Finite Group Databasebeta

← #11790561

Subgroups — #11790561

Order 1152.

822 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 110 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×#64102C211yesmaximal, characteristic
2C2×#63778C214yesmaximal, complemented
3C2×C4⋊#622C211yesmaximal, characteristic, complemented
4C2×C4×#622C211yesmaximal, characteristic, complemented
5C22×C4⋊(C3⋊D3)C411yescharacteristic
6C22×C4×C3⋊D3C2212yes—
7C22×#622C2212yes—
8C22×#622C2212yes—
9C2×C32×C4⋊C4C411yescharacteristic
10C2×#3752C412yes—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64102—22no—
13#64102—22no—
14#63778—28no—
15C4⋊#622—22no—
16C4×#622—22no—
17C2×#893—62no—
18C23×C3⋊D3C2×C412yes—
19C22×C32×C4C2×C412yes—
20C22×C32×C4C2×C411yescharacteristic
21C22×C3⋊Dic3C2×C411yescharacteristic
22C22×C3⋊Dic3C2311yescharacteristic
23C2×C4⋊(C3⋊D3)—22no—
24C2×C4⋊(C3⋊D3)—22no—
25C2×C4⋊(C3⋊D3)C814yescomplemented
26C2×C4×C3⋊D3—22no—
27C2×C4×C3⋊D3—22no—
28C2×C4×C3⋊D3—24no—
29C2×C4×C3⋊D3—24no—
30C2×#622—22no—
31C2×#622—22no—
32C2×#622—22no—
33C2×#622—24no—
34C2×#622D414yescomplemented
35C32×C4⋊C4—22no—
36#3752—24no—
37C4×C3⋊Dic3D412yes—
38C4×C3⋊Dic3D412yes—
39#1954—91nomaximal, Sylow
40C22×D12—62no—
41C22×C4×D3—64no—
42C2×C3×C4⋊C4—22no—
43C2×(C2×D3)⋊C4—64no—
44C2×C4×Dic3—62no—
45#893—68no—
46#893—68no—
47C23×C32C22×C411yescharacteristic
48C22×C3⋊D3—22no—
49C22×C3⋊D3—22no—
50C22×C3⋊D3—24no—
51C22×C3⋊D3—24no—
52C22×C3⋊D3C2×C814yes—
53C2×C32×C4—22no—
54C2×C32×C4—24no—
55C2×C32×C4C22⋊C412yes—
56C2×C32×C4C2×C812yes—
57C2×C32×C4M1612yes—
58C2×C3⋊Dic3—22no—
59C2×C3⋊Dic3C22⋊C412yes—
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3C2×D412yes—
62C2×C3⋊Dic3C2×D411yescharacteristic
63C2×C3⋊Dic3#4112yes—
64C4⋊(C3⋊D3)—28no—
65C4×C3⋊D3—44no—
66C4×C3⋊D3—42no—
67C4×C3⋊D3—42no—
68#622—24no—
69#622—42no—
70C2×C4×D4—91no—
71C2×C4⋊C8—91no—
72C2×C22⋊C8—94no—
73C2×C4×C8—91no—
74C23×D3—64no—
75C22×C3×C4—22no—
76C22×C3×C4—24no—
77C22×Dic3—62no—
78C22×Dic3—62no—
79C2×D12—68no—
80C2×D12—68no—
81C2×D12—68no—
82C2×C4×D3—68no—
83C2×C4×D3—68no—
84C2×C4×D3—128no—
85C2×C4×D3—128no—
86C3×C4⋊C4—28no—
87(C2×D3)⋊C4—616no—
88C4×Dic3—64no—
89C4×Dic3—64no—
90C22×C32C2×C22⋊C411yescharacteristic
91C22×C32C4×D412yes—
92C22×C32C22×C811yescharacteristic
93C22×C32C2×M1611yescharacteristic
94C22×C32#13112yes—
95C2×C3⋊D3—24no—
96C2×C3⋊D3—28no—
97C2×C3⋊D3—42no—
98C2×C3⋊D3—42no—
99C2×C3⋊D3—44no—
100C32×C4—42no—
101C32×C4C22⋊C814yescomplemented
102C3⋊Dic3—22no—
103C3⋊Dic3#12112yes—
104C3⋊Dic3#12411yescharacteristic
105C3⋊Dic3#12711yescharacteristic
106C22×D4—91no—
107C23×C4—92no—
108C22×C8—92no—
109C22×C8—92no—
110C4×D4—182no—
111C4×D4—182no—
112C2×C4⋊C4#15711yescharacteristic
113C2×C22⋊C4—92no—
