Finite Group Databasebeta

← #11797482

Subgroups — #11797482

Order 1152.

298 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 74 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×#63773C211yesmaximal, characteristic, complemented
2C22×#3708C211yesmaximal, characteristic, complemented
3D4×C3⋊(C3⋊C8)C211yesmaximal, characteristic
4C22⋊#3708C211yesmaximal, characteristic, complemented
5C22⋊#3708C211yesmaximal, characteristic, complemented
6#10590148C211yesmaximal, characteristic, complemented
7C4⋊#3708C211yesmaximal, characteristic, complemented
8C32×C4×D4C411yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11#63773—22no—
12C2×#3708—22no—
13C2×#3708C2211yescharacteristic
14C2×#3708C2211yescharacteristic
15C2×#3708C2211yescharacteristic
16C2×#3708C2211yescharacteristic
17#63657C411yescharacteristic
18#63657C411yescharacteristic
19C4⋊(C3⋊(C3⋊C8))C411yescharacteristic
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21D4×C3⋊C8—62no—
22C2×C32×D4C811yescharacteristic
23C22×C32×C4C2×C411yescharacteristic
24C22×C32×C4C2×C411yescharacteristic
25C32×C4⋊C4C811yescharacteristic
26C32×C22⋊C4C811yescharacteristic
27C32×C22⋊C4C811yescharacteristic
28C32×C42C2×C411yescharacteristic
29C2×C3⋊(C3⋊C8)—21no—
30C2×C3⋊(C3⋊C8)—21no—
31C2×C3⋊(C3⋊C8)—21no—
32C2×C3⋊(C3⋊C8)—21no—
33C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
34C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
35C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
36C2×C3⋊(C3⋊C8)C2311yescharacteristic
37#3708—21no—
38#3708—21no—
39#3708—21no—
40#3708D412yescomplemented
41#2168—91nomaximal, Sylow
42C3×C4×D4—22no—
43C22×C3⋊C8—62no—
44C22×C3⋊C8—62no—
45#830—62no—
46#830—62no—
47C4⋊(C3⋊C8)—62no—
48C4×C3⋊C8—62no—
49C23×C32C2×C811yescharacteristic
50C23×C32C2×C811yescharacteristic
51C32×D4—22no—
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4—21no—
55C2×C32×C4—21no—
56C2×C32×C4C2×C811yescharacteristic
57C2×C32×C4C2×C811yescharacteristic
58C2×C32×C4C2×C811yescharacteristic
59C2×C32×C4C2×C811yescharacteristic
60C2×C32×C4C22×C411yescharacteristic
61C3⋊(C3⋊C8)—21no—
62C3⋊(C3⋊C8)—21no—
63C3⋊(C3⋊C8)—21no—
64C3⋊(C3⋊C8)C2×D411yescharacteristic
65C3⋊(C3⋊C8)#4111yescharacteristic
66C2×M32—91no—
67C22×C16—91no—
68C8×D4—91no—
69C4⋊C16—91no—
70C22⋊C16—91no—
71C22⋊C16—91no—
72#346—91no—
73C2×C3×D4—22no—
74C22×C3×C4—22no—
75C22×C3×C4—22no—
76C3×C4⋊C4—22no—
77C3×C22⋊C4—22no—
78C3×C22⋊C4—22no—
79C3×C42—22no—
80C2×C3⋊C8—62no—
81C2×C3⋊C8—62no—
82C2×C3⋊C8—62no—
83C2×C3⋊C8—62no—
84C2×C3⋊C8—122no—
85C2×C3⋊C8—122no—
86C2×C3⋊C8—122no—
87C2×C3⋊C8—122no—
88C22×C32—21no—
89C22×C32—21no—
90C22×C32—21no—
91C22×C32—21no—
92C22×C32—21no—
93C22×C32M3212yescomplemented
94C22×C32C22×C811yescharacteristic
95C32×C4—21no—
96C32×C4—21no—
97C32×C4—21no—
98C32×C4—21no—
99C32×C4C4×D411yescharacteristic
