Finite Group Databasebeta

← C2×#10593508 #11867031

Subgroups — C2×#10593508 #11867031

Order 1152.

814 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 127 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×#3792C211yesmaximal, characteristic
2C22×#3776C211yesmaximal, characteristic, complemented
3C2×#63982C212yesmaximal
4C2×#63742C211yesmaximal, characteristic, complemented
5#10593508C218yesmaximal, direct product factor
6C2×#63740C212yesmaximal, complemented
7C23×C3⋊Dic3C2211yescharacteristic
8C22×#627C2212yes—
9C2×#3792—24no—
10C2×#3792C2214yes—
11C22×#622C2211yescharacteristic
12C22×#622C2211yescharacteristic
13C2×#3776—24no—
14C2×#3776C2214yescomplemented
15C2×C3×#217—22no—
16#63982—24no—
17#63982C2218yes—
18C2×#3724C2212yes—
19C2×Dic3⋊Dic3—22no—
20#63742C2214yescomplemented
21#63740C2218yescomplemented
22C2×#878—62no—
23C24×C32D411yescharacteristic
24C22×C3⋊Dic3—22no—
25C22×C3⋊Dic3—22no—
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3D412yes—
28C22×C3⋊Dic3C2312yes—
29C22×C3⋊Dic3C2311yescharacteristic
30C22×C3×Dic3—22no—
31C22×C3×Dic3—22no—
32C2×#627—24no—
33C2×#627—24no—
34C2×#627—22no—
35C2×#627C2314yes—
36#3792—28no—
37C2×#622—22no—
38C2×#622D414yes—
39C2×#622C2312yes—
40C2×#622C2312yes—
41#3776—28no—
42C3×#217—28no—
43#3724—22no—
44#3724C2314yes—
45Dic3⋊Dic3—28no—
46C2×#470—91nomaximal, Sylow
47C23×Dic3—62no—
48C22×Dic6—62no—
49C2×C3×C22⋊C4—62no—
50C2×#217—22no—
51C2×C4⋊Dic3—62no—
52C2×Dic3⋊C4—62no—
53C2×Dic3⋊C4—62no—
54#878—68no—
55#878—68no—
56C23×C32—24no—
57C23×C32—22no—
58C23×C32C2×D412yes—
59C23×C32C2×D411yescharacteristic
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3—24no—
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3C2×D412yes—
65C2×C3⋊Dic3C2×D411yescharacteristic
66C2×C3⋊Dic3C2×D412yes—
67C2×C3⋊Dic3#4112yes—
68C2×C3⋊Dic3C2411yescharacteristic
69C2×C3×Dic3—24no—
70C2×C3×Dic3—24no—
71C2×C3×Dic3—44no—
72C2×C3×Dic3—44no—
73#627—24no—
74#627—24no—
75#627—44no—
76#622—22no—
77#622C2×D414yes—
78C22×Q16—91no—
79C22×M16—91no—
80C2×C22⋊Q8—92no—
81#470—98no—
82C2×#106—91no—
83C2×#103—92no—
84C24×C3—22no—
85C22×C3×C4—62no—
86C22×C3×C4—62no—
87C22×Dic3—22no—
88C22×Dic3—22no—
89C22×Dic3—62no—
90C22×Dic3—64no—
91C22×Dic3—64no—
92C22×Dic3—62no—
93C22×Dic3—124no—
94C22×Dic3—124no—
95C2×Dic6—64no—
96C2×Dic6—64no—
97C2×Dic6—124no—
98C2×Dic6—124no—
99C3×C22⋊C4—68no—
100#217—28no—
101C4⋊Dic3—68no—
102Dic3⋊C4—64no—
103Dic3⋊C4—68no—
104Dic3⋊C4—64no—
105C22×C32—24no—
106C22×C32—22no—
107C22×C32—44no—
108C22×C32#12112yes—
109C22×C32#13714yes—
110C22×C32C22×D411yescharacteristic
111C3⋊Dic3—22no—
112C3⋊Dic3#12112yes—
113C3⋊Dic3C22×D411yescharacteristic
114C3⋊Dic3C2×#4111yescharacteristic
115C3×Dic3—44no—
116C3×Dic3—44no—
117C22×Q8—92no—
118C23×C4—91no—
