Finite Group Databasebeta

← C2×#10593446 #11866810

Subgroups — C2×#10593446 #11866810

Order 1152.

834 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 834 conjugacy classes of subgroups — too many to draw. Only its 135 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
2C22×#3776C211yesmaximal, characteristic, complemented
3C2×#63865C212yesmaximal
4C2×#63743C211yesmaximal, characteristic, complemented
5C2×#63740C212yesmaximal, complemented
6#10593446C218yesmaximal, direct product factor
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#627C2212yes—
9C22×#622C2211yescharacteristic
10C22×#622C2211yescharacteristic
11C2×#3787—24no—
12C2×#3787C2214yes—
13C2×#3776—24no—
14C2×#3776C2214yescomplemented
15C2×C3×Dic3⋊C4—22no—
16C2×#3724C2212yes—
17C2×#3722—22no—
18#63865—24no—
19#63865C2218yes—
20#63743C2214yescomplemented
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#3787—28no—
41#3776—28no—
42C3×Dic3⋊C4—28no—
43#3724—22no—
44#3724C2314yes—
45#3722—28no—
46C2×#467—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—22no—
58C22×C3⋊D3—22no—
59C22×C3⋊D3Q1614yescomplemented
60C22×C3⋊D3C2×D412yes—
61C2×C32×C4—22no—
62C2×C32×C4C2×D412yes—
63C2×C3⋊Dic3C2×D411yescharacteristic
64C2×C3⋊Dic3C2×D412yes—
65C2×C3⋊Dic3#4112yes—
66C2×C3⋊Dic3C2411yescharacteristic
67C4×C3⋊D3—24no—
68C4×C3⋊D3—22no—
69C4×C3⋊D3—22no—
70C2×C3×Dic3—24no—
71C2×C3×Dic3—24no—
72C2×C3×Dic3—44no—
73C2×C3×Dic3—44no—
74#627—24no—
75#627—24no—
76#627—44no—
77#622—22no—
78#622C2×D414yes—
79C22×Q16—91no—
80C23×C8—91no—
81C2×C22⋊Q8—92no—
82#467—98no—
83C2×#107—91no—
84C2×#103—92no—
85C23×D3—62no—
86C22×C3×C4—22no—
87C22×C3×C4—62no—
88C22×C3×C4—62no—
89C22×Dic3—22no—
90C22×Dic3—22no—
91C22×Dic3—62no—
92C2×C4×D3—64no—
93C2×C4×D3—64no—
94C2×C4×D3—124no—
95C2×C4×D3—124no—
96C2×Dic6—64no—
97C2×Dic6—64no—
98C2×Dic6—124no—
99C2×Dic6—124no—
100C3×C4⋊C4—68no—
101(C2×D3)⋊C4—68no—
102(C2×D3)⋊C4—68no—
103Dic3⋊C4—28no—
104Dic3⋊C4—64no—
105Dic3⋊C4—64no—
106C22×C32#12112yes—
107C22×C32C2×Q1612yes—
108C22×C32#13512yes—
109C22×C32C22×D411yescharacteristic
110C2×C3⋊D3—22no—
111C2×C3⋊D3—22no—
112C2×C3⋊D3—28no—
113C2×C3⋊D3C2×Q1614yescomplemented
114C32×C4—22no—
115C3⋊Dic3#12112yes—
116C3⋊Dic3C22×D411yescharacteristic
117C3⋊Dic3C2×#4111yescharacteristic
118C3×Dic3—44no—
119C3×Dic3—44no—
120C22×Q8—92no—
121C23×C4—91no—
122C2×Q16—94no—
123C2×Q16—184no—
124C22×C8—91no—
125C22×C8—94no—
126C22×C8—91no—
127C22×C8—184no—
128C22⋊Q8—98no—
129C22⋊Q8—184no—
130C2×C4⋊C4—62no—
131C2×C4⋊C4—92no—
132C2×C22⋊C4—182no—
133#107—94no—
134#103—98no—
135C23×C3—22no—
136C22×D3—68no—
