Finite Group Databasebeta

← C2×#79931 #11675628

Subgroups — C2×#79931 #11675628

Order 768.

1842 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5579C211yesmaximal, characteristic
2C2×#5567C211yesmaximal, characteristic, complemented
3C2×C3×C8×Q8C211yesmaximal, characteristic, complemented
4#79931C2116yesmaximal, direct product factor
5C2×#4829C212yesmaximal, complemented
6C2×#4850C211yesmaximal, characteristic, complemented
7C2×#4847C212yesmaximal
8C2×#4846C211yesmaximal, characteristic
9C2×C4×#204C211yesmaximal, characteristic
10C2×C4×#204C212yesmaximal
11C2×#4683C212yesmaximal, complemented
12C2×#4680C211yesmaximal, characteristic, complemented
13C2×#3381—31nomaximal, Sylow
14C2×C3×C4×Q8C2211yescharacteristic
15C2×#946—21no—
16C2×#944—21no—
17C22×#204C2211yescharacteristic
18#5579—24no—
19#5579C2218yes—
20#5567—24no—
21#5567C2218yescomplemented
22C2×#896—22no—
23C2×D3×C4⋊C4—21no—
24C2×#889—22no—
25C2×#887—21no—
26C2×C4×D12C2211yescharacteristic
27C2×C4×D12C2212yes—
28C2×#870C2212yes—
29C2×#870C2212yes—
30C2×#869C2211yescharacteristic
31C2×#869C2211yescharacteristic
32C2×C4×Dic6C2211yescharacteristic
33C2×C4×Dic6C2212yes—
34C3×C8×Q8C2218yescomplemented
35C2×C3×C4⋊C8C2211yescharacteristic
36C2×C3×C4⋊C8C2212yes—
37C2×C3×C4×C8C2211yescharacteristic
38C2×C3×C4×C8C2212yes—
39C2×#821C2212yes—
40C2×#821C2211yescharacteristic
41C2×#818C2212yes—
42C2×#818C2212yes—
43C2×#817C2212yes—
44C2×#817C2212yes—
45C2×#817C2211yescharacteristic
46C2×#816C2212yes—
47C2×#816C2211yescharacteristic
48#4850C2218yescomplemented
49#4847C22116yes—
50#4846C2218yes—
51#4829C22116yescomplemented
52C4×#204C2218yes—
53C4×#204C22116yes—
54#4683C22116yescomplemented
55#4680C2218yescomplemented
56C2×#557—31no—
57C2×#554—31no—
58#3381—316no—
59C2×#499—32no—
60C2×#498—31no—
61C2×#479—32no—
62C2×#477—31no—
63C2×#478—32no—
64C2×#474—31no—
65C2×C8×Q8D311yescharacteristic, complemented
66C2×C4×SD16—32no—
67C2×C4×SD16—31no—
68C22×C3×Q8D411yescharacteristic
69C22×D12C2311yescharacteristic
70C22×C4×D3—21no—
71C22×C4×D3—22no—
72C22×Dic6—21no—
73C22×Dic6—21no—
74C22×Dic6C2311yescharacteristic
75C22×C3×C8C2311yescharacteristic
76C22×C3×C8C2312yes—
77C22×C3×C8C2311yescharacteristic
78C3×C4×Q8D414yes—
79C3×C4×Q8C2314yes—
80C2×C3×C4⋊C4D411yescharacteristic
81C2×C3×C4⋊C4D412yes—
82C2×C3×C42C2311yescharacteristic
83C2×C3×C42C2312yes—
84#946—28no—
85#944—28no—
86C2×(C2×D3)⋊C4—21no—
87C2×(C2×D3)⋊C4—22no—
88C2×C4⋊Dic3—21no—
89C2×C4⋊Dic3—21no—
90C2×C4⋊Dic3C2312yes—
91C2×C4⋊Dic3C2311yescharacteristic
92C2×C4⋊Dic3C2312yes—
93C2×C4⋊Dic3C2311yescharacteristic
94C2×Dic3⋊C4—21no—
95C2×Dic3⋊C4—22no—
96C2×Dic3⋊C4—22no—
97C2×Dic3⋊C4—22no—
98C2×Dic3⋊C4—22no—
99C2×Dic3⋊C4—22no—
100C2×C4×Dic3—22no—
101C2×C4×Dic3—21no—
102C2×#204Q818yescomplemented
103C2×#204C2314yes—
