Finite Group Databasebeta

← #11775224

Subgroups — #11775224

Order 1152.

882 conjugacy classes of subgroups; only the 193 normal subgroups are shown.

normal subgroups only

This group has 882 conjugacy classes of subgroups — too many to draw. Only its 193 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×#64133C211yesmaximal, characteristic
2C32×C4×C22⋊C4C211yesmaximal, characteristic
3#10592906C211yesmaximal, characteristic
4#10589318C214yesmaximal, complemented
5#69445—34nomaximal
6C23×C32×C4C2211yescharacteristic
7C22×#634C411yescharacteristic, complemented
8C2×C32×C22⋊C4—21no—
9C2×C32×C42—21no—
10C2×#3757—21no—
11C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
12#64133—21no—
13#64133—21no—
14#64133C412yescomplemented
15#64133C2212yes—
16C2×#3750—21no—
17C2×#3748—21no—
18C32×#95C2212yes—
19#63657—21no—
20#63657C2212yes—
21C2×#924—34no—
22C3×C4×C22⋊C4D314yes—
23#5207—34no—
24#4452—316no—
25C24×C32D411yescharacteristic
26C22×C32×C4—22no—
27C22×C32×C4—42no—
28C22×C32×C4C2×C411yescharacteristic
29C22×C32×C4C2×C411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3—21no—
36C2×#634—21no—
37C2×#634—42no—
38C2×#634C2×C412yes—
39C32×C22⋊C4—24no—
40C32×C42—42no—
41#3757—22no—
42#3757—22no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)C2×C412yes—
45#3750—22no—
46#3750—22no—
47#3748—42no—
48C2×C3⋊(C3⋊C8)—22no—
49#1508—91noSylow
50C23×C3×C4C2×D314yes—
51C22×Dic6—34no—
52C2×C3×C22⋊C4—24no—
53C2×C3×C42—24no—
54C2×#217—64no—
55C2×C4⋊Dic3—34no—
56#924—38no—
57#924—38no—
58#924—64no—
59#924—64no—
60C2×Dic3⋊C4—64no—
61C2×#208—64no—
62C3×#95C2×D318yes—
63#830—38no—
64#830—64no—
65C23×C32—22no—
66C23×C32—22no—
67C23×C32—41no—
68C23×C32C22⋊C411yescharacteristic
69C23×C32C22⋊C411yescharacteristic
70C23×C32C2×D411yescharacteristic
71C2×C32×C4—22no—
72C2×C32×C4—22no—
73C2×C32×C4—22no—
74C2×C32×C4—24no—
75C2×C32×C4—41no—
76C2×C32×C4—41no—
77C2×C32×C4—41no—
78C2×C32×C4—42no—
79C2×C32×C4—42no—
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22⋊C411yescharacteristic
82C2×C32×C4C22×C411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—42no—
87C2×C3⋊Dic3—42no—
88#634—42no—
89#634—42no—
90C3⋊(C3⋊C8)—42no—
91C2×C22⋊Q8—91no—
92#407—91no—
93C4×C22⋊C4C3⋊D311yescharacteristic
94#328—94no—
95C24×C3#6714yes—
96C22×C3×C4—28no—
97C22×C3×C4—48no—
98C22×C3×C4C4×D314yes—
99C22×C3×C4C4×D314yes—
100C22×C3×C4D1214yes—
101C22×C3×C4D1214yes—
102C22×C3×C4#6714yes—
103C22×C3×C4C22×D314yes—
104C22×Dic3—64no—
105C22×Dic3—64no—
106C2×Dic6—38no—
107C2×Dic6—64no—
108C2×Dic6—128no—
109C3×C22⋊C4—216no—
110C3×C42—48no—
111#217—68no—
112#217—68no—
113C4⋊Dic3—38no—
114C4⋊Dic3—64no—
115Dic3⋊C4—68no—
116Dic3⋊C4—68no—
117#208—128no—
118C2×C3⋊C8—68no—
119C22×C32—21no—
120C22×C32—21no—
121C22×C32—21no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32—44no—
127C22×C32#10412yes—
128C22×C32C2×C22⋊C411yescharacteristic
129C22×C32#13712yes—
130C32×C4—21no—
131C32×C4—21no—
132C32×C4—21no—
133C32×C4—44no—
134C32×C4#9912yes—
135C3⋊Dic3—42no—
136C3⋊Dic3—42no—
137C22×Q8—91no—
138C23×C4C2×C3⋊D311yescharacteristic
139C2×M16—181no—
140C22⋊Q8—92no—
141C22⋊Q8—92no—
142C22⋊Q8—181no—
143C22⋊Q8—181no—
144C2×C4⋊C4—91no—
145C2×C4⋊C4—181no—
