Finite Group Databasebeta

← #13074516

Subgroups — #13074516

Order 1408.

562 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 129 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×#66951C211yesmaximal, characteristic, complemented
2C2×#66946C211yesmaximal, characteristic, complemented
3C11×#400C211yesmaximal, characteristic, complemented
4#10622605C211yesmaximal, characteristic, complemented
5#10622604C211yesmaximal, characteristic, complemented
6#10622289C212yesmaximal, complemented
7#10622285C212yesmaximal, complemented
8#10622284C211yesmaximal, characteristic
9#10622281C212yesmaximal, complemented
10#10622278C212yesmaximal, complemented
11#10622263C211yesmaximal, characteristic, complemented
12C22×D44C2211yescharacteristic
13C22×D44C2212yes—
14C22×C4×D11C2212yes—
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2211yescharacteristic
19C2×(C2×D11)⋊C4C2211yescharacteristic
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×C4⋊Dic11C2211yescharacteristic
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2212yes—
28C2×Dic11⋊C4C2212yes—
29C2×C4×Dic11C2211yescharacteristic
30#66951—24no—
31#66946—24no—
32C11×#95C2211yescharacteristic
33C11×#95C2212yes—
34C11×#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2211yescharacteristic
37C23×D11C2311yescharacteristic
38C23×D11C2312yes—
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×Dic11C2312yes—
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C2×D44—24no—
49C2×D44—24no—
50C2×D44—22no—
51C2×D44—42no—
52C2×D44—42no—
53C2×C4×D11—24no—
54C2×C4×D11—42no—
55C2×C4×D11—42no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4—22no—
58(C2×D11)⋊C4—24no—
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—24no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—42no—
64(C2×D11)⋊C4—42no—
65(C2×D11)⋊C4—42no—
66C4⋊Dic11—22no—
67Dic11⋊C4—22no—
68Dic11⋊C4—42no—
69Dic11⋊C4—42no—
70C4×Dic11D414yescomplemented
71#2636—111nomaximal, Sylow
72C23×C11C2411yescharacteristic
73C22×D11—22no—
74C22×D11—22no—
75C22×D11—22no—
76C22×D11—22no—
77C22×D11—22no—
78C22×D11—22no—
79C22×D11—21no—
80C22×D11—22no—
81C22×D11—22no—
82C22×D11—21no—
83C22×D11—21no—
84C22×D11#4114yes—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—21no—
97C2×C4×C11C2×D412yes—
98C2×Dic11—21no—
99C2×Dic11—22no—
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11C2×D412yes—
107C2×Dic11C2×D412yes—
108D44—28no—
109D44—48no—
110C4×D11—48no—
111C2×#126—111no—
112C2×C4×D4—111no—
113#400D1111yescharacteristic, complemented
114#399—111no—
115#396—112no—
116#394—111no—
117#394—112no—
118#392—111no—
119#386—112no—
120#385—112no—
121#382—111no—
122C22×C11C22×D411yescharacteristic
123C22×C11C2×#4112yes—
124C22×C11H(5,𝔽2)12yes—
125C22×C11H(5,𝔽2)11yescharacteristic
126C22×C112−1+411yescharacteristic
127C2×D11—24no—
128C2×D11—24no—
129C2×D11—24no—
130C2×D11—42no—
131C2×D11—42no—
132C2×D11—42no—
133C2×D11—42no—
134C2×D11—41no—
135C2×D11—41no—
136C2×D11—41no—
137C2×D11—42no—
138C2×D11—42no—
139C4×C11—22no—
140C4×C11—41no—
141C4×C11—42no—
142C4×C11—41no—
143C4×C11—42no—
144Dic11—22no—
145Dic11—22no—
146Dic11—41no—
147Dic11—42no—
148C22×D4—111no—
