Finite Group Databasebeta

← #11785348

Subgroups — #11785348

Order 1152.

674 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 674 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C22×C8×C3⋊D3C211yesmaximal, characteristic
2#10593812C212yesmaximal
3C2×#63768C212yesmaximal, complemented
4#10590182C212yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×C22⋊#157—22no—
7C2×C4⋊#157C2214yes—
8C22×C32×C8C411yescharacteristic, complemented
9C22×C3⋊(C3⋊C8)C411yescharacteristic, complemented
10C2×C8×C3⋊D3—24no—
11C2×C8×C3⋊D3C411yescharacteristic, complemented
12C2×C8×C3⋊D3C411yescharacteristic, complemented
13C2×C8×C3⋊D3C2211yescharacteristic
14C2×C8×C3⋊D3C2211yescharacteristic
15#63781—22no—
16#63768—24no—
17C22×D3×C8—62no—
18C23×C3⋊D3D411yescharacteristic
19C22×#157—24no—
20C22×C32×C4C2×C411yescharacteristic
21C22×C3⋊Dic3Q811yescharacteristic
22C2×C4×C3⋊D3—22no—
23C2×C4×C3⋊D3—22no—
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C4×C3⋊D3Q811yescharacteristic
27C2×C4×C3⋊D3C2311yescharacteristic
28C22⋊#157—44no—
29C4⋊#157—24no—
30C4⋊#157—24no—
31C2×C32×C8—22no—
32C2×C32×C8C2×C411yescharacteristic
33C2×C32×C8C2×C411yescharacteristic
34C2×C3⋊(C3⋊C8)—22no—
35C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
36C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
37C8×C3⋊D3—22no—
38C8×C3⋊D3—22no—
39C8×C3⋊D3—22no—
40C8×C3⋊D3D414yes—
41#1807—91nomaximal, Sylow
42C22×C4×D3—62no—
43C22×C3×C8—22no—
44C22×C3⋊C8—62no—
45C2×D3×C8—62no—
46C2×D3×C8—62no—
47C2×D3×C8—62no—
48C2×D3×C8—62no—
49C2×D3×C8—616no—
50C23×C32C4⋊C411yescharacteristic
51C22×C3⋊D3—22no—
52C22×C3⋊D3—22no—
53C22×C3⋊D3C4⋊C411yescharacteristic
54C22×C3⋊D3SD1614yes—
55C22×C3⋊D3C2×D411yescharacteristic
56C2×#157—44no—
57C2×#157—44no—
58C2×#157—44no—
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4C4⋊C411yescharacteristic
62C2×C32×C4C22×C411yescharacteristic
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3C4⋊C411yescharacteristic
65C2×C3⋊Dic3C2×Q811yescharacteristic
66C4×C3⋊D3—22no—
67C4×C3⋊D3—21no—
68C4×C3⋊D3—21no—
69C4×C3⋊D3—22no—
70C4×C3⋊D3C2×D412yes—
71C4×C3⋊D3#4112yes—
72C32×C8—21no—
73C32×C8C22⋊C412yescomplemented
74C3⋊(C3⋊C8)—21no—
75C3⋊(C3⋊C8)C22⋊C412yescomplemented
76C23×C8—91no—
77C2×#106—92no—
78#380—92no—
79#340—92no—
80C23×D3—62no—
81C22×C3×C4—22no—
82C22×Dic3—62no—
83C2×C4×D3—62no—
84C2×C4×D3—62no—
85C2×C4×D3—62no—
86C2×C4×D3—62no—
87C2×C4×D3—68no—
88C2×C4×D3—68no—
89C2×C3×C8—28no—
90C2×C3×C8—22no—
91C2×C3×C8—22no—
92C2×C3⋊C8—62no—
93C2×C3⋊C8—62no—
94C2×C3⋊C8—68no—
95D3×C8—68no—
96D3×C8—68no—
97D3×C8—68no—
98D3×C8—68no—
99C22×C32—21no—
100C22×C32—21no—
101C22×C32#10612yescomplemented
102C22×C32C2×C4⋊C411yescharacteristic
103C2×C3⋊D3—21no—
104C2×C3⋊D3—21no—
105C2×C3⋊D3—28no—
106C2×C3⋊D3#10612yescomplemented
107C2×C3⋊D3#12112yes—
108C2×C3⋊D3C2×SD1612yes—
109C2×C3⋊D3#13512yes—
110#157—84no—
111C32×C4—21no—
112C32×C4C2×C22⋊C411yescharacteristic
113C32×C4#11711yescharacteristic
114C3⋊Dic3—21no—
115C3⋊Dic3C22⋊Q812yes—
116C23×C4—91no—
117C22×C8—91no—
118C22×C8—91no—
119C22×C8—91no—
120C22×C8—91no—
121C22×C8—91no—
122C22×C8—184no—
