Finite Group Databasebeta

← #11795959

Subgroups — #11795959

Order 1152.

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

normal subgroups only

This group has 610 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
2C2×#63764C212yesmaximal, complemented
3C22⋊#3708C212yesmaximal, complemented
4#10590176C212yesmaximal, complemented
5C22×C4×C3⋊D3C411yescharacteristic
6C22×C32×C8C411yescharacteristic
7C22×C3⋊(C3⋊C8)C2211yescharacteristic
8C2×C8×C3⋊D3—24no—
9C2×C8×C3⋊D3C411yescharacteristic
10C2×C8×C3⋊D3C411yescharacteristic
11C2×C8×C3⋊D3C2211yescharacteristic
12C2×C8×C3⋊D3C2211yescharacteristic
13C2×#3708C2214yescomplemented
14#63764—24no—
15C22×D3×C8—62no—
16C23×C3⋊D3C811yescharacteristic
17C22×C32×C4C2×C411yescharacteristic
18C22×C3⋊Dic3C811yescharacteristic
19C2×C4×C3⋊D3—22no—
20C2×C4×C3⋊D3—22no—
21C2×C4×C3⋊D3C811yescharacteristic
22C2×C4×C3⋊D3C811yescharacteristic
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×C32×C8—22no—
26C2×C32×C8C2×C411yescharacteristic
27C2×C32×C8C2×C411yescharacteristic
28C2×C3⋊(C3⋊C8)—22no—
29C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
30C2×C3⋊(C3⋊C8)C2311yescharacteristic
31C8×C3⋊D3—22no—
32C8×C3⋊D3—22no—
33C8×C3⋊D3—22no—
34C8×C3⋊D3D414yes—
35#3708—24no—
36C2×C22⋊C16—91nomaximal, Sylow
37C22×C4×D3—62no—
38C22×C3×C8—22no—
39C22×C3⋊C8—62no—
40C2×D3×C8—62no—
41C2×D3×C8—62no—
42C2×D3×C8—62no—
43C2×D3×C8—62no—
44C2×D3×C8—616no—
45C23×C32C2×C811yescharacteristic
46C22×C3⋊D3—22no—
47C22×C3⋊D3—22no—
48C22×C3⋊D3C1614yescomplemented
49C22×C3⋊D3C2×C811yescharacteristic
50C22×C3⋊D3C2×C811yescharacteristic
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4C2×C811yescharacteristic
54C2×C32×C4C22×C411yescharacteristic
55C2×C3⋊Dic3—22no—
56C2×C3⋊Dic3C2×C811yescharacteristic
57C2×C3⋊Dic3C2×C811yescharacteristic
58C4×C3⋊D3—22no—
59C4×C3⋊D3—21no—
60C4×C3⋊D3—21no—
61C4×C3⋊D3—22no—
62C4×C3⋊D3C22⋊C412yes—
63C4×C3⋊D3M1612yes—
64C32×C8—21no—
65C32×C8C22⋊C412yes—
66C3⋊(C3⋊C8)—21no—
67C3⋊(C3⋊C8)C2×D412yes—
68C23×C8—91no—
69C22×C16—92no—
70C22⋊C16—92no—
71C22⋊C16—92no—
72C23×D3—62no—
73C22×C3×C4—22no—
74C22×Dic3—62no—
75C2×C4×D3—62no—
76C2×C4×D3—62no—
77C2×C4×D3—62no—
78C2×C4×D3—62no—
79C2×C4×D3—68no—
80C2×C4×D3—68no—
81C2×C3×C8—28no—
82C2×C3×C8—22no—
83C2×C3×C8—22no—
84C2×C3⋊C8—62no—
85C2×C3⋊C8—62no—
86C2×C3⋊C8—68no—
87D3×C8—68no—
88D3×C8—68no—
89D3×C8—68no—
90D3×C8—68no—
91C22×C32—21no—
92C22×C32—21no—
93C22×C32C2×C1612yescomplemented
94C22×C32C22×C811yescharacteristic
95C2×C3⋊D3—21no—
96C2×C3⋊D3—21no—
97C2×C3⋊D3—28no—
98C2×C3⋊D3C22⋊C812yes—
99C2×C3⋊D3C2×C1612yes—
100C2×C3⋊D3C2×C1612yescomplemented
101C2×C3⋊D3M3212yes—
102C32×C4—21no—
103C32×C4C2×C22⋊C411yescharacteristic
104C32×C4C2×M1611yescharacteristic
105C3⋊Dic3—21no—
106C3⋊Dic3C22⋊C812yes—
107C23×C4—91no—
108C22×C8—91no—
109C22×C8—91no—
110C22×C8—91no—
111C22×C8—91no—
112C22×C8—91no—
113C22×C8—184no—
114C22×C8#15711yescharacteristic
