Finite Group Databasebeta

← #11899658

Subgroups — #11899658

Order 1152.

630 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 107 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×#63822C212yesmaximal, complemented
2C2×#63773C211yesmaximal, characteristic, complemented
3#10593336C214yesmaximal, complemented
4#10593334C214yesmaximal, complemented
5#10593333C214yesmaximal, complemented
6C2×C3×#235—22no—
7C22×C3⋊(C3⋊C8)C2211yescharacteristic
8C2×#3718C2212yescomplemented
9C2×#3715—22no—
10#63822—22no—
11#63822—22no—
12#63822C2214yes—
13#63822C2214yescomplemented
14C2×#3713C2212yescomplemented
15#63773C2214yescomplemented
16C2×#3708C2212yescomplemented
17#63736C2214yescomplemented
18#63735C2218yescomplemented
19#63734C2214yescomplemented
20C2×#950—62no—
21C22×C32×C4D411yescharacteristic
22C2×C3×#67—42no—
23C3×#235—24no—
24C3×#235—24no—
25C3×#235—42no—
26C3×#235—42no—
27C2×C3×D12—22no—
28C2×C3×C4×D3—42no—
29C2×C3×Dic6—22no—
30C2×C3⋊(C3⋊C8)D411yescharacteristic
31C2×C3⋊(C3⋊C8)D412yes—
32C2×C3⋊(C3⋊C8)C2311yescharacteristic
33C2×C3⋊(C3⋊C8)C2312yes—
34#3718—22no—
35#3718C2314yes—
36#3715—24no—
37#3715—24no—
38#3713—22no—
39#3713C2314yes—
40#3708C2314yes—
41#3414—91nomaximal, Sylow
42C2×C3×#41—62no—
43C2×#235—22no—
44#950—64no—
45#950—64no—
46#950—64no—
47#950—64no—
48C2×#216—62no—
49C2×#215—62no—
50C2×#214—62no—
51C2×#213—62no—
52C22×C3⋊C8—62no—
53C23×C32D811yescharacteristic
54C22×C3×D3—42no—
55C2×C32×C4D812yes—
56C2×C32×C4D811yescharacteristic
57C2×C32×C4C2×D412yes—
58C2×C32×C4C2×D411yescharacteristic
59C3×#67—44no—
60C3×#67—44no—
61C2×C3×Dic3—42no—
62C3×D12—24no—
63C3×D12—42no—
64C3×C4×D3—44no—
65C3×C4×D3—44no—
66C3×Dic6—24no—
67C3×Dic6—42no—
68C3⋊(C3⋊C8)C2×D412yes—
69C3⋊(C3⋊C8)C2×D411yescharacteristic
70C3⋊(C3⋊C8)C2411yescharacteristic
71C2×#135—92no—
72#510—94no—
73#509—94no—
74#508—94no—
75C2×M32—91no—
76C3×#41—64no—
77C3×#41—64no—
78C3×#41—122no—
79C3×#41—122no—
80C2×C3×Q8—62no—
81C2×C3×D4—62no—
82C2×C3×D4—122no—
83C22×C3×C4—22no—
84C22×C3×C4—122no—
85C2×#67—42no—
86#235—24no—
87#235—24no—
88#235—42no—
89#235—42no—
90C2×D12—22no—
91C2×C4×D3—42no—
92C2×Dic6—22no—
93#216—64no—
94#216—64no—
95#215—64no—
96#215—64no—
97#214—64no—
98#214—64no—
99#213—64no—
100#213—64no—
101C2×C3⋊C8—62no—
102C2×C3⋊C8—62no—
103C2×C3⋊C8—62no—
104C2×C3⋊C8—62no—
105C2×C3⋊C8—62no—
106C2×C3⋊C8—62no—
107C22×C32—41no—
108C22×C32C2×D812yes—
109C22×C32C2×D811yescharacteristic
110C2×C3×D3—44no—
111C2×C3×D3—84no—
112C32×C4C2×D812yes—
113C32×C4C2×D811yescharacteristic
114C32×C4C22×D411yescharacteristic
115C3×Dic3—44no—
116C2×#41—62no—
117#135—94no—
118#135—94no—
119#135—182no—
120#135—182no—
121C2×Q16—92no—
122C2×SD16—182no—
123C2×D8—92no—
124C22×C8—91no—
