Finite Group Databasebeta

← #11904577

Subgroups — #11904577

Order 1152.

3205 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C22×C3×#239C211yesmaximal, characteristic, complemented
3#10596283C211yesmaximal, characteristic, complemented
4#10595412C218yesmaximal, complemented
5#10595409C218yesmaximal, complemented
6#10595040C216yesmaximal, complemented
7#10595022C216yesmaximal, complemented
8#87290—31nomaximal
9#87274—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C3×#1007—28no—
12C2×C3×#239—28no—
13C2×C3×#239C2218yes—
14C2×C3×#239C2214yescomplemented
15C2×C3×D3×Q8C2214yescomplemented
16C2×C3×#235C2216yes—
17C22×C3×D12C2213yes—
18C22×C3×C4×D3C2213yes—
19Q8×C3⋊Dic3C2218yescomplemented
20#64135C2216yes—
21#63976C22112yes—
22#63961C2214yes—
23#63914C22112yescomplemented
24#63908C22124yescomplemented
25#63908C22112yescomplemented
26C4×#625C22124yescomplemented
27#63863C22112yescomplemented
28#63856C22112yescomplemented
29C2×C3×2−1+4—31no—
30C22×C3×#41—31no—
31C2×#1007D311yescharacteristic, complemented
32C22×#239D311yescharacteristic, complemented
33#5834—38no—
34#5834—38no—
35#5831—38no—
36#5830—36no—
37#5828—36no—
38#5817—38no—
39#5812—31no—
40#5812—31no—
41#5812—61no—
42#5805—36no—
43#5791—36no—
44C23×C3×D3C2313yes—
45C2×C32×Q8D418yescomplemented
46C2×C32×Q8C2314yes—
47C22×C32×C4C2313yes—
48C2×C3×#67C2314yes—
49C22×C3×Dic3C2311yescharacteristic
50C3×#239—232no—
51C3×#239—216no—
52C3×D3×Q8—216no—
53C3×#235—224no—
54C2×C3×D12—212no—
55C2×C3×D12C23112yes—
56C2×C3×D12C2316yes—
57C2×C3×C4×D3—212no—
58C2×C3×C4×D3C23112yes—
59C2×C3×C4×D3C23112yes—
60C2×C3×Dic6C2316yes—
61C2×#625C23124yes—
62#3757C2314yes—
63C4⋊(C3⋊Dic3)C23112yes—
64C4×C3⋊Dic3C23112yes—
65#3724C2318yes—
66(C2×D3)⋊Dic3C23124yes—
67(C2×D3)⋊Dic3C2318yes—
68#3487—91noSylow
69C3×2−1+4—68no—
70C2×C3×#41—38no—
71C2×C3×#41—34no—
72C2×C3×#41—36no—
73C2×C3×#41—68no—
74C22×C3×Q8—21no—
75C22×C3×Q8—34no—
76C22×C3×Q8C2×D311yescharacteristic
77C22×C3×Q8C2×D311yescharacteristic
78C22×C3×D4—33no—
79C23×C3×C4—33no—
80#1007—28no—
81C2×#239—28no—
82C2×#239C2×D318yes—
83C2×#239C2×D314yescomplemented
84C2×D3×Q8C2×D314yescomplemented
85C2×#235C2×D316yes—
86C22×D12C2×D313yes—
87C22×C4×D3C2×D313yes—
88#953—312no—
89#947—312no—
90#946—312no—
91Q8×Dic3—38no—
92Q8×Dic3—38no—
93Q8×Dic3—68no—
94#940—312no—
95#940—312no—
96#938—324no—
97#938—312no—
98#937—312no—
99#936—312no—
100#935—34no—
101#930—312no—
102#930—324no—
103#929—34no—
104C4×#67—324no—
105C4×#67—324no—
106#926—36no—
107#926—36no—
108#926—66no—
109#924—312no—
110C23×C32C2411yescharacteristic
111C22×C3×D3—26no—
112C22×C3×D3—46no—
113C22×C3×D3C2416yes—
114C22×C3×D3C2414yes—
115C32×Q8C2×D4116yes—
116C2×C32×C4C2×D4112yes—
117C2×C32×C4C2416yes—
118C2×C3⋊Dic3C2418yes—
119C3×#67—28no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3C2414yes—
