Finite Group Databasebeta

← #11785848

Subgroups — #11785848

Order 1152.

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

normal subgroups only

This group has 636 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
1C2×#64101C211yesmaximal, characteristic
2C4×C22⋊#157C211yesmaximal, characteristic
3#10593803C211yesmaximal, characteristic
4#10590164C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×C22⋊#157—21no—
7C2×C4×#157C2212yes—
8C2×#3788C2212yes—
9C2×C32×C4⋊C4C411yescharacteristic, complemented
10C2×#3752—21no—
11C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
12C2×C4×C3⋊Dic3—21no—
13#64101—21no—
14#64101—21no—
15#64101C412yescomplemented
16#64101C2212yes—
17C22⋊#622—21no—
18#63781—21no—
19#63778—21no—
20C2×#892—62no—
21C23×C3⋊D3D411yescharacteristic
22C22×#157—22no—
23C22×C32×C4—21no—
24C22×C32×C4C2×C411yescharacteristic
25C22×C3⋊Dic3—21no—
26C22×C3⋊Dic3D411yescharacteristic
27C2×C4×C3⋊D3—24no—
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C4×C3⋊D3C2311yescharacteristic
32C22⋊#157—24no—
33C2×#622—22no—
34C4×#157—24no—
35#3788—24no—
36C32×C4⋊C4—21no—
37C32×C4⋊C4C2×C412yes—
38#3752—22no—
39#3752—22no—
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)C2×C412yes—
42C4×C3⋊Dic3—22no—
43C4×C3⋊Dic3—22no—
44#1826—91nomaximal, Sylow
45C22×C4×D3—62no—
46C2×C3×C4⋊C4—22no—
47C2×(C2×D3)⋊C4—64no—
48C2×C4⋊Dic3—62no—
49C2×C4×Dic3—64no—
50#892—64no—
51#892—64no—
52#892—64no—
53#892—64no—
54C23×C32C22⋊C411yescharacteristic
55C22×C3⋊D3—22no—
56C22×C3⋊D3—22no—
57C22×C3⋊D3—41no—
58C22×C3⋊D3C22⋊C411yescharacteristic
59C22×C3⋊D3C2×D411yescharacteristic
60C2×#157—24no—
61C2×#157—42no—
62C2×#157—42no—
63C2×C32×C4—22no—
64C2×C32×C4—22no—
65C2×C32×C4—42no—
66C2×C32×C4C22⋊C411yescharacteristic
67C2×C32×C4C22×C411yescharacteristic
68C2×C3⋊Dic3—22no—
69C2×C3⋊Dic3—22no—
70C2×C3⋊Dic3—42no—
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C2×D411yescharacteristic
73C4×C3⋊D3—22no—
74C4×C3⋊D3—22no—
75C4×C3⋊D3—22no—
76C4×C3⋊D3#4114yes—
77#622—42no—
78C2×#117—91no—
79#407—91no—
80C4×C22⋊C4—91no—
81#339—94no—
82C23×D3—62no—
83C22×C3×C4—24no—
84C22×C3×C4—22no—
85C22×Dic3—62no—
86C22×Dic3—64no—
87C2×C4×D3—62no—
88C2×C4×D3—62no—
89C2×C4×D3—62no—
90C2×C4×D3—62no—
91C2×C4×D3—616no—
92C3×C4⋊C4—24no—
93C3×C4⋊C4—24no—
94(C2×D3)⋊C4—68no—
95(C2×D3)⋊C4—68no—
96C4⋊Dic3—64no—
97C4⋊Dic3—64no—
98C4×Dic3—68no—
99C4×Dic3—68no—
100C22×C32—21no—
101C22×C32—21no—
102C22×C32#10412yes—
103C22×C32C2×C22⋊C411yescharacteristic
104C2×C3⋊D3—21no—
105C2×C3⋊D3—21no—
106C2×C3⋊D3—21no—
107C2×C3⋊D3—21no—
108C2×C3⋊D3—21no—
109C2×C3⋊D3—44no—
110C2×C3⋊D3#12312yes—
111#157—44no—
112C32×C4—21no—
113C32×C4—42no—
114C32×C4#11712yes—
115C3⋊Dic3—21no—
116C3⋊Dic3—42no—
117C3⋊Dic3#12312yes—
118C23×C4—91no—
