Finite Group Databasebeta

← C2×#10590075 #11783243

Subgroups — C2×#10590075 #11783243

Order 1152.

930 conjugacy classes of subgroups; only the 223 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 223 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
1C23×#622C211yesmaximal, characteristic
2C22×#3724C212yesmaximal
3#10590075C214yesmaximal, direct product factor
4C23×C3⋊Dic3C2211yescharacteristic
5C23×C3×Dic3—22no—
6C22×#622—24no—
7C22×#622C414yescomplemented
8C22×#622C2212yes—
9C2×#3724—22no—
10C2×#3724—24no—
11C2×#3724C418yescomplemented
12C2×#3724C2214yes—
13C22×Dic3⋊C4—62no—
14C24×C32D411yescharacteristic
15C22×C3⋊Dic3C2×C412yes—
16C22×C3⋊Dic3C2×C414yes—
17C22×C3⋊Dic3D411yescharacteristic
18C22×C3⋊Dic3D414yes—
19C22×C3⋊Dic3Q812yes—
20C22×C3⋊Dic3C2311yescharacteristic
21C22×C3×Dic3—28no—
22C22×C3×Dic3—24no—
23C22×C3×Dic3—44no—
24C22×C3×Dic3—44no—
25C2×#622—28no—
26C2×#622—24no—
27C2×#622C2×C414yescomplemented
28#3724—28no—
29#3724—24no—
30#3724C2×C418yescomplemented
31C2×#340—91nomaximal, Sylow
32C23×C3×C4—62no—
33C23×Dic3—22no—
34C23×Dic3—62no—
35C2×Dic3⋊C4—68no—
36C2×Dic3⋊C4—64no—
37C2×Dic3⋊C4—64no—
38C2×Dic3⋊C4—68no—
39C23×C32C22⋊C414yes—
40C23×C32C4⋊C412yes—
41C23×C32D812yes—
42C23×C32SD1614yes—
43C23×C32Q1612yes—
44C23×C32C2×D411yescharacteristic
45C2×C3⋊Dic3C4214yes—
46C2×C3⋊Dic3C22⋊C414yes—
47C2×C3⋊Dic3C22⋊C414yes—
48C2×C3⋊Dic3C4⋊C412yes—
49C2×C3⋊Dic3C4⋊C418yes—
50C2×C3⋊Dic3C22×C411yescharacteristic
51C2×C3⋊Dic3C22×C412yes—
52C2×C3⋊Dic3C2×D412yes—
53C2×C3⋊Dic3C2×Q811yescharacteristic
54C2×C3×Dic3—28no—
55C2×C3×Dic3—416no—
56C2×C3×Dic3—44no—
57C2×C3×Dic3—44no—
58#622—24no—
59C23×C8—91no—
60C22×C4⋊C4—92no—
61#340—94no—
62C24×C3—22no—
63C22×C3×C4—64no—
64C22×C3×C4—68no—
65C22×C3×C4—124no—
66C22×C3×C4—124no—
67C22×Dic3—24no—
68C22×Dic3—28no—
69C22×Dic3—44no—
70C22×Dic3—44no—
71C22×Dic3—64no—
72C22×Dic3—62no—
73C22×Dic3—64no—
74C22×Dic3—62no—
75C22×Dic3—64no—
76C22×Dic3—64no—
77C22×Dic3—64no—
78C22×Dic3—64no—
79Dic3⋊C4—68no—
80Dic3⋊C4—616no—
81Dic3⋊C4—68no—
82C22×C32#9514yes—
83C22×C32#10218yes—
84C22×C32#10318yes—
85C22×C32#10614yes—
86C22×C32#10714yes—
87C22×C32C2×C22⋊C412yes—
88C22×C32C2×C4⋊C411yescharacteristic
89C22×C32C2×D811yescharacteristic
90C22×C32C2×SD1612yes—
91C22×C32C2×Q1611yescharacteristic
92C3⋊Dic3#9514yes—
93C3⋊Dic3C2×C4211yescharacteristic
94C3⋊Dic3C2×C22⋊C411yescharacteristic
95C3⋊Dic3C2×C4⋊C412yes—
96C3×Dic3—48no—
97C23×C4—62no—
98C23×C4—91no—
99C22×C8—94no—
100C22×C8—92no—
101C22×C8—184no—
102C2×C4⋊C4—94no—
103C2×C4⋊C4—98no—
104C2×C4⋊C4—182no—
105C2×C4⋊C4—184no—
106C23×C3—22no—
107C23×C3—24no—
108C23×C3—24no—
109C23×C3—24no—
110C23×C3—24no—
111C23×C3—24no—
112C23×C3—24no—
113C23×C3—24no—
114C2×C3×C4—68no—
115C2×C3×C4—124no—
116C2×C3×C4—124no—
