Finite Group Databasebeta

← C2×#10593540 #11858297

Subgroups — C2×#10593540 #11858297

Order 1152.

630 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 199 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×#64286C211yesmaximal, characteristic
2C2×#64283C211yesmaximal, characteristic
3C22×#3787C211yesmaximal, characteristic
4#10593540C218yesmaximal, direct product factor
5C2×#63744C214yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157C412yes—
8C2×#3792—21no—
9C22×#622—21no—
10#64286C414yes—
11#64286C2214yes—
12C2×C4⋊#157C412yes—
13C2×C4×#157C2212yes—
14#64283—22no—
15#64283C2214yes—
16C2×#3788—21no—
17C2×#3787—21no—
18C2×#3787—22no—
19C2×#3787C2212yes—
20C2×#3787C2212yes—
21C2×#3787C2214yes—
22#63744C22116yescomplemented
23C23×C3⋊D3C2×C411yescharacteristic
24C22×#157C2×C414yes—
25C22×C32×C4Q811yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3C2×C412yes—
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D412yes—
31C2×C4×C3⋊D3Q812yes—
32C2×C4×C3⋊D3Q811yescharacteristic
33C2×C4×C3⋊D3C2311yescharacteristic
34C2×C4×C3⋊D3C2312yes—
35C22⋊#157C2×C418yes—
36#3792—24no—
37C2×#622—22no—
38C2×#622—24no—
39C2×#622—22no—
40C4⋊#157C2×C418yes—
41C4×#157C2×C414yes—
42C4×#157C2314yes—
43#3788—24no—
44#3787—22no—
45#3787—24no—
46#3787—22no—
47#3787C2314yes—
48#3787C2314yes—
49C2×#424—91nomaximal, Sylow
50C22×C4×D3—121no—
51C23×C32C4⋊C411yescharacteristic
52C22×C3⋊D3—24no—
53C22×C3⋊D3C4⋊C411yescharacteristic
54C22×C3⋊D3C4⋊C412yes—
55C22×C3⋊D3C22×C412yes—
56C22×C3⋊D3C22×C411yescharacteristic
57C2×#157—28no—
58C2×#157C22×C418yes—
59C2×C32×C4C4⋊C412yes—
60C2×C32×C4C4⋊C411yescharacteristic
61C2×C32×C4C2×Q812yes—
62C2×C32×C4C2×Q811yescharacteristic
63C2×C3⋊Dic3C4⋊C412yes—
64C2×C3⋊Dic3C4⋊C411yescharacteristic
65C2×C3⋊Dic3C2×D411yescharacteristic
66C2×C3⋊Dic3C2×D412yes—
67C4×C3⋊D3C4⋊C412yes—
68C4×C3⋊D3C4⋊C412yes—
69C4×C3⋊D3C4⋊C412yes—
70C4×C3⋊D3C22×C411yescharacteristic
71C4×C3⋊D3C22×C412yes—
72C4×C3⋊D3C2×D411yescharacteristic
73C4×C3⋊D3C2×D412yes—
74C4×C3⋊D3C2×Q812yes—
75C4×C3⋊D3C2×Q811yescharacteristic
76C4×C3⋊D3C2411yescharacteristic
77#622—24no—
78#622—24no—
79C22×M16—91no—
80C23×C8—91no—
81C2×#117—91no—
82#424—98no—
83C2×C4⋊C8—94no—
84C23×D3—121no—
85C22×C3×C4—41no—
86C22×Dic3—121no—
87C2×C4×D3—121no—
88C2×C4×D3—122no—
89C2×C4×D3—121no—
90C2×C4×D3—122no—
91C2×C4×D3—122no—
92C2×C4×D3—121no—
93C2×C4×D3—122no—
94C2×C4×D3—121no—
95C22×C32—22no—
96C22×C32C2×C4⋊C412yes—
97C22×C32C2×C4⋊C411yescharacteristic
98C2×C3⋊D3—22no—
99C2×C3⋊D3—24no—
100C2×C3⋊D3—24no—
101C2×C3⋊D3C2×C4⋊C412yes—
102C2×C3⋊D3C2×C4⋊C411yescharacteristic
103C2×C3⋊D3#13114yes—
104C2×C3⋊D3C23×C411yescharacteristic
105#157—28no—
106C32×C4C2×C4⋊C411yescharacteristic
107C32×C4C2×C4⋊C412yes—
108C32×C4C22×Q811yescharacteristic
109C3⋊Dic3C2×C4⋊C411yescharacteristic
110C3⋊Dic3C2×C4⋊C412yes—
111C3⋊Dic3C22×D411yescharacteristic
112C23×C4—91no—
113C2×M16—94no—
114C2×M16—181no—
