Finite Group Databasebeta

← #11795961

Subgroups — #11795961

Order 1152.

593 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 593 conjugacy classes of subgroups — too many to draw. Only its 130 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×D32×C8C211yesmaximal, characteristic
2C2×C16×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×#63542C211yesmaximal, characteristic, complemented
4C3×(C2×D3)⋊C16C212yesmaximal, complemented
5(C2×D3)⋊(C3⋊C16)C212yesmaximal, complemented
6D3×C22⋊C16—32nomaximal
7C2×C4×D32C411yescharacteristic
8C2×C8×C3⋊D3C2211yescharacteristic
9C2×C3×D3×C8C2212yes—
10C2×#3710C411yescharacteristic
11C2×D3×C3⋊C8C412yes—
12D32×C8—22no—
13D32×C8—22no—
14C2×C32×C16C2211yescharacteristic, complemented
15C2×C3⋊(C3⋊C16)C2211yescharacteristic, complemented
16C16×C3⋊D3—22no—
17C2×C3×C3⋊C16C2212yescomplemented
18#63542—22no—
19C22×D3×C8—32no—
20C2×D3×C16—32no—
21C2×D3×C16—32no—
22C2×D3×C16—61no—
23C3×C22⋊C16—32no—
24#4549—32no—
25(C2×D3)⋊C16—32no—
26(C2×D3)⋊C16D312yescomplemented
27C22×D32C811yescharacteristic
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C3×C4×D3C2×C412yes—
30C2×#624C811yescharacteristic
31C2×D3×Dic3C812yes—
32C4×D32—22no—
33C4×D32—22no—
34C2×C32×C8C2311yescharacteristic
35C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
36C8×C3⋊D3D412yes—
37C8×C3⋊D3D412yes—
38C2×C3×C3⋊C8C2×C412yes—
39C3×D3×C8—22no—
40C3×D3×C8—22no—
41#3710—22no—
42D3×C3⋊C8—24no—
43C32×C16—21no—
44C3⋊(C3⋊C16)—21no—
45C3×C3⋊C16—22no—
46C2×C22⋊C16—91noSylow
47C22×C4×D3—32no—
48C22×C3×C8—32no—
49C22×C3⋊C8—32no—
50C2×D3×C8—32no—
51C2×D3×C8—32no—
52C2×D3×C8—32no—
53C2×D3×C8—61no—
54C2×D3×C8—64no—
55C2×D3×C8—64no—
56C2×D3×C8C2×D312yes—
57C2×C3×C16—21no—
58C2×C3×C16—32no—
59C2×C3×C16C2×D312yescomplemented
60C2×C3⋊C16—32no—
61C2×C3⋊C16—61no—
62C2×C3⋊C16C2×D312yescomplemented
63D3×C16—64no—
64D3×C16—64no—
65D3×C16—64no—
66C22×C3⋊D3C2×C811yescharacteristic
67C22×C3×D3C2×C812yes—
68C2×D32—22no—
69C2×D32—22no—
70C2×D32C1614yescomplemented
71C2×C32×C4C22×C411yescharacteristic
72C2×C3⋊Dic3C2×C811yescharacteristic
73C4×C3⋊D3C22⋊C412yes—
74C4×C3⋊D3M1612yes—
75C2×C3×Dic3C2×C812yes—
76C3×C4×D3—22no—
77C3×C4×D3—22no—
78#624—22no—
79D3×Dic3—24no—
80C32×C8C2×D411yescharacteristic
81C32×C8C2×D411yescharacteristic
82C3⋊(C3⋊C8)C22⋊C412yes—
83C3×C3⋊C8—22no—
84C23×C8—91no—
85C22×C16—91no—
86C22×C16—91no—
87C22⋊C16—32no—
88C22⋊C16—92no—
89C23×D3—32no—
90C22×C3×C4—32no—
91C22×Dic3—32no—
92C2×C4×D3—32no—
93C2×C4×D3—32no—
94C2×C4×D3—32no—
95C2×C4×D3—61no—
96C2×C4×D3—64no—
97C2×C4×D3—64no—
98C2×C4×D3C4×D312yes—
99C2×C3×C8—21no—
100C2×C3×C8—32no—
101C2×C3×C8—62no—
102C2×C3×C8—62no—
103C2×C3×C8C22×D312yes—
104C2×C3⋊C8—32no—
105C2×C3⋊C8—61no—
106C2×C3⋊C8—64no—
107C2×C3⋊C8C4×D312yes—
108D3×C8—22no—
109D3×C8—22no—
110D3×C8—34no—
111D3×C8—34no—
112D3×C8—62no—
113D3×C8—62no—
114D3×C8—64no—
115D3×C8—64no—
116C3×C16—22no—
117C3×C16—22no—
118C3×C16—62no—
119C3⋊C16—22no—
120C3⋊C16—62no—
121C3⋊C16—62no—
122C22×C32C22×C811yescharacteristic
123C2×C3⋊D3C22⋊C812yes—
124C2×C3⋊D3C2×C1612yes—
125C2×C3⋊D3M3212yes—
126C2×C3×D3—22no—
127C2×C3×D3—22no—
128C2×C3×D3C2×C1614yescomplemented
129D32—28no—
130C32×C4C2×C22⋊C411yescharacteristic
131C32×C4C2×M1611yescharacteristic
132C3⋊Dic3C22⋊C812yes—
133C3×Dic3—22no—
134C23×C4—91no—
135C22×C8—32no—
136C22×C8—91no—
137C22×C8—92no—
138C22×C8—91no—
139C22×C8—182no—