117C2×C3×C4—1216no—
118C2×Dic3—28no—
119C2×Dic3—44no—
120C2×Dic3—44no—
121C2×Dic3—416no—
122C2×Dic3—68no—
123C2×Dic3—64no—
124C2×Dic3—64no—
125C2×Dic3—68no—
126C2×Dic3—64no—
127C2×Dic3—68no—
128C2×Dic3—68no—
129C2×Dic3—62no—
130C2×Dic3—62no—
131C2×Dic3—62no—
132C2×Dic3—62no—
133C2×Dic3—62no—
134C2×Dic3—62no—
135C2×C32#34018yescomplemented
136C2×C32C2×#9511yescharacteristic
137C2×C32C2×#10212yes—
138C2×C32C2×#10312yes—
139C2×C32C2×#10611yescharacteristic
140C2×C32C2×#10711yescharacteristic
141C24GO+(4,𝔽2)11yescharacteristic
142C22×C4—64no—
143C22×C4—68no—
144C22×C4—91no—
145C22×C4—91no—
146C22×C4—94no—
147C22×C4—94no—
148C22×C4—92no—
149C22×C4—92no—
150C22×C4—124no—
151C22×C4—124no—
152C2×C8—94no—
153C2×C8—184no—
154C2×C8—188no—
155C4⋊C4—98no—
156C4⋊C4—184no—
157C4⋊C4—188no—
158C22×C3—22no—
159C22×C3—22no—
160C22×C3—22no—
161C22×C3—22no—
162C22×C3—22no—
163C22×C3—22no—
164C22×C3—22no—
165C22×C3—28no—
166C22×C3—28no—
167C22×C3—28no—
168C22×C3—28no—
169C22×C3—28no—
170C22×C3—28no—
171C22×C3—28no—
172C3×C4—128no—
173Dic3—48no—
174Dic3—68no—
175Dic3—62no—
176Dic3—62no—
177Dic3—62no—
178Dic3—62no—
179C32C2×#34011yescharacteristic, complemented, Sylow
180C23D32⋊C414yes—
181C23#377312yes—
182C23#377412yes—
183C23#377514yes—
184C23#377612yes—
185C23C2×GO+(4,𝔽2)11yescharacteristic
186C2×C4—68no—
187C2×C4—92no—
188C2×C4—92no—
189C2×C4—94no—
190C2×C4—91no—
191C2×C4—91no—
192C2×C4—92no—
193C2×C4—94no—
194C2×C4—94no—
195C2×C4—98no—
196C2×C4—124no—
197C2×C4—124no—
198C2×C4—1216no—
199C8—184no—
200C2×C3—216no—
201C2×C3—22no—
202C2×C3—22no—
203C2×C3—22no—
204C2×C3—22no—
205C2×C3—22no—
206C2×C3—22no—
207C2×C3—22no—
208C22#6373714yes—
209C22#6373918yes—
210C22#6374018yes—
211C22#6374214yes—
212C22#6374314yes—
213C22C2×D32⋊C412yes—
214C22C2×#377311yescharacteristic
215C22C2×#377411yescharacteristic
216C22C2×#377512yes—
217C22C2×#377611yescharacteristic
218C4—91no—
219C4—91no—
220C4—92no—
221C4—94no—
222C4—128no—
223C3—22no—
224C2#1059007518yesdirect product factor
225C2C2×#6373711yescharacteristic
226C2C2×#6373912yes—
227C2C2×#6374012yes—
228C2C2×#6374211yescharacteristic
229C2C2×#6374311yescharacteristic
subgroupG/H
center, hypercenterC24GO+(4,𝔽2)
commutatorC3⋊Dic3C2×C42
FrattiniC23C2×GO+(4,𝔽2)
Fitting, socle, prime radicalC24×C32D4
cosocleC22×C3⋊Dic3C23
hypocenterC32C2×#340
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C24

Complements

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

NH ≅ G/Ntype
3. #10590075C2direct (N × H)
7. C22×#622C4semidirect
11. C2×#3724C4semidirect
27. C2×#622C2×C4semidirect
30. #3724C2×C4semidirect
135. C2×C32#340semidirect
179. C32C2×#340semidirect
224. C2#10590075direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6222
C22×#37242
#105900752
C2×#3409