Finite Group Databasebeta

← #11772616

Subgroups — #11772616

Order 1152.

358 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 44 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×#63780C212yesmaximal
2#10592628C211yesmaximal, characteristic
3C22×#634C2211yescharacteristic
4C2×#3792—22no—
5C2×C32×C42C411yescharacteristic
6C2×C4⋊(C3⋊Dic3)C411yescharacteristic
7#63780—22no—
8#63780C414yescomplemented
9#63658—22no—
10#4929—62no—
11C22×C32×C4—21no—
12C22×C32×C4C2×C411yescharacteristic
13C22×C3⋊Dic3—21no—
14C22×C3⋊Dic3D412yes—
15C2×#634—41no—
16C2×#634—41no—
17C2×#634C2×C412yes—
18C2×#634D411yescharacteristic
19C2×#634Q811yescharacteristic
20#3792—24no—
21#3792—42no—
22C2×#622—42no—
23C32×C42—41no—
24C4⋊(C3⋊Dic3)—41no—
25#1394—91nomaximal, Sylow
26C22×Dic6—62no—
27C2×C3×C42—22no—
28C2×C4⋊Dic3—62no—
29C3⋊#95—68no—
30C23×C32C22⋊C411yescharacteristic
31C2×C32×C4—21no—
32C2×C32×C4—21no—
33C2×C32×C4—22no—
34C2×C32×C4—41no—
35C2×C32×C4—41no—
36C2×C32×C4C4211yescharacteristic
37C2×C32×C4C4⋊C411yescharacteristic
38C2×C3⋊Dic3—22no—
39C2×C3⋊Dic3—22no—
40C2×C3⋊Dic3—42no—
41C2×C3⋊Dic3—41no—
42C2×C3⋊Dic3C22⋊C412yes—
43C2×C3⋊Dic3C4⋊C412yes—
44#634—42no—
45#634—41no—
46#634—41no—
47#622—44no—
48C2×#101—92no—
49#391—91no—
50C22×C3×C4—24no—
51C22×C3×C4—22no—
52C22×Dic3—64no—
53C22×Dic3—64no—
54C2×Dic6—64no—
55C2×Dic6—62no—
56C2×Dic6—62no—
57C2×Dic6—124no—
58C2×Dic6—124no—
59C3×C42—44no—
60C4⋊Dic3—124no—
61C22×C32—21no—
62C22×C32—21no—
63C22×C32#9511yescharacteristic
64C22×C32#9911yescharacteristic
65C22×C32#9911yescharacteristic
66C32×C4—21no—
67C32×C4—21no—
68C32×C4—42no—
69C3⋊Dic3—22no—
70C3⋊Dic3—22no—
71C3⋊Dic3—81no—
72C22×Q8—91no—
73C2×M16—182no—
74C2×C4⋊C4—91no—
75C2×C42#15711yescharacteristic
76#101—94no—
77#101—182no—
78#95—182no—
79C23×C3—22no—
80C2×C3×C4—24no—
81C2×C3×C4—24no—
82C2×C3×C4—28no—
83C2×C3×C4—22no—
84C2×C3×C4—22no—
85C2×C3×C4—44no—
86C2×C3×C4—44no—
87C2×Dic3—64no—
88C2×Dic3—64no—
89C2×Dic3—124no—
90C2×Dic3—124no—
91C2×Dic3—124no—
92C2×Dic3—128no—
93Dic6—128no—
94Dic6—124no—
95Dic6—124no—
96C2×C32—21no—
97C2×C32—21no—
98C2×C32#34211yescharacteristic
99C2×C32#35511yescharacteristic
100C2×C32#35611yescharacteristic
101C2×Q8—92no—
102C2×Q8—91no—
103C2×Q8—91no—
104C2×Q8—361no—
105C2×Q8—361no—
106C22×C4—21no—
107C22×C4—92no—
108C22×C4—181no—
109C22×C4C2×#15711yescharacteristic
110M16—184no—
111M16—362no—
112C2×C8—362no—
113C4⋊C4—361no—
114C42—41no—
115C22×C3—24no—
116C22×C3—24no—
117C22×C3—22no—
118C22×C3—22no—
119C22×C3—22no—
120C3×C4—24no—
121C3×C4—24no—
122C3×C4—48no—
123Dic3—124no—
124Dic3—124no—
125Dic3—244no—
126C32#139411yescharacteristic, complemented, Sylow
127C23C22⋊#15711yescharacteristic
128Q8—362no—
129Q8—361no—
130Q8—361no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—22no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—92no—
137C2×C4—92no—
138C2×C4—182no—
139C2×C4—182no—
140C2×C4—362no—
141C2×C4—361no—
142C2×C4C4×#15711yescharacteristic
143C2×C4C4⋊#15711yescharacteristic
144C8—364no—
145C2×C3—24no—
146C2×C3—24no—
147C2×C3—22no—
148C2×C3—22no—
149C2×C3—22no—
150C22—21no—
151C22—21no—
152C22#6377411yescharacteristic
153C22#6378111yescharacteristic
154C22#6378611yescharacteristic
155C4—21no—
156C4—21no—
157C4—42no—
158C4—182no—
159C4—182no—
160C4—721no—
161C3—22no—
162C2—21no—
163C2—21no—
164C2#1059014411yescharacteristic
165C2#1059014511yescharacteristic
166C2#1059020611yescharacteristic
subgroupG/H
centerC22#63774
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC2×C32×C42C4
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC22×#634C22
hypercenterC2×C42#157
hypocenterC32#1394
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
8. #63780C4semidirect
126. C32#1394semidirect

Maximal subgroups

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

subgroupindex
C2×#637802
#105926282
#13949