Finite Group Databasebeta

← #11771132

Subgroups — #11771132

Order 1152.

284 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 49 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#10593727C211yesmaximal, characteristic
2#10590340C211yesmaximal, characteristic
3C4×#3712C211yesmaximal, characteristic
4C42×C3⋊D3C2211yescharacteristic
5C2×#3712—21no—
6C2×#3712C412yes—
7#63778—21no—
8C4⋊#622C412yes—
9C4×#622—21no—
10C3×C4⋊(C3⋊C8)—21no—
11C3×C4×C3⋊C8—21no—
12#63572—21no—
13#63555C412yes—
14#4837—61no—
15C4×ΓL(1,𝔽25)—61no—
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×C4×C3⋊D3D411yescharacteristic
18C2×C4×C3⋊D3Q811yescharacteristic
19C2×#622—22no—
20C32×C42D411yescharacteristic
21C4×C3⋊Dic3C2×C411yescharacteristic
22C4×C3⋊Dic3C2×C411yescharacteristic
23C4×C3⋊Dic3D411yescharacteristic
24C2×C3×C3⋊C8—22no—
25C2×C3×C3⋊C8—22no—
26#3712—24no—
27#3712—42no—
28#1299—91nomaximal, Sylow
29C2×ΓL(1,𝔽25)—62no—
30C2×ΓL(1,𝔽25)—62no—
31C42×D3—61no—
32C42×D3—61no—
33C3×C4⋊C8—61no—
34C3×C4×C8—61no—
35#815—62no—
36Dic3⋊C8—62no—
37C4⋊(C3⋊C8)—21no—
38C4×C3⋊C8—21no—
39C22×C3⋊D3C4⋊C411yescharacteristic
40C2×C32×C4C22⋊C411yescharacteristic
41C2×C32×C4C22⋊C411yescharacteristic
42C2×C32×C4C4⋊C411yescharacteristic
43C2×C3⋊Dic3C4211yescharacteristic
44C2×C3⋊Dic3C22⋊C411yescharacteristic
45C2×C3⋊Dic3C4⋊C411yescharacteristic
46C4×C3⋊D3—21no—
47C4×C3⋊D3—21no—
48C4×C3⋊D3—22no—
49C4×C3⋊D3—22no—
50#622—42no—
51C3×C3⋊C8—24no—
52C3×C3⋊C8—42no—
53#431—91no—
54#423—91no—
55C4×M16—91no—
56C2×C4×D3—61no—
57C2×C4×D3—61no—
58C2×C4×D3—61no—
59C2×C4×D3—61no—
60C2×C4×D3—61no—
61C2×C4×D3—61no—
62C2×C3×C8—62no—
63C2×C3×C8—62no—
64C3×C42—21no—
65C3×C42—21no—
66C4×Dic3—61no—
67C4×Dic3—61no—
68C4×Dic3—61no—
69C4×Dic3—61no—
70C4×Dic3—61no—
71C4×Dic3—61no—
72C2×C3⋊C8—22no—
73C2×C3⋊C8—22no—
74ΓL(1,𝔽25)—68no—
75ΓL(1,𝔽25)—124no—
76C22×C32#9511yescharacteristic
77C2×C3⋊D3—21no—
78C2×C3⋊D3—21no—
79C2×C3⋊D3—21no—
80C32×C4—21no—
81C32×C4#10011yescharacteristic
82C32×C4#10111yescharacteristic
83C32×C4#10812yes—
84C3⋊Dic3—21no—
85C3⋊Dic3—21no—
86C3⋊Dic3#10412yes—
87C2×M16—92no—
88C2×M16—181no—
89C2×C42—91no—
90C4⋊C8—61no—
91C4⋊C8—92no—
92C4⋊C8—181no—
93C22⋊C8—181no—
94#97—92no—
95C4×C8—61no—
96C4×C8—181no—
97C22×D3—61no—
98C22×D3—61no—
99C2×C3×C4—21no—
100C2×C3×C4—21no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×Dic3—61no—
106C2×Dic3—61no—
107C2×Dic3—61no—
108C2×Dic3—61no—
109C2×Dic3—61no—
110C2×Dic3—61no—
111C4×D3—64no—
112C4×D3—62no—
113C4×D3—62no—
114C4×D3—122no—
115C4×D3—121no—
116C4×D3—121no—
117C4×D3—122no—
118C4×D3—122no—
119C3×C8—64no—
120C3×C8—122no—
121C3⋊C8—24no—
122C3⋊C8—42no—
123C2×C32#33911yescharacteristic
124C2×C32#34111yescharacteristic
125C2×C32#34311yescharacteristic
126C3⋊D3—41no—
127C22×C4—91no—
128C22×C4—91no—
129C22×C4—91no—
130M16—184no—
131M16—362no—
132C2×C8—62no—
133C2×C8—62no—
134C2×C8—182no—
135C42—91no—
136C42—91no—
137C42—91no—
138C42GO+(4,𝔽2)11yescharacteristic
139C22×C3—21no—
140C22×C3—21no—
141C2×D3—62no—
142C2×D3—62no—
143C2×D3—121no—
144C2×D3—121no—
145C2×D3—121no—
146C2×D3—121no—
147C3×C4—22no—
148C3×C4—21no—
149C3×C4—21no—
150C3×C4—21no—
151C3×C4—21no—
152C3×C4—22no—
153C3×C4—22no—
154C3×C4—41no—
155Dic3—62no—
156Dic3—62no—
157Dic3—62no—
158Dic3—121no—
159Dic3—121no—
160Dic3—121no—
161C32#129911yescharacteristic, complemented, Sylow
162C23—91no—
163C2×C4—91no—
164C2×C4—91no—
165C2×C4—91no—
166C2×C4—182no—
167C2×C4—181no—
168C2×C4—181no—
169C2×C4—182no—
170C2×C4D32⋊C411yescharacteristic
171C2×C4D32⋊C411yescharacteristic
172C2×C4#377311yescharacteristic
173C8—64no—
174C8—122no—
175C8—362no—
176C2×C3—21no—
177C2×C3—21no—
178C2×C3—21no—
179C2×C3—21no—
180C2×C3—21no—
181C2×C3—21no—
182D3—122no—
183D3—122no—
184C22—181no—
185C22—181no—
186C22—181no—
187C22#6373711yescharacteristic
188C4—21no—
189C4—92no—
190C4—181no—
191C4—181no—
192C4#6372711yescharacteristic
193C4#6372811yescharacteristic
194C4#6373312yes—
195C3—21no—
196C3—21no—
197C2—361no—
198C2#1059004811yescharacteristic
199C2#1059005111yescharacteristic
200C2#1059005211yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC42GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32#95
prime radicalC22×C3⋊D3C4⋊C4
cosocleC42×C3⋊D3C22
hypocenterC32#1299
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
161. C32#1299semidirect

Maximal subgroups

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

subgroupindex
#105937272
#105903402
C4×#37122
#12999