Finite Group Databasebeta

← #11771232

Subgroups — #11771232

Order 1152.

434 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 46 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#10593845C211yesmaximal, characteristic
2#10593845C211yesmaximal, characteristic
3#10592641C211yesmaximal, characteristic
4C23×C3⋊Dic3C2211yescharacteristic
5C2×#3792—21no—
6C2×#3792C412yescomplemented
7C2×C32×C22⋊C4C411yescharacteristic
8C2×#3757C411yescharacteristic
9C2×#3750—21no—
10C22⋊#622—21no—
11C22⋊#622—21no—
12C22⋊#622—21no—
13C22⋊#622C412yescomplemented
14#63658—21no—
15#4942—62no—
16C24×C32C2×C411yescharacteristic
17C22×C32×C4—21no—
18C22×C3⋊Dic3—21no—
19C22×C3⋊Dic3—42no—
20C22×C3⋊Dic3C2×C411yescharacteristic
21C22×C3⋊Dic3C2×C411yescharacteristic
22C22×C3⋊Dic3D411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C22×C3⋊Dic3Q811yescharacteristic
26#3792—42no—
27#3792—42no—
28C2×#622—22no—
29C2×#622—22no—
30C32×C22⋊C4—41no—
31#3757—41no—
32#3750—42no—
33#1305—91nomaximal, Sylow
34C23×Dic3—62no—
35C2×C3×C22⋊C4—22no—
36C2×#217—62no—
37C2×Dic3⋊C4—64no—
38C3⋊#95—64no—
39C23×C32—21no—
40C23×C32—21no—
41C23×C32—41no—
42C23×C32—41no—
43C23×C32C4211yescharacteristic
44C23×C32C22⋊C411yescharacteristic
45C23×C32C4⋊C411yescharacteristic
46C2×C32×C4—41no—
47C2×C32×C4—41no—
48C2×C32×C4—41no—
49C2×C3⋊Dic3—22no—
50C2×C3⋊Dic3—22no—
51C2×C3⋊Dic3—22no—
52C2×C3⋊Dic3—41no—
53C2×C3⋊Dic3—41no—
54C2×C3⋊Dic3—41no—
55C2×C3⋊Dic3—41no—
56C2×C3⋊Dic3—41no—
57C2×C3⋊Dic3—41no—
58C2×C3⋊Dic3C22⋊C411yescharacteristic
59C2×C3⋊Dic3C22⋊C411yescharacteristic
60C2×C3⋊Dic3C4⋊C411yescharacteristic
61C2×C3⋊Dic3C4⋊C411yescharacteristic
62#622—42no—
63#622—42no—
64#407—91no—
65#407—91no—
66#380—91no—
67C24×C3—22no—
68C22×C3×C4—24no—
69C22×Dic3—62no—
70C22×Dic3—62no—
71C22×Dic3—62no—
72C22×Dic3—62no—
73C22×Dic3—62no—
74C22×Dic3—62no—
75C22×Dic3—64no—
76C22×Dic3—128no—
77C3×C22⋊C4—44no—
78#217—124no—
79Dic3⋊C4—128no—
80C22×C32—21no—
81C22×C32—21no—
82C22×C32—21no—
83C22×C32—21no—
84C22×C32—21no—
85C22×C32—21no—
86C22×C32—21no—
87C22×C32—21no—
88C22×C32—42no—
89C22×C32—42no—
90C22×C32#9511yescharacteristic
91C22×C32#10011yescharacteristic
92C22×C32#10111yescharacteristic
93C32×C4—81no—
94C3⋊Dic3—21no—
95C3⋊Dic3—21no—
96C3⋊Dic3—21no—
97C3⋊Dic3—81no—
98C3⋊Dic3#9912yes—
99C23×C4—91no—
100C2×M16—92no—
101C2×M16—181no—
102C2×C4⋊C4—181no—
103C2×C22⋊C4—91no—
104C2×C22⋊C4#15711yescharacteristic
105C22⋊C8—92no—
106C22⋊C8—181no—
107C22⋊C8—181no—
108C22⋊C8—181no—
109#95—181no—
110C23×C3—24no—
111C23×C3—24no—
112C23×C3—22no—