104#896—216no—
105D3×C4⋊C4—28no—
106#889—216no—
107#887—28no—
108C4×D12—24no—
109C4×D12—22no—
110C4×D12C2314yes—
111C4×D12C2318yes—
112#870—24no—
113#870—24no—
114#870C2318yes—
115#870C2318yes—
116#869—22no—
117#869—22no—
118#869C2314yes—
119#869C2314yes—
120C4×Dic6—24no—
121C4×Dic6—22no—
122C4×Dic6C2318yes—
123C4×Dic6C2314yes—
124C3×C4⋊C8C2318yes—
125C3×C4⋊C8C2314yes—
126C3×C4×C8C2314yes—
127C3×C4×C8C2318yes—
128#821C2318yes—
129#821C2314yes—
130#818C2318yes—
131#818C2318yes—
132#817C2318yes—
133#817C2318yes—
134#817C2314yes—
135#816C2314yes—
136#816C2318yes—
137C22×SD16—31no—
138#557—38no—
139#557—64no—
140#554—38no—
141#554—64no—
142C2×C4⋊Q8—31no—
143C2×C4⋊Q8—31no—
144C2×C4⋊Q8—61no—
145C2×#125—32no—
146C2×#125—32no—
147C2×#125—62no—
148C2×C22⋊Q8—61no—
149C2×C22⋊Q8—62no—
150C2×C4×Q8—31no—
151C2×C4×Q8—32no—
152C2×C4×Q8—61no—
153C2×C4×Q8C2×D311yescharacteristic
154C2×C4×D4—32no—
155C2×C4×D4—31no—
156C22×C4⋊C4—61no—
157#499—316no—
158#498—38no—
159#479—316no—
160#478—316no—
161#477—38no—
162#474—38no—
163C8×Q8C2×D318yescomplemented
164C4×SD16—38no—
165C4×SD16—316no—
166C2×#107—32no—
167C2×#107—32no—
168C2×#106—32no—
169C2×#106—32no—
170C2×#106—31no—
171C2×C4⋊C8C2×D312yes—
172C2×C4⋊C8C2×D311yescharacteristic
173C2×#103—32no—
174C2×#103—31no—
175C2×#102—31no—
176C2×#102—32no—
177C2×C4×C8C2×D311yescharacteristic
178C2×C4×C8C2×D312yes—
179C23×D3—21no—
180C2×C3×Q8—24no—
181C2×C3×Q8C2×D414yes—
182C22×C3×C4C2×D412yes—
183C22×C3×C4C2×D412yes—
184C22×C3×C4C2×D411yescharacteristic
185C22×C3×C4C2×D411yescharacteristic
186C22×C3×C4C2411yescharacteristic
187C22×Dic3—21no—
188C22×Dic3—21no—
189C22×Dic3—22no—
190C22×Dic3—21no—
191C22×Dic3—22no—
192C2×D12—21no—
193C2×D12—22no—
194C2×D12C2×Q814yes—
195C2×D12C2412yes—
196C2×C4×D3—24no—
197C2×C4×D3—28no—
198C2×C4×D3—44no—
199C2×C4×D3—84no—
200C2×Dic6—21no—
201C2×Dic6—22no—
202C2×Dic6—24no—
203C2×Dic6—24no—
204C2×Dic6—44no—
205C2×Dic6—82no—
206C2×Dic6C2×Q814yes—
207C2×Dic6C2412yes—
208C2×C3×C8—22no—
209C2×C3×C8—24no—
210C2×C3×C8C2×Q814yes—
211C2×C3×C8C2412yes—
212C2×C3×C8C2414yes—
213C2×C3×C8C2412yes—
214C3×C4⋊C4C2×D414yes—
215C3×C4⋊C4C2×D418yes—
216C3×C42C2×D412yes—
217C3×C42C2×D414yes—
218C3×C42C2412yes—
219C3×C42C2414yes—
220(C2×D3)⋊C4—24no—
221(C2×D3)⋊C4—28no—
222C4⋊Dic3—22no—
223C4⋊Dic3—21no—
224C4⋊Dic3—22no—
225C4⋊Dic3—24no—
226C4⋊Dic3—24no—
227C4⋊Dic3—21no—
228C4⋊Dic3C2414yes—
229C4⋊Dic3C2412yes—
230C4⋊Dic3C2414yes—
231C4⋊Dic3C2412yes—
232Dic3⋊C4—24no—
233Dic3⋊C4—28no—
234Dic3⋊C4—28no—
235Dic3⋊C4—28no—
236Dic3⋊C4—28no—
237Dic3⋊C4—28no—
238C4×Dic3—28no—
239C4×Dic3—24no—
240#204C2×Q8116yescomplemented
241C22×Q8—31no—
242C22×Q8—61no—
243C22×Q8—61no—
244C22×Q8D1211yescharacteristic
245C22×D4—31no—
246C23×C4—61no—
247C23×C4—62no—
248C2×SD16—38no—
249C2×SD16—34no—
250C22×C8C22×D311yescharacteristic
