Finite Group Databasebeta

← #11775903

Subgroups — #11775903

Order 1152.

434 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 60 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#10596199C211yesmaximal, characteristic
2#10593730C211yesmaximal, characteristic
3#10593723C211yesmaximal, characteristic
4#10590159C214yesmaximal, complemented
5C2×#3787—21no—
6C32×C4⋊Q8C411yescharacteristic
7#64155—21no—
8Q8×C3⋊Dic3—21no—
9#64106—21no—
10#64101C412yes—
11#64099C2212yes—
12#64096—21no—
13C42×C3⋊D3C2211yescharacteristic
14#64078C411yescharacteristic
15#63778—21no—
16#63777—21no—
17#63777C2212yes—
18#63777C2212yes—
19C4⋊#622—21no—
20#5728—62no—
21C2×C32×Q8—21no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×#634—21no—
26C2×#622—22no—
27C2×#622—22no—
28#3787—24no—
29C32×C4⋊C4—21no—
30C32×C4⋊C4C2×C412yes—
31C32×C42C2×C411yescharacteristic
32#3752—22no—
33C4⋊(C3⋊Dic3)—21no—
34C4⋊(C3⋊Dic3)—22no—
35C4⋊(C3⋊Dic3)C2×C412yes—
36#3750—22no—
37C4×C3⋊Dic3—22no—
38C4×C3⋊Dic3D411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3C2311yescharacteristic
41#1531—91nomaximal, Sylow
42C3×C4⋊Q8—22no—
43#946—64no—
44Q8×Dic3—64no—
45#897—64no—
46#892—64no—
47#890—64no—
48#887—64no—
49C42×D3—62no—
50#869—62no—
51C22×C3⋊D3C22⋊C411yescharacteristic
52C32×Q8—42no—
53C2×C32×C4—22no—
54C2×C32×C4C22⋊C411yescharacteristic
55C2×C32×C4C22⋊C411yescharacteristic
56C2×C32×C4C22×C411yescharacteristic
57C2×C3⋊Dic3—22no—
58C2×C3⋊Dic3C22⋊C411yescharacteristic
59C2×C3⋊Dic3C2×D411yescharacteristic
60C2×C3⋊Dic3C2×D411yescharacteristic
61C4×C3⋊D3—22no—
62C4×C3⋊D3—22no—
63C4×C3⋊D3—41no—
64#634—42no—
65#622—24no—
66#622—42no—
67#533—91no—
68#432—91no—
69C2×#97—91no—
70#330—94no—
71C2×C3×Q8—24no—
72C2×C4×D3—62no—
73C2×C4×D3—62no—
74C2×C4×D3—62no—
75C2×Dic6—64no—
76C3×C4⋊C4—24no—
77C3×C4⋊C4—24no—
78C3×C42—22no—
79(C2×D3)⋊C4—68no—
80C4⋊Dic3—64no—
81C4⋊Dic3—64no—
82C4⋊Dic3—68no—
83Dic3⋊C4—68no—
84C4×Dic3—62no—
85C4×Dic3—62no—
86C4×Dic3—62no—
87C4×Dic3—68no—
88C22×C32C2×C22⋊C411yescharacteristic
89C2×C3⋊D3—21no—
90C2×C3⋊D3—21no—
91C2×C3⋊D3#10112yes—
92C32×C4—21no—
93C32×C4—21no—
94C32×C4—42no—
95C32×C4#10412yes—
96C3⋊Dic3—21no—
97C3⋊Dic3—21no—
98C3⋊Dic3—21no—
99C3⋊Dic3—42no—
100C22×C8—181no—
101C4⋊Q8—91no—
102C4⋊Q8#15711yescharacteristic
103#125—92no—
104C22⋊Q8—181no—
105C22⋊Q8—181no—
106C4×Q8—181no—
107C4×Q8—181no—
108#117—92no—
109C2×C42—91no—
110C4⋊C8—181no—
111C22⋊C8—181no—
112#97—92no—
113#97—92no—
114#97—181no—
115C22×D3—62no—
116C3×Q8—48no—
117C2×C3×C4—28no—
118C2×C3×C4—22no—
119C2×C3×C4—22no—
120C2×C3×C4—22no—
121C2×Dic3—62no—
122C2×Dic3—62no—
123C2×Dic3—62no—
124C2×Dic3—68no—
125C4×D3—68no—
126C4×D3—124no—
127C4×D3—124no—
128Dic6—128no—
129C2×C32C2×#10111yescharacteristic
130C2×C32C2×#10411yescharacteristic
131C2×C32#42111yescharacteristic
132C3⋊D3—22no—
133C2×Q8—21no—
134C2×Q8—181no—
135C22×C4—91no—
136C22×C4—91no—
137C22×C4—91no—
138C2×C8—182no—
139C2×C8—184no—
140C2×C8—182no—
141C4⋊C4—21no—
142C4⋊C4—92no—
143C4⋊C4—182no—
144C4⋊C4—182no—
145C4⋊C4—181no—
146C4⋊C4C2×#15712yes—
147C22⋊C4—182no—
148C42—91no—
149C42—91no—
150C42—91no—
151C42—182no—
152C42C2×#15711yescharacteristic
153C22×C3—22no—
154C2×D3—64no—
155C2×D3—122no—
156C2×D3—122no—
157C3×C4—24no—
158C3×C4—24no—
159C3×C4—24no—
160C3×C4—48no—
161Dic3—64no—
162Dic3—122no—
163Dic3—122no—
164Dic3—128no—
165C32#153111yescharacteristic, complemented, Sylow
166C23—91no—
167Q8—42no—
168Q8—362no—
169C2×C4—22no—
170C2×C4—91no—
171C2×C4—91no—
172C2×C4—91no—
173C2×C4—182no—
174C2×C4—182no—
175C2×C4—182no—
176C2×C4—361no—
177C2×C4C22⋊#15711yescharacteristic
178C2×C4C22⋊#15711yescharacteristic
179C2×C4C22×#15711yescharacteristic
180C8—184no—
181C8—362no—
182C2×C3—22no—
183C2×C3—22no—
184C2×C3—22no—
185D3—124no—
186C22—92no—
187C22—181no—
188C22—181no—
189C22C2×C22⋊#15711yescharacteristic
190C4—21no—
191C4—21no—
192C4—42no—
193C4—181no—
194C4—181no—
195C4—181no—
196C4—362no—
197C4#6378312yes—
198C3—22no—
199C2—182no—
200C2C2×#6378311yescharacteristic
201C2#1059383111yescharacteristic
202C2#1059383611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4⋊Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC4⋊Q8#157
hypocenterC32#1531
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #10590159C2semidirect
165. C32#1531semidirect

Maximal subgroups

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

subgroupindex
#105961992
#105937302
#105937232
#105901592
#15319