113C23×C3—22no—
114C23×C3—22no—
115C23×C3—44no—
116C23×C3—44no—
117C2×C3×C4—44no—
118C2×C3×C4—44no—
119C2×C3×C4—44no—
120C2×Dic3—62no—
121C2×Dic3—62no—
122C2×Dic3—62no—
123C2×Dic3—62no—
124C2×Dic3—68no—
125C2×Dic3—124no—
126C2×Dic3—124no—
127C2×Dic3—124no—
128C2×Dic3—124no—
129C2×Dic3—124no—
130C2×Dic3—124no—
131C2×Dic3—124no—
132C2×Dic3—124no—
133C2×C32—21no—
134C2×C32—21no—
135C2×C32—41no—
136C2×C32—41no—
137C2×C32#34211yescharacteristic
138C2×C32#34311yescharacteristic
139C2×C32#34411yescharacteristic
140C24C2×#15711yescharacteristic
141C22×C4—21no—
142C22×C4—91no—
143C22×C4—91no—
144C22×C4—91no—
145C22×C4—91no—
146C22×C4—91no—
147C22×C4—91no—
148C22×C4—181no—
149C22×C4—362no—
150M16—362no—
151M16—362no—
152C2×C8—182no—
153C2×C8—182no—
154C4⋊C4—362no—
155C22⋊C4—41no—
156C22⋊C4—361no—
157C22×C3—24no—
158C22×C3—24no—
159C22×C3—24no—
160C22×C3—24no—
161C22×C3—22no—
162C22×C3—22no—
163C22×C3—22no—
164C22×C3—42no—
165C22×C3—42no—
166C22×C3—42no—
167C22×C3—42no—
168C22×C3—48no—
169C22×C3—48no—
170C3×C4—84no—
171Dic3—64no—
172Dic3—64no—
173Dic3—122no—
174Dic3—122no—
175Dic3—244no—
176C32#130511yescharacteristic, complemented, Sylow
177C23—21no—
178C23—21no—
179C23—41no—
180C23—41no—
181C23C4×#15711yescharacteristic
182C23C4⋊#15711yescharacteristic
183C23C22⋊#15711yescharacteristic
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—91no—
188C2×C4—91no—
189C2×C4—91no—
190C2×C4—91no—
191C2×C4—182no—
192C2×C4—182no—
193C2×C4—182no—
194C2×C4—361no—
195C2×C4—361no—
196C2×C4—361no—
197C2×C4—361no—
198C2×C4—361no—
199C2×C4—361no—
200C8—362no—
201C8—362no—
202C2×C3—24no—
203C2×C3—24no—
204C2×C3—22no—
205C2×C3—22no—
206C2×C3—22no—
207C2×C3—44no—
208C2×C3—44no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—42no—
218C22—42no—
219C22#6378011yescharacteristic
220C22#6378111yescharacteristic
221C22#6378811yescharacteristic
222C4—81no—
223C4—92no—
224C4—181no—
225C4—181no—
226C4—181no—
227C4—721no—
228C3—22no—
229C2—21no—
230C2—21no—
231C2—41no—
232C2—41no—
233C2#1059015511yescharacteristic
234C2#1059015611yescharacteristic
235C2#1059020811yescharacteristic
subgroupG/H
centerC22#63781
commutatorC23×C32C42
FrattiniC24C2×#157
FittingC2×C32×C22⋊C4C4
socleC22×C32#95
prime radicalC24×C32C2×C4
cosocleC23×C3⋊Dic3C22
hypercenterC2×C22⋊C4#157
hypocenterC32#1305
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. C2×#3792C4semidirect
13. C22⋊#622C4semidirect
176. C32#1305semidirect

Maximal subgroups

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

subgroupindex
#105938452
#105926412
#13059