125Q32—94no—
126SD32—98no—
127D16—94no—
128M32—94no—
129C2×C16—92no—
130C23×C3—22no—
131C23×C3—122no—
132C22×D3—42no—
133C3×Q8—64no—
134C3×Q8—122no—
135C3×D4—64no—
136C3×D4—122no—
137C3×D4—124no—
138C3×D4—124no—
139C2×C3×C4—22no—
140C2×C3×C4—22no—
141C2×C3×C4—22no—
142C2×C3×C4—22no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×C3×C4—124no—
146C2×C3×C4—124no—
147C2×C3×C4—122no—
148#67—44no—
149#67—44no—
150C2×Dic3—42no—
151D12—24no—
152D12—42no—
153C4×D3—44no—
154C4×D3—44no—
155Dic6—24no—
156Dic6—42no—
157C3⋊C8—62no—
158C3⋊C8—62no—
159C3⋊C8—62no—
160C3⋊C8—62no—
161C2×C32—22no—
162C2×C32—21no—
163C2×C32C22×D811yescharacteristic
164C3×D3—84no—
165#41—64no—
166#41—64no—
167#41—122no—
168#41—122no—
169C2×Q8—62no—
170C2×D4—62no—
171C2×D4—122no—
172C22×C4—122no—
173C22×C4GO+(4,𝔽2)11yescharacteristic
174Q16—94no—
175Q16—182no—
176SD16—184no—
177SD16—184no—
178D8—94no—
179D8—182no—
180C2×C8—91no—
181C2×C8—92no—
182C2×C8—92no—
183C2×C8—91no—
184C16—94no—
185C22×C3—22no—
186C22×C3—22no—
187C22×C3—22no—
188C22×C3—44no—
189C22×C3—124no—
190C22×C3—244no—
191C2×D3—44no—
192C2×D3—84no—
193C3×C4—22no—
194C3×C4—22no—
195C3×C4—22no—
196C3×C4—22no—
197C3×C4—124no—
198Dic3—44no—
199C32#341411yescharacteristic, complemented, Sylow
200C23—122no—
201C23#377411yescharacteristic
202Q8—64no—
203Q8—122no—
204D4—64no—
205D4—124no—
206D4—124no—
207D4—122no—
208C2×C4—122no—
209C2×C4—124no—
210C2×C4—124no—
211C2×C4#377411yescharacteristic
212C2×C4#377412yes—
213C2×C4C2×GO+(4,𝔽2)12yes—
214C2×C4C2×GO+(4,𝔽2)11yescharacteristic
215C8—91no—
216C8—92no—
217C8—91no—
218C2×C3—24no—
219C2×C3—22no—
220C2×C3—42no—
221C2×C3—42no—
222C2×C3—244no—
223D3—84no—
224C22—41no—
225C22—124no—
226C22—244no—
227C22C2×#377412yes—
228C22C2×#377411yescharacteristic
229C4—124no—
230C4C2×#377412yes—
231C4C2×#377411yescharacteristic
232C4C22×GO+(4,𝔽2)11yescharacteristic
233C3—22no—
234C2—22no—
235C2—21no—
236C2—244no—
237C2C22×#377411yescharacteristic
subgroupG/H
centerC4C2×#3774
commutator, cosocleC3⋊(C3⋊C8)C24
FrattiniC4C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32C22×D8
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#3414
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#63822C2semidirect
2. C2×#63773C2semidirect
3. #10593336C2semidirect
4. #10593334C2semidirect
5. #10593333C2semidirect
8. C2×#3718C22semidirect
13. #63822C22semidirect
14. C2×#3713C22semidirect
15. #63773C22semidirect
16. C2×#3708C22semidirect
17. #63736C22semidirect
18. #63735C22semidirect
19. #63734C22semidirect
199. C32#3414semidirect

Maximal subgroups

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

subgroupindex
C2×#638222
C2×#637732
#105933362
#105933342
#105933332
#34149