Finite Group Databasebeta

← #11904515

Subgroups — #11904515

Order 1152.

3117 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
3#10596283C211yesmaximal, characteristic, complemented
4#10595409C218yesmaximal, complemented
5Q8×#625C218yesmaximal, complemented
6#10595022C216yesmaximal, complemented
7#10594855C216yesmaximal, complemented
8#87294—31nomaximal
9#87251—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C3×#1007—28no—
12C2×C3×#239C2214yescomplemented
13C2×C3×D3×Q8—28no—
14C2×C3×D3×Q8C2218yes—
15C2×C3×D3×Q8C2214yescomplemented
16C2×C3×#235C2216yes—
17C22×C3×C4×D3C2213yes—
18C22×C3×Dic6C2213yes—
19Q8×C3⋊Dic3C2218yescomplemented
20#64135C2216yes—
21#63976C2214yes—
22#63961C22112yes—
23#63908C22112yes—
24C4×#625C22124yes—
25#63873C22112yescomplemented
26#63863C22112yescomplemented
27#63856C22112yes—
28#63856C22124yescomplemented
29C2×C3×2−1+4—31no—
30C23×C3×Q8—31no—
31C2×#1007D311yescharacteristic, complemented
32C22×D3×Q8D311yescharacteristic, complemented
33#5831—38no—
34#5828—36no—
35#5825—36no—
36#5817—38no—
37#5816—36no—
38Q8×#67—38no—
39Q8×#67—38no—
40#5812—31no—
41#5812—31no—
42#5812—61no—
43#5791—36no—
44C23×C3×D3C2311yescharacteristic
45C2×C32×Q8D418yescomplemented
46C2×C32×Q8C2314yes—
47C22×C32×C4C2313yes—
48C2×C3×#67C2314yes—
49C22×C3×Dic3C2313yes—
50C3×#239—216no—
51C3×D3×Q8—232no—
52C3×D3×Q8—216no—
53C3×#235—224no—
54C2×C3×D12C2316yes—
55C2×C3×C4×D3—212no—
56C2×C3×C4×D3C23112yes—
57C2×C3×C4×D3C23112yes—
58C2×C3×Dic6—212no—
59C2×C3×Dic6C23112yes—
60C2×C3×Dic6C2316yes—
61C2×#625C2318yes—
62#3757C2314yes—
63C4⋊(C3⋊Dic3)C23112yes—
64C4×C3⋊Dic3C23112yes—
65#3724C23124yes—
66(C2×D3)⋊Dic3C2318yes—
67(C2×D3)⋊Dic3C23124yes—
68#3486—91noSylow
69C3×2−1+4—68no—
70C2×C3×#41—34no—
71C2×C3×#41—36no—
72C22×C3×Q8—21no—
73C22×C3×Q8—38no—
74C22×C3×Q8—34no—
75C22×C3×Q8—33no—
76C22×C3×Q8—68no—
77C22×C3×Q8C2×D311yescharacteristic
78C22×C3×Q8C2×D311yescharacteristic
79C23×C3×C4—33no—
80#1007—28no—
81C2×#239C2×D314yescomplemented
82C2×D3×Q8—28no—
83C2×D3×Q8C2×D318yes—
84C2×D3×Q8C2×D314yescomplemented
85C2×#235C2×D316yes—
86C22×C4×D3C2×D313yes—
87C22×Dic6C2×D313yes—
88#953—34no—
89#947—312no—
90#946—312no—
91#946—324no—
92Q8×Dic3—38no—
93Q8×Dic3—38no—
94Q8×Dic3—68no—
95#944—312no—
96#944—312no—
97#938—312no—
98#937—34no—
99#936—312no—
100#935—312no—
101#930—312no—
102#929—312no—
103C4×#67—324no—
104C4×#67—324no—
105#926—36no—
106#926—36no—
107#926—66no—
108#924—312no—
109#924—324no—
110C23×C32C2411yescharacteristic
111C22×C3×D3—22no—
112C22×C3×D3—24no—
113C22×C3×D3C2414yes—
114C22×C3×D3C2412yes—
115C32×Q8C2×D4116yes—
116C2×C32×C4C2×D4112yes—
117C2×C32×C4C2416yes—
118C2×C3⋊Dic3C2418yes—
119C3×#67—28no—
120C2×C3×Dic3—26no—
121C2×C3×Dic3C2416yes—
122C2×C3×Dic3C2414yes—
123C3×D12—212no—
124C3×C4×D3—224no—
125C3×C4×D3—224no—
