Finite Group Databasebeta

← #11796527

Subgroups — #11796527

Order 1152.

500 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 54 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
1#10595997C211yesmaximal, characteristic
2C2×#63780C212yesmaximal, complemented
3#10590145C212yesmaximal, complemented
4#10590144C212yesmaximal, complemented
5C2×#3828C411yescharacteristic
6C22×#634C2211yescharacteristic
7C2×#3792—22no—
8C32×#117C411yescharacteristic
9#64106—22no—
10#64095—22no—
11#64084C411yescharacteristic
12#64084C2211yescharacteristic
13#64078C411yescharacteristic
14#64078C2211yescharacteristic
15#63780—22no—
16#63780C2214yes—
17#5526—62no—
18C22×C32×C4C2×C411yescharacteristic
19C2×#638—21no—
20C22×C3⋊Dic3D412yes—
21#3828—42no—
22C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
23C2×C4×C3⋊D3—21no—
24C2×#634—42no—
25C2×#634C2×C411yescharacteristic
26C2×#634C2×C411yescharacteristic
27C2×#634D412yes—
28C2×#634C2311yescharacteristic
29#3792—24no—
30#3792—42no—
31C2×#622—42no—
32C32×C4⋊C4—21no—
33C32×C22⋊C4—21no—
34C32×C42C2×C411yescharacteristic
35C32×C42C2×C411yescharacteristic
36#3752—22no—
37#3752—22no—
38C4⋊(C3⋊Dic3)—22no—
39C4⋊(C3⋊Dic3)—22no—
40#2133—91nomaximal, Sylow
41C2×#235—62no—
42C22×Dic6—62no—
43C3×#117—22no—
44#897—68no—
45#886—68no—
46#875—62no—
47#875—62no—
48#869—62no—
49#869—62no—
50C23×C32C22⋊C411yescharacteristic
51C22×C3⋊D3—21no—
52C2×C32×C4—22no—
53C2×C32×C4—21no—
54C2×C32×C4—21no—
55C2×C32×C4C22⋊C411yescharacteristic
56C2×C32×C4C22×C411yescharacteristic
57#638—42no—
58C2×C3⋊Dic3—21no—
59C2×C3⋊Dic3—22no—
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3C22⋊C412yes—
62C2×C3⋊Dic3C2×D412yes—
63C4⋊(C3⋊D3)—41no—
64C4×C3⋊D3—42no—
65#634—41no—
66#634—42no—
67#634—41no—
68#634—41no—
69#622—44no—
70#536—91no—
71C2×#101—92no—
72#356—92no—
73#355—92no—
74C22×C3×C4—22no—
75C2×#67—64no—
76C22×Dic3—64no—
77#235—128no—
78C2×D12—62no—
79C2×C4×D3—64no—
80C2×Dic6—62no—
81C2×Dic6—62no—
82C2×Dic6—62no—
83C2×Dic6—64no—
84C2×Dic6—128no—
85C3×C4⋊C4—24no—
86C3×C22⋊C4—24no—
87C3×C42—22no—
88C3×C42—22no—
89(C2×D3)⋊C4—68no—
90(C2×D3)⋊C4—68no—
91C4⋊Dic3—68no—
92C4⋊Dic3—68no—
93C22×C32—41no—
94C22×C32#9912yes—
95C22×C32C2×C22⋊C411yescharacteristic
96C2×C3⋊D3—42no—
97C2×C3⋊D3—41no—
98C32×C4—21no—
99C32×C4—21no—
100C32×C4—41no—
101C32×C4—41no—
102C3⋊Dic3—22no—
103C3⋊Dic3—22no—
104C3⋊Dic3—41no—
105C2×#41—91no—
106C22×Q8—91no—
107C2×M16—182no—
108C4⋊Q8—91no—
109C4⋊Q8—91no—
110#124—91no—
111#124—91no—
112#123—182no—
113C22⋊Q8—182no—
114#117#15711yescharacteristic
115#101—94no—
116#101—182no—
117C23×C3—22no—
118C22×D3—64no—
119C2×C3×C4—28no—
120C2×C3×C4—24no—
121C2×C3×C4—24no—
122C2×C3×C4—22no—
123C2×C3×C4—22no—
124#67—128no—
125C2×Dic3—64no—
126C2×Dic3—64no—
127C2×Dic3—64no—
128C2×Dic3—124no—
129C2×Dic3—124no—
130D12—124no—
131C4×D3—128no—
132Dic6—124no—
133Dic6—124no—
134Dic6—128no—
135Dic6—124no—
136C2×C32—21no—
137C2×C32—22no—
138C2×C32C2×#9911yescharacteristic
139C3⋊D3—81no—
140#41—362no—
141C2×Q8—91no—
142C2×Q8—91no—
143C2×Q8—92no—
144C2×Q8—91no—
145C2×Q8—362no—
146C2×D4—91no—
147C2×D4—181no—
148C22×C4—92no—
149C22×C4—181no—
150C22×C4C2×#15711yescharacteristic
151M16—184no—
152M16—362no—
153C2×C8—362no—
154C4⋊C4—21no—
155C4⋊C4—182no—
156C4⋊C4—182no—
157C22⋊C4—21no—
158C22⋊C4—182no—
159C22⋊C4—182no—
160C42C2×#15711yescharacteristic
161C42C2×#15711yescharacteristic
162C22×C3—24no—
163C22×C3—22no—
164C22×C3—44no—
165C2×D3—124no—
166C2×D3—128no—
167C3×C4—24no—
168C3×C4—24no—
169C3×C4—44no—
170C3×C4—44no—
171Dic3—124no—
172Dic3—124no—
173Dic3—124no—
174C32#213311yescharacteristic, complemented, Sylow
175C23—181no—
176C23C22⋊#15711yescharacteristic
177Q8—362no—
178Q8—361no—
179Q8—361no—
180Q8—361no—
181D4—361no—
182D4—362no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—92no—
187C2×C4—92no—
188C2×C4—182no—
189C2×C4—182no—
190C2×C4—181no—
191C2×C4—362no—
192C2×C4C22⋊#15711yescharacteristic
193C2×C4C22×#15711yescharacteristic
194C8—364no—
195C2×C3—24no—
196C2×C3—22no—
197C2×C3—44no—
198D3—244no—
199C22—41no—
200C22—362no—
201C22—361no—
202C22#6377412yes—
203C22C2×C22⋊#15711yescharacteristic
204C4—21no—
205C4—21no—
206C4—41no—
207C4—41no—
208C4—182no—
209C4—182no—
210C4—361no—
211C3—22no—
212C2—21no—
213C2—22no—
214C2—721no—
215C2C2×#6377411yescharacteristic
subgroupG/H
centerC2C2×#63774
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#117C4
socleC2×C32C2×#99
prime radicalC2×#3828C4
cosocleC2×#634C23
hypercenter#117#157
hypocenterC32#2133
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#63780C2semidirect
3. #10590145C2semidirect
4. #10590144C2semidirect
174. C32#2133semidirect

Maximal subgroups

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

subgroupindex
#105959972
C2×#637802
#105901452
#105901442
#21339