Finite Group Databasebeta

← #11772620

Subgroups — #11772620

Order 1152.

318 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 39 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#10593837C211yesmaximal, characteristic
2#10591639C212yesmaximal
3C2×Q8×C3⋊D3C2211yescharacteristic
4C2×C4⋊#157C411yescharacteristic
5C2×C4×#157C411yescharacteristic
6#63818—22no—
7#63781—22no—
8C3×#836—22no—
9#63561C414yescomplemented
10D3×#101—62no—
11C22×#157—21no—
12C22×#157—21no—
13C2×C32×Q8D411yescharacteristic
14Q8×C3⋊D3—41no—
15Q8×C3⋊D3—41no—
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×C4×C3⋊D3D412yes—
18C2×#634C2×C412yes—
19C2×#634Q811yescharacteristic
20C4⋊#157—41no—
21C4×#157—41no—
22C3×#208—24no—
23#3712—42no—
24#3710—42no—
25#1394—91nomaximal, Sylow
26C2×D3×Q8—62no—
27D3×M16—64no—
28C3×#101—62no—
29#836—22no—
30#824—64no—
31C22×C3⋊D3C22⋊C411yescharacteristic
32C2×#157—22no—
33C2×#157—41no—
34C2×#157—41no—
35C2×#157—42no—
36C2×#157—41no—
37C32×Q8—41no—
38C2×C32×C4C22⋊C412yes—
39C2×C32×C4C4⋊C411yescharacteristic
40C2×C3⋊Dic3C4211yescharacteristic
41C2×C3⋊Dic3C4⋊C412yes—
42C4×C3⋊D3—22no—
43C4×C3⋊D3—22no—
44C4×C3⋊D3—21no—
45C4×C3⋊D3—21no—
46#634—42no—
47#634—41no—
48C3×C3⋊C8—44no—
49C2×#101—92no—
50#391—91no—
51C2×C3×Q8—22no—
52D3×Q8—124no—
53D3×Q8—124no—
54C2×C4×D3—62no—
55C2×C4×D3—62no—
56C2×C4×D3—62no—
57C2×Dic6—62no—
58C2×Dic6—62no—
59C2×Dic6—62no—
60C3×M16—64no—
61#208—24no—
62ΓL(1,𝔽25)—124no—
63D3×C8—124no—
64C22×C32#9511yescharacteristic
65C2×C3⋊D3—21no—
66C2×C3⋊D3—21no—
67C2×C3⋊D3#9911yescharacteristic
68C2×C3⋊D3#9911yescharacteristic
69#157—42no—
70#157—81no—
71C32×C4—22no—
72C32×C4—21no—
73C3⋊Dic3—22no—
74C3⋊Dic3—21no—
75C22×Q8—91no—
76C2×M16—182no—
77C2×C4⋊C4—91no—
78C2×C42—91no—
79#101—62no—
80#101—94no—
81#95—182no—
82C22×D3—62no—
83C3×Q8—44no—
84C2×C3×C4—22no—
85C2×C3×C4—22no—
86C2×C3×C4—22no—
87C2×Dic3—62no—
88C2×Dic3—62no—
89C2×Dic3—62no—
90C4×D3—64no—
91C4×D3—64no—
92C4×D3—122no—
93C4×D3—122no—
94C4×D3—122no—
95C4×D3—122no—
96Dic6—124no—
97Dic6—124no—
98Dic6—124no—
99C3×C8—124no—
100C3⋊C8—44no—
101C2×C32—21no—
102C2×C32#34211yescharacteristic
103C3⋊D3—21no—
104C3⋊D3#35511yescharacteristic
105C3⋊D3#35611yescharacteristic
106C2×Q8—92no—
107C2×Q8—91no—
108C2×Q8—361no—
109C2×Q8—361no—
110C2×Q8GO+(4,𝔽2)11yescharacteristic
111C22×C4—92no—
112C22×C4—91no—
113C22×C4—181no—
114C22×C4—181no—
115M16—64no—
116M16—362no—
117C2×C8—362no—
118C4⋊C4—361no—
119C42—361no—
120C22×C3—22no—
121C2×D3—62no—
122C2×D3—62no—
123C2×D3—122no—
124C2×D3—122no—
125C3×C4—24no—
126C3×C4—42no—
127C3×C4—42no—
128Dic3—64no—
129Dic3—122no—
130Dic3—122no—
131C32#139411yescharacteristic, complemented, Sylow
132C23—91no—
133Q8—41no—
134Q8—362no—
135Q8—361no—
136C2×C4—92no—
137C2×C4—91no—
138C2×C4—181no—
139C2×C4—181no—
140C2×C4—182no—
141C2×C4—182no—
142C2×C4—182no—
143C2×C4—361no—
144C2×C4—361no—
145C2×C4—361no—
146C2×C4—362no—
147C2×C4D32⋊C412yes—
148C2×C4#377311yescharacteristic
149C8—124no—
150C2×C3—22no—
151C2×C3—42no—
152D3—62no—
153D3—62no—
154D3—122no—
155C22—91no—
156C22—91no—
157C22—181no—
158C22—181no—
159C22#6373711yescharacteristic
160C4—22no—
161C4—21no—
162C4—182no—
163C4—181no—
164C4—362no—
165C4—721no—
166C3—22no—
167C2—21no—
168C2—91no—
169C2—91no—
170C2—181no—
171C2#1059007711yescharacteristic
subgroupG/H
centerC2#10590077
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC2×Q8GO+(4,𝔽2)
FittingC2×C32×Q8D4
socleC2×C32#342
prime radicalC22×C3⋊D3C22⋊C4
cosocleC2×Q8×C3⋊D3C22
hypocenterC32#1394
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
9. #63561C4semidirect
131. C32#1394semidirect

Maximal subgroups

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

subgroupindex
#105938372
#105916392
#13949