Finite Group Databasebeta

← #11776293

Subgroups — #11776293

Order 1152.

530 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2#10593729C211yesmaximal, characteristic
3#10593725C211yesmaximal, characteristic
4#10590162C214yesmaximal, complemented
5C2×Q8×C3⋊D3—21no—
6C2×#3788—21no—
7C32×C4⋊Q8C411yescharacteristic
8#64153—21no—
9C4⋊C4×C3⋊D3—21no—
10C4⋊C4×C3⋊D3C412yes—
11#64097—21no—
12#64097C2212yes—
13C42×C3⋊D3C2211yescharacteristic
14#64078C411yescharacteristic
15#63779—21no—
16#63779C2212yes—
17#63779C2212yes—
18#63778—21no—
19C4×#622—21no—
20D3×C4⋊Q8—62no—
21C2×C32×Q8—21no—
22Q8×C3⋊D3—42no—
23Q8×C3⋊D3—42no—
24C2×C4×C3⋊D3—22no—
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×#634—21no—
29C2×#634—22no—
30C2×#622—22no—
31C2×#622—22no—
32#3788—42no—
33C32×C4⋊C4—21no—
34C32×C4⋊C4C2×C412yes—
35C32×C42C2×C411yescharacteristic
36C4⋊(C3⋊Dic3)—21no—
37C4⋊(C3⋊Dic3)C2×C412yes—
38#3750—22no—
39#3750—22no—
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3C2311yescharacteristic
43#1546—91nomaximal, Sylow
44C2×D3×Q8—64no—
45C3×C4⋊Q8—22no—
46#944—64no—
47D3×C4⋊C4—64no—
48D3×C4⋊C4—64no—
49#888—64no—
50#888—64no—
51C42×D3—62no—
52#869—62no—
53C22×C3⋊D3C22⋊C411yescharacteristic
54C32×Q8—42no—
55C2×C32×C4—22no—
56C2×C32×C4C22⋊C411yescharacteristic
57C2×C32×C4C22⋊C411yescharacteristic
58C2×C32×C4C22×C411yescharacteristic
59C2×C3⋊Dic3—22no—
60C2×C3⋊Dic3C22⋊C411yescharacteristic
61C2×C3⋊Dic3C2×D411yescharacteristic
62C2×C3⋊Dic3C2×D411yescharacteristic
63C4×C3⋊D3—22no—
64C4×C3⋊D3—22no—
65C4×C3⋊D3—44no—
66C4×C3⋊D3D812yes—
67C4×C3⋊D3SD1612yes—
68#634—42no—
69#634—42no—
70#634—42no—
71#622—42no—
72#622—42no—
73C2×C4⋊Q8—91no—
74#431—91no—
75#423—91no—
76#332—94no—
77C2×C3×Q8—24no—
78D3×Q8—128no—
79D3×Q8—128no—
80C2×C4×D3—62no—
81C2×C4×D3—62no—
82C2×C4×D3—62no—
83C2×C4×D3—68no—
84C2×Dic6—64no—
85C2×Dic6—68no—
86C3×C4⋊C4—24no—
87C3×C4⋊C4—24no—
88C3×C42—22no—
89C4⋊Dic3—64no—
90C4⋊Dic3—64no—
91Dic3⋊C4—68no—
92Dic3⋊C4—68no—
93C4×Dic3—62no—
94C4×Dic3—62no—
95C4×Dic3—62no—
96C22×C32C2×C22⋊C411yescharacteristic
97C2×C3⋊D3—21no—
98C2×C3⋊D3—21no—
99C2×C3⋊D3#10212yes—
100C32×C4—21no—
101C32×C4—21no—
102C32×C4—42no—
103C32×C4#10212yes—
104C3⋊Dic3—42no—
105C3⋊Dic3#10112yes—
106C3⋊Dic3C2×D811yescharacteristic
107C3⋊Dic3C2×SD1611yescharacteristic
108C3⋊Dic3#13712yes—
109C22×Q8—181no—
110C2×M16—181no—
111C4⋊Q8—92no—
112C4⋊Q8—91no—
113C4⋊Q8—181no—
114C4⋊Q8—181no—
115C4⋊Q8#15711yescharacteristic
116C2×C4⋊C4—92no—
117C2×C4⋊C4—181no—
118C2×C42—91no—
119C4⋊C8—92no—
120C4⋊C8—92no—
121C4⋊C8—181no—
122C22⋊C8—181no—
123C4×C8—181no—
124C22×D3—62no—
125C3×Q8—48no—
126C2×C3×C4—28no—
127C2×C3×C4—22no—
128C2×C3×C4—22no—
129C2×C3×C4—22no—
130C2×Dic3—62no—
131C2×Dic3—62no—
132C2×Dic3—62no—
133C2×Dic3—68no—
134C4×D3—64no—
135C4×D3—64no—
136C4×D3—68no—
137C4×D3—68no—
138C4×D3—1216no—
139Dic6—128no—
140Dic6—128no—
141Dic6—128no—
142C2×C32C2×#10111yescharacteristic
143C2×C32C2×#10211yescharacteristic
144C2×C32#41911yescharacteristic
145C3⋊D3—22no—
146C2×Q8—21no—
147C2×Q8—182no—
148C2×Q8—181no—
149C2×Q8—362no—
150C2×Q8—362no—
151C22×C4—91no—
152C22×C4—91no—
153C22×C4—91no—
154C22×C4—182no—
155M16—362no—
156C2×C8—182no—
157C2×C8—182no—
158C4⋊C4—21no—
159C4⋊C4—92no—
160C4⋊C4—182no—
161C4⋊C4—182no—
162C4⋊C4—181no—
163C4⋊C4C2×#15712yes—
164C42—91no—
165C42—91no—
166C42—91no—
167C42C2×#15711yescharacteristic
168C22×C3—22no—
169C2×D3—64no—
170C2×D3—64no—
171C2×D3—64no—
172C3×C4—24no—
173C3×C4—24no—
174C3×C4—24no—
175C3×C4—48no—
176Dic3—62no—
177Dic3—62no—
178Dic3—64no—
179Dic3—64no—
180Dic3—128no—
181C32#154611yescharacteristic, complemented, Sylow
182C23—91no—
183Q8—42no—
184Q8—362no—
185Q8—362no—
186Q8—362no—
187C2×C4—22no—
188C2×C4—91no—
189C2×C4—91no—
190C2×C4—91no—
191C2×C4—92no—
192C2×C4—92no—
193C2×C4—182no—
194C2×C4—182no—
195C2×C4—182no—
196C2×C4—364no—
197C2×C4C22⋊#15711yescharacteristic
198C2×C4C22⋊#15711yescharacteristic
199C2×C4C22×#15711yescharacteristic
200C8—362no—
201C8—362no—
202C2×C3—22no—
203C2×C3—22no—
204C2×C3—22no—
205D3—68no—
206C22—92no—
207C22—181no—
208C22—181no—
209C22C2×C22⋊#15711yescharacteristic
210C4—21no—
211C4—21no—
212C4—42no—
213C4—91no—
214C4—91no—
215C4—92no—
216C4—92no—
217C4—362no—
218C4#6378212yes—
219C3—22no—
220C2—182no—
221C2C2×#6378211yescharacteristic
222C2#1059382911yescharacteristic
223C2#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#1546
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. #10590162C2semidirect
181. C32#1546semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
#105937292
#105937252
#105901622
#15469