Finite Group Databasebeta

← #11770881

Subgroups — #11770881

Order 1152.

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

normal subgroups only

This group has 484 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#10593811C211yesmaximal, characteristic
2#10593802C211yesmaximal, characteristic
3C4×#3752C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×C22⋊#157—21no—
6C2×#3792—21no—
7C2×C32×C42C411yescharacteristic, complemented
8C2×#3752—21no—
9C2×C4×C3⋊Dic3C411yescharacteristic, complemented
10#63781—21no—
11#63781C412yescomplemented
12#63778—21no—
13#63778C412yescomplemented
14#63658—21no—
15C4×(C2×D3)⋊C4—62no—
16C23×C3⋊D3D411yescharacteristic
17C22×#157—22no—
18C22×C32×C4—21no—
19C22×C32×C4C2×C411yescharacteristic
20C22×C3⋊Dic3—21no—
21C22×C3⋊Dic3D411yescharacteristic
22C2×C4×C3⋊D3—41no—
23C2×C4×C3⋊D3—41no—
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3Q811yescharacteristic
28C22⋊#157—41no—
29C22⋊#157—41no—
30#3792—41no—
31#3792—41no—
32C2×#622—22no—
33C32×C42—41no—
34#3752—24no—
35C4×C3⋊Dic3—41no—
36#1284—91nomaximal, Sylow
37C22×C4×D3—62no—
38C2×C3×C42—22no—
39C2×(C2×D3)⋊C4—64no—
40C2×C4×Dic3—62no—
41C3⋊#95—64no—
42C23×C32C22⋊C411yescharacteristic
43C22×C3⋊D3—22no—
44C22×C3⋊D3—21no—
45C22×C3⋊D3—21no—
46C22×C3⋊D3—41no—
47C22×C3⋊D3C22⋊C411yescharacteristic
48C22×C3⋊D3C4⋊C411yescharacteristic
49C2×#157—42no—
50C2×#157—42no—
51C2×#157—42no—
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4—22no—
55C2×C32×C4—41no—
56C2×C32×C4—41no—
57C2×C32×C4C4211yescharacteristic
58C2×C32×C4C4⋊C411yescharacteristic
59C2×C3⋊Dic3—22no—
60C2×C3⋊Dic3—21no—
61C2×C3⋊Dic3—21no—
62C2×C3⋊Dic3—41no—
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3C22⋊C411yescharacteristic
65C2×C3⋊Dic3C4⋊C411yescharacteristic
66C4×C3⋊D3—41no—
67C4×C3⋊D3—41no—
68C4×C3⋊D3—41no—
69C4×C3⋊D3—41no—
70#622—42no—
71#407—91no—
72#381—91no—
73C4×C22⋊C4—91no—
74C23×D3—62no—
75C22×C3×C4—24no—
76C22×C3×C4—22no—
77C22×Dic3—62no—
78C22×Dic3—64no—
79C2×C4×D3—62no—
80C2×C4×D3—62no—
81C2×C4×D3—62no—
82C2×C4×D3—62no—
83C2×C4×D3—124no—
84C2×C4×D3—124no—
85C3×C42—44no—
86(C2×D3)⋊C4—616no—
87C4×Dic3—124no—
88C22×C32—21no—
89C22×C32—21no—
90C22×C32#9511yescharacteristic
91C22×C32#9911yescharacteristic
92C22×C32#9911yescharacteristic
93C2×C3⋊D3—21no—
94C2×C3⋊D3—21no—
95C2×C3⋊D3—21no—
96C2×C3⋊D3—21no—
97C2×C3⋊D3—21no—
98C2×C3⋊D3—42no—
99C2×C3⋊D3—42no—
100C2×C3⋊D3#10412yes—
101#157—82no—
102C32×C4—21no—
103C32×C4—21no—
104C32×C4—42no—
105C3⋊Dic3—21no—
106C3⋊Dic3—21no—
107C3⋊Dic3—42no—
108C23×C4—91no—
109C2×M16—181no—
110C2×C22⋊C4—181no—
111C2×C22⋊C4—181no—
112C2×C42—91no—
113C2×C42#15711yescharacteristic, complemented
114C22⋊C8—92no—
115C22⋊C8—181no—
116#95—92no—
117#95—181no—
118#95—181no—
119C23×C3—22no—
120C22×D3—62no—
121C22×D3—62no—