119C2×Q16—94no—
120C2×Q16—184no—
121C2×M16—94no—
122C2×M16—184no—
123C22×C8—91no—
124C22×C8—91no—
125C22⋊Q8—98no—
126C22⋊Q8—184no—
127C2×C4⋊C4—92no—
128C2×C4⋊C4—182no—
129C2×C22⋊C4—62no—
130#106—94no—
131#103—98no—
132C23×C3—28no—
133C23×C3—24no—
134C23×C3—22no—
135C23×C3—44no—
136C23×C3—44no—
137C2×C3×C4—64no—
138C2×C3×C4—64no—
139C2×C3×C4—124no—
140C2×C3×C4—124no—
141C2×Dic3—24no—
142C2×Dic3—24no—
143C2×Dic3—44no—
144C2×Dic3—44no—
145C2×Dic3—62no—
146C2×Dic3—64no—
147C2×Dic3—64no—
148C2×Dic3—62no—
149C2×Dic3—64no—
150C2×Dic3—124no—
151C2×Dic3—128no—
152C2×Dic3—124no—
153C2×Dic3—124no—
154Dic6—124no—
155Dic6—124no—
156Dic6—128no—
157C2×C32—42no—
158C2×C32#47014yescomplemented
159C2×C32C2×#12111yescharacteristic
160C2×C32C2×#13712yes—
161C24GO+(4,𝔽2)11yescharacteristic
162C2×Q8—94no—
163C2×Q8—182no—
164C2×Q8—184no—
165C2×Q8—184no—
166C22×C4—62no—
167C22×C4—62no—
168C22×C4—91no—
169C22×C4—92no—
170C22×C4—92no—
171C22×C4—91no—
172C22×C4—182no—
173C22×C4—182no—
174Q16—188no—
175M16—188no—
176C2×C8—92no—
177C2×C8—94no—
178C2×C8—92no—
179C2×C8—182no—
180C4⋊C4—94no—
181C4⋊C4—182no—
182C4⋊C4—188no—
183C22⋊C4—68no—
184C22×C3—28no—
185C22×C3—22no—
186C22×C3—24no—
187C22×C3—24no—
188C22×C3—24no—
189C22×C3—44no—
190C22×C3—44no—
191C22×C3—416no—
192C3×C4—124no—
193C3×C4—124no—
194Dic3—44no—
195Dic3—44no—
196Dic3—64no—
197Dic3—62no—
198Dic3—62no—
199Dic3—124no—
200C32C2×#47011yescharacteristic, complemented, Sylow
201C23—24no—
202C23—22no—
203C23C2×GO+(4,𝔽2)12yes—
204C23C2×GO+(4,𝔽2)11yescharacteristic
205Q8—184no—
206Q8—184no—
207Q8—364no—
208C2×C4—64no—
209C2×C4—64no—
210C2×C4—91no—
211C2×C4—91no—
212C2×C4—92no—
213C2×C4—92no—
214C2×C4—92no—
215C2×C4—124no—
216C2×C4—124no—
217C2×C4—182no—
218C2×C4—182no—
219C2×C4—184no—
220C2×C4—182no—
221C8—94no—
222C8—182no—
223C2×C3—22no—
224C2×C3—22no—
225C2×C3—22no—
226C2×C3—28no—
227C2×C3—48no—
228C22—24no—
229C22—22no—
230C22—44no—
231C22#6423914yes—
232C22#6424212yes—
233C22C22×GO+(4,𝔽2)11yescharacteristic
234C4—91no—
235C4—91no—
236C4—92no—
237C4—124no—
238C4—124no—
239C4—182no—
240C3—22no—
241C2—42no—
242C2#1059350814yesdirect product factor
243C2C2×#6423912yes—
244C2C2×#6424211yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
Fitting, prime radicalC24×C32D4
socleC23×C32C2×D4
hypercenterC24GO+(4,𝔽2)
hypocenterC32C2×#470
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C22×#3776C2semidirect
4. C2×#63742C2semidirect
5. #10593508C2direct (N × H)
6. C2×#63740C2semidirect
14. C2×#3776C22semidirect
20. #63742C22semidirect
21. #63740C22semidirect
158. C2×C32#470semidirect
200. C32C2×#470semidirect
242. C2#10593508direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37922
C22×#37762
C2×#639822
C2×#637422
#105935082
C2×#637402
C2×#4709