Finite Group Databasebeta

← C2×#10593449 #11867032

Subgroups — C2×#10593449 #11867032

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×#3788C211yesmaximal, characteristic
2C22×#3776C211yesmaximal, characteristic, complemented
3C2×#63865C212yesmaximal
4C2×#63742C211yesmaximal, characteristic, complemented
5C2×#63740C212yesmaximal, complemented
6#10593449C218yesmaximal, direct product factor
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#627C2212yes—
9C22×#622C2211yescharacteristic
10C22×#622C2211yescharacteristic
11C2×#3788—24no—
12C2×#3788C2214yes—
13C2×#3776—24no—
14C2×#3776C2214yescomplemented
15C2×C3×Dic3⋊C4—22no—
16C2×#3724C2212yes—
17C2×#3722—22no—
18#63865—24no—
19#63865C2218yes—
20#63742C2214yescomplemented
21#63740C2218yescomplemented
22C2×#896—62no—
23C23×C3⋊D3D411yescharacteristic
24C22×C32×C4D411yescharacteristic
25C22×C3⋊Dic3C2311yescharacteristic
26C2×C4×C3⋊D3—22no—
27C2×C4×C3⋊D3—22no—
28C2×C4×C3⋊D3D412yes—
29C2×C4×C3⋊D3C2312yes—
30C22×C3×Dic3—22no—
31C22×C3×Dic3—22no—
32C2×#627—24no—
33C2×#627—24no—
34C2×#627—22no—
35C2×#627C2314yes—
36C2×#622—22no—
37C2×#622D414yes—
38C2×#622C2312yes—
39C2×#622C2312yes—
40#3788—28no—
41#3776—28no—
42C3×Dic3⋊C4—28no—
43#3724—22no—
44#3724C2314yes—
45#3722—28no—
46C2×#470—91nomaximal, Sylow
47C22×C4×D3—62no—
48C22×Dic6—62no—
49C2×C3×C4⋊C4—62no—
50C2×(C2×D3)⋊C4—62no—
51C2×(C2×D3)⋊C4—62no—
52C2×Dic3⋊C4—22no—
53C2×Dic3⋊C4—62no—
54#896—68no—
55#896—68no—
56C23×C32C2×D411yescharacteristic
57C22×C3⋊D3—24no—
58C22×C3⋊D3—22no—
59C22×C3⋊D3C2×D412yes—
60C2×C32×C4—22no—
61C2×C32×C4C2×D412yes—
62C2×C3⋊Dic3C2×D411yescharacteristic
63C2×C3⋊Dic3C2×D412yes—
64C2×C3⋊Dic3#4112yes—
65C2×C3⋊Dic3C2411yescharacteristic
66C4×C3⋊D3—24no—
67C4×C3⋊D3—22no—
68C4×C3⋊D3—22no—
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—
84C23×D3—62no—
85C22×C3×C4—22no—
86C22×C3×C4—62no—
87C22×C3×C4—62no—
88C22×Dic3—22no—
89C22×Dic3—22no—
90C22×Dic3—62no—
91C2×C4×D3—64no—
92C2×C4×D3—64no—
93C2×C4×D3—124no—
94C2×C4×D3—124no—
95C2×Dic6—64no—
96C2×Dic6—64no—
97C2×Dic6—124no—
98C2×Dic6—124no—
99C3×C4⋊C4—68no—
100(C2×D3)⋊C4—68no—
101(C2×D3)⋊C4—68no—
102Dic3⋊C4—28no—
103Dic3⋊C4—64no—
104Dic3⋊C4—64no—
105C22×C32#12112yes—
106C22×C32#13714yes—
107C22×C32C22×D411yescharacteristic
108C2×C3⋊D3—24no—
109C2×C3⋊D3—22no—
110C2×C3⋊D3—44no—
111C32×C4—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—62no—
128C2×C4⋊C4—92no—
129C2×C22⋊C4—182no—
130#106—94no—
131#103—98no—
132C23×C3—22no—
133C22×D3—64no—
134C22×D3—68no—
135C22×D3—124no—
136C22×D3—124no—
137C2×C3×C4—24no—
138C2×C3×C4—44no—
139C2×C3×C4—64no—
140C2×C3×C4—64no—
141C2×C3×C4—124no—
142C2×C3×C4—124no—
143C2×Dic3—24no—
144C2×Dic3—24no—
145C2×Dic3—44no—
146C2×Dic3—44no—
147C2×Dic3—62no—
148C2×Dic3—64no—
149C2×Dic3—64no—
150C2×Dic3—62no—
151C4×D3—124no—
152C4×D3—128no—
153C4×D3—124no—
154Dic6—124no—
155Dic6—124no—
156Dic6—128no—
157C2×C32#47014yescomplemented
158C2×C32C2×#12111yescharacteristic
159C2×C32C2×#13712yes—
160C3⋊D3—42no—
161C24—91no—
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—182no—
172C22×C4—182no—
173C22×C4GO+(4,𝔽2)11yescharacteristic
174Q16—188no—
175M16—188no—
176C2×C8—92no—
177C2×C8—94no—
178C2×C8—92no—
179C2×C8—182no—
180C4⋊C4—68no—
181C4⋊C4—94no—
182C4⋊C4—182no—
183C22⋊C4—188no—
184C22×C3—22no—
185C22×C3—24no—
186C22×C3—24no—
187C22×C3—24no—
188C2×D3—68no—
189C2×D3—124no—
190C2×D3—124no—
191C2×D3—1216no—
192C3×C4—44no—
193C3×C4—124no—
194C3×C4—124no—
195Dic3—44no—
196Dic3—44no—
197Dic3—64no—
198Dic3—62no—
199Dic3—62no—
200C32C2×#47011yescharacteristic, complemented, Sylow
201C23—92no—
202C23—184no—
203C23—182no—
204C23C2×GO+(4,𝔽2)11yescharacteristic
205Q8—184no—
206Q8—184no—
207Q8—364no—
208C2×C4—22no—
209C2×C4—64no—
210C2×C4—64no—
211C2×C4—91no—
212C2×C4—91no—
213C2×C4—92no—
214C2×C4—92no—
215C2×C4—124no—
216C2×C4—124no—
217C2×C4—182no—
218C2×C4—182no—
219C2×C4—184no—
220C2×C4C2×GO+(4,𝔽2)12yes—
221C8—94no—
222C8—182no—
223C2×C3—22no—
224C2×C3—22no—
225C2×C3—28no—
226C2×C3—22no—
227D3—128no—
228C22—184no—
229C22—182no—
230C22—364no—
231C22#6422614yes—
232C22#6424212yes—
233C22C22×GO+(4,𝔽2)11yescharacteristic
234C4—22no—
235C4—91no—
236C4—91no—
237C4—92no—
238C4—124no—
239C4—124no—
240C3—22no—
241C2—362no—
242C2#1059344914yesdirect product factor
243C2C2×#6422612yes—
244C2C2×#6424211yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#470
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3776C2semidirect
4. C2×#63742C2semidirect
5. C2×#63740C2semidirect
6. #10593449C2direct (N × H)
14. C2×#3776C22semidirect
20. #63742C22semidirect
21. #63740C22semidirect
157. C2×C32#470semidirect
200. C32C2×#470semidirect
242. C2#10593449direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37882
C22×#37762
C2×#638652
C2×#637422
C2×#637402
#105934492
C2×#4709