Finite Group Databasebeta

← #11772635

Subgroups — #11772635

Order 1152.

312 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 38 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#10593834C211yesmaximal, characteristic
2#10593832C211yesmaximal, characteristic
3#10592450C211yesmaximal, characteristic
4C2×#3832C2211yescharacteristic
5#64286—21no—
6C2×#3788C411yescharacteristic, complemented
7C2×#3787C411yescharacteristic, complemented
8M16×C3⋊D3—21no—
9#63778—21no—
10#63778—21no—
11#63774—21no—
12#63774C412yes—
13C32×#101C411yescharacteristic, complemented
14#63663C411yescharacteristic, complemented
15#63650—21no—
16#4751—62no—
17C2×C32×Q8C2×C411yescharacteristic
18#3832—41no—
19#3832—41no—
20C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
21C2×C4⋊(C3⋊D3)D411yescharacteristic
22C2×C4⋊(C3⋊D3)Q811yescharacteristic
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3D411yescharacteristic
26C22⋊#157—22no—
27C2×#622—21no—
28C2×#622—21no—
29C4⋊#157—41no—
30C4×#157—41no—
31#3788—41no—
32#3787—41no—
33C32×M16—21no—
34#3748—21no—
35#3743—41no—
36C8×C3⋊D3—41no—
37#1395—91nomaximal, Sylow
38C2×#239—62no—
39D3×M16—64no—
40C3×#101—22no—
41#836—62no—
42#823—64no—
43C22×C3⋊D3C22⋊C411yescharacteristic
44C22×C3⋊D3C4⋊C411yescharacteristic
45C22×C3⋊D3C4⋊C411yescharacteristic
46C2×#157—42no—
47C32×Q8—41no—
48C2×C32×C4C4211yescharacteristic
49C2×C32×C4C22⋊C411yescharacteristic
50C2×C32×C4C4⋊C411yescharacteristic
51C2×C3⋊Dic3C22⋊C411yescharacteristic
52C4⋊(C3⋊D3)—41no—
53C4⋊(C3⋊D3)—41no—
54C4⋊(C3⋊D3)—41no—
55C4×C3⋊D3—21no—
56C4×C3⋊D3—21no—
57C4×C3⋊D3—21no—
58C4×C3⋊D3—21no—
59C4×C3⋊D3—21no—
60C4×C3⋊D3—21no—
61#622—41no—
62#622—41no—
63C32×C8—41no—
64C3⋊(C3⋊C8)—41no—
65#413—91no—
66#410—91no—
67#408—91no—
68C2×C3×Q8—22no—
69#239—124no—
70#239—124no—
71C2×D12—62no—
72C2×D12—62no—
73C2×D12—62no—
74C2×C4×D3—62no—
75C2×C4×D3—62no—
76C2×C4×D3—62no—
77C3×M16—24no—
78#208—64no—
79ΓL(1,𝔽25)—124no—
80D3×C8—124no—
81C22×C32#9511yescharacteristic
82C2×C3⋊D3—21no—
83C2×C3⋊D3—21no—
84C2×C3⋊D3—21no—
85C2×C3⋊D3—41no—
86C2×C3⋊D3—41no—
87C2×C3⋊D3—41no—
88#157—82no—
89C32×C4—21no—
90C32×C4—21no—
91C32×C4—21no—
92C3⋊Dic3#9911yescharacteristic
93C3⋊Dic3#9911yescharacteristic
94C2×#41—91no—
95C2×M16—91no—
96C2×M16—181no—
97C22×C8—91no—
98#117—181no—
99#101—91no—
100#101#15711yescharacteristic, complemented
101#100—181no—
102#99—92no—
103#99—181no—
104C22⋊C8—181no—
105C22⋊C8—181no—
106C22×D3—62no—
107C22×D3—62no—
108C22×D3—62no—
109C3×Q8—44no—
110C2×C3×C4—22no—
111C2×C3×C4—22no—
112C2×C3×C4—22no—
113C2×Dic3—62no—
114D12—124no—
115D12—124no—
116D12—124no—
117C4×D3—64no—
118C4×D3—64no—
119C4×D3—122no—
120C4×D3—122no—
121C4×D3—122no—
122C4×D3—122no—
123C3×C8—44no—
124C3⋊C8—124no—
125C2×C32—21no—
126C2×C32#34211yescharacteristic
127C3⋊D3—41no—
128C3⋊D3—41no—
129C3⋊D3—41no—
130#41—361no—
131#41—361no—
132C2×Q8C2×#15711yescharacteristic
133C2×D4—91no—
134C2×D4—91no—
135C2×D4—91no—
136C22×C4—91no—
137C22×C4—91no—
138C22×C4—91no—
139M16—21no—
140M16—181no—
141M16—361no—
142M16—361no—
143C2×C8—181no—
144C2×C8—181no—
145C2×C8—361no—
146C2×C8—361no—
147C4⋊C4—361no—
148C22⋊C4—182no—
149C42—361no—
150C22×C3—22no—
151C2×D3—64no—
152C2×D3—122no—
153C2×D3—122no—
154C2×D3—242no—
155C2×D3—242no—
156C2×D3—242no—
157C3×C4—24no—
158C3×C4—42no—
159C3×C4—42no—
160Dic3—62no—
161Dic3—62no—
162C32#139511yescharacteristic, complemented, Sylow
163C23—91no—
164C23—91no—
165C23—91no—
166Q8—41no—
167D4—361no—
168D4—361no—
169D4—361no—
170C2×C4—91no—
171C2×C4—181no—
172C2×C4—181no—
173C2×C4—181no—
174C2×C4—181no—
175C2×C4—181no—
176C2×C4—181no—
177C2×C4—362no—
178C2×C4C4×#15711yescharacteristic
179C2×C4C4⋊#15711yescharacteristic
180C2×C4C22⋊#15711yescharacteristic
181C8—41no—
182C8—361no—
183C8—361no—
184C8—361no—
185C2×C3—22no—
186C2×C3—42no—
187D3—124no—
188D3—242no—
189D3—242no—
190C22—181no—
191C22—181no—
192C22—181no—
193C22—361no—
194C22—361no—
195C22—361no—
196C22#6378111yescharacteristic
197C4—21no—
198C4—21no—
199C4—21no—
200C4—91no—
201C4—91no—
202C4—722no—
203C3—22no—
204C2—21no—
205C2—361no—
206C2—361no—
207C2—361no—
208C2#1059015511yescharacteristic
subgroupG/H
centerC2#10590155
commutatorC2×C32×C4C42
FrattiniC2×Q8C2×#157
FittingC32×#101C4
socleC2×C32#342
prime radical, cosocleC2×#3832C22
hypercenter#101#157
hypocenterC32#1395
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
6. C2×#3788C4semidirect
7. C2×#3787C4semidirect
13. C32×#101C4semidirect
14. #63663C4semidirect
100. #101#157semidirect
162. C32#1395semidirect

Maximal subgroups

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

subgroupindex
#105938342
#105938322
#105924502
#13959