Finite Group Databasebeta

← #11895489

Subgroups — #11895489

Order 1152.

772 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596041C211yesmaximal, characteristic
2C3×Q8×Dic6C211yesmaximal, characteristic
3C3×Q8×C3⋊C8C211yesmaximal, characteristic
4#10590385C213yesmaximal
5C4×#3719C213yesmaximal
6#10590288C213yesmaximal
7#10590284C213yesmaximal
8#83707—31nomaximal
9#79933—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11Q8×C3⋊Dic3—21no—
12#64099—23no—
13#64078C2213yes—
14C4×#634C2213yes—
15C3×Q8×Dic3—21no—
16C3×#888—23no—
17C3×#869C2213yes—
18C3×C4×Dic6C2213yes—
19C2×#3719C2213yes—
20C3×C4⋊(C3⋊C8)C2213yes—
21C3×C4×C3⋊C8C2213yes—
22#63575C2213yes—
23#63567C2216yes—
24#63567C2213yes—
25#63566C2211yescharacteristic
26C3×Q82—31no—
27#5570—31no—
28#5570—31no—
29#5570—61no—
30Q8×Dic6D311yescharacteristic
31C3×C8×Q8—31no—
32#5093—33no—
33#5091—33no—
34#5031—33no—
35C4×#216—33no—
36Q8×C3⋊C8D311yescharacteristic
37#4850—33no—
38#4849—33no—
39C4×Dic12—33no—
40#4681—33no—
41C2×C32×Q8D411yescharacteristic
42C2×#634C2313yes—
43C2×C3×Dic6—23no—
44C2×C3×Dic6C2311yescharacteristic
45C32×C4⋊C4D413yes—
46C32×C42C2313yes—
47C4⋊(C3⋊Dic3)—23no—
48C4⋊(C3⋊Dic3)—23no—
49C4⋊(C3⋊Dic3)C2311yescharacteristic
50#3750—23no—
51C4×C3⋊Dic3—23no—
52C3×C4⋊Dic3—23no—
53C3×C4⋊Dic3C2313yes—
54C3×Dic3⋊C4—23no—
55C3×C4×Dic3—23no—
56C2×C3×C3⋊C8C2311yescharacteristic
57C2×C3×C3⋊C8C2313yes—
58#3719—26no—
59#3363—91noSylow
60C3×C4⋊Q8—33no—
61C3×C4⋊Q8—63no—
62C3×C4×Q8—21no—
63C3×C4×Q8—33no—
64C3×C4×Q8—61no—
65C3×C4×Q8C2×D311yescharacteristic
66C3×C4×Q8C2×D311yescharacteristic
67Q8×Dic3—21no—
68Q8×Dic3—62no—
69Q8×Dic3—61no—
70Q8×Dic3—61no—
71C2×#216—33no—
72C2×Dic12—33no—
73#890—66no—
74#890—63no—
75#890—63no—
76#888—23no—
77#869—33no—
78#869—33no—
79#869—63no—
80#869C2×D313yes—
81C4×Dic6—33no—
82C4×Dic6—33no—
83C4×Dic6—63no—
84C4×Dic6C2×D313yes—
85C3×C4⋊C8—33no—
86C3×C4×C8—33no—
87#835—31no—
88#818—33no—
89#816—31no—
90#816—33no—
91#816—36no—
92#810—33no—
93#810—36no—
94#807—33no—
95C4⋊(C3⋊C8)C2×D313yes—
96C4×C3⋊C8C2×D313yes—
97C32×Q8Q1614yescomplemented
98C2×C32×C4C2×D413yes—
99C2×C32×C4C2×D413yes—
100C2×C32×C4C2411yescharacteristic
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—23no—
103#634—23no—
104#634—23no—
105C2×C3×Dic3—21no—
106C2×C3×Dic3—23no—
107C3×Dic6—21no—
108C3×Dic6—83no—
109C3×Dic6#4112yes—
110C3×C3⋊C8—23no—
111C3×C3⋊C8—21no—
112Q82—31no—
113#557—91no—
114#487—93no—
115#477—93no—
116#462—93no—
117C8×Q8—31no—
118C4×Q16—93no—
119C2×C3×Q8—21no—
120C2×C3×Q8—31no—
121C2×C3×Q8—63no—
122C2×C3×Q8D1211yescharacteristic
123C2×C3×Q8#6711yescharacteristic
124C2×Dic6—23no—
125C2×Dic6—33no—
126C2×Dic6—33no—
127C2×Dic6—63no—
128C2×Dic6C22×D311yescharacteristic
129C2×C3×C8—31no—
130C2×C3×C8—33no—
131C3×C4⋊C4—23no—
132C3×C4⋊C4—33no—
133C3×C4⋊C4—63no—
134C3×C4⋊C4—63no—
135C3×C4⋊C4D1213yes—
136C3×C4⋊C4#6713yes—
137C3×C42—23no—
138C3×C42—63no—
139C3×C42C22×D313yes—
140C3×C42C22×D313yes—
141#216—66no—
142C4⋊Dic3—23no—
143C4⋊Dic3—31no—
144C4⋊Dic3—31no—
145C4⋊Dic3—61no—
146C4⋊Dic3—66no—
147C4⋊Dic3—66no—
148C4⋊Dic3—63no—
149C4⋊Dic3—63no—
150C4⋊Dic3—63no—
151C4⋊Dic3—63no—
152C4⋊Dic3C22×D313yes—
153Dic3⋊C4—23no—
154Dic3⋊C4—66no—
155Dic3⋊C4—63no—
156Dic3⋊C4—63no—
157C4×Dic3—23no—
158C4×Dic3—66no—
159C4×Dic3—63no—
160C4×Dic3—63no—
161C2×C3⋊C8C22×D311yescharacteristic
162C2×C3⋊C8C22×D313yes—
163Dic12—66no—
164C22×C32C22×D411yescharacteristic
165C32×C4—23no—
166C32×C4C2×Q1616yes—
167C32×C4C2×#4111yescharacteristic
