Finite Group Databasebeta

← C2×#10590021 #11796925

Subgroups — C2×#10590021 #11796925

Order 1152.

390 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#63802C211yesmaximal, characteristic
2C2×#63771C211yesmaximal, characteristic
3C2×#63544C211yesmaximal, characteristic
4#10590021C214yesmaximal, direct product factor
5C2×#3797—21no—
6C2×#3788—21no—
7C2×C8×C3⋊D3C2211yescharacteristic
8C2×C3×Dic12—21no—
9C2×#3718C412yes—
10#63802—21no—
11#63802—21no—
12#63802C412yes—
13#63802C2212yes—
14#63771—21no—
15#63771C2212yes—
16C2×C3×C3⋊C16—21no—
17#63544—21no—
18#63544C2212yes—
19C2×D3×Q16—61no—
20C2×#798—61no—
21C2×C4×C3⋊D3D411yescharacteristic
22C2×C3×Dic6—22no—
23C2×#627—41no—
24C2×#624—41no—
25#3797—22no—
26#3797—22no—
27#3797—41no—
28#3797—41no—
29C2×#622—41no—
30#3788—22no—
31#3788—41no—
32C2×C32×C8D411yescharacteristic
33C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
34C8×C3⋊D3C2×C411yescharacteristic
35C8×C3⋊D3D411yescharacteristic
36C8×C3⋊D3D411yescharacteristic
37C8×C3⋊D3C2311yescharacteristic
38C3×Dic12—22no—
39C3×Dic12—22no—
40#3718—22no—
41#3718C2×C414yes—
42C3×C3⋊C16—22no—
43C2×#362—91nomaximal, Sylow
44C2×D3×Q8—62no—
45C2×C3×Q16—61no—
46C2×#216—62no—
47D3×Q16—62no—
48D3×Q16—62no—
49D3×Q16—62no—
50D3×Q16—62no—
51C2×Dic12—21no—
52C2×D3×C8—61no—
53C2×D3×C8—61no—
54C2×C3×C16—61no—
55C2×C3⋊C16—21no—
56#798—62no—
57#798—62no—
58C22×C3⋊D3SD1611yescharacteristic
59C2×C32×C4C22⋊C411yescharacteristic
60C2×C3⋊Dic3D811yescharacteristic
61C4×C3⋊D3C22⋊C411yescharacteristic
62C4×C3⋊D3D811yescharacteristic
63C4×C3⋊D3SD1611yescharacteristic
64C4×C3⋊D3C2×D411yescharacteristic
65C2×C3×Dic3—42no—
66C3×Dic6—24no—
67C3×Dic6—42no—
68#627—42no—
69#627—42no—
70#624—42no—
71#624—42no—
72#622—42no—
73C32×C8C22⋊C411yescharacteristic
74C32×C8C2×D411yescharacteristic
75C3⋊(C3⋊C8)C22⋊C411yescharacteristic
76C3⋊(C3⋊C8)C22×C411yescharacteristic
77C22×Q16—91no—
78C2×M32—91no—
79C2×#108—91no—
80#362—94no—
81C2×C3×Q8—62no—
82D3×Q8—64no—
83D3×Q8—64no—
84D3×Q8—122no—
85D3×Q8—122no—
86C2×C4×D3—61no—
87C2×C4×D3—61no—
88C2×C4×D3—122no—
89C2×Dic6—22no—
90C2×Dic6—122no—
91C3×Q16—62no—
92C3×Q16—62no—
93C2×C3×C8—21no—
94C2×C3×C8—21no—
95#216—64no—
96#216—64no—
97C2×C3⋊C8—61no—
98C2×C3⋊C8—61no—
99Dic12—22no—
100Dic12—22no—
101D3×C8—61no—
102D3×C8—61no—
103D3×C8—61no—
104D3×C8—61no—
105D3×C8—61no—
106D3×C8—61no—
107D3×C8—61no—
108D3×C8—61no—
109C3×C16—62no—
110C3⋊C16—22no—
111C22×C32#10211yescharacteristic
112C2×C3⋊D3—22no—
113C2×C3⋊D3#10211yescharacteristic
114C2×C3⋊D3C2×SD1611yescharacteristic
115C32×C4#10211yescharacteristic
116C32×C4C2×C22⋊C411yescharacteristic
117C3⋊Dic3#10211yescharacteristic
118C3⋊Dic3C2×D811yescharacteristic
119C3×Dic3—44no—
120C22×Q8—181no—
121C2×Q16—61no—
