Finite Group Databasebeta

← #13074513

Subgroups — #13074513

Order 1408.

562 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 137 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×C11×#126C211yesmaximal, characteristic, complemented
2C2×C4×D44C211yesmaximal, characteristic, complemented
3#10622607C212yesmaximal, complemented
4#10622604C211yesmaximal, characteristic, complemented
5#10622602C212yesmaximal, complemented
6#10622599C211yesmaximal, characteristic, complemented
7#10622574C212yesmaximal, complemented
8#10622573C211yesmaximal, characteristic
9#10622569C212yesmaximal, complemented
10#10622562C211yesmaximal, characteristic, complemented
11#10622549C211yesmaximal, characteristic, complemented
12C22×C22⋊D11C2212yes—
13C22×D44C2211yescharacteristic
14C22×C4×D11C2212yes—
15C11×#126—24no—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C42×C11C2211yescharacteristic
23C2×C22⋊Dic11C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×C4⋊Dic11C2211yescharacteristic
29C2×C4⋊Dic11C2212yes—
30C2×Dic11⋊C4C2212yes—
31C4×D44—24no—
32C11⋊#95C2211yescharacteristic
33C11⋊#95C2212yes—
34C11⋊#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C23×D11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C2×C22⋊D11—24no—
46C2×C22⋊D11—42no—
47C2×C22⋊D11—42no—
48C22×Dic11C2312yes—
49C22×Dic11C2312yes—
50C22×Dic11C2312yes—
51C2×D44—24no—
52C2×D44—22no—
53C2×C4×D11—24no—
54C2×C4×D11—42no—
55C2×C4×D11—42no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—22no—
59C11×C22⋊C4—22no—
60C11×C22⋊C4—22no—
61C11×C22⋊C4—22no—
62C42×C11D414yescomplemented
63C22⋊Dic11—42no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—42no—
67(C2×D11)⋊C4—42no—
68C4⋊Dic11—22no—
69C4⋊Dic11—42no—
70Dic11⋊C4—42no—
71#2636—111nomaximal, Sylow
72C23×C11—21no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—21no—
76C23×C11—21no—
77C23×C11C2411yescharacteristic
78C22×D11—22no—
79C22×D11—22no—
80C22×D11—22no—
81C22×D11—22no—
82C22×D11—22no—
83C22×D11—22no—
84C22×D11#4114yes—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11C2×D412yes—
97C2×C4×C11C2×D412yes—
98C2×C4×C11C2×D412yes—
99C22⋊D11—48no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109D44—28no—
110C4×D11—48no—
111C2×#126D1111yescharacteristic, complemented
112C2×C4×D4—111no—
113#400—111no—
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×C11—41no—
123C22×C11—41no—
124C22×C11—41no—
125C22×C11—42no—
126C22×C11—42no—
127C22×C11C22×D411yescharacteristic
128C22×C11C2×#4112yes—
129C22×C11H(5,𝔽2)12yes—
130C22×C11H(5,𝔽2)11yescharacteristic
131C22×C112−1+411yescharacteristic
132C2×D11—24no—
133C2×D11—24no—
134C2×D11—24no—
135C2×D11—42no—
136C2×D11—42no—
137C2×D11—42no—
138C2×D11—42no—
139C4×C11—22no—
140C4×C11—22no—
141C4×C11—22no—
142C4×C11—41no—
143C4×C11—41no—
144C4×C11—41no—
145Dic11—42no—
146Dic11—42no—
147Dic11—42no—
148C22×D4—112no—
149C22×D4—111no—
150C23×C4—112no—
151#126—24no—
152C4×D4—224no—
153C2×C4⋊C4—111no—
154C2×C4⋊C4—112no—
155C2×C4⋊C4—112no—
156C2×C4⋊C4C2×D1111yescharacteristic
