24no—
453D4—22no—
454D4C2×D3×Q814yes—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—34no—
459C2×C4—34no—
460C2×C4—42no—
461C2×C4—44no—
462C2×C4—48no—
463C2×C4—64no—
464C2×C4—62no—
465C2×C4—64no—
466C2×C4—64no—
467C2×C4—62no—
468C2×C4—64no—
469C2×C4—1216no—
470C2×C4—124no—
471C2×C4—122no—
472C2×C4#91114yes—
473C2×C4C2×D3×D412yes—
474C2×C4C2×D3×D411yescharacteristic
475C2×C4C2×D3×D412yes—
476C2×C4C2×D3×Q812yes—
477C2×C4#101012yes—
478C2×C4C24×D311yescharacteristic
479C8—24no—
480C8—34no—
481C8—62no—
482C2×C3—44no—
483C2×C3#338614yescomplemented
484C2×C3C2×D4×Q811yescharacteristic
485C2×C3C22×AGL(1,ℤ/8)11yescharacteristic
486C2×C3C2×#57811yescharacteristic
487C22—24no—
488C22—48no—
489C22—42no—
490C22—42no—
491C22#563212yes—
492C22C2×#91112yes—
493C22#577912yes—
494C22C22×D3×D411yescharacteristic
495C4—22no—
496C4—42no—
497C4—44no—
498C4—64no—
499C4—64no—
500C4—64no—
501C4—124no—
502C4—122no—
503C4#563212yes—
504C4C2×#91114yes—
505C4C22×D3×Q811yescharacteristic
506C4C2×#101011yescharacteristic
507C3C2×#338611yescharacteristic, complemented, Sylow
508C2—44no—
509C2#8096114yesdirect product factor
510C2C2×#563211yescharacteristic
511C2C22×#91111yescharacteristic
512C2C2×#577911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#474C2
socleC23×C3C22×D4
prime radicalC22×C3×D4C23
hypercenterC2×#474D3
hypocenterC3C2×#3386
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#5721C2semidirect
4. C2×#5078C2semidirect
6. #80961C2direct (N × H)
7. C2×#4875C2semidirect
8. C2×#4876C2semidirect
9. C2×#4851C2semidirect
10. C2×#4831C2semidirect
23. #5721C22semidirect
43. #5078C22semidirect
50. #4876C22semidirect
51. #4875C22semidirect
52. #4851C22semidirect
53. #4831C22semidirect
93. C2×#214Q8semidirect
210. C2×Dic6C2×Q8semidirect
223. #214C2×Q8semidirect
241. C2×C3⋊C8C2×Q8semidirect
352. Dic6C22×Q8semidirect
355. C3⋊C8C22×Q8semidirect
483. C2×C3#3386semidirect
507. C3C2×#3386semidirect
509. C2#80961direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#57212
C2×D4×Dic62
C2×C3×#4742
C2×#50782
C2×C4×#2142
#809612
C2×#48752
C2×#48762
C2×#48512
C2×#48312
C2×#47632
C2×#47572
C2×#33863