122C2×Q16—92no—
123C2×Q16—92no—
124C2×Q16—92no—
125C2×Q16—181no—
126C2×Q16—181no—
127C2×M16—181no—
128C22×C8—91no—
129M32—92no—
130M32—181no—
131C2×C16—61no—
132#108—92no—
133#108—181no—
134C22×D3—61no—
135C22×D3—61no—
136C3×Q8—64no—
137C3×Q8—122no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—122no—
141C2×Dic3—42no—
142C2×Dic3—61no—
143C2×Dic3—61no—
144C4×D3—61no—
145C4×D3—61no—
146C4×D3—61no—
147C4×D3—61no—
148C4×D3—61no—
149C4×D3—61no—
150C4×D3—61no—
151C4×D3—61no—
152C4×D3—124no—
153C4×D3—124no—
154Dic6—24no—
155Dic6—42no—
156Dic6—124no—
157Dic6—124no—
158C3×C8—21no—
159C3×C8—21no—
160C3×C8—21no—
161C3×C8—21no—
162C3⋊C8—61no—
163C3⋊C8—61no—
164C3⋊C8—61no—
165C3⋊C8—61no—
166C2×C32#36212yescomplemented
167C2×C32C2×#10211yescharacteristic
168C3⋊D3—21no—
169C3⋊D3—21no—
170C2×Q8—62no—
171C2×Q8—182no—
172C2×Q8—182no—
173C2×Q8—361no—
174C2×Q8—361no—
175C2×Q8—361no—
176C22×C4—91no—
177C22×C4—361no—
178Q16—62no—
179Q16—62no—
180Q16—94no—
181Q16—182no—
182M16—182no—
183M16—361no—
184C2×C8—91no—
185C2×C8—91no—
186C2×C8—91no—
187C2×C8—91no—
188C2×C8—91no—
189C2×C8—361no—
190C2×C8GO+(4,𝔽2)11yescharacteristic
191C16—62no—
192C22×C3—21no—
193C22×C3—21no—
194C2×D3—61no—
195C2×D3—61no—
196C2×D3—61no—
197C2×D3—61no—
198C2×D3—64no—
199C2×D3—122no—
200C3×C4—21no—
201C3×C4—21no—
202C3×C4—21no—
203C3×C4—21no—
204C3×C4—124no—
205Dic3—44no—
206Dic3—61no—
207Dic3—61no—
208Dic3—61no—
209Dic3—61no—
210C32C2×#36211yescharacteristic, complemented, Sylow
211C23—91no—
212Q8—64no—
213Q8—122no—
214Q8—362no—
215Q8—362no—
216C2×C4—91no—
217C2×C4—91no—
218C2×C4—91no—
219C2×C4—91no—
220C2×C4—91no—
221C2×C4—122no—
222C2×C4—362no—
223C2×C4—362no—
224C2×C4D32⋊C411yescharacteristic
225C8—91no—
226C8—91no—
227C8—362no—
228C8D32⋊C411yescharacteristic
229C8C2×GO+(4,𝔽2)11yescharacteristic
230C2×C3—21no—
231C2×C3—21no—
232C2×C3—22no—
233C2×C3—22no—
234D3—62no—
235D3—62no—
236D3—121no—
237D3—121no—
238C22—91no—
239C22—91no—
240C22—182no—
241C22#6372911yescharacteristic
242C4—91no—
243C4—91no—
244C4—124no—
245C4#6372911yescharacteristic
246C4C2×D32⋊C411yescharacteristic
247C3—21no—
248C3—21no—
249C2—181no—
250C2—181no—
251C2#1059002112yesdirect product factor
252C2C2×#6372911yescharacteristic
subgroupG/H
centerC22#63729
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC8C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#102
prime radicalC22×C3⋊D3SD16
cosocleC8×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32C2×#362
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
4. #10590021C2direct (N × H)
166. C2×C32#362semidirect
210. C32C2×#362semidirect
251. C2#10590021direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638022
C2×#637712
C2×#635442
#105900212
C2×#3629