Finite Group Databasebeta

← #11797714

Subgroups — #11797714

Order 1152.

341 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 341 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63656C211yesmaximal, characteristic
2C3×Dic3×Q16C211yesmaximal, characteristic
3#10590807C211yesmaximal, characteristic
4C3×#4564C211yesmaximal, characteristic
5#10589140C211yesmaximal, characteristic
6#10589119C211yesmaximal, characteristic
7Dic3×C3⋊C16C211yesmaximal, characteristic
8C4×#829—31nomaximal
9#69207—31nomaximal
10C2×C32×Q16C2211yescharacteristic
11C2×#3746C2211yescharacteristic
12C3×Q8×Dic3—21no—
13#63844—21no—
14#63656C414yescomplemented
15C2×C3⋊(C3⋊C16)C2211yescharacteristic
16C3×#835—21no—
17C3×#818C2211yescharacteristic
18C3×#818C2211yescharacteristic
19C3×C8×Dic3C2211yescharacteristic
20C2×C3×C3⋊C16C2211yescharacteristic
21#63567—21no—
22C3×C4×Q16—31no—
23Dic3×Q16D311yescharacteristic
24C2×#829—31no—
25C2×#829—31no—
26C2×#829—61no—
27#4873—31no—
28C4×Dic12—31no—
29C3×#358—31no—
30#4564D311yescharacteristic
31#4503—31no—
32Dic3×C16—31no—
33#4492—31no—
34#4489—31no—
35#4489—31no—
36C4×C3⋊C16—31no—
37C2×C32×Q8—21no—
38C2×#634—21no—
39C32×Q16—21no—
40C32×Q16C2×C412yes—
41C2×C32×C8C2311yescharacteristic
42#3746—21no—
43#3746C2×C412yes—
44C3×C4⋊Dic3—21no—
45C3×C4⋊Dic3—21no—
46C3×C4⋊Dic3—41no—
47C3×C4×Dic3—41no—
48C3×C4×Dic3D411yescharacteristic
49C2×C3×C3⋊C8D411yescharacteristic
50#3724—41no—
51Dic32—41no—
52C3⋊(C3⋊C16)C2×C412yes—
53C3×C3⋊C16—21no—
54C4×Q32—91noSylow
55C2×C3×Q16—21no—
56C2×C3×Q16C2×D311yescharacteristic
57C2×C3×Q16C2×D311yescharacteristic
58C3×C4×Q8—61no—
59Q8×Dic3—21no—
60C2×Dic12—31no—
61C2×Dic12—31no—
62C2×Dic12—61no—
63#887—61no—
64C4×Dic6—61no—
65C2×C3×C16—31no—
66C3×#107—31no—
67C3×#107—31no—
68C3×#103—61no—
69C3×C4×C8—31no—
70#835—21no—
71#829—34no—
72#829—34no—
73#829—64no—
74#818C2×D311yescharacteristic
75#818C2×D311yescharacteristic
76#816—61no—
77C8×Dic3C2×D311yescharacteristic
78C2×C3⋊C16—31no—
79C2×C3⋊C16—31no—
80C2×C3⋊C16—61no—
81C2×C3⋊C16C2×D311yescharacteristic
82#810—61no—
83C32×Q8—22no—
84C32×Q8—41no—
85C2×C32×C4—41no—
86C2×C32×C4C2×D411yescharacteristic
87C2×C3⋊Dic3—41no—
88#634—22no—
89#634—41no—
90C2×C3×Dic3—41no—
91C2×C3×Dic3—41no—
92C2×C3×Dic3D811yescharacteristic
93C2×C3×Dic3D811yescharacteristic
94C32×C8C22×C411yescharacteristic
95C32×C8#4111yescharacteristic
96C3×C3⋊C8—21no—
97C2×Q32—91no—
98C4×Q16—31no—
99C4×Q16—91no—
100#366—91no—
101#358—31no—
102#358—91no—
103C4×C16—91no—
104C2×C3×Q8—21no—
105C2×C3×Q8—21no—
106C2×C3×Q8—41no—
107C2×Dic6—61no—
108C2×Dic6—61no—
109C2×Dic6—121no—
110C3×Q16—21no—
111C3×Q16—21no—
112C3×Q16—22no—
113C3×Q16—41no—
114C3×Q16C4×D312yes—
115C3×Q16C4×D312yes—
116C2×C3×C8—21no—
117C2×C3×C8—31no—
118C2×C3×C8C22×D311yescharacteristic
119C2×C3×C8C22×D311yescharacteristic
120C3×C4⋊C4—61no—
121C3×C4⋊C4—61no—
122C3×C4⋊C4—121no—
123C3×C42—31no—
124C3×C42—121no—
125C4⋊Dic3—21no—
126C4⋊Dic3—21no—
127C4⋊Dic3—41no—
128Dic3⋊C4—121no—
129Dic3⋊C4—121no—
130C4×Dic3—41no—
131C4×Dic3—121no—
132C4×Dic3—121no—
133C4×Dic3#6711yescharacteristic
134C2×C3⋊C8#6711yescharacteristic
135Dic12—32no—
136Dic12—32no—
137Dic12—62no—
138Dic12—61no—
139Dic12—61no—
140Dic12—121no—
141C3×C16—61no—
142C3⋊C16—21no—
143C3⋊C16—32no—
144C3⋊C16—32no—
145C3⋊C16—62no—
146C22×C32C2×D811yescharacteristic
147C32×C4—42no—
148C32×C4C4×D411yescharacteristic
149C32×C4#13511yescharacteristic