122C22×D3—68no—
123C22×D3—122no—
124C22×D3—122no—
125C22×D3—124no—
126C2×C3×C4—24no—
127C2×C3×C4—24no—
128C2×C3×C4—28no—
129C2×C3×C4—22no—
130C2×C3×C4—22no—
131C2×C3×C4—44no—
132C2×C3×C4—44no—
133C2×Dic3—62no—
134C2×Dic3—62no—
135C2×Dic3—68no—
136C2×Dic3—122no—
137C2×Dic3—122no—
138C2×Dic3—124no—
139C2×Dic3—124no—
140C4×D3—124no—
141C4×D3—124no—
142C4×D3—124no—
143C4×D3—124no—
144C2×C32—21no—
145C2×C32—21no—
146C2×C32H(3,ℤ/4)11yescharacteristic
147C2×C32#33911yescharacteristic
148C2×C32#34211yescharacteristic
149C3⋊D3—22no—
150C3⋊D3—41no—
151C24—91no—
152C22×C4—21no—
153C22×C4—91no—
154C22×C4—91no—
155C22×C4—91no—
156C22×C4—91no—
157C22×C4—91no—
158C22×C4—181no—
159C22×C4—182no—
160C22×C4—361no—
161C22×C4—361no—
162C22×C4C2×#15711yescharacteristic
163M16—361no—
164M16—361no—
165C2×C8—182no—
166C22⋊C4—184no—
167C22⋊C4—361no—
168C22⋊C4—361no—
169C42—41no—
170C42—361no—
171C22×C3—24no—
172C22×C3—24no—
173C22×C3—22no—
174C22×C3—22no—
175C22×C3—22no—
176C2×D3—64no—
177C2×D3—64no—
178C2×D3—122no—
179C2×D3—122no—
180C2×D3—122no—
181C2×D3—122no—
182C2×D3—128no—
183C2×D3—128no—
184C3×C4—24no—
185C3×C4—24no—
186C3×C4—48no—
187Dic3—122no—
188Dic3—122no—
189Dic3—128no—
190C32#128411yescharacteristic, complemented, Sylow
191C23—91no—
192C23—91no—
193C23—182no—
194C23—181no—
195C23—181no—
196C23—361no—
197C23C22⋊#15711yescharacteristic
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—91no—
204C2×C4—91no—
205C2×C4—181no—
206C2×C4—181no—
207C2×C4—182no—
208C2×C4—361no—
209C2×C4—361no—
210C2×C4—361no—
211C2×C4—361no—
212C2×C4—361no—
213C2×C4—361no—
214C2×C4—362no—
215C2×C4—362no—
216C2×C4—362no—
217C2×C4C4×#15711yescharacteristic
218C2×C4C4⋊#15711yescharacteristic
219C8—362no—
220C2×C3—24no—
221C2×C3—24no—
222C2×C3—22no—
223C2×C3—22no—
224C2×C3—22no—
225D3—124no—
226D3—124no—
227C22—21no—
228C22—21no—
229C22—92no—
230C22—181no—
231C22—181no—
232C22—181no—
233C22—181no—
234C22—181no—
235C22—362no—
236C22—362no—
237C22#6377411yescharacteristic
238C22#6378111yescharacteristic
239C22#6378611yescharacteristic
240C4—21no—
241C4—21no—
242C4—42no—
243C4—181no—
244C4—181no—
245C4—362no—
246C4—722no—
247C3—22no—
248C2—21no—
249C2—21no—
250C2—182no—
251C2—361no—
252C2#1059015111yescharacteristic
253C2#1059015211yescharacteristic
254C2#1059020611yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC2×C32×C42C4
socleC22×C32#95
prime radicalC23×C3⋊D3D4
cosocleC22×C4×C3⋊D3C22
hypercenterC2×C42#157
hypocenterC32#1284
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
7. C2×C32×C42C4semidirect
9. C2×C4×C3⋊Dic3C4semidirect
11. #63781C4semidirect
13. #63778C4semidirect
113. C2×C42#157semidirect
190. C32#1284semidirect

Maximal subgroups

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

subgroupindex
#105938112
#105938022
C4×#37522
#12849