100C32×C4#13111yescharacteristic
101C22×C8—91no—
102C22×C8—91no—
103C4×D4#15711yescharacteristic
104M32—182no—
105C2×C16—91no—
106C2×C16—91no—
107C2×C16—91no—
108C2×C16—91no—
109C2×C16—182no—
110C4⋊C8—91no—
111C22⋊C8—91no—
112C22⋊C8—91no—
113C4×C8—91no—
114C23×C3—22no—
115C23×C3—22no—
116C3×D4—28no—
117C2×C3×C4—22no—
118C2×C3×C4—22no—
119C2×C3×C4—22no—
120C2×C3×C4—22no—
121C2×C3×C4—22no—
122C2×C3×C4—42no—
123C2×C3×C4—42no—
124C2×C3×C4—42no—
125C2×C3×C4—42no—
126C3⋊C8—62no—
127C3⋊C8—62no—
128C3⋊C8—122no—
129C3⋊C8—122no—
130C3⋊C8—122no—
131C2×C32—22no—
132C2×C32—41no—
133C2×C32C8×D411yescharacteristic
134C2×C32C2×M3211yescharacteristic
135C2×C32#50411yescharacteristic
136C2×D4#62211yescharacteristic
137C22×C4C2×#15711yescharacteristic
138C22×C4C2×#15711yescharacteristic
139C2×C8—91no—
140C2×C8—91no—
141C2×C8—91no—
142C2×C8—91no—
143C2×C8—181no—
144C2×C8—181no—
145C2×C8—181no—
146C2×C8—181no—
147C4⋊C4#62211yescharacteristic
148C22⋊C4#62211yescharacteristic
149C22⋊C4#62211yescharacteristic
150C42C2×#15711yescharacteristic
151C16—92no—
152C16—181no—
153C16—181no—
154C16—181no—
155C22×C3—24no—
156C22×C3—24no—
157C22×C3—22no—
158C22×C3—42no—
159C22×C3—42no—
160C22×C3—42no—
161C22×C3—42no—
162C3×C4—24no—
163C3×C4—22no—
164C3×C4—22no—
165C3×C4—42no—
166C3×C4—42no—
167C3×C4—42no—
168C32#216811yescharacteristic, complemented, Sylow
169C23C2×#62211yescharacteristic
170C23C2×#62211yescharacteristic
171D4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4C2×#62211yescharacteristic
177C2×C4C2×#62211yescharacteristic
178C2×C4C2×#62211yescharacteristic
179C2×C4C2×#62211yescharacteristic
180C2×C4C22×#15711yescharacteristic
181C8—91no—
182C8—91no—
183C8—181no—
184C8—181no—
185C8—181no—
186C2×C3—22no—
187C2×C3—22no—
188C2×C3—22no—
189C2×C3—44no—
190C2×C3—44no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—21no—
196C22#6377312yescomplemented
197C22C22×#62211yescharacteristic
198C4—21no—
199C4—21no—
200C4—21no—
201C4—21no—
202C4#6428711yescharacteristic
203C4D4×#15711yescharacteristic
204C3—22no—
205C2—22no—
206C2—41no—
207C2C2×#6377311yescharacteristic
208C2D4×#62211yescharacteristic
209C2#1059383811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#157
commutator, socleC22×C32C22×C8
FittingC32×C4×D4C4
prime radicalC2×C32×D4C8
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC4×D4#157
hypocenterC32#2168
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#63773C2semidirect
2. C22×#3708C2semidirect
4. C22⋊#3708C2semidirect
5. C22⋊#3708C2semidirect
6. #10590148C2semidirect
7. C4⋊#3708C2semidirect
40. #3708D4semidirect
93. C22×C32M32semidirect
168. C32#2168semidirect
196. C22#63773semidirect

Maximal subgroups

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

subgroupindex
C2×#637732
C22×#37082
D4×C3⋊(C3⋊C8)2
C22⋊#37082
#105901482
C4⋊#37082
#21689