126C3×Dic6—224no—
127C3×Dic6—212no—
128#625—216no—
129C2×2−1+4—31no—
130C23×Q8—31no—
131D4×Q8—98no—
132#548—98no—
133#536—96no—
134#525—96no—
135#519—91no—
136C24×C3—31no—
137C23×D3C22×D311yescharacteristic
138C3×#41—616no—
139C3×#41—624no—
140C2×C3×Q8—28no—
141C2×C3×Q8—24no—
142C2×C3×Q8—36no—
143C2×C3×Q8—312no—
144C2×C3×Q8—632no—
145C2×C3×Q8—616no—
146C2×C3×Q8—612no—
147C2×C3×Q8#6718yescomplemented
148C2×C3×Q8#6718yescomplemented
149C2×C3×Q8C22×D314yes—
150C2×C3×Q8C22×D314yes—
151C2×C3×D4—34no—
152C2×C3×D4—36no—
153C22×C3×C4—23no—
154C22×C3×C4—33no—
155C22×C3×C4—312no—
156C22×C3×C4—312no—
157C22×C3×C4—612no—
158C22×C3×C4C22×D313yes—
159C22×C3×C4C22×D313yes—
160C2×#67—38no—
161C2×#67—38no—
162C2×#67C22×D314yes—
163C22×Dic3C22×D313yes—
164#239—216no—
165D3×Q8—232no—
166D3×Q8—216no—
167#235—224no—
168C2×D12C22×D316yes—
169C2×C4×D3—212no—
170C2×C4×D3C22×D3112yes—
171C2×C4×D3C22×D3112yes—
172C2×Dic6—212no—
173C2×Dic6C22×D3112yes—
174C2×Dic6C22×D316yes—
175#217—34no—
176#217—34no—
177#217—38no—
178#217—324no—
179#217—64no—
180(C2×D3)⋊C4—38no—
181(C2×D3)⋊C4—324no—
182C4⋊Dic3—312no—
183C4⋊Dic3—312no—
184C4⋊Dic3—612no—
185Dic3⋊C4—324no—
186Dic3⋊C4—324no—
187C4×Dic3—312no—
188C4×Dic3—312no—
189C4×Dic3—612no—
190C22×C32—22no—
191C22×C32C22×D412yes—
192C22×C32C2511yescharacteristic
193C2×C3×D3—28no—
194C2×C3×D3—22no—
195C2×C3×D3—22no—
196C2×C3×D3—24no—
197C2×C3×D3—28no—
198C2×C3×D32−1+414yescomplemented
199C32×C4C22×D4112yes—
200C3⋊Dic3—28no—
201C3×Dic3—26no—
202C3×Dic3—24no—
2032−1+4—68no—
204C2×#41—34no—
205C2×#41—36no—
206C22×Q8—38no—
207C22×Q8—34no—
208C22×Q8—33no—
209C22×Q8—68no—
210C22×Q8D3211yescharacteristic
211C23×C4—33no—
212C4⋊Q8—912no—
213#124—912no—
214#123—912no—
215C22⋊Q8—912no—
216C22⋊Q8—924no—
217#121—912no—
218#120—94no—
219C4×Q8—98no—
220C4×D4—924no—
221#117—96no—
222C23×C3—21no—
223C23×C3—32no—
224C23×C3—34no—
225C23×C3—64no—
226C23×C3—62no—
227C23×C3C23×D311yescharacteristic
228C23×C3C23×D311yescharacteristic
229C22×D3—22no—
230C22×D3—24no—
231C22×D3C23×D314yes—
232C22×D3C23×D312yes—
233C3×Q8—216no—
234C3×Q8—624no—
235C3×Q8—612no—
236C3×Q8C2×#67116yes—
237C3×Q8C2×#67116yes—
238C3×D4—68no—
239C3×D4—612no—
240C2×C3×C4—26no—
241C2×C3×C4—212no—
242C2×C3×C4—34no—
243C2×C3×C4—36no—
244C2×C3×C4—66no—
245C2×C3×C4—624no—
246C2×C3×C4—624no—
247C2×C3×C4C2×#67112yes—
248C2×C3×C4C2×#67112yes—
249C2×C3×C4C23×D316yes—
250C2×C3×C4C23×D316yes—
251#67—28no—
252#67—616no—
253#67—616no—
254C2×Dic3—26no—
255C2×Dic3—38no—
256C2×Dic3—38no—
257C2×Dic3—68no—
258C2×Dic3C23×D314yes—
259C2×Dic3C23×D316yes—
260D12—212no—
261C4×D3—224no—
262C4×D3—224no—
263Dic6—224no—
264Dic6—212no—
265C2×C32—22no—
266C2×C32C23×D411yescharacteristic
267C2×C32C2×2−1+412yes—
268C3×D3—24no—
269C3×D3—44no—
270C24—31no—
271#41—616no—
272#41—624no—
273C2×Q8—312no—
