Finite Group Databasebeta

← #13079540

Subgroups — #13079540

Order 1408.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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
1D11×C4⋊Q8C211yesmaximal, characteristic, complemented
2#10623079C211yesmaximal, characteristic
3C11×#461C211yesmaximal, characteristic, complemented
4#10622788C212yesmaximal, complemented
5#10622783C212yesmaximal, complemented
6#10622696C211yesmaximal, characteristic, complemented
7#10622632C211yesmaximal, characteristic, complemented
8#10622454C211yesmaximal, characteristic, complemented
9#10622446C211yesmaximal, characteristic, complemented
10#10622419C212yesmaximal, complemented
11#10622405C212yesmaximal, complemented
12C2×Q8×D11C2212yes—
13C2×#4339—21no—
14C2×C11×SD16C2212yes—
15C11×C4⋊Q8C2211yescharacteristic
16C4×D4×C11C2211yescharacteristic
17#66997C2212yes—
18C2×#4325C2212yes—
19#66993C2211yescharacteristic
20#66991C2211yescharacteristic
21C2×#4324C2212yes—
22C4×C22⋊D11—21no—
23C2×#4314C2212yes—
24#66948C2211yescharacteristic
25C4⋊C4×D11—21no—
26C4⋊C4×D11—21no—
27#66941—21no—
28#66941—21no—
29#66941C2211yescharacteristic
30#66938—21no—
31#66937—21no—
32C4×D44C2211yescharacteristic
33C42×D11C2211yescharacteristic
34#66922C2211yescharacteristic
35C11×C4⋊C8C2211yescharacteristic
36C11×#103C2212yes—
37#66899C2212yes—
38(C2×D11)⋊C8C2212yes—
39#66880C2212yes—
40C8×Dic11C2212yes—
41#66874C2212yes—
42C4⋊(C11⋊C8)C2211yescharacteristic
43C2×Q8×C11C2312yes—
44C2×D4×C11C2311yescharacteristic
45C22×C4×C11—21no—
46C2×C22⋊D11—21no—
47C2×C22⋊D11—21no—
48C2×C22⋊D11—21no—
49Q8×D11—42no—
50Q8×D11—42no—
51#4339—44no—
52C2×D44—21no—
53C2×D44C2311yescharacteristic
54C2×C4×D11—22no—
55C2×C4×D11—21no—
56C2×C4×D11D411yescharacteristic
57C2×C4×D11D411yescharacteristic
58C2×C4×D11C2311yescharacteristic
59C2×Dic22—21no—
60C2×Dic22—22no—
61C2×Dic22C2312yes—
62C11×SD16—42no—
63C2×C8×C11C2312yes—
64C11×C4⋊C4—21no—
65C11×C4⋊C4—21no—
66C11×C4⋊C4C2311yescharacteristic
67C11×C22⋊C4—21no—
68C42×C11C2311yescharacteristic
69C22⋊Dic11—21no—
70#4325—42no—
71#4324—42no—
72(C2×D11)⋊C4—21no—
73(C2×D11)⋊C4—21no—
74C4⋊Dic11—21no—
75C4⋊Dic11—21no—
76C4⋊Dic11C2311yescharacteristic
77Dic11⋊C4—21no—
78Dic11⋊C4—22no—
79Dic11⋊C4—22no—
80C4×Dic11D411yescharacteristic
81C4×Dic11D411yescharacteristic
82C4×Dic11C2311yescharacteristic
83C2×C11⋊C8C2312yes—
84#4314—42no—
85#3206—111nomaximal, Sylow
86C23×C11—21no—
87C22×D11—21no—
88C22×D11C2×D411yescharacteristic
89Q8×C11—22no—
90Q8×C11—22no—
91D4×C11—21no—
92D4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—42no—
96C2×C4×C11C2×D411yescharacteristic
97C2×C4×C11C2×D411yescharacteristic
98C2×C4×C11C2411yescharacteristic
99C22⋊D11—42no—
100C22⋊D11—42no—
101C22⋊D11—42no—
102C2×Dic11—22no—
103C2×Dic11—21no—
104C2×Dic11C2×D411yescharacteristic
105C2×Dic11C2×D411yescharacteristic
106C2×Dic11C2×D411yescharacteristic
107D44—21no—
108D44—21no—
109D44—42no—
110C4×D11—21no—
111C4×D11—21no—
112C4×D11—22no—
113C4×D11—44no—
114C4×D11—42no—
115C4×D11SD1614yescomplemented
116Dic22—22no—
117Dic22—22no—
118Dic22—44no—
119Dic22—42no—
120C8×C11—22no—
121C11⋊C8—22no—
122#532—111no—
123C2×C4⋊Q8—111no—
124#492—112no—
125#487—112no—
126#461—111no—
127#461—111no—
128#461—111no—
129#461D1111yescharacteristic, complemented
130#448—112no—
131#448—112no—
132#431—111no—
133C22×C11—41no—
134C22×C11—41no—
135C22×C11—41no—
136C22×C11C22×D411yescharacteristic
137C2×D11—21no—
138C2×D11—21no—
139C2×D11—41no—
140C2×D11—41no—
141C2×D11—41no—
142C2×D11C2×SD1612yes—
143C4×C11—21no—
