Finite Group Databasebeta

← #11774425

Subgroups — #11774425

Order 1152.

636 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 181 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#10595950C211yesmaximal, characteristic
2C32×#431C211yesmaximal, characteristic, complemented
3#10592624C211yesmaximal, characteristic, complemented
4#10589325C212yesmaximal, complemented
5#10589322C212yesmaximal, complemented
6#70760—34nomaximal
7C2×C32×C42C2211yescharacteristic
8#64139C411yescharacteristic
9#64138—21no—
10C4×#638—21no—
11#64133C411yescharacteristic
12#64085—21no—
13#64084C411yescharacteristic
14C4×C4⋊(C3⋊D3)C2211yescharacteristic
15#64081—21no—
16#64079C411yescharacteristic
17C4×#634C2211yescharacteristic
18C32×C4⋊C8—21no—
19C32×C22⋊C8—21no—
20C32×C4×C8C2212yes—
21#63657—21no—
22C4⋊(C3⋊(C3⋊C8))C2212yes—
23C4×C3⋊(C3⋊C8)—21no—
24#5479—34no—
25C3×#431D314yescomplemented
26#4925—34no—
27#4459—38no—
28#4456—38no—
29C22×C32×C4C2×C411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C32×C4D411yescharacteristic
32C2×#638—21no—
33C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
34C2×C4×C3⋊D3—21no—
35C2×#634C2×C411yescharacteristic
36C2×C32×C8—22no—
37C32×C42C2×C411yescharacteristic
38C32×C42D411yescharacteristic
39C32×C42D411yescharacteristic
40C32×C42C2311yescharacteristic
41#3757—21no—
42#3752—21no—
43#3752—21no—
44#3752—21no—
45#3752—21no—
46C4⋊(C3⋊Dic3)C2×C411yescharacteristic
47C4⋊(C3⋊Dic3)C2×C411yescharacteristic
48#3750—21no—
49#3750—21no—
50#3750—21no—
51#3750—21no—
52C4×C3⋊Dic3—21no—
53C2×C3⋊(C3⋊C8)—22no—
54#1482—91noSylow
55C2×C3×C42C2×D314yes—
56#930—34no—
57#929—64no—
58C4×#67—64no—
59#924—34no—
60#876—64no—
61#875—34no—
62C4×D12—34no—
63#872—64no—
64#870—34no—
65C4×Dic6—34no—
66C3×C4⋊C8—24no—
67C3×C22⋊C8—24no—
68C3×C4×C8C2×D318yes—
69#830—64no—
70C4⋊(C3⋊C8)—38no—
71C4×C3⋊C8—64no—
72C23×C32C22⋊C411yescharacteristic
73C22×C3⋊D3—21no—
74C2×C32×C4—22no—
75C2×C32×C4—22no—
76C2×C32×C4—41no—
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C22⋊C411yescharacteristic
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83#638—42no—
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3—21no—
86C2×C3⋊Dic3—21no—
87C4⋊(C3⋊D3)—22no—
88C4×C3⋊D3—42no—
89#634—22no—
90C32×C8—42no—
91C3⋊(C3⋊C8)—42no—
92#529—91no—
93#431—91no—
94#431C3⋊D311yescharacteristic, complemented
95Q8⋊C8—92no—
96D4⋊C8—92no—
97C22×C3×C4C4×D314yes—
98C22×C3×C4D1214yes—
99C22×C3×C4#6714yes—
100C2×#67—64no—
101C2×D12—34no—
102C2×C4×D3—64no—
103C2×Dic6—34no—
104C2×C3×C8—28no—
105C3×C42C4×D314yes—
106C3×C42D1214yes—
107C3×C42#6714yes—
108C3×C42C22×D314yes—
109#217—64no—
110(C2×D3)⋊C4—64no—
111(C2×D3)⋊C4—64no—
112(C2×D3)⋊C4—64no—
113(C2×D3)⋊C4—64no—
114C4⋊Dic3—34no—
115C4⋊Dic3—34no—
116Dic3⋊C4—64no—
117Dic3⋊C4—64no—
118Dic3⋊C4—64no—
119Dic3⋊C4—64no—
120C4×Dic3—64no—
121C2×C3⋊C8—68no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32C2×C22⋊C411yescharacteristic
126C2×C3⋊D3—41no—
127C2×C3⋊D3—41no—
128C2×C3⋊D3—41no—
129C32×C4—21no—
130C32×C4—21no—
131C32×C4—21no—
132C32×C4—21no—
133C32×C4#13112yes—
134C32×C4#13512yes—
135C3⋊Dic3—41no—
136C3⋊Dic3—41no—
137C3⋊Dic3—41no—
138#126—181no—
139#125—91no—
140#124—91no—
141#123—181no—
