Finite Group Databasebeta

← #11773758

Subgroups — #11773758

Order 1152.

594 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 90 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×#64135C211yesmaximal, characteristic
2#10593795C212yesmaximal, complemented
3#10590222C212yesmaximal
4#10590202C212yesmaximal, complemented
5C23×C32×C4C411yescharacteristic
6C2×#3757C411yescharacteristic
7C2×#3757C2211yescharacteristic
8#64135—22no—
9#64135—22no—
10C2×C4⋊(C3⋊Dic3)C411yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×C4×C3⋊Dic3C411yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22⋊#622C2214yes—
15C4⋊#622—22no—
16C4×#622—22no—
17C2×#926—62no—
18C24×C32C2×C411yescharacteristic
19C22×C32×C4—21no—
20C22×C32×C4—21no—
21C22×C32×C4—22no—
22C22×C32×C4C814yescomplemented
23C22×C32×C4C2×C411yescharacteristic
24C22×C32×C4C2×C411yescharacteristic
25C22×C3⋊Dic3C2×C411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C2×#622—24no—
30#3757—22no—
31#3757—22no—
32C4⋊(C3⋊Dic3)—22no—
33C4⋊(C3⋊Dic3)—22no—
34C4×C3⋊Dic3—21no—
35C4×C3⋊Dic3—21no—
36C4×C3⋊Dic3D412yes—
37C4×C3⋊Dic3D412yes—
38#1458—91nomaximal, Sylow
39C23×C3×C4—22no—
40C2×#217—62no—
41C2×#217—62no—
42#926—68no—
43#926—68no—
44C2×C4⋊Dic3—62no—
45C2×C4⋊Dic3—62no—
46C2×C4×Dic3—62no—
47C2×C4×Dic3—62no—
48C23×C32—21no—
49C23×C32—21no—
50C23×C32—41no—
51C23×C32—41no—
52C23×C32C2×C812yes—
53C23×C32C22×C411yescharacteristic
54C2×C32×C4—21no—
55C2×C32×C4—21no—
56C2×C32×C4—24no—
57C2×C32×C4—24no—
58C2×C32×C4C22⋊C411yescharacteristic
59C2×C32×C4C22⋊C411yescharacteristic
60C2×C32×C4C2×C812yes—
61C2×C32×C4C2×C812yes—
62C2×C32×C4M1612yes—
63C2×C3⋊Dic3—21no—
64C2×C3⋊Dic3—21no—
65C2×C3⋊Dic3—41no—
66C2×C3⋊Dic3—41no—
67C2×C3⋊Dic3—41no—
68C2×C3⋊Dic3—41no—
69C2×C3⋊Dic3C22⋊C412yes—
70C2×C3⋊Dic3C2×D412yes—
71#622—44no—
72C2×#117—91no—
73#431—92no—
74#324—92no—
75#323—92no—
76C24×C3—22no—
77C22×C3×C4—24no—
78C22×C3×C4—24no—
79C22×C3×C4—28no—
80C22×C3×C4—28no—
81C22×C3×C4—22no—
82C22×C3×C4—22no—
83C22×Dic3—62no—
84C22×Dic3—62no—
85C22×Dic3—62no—
86C22×Dic3—62no—
87#217—68no—
88#217—68no—
89C4⋊Dic3—68no—
90C4⋊Dic3—68no—
91C4×Dic3—64no—
92C4×Dic3—64no—
93C4×Dic3—64no—
94C4×Dic3—64no—
95C22×C32—21no—
96C22×C32—21no—
97C22×C32—22no—
98C22×C32—42no—
99C22×C32—42no—
100C22×C32—41no—
101C22×C32—41no—
102C22×C32C2×C22⋊C411yescharacteristic
103C22×C32C22×C811yescharacteristic
104C22×C32C2×M1611yescharacteristic
105C32×C4—22no—
106C32×C4C22⋊C812yes—
107C32×C4C22⋊C812yes—
108C3⋊Dic3—22no—
109C3⋊Dic3—22no—
110C3⋊Dic3—41no—
111C3⋊Dic3—41no—
112C23×C4#15711yescharacteristic
113#117—182no—
114#117—182no—
115C2×C4⋊C4—91no—
116C2×C4⋊C4—91no—
117C2×C22⋊C4—91no—
118C2×C22⋊C4—91no—
119C2×C42—91no—
120C2×C42—91no—
121C4⋊C8—182no—
122C22⋊C8—94no—