251C22×C8C22×D312yes—
252C22×C8C22×D311yescharacteristic
253C4⋊Q8—34no—
254C4⋊Q8—34no—
255C4⋊Q8—68no—
256C4⋊Q8—62no—
257C4⋊Q8—62no—
258#125—38no—
259#125—38no—
260#125—616no—
261#125—64no—
262#125—64no—
263C22⋊Q8—68no—
264C22⋊Q8—616no—
265C4×Q8—34no—
266C4×Q8—38no—
267C4×Q8—68no—
268C4×Q8—64no—
269C4×Q8—62no—
270C4×Q8D1214yes—
271C4×Q8C22×D314yes—
272C4×D4—34no—
273C4×D4—38no—
274C4×D4—64no—
275C4×D4—62no—
276C2×C4⋊C4—31no—
277C2×C4⋊C4—32no—
278C2×C4⋊C4—31no—
279C2×C4⋊C4—32no—
280C2×C4⋊C4—62no—
281C2×C4⋊C4—61no—
282C2×C4⋊C4—61no—
283C2×C4⋊C4—62no—
284C2×C4⋊C4—62no—
285C2×C4⋊C4—62no—
286C2×C4⋊C4—62no—
287C2×C4⋊C4—61no—
288C2×C4⋊C4—68no—
289C2×C4⋊C4D1211yescharacteristic
290C2×C4⋊C4D1212yes—
291C2×C22⋊C4—61no—
292C2×C22⋊C4—62no—
293C2×C42—62no—
294C2×C42—61no—
295C2×C42C22×D312yes—
296C2×C42C22×D311yescharacteristic
297#107—38no—
298#107—38no—
299#106—38no—
300#106—34no—
301#106—38no—
302C4⋊C8C22×D314yes—
303C4⋊C8C22×D318yes—
304#103—38no—
305#103—34no—
306#102—38no—
307#102—34no—
308C4×C8C22×D314yes—
309C4×C8C22×D318yes—
310C23×C3C22×D411yescharacteristic
311C22×D3—24no—
312C22×D3—22no—
313C22×D3—42no—
314C22×D3—42no—
315C3×Q8—28no—
316C2×C3×C4—24no—
317C2×C3×C4—22no—
318C2×C3×C4—24no—
319C2×C3×C4#13514yes—
320C2×C3×C4C22×D414yes—
321C2×C3×C4C22×D414yes—
322C2×C3×C4C22×D412yes—
323C2×C3×C4C22×D411yescharacteristic
324C2×C3×C4C22×D412yes—
325C2×C3×C4C22×Q812yes—
326C2×C3×C42−1+412yes—
327C2×C3×C4C2511yescharacteristic
328C2×Dic3—24no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—24no—
332C2×Dic3—22no—
333C2×Dic3—24no—
334C2×Dic3—44no—
335C2×Dic3—42no—
336C2×Dic3—44no—
337C2×Dic3—42no—
338D12—24no—
339D12—22no—
340D12C22×Q814yes—
341C4×D3—48no—
342C4×D3—88no—
343Dic6—24no—
344Dic6—22no—
345Dic6—48no—
346Dic6—84no—
347Dic6C22×Q814yes—
348C3×C8—22no—
349C3×C8—24no—
350C3×C8C22×Q814yes—
351C24—61no—
352C2×Q8—24no—
353C2×Q8—34no—
354C2×Q8—32no—
355C2×Q8—61no—
356C2×Q8—64no—
357C2×Q8—64no—
358C2×Q8—62no—
359C2×Q8—124no—
360C2×Q8—242no—
361C2×Q8C2×D1214yes—
362C2×D4—34no—
363C2×D4—32no—
364C2×D4—61no—
365C2×D4—62no—
366C22×C4—61no—
367C22×C4—61no—
368C22×C4—62no—
369C22×C4—61no—
370C22×C4—62no—
371C22×C4—64no—
372C22×C4—68no—
373C22×C4—124no—
374C22×C4—244no—
375C22×C4C2×D1212yes—
376C22×C4C2×D1212yes—
377C22×C4C2×D1211yescharacteristic
378C22×C4C2×D1211yescharacteristic
379C22×C4C23×D311yescharacteristic
380SD16—316no—
381C2×C8—22no—
382C2×C8—24no—
383C2×C8D3×Q814yes—
384C2×C8C23×D312yes—
385C2×C8C23×D314yes—
386C2×C8C23×D312yes—
387C4⋊C4—34no—
388C4⋊C4—32no—
389C4⋊C4—34no—
390C4⋊C4—32no—
391C4⋊C4—61no—
392C4⋊C4—62no—
393C4⋊C4—61no—
394C4⋊C4—62no—
395C4⋊C4—68no—
396C4⋊C4—64no—
397C4⋊C4—64no—
398C4⋊C4—68no—
399C4⋊C4—68no—
400C4⋊C4—68no—
401C4⋊C4—68no—
402C4⋊C4—64no—
403C4⋊C4C2×D1214yes—