115C2×C16—94no—
116C2×C16—184no—
117C23×C3—22no—
118C22×D3—68no—
119C22×D3—62no—
120C22×D3—62no—
121C22×D3—68no—
122C22×D3—68no—
123C2×C3×C4—24no—
124C2×C3×C4—24no—
125C2×C3×C4—22no—
126C2×C3×C4—22no—
127C2×Dic3—62no—
128C2×Dic3—62no—
129C2×Dic3—68no—
130C4×D3—64no—
131C4×D3—64no—
132C4×D3—64no—
133C4×D3—68no—
134C4×D3—68no—
135C4×D3—64no—
136C3×C8—24no—
137C3×C8—24no—
138C3⋊C8—64no—
139C3⋊C8—64no—
140C2×C32—22no—
141C2×C32C2×C22⋊C811yescharacteristic
142C2×C32C22×C1611yescharacteristic
143C2×C32C2×M3211yescharacteristic
144C3⋊D3—22no—
145C3⋊D3C22⋊C1614yescomplemented
146C24—91no—
147C22×C4—91no—
148C22×C4—91no—
149C22×C4—91no—
150C22×C4—91no—
151C22×C4—91no—
152C22×C4—182no—
153C22×C4—182no—
154C22×C4C2×#15711yescharacteristic
155C2×C8—22no—
156C2×C8—91no—
157C2×C8—94no—
158C2×C8—91no—
159C2×C8—182no—
160C2×C8—182no—
161C2×C8—182no—
162C2×C8—182no—
163C2×C8C2×#15711yescharacteristic
164C2×C8C2×#15711yescharacteristic
165C16—184no—
166C22×C3—24no—
167C22×C3—24no—
168C22×C3—24no—
169C22×C3—22no—
170C2×D3—64no—
171C2×D3—64no—
172C2×D3—64no—
173C2×D3—64no—
174C2×D3—64no—
175C2×D3—632no—
176C2×D3—64no—
177C3×C4—24no—
178C3×C4—22no—
179C3×C4—22no—
180Dic3—64no—
181Dic3—64no—
182C32C2×C22⋊C1611yescharacteristic, complemented, Sylow
183C23—91no—
184C23—94no—
185C23—91no—
186C23—182no—
187C23—182no—
188C23#378711yescharacteristic
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—91no—
192C2×C4—92no—
193C2×C4—92no—
194C2×C4—91no—
195C2×C4—182no—
196C2×C4—182no—
197C2×C4—182no—
198C2×C4—181no—
199C2×C4—181no—
200C2×C4#378711yescharacteristic
201C2×C4C22×#15711yescharacteristic
202C8—21no—
203C8—92no—
204C8—181no—
205C8C22⋊#15712yes—
206C2×C3—28no—
207C2×C3—22no—
208C2×C3—22no—
209C2×C3—22no—
210D3—68no—
211D3—68no—
212C22—21no—
213C22—21no—
214C22—92no—
215C22—92no—
216C22—92no—
217C22—92no—
218C22—188no—
219C22—181no—
220C22—181no—
221C22#6376412yescomplemented
222C22C2×#378711yescharacteristic
223C4—21no—
224C4—92no—
225C4—181no—
226C4#6428311yescharacteristic
227C4C2×C22⋊#15711yescharacteristic
228C3—22no—
229C2—22no—
230C2—94no—
231C2—182no—
232C2C2×#6376411yescharacteristic
233C2#1059376211yescharacteristic
234C2#1059380011yescharacteristic
subgroupG/H
centerC2×C8C2×#157
commutatorC2×C32C22×C16
FrattiniC2×C4C22×#157
FittingC22×C32×C8C4
socleC22×C32C22×C8
prime radicalC23×C3⋊D3C8
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC22×C8#157
hypocenterC32C2×C22⋊C16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63764C2semidirect
3. C22⋊#3708C2semidirect
4. #10590176C2semidirect
13. C2×#3708C22semidirect
48. C22×C3⋊D3C16semidirect
93. C22×C32C2×C16semidirect
100. C2×C3⋊D3C2×C16semidirect
145. C3⋊D3C22⋊C16semidirect
182. C32C2×C22⋊C16semidirect
221. C22#63764semidirect

Maximal subgroups

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

subgroupindex
C22×C8×C3⋊D32
C2×#637642
C22⋊#37082
#105901762
C2×C22⋊C169