157C2×C4⋊C4C2×D1111yescharacteristic
158C2×C4⋊C4C2×D1111yescharacteristic
159C2×C22⋊C4—112no—
160C2×C22⋊C4—112no—
161C2×C22⋊C4—112no—
162C2×C22⋊C4—112no—
163C2×C22⋊C4—112no—
164C2×C22⋊C4C2×D1111yescharacteristic
165C2×C22⋊C4C2×D1111yescharacteristic
166C2×C22⋊C4C2×D1111yescharacteristic
167C2×C42C2×D1111yescharacteristic
168#95—112no—
169#95—111no—
170#95—111no—
171#95—112no—
172#95—112no—
173C2×C11—81no—
174C2×C11#52511yescharacteristic
175C2×C11#53511yescharacteristic
176C2×C11#53711yescharacteristic
177C2×C11#53812yes—
178C2×C11#53912yes—
179D11—44no—
180C24—112no—
181C24C22×D1111yescharacteristic
182C2×D4—224no—
183C2×D4—224no—
184C2×D4—222no—
185C2×D4—442no—
186C2×D4—442no—
187C22×C4—112no—
188C22×C4—112no—
189C22×C4—112no—
190C22×C4—224no—
191C22×C4—442no—
192C22×C4—442no—
193C22×C4C22×D1111yescharacteristic
194C22×C4C22×D1111yescharacteristic
195C22×C4C22×D1111yescharacteristic
196C22×C4C22×D1111yescharacteristic
197C22×C4C22×D1111yescharacteristic
198C22×C4C22×D1111yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—222no—
203C4⋊C4—442no—
204C4⋊C4—442no—
205C22⋊C4—22no—
206C22⋊C4—22no—
207C22⋊C4—22no—
208C22⋊C4—224no—
209C22⋊C4—224no—
210C22⋊C4—442no—
211C22⋊C4—442no—
212C22⋊C4—442no—
213C42C22⋊D1114yescomplemented
214C11#263611yescharacteristic, complemented, Sylow
215C23—22no—
216C23—22no—
217C23—21no—
218C23—21no—
219C23—21no—
220C23—114no—
221C23—222no—
222C23—222no—
223C23—222no—
224C23—222no—
225C23—222no—
226C23—222no—
227C23C23×D1111yescharacteristic
228D4—228no—
229D4—448no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—222no—
244C2×C4—222no—
245C2×C4—222no—
246C2×C4—222no—
247C2×C4—222no—
248C2×C4—222no—
249C2×C4—222no—
250C2×C4—448no—
251C2×C4C2×C22⋊D1112yes—
252C2×C4C2×C22⋊D1112yes—
253C2×C4C2×C22⋊D1112yes—
254C22—42no—
255C22—42no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—224no—
260C22—224no—
261C22—224no—
262C22—442no—
263C22—442no—
264C22—442no—
265C22—442no—
266C22#41×D1112yes—
267C22#6704211yescharacteristic
268C22#6704212yes—
269C22#6704311yescharacteristic
270C22C22×C22⋊D1111yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—442no—
278C4—442no—
279C4—442no—
280C2—81no—
281C2—444no—
282C2#1062323512yes—
283C2#1062323812yes—
284C2#1062335911yescharacteristic
285C2#1062336111yescharacteristic
286C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#126C2
prime radical#10622573C2
hypercenterC2×#126D11
hypocenterC11#2636
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×C11×#126C2semidirect
2. C2×C4×D44C2semidirect
3. #10622607C2semidirect
4. #10622604C2semidirect
5. #10622602C2semidirect
6. #10622599C2semidirect
7. #10622574C2semidirect
9. #10622569C2semidirect
10. #10622562C2semidirect
11. #10622549C2semidirect
62. C42×C11D4semidirect
111. C2×#126D11semidirect
213. C42C22⋊D11semidirect
214. C11#2636semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1262
C2×C4×D442
#106226072
#106226042
#106226022
#106225992
#106225742
#106225732
#106225692
#106225622
#106225492
#263611