274C2×Q8—36no—
275C2×Q8—632no—
276C2×Q8—616no—
277C2×Q8—612no—
278C2×Q8#62518yescomplemented
279C2×Q8C2×D3214yes—
280C2×D4—34no—
281C2×D4—36no—
282C2×D4—98no—
283C22×C4—33no—
284C22×C4—312no—
285C22×C4—312no—
286C22×C4—612no—
287C22×C4C2×D3213yes—
288C4⋊C4—924no—
289C4⋊C4—912no—
290C22⋊C4—98no—
291C22⋊C4—924no—
292C22⋊C4—94no—
293C42—912no—
294C22×C3—22no—
295C22×C3—22no—
296C22×C3—22no—
297C22×C3—21no—
298C22×C3—34no—
299C22×C3—42no—
300C22×C3—68no—
301C22×C3—62no—
302C22×C3—62no—
303C22×C3—68no—
304C22×C3—64no—
305C22×C3C22×#6712yes—
306C22×C3C22×#6712yes—
307C22×C3C24×D311yescharacteristic
308C22×C3C24×D311yescharacteristic
309C2×D3—28no—
310C2×D3—22no—
311C2×D3—22no—
312C2×D3—28no—
313C2×D3—24no—
314C2×D3#100714yescomplemented
315C3×C4—212no—
316C3×C4—64no—
317C3×C4—66no—
318C3×C4C22×#67112yes—
319C3×C4C22×#67112yes—
320Dic3—26no—
321Dic3—24no—
322Dic3—68no—
323Dic3—68no—
324Dic3—128no—
325C32#348611yescharacteristic, complemented, Sylow
326C23—32no—
327C23—34no—
328C23—64no—
329C23—62no—
330C23C22×D3211yescharacteristic
331Q8—624no—
332Q8—612no—
333Q8C2×#625116yes—
334D4—68no—
335D4—612no—
336D4—1816no—
337C2×C4—36no—
338C2×C4—34no—
339C2×C4—66no—
340C2×C4—624no—
341C2×C4—624no—
342C2×C4—98no—
343C2×C4C2×#625112yes—
344C2×C4C22×D3216yes—
345C2×C3—22no—
346C2×C3—22no—
347C2×C3—22no—
348C2×C3—21no—
349C2×C3—42no—
350C2×C3—64no—
351C2×C3—124no—
352C2×C3C2×#100712yes—
353C2×C3D3×2−1+412yes—
354C2×C3C23×#6711yescharacteristic
355C2×C3C23×#6711yescharacteristic
356D3—24no—
357D3—44no—
358C22—22no—
359C22—34no—
360C22—68no—
361C22—62no—
362C22—62no—
363C22—68no—
364C22—64no—
365C22C22×#62512yes—
366C22C23×D3211yescharacteristic
367C4—64no—
368C4—66no—
369C4—188no—
370C4C22×#625112yes—
371C3—21no—
372C3#8725111yescharacteristic, complemented
373C3#8729411yescharacteristic, complemented
374C2—22no—
375C2—64no—
376C2—124no—
377C2D3×#100712yes—
378C2C23×#62511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#3486
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C22×C3×D3×Q8C2semidirect
3. #10596283C2semidirect
4. #10595409C2semidirect
5. Q8×#625C2semidirect
6. #10595022C2semidirect
7. #10594855C2semidirect
12. C2×C3×#239C22semidirect
15. C2×C3×D3×Q8C22semidirect
19. Q8×C3⋊Dic3C22semidirect
25. #63873C22semidirect
26. #63863C22semidirect
28. #63856C22semidirect
31. C2×#1007D3semidirect
32. C22×D3×Q8D3semidirect
45. C2×C32×Q8D4semidirect
81. C2×#239C2×D3semidirect
84. C2×D3×Q8C2×D3semidirect
147. C2×C3×Q8#67semidirect
148. C2×C3×Q8#67semidirect
198. C2×C3×D32−1+4semidirect
278. C2×Q8#625semidirect
314. C2×D3#1007semidirect
325. C32#3486semidirect
372. C3#87251semidirect
373. C3#87294semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C22×C3×D3×Q82
#105962832
#105954092
Q8×#6252
#105950222
#105948552
#872943
#872513