123C22×C8#15711yescharacteristic, complemented
124C2×C4⋊C4—94no—
125C2×C22⋊C4—182no—
126#106—184no—
127#95—182no—
128C23×C3—22no—
129C22×D3—62no—
130C22×D3—68no—
131C22×D3—62no—
132C22×D3—68no—
133C22×D3—68no—
134C2×C3×C4—24no—
135C2×C3×C4—24no—
136C2×C3×C4—22no—
137C2×C3×C4—22no—
138C2×Dic3—62no—
139C2×Dic3—62no—
140C2×Dic3—68no—
141C4×D3—64no—
142C4×D3—64no—
143C4×D3—64no—
144C4×D3—68no—
145C4×D3—68no—
146C4×D3—64no—
147C3×C8—24no—
148C3×C8—24no—
149C3⋊C8—64no—
150C3⋊C8—64no—
151C2×C32—22no—
152C2×C32#38011yescharacteristic
153C2×C32C2×#10611yescharacteristic
154C2×C32#42711yescharacteristic
155C3⋊D3—22no—
156C3⋊D3#46514yes—
157C24—91no—
158C22×C4—91no—
159C22×C4—91no—
160C22×C4—91no—
161C22×C4—91no—
162C22×C4—91no—
163C22×C4—182no—
164C22×C4—182no—
165C22×C4—184no—
166C22×C4C2×#15711yescharacteristic
167C2×C8—22no—
168C2×C8—91no—
169C2×C8—94no—
170C2×C8—91no—
171C2×C8—182no—
172C2×C8—182no—
173C2×C8—182no—
174C2×C8—182no—
175C2×C8C2×#15711yescharacteristic
176C2×C8C2×#15711yescharacteristic
177C4⋊C4—184no—
178C4⋊C4—184no—
179C22⋊C4—364no—
180C22×C3—24no—
181C22×C3—24no—
182C22×C3—24no—
183C22×C3—22no—
184C2×D3—64no—
185C2×D3—64no—
186C2×D3—64no—
187C2×D3—64no—
188C2×D3—64no—
189C2×D3—632no—
190C2×D3—64no—
191C3×C4—24no—
192C3×C4—22no—
193C3×C4—22no—
194Dic3—64no—
195Dic3—64no—
196C32#180711yescharacteristic, complemented, Sylow
197C23—91no—
198C23—94no—
199C23—91no—
200C23—182no—
201C23—182no—
202C23C4⋊#15711yescharacteristic
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—91no—
206C2×C4—92no—
207C2×C4—92no—
208C2×C4—91no—
209C2×C4—182no—
210C2×C4—182no—
211C2×C4—182no—
212C2×C4—181no—
213C2×C4—181no—
214C2×C4—364no—
215C2×C4—364no—
216C2×C4—364no—
217C2×C4C4⋊#15711yescharacteristic
218C2×C4C22×#15711yescharacteristic
219C8—21no—
220C8—92no—
221C8—181no—
222C8C22⋊#15712yescomplemented
223C2×C3—28no—
224C2×C3—22no—
225C2×C3—22no—
226C2×C3—22no—
227D3—68no—
228D3—68no—
229C22—21no—
230C22—21no—
231C22—92no—
232C22—92no—
233C22—92no—
234C22—92no—
235C22—188no—
236C22—181no—
237C22—181no—
238C22#6376812yescomplemented
239C22C2×C4⋊#15711yescharacteristic
240C4—21no—
241C4—92no—
242C4—181no—
243C4—724no—
244C4#6428611yescharacteristic
245C4C2×C22⋊#15711yescharacteristic
246C3—22no—
247C2—22no—
248C2—94no—
249C2—182no—
250C2C2×#6376811yescharacteristic
251C2#1059376811yescharacteristic
252C2#1059381211yescharacteristic
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC22×C32×C8C4
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C8#157
hypocenterC32#1807
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×#63768C2semidirect
4. #10590182C2semidirect
8. C22×C32×C8C4semidirect
9. C22×C3⋊(C3⋊C8)C4semidirect
11. C2×C8×C3⋊D3C4semidirect
12. C2×C8×C3⋊D3C4semidirect
73. C32×C8C22⋊C4semidirect
75. C3⋊(C3⋊C8)C22⋊C4semidirect
101. C22×C32#106semidirect
106. C2×C3⋊D3#106semidirect
123. C22×C8#157semidirect
196. C32#1807semidirect
222. C8C22⋊#157semidirect
238. C22#63768semidirect

Maximal subgroups

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

subgroupindex
C22×C8×C3⋊D32
#105938122
C2×#637682
#105901822
#18079