150C3⋊Dic3—42no—
151C3×Dic3—21no—
152C3×Dic3—81no—
153C3×Dic3—81no—
154C3×Dic3Q3212yescomplemented
155C2×Q16—91no—
156C2×Q16D3211yescharacteristic
157C4×Q8—61no—
158C4×Q8—181no—
159Q32—94no—
160C2×C16—31no—
161C2×C16—91no—
162#107—31no—
163#107—31no—
164#103—61no—
165#103—181no—
166C4×C8—31no—
167C3×Q8—22no—
168C3×Q8—22no—
169C3×Q8—42no—
170C3×Q8—41no—
171C3×Q8—41no—
172C3×Q8—81no—
173C2×C3×C4—21no—
174C2×C3×C4—31no—
175C2×C3×C4—31no—
176C2×C3×C4—41no—
177C2×C3×C4—41no—
178C2×C3×C4—81no—
179C2×C3×C4—121no—
180C2×C3×C4—121no—
181C2×C3×C4D3×D411yescharacteristic
182C2×C3×C4C2×#6711yescharacteristic
183C2×Dic3—41no—
184C2×Dic3—41no—
185C2×Dic3—121no—
186C2×Dic3—121no—
187C2×Dic3—241no—
188C2×Dic3#21311yescharacteristic
189C2×Dic3#21311yescharacteristic
190Dic6—62no—
191Dic6—62no—
192Dic6—122no—
193Dic6—121no—
194Dic6—121no—
195Dic6—241no—
196C3×C8—21no—
197C3×C8—21no—
198C3×C8—61no—
199C3×C8C2×C4×D311yescharacteristic
200C3×C8C2×C4×D311yescharacteristic
201C3×C8#23511yescharacteristic
202C3×C8#23711yescharacteristic
203C3⋊C8—21no—
204C2×C32C4×D811yescharacteristic
205C2×C32C2×Q3211yescharacteristic
206C2×C32#50811yescharacteristic
207C2×Q8—21no—
208C2×Q8—181no—
209Q16—21no—
210Q16—92no—
211Q16—181no—
212Q16#62412yes—
213C2×C8—31no—
214C2×C8C2×D3211yescharacteristic
215C4⋊C4—61no—
216C4⋊C4—61no—
217C4⋊C4—121no—
218C4⋊C4—361no—
219C42—31no—
220C42—121no—
221C42—361no—
222C16—61no—
223C16—92no—
224C22×C3—21no—
225C22×C3D3×D811yescharacteristic
226C22×C3C2×#21311yescharacteristic
227C3×C4—21no—
228C3×C4—21no—
229C3×C4—32no—
230C3×C4—42no—
231C3×C4—42no—
232C3×C4—61no—
233C3×C4—82no—
234C3×C4—241no—
235C3×C4—241no—
236C3×C4#67⋊C411yescharacteristic
237C3×C4#91611yescharacteristic
238C3×C4C4×#6711yescharacteristic
239C3×C4#95011yescharacteristic
240Dic3—21no—
241Dic3—81no—
242Dic3—81no—
243Dic3—122no—
244Dic3—122no—
245Dic3—242no—
246Dic3#82912yescomplemented
247C32C4×Q3211yescharacteristic, complemented, Sylow
248Q8—22no—
249Q8—41no—
250Q8—182no—
251Q8—361no—
252C2×C4—31no—
253C2×C4—31no—
254C2×C4—41no—
255C2×C4—121no—
256C2×C4—121no—
257C2×C4—361no—
258C2×C4D3×#6711yescharacteristic
259C8—61no—
260C8#380411yescharacteristic
261C8C2×#62411yescharacteristic
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3#475611yescharacteristic
266C2×C3#491611yescharacteristic
267C2×C3D3×Q3211yescharacteristic
268C2×C3C4×#21311yescharacteristic
269C2×C3C2×#82911yescharacteristic
270C2×C3#519411yescharacteristic
271C22D3×#21311yescharacteristic
272C4—32no—
273C4—42no—
274C4—61no—
275C4—241no—
276C4—241no—
277C4—362no—
278C4#6393511yescharacteristic
279C4#6395211yescharacteristic
280C3—21no—
281C3#6920711yescharacteristic, complemented
282C3C4×#82911yescharacteristic, complemented
283C2D3×#82911yescharacteristic
284C2#1059104611yescharacteristic
285C2#1059140011yescharacteristic
subgroupG/H
centerC22D3×#213
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socle, prime radicalC22×C32C2×D8
cosocleC2×C32×C8C23
hypercenterC2×Q16D32
hypocenterC32C4×Q32
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
14. #63656C4semidirect
154. C3×Dic3Q32semidirect
246. Dic3#829semidirect
247. C32C4×Q32semidirect
281. C3#69207semidirect
282. C3C4×#829semidirect

Maximal subgroups

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

subgroupindex
C2×#636562
C3×Dic3×Q162
#105908072
C3×#45642
#105891402
#105891192
Dic3×C3⋊C162
C4×#8293
#692073