Finite Group Databasebeta

← C2×#10593527 #11866809

Subgroups — C2×#10593527 #11866809

Order 1152.

834 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 834 conjugacy classes of subgroups — too many to draw. Only its 143 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×#3776C211yesmaximal, characteristic, complemented
3C2×#63982C212yesmaximal
4#10593527C218yesmaximal, direct product factor
5C2×#63743C211yesmaximal, characteristic, complemented
6C2×#63740C212yesmaximal, complemented
7C23×C3⋊Dic3C2211yescharacteristic
8C22×#627C2212yes—
9C22×#622—24no—
10C22×#622C2211yescharacteristic
11C22×#622C2214yes—
12C22×#622C2211yescharacteristic
13C2×#3776—24no—
14C2×#3776C2214yescomplemented
15C2×C3×#217—22no—
16#63982—24no—
17#63982C2218yes—
18C2×#3724C2212yes—
19C2×Dic3⋊Dic3—22no—
20#63743C2214yescomplemented
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—
36C2×#622—22no—
37C2×#622—28no—
38C2×#622D414yes—
39C2×#622C2312yes—
40C2×#622C2312yes—
41#3776—28no—
42C3×#217—28no—
43#3724—22no—
44#3724C2314yes—
45Dic3⋊Dic3—28no—
46C2×#467—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—22no—
57C23×C32—22no—
58C23×C32Q1614yescomplemented
59C23×C32C2×D412yes—
60C23×C32C2×D411yescharacteristic
61C2×C3⋊Dic3—22no—
62C2×C3⋊Dic3—24no—
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3C2×D412yes—
66C2×C3⋊Dic3C2×D411yescharacteristic
67C2×C3⋊Dic3C2×D412yes—
68C2×C3⋊Dic3#4112yes—
69C2×C3⋊Dic3C2411yescharacteristic
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—
85C24×C3—22no—
86C22×C3×C4—62no—
87C22×C3×C4—62no—
88C22×Dic3—22no—
89C22×Dic3—22no—
90C22×Dic3—62no—
91C22×Dic3—64no—
92C22×Dic3—64no—
93C22×Dic3—62no—
94C22×Dic3—124no—
95C22×Dic3—124no—
96C2×Dic6—64no—
97C2×Dic6—64no—
98C2×Dic6—124no—
99C2×Dic6—124no—
100C3×C22⋊C4—68no—
101#217—28no—
102C4⋊Dic3—68no—
103Dic3⋊C4—64no—
104Dic3⋊C4—68no—
105Dic3⋊C4—64no—
106C22×C32—22no—
107C22×C32—22no—
108C22×C32—28no—
109C22×C32#12112yes—
110C22×C32C2×Q1612yes—
111C22×C32C2×Q1614yescomplemented
112C22×C32#13512yes—
113C22×C32C22×D411yescharacteristic
114C3⋊Dic3—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—91no—
126C22×C8—94no—
127C22×C8—184no—
128C22⋊Q8—98no—
129C22⋊Q8—184no—
130C2×C4⋊C4—92no—
131C2×C4⋊C4—182no—
132C2×C22⋊C4—62no—
133#107—94no—
134#103—98no—
135C23×C3—24no—
136C23×C3—22no—
137C23×C3—28no—
138C23×C3—44no—
139C23×C3—44no—
140C2×C3×C4—64no—
141C2×C3×C4—64no—
142C2×C3×C4—124no—
143C2×C3×C4—124no—
144C2×Dic3—24no—
145C2×Dic3—24no—
146C2×Dic3—44no—
147C2×Dic3—44no—
148C2×Dic3—62no—
149C2×Dic3—64no—
150C2×Dic3—64no—
151C2×Dic3—62no—
152C2×Dic3—64no—
153C2×Dic3—124no—
154C2×Dic3—128no—
155C2×Dic3—124no—
156C2×Dic3—124no—
157Dic6—124no—
158Dic6—124no—
159Dic6—128no—
160C2×C32—24no—
161C2×C32#46714yescomplemented
162C2×C32C2×#12111yescharacteristic
163C2×C32C22×Q1611yescharacteristic
164C2×C32C2×#13511yescharacteristic
165C24GO+(4,𝔽2)11yescharacteristic
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—91no—
176C22×C4—182no—
177C22×C4—182no—
178Q16—188no—
179C2×C8—92no—
180C2×C8—94no—
181C2×C8—92no—
182C2×C8—188no—
183C2×C8—182no—
184C4⋊C4—94no—
185C4⋊C4—182no—
186C4⋊C4—188no—
187C22⋊C4—68no—
188C22×C3—22no—
189C22×C3—24no—
190C22×C3—24no—
191C22×C3—28no—
192C22×C3—24no—
193C22×C3—44no—
194C22×C3—44no—
195C22×C3—416no—
196C3×C4—124no—
197C3×C4—124no—
198Dic3—44no—
199Dic3—44no—
200Dic3—64no—
201Dic3—62no—
202Dic3—62no—
203Dic3—124no—
204C32C2×#46711yescharacteristic, complemented, Sylow
205C23—22no—
206C23—22no—
207C23#377614yescomplemented
208C23C2×GO+(4,𝔽2)12yes—
209C23C2×GO+(4,𝔽2)11yescharacteristic
210Q8—184no—
211Q8—184no—
212Q8—364no—
213C2×C4—64no—
214C2×C4—64no—
215C2×C4—91no—
216C2×C4—91no—
217C2×C4—92no—
218C2×C4—92no—
219C2×C4—92no—
220C2×C4—124no—
221C2×C4—124no—
222C2×C4—182no—
223C2×C4—182no—
224C2×C4—184no—
225C2×C4—182no—
226C8—94no—
227C8—182no—
228C2×C3—22no—
229C2×C3—22no—
230C2×C3—22no—
231C2×C3—28no—
232C2×C3—48no—
233C22—22no—
234C22—22no—
235C22—28no—
236C22#6423712yes—
237C22C2×#377612yes—
238C22C2×#377614yescomplemented
239C22#6424212yes—
240C22C22×GO+(4,𝔽2)11yescharacteristic
241C4—91no—
242C4—91no—
243C4—92no—
244C4—124no—
245C4—124no—
246C4—182no—
247C3—22no—
248C2—24no—
249C2#1059352714yesdirect product factor
250C2C2×#6423711yescharacteristic
251C2C22×#377611yescharacteristic
252C2C2×#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×#467
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. #10593527C2direct (N × H)
5. C2×#63743C2semidirect
6. C2×#63740C2semidirect
14. C2×#3776C22semidirect
20. #63743C22semidirect
21. #63740C22semidirect
58. C23×C32Q16semidirect
111. C22×C32C2×Q16semidirect
161. C2×C32#467semidirect
204. C32C2×#467semidirect
207. C23#3776semidirect
238. C22C2×#3776semidirect
249. C2#10593527direct (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×#37762
C2×#639822
#105935272
C2×#637432
C2×#637402
C2×#4679