137C22×D3—64no—
138C22×D3—124no—
139C22×D3—124no—
140C2×C3×C4—24no—
141C2×C3×C4—44no—
142C2×C3×C4—64no—
143C2×C3×C4—64no—
144C2×C3×C4—124no—
145C2×C3×C4—124no—
146C2×Dic3—24no—
147C2×Dic3—24no—
148C2×Dic3—44no—
149C2×Dic3—44no—
150C2×Dic3—62no—
151C2×Dic3—64no—
152C2×Dic3—64no—
153C2×Dic3—62no—
154C4×D3—124no—
155C4×D3—128no—
156C4×D3—124no—
157Dic6—124no—
158Dic6—124no—
159Dic6—128no—
160C2×C32#46714yescomplemented
161C2×C32C2×#12111yescharacteristic
162C2×C32C22×Q1611yescharacteristic
163C2×C32C2×#13511yescharacteristic
164C3⋊D3—24no—
165C24—91no—
166C2×Q8—94no—
167C2×Q8—182no—
168C2×Q8—184no—
169C2×Q8—184no—
170C22×C4—62no—
171C22×C4—62no—
172C22×C4—91no—
173C22×C4—92no—
174C22×C4—92no—
175C22×C4—182no—
176C22×C4—182no—
177C22×C4GO+(4,𝔽2)11yescharacteristic
178Q16—188no—
179C2×C8—92no—
180C2×C8—94no—
181C2×C8—92no—
182C2×C8—188no—
183C2×C8—182no—
184C4⋊C4—68no—
185C4⋊C4—94no—
186C4⋊C4—182no—
187C22⋊C4—188no—
188C22×C3—22no—
189C22×C3—24no—
190C22×C3—24no—
191C22×C3—24no—
192C2×D3—68no—
193C2×D3—124no—
194C2×D3—124no—
195C2×D3—1216no—
196C3×C4—44no—
197C3×C4—124no—
198C3×C4—124no—
199Dic3—44no—
200Dic3—44no—
201Dic3—64no—
202Dic3—62no—
203Dic3—62no—
204C32C2×#46711yescharacteristic, complemented, Sylow
205C23—92no—
206C23—94no—
207C23—182no—
208C23—182no—
209C23C2×GO+(4,𝔽2)11yescharacteristic
210Q8—184no—
211Q8—184no—
212Q8—364no—
213C2×C4—22no—
214C2×C4—64no—
215C2×C4—64no—
216C2×C4—91no—
217C2×C4—91no—
218C2×C4—92no—
219C2×C4—92no—
220C2×C4—124no—
221C2×C4—124no—
222C2×C4—182no—
223C2×C4—182no—
224C2×C4—184no—
225C2×C4C2×GO+(4,𝔽2)12yes—
226C8—94no—
227C8—182no—
228C2×C3—22no—
229C2×C3—22no—
230C2×C3—28no—
231C2×C3—22no—
232D3—128no—
233C22—94no—
234C22—182no—
235C22—188no—
236C22—182no—
237C22#6422312yes—
238C22#6422812yes—
239C22#6424212yes—
240C22C22×GO+(4,𝔽2)11yescharacteristic
241C4—22no—
242C4—91no—
243C4—91no—
244C4—92no—
245C4—124no—
246C4—124no—
247C3—22no—
248C2—184no—
249C2#1059344614yesdirect product factor
250C2C2×#6422311yescharacteristic
251C2C2×#6422811yescharacteristic
252C2C2×#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×#467
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×#63743C2semidirect
5. C2×#63740C2semidirect
6. #10593446C2direct (N × H)
14. C2×#3776C22semidirect
20. #63743C22semidirect
21. #63740C22semidirect
59. C22×C3⋊D3Q16semidirect
113. C2×C3⋊D3C2×Q16semidirect
160. C2×C32#467semidirect
204. C32C2×#467semidirect
249. C2#10593446direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37872
C22×#37762
C2×#638652
C2×#637432
C2×#637402
#105934462
C2×#4679