149C22×D4—112no—
150C23×C4—112no—
151#126—224no—
152C4×D4—224no—
153C2×C4⋊C4—111no—
154C2×C4⋊C4—111no—
155C2×C4⋊C4—112no—
156C2×C4⋊C4—112no—
157C2×C4⋊C4C2×D1111yescharacteristic
158C2×C4⋊C4C2×D1111yescharacteristic
159C2×C22⋊C4—112no—
160C2×C22⋊C4—111no—
161C2×C22⋊C4—111no—
162C2×C22⋊C4—111no—
163C2×C22⋊C4—112no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4—112no—
166C2×C22⋊C4—112no—
167C2×C42—111no—
168#95—112no—
169#95—111no—
170#95C2×D1111yescharacteristic
171#95C2×D1112yes—
172#95C2×D1112yes—
173C2×C11#52511yescharacteristic
174C2×C11#53511yescharacteristic
175C2×C11#53711yescharacteristic
176C2×C11#53812yes—
177C2×C11#53912yes—
178D11—44no—
179D11—81no—
180C24—112no—
181C24—111no—
182C2×D4—224no—
183C2×D4—224no—
184C2×D4—222no—
185C2×D4—442no—
186C2×D4—442no—
187C22×C4—111no—
188C22×C4—111no—
189C22×C4—112no—
190C22×C4—111no—
191C22×C4—224no—
192C22×C4—442no—
193C22×C4—442no—
194C22×C4C22×D1112yes—
195C22×C4C22×D1111yescharacteristic
196C22×C4C22×D1111yescharacteristic
197C22×C4C22×D1112yes—
198C22×C4C22×D1111yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—222no—
202C4⋊C4—222no—
203C4⋊C4—442no—
204C4⋊C4—442no—
205C22⋊C4—224no—
206C22⋊C4—222no—
207C22⋊C4—222no—
208C22⋊C4—224no—
209C22⋊C4—222no—
210C22⋊C4—442no—
211C22⋊C4—442no—
212C22⋊C4—442no—
213C42—114no—
214C11#263611yescharacteristic, complemented, Sylow
215C23—114no—
216C23—222no—
217C23—222no—
218C23—222no—
219C23—222no—
220C23—222no—
221C23—222no—
222C23—221no—
223C23—221no—
224C23—222no—
225C23—222no—
226C23—221no—
227C23C23×D1111yescharacteristic
228D4—228no—
229D4—448no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—112no—
243C2×C4—112no—
244C2×C4—221no—
245C2×C4—221no—
246C2×C4—222no—
247C2×C4—221no—
248C2×C4—222no—
249C2×C4—222no—
250C2×C4—222no—
251C2×C4—222no—
252C2×C4—448no—
253C2×C4D4×D1112yes—
254C22—224no—
255C22—224no—
256C22—224no—
257C22—442no—
258C22—442no—
259C22—442no—
260C22—442no—
261C22—442no—
262C22—441no—
263C22—441no—
264C22—441no—
265C22—442no—
266C22C2×D4×D1111yescharacteristic
267C22#6704011yescharacteristic
268C22#41×D1112yes—
269C22#6704211yescharacteristic
270C22#6704212yes—
271C4—22no—
272C4—42no—
273C4—41no—
274C4—41no—
275C4—42no—
276C4—222no—
277C4—222no—
278C4—442no—
279C4—441no—
280C2—444no—
281C2—881no—
282C2#1062316011yescharacteristic
283C2#1062318711yescharacteristic
284C2#1062320511yescharacteristic
285C2#1062322312yes—
286C2#1062323512yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#400C2
prime radical#10622284C2
hypercenter#400D11
hypocenterC11#2636
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#66951C2semidirect
2. C2×#66946C2semidirect
3. C11×#400C2semidirect
4. #10622605C2semidirect
5. #10622604C2semidirect
6. #10622289C2semidirect
7. #10622285C2semidirect
9. #10622281C2semidirect
10. #10622278C2semidirect
11. #10622263C2semidirect
70. C4×Dic11D4semidirect
113. #400D11semidirect
214. C11#2636semidirect

Maximal subgroups

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

subgroupindex
C2×#669512
C2×#669462
C11×#4002
#106226052
#106226042
#106222892
#106222852
#106222842
#106222812
#106222782
#106222632
#263611