Finite Group Databasebeta

← C2×#10593539 #11858260

Subgroups — C2×#10593539 #11858260

Order 1152.

694 conjugacy classes of subgroups; only the 215 normal subgroups are shown.

normal subgroups only

This group has 694 conjugacy classes of subgroups — too many to draw. Only its 215 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
1C22×C4×#157C211yesmaximal, characteristic
2C2×#64283C212yesmaximal
3#10593539C218yesmaximal, direct product factor
4C2×#63744C214yesmaximal, complemented
5C23×#157C412yes—
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×#3792—22no—
8C2×C4×#157C411yescharacteristic
9C2×C4×#157C414yes—
10C2×C4×#157C411yescharacteristic
11C2×C4×#157C2212yes—
12C2×C4×#157C2214yes—
13#64283—24no—
14#64283C2218yes—
15C2×#3788—22no—
16C2×#3787C2214yes—
17#63744C22116yescomplemented
18C23×C3⋊D3C2×C411yescharacteristic
19C22×#157—28no—
20C22×#157C2×C412yes—
21C22×#157C2×C418yes—
22C22×#157C2×C412yes—
23C22×C32×C4Q811yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C2×C4×C3⋊D3C2×C412yes—
26C2×C4×C3⋊D3C2×C411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3D412yes—
29C2×C4×C3⋊D3Q812yes—
30C2×C4×C3⋊D3Q811yescharacteristic
31C2×C4×C3⋊D3C2311yescharacteristic
32C2×C4×C3⋊D3C2312yes—
33#3792—28no—
34C2×#622—24no—
35C4×#157C2×C414yes—
36C4×#157C2×C414yes—
37C4×#157C2×C414yes—
38C4×#157C2314yes—
39#3788—28no—
40#3787—24no—
41#3787C2318yes—
42C2×#423—91nomaximal, Sylow
43C22×C4×D3—121no—
44C23×C32C4⋊C411yescharacteristic
45C22×C3⋊D3—24no—
46C22×C3⋊D3C4⋊C411yescharacteristic
47C22×C3⋊D3C4⋊C412yes—
48C22×C3⋊D3C22×C412yes—
49C22×C3⋊D3C22×C411yescharacteristic
50C2×#157—24no—
51C2×#157—216no—
52C2×#157M1618yescomplemented
53C2×#157C22×C414yes—
54C2×#157C22×C414yes—
55C2×C32×C4C4⋊C412yes—
56C2×C32×C4C4⋊C411yescharacteristic
57C2×C32×C4C2×Q812yes—
58C2×C32×C4C2×Q811yescharacteristic
59C2×C3⋊Dic3C4⋊C412yes—
60C2×C3⋊Dic3C4⋊C411yescharacteristic
61C2×C3⋊Dic3C2×D411yescharacteristic
62C2×C3⋊Dic3C2×D412yes—
63C4×C3⋊D3C4⋊C412yes—
64C4×C3⋊D3C4⋊C412yes—
65C4×C3⋊D3C4⋊C412yes—
66C4×C3⋊D3C22×C411yescharacteristic
67C4×C3⋊D3C22×C412yes—
68C4×C3⋊D3C2×D411yescharacteristic
69C4×C3⋊D3C2×D412yes—
70C4×C3⋊D3C2×Q812yes—
71C4×C3⋊D3C2×Q811yescharacteristic
72C4×C3⋊D3C2411yescharacteristic
73#622—28no—
74C22×M16—92no—
75C22×C42—91no—
76#423—98no—
77C2×C4⋊C8—94no—
78C23×D3—121no—
79C22×C3×C4—41no—
80C22×Dic3—121no—
81C2×C4×D3—121no—
82C2×C4×D3—122no—
83C2×C4×D3—121no—
84C2×C4×D3—122no—
85C2×C4×D3—122no—
86C2×C4×D3—121no—
87C2×C4×D3—122no—
88C2×C4×D3—121no—
89C22×C32—22no—
90C22×C32C2×C4⋊C412yes—
91C22×C32C2×C4⋊C411yescharacteristic
92C2×C3⋊D3—22no—
93C2×C3⋊D3—24no—
94C2×C3⋊D3—24no—
95C2×C3⋊D3C2×C4⋊C412yes—
96C2×C3⋊D3C2×C4⋊C411yescharacteristic
97C2×C3⋊D3C2×M1614yes—
98C2×C3⋊D3C23×C411yescharacteristic
99#157—24no—
100#157C2×M1618yescomplemented
101C32×C4C2×C4⋊C411yescharacteristic
102C32×C4C2×C4⋊C412yes—
103C32×C4C22×Q811yescharacteristic
104C3⋊Dic3C2×C4⋊C411yescharacteristic
105C3⋊Dic3C2×C4⋊C412yes—
106C3⋊Dic3C22×D411yescharacteristic
107C23×C4—91no—
108C23×C4—92no—
109C2×M16—98no—
110C2×M16—182no—
