Finite Group Databasebeta

← #11773875

Subgroups — #11773875

Order 1152.

730 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 68 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×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2#10593803C212yesmaximal
3#10590203C212yesmaximal, complemented
4#10590202C212yesmaximal, complemented
5C22×C4×C3⋊D3C411yescharacteristic
6C22×C4×C3⋊D3C411yescharacteristic
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×#3788—22no—
9C2×C32×C4⋊C4C411yescharacteristic
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C2×#3750C411yescharacteristic
12C2×#3750C2211yescharacteristic
13C4⋊C4×C3⋊D3—22no—
14C4⋊C4×C3⋊D3—22no—
15C22⋊#622C2214yes—
16#63778—22no—
17C2×D3×C4⋊C4—62no—
18C23×C3⋊D3C2×C411yescharacteristic
19C22×C32×C4C2×C411yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4C2×C411yescharacteristic
22C22×C3⋊Dic3C2×C411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C2×C4×C3⋊D3—21no—
26C2×C4×C3⋊D3—21no—
27C2×C4×C3⋊D3—22no—
28C2×C4×C3⋊D3—22no—
29C2×C4×C3⋊D3—21no—
30C2×C4×C3⋊D3—21no—
31C2×C4×C3⋊D3—42no—
32C2×C4×C3⋊D3—42no—
33C2×C4×C3⋊D3D412yes—
34C2×C4×C3⋊D3D412yes—
35C2×#622—24no—
36#3788—44no—
37C32×C4⋊C4—22no—
38C4⋊(C3⋊Dic3)—22no—
39#3750—22no—
40#3750—22no—
41#1463—91nomaximal, Sylow
42C22×C4×D3—62no—
43C22×C4×D3—62no—
44C22×C4×D3—62no—
45C2×C3×C4⋊C4—22no—
46C2×C4⋊Dic3—62no—
47C2×Dic3⋊C4—62no—
48C2×Dic3⋊C4—62no—
49D3×C4⋊C4—68no—
50D3×C4⋊C4—68no—
51C23×C32C22×C411yescharacteristic
52C22×C3⋊D3—21no—
53C22×C3⋊D3—21no—
54C22×C3⋊D3—22no—
55C22×C3⋊D3—22no—
56C22×C3⋊D3C22⋊C411yescharacteristic
57C22×C3⋊D3C22⋊C411yescharacteristic
58C2×C32×C4—21no—
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4—41no—
62C2×C32×C4—41no—
63C2×C32×C4C22⋊C412yes—
64C2×C32×C4M1612yescomplemented
65C2×C3⋊Dic3—21no—
66C2×C3⋊Dic3—21no—
67C2×C3⋊Dic3—21no—
68C2×C3⋊Dic3—41no—
69C2×C3⋊Dic3—41no—
70C2×C3⋊Dic3M1612yescomplemented
71C2×C3⋊Dic3C2×D412yes—
72C4×C3⋊D3—24no—
73C4×C3⋊D3—24no—
74C4×C3⋊D3—24no—
75C4×C3⋊D3—42no—
76C4×C3⋊D3—42no—
77C4×C3⋊D3—42no—
78#622—44no—
79C22×C4⋊C4—91no—
80#407—92no—
81#324—92no—
82#324—92no—
83C23×D3—62no—
84C22×C3×C4—22no—
85C22×C3×C4—22no—
86C22×C3×C4—22no—
87C22×Dic3—62no—
88C22×Dic3—62no—
89C22×Dic3—62no—
90C2×C4×D3—64no—
91C2×C4×D3—64no—
92C2×C4×D3—64no—
93C2×C4×D3—64no—
94C2×C4×D3—68no—
95C2×C4×D3—68no—
96C2×C4×D3—64no—
97C2×C4×D3—64no—
98C2×C4×D3—128no—
99C2×C4×D3—128no—
100C3×C4⋊C4—28no—
101C4⋊Dic3—68no—
102Dic3⋊C4—68no—
103Dic3⋊C4—68no—
104C22×C32—21no—
105C22×C32—21no—
106C22×C32C2×C22⋊C411yescharacteristic
107C22×C32C2×M1611yescharacteristic
108C22×C32C2×M1611yescharacteristic
109C2×C3⋊D3—24no—
110C2×C3⋊D3—24no—
111C2×C3⋊D3—21no—
112C2×C3⋊D3—21no—
113C2×C3⋊D3—21no—
114C2×C3⋊D3—21no—
115C2×C3⋊D3#9912yes—
116C2×C3⋊D3#10112yes—
117C32×C4—22no—
118C32×C4—22no—
119C32×C4—41no—
120C3⋊Dic3—22no—
121C3⋊Dic3—22no—
122C3⋊Dic3—41no—
123C23×C4—91no—
124C23×C4—91no—
125C23×C4—91no—
126C2×M16—182no—
127C2×C4⋊C4—91no—
128C2×C4⋊C4—91no—
