Finite Group Databasebeta

← #11775163

Subgroups — #11775163

Order 1152.

482 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 55 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#10593971C211yesmaximal, characteristic
2#10593733C211yesmaximal, characteristic, complemented
3#10590299C211yesmaximal, characteristic, complemented
4#10590033C214yesmaximal, complemented
5C2×#3796—21no—
6C2×C4×#157—21no—
7C42×C3⋊D3C2211yescharacteristic
8C3×#875—21no—
9#63914C411yescharacteristic, complemented
10#63912—21no—
11#63912C2212yes—
12#63902—21no—
13#63902C412yescomplemented
14#63873C411yescharacteristic, complemented
15#63781—21no—
16#63781C2212yes—
17C3×#803—21no—
18#63572—21no—
19#63557C2212yes—
20#5668—61no—
21#4705—61no—
22C22×#157—22no—
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3C2311yescharacteristic
26C2×C3×D12—21no—
27C2×C3×Dic6—21no—
28C2×#626—22no—
29C2×#625—21no—
30C2×#625C2×C412yes—
31C2×D3×Dic3—22no—
32#3796—44no—
33C4×#157—24no—
34C32×C42D411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C3×(C2×D3)⋊C4—22no—
39C3×(C2×D3)⋊C4—22no—
40C2×C3×C3⋊C8—22no—
41#3724—21no—
42#3724C2×C412yes—
43#1505—91nomaximal, Sylow
44C2×#239—61no—
45C2×#237—61no—
46C3×#124—61no—
47#944—61no—
48#940—61no—
49#884—62no—
50#884—62no—
51#67⋊C4—62no—
52#67⋊C4—62no—
53#875—21no—
54C42×D3—61no—
55C42×D3—61no—
56C3×#97—61no—
57(C2×D3)⋊C8—62no—
58Dic3⋊C8—62no—
59#803—21no—
60C22×C3⋊D3C2×D411yescharacteristic
61C22×C3×D3—22no—
62C2×#157—24no—
63C2×#157—42no—
64C2×#157—42no—
65C2×C32×C4C22⋊C411yescharacteristic
66C2×C32×C4C22⋊C411yescharacteristic
67C2×C32×C4C2×D411yescharacteristic
68C2×C3⋊Dic3C22⋊C411yescharacteristic
69C2×C3⋊Dic3C22⋊C411yescharacteristic
70C2×C3⋊Dic3C22×C411yescharacteristic
71C4×C3⋊D3—22no—
72C4×C3⋊D3—22no—
73C4×C3⋊D3—41no—
74C2×C3×Dic3—22no—
75C3×D12—42no—
76C3×Dic6—42no—
77#626—44no—
78#625—42no—
79#625—42no—
80D3×Dic3—44no—
81C3×C3⋊C8—42no—
82#532—91no—
83#432—91no—
84#376—91no—
85#327—94no—
86C2×C3×Q8—61no—
87C2×C3×D4—61no—
88C2×#67—62no—
89C2×#67—62no—
90C2×#67—62no—
91C22×Dic3—62no—
92#239—124no—
93#237—124no—
94C2×D12—21no—
95C2×D12—62no—
96C2×C4×D3—61no—
97C2×C4×D3—61no—
98C2×C4×D3—61no—
99C2×C4×D3—61no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×C4×D3—62no—
103C2×Dic6—21no—
104C2×C3×C8—62no—
105C3×C22⋊C4—62no—
106C3×C22⋊C4—62no—
107C3×C42—21no—
108C3×C42—21no—
109(C2×D3)⋊C4—22no—
110(C2×D3)⋊C4—22no—
111Dic3⋊C4—62no—
112Dic3⋊C4—62no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C2×C3⋊C8—22no—
120C22×C32C2×C22⋊C411yescharacteristic
121C2×C3⋊D3—21no—
122C2×C3⋊D3—21no—
123C2×C3⋊D3AGL(1,ℤ/8)12yes—
124C2×C3×D3—42no—
125C2×C3×D3—42no—
126C2×C3×D3—42no—
127#157—44no—
128C32×C4—21no—
129C32×C4—21no—
130C32×C4—21no—
131C3⋊Dic3—21no—
132C3⋊Dic3—21no—
133C3⋊Dic3#10412yes—
134C3×Dic3—42no—
135C2×#41—181no—
136C4⋊Q8—91no—
137#127—91no—
138#124—61no—
139#121—92no—
140#121—181no—