168C32×C42−1+411yescharacteristic
169C3⋊Dic3—43no—
170C3⋊Dic3—41no—
171C3×Dic3—22no—
172C3×Dic3—43no—
173C2×Q16—93no—
174C4⋊Q8—33no—
175C4⋊Q8—63no—
176C4⋊Q8—93no—
177#125—183no—
178C4×Q8—33no—
179C4×Q8—61no—
180C4×Q8—93no—
181C4×Q8—181no—
182C4×Q8D3211yescharacteristic
183#107—93no—
184C4⋊C8—33no—
185#103—93no—
186#103—96no—
187#103—91no—
188C4×C8—33no—
189C3×Q8—24no—
190C3×Q8—32no—
191C3×Q8—61no—
192C3×Q8—243no—
193C3×Q8Dic1214yescomplemented
194C3×Q8#21614yescomplemented
195C2×C3×C4—21no—
196C2×C3×C4—23no—
197C2×C3×C4—23no—
198C2×C3×C4—61no—
199C2×C3×C4—63no—
200C2×C3×C4C2×D1213yes—
201C2×C3×C4C2×D1213yes—
202C2×C3×C4C2×#6713yes—
203C2×C3×C4C2×#6713yes—
204C2×C3×C4C23×D311yescharacteristic
205C2×C3×C4C23×D311yescharacteristic
206C2×Dic3—21no—
207C2×Dic3—23no—
208C2×Dic3—62no—
209C2×Dic3—66no—
210C2×Dic3—61no—
211C2×Dic3—63no—
212C2×Dic3—61no—
213C2×Dic3—63no—
214Dic6—21no—
215Dic6—63no—
216Dic6—63no—
217Dic6—63no—
218Dic6—63no—
219Dic6—83no—
220Dic6—123no—
221Dic6—123no—
222Dic6#23912yes—
223C3×C8—63no—
224C3×C8—61no—
225C3⋊C8—21no—
226C3⋊C8—23no—
227C2×C32#54811yescharacteristic
228C2×C32C22×Q1611yescharacteristic
229C2×C32#57711yescharacteristic
230C2×Q8—31no—
231C2×Q8—63no—
232C2×Q8—93no—
233C2×Q8#62611yescharacteristic
234Q16—186no—
235C2×C8—31no—
236C2×C8—33no—
237C4⋊C4—33no—
238C4⋊C4—63no—
239C4⋊C4—63no—
240C4⋊C4—91no—
241C4⋊C4—183no—
242C4⋊C4—183no—
243C4⋊C4—183no—
244C4⋊C4#62613yes—
245C42—63no—
246C42—183no—
247C42C2×D3213yes—
248C22×C3—21no—
249C22×C3C22×D1211yescharacteristic
250C22×C3C22×#6711yescharacteristic
251C3×C4—23no—
252C3×C4—23no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—26no—
256C3×C4—43no—
257C3×C4—62no—
258C3×C4—123no—
259C3×C4C2×Dic1216yes—
260C3×C4C2×#21616yes—
261C3×C4C2×#23911yescharacteristic
262C3×C4#100711yescharacteristic
263C3×C4#100711yescharacteristic
264C3×C4D3×#4111yescharacteristic
265Dic3—22no—
266Dic3—43no—
267Dic3—126no—
268Dic3—122no—
269Dic3—121no—
270Dic3—123no—
271Dic3—123no—
272Dic3—121no—
273C32#336311yescharacteristic, complemented, Sylow
274Q8—32no—
275Q8—61no—
276Q8—183no—
277Q8—183no—
278Q8—243no—
279Q8#371914yescomplemented
280C2×C4—61no—
281C2×C4—63no—
282C2×C4—181no—
283C2×C4—183no—
284C2×C4C2×#62613yes—
285C2×C4C2×#62613yes—
286C2×C4C22×D3211yescharacteristic
287C8—61no—
288C8—63no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3#557611yescharacteristic
293C2×C3C22×Dic1211yescharacteristic
294C2×C3#575111yescharacteristic
295C2×C3C22×#21611yescharacteristic
296C2×C3#581711yescharacteristic
297C2×C3#583611yescharacteristic
298C22C22×#62611yescharacteristic
299C4—23no—
300C4—62no—
301C4—123no—
302C4—363no—
303C4—361no—
304C4C2×#371916yes—
305C4#6431611yescharacteristic
306C4D3×#23911yescharacteristic
307C3—21no—
308C3#7993311yescharacteristic, complemented
309C3#8370711yescharacteristic, complemented
310C2C22×#371911yescharacteristic
311C2#1059534211yescharacteristic
312C2#1059544711yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32C22×D4
hypercenterC4×Q8D32
hypocenterC32#3363
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
97. C32×Q8Q16semidirect
193. C3×Q8Dic12semidirect
194. C3×Q8#216semidirect
273. C32#3363semidirect
279. Q8#3719semidirect
308. C3#79933semidirect
309. C3#83707semidirect

Maximal subgroups

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

subgroupindex
#105960412
C3×Q8×Dic62
C3×Q8×C3⋊C82
#105903852
C4×#37192
#105902882
#105902842
#837073
#799333