122C2×C3×Dic3C2412yes—
123C3×D12—224no—
124C3×D12—212no—
125C3×C4×D3—224no—
126C3×C4×D3—224no—
127C3×Dic6—212no—
128#625—424no—
129C2×2−1+4—31no—
130C22×#41—31no—
131#550—98no—
132#548—98no—
133#535—96no—
134#525—96no—
135#519—91no—
136C24×C3—33no—
137C23×D3C22×D313yes—
138C3×#41—632no—
139C3×#41—616no—
140C3×#41—624no—
141C2×C3×Q8—28no—
142C2×C3×Q8—24no—
143C2×C3×Q8—36no—
144C2×C3×Q8—616no—
145C2×C3×Q8#6718yescomplemented
146C2×C3×Q8#6718yescomplemented
147C2×C3×Q8C22×D314yes—
148C2×C3×Q8C22×D314yes—
149C2×C3×D4—34no—
150C2×C3×D4—312no—
151C2×C3×D4—36no—
152C2×C3×D4—612no—
153C22×C3×C4—23no—
154C22×C3×C4—31no—
155C22×C3×C4—312no—
156C22×C3×C4—312no—
157C22×C3×C4—612no—
158C22×C3×C4C22×D313yes—
159C22×C3×C4C22×D313yes—
160C2×#67—324no—
161C2×#67—324no—
162C2×#67C22×D314yes—
163C22×Dic3C22×D311yescharacteristic
164#239—232no—
165#239—216no—
166D3×Q8—216no—
167#235—224no—
168C2×D12—212no—
169C2×D12C22×D316yes—
170C2×D12C22×D3112yes—
171C2×C4×D3—212no—
172C2×C4×D3C22×D3112yes—
173C2×C4×D3C22×D3112yes—
174C2×Dic6C22×D316yes—
175#217—34no—
176#217—34no—
177#217—324no—
178#217—38no—
179#217—64no—
180(C2×D3)⋊C4—38no—
181(C2×D3)⋊C4—324no—
182C4⋊Dic3—312no—
183C4⋊Dic3—312no—
184C4⋊Dic3—612no—
185Dic3⋊C4—38no—
186Dic3⋊C4—38no—
187C4×Dic3—312no—
188C4×Dic3—312no—
189C4×Dic3—612no—
190C22×C32—22no—
191C22×C32C22×D412yes—
192C22×C32C2511yescharacteristic
193C2×C3×D3—24no—
194C2×C3×D3—26no—
195C2×C3×D3—28no—
196C2×C3×D3—212no—
197C2×C3×D3—412no—
198C32×C4C22×D4112yes—
199C3⋊Dic3—28no—
200C3×Dic3—24no—
201C3×Dic3—22no—
2022−1+4—68no—
203C2×#41—38no—
204C2×#41—34no—
205C2×#41—36no—
206C2×#41—68no—
207C22×Q8—34no—
208C22×Q8D3211yescharacteristic
209C22×D4—33no—
210C23×C4—33no—
211#127—912no—
212#124—912no—
213#123—94no—
214C22⋊Q8—912no—
215#121—912no—
216#121—924no—
217#120—912no—
218C4×Q8—98no—
219C4×D4—924no—
220#117—96no—
221C23×C3—21no—
222C23×C3—36no—
223C23×C3—34no—
224C23×C3—66no—
225C23×C3—126no—
226C23×C3C23×D311yescharacteristic
227C23×C3C23×D311yescharacteristic
228C22×D3—26no—
229C22×D3—46no—
230C22×D3C23×D316yes—
231C22×D3C23×D314yes—
232C3×Q8—216no—
233C3×Q8—612no—
234C3×Q8C2×#67116yes—
235C3×Q8C2×#67116yes—
236C3×D4—68no—
237C3×D4—624no—
238C3×D4—612no—
239C2×C3×C4—26no—
240C2×C3×C4—212no—
241C2×C3×C4—32no—
242C2×C3×C4—34no—
243C2×C3×C4—62no—
244C2×C3×C4—624no—
245C2×C3×C4—624no—
246C2×C3×C4C2×#67112yes—
247C2×C3×C4C2×#67112yes—
248C2×C3×C4C23×D316yes—
249C2×C3×C4C23×D316yes—
250#67—28no—
251#67—1224no—
252#67—1224no—
253C2×Dic3—22no—
254C2×Dic3—38no—
255C2×Dic3—38no—
256C2×Dic3—68no—
257C2×Dic3C23×D312yes—
258C2×Dic3C23×D314yes—
259D12—224no—
260D12—212no—
261C4×D3—224no—
262C4×D3—224no—
263Dic6—212no—
264C2×C32—22no—
265C2×C32C23×D411yescharacteristic
266C2×C32#58512yes—
267C3×D3—44no—
268C3×D3—46no—
269C24—33no—
