Finite Group Databasebeta

← C2×#10593331 #11858625

Subgroups — C2×#10593331 #11858625

Order 1152.

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

normal subgroups only

This group has 778 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
1C22×#3787C211yesmaximal, characteristic
2C2×#63818C212yesmaximal
3#10593331C218yesmaximal, direct product factor
4C2×#63733C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#622C412yes—
7C2×#3787C414yes—
8C2×#3787C412yes—
9C2×#3787C2212yes—
10C2×#3787C2214yes—
11C2×C3×#208—22no—
12C2×#3712C2214yes—
13#63818—24no—
14#63818C2218yes—
15C2×#3710—22no—
16#63733C22116yescomplemented
17C2×D3×M16—62no—
18C23×C3⋊D3Q811yescharacteristic
19C22×C32×C4D411yescharacteristic
20C22×C3⋊Dic3C2×C411yescharacteristic
21C2×C4×C3⋊D3C2×C412yes—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D412yes—
25C2×C4×C3⋊D3Q811yescharacteristic
26C2×C4×C3⋊D3Q812yes—
27C2×C4×C3⋊D3C2312yes—
28C2×C4×C3⋊D3C2311yescharacteristic
29C2×#622C2×C414yes—
30C2×#622C2×C418yes—
31#3787C2×C414yes—
32#3787C2×C418yes—
33#3787C2314yes—
34C3×#208—28no—
35C2×C3×C3⋊C8—24no—
36#3712—24no—
37#3712C2318yes—
38#3710—28no—
39C22×#108—91nomaximal, Sylow
40C22×C4×D3—62no—
41C2×C3×M16—62no—
42C2×#208—22no—
43D3×M16—68no—
44D3×M16—68no—
45C2×ΓL(1,𝔽25)—64no—
46C2×D3×C8—64no—
47C23×C32C4⋊C411yescharacteristic
48C22×C3⋊D3—24no—
49C22×C3⋊D3C4⋊C412yes—
50C22×C3⋊D3C4⋊C411yescharacteristic
51C22×C3⋊D3C2×Q811yescharacteristic
52C22×C3⋊D3C2×Q812yes—
53C2×C32×C4C4⋊C412yes—
54C2×C32×C4C4⋊C411yescharacteristic
55C2×C32×C4C2×D411yescharacteristic
56C2×C32×C4C2×D412yes—
57C2×C3⋊Dic3C4⋊C412yes—
58C2×C3⋊Dic3C4⋊C411yescharacteristic
59C2×C3⋊Dic3C22×C412yes—
60C2×C3⋊Dic3C22×C411yescharacteristic
61C4×C3⋊D3C4⋊C412yes—
62C4×C3⋊D3C4⋊C412yes—
63C4×C3⋊D3C4⋊C412yes—
64C4×C3⋊D3C22×C411yescharacteristic
65C4×C3⋊D3C22×C412yes—
66C4×C3⋊D3C2×D412yes—
67C4×C3⋊D3C2×D411yescharacteristic
68C4×C3⋊D3C2×Q812yes—
69C4×C3⋊D3C2×Q811yescharacteristic
70C4×C3⋊D3C2411yescharacteristic
71#622C22×C418yes—
72C3×C3⋊C8—28no—
73C22×M16—92no—
74C23×C8—91no—
75C2×#108—94no—
76C2×#108—98no—
77C23×D3—62no—
78C22×C3×C4—22no—
79C22×Dic3—62no—
80C2×C4×D3—62no—
81C2×C4×D3—62no—
82C2×C4×D3—64no—
83C2×C4×D3—64no—
84C2×C4×D3—62no—
85C2×C4×D3—64no—
86C2×C4×D3—64no—
87C2×C4×D3—62no—
88C3×M16—68no—
89C2×C3×C8—64no—
90#208—28no—
91C2×C3⋊C8—24no—
92ΓL(1,𝔽25)—68no—
93ΓL(1,𝔽25)—68no—
94D3×C8—616no—
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⋊D3#10814yescomplemented
102C2×C3⋊D3C2×C4⋊C411yescharacteristic
103C2×C3⋊D3C2×C4⋊C412yes—
104C2×C3⋊D3C22×Q811yescharacteristic
105C32×C4C2×C4⋊C411yescharacteristic
106C32×C4C2×C4⋊C412yes—
107C32×C4C22×D411yescharacteristic
108C3⋊Dic3C2×C4⋊C412yes—
109C3⋊Dic3C2×C4⋊C411yescharacteristic
110C3⋊Dic3C23×C411yescharacteristic
111C23×C4—91no—
112C2×M16—62no—
113C2×M16—94no—
114C2×M16—98no—
