Finite Group Databasebeta

← #11772500

Subgroups — #11772500

Order 1152.

246 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 51 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×#63771C211yesmaximal, characteristic
2#10590687C211yesmaximal, characteristic
3C2×#63544C211yesmaximal, characteristic
4C2×#3788—21no—
5C2×C8×C3⋊D3C2211yescharacteristic
6#63900—21no—
7#63771—21no—
8#63771C412yescomplemented
9C3×#818—21no—
10C2×C3×C3⋊C16—21no—
11#63576C412yes—
12#63544—21no—
13#63544C412yescomplemented
14C2×#798—61no—
15D3×#107—61no—
16C2×C4×C3⋊D3D411yescharacteristic
17C2×#624—41no—
18C2×#622—41no—
19#3788—22no—
20#3788—41no—
21C2×C32×C8D411yescharacteristic
22C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
23C8×C3⋊D3C2×C411yescharacteristic
24C8×C3⋊D3C2×C411yescharacteristic
25C8×C3⋊D3D411yescharacteristic
26C8×C3⋊D3Q811yescharacteristic
27C3×C4⋊Dic3—22no—
28#3724—41no—
29C3×C3⋊C16—22no—
30#1387—91nomaximal, Sylow
31C2×D3×C8—61no—
32C2×D3×C8—61no—
33D3×C4⋊C4—62no—
34C2×C3×C16—61no—
35C3×#107—61no—
36#818—21no—
37C2×C3⋊C16—21no—
38#807—62no—
39#798—62no—
40#798—62no—
41C22×C3⋊D3SD1611yescharacteristic
42C2×C32×C4C22⋊C411yescharacteristic
43C2×C3⋊Dic3D811yescharacteristic
44C4×C3⋊D3C22⋊C411yescharacteristic
45C4×C3⋊D3C4⋊C411yescharacteristic
46C4×C3⋊D3SD1611yescharacteristic
47C4×C3⋊D3Q1611yescharacteristic
48C2×C3×Dic3—42no—
49#624—82no—
50#622—42no—
51C32×C8C22⋊C411yescharacteristic
52C32×C8C4⋊C411yescharacteristic
53C3⋊(C3⋊C8)C4211yescharacteristic
54C3⋊(C3⋊C8)C4⋊C411yescharacteristic
55C2×M32—91no—
56C2×#108—91no—
57C2×#107—91no—
58C2×C4×D3—61no—
59C2×C4×D3—61no—
60C2×C4×D3—122no—
61C2×C3×C8—21no—
62C2×C3×C8—21no—
63C3×C4⋊C4—62no—
64C4⋊Dic3—22no—
65Dic3⋊C4—122no—
66C2×C3⋊C8—61no—
67C2×C3⋊C8—61no—
68D3×C8—61no—
69D3×C8—61no—
70D3×C8—61no—
71D3×C8—61no—
72D3×C8—61no—
73D3×C8—61no—
74D3×C8—61no—
75D3×C8—61no—
76C3×C16—62no—
77C3⋊C16—22no—
78C22×C32#10211yescharacteristic
79C2×C3⋊D3—21no—
80C2×C3⋊D3—21no—
81C2×C3⋊D3#10311yescharacteristic
82C2×C3⋊D3#10611yescharacteristic
83C32×C4#9511yescharacteristic
84C32×C4#10311yescharacteristic
85C3⋊Dic3#10211yescharacteristic
86C3⋊Dic3#10711yescharacteristic
87C3×Dic3—82no—
88C2×M16—181no—
89C22×C8—91no—
90C2×C4⋊C4—181no—
91M32—92no—
92M32—181no—
93C2×C16—61no—
94#108—92no—
95#108—181no—
96#107—61no—
97#107—92no—
98C22×D3—61no—
99C22×D3—61no—
100C2×C3×C4—21no—
101C2×C3×C4—21no—
102C2×C3×C4—122no—
103C2×Dic3—42no—
104C2×Dic3—61no—
105C2×Dic3—61no—
106C4×D3—61no—
107C4×D3—61no—
108C4×D3—61no—
109C4×D3—61no—
110C4×D3—61no—
111C4×D3—61no—
112C4×D3—61no—
113C4×D3—61no—
114C4×D3—244no—
115C3×C8—21no—
116C3×C8—21no—
117C3×C8—21no—
118C3×C8—21no—
119C3⋊C8—61no—
120C3⋊C8—61no—
121C3⋊C8—61no—
122C3⋊C8—61no—
123C2×C32#34011yescharacteristic
124C2×C32#36111yescharacteristic
125C2×C32#36211yescharacteristic
126C3⋊D3—21no—
127C3⋊D3—21no—
128C22×C4—91no—
129C22×C4—361no—
130M16—182no—
131M16—361no—
132C2×C8—91no—
133C2×C8—91no—
134C2×C8—91no—
135C2×C8—91no—
136C2×C8—91no—
137C2×C8—361no—
138C2×C8GO+(4,𝔽2)11yescharacteristic
139C4⋊C4—62no—
140C4⋊C4—361no—
141C16—62no—
142C22×C3—21no—
143C22×C3—21no—
144C2×D3—61no—
145C2×D3—61no—
146C2×D3—61no—
147C2×D3—61no—
148C2×D3—62no—
149C2×D3—62no—
150C2×D3—121no—
151C2×D3—121no—
152C3×C4—21no—
153C3×C4—21no—
154C3×C4—21no—
155C3×C4—21no—
156C3×C4—242no—
157Dic3—61no—
158Dic3—61no—
159Dic3—61no—
160Dic3—61no—
161Dic3—82no—
162C32#138711yescharacteristic, complemented, Sylow
163C23—91no—
164C2×C4—91no—
165C2×C4—91no—
166C2×C4—91no—
167C2×C4—91no—
168C2×C4—91no—
169C2×C4—122no—
170C2×C4—722no—
171C2×C4D32⋊C411yescharacteristic
172C8—91no—
173C8—91no—
174C8—362no—
175C8D32⋊C411yescharacteristic
176C8#377311yescharacteristic
177C2×C3—21no—
178C2×C3—21no—
179C2×C3—21no—
180C2×C3—21no—
181C2×C3—21no—
182C2×C3—21no—
183D3—62no—
184D3—62no—
185D3—121no—
186D3—121no—
187C22—91no—
188C22—91no—
189C22—181no—
190C22—181no—
191C22#6372911yescharacteristic
192C4—91no—
193C4—91no—
194C4—242no—
195C4#6373011yescharacteristic
196C4#6373711yescharacteristic
197C3—21no—
198C3—21no—
199C2—181no—
200C2—181no—
201C2#1059002011yescharacteristic
202C2#1059002111yescharacteristic
203C2#1059004911yescharacteristic
subgroupG/H
centerC22#63729
commutatorC3⋊(C3⋊C8)C42
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#102
prime radicalC22×C3⋊D3SD16
cosocleC2×C8×C3⋊D3C22
hypocenterC32#1387
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
8. #63771C4semidirect
13. #63544C4semidirect
162. C32#1387semidirect

Maximal subgroups

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

subgroupindex
C2×#637712
#105906872
C2×#635442
#13879