115C2×M16—182no—
116C2×M16—181no—
117C22×C8—92no—
118C22×C8—94no—
119C22×C8—92no—
120C22×C8—182no—
121C22×C8—181no—
122C22×C8—181no—
123#117—94no—
124#117—94no—
125C2×C4⋊C4—92no—
126C2×C22⋊C4—92no—
127C2×C42—92no—
128C4⋊C8—916no—
129C23×C3—41no—
130C22×D3—122no—
131C22×D3—121no—
132C22×D3—121no—
133C22×D3—122no—
134C22×D3—128no—
135C2×C3×C4—42no—
136C2×C3×C4—41no—
137C2×C3×C4—41no—
138C2×C3×C4—42no—
139C2×Dic3—122no—
140C2×Dic3—121no—
141C2×Dic3—121no—
142C2×Dic3—122no—
143C4×D3—122no—
144C4×D3—122no—
145C4×D3—122no—
146C4×D3—121no—
147C4×D3—122no—
148C4×D3—121no—
149C4×D3—122no—
150C4×D3—121no—
151C4×D3—122no—
152C4×D3—121no—
153C2×C32—22no—
154C2×C32#42412yescomplemented
155C2×C32C22×C4⋊C411yescharacteristic
156C3⋊D3—22no—
157C3⋊D3#42412yescomplemented
158C3⋊D3C2×#13112yes—
159C24—91no—
160C22×C4—91no—
161C22×C4—92no—
162C22×C4—92no—
163C22×C4—91no—
164C22×C4—91no—
165C22×C4—91no—
166C22×C4—92no—
167C22×C4—91no—
168C22×C4—92no—
169C22×C4—94no—
170C22×C4PSU(3,𝔽2)11yescharacteristic
171M16—184no—
172M16—184no—
173C2×C8—94no—
174C2×C8—94no—
175C2×C8—182no—
176C2×C8—184no—
177C2×C8—182no—
178C2×C8—184no—
179C2×C8—182no—
180C2×C8—182no—
181C4⋊C4—98no—
182C22⋊C4—98no—
183C42—94no—
184C42—94no—
185C22×C3—44no—
186C22×C3—42no—
187C22×C3—41no—
188C2×D3—121no—
189C2×D3—122no—
190C2×D3—121no—
191C2×D3—124no—
192C2×D3—128no—
193C2×D3—128no—
194C2×D3—124no—
195C3×C4—41no—
196C3×C4—42no—
197C3×C4—41no—
198Dic3—121no—
199Dic3—122no—
200Dic3—121no—
201C32C2×#42411yescharacteristic, complemented, Sylow
202C23—91no—
203C23—92no—
204C23—92no—
205C23—91no—
206C23—184no—
207C23#377711yescharacteristic
208C2×C4—91no—
209C2×C4—92no—
210C2×C4—92no—
211C2×C4—91no—
212C2×C4—91no—
213C2×C4—91no—
214C2×C4—92no—
215C2×C4—91no—
216C2×C4—92no—
217C2×C4—91no—
218C2×C4—92no—
219C2×C4—92no—
220C2×C4—92no—
221C2×C4—92no—
222C2×C4—98no—
223C2×C4—188no—
224C2×C4#377711yescharacteristic
225C2×C4#377712yes—
226C2×C4C2×PSU(3,𝔽2)12yes—
227C2×C4C2×PSU(3,𝔽2)11yescharacteristic
228C8—184no—
229C8—184no—
230C2×C3—44no—
231C2×C3—42no—
232C2×C3—41no—
233D3—122no—
234D3—122no—
235D3—124no—
236C22—22no—
237C22—94no—
238C22—91no—
239C22—91no—
240C22—92no—
241C22—184no—
242C22—184no—
243C22—182no—
244C22C2×#377712yes—
245C22C2×#377711yescharacteristic
246C4—91no—
247C4—91no—
248C4—92no—
249C4—188no—
250C4C2×#377712yes—
251C4C2×#377711yescharacteristic
252C4C22×PSU(3,𝔽2)11yescharacteristic
253C3—41no—
254C2—22no—
255C2—92no—
256C2—92no—
257C2—182no—
258C2#1059354012yesdirect product factor
259C2C22×#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×#424
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10593540C2direct (N × H)
5. C2×#63744C2semidirect
22. #63744C22semidirect
154. C2×C32#424semidirect
157. C3⋊D3#424semidirect
201. C32C2×#424semidirect
258. C2#10593540direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642862
C2×#642832
C22×#37872
#105935402
C2×#637442
C2×#4249