404C4⋊C4C2×D1218yes—
405C22⋊C4—64no—
406C22⋊C4—68no—
407C42—68no—
408C42—64no—
409C42C2×D1214yes—
410C42C2×D1212yes—
411C42C23×D314yes—
412C42C23×D312yes—
413C22×C3D4×Q812yes—
414C22×C3C2×#13512yes—
415C22×C3#57712yes—
416C22×C3C23×D411yescharacteristic
417C2×D3—24no—
418C2×D3—48no—
419C2×D3—42no—
420C2×D3—42no—
421C3×C4—24no—
422C3×C4—22no—
423C3×C4—24no—
424C3×C4D4×Q812yes—
425C3×C4C2×#13514yes—
426C3×C4C23×Q811yescharacteristic
427C3×C4C2×2−1+411yescharacteristic
428Dic3—24no—
429Dic3—44no—
430Dic3—42no—
431Dic3—44no—
432Dic3—42no—
433C23—62no—
434C23—64no—
435C23—122no—
436C23—122no—
437C23C22×D1211yescharacteristic
438Q8—28no—
439Q8—34no—
440Q8—62no—
441Q8—64no—
442Q8—128no—
443Q8—244no—
444D4—34no—
445D4—62no—
446D4—64no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—62no—
451C2×C4—64no—
452C2×C4—62no—
453C2×C4—64no—
454C2×C4—62no—
455C2×C4—64no—
456C2×C4—122no—
457C2×C4—124no—
458C2×C4—124no—
459C2×C4—122no—
460C2×C4—128no—
461C2×C4—248no—
462C2×C4#90414yes—
463C2×C4C22×D1214yes—
464C2×C4C22×D1214yes—
465C2×C4C22×D1212yes—
466C2×C4C22×D1212yes—
467C2×C4C22×D1211yescharacteristic
468C2×C4C2×D3×Q812yes—
469C2×C4#101012yes—
470C2×C4C24×D311yescharacteristic
471C8—22no—
472C8—24no—
473C8C2×D3×Q814yes—
474C2×C3#338114yescomplemented
475C2×C3C2×D4×Q811yescharacteristic
476C2×C3C22×#13511yescharacteristic
477C2×C3C2×#57711yescharacteristic
478D3—44no—
479C22—64no—
480C22—128no—
481C22—122no—
482C22—122no—
483C22Q8×D1212yes—
484C22C2×#90412yes—
485C22#575112yes—
486C22C23×D1211yescharacteristic
487C4—24no—
488C4—24no—
489C4—22no—
490C4—64no—
491C4—122no—
492C4—124no—
493C4—124no—
494C4—122no—
495C4Q8×D1212yes—
496C4C2×#90414yes—
497C4C22×D3×Q811yescharacteristic
498C4C2×#101011yescharacteristic
499C3C2×#338111yescharacteristic, complemented, Sylow
500C2—124no—
501C2#7993114yesdirect product factor
502C2C2×Q8×D1211yescharacteristic
503C2C22×#90411yescharacteristic
504C2C2×#575111yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×C8×Q8C2
socleC23×C3C22×D4
prime radicalC22×D12C23
hypercenterC2×C8×Q8D3
hypocenterC3C2×#3381
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#5567C2semidirect
3. C2×C3×C8×Q8C2semidirect
4. #79931C2direct (N × H)
5. C2×#4829C2semidirect
6. C2×#4850C2semidirect
11. C2×#4683C2semidirect
12. C2×#4680C2semidirect
21. #5567C22semidirect
34. C3×C8×Q8C22semidirect
48. #4850C22semidirect
51. #4829C22semidirect
54. #4683C22semidirect
55. #4680C22semidirect
65. C2×C8×Q8D3semidirect
102. C2×#204Q8semidirect
163. C8×Q8C2×D3semidirect
240. #204C2×Q8semidirect
474. C2×C3#3381semidirect
499. C3C2×#3381semidirect
501. C2#79931direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#55792
C2×#55672
C2×C3×C8×Q82
#799312
C2×#48292
C2×#48502
C2×#48472
C2×#48462
C2×C4×#2042
C2×#46832
C2×#46802
C2×#33813