115C2×M16—184no—
116C22×C8—92no—
117C22×C8—94no—
118C22×C8—94no—
119C22×C8—92no—
120C22×C8—92no—
121C22×C8—182no—
122#108—916no—
123C23×C3—22no—
124C22×D3—62no—
125C22×D3—64no—
126C22×D3—64no—
127C22×D3—62no—
128C22×D3—128no—
129C2×C3×C4—24no—
130C2×C3×C4—22no—
131C2×C3×C4—22no—
132C2×C3×C4—24no—
133C2×Dic3—62no—
134C2×Dic3—64no—
135C2×Dic3—62no—
136C2×Dic3—64no—
137C4×D3—64no—
138C4×D3—64no—
139C4×D3—64no—
140C4×D3—64no—
141C4×D3—62no—
142C4×D3—64no—
143C4×D3—62no—
144C4×D3—62no—
145C4×D3—64no—
146C4×D3—62no—
147C3×C8—68no—
148C3⋊C8—28no—
149C2×C32—22no—
150C2×C32C2×#10812yescomplemented
151C2×C32C22×C4⋊C411yescharacteristic
152C3⋊D3—21no—
153C3⋊D3—21no—
154C3⋊D3C2×#10814yescomplemented
155C24—91no—
156C22×C4—91no—
157C22×C4—92no—
158C22×C4—92no—
159C22×C4—91no—
160C22×C4—91no—
161C22×C4—91no—
162C22×C4—92no—
163C22×C4—92no—
164C22×C4—91no—
165C22×C4GO+(4,𝔽2)11yescharacteristic
166M16—68no—
167M16—98no—
168M16—184no—
169C2×C8—64no—
170C2×C8—94no—
171C2×C8—98no—
172C2×C8—94no—
173C2×C8—98no—
174C2×C8—94no—
175C2×C8—188no—
176C22×C3—22no—
177C22×C3—24no—
178C22×C3—44no—
179C2×D3—64no—
180C2×D3—68no—
181C2×D3—62no—
182C2×D3—62no—
183C2×D3—128no—
184C2×D3—128no—
185C2×D3—124no—
186C3×C4—22no—
187C3×C4—24no—
188C3×C4—22no—
189Dic3—64no—
190Dic3—62no—
191Dic3—62no—
192C32C22×#10811yescharacteristic, complemented, Sylow
193C23—91no—
194C23—92no—
195C23—92no—
196C23—91no—
197C23—184no—
198C23#377311yescharacteristic
199C2×C4—92no—
200C2×C4—91no—
201C2×C4—92no—
202C2×C4—91no—
203C2×C4—91no—
204C2×C4—92no—
205C2×C4—91no—
206C2×C4—92no—
207C2×C4—91no—
208C2×C4—92no—
209C2×C4—92no—
210C2×C4—92no—
211C2×C4—92no—
212C2×C4—91no—
213C2×C4#377311yescharacteristic
214C2×C4#377312yes—
215C2×C4C2×GO+(4,𝔽2)12yes—
216C2×C4C2×GO+(4,𝔽2)11yescharacteristic
217C8—68no—
218C8—98no—
219C2×C3—24no—
220C2×C3—22no—
221C2×C3—44no—
222D3—68no—
223D3—122no—
224D3—122no—
225C22—22no—
226C22—94no—
227C22—92no—
228C22—91no—
229C22—91no—
230C22—184no—
231C22—184no—
232C22—182no—
233C22C2×#377312yes—
234C22C2×#377311yescharacteristic
235C4—91no—
236C4—92no—
237C4—91no—
238C4C2×#377312yes—
239C4C2×#377311yescharacteristic
240C4C22×GO+(4,𝔽2)11yescharacteristic
241C3—22no—
242C2—22no—
243C2—94no—
244C2—181no—
245C2—181no—
246C2#1059333112yesdirect product factor
247C2C22×#377311yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC4C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3Q8
cosocleC4×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C22×#108
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #10593331C2direct (N × H)
4. C2×#63733C2semidirect
16. #63733C22semidirect
101. C2×C3⋊D3#108semidirect
150. C2×C32C2×#108semidirect
154. C3⋊D3C2×#108semidirect
192. C32C22×#108semidirect
246. C2#10593331direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37872
C2×#638182
#105933312
C2×#637332
C22×#1089