270#41—632no—
271#41—616no—
272#41—624no—
273C2×Q8—36no—
274C2×Q8—616no—
275C2×Q8#62518yescomplemented
276C2×Q8C2×D3214yes—
277C2×D4—34no—
278C2×D4—312no—
279C2×D4—36no—
280C2×D4—612no—
281C2×D4—924no—
282C22×C4—31no—
283C22×C4—312no—
284C22×C4—312no—
285C22×C4—612no—
286C22×C4C2×D3213yes—
287C4⋊C4—98no—
288C4⋊C4—912no—
289C22⋊C4—98no—
290C22⋊C4—924no—
291C22⋊C4—94no—
292C42—912no—
293C22×C3—22no—
294C22×C3—22no—
295C22×C3—22no—
296C22×C3—21no—
297C22×C3—42no—
298C22×C3—68no—
299C22×C3—612no—
300C22×C3—64no—
301C22×C3—66no—
302C22×C3—1212no—
303C22×C3C22×#6712yes—
304C22×C3C22×#6712yes—
305C22×C3C24×D311yescharacteristic
306C22×C3C24×D311yescharacteristic
307C2×D3—212no—
308C2×D3—28no—
309C2×D3—24no—
310C2×D3—26no—
311C2×D3—412no—
312C3×C4—212no—
313C3×C4—62no—
314C3×C4—64no—
315C3×C4C22×#67112yes—
316C3×C4C22×#67112yes—
317Dic3—24no—
318Dic3—22no—
319Dic3—68no—
320Dic3—68no—
321Dic3—128no—
322C32#348711yescharacteristic, complemented, Sylow
323C23—36no—
324C23—34no—
325C23—66no—
326C23—126no—
327C23C22×D3211yescharacteristic
328Q8—612no—
329Q8C2×#625116yes—
330D4—68no—
331D4—624no—
332D4—612no—
333D4—3624no—
334C2×C4—34no—
335C2×C4—32no—
336C2×C4—62no—
337C2×C4—624no—
338C2×C4—624no—
339C2×C4—98no—
340C2×C4C2×#625112yes—
341C2×C4C22×D3216yes—
342C2×C3—22no—
343C2×C3—22no—
344C2×C3—22no—
345C2×C3—21no—
346C2×C3—42no—
347C2×C3—124no—
348C2×C3—126no—
349C2×C3#596412yes—
350C2×C3#596812yes—
351C2×C3C23×#6711yescharacteristic
352C2×C3C23×#6711yescharacteristic
353D3—46no—
354D3—44no—
355C22—22no—
356C22—68no—
357C22—612no—
358C22—64no—
359C22—66no—
360C22—1212no—
361C22C22×#62512yes—
362C22C23×D3211yescharacteristic
363C4—62no—
364C4—64no—
365C4—188no—
366C4C22×#625112yes—
367C3—21no—
368C3#8727411yescharacteristic, complemented
369C3#8729011yescharacteristic, complemented
370C2—22no—
371C2—126no—
372C2—124no—
373C2#1059668812yes—
374C2C23×#62511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#3487
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×#239C2semidirect
3. #10596283C2semidirect
4. #10595412C2semidirect
5. #10595409C2semidirect
6. #10595040C2semidirect
7. #10595022C2semidirect
14. C2×C3×#239C22semidirect
15. C2×C3×D3×Q8C22semidirect
19. Q8×C3⋊Dic3C22semidirect
23. #63914C22semidirect
24. #63908C22semidirect
25. #63908C22semidirect
26. C4×#625C22semidirect
27. #63863C22semidirect
28. #63856C22semidirect
31. C2×#1007D3semidirect
32. C22×#239D3semidirect
45. C2×C32×Q8D4semidirect
83. C2×#239C2×D3semidirect
84. C2×D3×Q8C2×D3semidirect
145. C2×C3×Q8#67semidirect
146. C2×C3×Q8#67semidirect
275. C2×Q8#625semidirect
322. C32#3487semidirect
368. C3#87274semidirect
369. C3#87290semidirect

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×#2392
#105962832
#105954122
#105954092
#105950402
#105950222
#872903
#872743