Finite Group Databasebeta

← #11784239

Subgroups — #11784239

Order 1152.

414 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 95 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#10593733C211yesmaximal, characteristic
2C2×#63732C212yesmaximal
3#10590322C211yesmaximal, characteristic
4C4×#3710C211yesmaximal, characteristic
5#10590044C212yesmaximal
6C2×C4×#157C2211yescharacteristic
7C2×C4×#157C2211yescharacteristic
8C42×C3⋊D3C2211yescharacteristic
9C2×#3710C2212yes—
10C2×#3710C2212yes—
11#63781C414yes—
12#63732C418yescomplemented
13C3×#803—21no—
14C3×C4×C3⋊C8—21no—
15#63555—21no—
16#63553—21no—
17D3×#97—61no—
18C4×D3×C8—61no—
19C22×#157C2×C412yes—
20C22×#157C2×C412yes—
21C2×C4×C3⋊D3C2×C412yes—
22C2×C4×C3⋊D3C2311yescharacteristic
23C4×#157—22no—
24C4×#157C2×C414yes—
25C32×C42D411yescharacteristic
26C4×C3⋊Dic3D411yescharacteristic
27C4×C3⋊Dic3Q812yes—
28C2×C3×C3⋊C8—22no—
29C2×C3×C3⋊C8—22no—
30#3710—22no—
31#3710—22no—
32#3710C2×C414yes—
33#3710C2×C414yes—
34#1768—91nomaximal, Sylow
35C2×D3×C8—62no—
36C2×D3×C8—62no—
37C42×D3—61no—
38C42×D3—61no—
39C3×#97—61no—
40C3×C4×C8—61no—
41#815—62no—
42C8×Dic3—62no—
43#803—21no—
44C4×C3⋊C8—21no—
45C22×C3⋊D3C22×C411yescharacteristic
46C2×#157—24no—
47C2×#157—22no—
48C2×#157—24no—
49C2×#157C4214yes—
50C2×C32×C4C4⋊C412yes—
51C2×C32×C4C2×D411yescharacteristic
52C2×C3⋊Dic3C4⋊C412yes—
53C2×C3⋊Dic3C2×Q811yescharacteristic
54C4×C3⋊D3—24no—
55C4×C3⋊D3C22×C412yes—
56C4×C3⋊D3#4112yes—
57C3×C3⋊C8—24no—
58C3×C3⋊C8—24no—
59C2×C4⋊C8—92no—
60C2×#97—91no—
61C2×C4×C8—91no—
62#376—91no—
63#336—92no—
64C2×C4×D3—61no—
65C2×C4×D3—61no—
66C2×C4×D3—62no—
67C2×C4×D3—62no—
68C2×C3×C8—62no—
69C2×C3×C8—62no—
70C3×C42—21no—
71C3×C42—21no—
72C4×Dic3—61no—
73C4×Dic3—61no—
74C4×Dic3—62no—
75C4×Dic3—62no—
76C2×C3⋊C8—22no—
77C2×C3⋊C8—22no—
78D3×C8—64no—
79D3×C8—64no—
80D3×C8—64no—
81D3×C8—64no—
82C22×C32C2×C4⋊C411yescharacteristic
83C2×C3⋊D3C2×C4211yescharacteristic
84C2×C3⋊D3#11711yescharacteristic
85C2×C3⋊D3#13114yes—
86#157—24no—
87#157—42no—
88C32×C4—22no—
89C32×C4C4×D412yes—
90C3⋊Dic3—22no—
91C3⋊Dic3C4×Q812yes—
92C22×C8—92no—
93C22×C8—92no—
94C2×C42—91no—
95C2×C42—91no—
96C2×C42—91no—
97C4⋊C8—98no—
98#97—61no—
99#97—181no—
100C4×C8—61no—
101C4×C8—181no—
102#95—94no—
103C22×D3—61no—
104C22×D3—61no—
105C2×C3×C4—21no—
106C2×C3×C4—21no—
107C2×C3×C4—22no—
108C2×C3×C4—22no—
109C2×Dic3—62no—
110C2×Dic3—61no—
111C2×Dic3—61no—
112C2×Dic3—62no—
113C4×D3—62no—
114C4×D3—62no—
115C4×D3—62no—
116C4×D3—62no—
117C4×D3—68no—
118C4×D3—124no—
119C3×C8—64no—
120C3×C8—64no—
121C3⋊C8—24no—
122C3⋊C8—24no—
123C2×C32C4×C4⋊C411yescharacteristic
124C2×C32#42412yes—
125C3⋊D3#40512yes—
126C3⋊D3#43312yes—
127C22×C4—91no—
128C22×C4—92no—
129C22×C4—92no—
130C22×C4—92no—
131C2×C8—62no—
132C2×C8—62no—
133C2×C8—94no—
134C2×C8—94no—
135C2×C8—182no—
136C2×C8—182no—
137C42—94no—
138C42—91no—
139C42—92no—
140C42—182no—
141C42GO+(4,𝔽2)11yescharacteristic
142C22×C3—21no—
143C22×C3—21no—
144C2×D3—61no—
145C2×D3—61no—
146C2×D3—61no—
147C2×D3—61no—
148C2×D3—64no—
149C2×D3—64no—
150C3×C4—24no—
151C3×C4—22no—
152C3×C4—22no—
153C3×C4—42no—
154Dic3—62no—
155Dic3—62no—
156Dic3—64no—
157Dic3—122no—
158C32#176811yescharacteristic, complemented, Sylow
159C23—91no—
160C2×C4—91no—
161C2×C4—92no—
162C2×C4—92no—
163C2×C4—94no—
164C2×C4—92no—
165C2×C4—184no—
166C2×C4—184no—
167C2×C4—182no—
168C2×C4—184no—
169C2×C4#377312yes—
170C2×C4C2×GO+(4,𝔽2)11yescharacteristic
171C8—64no—
172C8—64no—
173C2×C3—22no—
174C2×C3—22no—
175C2×C3—21no—
176C2×C3—21no—
177D3—62no—
178D3—62no—
179D3—62no—
180D3—62no—
181C22—94no—
182C22—91no—
183C22—91no—
184C22C2×#377311yescharacteristic
185C4—22no—
186C4—92no—
187C4—184no—
188C4—182no—
189C4—362no—
190C4C4×GO+(4,𝔽2)12yes—
191C3—21no—
192C3—21no—
193C2—92no—
194C2—92no—
195C2#1059332712yes—
196C2C4×#377311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C2×C42
FittingC32×C42D4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1768
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
12. #63732C4semidirect
158. C32#1768semidirect

Maximal subgroups

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

subgroupindex
#105937332
C2×#637322
#105903222
C4×#37102
#105900442
#17689