142C22⋊Q8—91no—
143#121—91no—
144C4×Q8—91no—
145C4×D4—91no—
146C4×D4—181no—
147#117—181no—
148C2×C42C2×C3⋊D311yescharacteristic
149C4⋊C8—21no—
150C4⋊C8—92no—
151C22⋊C8—21no—
152C22⋊C8—181no—
153C4×C8—181no—
154C4×C8C2×C3⋊D312yes—
155C23×C3(C2×D3)⋊C414yes—
156C22×D3—64no—
157C2×C3×C4—28no—
158C2×C3×C4—28no—
159C2×C3×C4—44no—
160C2×C3×C4(C2×D3)⋊C414yes—
161C2×C3×C4(C2×D3)⋊C414yes—
162C2×C3×C4(C2×D3)⋊C414yes—
163C2×C3×C4C2×C4×D314yes—
164C2×C3×C4C2×D1214yes—
165C2×C3×C4C2×#6714yes—
166#67—128no—
167C2×Dic3—64no—
168C2×Dic3—64no—
169C2×Dic3—64no—
170D12—68no—
171C4×D3—128no—
172Dic6—68no—
173C3×C8—48no—
174C3⋊C8—128no—
175C2×C32—41no—
176C2×C32#40811yescharacteristic
177C2×C32#41611yescharacteristic
178C2×C32#42111yescharacteristic
179C3⋊D3—81no—
180C2×Q8—91no—
181C2×D4—91no—
182C2×D4—181no—
183C22×C4—181no—
184C22×C4C4×C3⋊D311yescharacteristic
185C22×C4C4⋊(C3⋊D3)11yescharacteristic
186C22×C4#63811yescharacteristic
187C2×C8—22no—
188C2×C8—182no—
189C4⋊C4—91no—
190C4⋊C4—91no—
191C4⋊C4—181no—
192C4⋊C4—181no—
193C4⋊C4—181no—
194C4⋊C4—181no—
195C22⋊C4—181no—
196C22⋊C4—181no—
197C22⋊C4—181no—
198C22⋊C4—181no—
199C22⋊C4—181no—
200C42—181no—
201C42C4×C3⋊D311yescharacteristic
202C42C4⋊(C3⋊D3)11yescharacteristic
203C42#63811yescharacteristic
204C42C22×C3⋊D311yescharacteristic
205C22×C3—24no—
206C22×C3—24no—
207C22×C3—24no—
208C22×C3C2×(C2×D3)⋊C414yes—
209C2×D3—124no—
210C2×D3—124no—
211C2×D3—124no—
212C3×C4—24no—
213C3×C4—24no—
214C3×C4—24no—
215C3×C4—24no—
216C3×C4#90418yes—
217C3×C4#90718yes—
218Dic3—124no—
219Dic3—124no—
220Dic3—124no—
221C32#148211yescharacteristic, complemented, Sylow
222C23—181no—
223C23#375211yescharacteristic
224Q8—182no—
225D4—182no—
226D4—362no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—41no—
230C2×C4—181no—
231C2×C4—181no—
232C2×C4—181no—
233C2×C4—362no—
234C2×C4#375211yescharacteristic
235C2×C4#375211yescharacteristic
236C2×C4#375211yescharacteristic
237C2×C4C2×C4×C3⋊D311yescharacteristic
238C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
239C2×C4C2×#63811yescharacteristic
240C8—42no—
241C8—362no—
242C2×C3—44no—
243C2×C3#500514yes—
244C2×C3#511314yes—
245C2×C3#512914yes—
246D3—244no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—361no—
251C22—361no—
252C22—361no—
253C22C2×#375211yescharacteristic
254C4—21no—
255C4—21no—
256C4—21no—
257C4—21no—
258C4—361no—
259C4—361no—
260C4—361no—
261C4#6411312yes—
262C4#6411612yes—
263C3#7076014yescomplemented
264C2—41no—
265C2—721no—
266C2#1059270411yescharacteristic
267C2#1059281211yescharacteristic
268C2#1059282811yescharacteristic
subgroupG/H
centerC2×C4C2×C4⋊(C3⋊D3)
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×#431C2
socleC22×C32C2×C22⋊C4
prime radical#64139C4
cosocleC32×C42C23
hypercenter#431C3⋊D3
hypocenterC32#1482
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. C32×#431C2semidirect
3. #10592624C2semidirect
4. #10589325C2semidirect
5. #10589322C2semidirect
25. C3×#431D3semidirect
94. #431C3⋊D3semidirect
221. C32#1482semidirect
263. C3#70760semidirect

Maximal subgroups

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

subgroupindex
#105959502
C32×#4312
#105926242
#105893252
#105893222
#707603