Finite Group Databasebeta

← #11791872

Subgroups — #11791872

Order 1152.

550 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 76 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×#64153C211yesmaximal, characteristic
2#10593805C211yesmaximal, characteristic
3C4×#3792C211yesmaximal, characteristic
4#10590208C214yesmaximal
5C22×C32×Q8C411yescharacteristic
6C22×#634C411yescharacteristic
7C2×#3792C2212yes—
8C2×#3792C2212yes—
9#64153—21no—
10#64153—21no—
11#64153—21no—
12#64153—21no—
13C2×#3750C412yes—
14C2×#3750C2212yes—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#63779—21no—
17#63777—21no—
18C4⋊#622—21no—
19C4×#622—21no—
20C2×#944—62no—
21C2×C32×Q8—21no—
22C2×C32×Q8—21no—
23C2×C32×Q8—42no—
24C22×C32×C4C2×C411yescharacteristic
25C22×C32×C4C2×C412yes—
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3C2×C412yes—
28C22×C3⋊Dic3C2311yescharacteristic
29C2×#634—21no—
30C2×#634—21no—
31C2×#634—42no—
32#3792—22no—
33#3792—24no—
34#3792Q814yescomplemented
35C2×#622—22no—
36C2×#622—22no—
37#3750—22no—
38#3750—22no—
39#3750—22no—
40#3750—22no—
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C4×C3⋊Dic3D411yescharacteristic
44C4×C3⋊Dic3D411yescharacteristic
45#1997—91nomaximal, Sylow
46C22×C3×Q8—22no—
47C22×Dic6—62no—
48#944—64no—
49#944—64no—
50#944—64no—
51#944—64no—
52C2×Dic3⋊C4—64no—
53C2×Dic3⋊C4—64no—
54C2×C4×Dic3—62no—
55C23×C32C22×C411yescharacteristic
56C32×Q8—42no—
57C32×Q8—42no—
58C2×C32×C4—22no—
59C2×C32×C4—22no—
60C2×C32×C4—42no—
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3—42no—
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C2×D411yescharacteristic
69C2×C3⋊Dic3C2×D411yescharacteristic
70C2×C3⋊Dic3C2×Q812yes—
71C2×C3⋊Dic3#4112yes—
72#634—42no—
73#634—42no—
74#622—24no—
75#622—42no—
76C2×C4⋊Q8—91no—
77#423—91no—
78C4×M16—91no—
79#343—94no—
80C2×C3×Q8—24no—
81C2×C3×Q8—24no—
82C2×C3×Q8—48no—
83C22×C3×C4—24no—
84C22×C3×C4—22no—
85C22×Dic3—62no—
86C22×Dic3—62no—
87C22×Dic3—64no—
88C2×Dic6—64no—
89C2×Dic6—64no—
90C2×Dic6—128no—
91Dic3⋊C4—68no—
92Dic3⋊C4—68no—
93Dic3⋊C4—68no—
94Dic3⋊C4—68no—
95C4×Dic3—62no—
96C4×Dic3—62no—
97C4×Dic3—62no—
98C4×Dic3—62no—
99C22×C32—21no—
100C22×C32—21no—
101C22×C32C2×C22⋊C411yescharacteristic
102C22×C32C4×Q812yes—
103C32×C4—21no—
104C32×C4—42no—
105C32×C4#10012yes—
106C3⋊Dic3—21no—
107C3⋊Dic3—42no—
108C3⋊Dic3#10112yes—
109C3⋊Dic3C22⋊Q812yes—
110C3⋊Dic3#12411yescharacteristic
111C3⋊Dic3C4⋊Q811yescharacteristic
112C22×Q8—91no—
113C22×Q8#15711yescharacteristic
114C2×M16—92no—
115C2×M16—92no—
116C4⋊Q8—181no—
117C4⋊Q8—181no—
118C4⋊Q8—181no—
119C4⋊Q8—181no—
120C2×C4⋊C4—92no—
121C2×C4⋊C4—92no—
122C2×C42—91no—
123C4⋊C8—181no—
124C4⋊C8—181no—
125#97—181no—
126C4×C8—181no—
127C23×C3—22no—
128C3×Q8—48no—
129C3×Q8—48no—
130C2×C3×C4—28no—
131C2×C3×C4—28no—
132C2×C3×C4—22no—
133C2×C3×C4—22no—
134C2×C3×C4—48no—
135C2×Dic3—62no—
136C2×Dic3—62no—
137C2×Dic3—62no—
138C2×Dic3—62no—
139C2×Dic3—64no—
140C2×Dic3—64no—
141C2×Dic3—68no—
142C2×Dic3—68no—
143C2×Dic3—128no—
144Dic6—128no—
145Dic6—128no—
146C2×C32—22no—
147C2×C32#39111yescharacteristic
148C2×C32C2×#10011yescharacteristic
149C2×C32C2×#10111yescharacteristic
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—42no—
153C2×Q8—181no—
154C2×Q8—181no—
155C2×Q8—362no—
156C22×C4—91no—
157C22×C4—91no—
158C22×C4—92no—
159C22×C4C2×#15712yes—
160C22×C4C2×#15711yescharacteristic
161M16—94no—
162M16—182no—
163M16—184no—
164C2×C8—182no—
165C2×C8—182no—
166C4⋊C4—182no—
167C4⋊C4—182no—
168C4⋊C4—182no—
169C4⋊C4—182no—
170C42—91no—
171C42—91no—
172C42—91no—
173C42—91no—
174C22×C3—24no—
175C22×C3—24no—
176C22×C3—24no—
177C22×C3—22no—
178C3×C4—24no—
179C3×C4—24no—
180C3×C4—48no—
181Dic3—64no—
182Dic3—64no—
183Dic3—62no—
184Dic3—62no—
185Dic3—64no—
186Dic3—128no—
187C32#199711yescharacteristic, complemented, Sylow
188C23C22×#15711yescharacteristic
189Q8—42no—
190Q8—42no—
191Q8—362no—
192Q8—362no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—42no—
196C2×C4—92no—
197C2×C4—92no—
198C2×C4—91no—
199C2×C4—91no—
200C2×C4—91no—
201C2×C4—91no—
202C2×C4—182no—
203C2×C4—182no—
204C2×C4—362no—
205C2×C4C22⋊#15711yescharacteristic
206C2×C4C22⋊#15711yescharacteristic
207C8—184no—
208C8—362no—
209C2×C3—28no—
210C2×C3—22no—
211C2×C3—22no—
212C2×C3—22no—
213C22—21no—
214C22—21no—
215C22Q8×#15712yes—
216C22C2×C22⋊#15711yescharacteristic
217C4—21no—
218C4—42no—
219C4—92no—
220C4—92no—
221C4—91no—
222C4—91no—
223C4—181no—
224C4—362no—
225C4#6378812yes—
226C3—22no—
227C2—22no—
228C2#1059383611yescharacteristic
229C2#1059383711yescharacteristic
230C2C2×#6378811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutator, prime radicalC23×C32C22×C4
FrattiniC23C22×#157
FittingC22×C32×Q8C4
socleC22×C32C2×C22⋊C4
cosocleC22×C3⋊Dic3C23
hypercenterC22×Q8#157
hypocenterC32#1997
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
34. #3792Q8semidirect
187. C32#1997semidirect

Maximal subgroups

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

subgroupindex
C2×#641532
#105938052
C4×#37922
#105902082
#19979