119C2×M16—92no—
120#117—92no—
121#117—92no—
122#117—181no—
123#117—181no—
124C2×C4⋊C4—91no—
125C2×C4⋊C4#15711yescharacteristic, complemented
126C2×C22⋊C4—181no—
127C2×C22⋊C4—181no—
128C2×C42—92no—
129C2×C42—181no—
130C22⋊C8—181no—
131C22⋊C8—181no—
132#95—181no—
133C23×C3—22no—
134C22×D3—62no—
135C22×D3—62no—
136C22×D3—68no—
137C22×D3—124no—
138C22×D3—124no—
139C2×C3×C4—28no—
140C2×C3×C4—28no—
141C2×C3×C4—22no—
142C2×C3×C4—22no—
143C2×C3×C4—48no—
144C2×Dic3—62no—
145C2×Dic3—62no—
146C2×Dic3—68no—
147C2×Dic3—68no—
148C2×Dic3—128no—
149C4×D3—68no—
150C4×D3—68no—
151C4×D3—68no—
152C4×D3—68no—
153C2×C32—22no—
154C2×C32#38111yescharacteristic
155C2×C32C2×#10411yescharacteristic
156C2×C32#42111yescharacteristic
157C3⋊D3—22no—
158C3⋊D3—41no—
159C24—91no—
160C22×C4—21no—
161C22×C4—91no—
162C22×C4—91no—
163C22×C4—91no—
164C22×C4—91no—
165C22×C4—91no—
166C22×C4—184no—
167C22×C4—182no—
168C22×C4—181no—
169C22×C4C2×#15711yescharacteristic
170M16—184no—
171C2×C8—182no—
172C4⋊C4—21no—
173C4⋊C4—92no—
174C4⋊C4—181no—
175C4⋊C4C2×#15712yes—
176C22⋊C4—182no—
177C22⋊C4—182no—
178C22⋊C4—184no—
179C42—182no—
180C42—182no—
181C42—184no—
182C22×C3—24no—
183C22×C3—24no—
184C22×C3—22no—
185C22×C3—24no—
186C2×D3—64no—
187C2×D3—64no—
188C2×D3—122no—
189C2×D3—122no—
190C2×D3—122no—
191C2×D3—122no—
192C2×D3—1216no—
193C3×C4—24no—
194C3×C4—24no—
195C3×C4—48no—
196Dic3—64no—
197Dic3—64no—
198Dic3—128no—
199C32#182611yescharacteristic, complemented, Sylow
200C23—91no—
201C23—91no—
202C23—182no—
203C23—182no—
204C23—361no—
205C23C22⋊#15711yescharacteristic
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—91no—
210C2×C4—94no—
211C2×C4—91no—
212C2×C4—182no—
213C2×C4—182no—
214C2×C4—182no—
215C2×C4—182no—
216C2×C4—184no—
217C2×C4—182no—
218C2×C4—362no—
219C2×C4—362no—
220C2×C4—362no—
221C2×C4C22⋊#15711yescharacteristic
222C2×C4C22×#15711yescharacteristic
223C8—362no—
224C2×C3—28no—
225C2×C3—22no—
226C2×C3—22no—
227C2×C3—22no—
228D3—124no—
229D3—124no—
230C22—21no—
231C22—21no—
232C22—92no—
233C22—181no—
234C22—181no—
235C22—181no—
236C22—181no—
237C22—181no—
238C22—364no—
239C22#6378512yes—
240C22C2×C22⋊#15711yescharacteristic
241C4—21no—
242C4—42no—
243C4—92no—
244C4—181no—
245C4—364no—
246C4—362no—
247C4#6428612yes—
248C3—22no—
249C2—22no—
250C2—182no—
251C2—361no—
252C2#1059381111yescharacteristic
253C2#1059381611yescharacteristic
254C2C2×#6378511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1826
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10590164C2semidirect
9. C2×C32×C4⋊C4C4semidirect
11. C2×C4⋊(C3⋊Dic3)C4semidirect
15. #64101C4semidirect
125. C2×C4⋊C4#157semidirect
199. C32#1826semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C4×C22⋊#1572
#105938032
#105901642
#18269