Finite Group Databasebeta

← #11796915

Subgroups — #11796915

Order 1152.

485 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 485 conjugacy classes of subgroups — too many to draw. Only its 92 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×#63802C211yesmaximal, characteristic
2C3⋊D3×#108C211yesmaximal, characteristic
3#10590625C211yesmaximal, characteristic
4C3×#4496C212yesmaximal, complemented
5#10589130C212yesmaximal, complemented
6D3×#362—32nomaximal
7C2×#3797—21no—
8M16×C3⋊D3—21no—
9C2×C8×C3⋊D3C2211yescharacteristic
10C2×C3×Dic12C2212yes—
11C2×#3718—21no—
12#63802—21no—
13#63802—21no—
14#63802C412yes—
15#63802C412yes—
16C32×#108C2211yescharacteristic
17#63649—21no—
18#63646C2211yescharacteristic
19C3×#812C2212yes—
20#63544—21no—
21#63542—21no—
22C2×D3×Q16—32no—
23D3×M32—32no—
24D3×#108—32no—
25D3×#108—61no—
26C3×#362—32no—
27#4565—32no—
28#4517—32no—
29#4496D312yescomplemented
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C3×Dic6—22no—
32C2×#627—41no—
33C2×#624—41no—
34#3797—22no—
35#3797—22no—
36#3797—41no—
37#3797—41no—
38C32×M16—21no—
39C2×C32×C8C2311yescharacteristic
40#3748—21no—
41C2×C3⋊(C3⋊C8)D411yescharacteristic
42#3743—41no—
43C8×C3⋊D3—41no—
44C8×C3⋊D3C2×C411yescharacteristic
45C8×C3⋊D3C2×C411yescharacteristic
46C8×C3⋊D3D411yescharacteristic
47C8×C3⋊D3D411yescharacteristic
48C3×Dic12—22no—
49C3×Dic12C2×C414yes—
50#3718—22no—
51#3718—22no—
52C3×C3⋊C16—22no—
53C2×#362—91noSylow
54C2×D3×Q8—62no—
55C2×C3×Q16—32no—
56C2×#216—62no—
57D3×Q16—34no—
58D3×Q16—34no—
59D3×Q16—62no—
60D3×Q16—62no—
61D3×M16—62no—
62D3×M16—62no—
63C2×Dic12C2×D312yes—
64C2×D3×C8—32no—
65C2×D3×C8—61no—
66C3×M32—32no—
67C3×#108—21no—
68C3×#108C2×D312yes—
69#822—62no—
70#822—62no—
71#819—32no—
72#819—61no—
73#812C2×D312yes—
74#798—62no—
75D3×C16—62no—
76C22×C3⋊D3SD1611yescharacteristic
77C2×C32×C4C2×D411yescharacteristic
78C2×C3⋊Dic3SD1611yescharacteristic
79C4×C3⋊D3C22⋊C411yescharacteristic
80C4×C3⋊D3C22⋊C411yescharacteristic
81C4×C3⋊D3D811yescharacteristic
82C4×C3⋊D3D811yescharacteristic
83C2×C3×Dic3—42no—
84C3×Dic6—24no—
85C3×Dic6—42no—
86#627—42no—
87#627—42no—
88#624—42no—
89#624—42no—
90C32×C8—41no—
91C32×C8C22×C411yescharacteristic
92C32×C8C2×D411yescharacteristic
93C3⋊(C3⋊C8)—41no—
94C3⋊(C3⋊C8)C22⋊C411yescharacteristic
95C3⋊(C3⋊C8)C22⋊C411yescharacteristic
96C22×Q16—91no—
97C2×M32—91no—
98C2×#108—91no—
99#362—32no—
100#362—92no—
101C2×C3×Q8—62no—
102D3×Q8—64no—
103D3×Q8—64no—
104D3×Q8—122no—
105D3×Q8—122no—
106C2×C4×D3—32no—
107C2×C4×D3—61no—
108C2×C4×D3—122no—
109C2×Dic6—22no—
110C2×Dic6—122no—
111C3×Q16—34no—
112C3×Q16—62no—
113C3×M16—22no—
114C3×M16—22no—
115C2×C3×C8—21no—
116C2×C3×C8C22×D312yes—
117#216—64no—
118#216—64no—
119#208—62no—
120#208—62no—
121C2×C3⋊C8—32no—
122C2×C3⋊C8—61no—
123Dic12—22no—
124Dic12C4×D314yes—
125ΓL(1,𝔽25)—122no—
126ΓL(1,𝔽25)—122no—
127D3×C8—32no—
128D3×C8—32no—
129D3×C8—32no—
130D3×C8—32no—
131D3×C8—61no—
132D3×C8—61no—
133D3×C8—61no—
134D3×C8—61no—
135D3×C8—122no—
136D3×C8—122no—
137C3×C16—62no—
138C3⋊C16—22no—
139C22×C32C2×SD1611yescharacteristic
140C2×C3⋊D3—22no—
141C2×C3⋊D3#10211yescharacteristic