140C22×C8—182no—
141C2×C16—32no—
142C2×C16—91no—
143C2×C16—182no—
144C2×C16—182no—
145C2×C16D3211yescharacteristic, complemented
146C23×C3—32no—
147C22×D3—32no—
148C22×D3—38no—
149C22×D3—61no—
150C22×D3—64no—
151C22×D3—64no—
152C22×D3D3×C812yes—
153C2×C3×C4—21no—
154C2×C3×C4—32no—
155C2×C3×C4—62no—
156C2×C3×C4—62no—
157C2×C3×C4C2×C4×D312yes—
158C2×Dic3—32no—
159C2×Dic3—61no—
160C2×Dic3—64no—
161C2×Dic3D3×C812yes—
162C4×D3—22no—
163C4×D3—22no—
164C4×D3—34no—
165C4×D3—34no—
166C4×D3—62no—
167C4×D3—62no—
168C4×D3—64no—
169C4×D3—64no—
170C3×C8—21no—
171C3×C8—21no—
172C3×C8—62no—
173C3×C8D3×D412yes—
174C3×C8D3×D412yes—
175C3⋊C8—22no—
176C3⋊C8—34no—
177C3⋊C8—62no—
178C2×C32C2×C22⋊C811yescharacteristic
179C2×C32C22×C1611yescharacteristic
180C2×C32C2×M3211yescharacteristic
181C3⋊D3C22⋊C1614yescomplemented
182C3×D3—24no—
183C24—91no—
184C22×C4—32no—
185C22×C4—91no—
186C22×C4—92no—
187C22×C4—91no—
188C22×C4—182no—
189C22×C4—182no—
190C2×C8—32no—
191C2×C8—62no—
192C2×C8—62no—
193C2×C8—91no—
194C2×C8—92no—
195C2×C8—92no—
196C2×C8—182no—
197C2×C8—184no—
198C2×C8C2×D3211yescharacteristic
199C16—21no—
200C16—62no—
201C16—181no—
202C22×C3—21no—
203C22×C3—34no—
204C22×C3—62no—
205C22×C3—62no—
206C22×C3C2×D3×C812yes—
207C2×D3—22no—
208C2×D3—22no—
209C2×D3—34no—
210C2×D3—34no—
211C2×D3—34no—
212C2×D3—62no—
213C2×D3—62no—
214C2×D3—62no—
215C2×D3—616no—
216C2×D3D3×C1614yescomplemented
217C3×C4—21no—
218C3×C4—21no—
219C3×C4—62no—
220C3×C4D3×C22⋊C412yes—
221C3×C4D3×M1612yes—
222Dic3—22no—
223Dic3—34no—
224Dic3—62no—
225C32C2×C22⋊C1611yescharacteristic, complemented, Sylow
226C23—32no—
227C23—94no—
228C23—91no—
229C23—182no—
230C23—182no—
231C2×C4—32no—
232C2×C4—62no—
233C2×C4—62no—
234C2×C4—91no—
235C2×C4—92no—
236C2×C4—92no—
237C2×C4—182no—
238C2×C4—184no—
239C2×C4C4×D3211yescharacteristic
240C8—62no—
241C8—92no—
242C8#380211yescharacteristic
243C8#381111yescharacteristic
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—64no—
248C2×C3D3×C22⋊C812yes—
249C2×C3C2×D3×C1612yes—
250C2×C3D3×M3212yes—
251D3—24no—
252D3—38no—
253D3—64no—
254C22—34no—
255C22—62no—
256C22—62no—
257C22—92no—
258C22—92no—
259C22—92no—
260C22—188no—
261C22D32×C811yescharacteristic
262C4—62no—
263C4—92no—
264C4#6379111yescharacteristic
265C4#6392111yescharacteristic
266C3—21no—
267C3D3×C22⋊C1612yescomplemented
268C2—64no—
269C2—94no—
270C2D32×C1611yescharacteristic
271C2#1059022611yescharacteristic
272C2#1059093511yescharacteristic
subgroupG/H
center, FrattiniC2×C8C2×D32
commutatorC2×C32C22×C16
FittingC2×C32×C16C22
socleC22×C32C22×C8
prime radicalC22×D32C8
cosocleC2×C32×C8C23
hypercenterC2×C16D32
hypocenterC32C2×C22⋊C16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
2. C2×C16×C3⋊D3C2semidirect
3. C2×#63542C2semidirect
4. C3×(C2×D3)⋊C16C2semidirect
5. (C2×D3)⋊(C3⋊C16)C2semidirect
14. C2×C32×C16C22semidirect
15. C2×C3⋊(C3⋊C16)C22semidirect
17. C2×C3×C3⋊C16C22semidirect
26. (C2×D3)⋊C16D3semidirect
59. C2×C3×C16C2×D3semidirect
62. C2×C3⋊C16C2×D3semidirect
70. C2×D32C16semidirect
128. C2×C3×D3C2×C16semidirect
145. C2×C16D32semidirect
181. C3⋊D3C22⋊C16semidirect
216. C2×D3D3×C16semidirect
225. C32C2×C22⋊C16semidirect
267. C3D3×C22⋊C16semidirect

Maximal subgroups

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

subgroupindex
C2×D32×C82
C2×C16×C3⋊D32
C2×#635422
C3×(C2×D3)⋊C162
(C2×D3)⋊(C3⋊C16)2
D3×C22⋊C163