Finite Group Databasebeta

← #11775761

Subgroups — #11775761

Order 1152.

448 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 64 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
2C4×#3788C211yesmaximal, characteristic
3C4×#3788C211yesmaximal, characteristic
4#10590159C214yesmaximal, complemented
5C2×#3788—21no—
6C2×#3788—21no—
7C32×C4⋊Q8C411yescharacteristic
8#64155—21no—
9Q8×C3⋊Dic3—21no—
10#64106—21no—
11#64101C412yes—
12#64099C2212yes—
13#64096—21no—
14C42×C3⋊D3C2211yescharacteristic
15#64078C411yescharacteristic
16#63777C2212yes—
17#63777C2212yes—
18C4×#622—21no—
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#3788—24no—
29#3788—24no—
30C32×C4⋊C4—21no—
31C32×C4⋊C4C2×C412yes—
32C32×C42C2×C411yescharacteristic
33#3752—22no—
34C4⋊(C3⋊Dic3)—21no—
35C4⋊(C3⋊Dic3)—22no—
36C4⋊(C3⋊Dic3)C2×C412yes—
37#3750—22no—
38C4×C3⋊Dic3—22no—
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3C2311yescharacteristic
42#1526—91nomaximal, Sylow
43C3×C4⋊Q8—22no—
44#946—64no—
45Q8×Dic3—64no—
46#897—64no—
47#892—64no—
48#890—64no—
49#887—64no—
50C42×D3—62no—
51#869—62no—
52C22×C3⋊D3C22⋊C411yescharacteristic
53C32×Q8—42no—
54C2×C32×C4—22no—
55C2×C32×C4C22⋊C411yescharacteristic
56C2×C32×C4C22⋊C411yescharacteristic
57C2×C32×C4C22×C411yescharacteristic
58C2×C3⋊Dic3—22no—
59C2×C3⋊Dic3C22⋊C411yescharacteristic
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3C2×D411yescharacteristic
62C4×C3⋊D3—22no—
63C4×C3⋊D3—22no—
64C4×C3⋊D3—22no—
65#634—42no—
66#622—24no—
67#622—24no—
68#533—91no—
69C4×M16—91no—
70C4×M16—91no—
71#330—94no—
72C2×C3×Q8—24no—
73C2×C4×D3—62no—
74C2×C4×D3—62no—
75C2×C4×D3—62no—
76C2×Dic6—64no—
77C3×C4⋊C4—24no—
78C3×C4⋊C4—24no—
79C3×C42—22no—
80(C2×D3)⋊C4—68no—
81C4⋊Dic3—64no—
82C4⋊Dic3—64no—
83C4⋊Dic3—68no—
84Dic3⋊C4—68no—
85C4×Dic3—62no—
86C4×Dic3—62no—
87C4×Dic3—62no—
88C4×Dic3—68no—
89C22×C32C2×C22⋊C411yescharacteristic
90C2×C3⋊D3—21no—
91C2×C3⋊D3—21no—
92C2×C3⋊D3—21no—
93C32×C4—21no—
94C32×C4—42no—
95C32×C4#10412yes—
96C32×C4#10412yes—
97C3⋊Dic3—21no—
98C3⋊Dic3—21no—
99C3⋊Dic3—42no—
100C3⋊Dic3#10112yes—
101C2×M16—181no—
102C2×M16—181no—
103C4⋊Q8—91no—
104C4⋊Q8#15711yescharacteristic
105#125—92no—
106C22⋊Q8—181no—
107C22⋊Q8—181no—
108C4×Q8—181no—
109C4×Q8—181no—
110#117—92no—
111C2×C42—91no—
112#97—92no—
113#97—92no—
114C4×C8—181no—
115C4×C8—181no—
116C22×D3—62no—
117C3×Q8—48no—
118C2×C3×C4—28no—
119C2×C3×C4—22no—
120C2×C3×C4—22no—
121C2×C3×C4—22no—
122C2×Dic3—62no—
123C2×Dic3—62no—
124C2×Dic3—62no—
125C2×Dic3—68no—
126C4×D3—68no—
127C4×D3—124no—
128C4×D3—124no—
129Dic6—128no—
130C2×C32C2×#10111yescharacteristic
131C2×C32C2×#10411yescharacteristic
132C2×C32C2×#10411yescharacteristic
133C3⋊D3—41no—
134C2×Q8—21no—
135C2×Q8—181no—
136C22×C4—91no—
137C22×C4—91no—
138C22×C4—91no—
139M16—184no—
140M16—184no—
141C2×C8—182no—
142C2×C8—182no—
143C4⋊C4—21no—
144C4⋊C4—92no—
145C4⋊C4—182no—
146C4⋊C4—182no—
147C4⋊C4—181no—
148C4⋊C4C2×#15712yes—
149C22⋊C4—182no—
150C42—91no—
151C42—91no—
152C42—91no—
153C42—182no—
154C42C2×#15711yescharacteristic
155C22×C3—22no—
156C2×D3—64no—
157C2×D3—122no—
158C2×D3—122no—
159C3×C4—24no—
160C3×C4—24no—
161C3×C4—24no—
162C3×C4—48no—
163Dic3—64no—
164Dic3—122no—
165Dic3—122no—
166Dic3—128no—
167C32#152611yescharacteristic, complemented, Sylow
168C23—91no—
169Q8—42no—
170Q8—362no—
171C2×C4—22no—
172C2×C4—91no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—182no—
176C2×C4—182no—
177C2×C4—182no—
178C2×C4—182no—
179C2×C4C22⋊#15711yescharacteristic
180C2×C4C22⋊#15711yescharacteristic
181C2×C4C22×#15711yescharacteristic
182C8—184no—
183C8—184no—
184C2×C3—22no—
185C2×C3—22no—
186C2×C3—22no—
187D3—124no—
188C22—181no—
189C22—181no—
190C22—181no—
191C22C2×C22⋊#15711yescharacteristic
192C4—21no—
193C4—42no—
194C4—92no—
195C4—181no—
196C4—181no—
197C4—362no—
198C4#6378312yes—
199C4#6378512yes—
200C3—22no—
201C2—361no—
202C2C2×#6378311yescharacteristic
203C2C2×#6378511yescharacteristic
204C2#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#1526
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
167. C32#1526semidirect

Maximal subgroups

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

subgroupindex
#105961992
C4×#37882
#105901592
#15269