129C2×C4⋊C4—91no—
130C2×C4⋊C4—182no—
131C2×C4⋊C4—182no—
132C2×C4⋊C4#15711yescharacteristic
133C22⋊C8—94no—
134C22⋊C8—182no—
135C23×C3—22no—
136C22×D3—62no—
137C22×D3—62no—
138C22×D3—64no—
139C22×D3—64no—
140C22×D3—68no—
141C22×D3—68no—
142C2×C3×C4—24no—
143C2×C3×C4—24no—
144C2×C3×C4—24no—
145C2×C3×C4—24no—
146C2×C3×C4—24no—
147C2×C3×C4—44no—
148C2×C3×C4—44no—
149C2×Dic3—64no—
150C2×Dic3—64no—
151C2×Dic3—64no—
152C2×Dic3—64no—
153C2×Dic3—64no—
154C2×Dic3—124no—
155C2×Dic3—124no—
156C4×D3—616no—
157C4×D3—616no—
158C4×D3—128no—
159C4×D3—128no—
160C4×D3—128no—
161C4×D3—128no—
162C2×C32—21no—
163C2×C32—21no—
164C2×C32#40711yescharacteristic
165C2×C32C2×#9911yescharacteristic
166C2×C32C2×#10111yescharacteristic
167C3⋊D3—22no—
168C3⋊D3—22no—
169C24—91no—
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—92no—
173C22×C4—92no—
174C22×C4—91no—
175C22×C4—182no—
176C22×C4—181no—
177C22×C4—181no—
178C22×C4—181no—
179C22×C4—181no—
180C22×C4—182no—
181C22×C4—362no—
182C22×C4—362no—
183C22×C4C2×#15711yescharacteristic
184C22×C4C2×#15711yescharacteristic
185C22×C4C2×#15711yescharacteristic
186M16—364no—
187C2×C8—184no—
188C4⋊C4—22no—
189C4⋊C4—182no—
190C4⋊C4—182no—
191C4⋊C4—182no—
192C22×C3—24no—
193C22×C3—24no—
194C22×C3—22no—
195C22×C3—22no—
196C22×C3—22no—
197C2×D3—64no—
198C2×D3—64no—
199C2×D3—64no—
200C2×D3—64no—
201C2×D3—64no—
202C2×D3—616no—
203C2×D3—616no—
204C2×D3—64no—
205C3×C4—28no—
206C3×C4—44no—
207C3×C4—44no—
208Dic3—68no—
209Dic3—124no—
210Dic3—124no—
211C32#146311yescharacteristic, complemented, Sylow
212C23—91no—
213C23—91no—
214C23—182no—
215C23—182no—
216C23—181no—
217C23—181no—
218C23C22×#15711yescharacteristic
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—92no—
225C2×C4—92no—
226C2×C4—184no—
227C2×C4—184no—
228C2×C4—184no—
229C2×C4—181no—
230C2×C4—181no—
231C2×C4—181no—
232C2×C4—362no—
233C2×C4—362no—
234C2×C4—362no—
235C2×C4—361no—
236C2×C4—361no—
237C2×C4#378812yescomplemented
238C2×C4C22⋊#15712yes—
239C8—364no—
240C2×C3—24no—
241C2×C3—24no—
242C2×C3—22no—
243C2×C3—22no—
244C2×C3—22no—
245D3—68no—
246D3—68no—
247C22—21no—
248C22—21no—
249C22—92no—
250C22—92no—
251C22—184no—
252C22—184no—
253C22—181no—
254C22—181no—
255C22—181no—
256C22—181no—
257C22C2×#378811yescharacteristic
258C22#6428311yescharacteristic
259C22C2×C22⋊#15711yescharacteristic
260C4—22no—
261C4—22no—
262C4—41no—
263C4—182no—
264C4—182no—
265C4—361no—
266C3—22no—
267C2—21no—
268C2—21no—
269C2—182no—
270C2—182no—
271C2#1059380311yescharacteristic
272C2#1059381711yescharacteristic
273C2#1059383611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC23×C32C22×C4
FrattiniC23C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1463
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10590203C2semidirect
4. #10590202C2semidirect
64. C2×C32×C4M16semidirect
70. C2×C3⋊Dic3M16semidirect
211. C32#1463semidirect
237. C2×C4#3788semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
#105938032
#105902032
#105902022
#14639