111C2×M16—184no—
112C2×M16—182no—
113C22×C8—94no—
114C2×C42—91no—
115C2×C42—94no—
116C2×C42—91no—
117C2×C42—92no—
118C2×C42—94no—
119C4⋊C8—916no—
120C23×C3—41no—
121C22×D3—122no—
122C22×D3—121no—
123C22×D3—121no—
124C22×D3—122no—
125C22×D3—128no—
126C2×C3×C4—42no—
127C2×C3×C4—41no—
128C2×C3×C4—41no—
129C2×C3×C4—42no—
130C2×Dic3—122no—
131C2×Dic3—121no—
132C2×Dic3—121no—
133C2×Dic3—122no—
134C4×D3—122no—
135C4×D3—122no—
136C4×D3—122no—
137C4×D3—122no—
138C4×D3—121no—
139C4×D3—121no—
140C4×D3—122no—
141C4×D3—121no—
142C4×D3—122no—
143C4×D3—121no—
144C2×C32—22no—
145C2×C32#42312yescomplemented
146C2×C32C22×C4⋊C411yescharacteristic
147C3⋊D3—22no—
148C3⋊D3#42312yescomplemented
149C3⋊D3C22×M1612yes—
150C24—91no—
151C22×C4—92no—
152C22×C4—91no—
153C22×C4—92no—
154C22×C4—92no—
155C22×C4—91no—
156C22×C4—91no—
157C22×C4—91no—
158C22×C4—92no—
159C22×C4—91no—
160C22×C4—92no—
161C22×C4—98no—
162C22×C4—92no—
163C22×C4—188no—
164C22×C4PSU(3,𝔽2)11yescharacteristic
165M16—188no—
166M16—188no—
167C2×C8—98no—
168C2×C8—184no—
169C2×C8—184no—
170C42—94no—
171C42—94no—
172C42—94no—
173C42—94no—
174C22×C3—44no—
175C22×C3—42no—
176C22×C3—41no—
177C2×D3—121no—
178C2×D3—122no—
179C2×D3—121no—
180C2×D3—124no—
181C2×D3—128no—
182C2×D3—128no—
183C2×D3—124no—
184C3×C4—41no—
185C3×C4—42no—
186C3×C4—41no—
187Dic3—121no—
188Dic3—122no—
189Dic3—121no—
190C32C2×#42311yescharacteristic, complemented, Sylow
191C23—91no—
192C23—92no—
193C23—92no—
194C23—91no—
195C23—184no—
196C23#377711yescharacteristic
197C2×C4—94no—
198C2×C4—98no—
199C2×C4—91no—
200C2×C4—92no—
201C2×C4—92no—
202C2×C4—91no—
203C2×C4—91no—
204C2×C4—91no—
205C2×C4—92no—
206C2×C4—92no—
207C2×C4—91no—
208C2×C4—91no—
209C2×C4—92no—
210C2×C4—92no—
211C2×C4—92no—
212C2×C4—92no—
213C2×C4—94no—
214C2×C4—1816no—
215C2×C4—184no—
216C2×C4#377711yescharacteristic
217C2×C4#377712yes—
218C2×C4C2×PSU(3,𝔽2)12yes—
219C2×C4C2×PSU(3,𝔽2)11yescharacteristic
220C8—188no—
221C2×C3—44no—
222C2×C3—42no—
223C2×C3—41no—
224D3—122no—
225D3—122no—
226D3—124no—
227C22—22no—
228C22—94no—
229C22—91no—
230C22—91no—
231C22—92no—
232C22—184no—
233C22—184no—
234C22—182no—
235C22C2×#377712yes—
236C22C2×#377711yescharacteristic
237C4—98no—
238C4—91no—
239C4—91no—
240C4—92no—
241C4—184no—
242C4C2×#377712yes—
243C4C2×#377711yescharacteristic
244C4C22×PSU(3,𝔽2)11yescharacteristic
245C3—41no—
246C2—22no—
247C2—92no—
248C2—92no—
249C2—182no—
250C2#1059353912yesdirect product factor
251C2C22×#377711yescharacteristic
subgroupG/H
centerC2×C4C2×PSU(3,𝔽2)
commutatorC2×C3⋊D3C23×C4
FrattiniC4C22×PSU(3,𝔽2)
FittingC22×C32×C4Q8
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC4×C3⋊D3C24
hypercenterC22×C4PSU(3,𝔽2)
hypocenterC32C2×#423
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #10593539C2direct (N × H)
4. C2×#63744C2semidirect
17. #63744C22semidirect
52. C2×#157M16semidirect
100. #157C2×M16semidirect
145. C2×C32#423semidirect
148. C3⋊D3#423semidirect
190. C32C2×#423semidirect
250. C2#10593539direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×#1572
C2×#642832
#105935392
C2×#637442
C2×#4239