144C4×C11—42no—
145C4×C11—41no—
146C4×C11C2×SD1612yes—
147C4×C11H(5,𝔽2)11yescharacteristic
148C4×C11H(5,𝔽2)11yescharacteristic
149Dic11—21no—
150Dic11—42no—
151Dic11—41no—
152Dic11C2×SD1612yes—
153Dic11#13712yes—
154C2×#41—221no—
155C22×Q8—112no—
156C2×SD16—112no—
157C2×SD16—112no—
158C2×SD16—112no—
159C2×SD16C2×D1112yes—
160C4⋊Q8—111no—
161C4⋊Q8—112no—
162C4⋊Q8—111no—
163C4⋊Q8—221no—
164C4⋊Q8—221no—
165C4⋊Q8C2×D1111yescharacteristic
166#127—111no—
167#124—221no—
168#121—111no—
169#121—111no—
170#121—221no—
171C4×D4—111no—
172C4×D4—221no—
173C4×D4C2×D1111yescharacteristic
174C2×C4⋊C4—221no—
175C2×C4⋊C4—221no—
176C2×C42—111no—
177C4⋊C8—111no—
178C4⋊C8C2×D1111yescharacteristic
179#103—112no—
180#103—112no—
181#103—112no—
182#103C2×D1112yes—
183C22⋊C8—112no—
184C4×C8—112no—
185C2×C11—81no—
186C2×C11#53511yescharacteristic
187C2×C11C22×SD1611yescharacteristic
188C2×C11C2×#13711yescharacteristic
189D11—22no—
190D11—81no—
191#41—444no—
192C2×Q8—112no—
193C2×Q8—221no—
194C2×Q8—222no—
195C2×Q8—442no—
196C2×Q8—442no—
197C2×Q8C22×D1112yes—
198C2×D4—111no—
199C2×D4—221no—
200C2×D4—221no—
201C2×D4—221no—
202C2×D4—221no—
203C2×D4C22×D1111yescharacteristic
204C22×C4—21no—
205C22×C4—111no—
206C22×C4—111no—
207C22×C4—111no—
208C22×C4—222no—
209C22×C4—221no—
210SD16—42no—
211SD16—442no—
212SD16—442no—
213SD16—442no—
214C2×C8—112no—
215C2×C8C22×D1112yes—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—111no—
219C4⋊C4—222no—
220C4⋊C4—222no—
221C4⋊C4—221no—
222C4⋊C4—221no—
223C4⋊C4—221no—
224C4⋊C4C22×D1111yescharacteristic
225C22⋊C4—21no—
226C22⋊C4—221no—
227C22⋊C4—221no—
228C22⋊C4—221no—
229C42—111no—
230C42—111no—
231C42—111no—
232C42C22×D1111yescharacteristic
233C11#320611yescharacteristic, complemented, Sylow
234C23—21no—
235C23—111no—
236C23—221no—
237Q8—22no—
238Q8—22no—
239Q8—222no—
240Q8—222no—
241Q8—442no—
242Q8—444no—
243D4—21no—
244D4—21no—
245D4—221no—
246D4—221no—
247D4—442no—
248D4—442no—
249D4—442no—
250D4—442no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—111no—
255C2×C4—111no—
256C2×C4—114no—
257C2×C4—111no—
258C2×C4—222no—
259C2×C4—221no—
260C2×C4—221no—
261C2×C4—221no—
262C2×C4—222no—
263C2×C4—444no—
264C2×C4—442no—
265C2×C4D4×D1111yescharacteristic
266C2×C4D4×D1111yescharacteristic
267C2×C4C23×D1111yescharacteristic
268C8—22no—
269C8—222no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—112no—
274C22—221no—
275C22—221no—
276C22—441no—
277C22—441no—
278C22—441no—
279C22C2×D4×D1111yescharacteristic
280C4—21no—
281C4—41no—
282C4—42no—
283C4—112no—
284C4—112no—
285C4—221no—
286C4—441no—
287C4—442no—
288C4SD16×D1112yes—
289C4#6703711yescharacteristic
290C4#6704211yescharacteristic
291C2—81no—
292C2—222no—
293C2—881no—
294C2#1062313811yescharacteristic
295C2C2×SD16×D1111yescharacteristic
296C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#461C2
socleC22×C11C22×D4
prime radical#10623079C2
hypercenter#461D11
hypocenterC11#3206
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. D11×C4⋊Q8C2semidirect
3. C11×#461C2semidirect
4. #10622788C2semidirect
5. #10622783C2semidirect
6. #10622696C2semidirect
7. #10622632C2semidirect
8. #10622454C2semidirect
9. #10622446C2semidirect
10. #10622419C2semidirect
11. #10622405C2semidirect
115. C4×D11SD16semidirect
129. #461D11semidirect
233. C11#3206semidirect

Maximal subgroups

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

subgroupindex
D11×C4⋊Q82
#106230792
C11×#4612
#106227882
#106227832
#106226962
#106226322
#106224542
#106224462
#106224192
#106224052
#320611