114C2×C42—91no—
115C4⋊C8—182no—
116C22⋊C8—188no—
117C4×C8—182no—
118C23×C3—22no—
119C22×D3—68no—
120C22×D3—68no—
121C22×D3—68no—
122C22×D3—128no—
123C22×D3—128no—
124C2×C3×C4—28no—
125C2×C3×C4—24no—
126C2×C3×C4—24no—
127C2×C3×C4—24no—
128C2×C3×C4—48no—
129C2×Dic3—62no—
130C2×Dic3—62no—
131C2×Dic3—64no—
132C2×Dic3—64no—
133C2×Dic3—64no—
134C2×Dic3—124no—
135D12—632no—
136C4×D3—1216no—
137C4×D3—128no—
138C4×D3—128no—
139C2×C32#39011yescharacteristic
140C2×C32C2×C22⋊C811yescharacteristic
141C2×C32#40811yescharacteristic
142C2×C32C8×D412yes—
143C2×C32#43612yes—
144C3⋊D3—44no—
145C24—92no—
146C2×D4—94no—
147C2×D4—182no—
148C2×D4—182no—
149C22×C4—91no—
150C22×C4—91no—
151C22×C4—184no—
152C22×C4—182no—
153C22×C4—182no—
154C22×C4—184no—
155C22×C4C2×#15712yes—
156C22×C4C2×#15711yescharacteristic
157C2×C8—94no—
158C2×C8—182no—
159C2×C8—182no—
160C2×C8—184no—
161C2×C8—182no—
162C4⋊C4—22no—
163C22⋊C4—184no—
164C42—92no—
165C42—92no—
166C22×C3—22no—
167C22×C3—22no—
168C22×C3—24no—
169C22×C3—24no—
170C22×C3—22no—
171C2×D3—616no—
172C2×D3—1216no—
173C2×D3—128no—
174C2×D3—128no—
175C2×D3—1216no—
176C3×C4—28no—
177C3×C4—48no—
178Dic3—64no—
179Dic3—62no—
180Dic3—62no—
181Dic3—124no—
182C32#195411yescharacteristic, complemented, Sylow
183C23—94no—
184C23—182no—
185C23—184no—
186C23—184no—
187C23—182no—
188C23C22×#15711yescharacteristic
189D4—188no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—92no—
193C2×C4—92no—
194C2×C4—91no—
195C2×C4—91no—
196C2×C4—92no—
197C2×C4—182no—
198C2×C4—364no—
199C2×C4—362no—
200C2×C4—362no—
201C2×C4#378712yes—
202C2×C4#378812yes—
203C2×C4C22⋊#15712yes—
204C8—184no—
205C8—362no—
206C2×C3—22no—
207C2×C3—22no—
208C2×C3—22no—
209C2×C3—24no—
210C2×C3—24no—
211D3—1216no—
212C22—184no—
213C22—188no—
214C22—362no—
215C22—362no—
216C22—364no—
217C22C2×#378711yescharacteristic
218C22C2×#378811yescharacteristic
219C22D4×#15712yes—
220C22#6428912yes—
221C22C2×C22⋊#15711yescharacteristic
222C4—42no—
223C4—92no—
224C4—91no—
225C4—91no—
226C4—182no—
227C4#6377814yescomplemented
228C3—22no—
229C2—364no—
230C2#1059374912yes—
231C2#1059375212yes—
232C2C2×#6377811yescharacteristic
233C2#1059382711yescharacteristic
234C2#1059383411yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C22×C8
FittingC2×C32×C4⋊C4C4
socleC23×C32C22×C4
prime radicalC22×C4⋊(C3⋊D3)C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1954
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63778C2semidirect
3. C2×C4⋊#622C2semidirect
4. C2×C4×#622C2semidirect
25. C2×C4⋊(C3⋊D3)C8semidirect
34. C2×#622D4semidirect
101. C32×C4C22⋊C8semidirect
182. C32#1954semidirect
227. C4#63778semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#637782
C2×C4⋊#6222
C2×C4×#6222
#19549