Finite Group Databasebeta

← #11772890

Subgroups — #11772890

Order 1152.

153 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 153 conjugacy classes of subgroups — too many to draw. Only its 19 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#10591616C211yesmaximal, characteristic
2#10590218C211yesmaximal, characteristic
3#10589185C211yesmaximal, characteristic
4#64153C2211yescharacteristic
5#63872C411yescharacteristic
6#63780—21no—
7C3×#836—21no—
8C3×#835—21no—
9#63567—21no—
10#63555C411yescharacteristic
11#4797—61no—
12#4478—61no—
13C2×C32×Q8D411yescharacteristic
14C2×#634D411yescharacteristic
15#3792—41no—
16#3750—41no—
17C4×C3⋊Dic3C2×C411yescharacteristic
18C3×C4⋊Dic3—21no—
19C3×#208—41no—
20C2×C3×C3⋊C8—21no—
21Dic3⋊Dic3—41no—
22#1413—91nomaximal, Sylow
23#944—61no—
24#944—61no—
25#890—61no—
26C3×#103—61no—
27C3×#101—61no—
28#836—21no—
29#835—21no—
30#816—61no—
31#815—61no—
32#810—61no—
33C32×Q8—41no—
34C2×C32×C4—21no—
35C2×C32×C4C22⋊C411yescharacteristic
36C2×C3⋊Dic3—21no—
37C2×C3⋊Dic3—21no—
38#634—41no—
39C2×C3×Dic3—41no—
40#622—81no—
41C3×C3⋊C8—41no—
42C3×C3⋊C8—81no—
43#491—91no—
44#356—91no—
45#356—91no—
46C2×C3×Q8—21no—
47C2×C3×Q8—21no—
48C2×Dic6—61no—
49C2×Dic6—61no—
50C3×M16—121no—
51C2×C3×C8—61no—
52C3×C4⋊C4—61no—
53C4⋊Dic3—21no—
54C4⋊Dic3—121no—
55Dic3⋊C4—121no—
56Dic3⋊C4—121no—
57Dic3⋊C4—121no—
58Dic3⋊C4—121no—
59Dic3⋊C4—121no—
60C4×Dic3—61no—
61C4×Dic3—61no—
62#208—41no—
63C2×C3⋊C8—21no—
64C22×C32#9911yescharacteristic
65C32×C4—21no—
66C32×C4—41no—
67C3⋊Dic3—41no—
68C3⋊Dic3—41no—
69C3×Dic3—81no—
70C4⋊Q8—91no—
71#125—91no—
72#103—61no—
73#103—181no—
74#101—61no—
75#101—181no—
76#97—91no—
77C3×Q8—41no—
78C3×Q8—41no—
79C3×Q8—81no—
80C2×C3×C4—21no—
81C2×C3×C4—21no—
82C2×C3×C4—21no—
83C2×C3×C4—21no—
84C2×C3×C4—41no—
85C2×C3×C4—121no—
86C2×Dic3—41no—
87C2×Dic3—61no—
88C2×Dic3—61no—
89C2×Dic3—121no—
90C2×Dic3—121no—
91C2×Dic3—121no—
92Dic6—121no—
93Dic6—121no—
94Dic6—241no—
95C3×C8—121no—
96C3×C8—241no—
97C3⋊C8—41no—
98C3⋊C8—81no—
99C2×C32—21no—
100C2×C32#35411yescharacteristic
101C2×Q8—91no—
102C2×Q8GO+(4,𝔽2)11yescharacteristic
103M16—121no—
104M16—361no—
105C2×C8—61no—
106C4⋊C4—61no—
107C4⋊C4—361no—
108C4⋊C4—361no—
109C42—91no—
110C22×C3—21no—
111C22×C3—21no—
112C3×C4—21no—
113C3×C4—21no—
114C3×C4—41no—
115C3×C4—41no—
116C3×C4—41no—
117C3×C4—81no—
118C3×C4—241no—
119Dic3—81no—
120Dic3—121no—
121Dic3—121no—
122Dic3—122no—
123Dic3—241no—
124Dic3—241no—
125C32#141311yescharacteristic, complemented, Sylow
126Q8—41no—
127Q8—361no—
128C2×C4—21no—
129C2×C4—121no—
130C2×C4—181no—
131C2×C4—181no—
132C2×C4D32⋊C411yescharacteristic
133C8—121no—
134C8—241no—
135C8—721no—
136C2×C3—21no—
137C2×C3—21no—
138C2×C3—21no—
139C2×C3—21no—
140C2×C3—41no—
141C22#6373811yescharacteristic
142C4—21no—
143C4—41no—
144C4—241no—
145C4—361no—
146C4—361no—
147C3—21no—
148C3—21no—
149C2—21no—
150C2#1059008111yescharacteristic
subgroupG/H
centerC2#10590081
commutatorC4×C3⋊Dic3C2×C4
Frattini, hypercenterC2×Q8GO+(4,𝔽2)
FittingC2×C32×Q8D4
socleC2×C32#354
prime radicalC22×C32#99
cosocle#64153C22
hypocenterC32#1413
LCSG ▷ C4×C3⋊Dic3 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
125. C32#1413semidirect

Maximal subgroups

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

subgroupindex
#105916162
#105902182
#105891852
#14139