141C4×D4—92no—
142C4×D4—181no—
143C2×C42—91no—
144C2×C42—181no—
145C4⋊C8—181no—
146C22⋊C8—92no—
147#97—61no—
148#95—92no—
149#95—181no—
150C23×C3—62no—
151C22×D3—22no—
152C22×D3—61no—
153C22×D3—61no—
154C3×Q8—122no—
155C3×D4—122no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—62no—
163#67—124no—
164#67—124no—
165#67—124no—
166C2×Dic3—22no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—124no—
174D12—42no—
175D12—124no—
176C4×D3—64no—
177C4×D3—122no—
178C4×D3—122no—
179C4×D3—122no—
180C4×D3—122no—
181C4×D3—124no—
182C4×D3—122no—
183Dic6—42no—
184C3×C8—122no—
185C3⋊C8—42no—
186C2×C32#41011yescharacteristic
187C2×C32#41811yescharacteristic
188C2×C32C2×#10411yescharacteristic
189C3⋊D3—22no—
190C3×D3—82no—
191#41—364no—
192C2×Q8—61no—
193C2×D4—61no—
194C2×D4—92no—
195C2×D4—182no—
196C2×D4—181no—
197C22×C4—91no—
198C22×C4—91no—
199C22×C4—91no—
200C22×C4—182no—
201C22×C4—182no—
202C2×C8—62no—
203C4⋊C4—92no—
204C4⋊C4—181no—
205C22⋊C4—62no—
206C22⋊C4—62no—
207C42—91no—
208C42—91no—
209C42—91no—
210C42—184no—
211C42GO+(4,𝔽2)11yescharacteristic
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—122no—
215C22×C3—122no—
216C22×C3—122no—
217C2×D3—42no—
218C2×D3—42no—
219C2×D3—42no—
220C2×D3—62no—
221C2×D3—62no—
222C2×D3—121no—
223C2×D3—121no—
224C2×D3—121no—
225C2×D3—121no—
226C3×C4—22no—
227C3×C4—22no—
228C3×C4—41no—
229C3×C4—41no—
230C3×C4—41no—
231C3×C4—41no—
232C3×C4—122no—
233Dic3—42no—
234Dic3—62no—
235Dic3—62no—
236Dic3—62no—
237Dic3—62no—
238Dic3—121no—
239Dic3—121no—
240C32#150511yescharacteristic, complemented, Sylow
241C23—62no—
242C23—91no—
243Q8—122no—
244D4—122no—
245D4—362no—
246D4—364no—
247D4—362no—
248C2×C4—62no—
249C2×C4—91no—
250C2×C4—91no—
251C2×C4—91no—
252C2×C4—182no—
253C2×C4—182no—
254C2×C4—184no—
255C2×C4—361no—
256C2×C4—364no—
257C2×C4—362no—
258C2×C4—362no—
259C2×C4D32⋊C411yescharacteristic
260C2×C4D32⋊C411yescharacteristic
261C2×C4C2×GO+(4,𝔽2)11yescharacteristic
262C8—122no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—242no—
270D3—82no—
271D3—122no—
272D3—122no—
273C22—92no—
274C22—122no—
275C22—122no—
276C22—122no—
277C22—181no—
278C22—181no—
279C22C2×D32⋊C411yescharacteristic
280C4—21no—
281C4—21no—
282C4—21no—
283C4—92no—
284C4—122no—
285C4—181no—
286C4—181no—
287C4—364no—
288C3—21no—
289C3—21no—
290C2—182no—
291C2—242no—
292C2#1059331811yescharacteristic
293C2#1059332511yescharacteristic
294C2#1059334511yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10593971C2
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1505
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593733C2semidirect
3. #10590299C2semidirect
4. #10590033C2semidirect
9. #63914C4semidirect
13. #63902C4semidirect
14. #63873C4semidirect
240. C32#1505semidirect

Maximal subgroups

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

subgroupindex
#105939712
#105937332
#105902992
#105900332
#15059