146C2×C22⋊C4—21no—
147C2×C22⋊C4—181no—
148C2×C42—21no—
149C22⋊C8—92no—
150C22⋊C8—181no—
151#95C2×C3⋊D312yes—
152C23×C3—28no—
153C23×C3—28no—
154C23×C3—44no—
155C23×C3(C2×D3)⋊C414yes—
156C23×C3(C2×D3)⋊C414yes—
157C23×C3C2×#6714yes—
158C2×C3×C4—28no—
159C2×C3×C4—28no—
160C2×C3×C4—28no—
161C2×C3×C4—216no—
162C2×C3×C4—44no—
163C2×C3×C4—44no—
164C2×C3×C4—44no—
165C2×C3×C4—48no—
166C2×C3×C4—48no—
167C2×C3×C4(C2×D3)⋊C414yes—
168C2×C3×C4(C2×D3)⋊C414yes—
169C2×C3×C4C2×C4×D314yes—
170C2×C3×C4C2×D1214yes—
171C2×Dic3—68no—
172C2×Dic3—68no—
173C2×Dic3—128no—
174C2×Dic3—128no—
175Dic6—128no—
176Dic6—128no—
177C3⋊C8—128no—
178C2×C32—22no—
179C2×C32—22no—
180C2×C32—41no—
181C2×C32C2×#9911yescharacteristic
182C2×C32#41911yescharacteristic
183C2×C32C2×#10411yescharacteristic
184C24#63811yescharacteristic
185C2×Q8—92no—
186C2×Q8—181no—
187C2×Q8—362no—
188C22×C4—22no—
189C22×C4—42no—
190C22×C4—181no—
191C22×C4—181no—
192C22×C4C4×C3⋊D311yescharacteristic
193C22×C4C4×C3⋊D311yescharacteristic
194C22×C4C4⋊(C3⋊D3)11yescharacteristic
195C22×C4C4⋊(C3⋊D3)11yescharacteristic
196C22×C4#63811yescharacteristic
197C22×C4C22×C3⋊D311yescharacteristic
198M16—362no—
199C2×C8—182no—
200C4⋊C4—92no—
201C4⋊C4—181no—
202C4⋊C4—182no—
203C4⋊C4—182no—
204C22⋊C4—24no—
205C22⋊C4—182no—
206C22⋊C4—182no—
207C42—42no—
208C22×C3—24no—
209C22×C3—24no—
210C22×C3—24no—
211C22×C3—24no—
212C22×C3—24no—
213C22×C3—24no—
214C22×C3—24no—
215C22×C3—416no—
216C22×C3#80518yes—
217C22×C3C2×(C2×D3)⋊C414yes—
218C22×C3#95118yes—
219C3×C4—24no—
220C3×C4—24no—
221C3×C4—24no—
222C3×C4—416no—
223C3×C4#80618yes—
224Dic3—128no—
225Dic3—128no—
226C32#150811yescharacteristic, complemented, Sylow
227C23—22no—
228C23—22no—
229C23—41no—
230C23#375211yescharacteristic
231C23#375211yescharacteristic
232C23C2×#63811yescharacteristic
233Q8—362no—
234Q8—362no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—182no—
245C2×C4—182no—
246C2×C4—362no—
247C2×C4—362no—
248C2×C4#375211yescharacteristic
249C2×C4#375211yescharacteristic
250C2×C4C2×C4×C3⋊D311yescharacteristic
251C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
252C8—362no—
253C2×C3—28no—
254C2×C3—28no—
255C2×C3—44no—
256C2×C3C2×#80514yes—
257C2×C3C2×#80614yes—
258C2×C3#500414yes—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—44no—
267C22#6363212yes—
268C22C2×#375211yescharacteristic
269C22#6416012yes—
270C4—21no—
271C4—21no—
272C4—21no—
273C4—44no—
274C4—362no—
275C4—362no—
276C4#6363312yes—
277C3#6944514yescomplemented
278C2—22no—
279C2—22no—
280C2—41no—
281C2C2×#6363211yescharacteristic
282C2C2×#6363311yescharacteristic
283C2#1059270311yescharacteristic
subgroupG/H
centerC22C2×#3752
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×C4×C22⋊C4C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32D4
cosocleC22×C32×C4C23
hypercenterC4×C22⋊C4C3⋊D3
hypocenterC32#1508
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. #10589318C2semidirect
7. C22×#634C4semidirect
11. C2×C4⋊(C3⋊Dic3)C4semidirect
14. #64133C4semidirect
226. C32#1508semidirect
277. C3#69445semidirect

Maximal subgroups

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

subgroupindex
C2×#641332
C32×C4×C22⋊C42
#105929062
#105893182
#694453