142C2×C3⋊D3#10211yescharacteristic
143C32×C4C2×C22⋊C411yescharacteristic
144C32×C4C2×D811yescharacteristic
145C3⋊Dic3#10211yescharacteristic
146C3⋊Dic3#10211yescharacteristic
147C3×Dic3—44no—
148C22×Q8—181no—
149C2×Q16—32no—
150C2×Q16—92no—
151C2×Q16—92no—
152C2×Q16—181no—
153C2×Q16—181no—
154C2×Q16—181no—
155C2×M16—181no—
156C22×C8—91no—
157M32—32no—
158M32—181no—
159C2×C16—181no—
160#108—91no—
161#108—181no—
162#108D3211yescharacteristic
163C22×D3—32no—
164C22×D3—61no—
165C3×Q8—64no—
166C3×Q8—122no—
167C2×C3×C4—21no—
168C2×C3×C4—122no—
169C2×C3×C4D3×D412yes—
170C2×Dic3—32no—
171C2×Dic3—42no—
172C2×Dic3—61no—
173C4×D3—32no—
174C4×D3—32no—
175C4×D3—32no—
176C4×D3—32no—
177C4×D3—61no—
178C4×D3—61no—
179C4×D3—61no—
180C4×D3—61no—
181C4×D3—124no—
182C4×D3—124no—
183Dic6—24no—
184Dic6—42no—
185Dic6—124no—
186Dic6—124no—
187C3×C8—21no—
188C3×C8—21no—
189C3×C8—42no—
190C3×C8—42no—
191C3×C8C2×C4×D312yes—
192C3×C8D3×D412yes—
193C3⋊C8—32no—
194C3⋊C8—32no—
195C3⋊C8—61no—
196C3⋊C8—61no—
197C3⋊C8—122no—
198C3⋊C8—122no—
199C2×C32—21no—
200C2×C32C2×#10211yescharacteristic
201C3⋊D3—21no—
202C3⋊D3#36212yescomplemented
203C2×Q8—62no—
204C2×Q8—182no—
205C2×Q8—182no—
206C2×Q8—361no—
207C2×Q8—361no—
208C2×Q8—361no—
209C22×C4—91no—
210C22×C4—361no—
211Q16—34no—
212Q16—62no—
213Q16—182no—
214Q16—182no—
215M16—21no—
216M16—181no—
217M16—361no—
218C2×C8—91no—
219C2×C8—91no—
220C2×C8—91no—
221C2×C8—91no—
222C2×C8—91no—
223C2×C8—361no—
224C2×C8C2×D3211yescharacteristic
225C16—62no—
226C22×C3—21no—
227C22×C3D3×SD1612yes—
228C2×D3—32no—
229C2×D3—32no—
230C2×D3—61no—
231C2×D3—61no—
232C2×D3—64no—
233C2×D3—122no—
234C3×C4—21no—
235C3×C4—21no—
236C3×C4—124no—
237C3×C4D3×C22⋊C412yes—
238C3×C4D3×D812yes—
239Dic3—32no—
240Dic3—32no—
241Dic3—44no—
242Dic3—61no—
243Dic3—61no—
244C32C2×#36211yescharacteristic, complemented, Sylow
245C23—91no—
246Q8—64no—
247Q8—122no—
248Q8—362no—
249Q8—362no—
250C2×C4—91no—
251C2×C4—91no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—91no—
255C2×C4—122no—
256C2×C4—362no—
257C2×C4—362no—
258C2×C4#381111yescharacteristic
259C8—41no—
260C8—91no—
261C8—91no—
262C8—361no—
263C8C4×D3211yescharacteristic
264C8#380211yescharacteristic
265C2×C3—22no—
266C2×C3—21no—
267C2×C3—41no—
268C2×C3D3×#10212yes—
269D3—34no—
270D3—62no—
271D3—62no—
272D3—121no—
273C22—91no—
274C22—91no—
275C22—182no—
276C22#6394011yescharacteristic
277C4—91no—
278C4—91no—
279C4—124no—
280C4#6392111yescharacteristic
281C4#6392611yescharacteristic
282C3—21no—
283C3D3×#36212yescomplemented
284C2—21no—
285C2—92no—
286C2—181no—
287C2#1059059311yescharacteristic
subgroupG/H
centerC2#10590593
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#108C22
socleC2×C32C2×#102
prime radicalC22×C3⋊D3SD16
cosocleC2×C32×C8C23
hypercenter#108D32
hypocenterC32C2×#362
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
4. C3×#4496C2semidirect
5. #10589130C2semidirect
29. #4496D3semidirect
202. C3⋊D3#362semidirect
244. C32C2×#362semidirect
283. C3D3×#362semidirect

Maximal subgroups

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

subgroupindex
C2×#638022
C3⋊D3×#1082
#105906252
C3×#44962
#105891302
D3×#3623