123C4×C8—182no—
124C23×C3—24no—
125C23×C3—24no—
126C23×C3—22no—
127C23×C3—24no—
128C23×C3—44no—
129C23×C3—44no—
130C2×C3×C4—24no—
131C2×C3×C4—24no—
132C2×C3×C4—216no—
133C2×C3×C4—216no—
134C2×C3×C4—24no—
135C2×C3×C4—24no—
136C2×C3×C4—24no—
137C2×C3×C4—22no—
138C2×C3×C4—22no—
139C2×Dic3—64no—
140C2×Dic3—64no—
141C2×Dic3—64no—
142C2×Dic3—64no—
143C2×Dic3—124no—
144C2×Dic3—124no—
145C2×Dic3—124no—
146C2×Dic3—124no—
147C2×C32—21no—
148C2×C32—21no—
149C2×C32—42no—
150C2×C32C2×C22⋊C811yescharacteristic
151C2×C32#41011yescharacteristic
152C2×C32#41311yescharacteristic
153C24C2×#15711yescharacteristic
154C22×C4—22no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—91no—
158C22×C4—91no—
159C22×C4—91no—
160C22×C4—91no—
161C22×C4#62214yescomplemented
162C22×C4C2×#15711yescharacteristic
163C22×C4C2×#15711yescharacteristic
164C2×C8—184no—
165C4⋊C4—182no—
166C4⋊C4—182no—
167C22⋊C4—182no—
168C22⋊C4—182no—
169C42—92no—
170C42—92no—
171C42—181no—
172C42—181no—
173C22×C3—24no—
174C22×C3—24no—
175C22×C3—28no—
176C22×C3—22no—
177C22×C3—22no—
178C22×C3—22no—
179C22×C3—48no—
180C22×C3—48no—
181C22×C3—44no—
182C22×C3—44no—
183C3×C4—28no—
184C3×C4—24no—
185C3×C4—24no—
186Dic3—124no—
187Dic3—124no—
188Dic3—124no—
189Dic3—124no—
190C32#145811yescharacteristic, complemented, Sylow
191C23—21no—
192C23—21no—
193C23—41no—
194C23—41no—
195C23C2×#62212yes—
196C23C22×#15711yescharacteristic
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—24no—
200C2×C4—24no—
201C2×C4—92no—
202C2×C4—92no—
203C2×C4—181no—
204C2×C4—181no—
205C2×C4—361no—
206C2×C4—361no—
207C2×C4—361no—
208C2×C4—361no—
209C2×C4C2×#62212yes—
210C2×C4C2×#62212yes—
211C2×C4#379212yes—
212C2×C4C22⋊#15711yescharacteristic
213C2×C4C22⋊#15711yescharacteristic
214C8—364no—
215C2×C3—24no—
216C2×C3—24no—
217C2×C3—22no—
218C2×C3—22no—
219C2×C3—22no—
220C2×C3—48no—
221C22—21no—
222C22—21no—
223C22—22no—
224C22—42no—
225C22—42no—
226C22—41no—
227C22—41no—
228C22C22×#62211yescharacteristic
229C22C2×#379211yescharacteristic
230C22C2×C22⋊#15711yescharacteristic
231C4—22no—
232C4—182no—
233C4—182no—
234C4—361no—
235C4—361no—
236C4C22⋊#62212yes—
237C4C22⋊#62212yes—
238C3—22no—
239C2—21no—
240C2—21no—
241C2—42no—
242C2#1059379211yescharacteristic
243C2#1059380811yescharacteristic
244C2C2×C22⋊#62211yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC22×C32C22×C8
FrattiniC23C22×#157
FittingC23×C32×C4C4
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC23×C4#157
hypocenterC32#1458
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #10593795C2semidirect
4. #10590202C2semidirect
22. C22×C32×C4C8semidirect
161. C22×C4#622semidirect
190. C32#1458semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
#105937952
#105902222
#105902022
#14589