Finite Group Databasebeta

← #13077913

Subgroups — #13077913

Order 1408.

700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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×#67043C211yesmaximal, characteristic
2#10623356C211yesmaximal, characteristic, complemented
3C2×#66962C211yesmaximal, characteristic, complemented
4C22×Dic44C211yesmaximal, characteristic, complemented
5C11×#408C211yesmaximal, characteristic, complemented
6#10622733C211yesmaximal, characteristic, complemented
7#10622726C211yesmaximal, characteristic, complemented
8#10622352C214yesmaximal, complemented
9#10622346C214yesmaximal, complemented
10C2×C11×#41C2211yescharacteristic
11#67043—24no—
12#67043—24no—
13C2×Q8×D11—21no—
14C2×#4341—22no—
15C2×#4341—21no—
16C2×#4339C2212yes—
17C2×#4339C2211yescharacteristic
18C22×Dic22C2211yescharacteristic
19C22×Dic22C2212yes—
20C22×Dic22C2211yescharacteristic
21C2×C11×M16C2211yescharacteristic
22C22×C8×C11C2211yescharacteristic
23#66997—21no—
24#66989—21no—
25#66988—22no—
26#66979C2211yescharacteristic
27#66977C2214yes—
28#66962—24no—
29C2×Dic44—24no—
30C2×Dic44C2214yes—
31C2×Dic44C2212yes—
32C2×#4314C2212yes—
33C11×C22⋊C8C2214yes—
34#66885C2212yes—
35#66880C2212yes—
36#66880C2214yes—
37C11×#41—22no—
38C11×#41—22no—
39C2×Q8×C11D411yescharacteristic
40C2×D4×C11D412yes—
41C2×D4×C11D411yescharacteristic
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C2×C22⋊D11—22no—
45C2×C22⋊D11—21no—
46C22×Dic11—22no—
47C22×Dic11—21no—
48C22×Dic11—21no—
49Q8×D11—28no—
50#4341—216no—
51#4341—28no—
52#4339—24no—
53#4339—24no—
54#4339—22no—
55#4339D414yes—
56C2×D44C2311yescharacteristic
57C2×C4×D11—22no—
58C2×C4×D11—21no—
59C2×Dic22—24no—
60C2×Dic22—24no—
61C2×Dic22—22no—
62C2×Dic22—21no—
63C2×Dic22—22no—
64C2×Dic22—22no—
65C2×Dic22—22no—
66C2×Dic22—21no—
67C2×Dic22D414yes—
68C2×Dic22C2312yes—
69C2×Dic22C2311yescharacteristic
70C2×Dic22C2312yes—
71C11×M16—22no—
72C2×C8×C11—22no—
73C2×C8×C11C2312yes—
74C2×C8×C11C2312yes—
75C22⋊Dic11—24no—
76C22⋊Dic11—21no—
77C4⋊Dic11C2312yes—
78Dic11⋊C4—24no—
79C4×Dic11—21no—
80Dic44—28no—
81Dic44—24no—
82#4314—24no—
83#3011—111nomaximal, Sylow
84C23×C11C2×D412yes—
85C23×C11C2×D411yescharacteristic
86C22×D11—21no—
87Q8×C11—22no—
88D4×C11—24no—
89D4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11C2×D412yes—
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2×D412yes—
95C2×C4×C11C2×D412yes—
96C2×C4×C11C2411yescharacteristic
97C22⋊D11—28no—
98C22⋊D11—24no—
99C2×Dic11—28no—
100C2×Dic11—24no—
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—42no—
106D44—21no—
107D44C2×D412yes—
108C4×D11—28no—
109C4×D11—24no—
110Dic22—28no—
111Dic22—24no—
112Dic22—22no—
113Dic22—21no—
114Dic22—22no—
115Dic22—22no—
116Dic22—42no—
117Dic22C2×D412yes—
118Dic22C2×D414yes—
119C8×C11—22no—
120C8×C11—22no—
121C2×2−1+4—111no—
122C2×#137—111no—
123C22×Q16—111no—
124#536—111no—
125#452—114no—
126#451—114no—
127#419—111no—
128#416—111no—
129#408D1111yescharacteristic, complemented
130C22×C11—22no—
131C22×C11—22no—
132C22×C11—24no—
133C22×C11#12012yes—
134C22×C11C22×D411yescharacteristic
135C2×D11—22no—
136C2×D11—42no—
137C4×C11—22no—
138C4×C11#12012yes—
139C4×C11C22×D411yescharacteristic
140C4×C11C22×D411yescharacteristic
141Dic11—22no—
142Dic11—24no—
143Dic11—42no—
144Dic11—42no—
1452−1+4—224no—
1462−1+4—224no—
147C2×#41—111no—
148C2×#41—112no—
149C2×#41—222no—
150C2×#41—221no—
151C2×#41C2×D1111yescharacteristic
152C22×Q8—111no—
153C22×Q8—111no—
154C22×Q8—112no—
155C22×Q8—221no—
156#137—224no—
157C2×Q16—114no—
158C2×Q16—112no—
159C2×Q16—224no—
160C2×SD16—112no—
161C2×M16C2×D1111yescharacteristic
162C22×C8C2×D1111yescharacteristic
163C4⋊Q8—221no—
164#124—221no—
165#123—222no—
166C22⋊Q8—114no—
167#117—111no—
168#103—112no—
169#103—114no—
170#102—112no—
171C22⋊C8C2×D1114yes—
172C2×C11—22no—
173C2×C11—42no—
174C2×C11C2×#12011yescharacteristic
175C2×C11#57812yes—
176D11—42no—
177#41—22no—
178#41—22no—
179#41—114no—
180#41—224no—
181#41—224no—
182#41—2216no—
183#41—228no—
184#41—222no—
185C2×Q8—114no—
186C2×Q8—112no—
187C2×Q8—111no—
188C2×Q8—112no—
189C2×Q8—224no—
190C2×Q8—224no—
191C2×Q8—228no—
192C2×Q8—222no—
193C2×Q8—221no—
194C2×Q8—221no—
195C2×Q8—222no—
196C2×Q8—222no—
197C2×Q8—222no—
198C2×Q8D4411yescharacteristic
199C2×D4—111no—
200C2×D4—222no—
201C2×D4—221no—
202C2×D4D4412yes—
203C2×D4D4411yescharacteristic
204C22×C4—222no—
205C22×C4—221no—
206C22×C4—222no—
207C22×C4—221no—
208C22×C4—221no—
209C22×C4C22×D1112yes—
210C22×C4C22×D1111yescharacteristic
211Q16—228no—
212Q16—224no—
213SD16—224no—
214M16—22no—
215C2×C8—22no—
216C2×C8C22×D1112yes—
217C2×C8C22×D1112yes—
218C4⋊C4—112no—
219C4⋊C4—224no—
220C22⋊C4—221no—
221C22⋊C4—224no—
222C42—221no—
223C11#301111yescharacteristic, complemented, Sylow
224C23—221no—
225C23C2×D4412yes—
226C23C2×D4411yescharacteristic
227Q8—22no—
228Q8—114no—
229Q8—112no—
230Q8—228no—
231Q8—224no—
232Q8—222no—
233Q8—221no—
234Q8—222no—
235Q8—222no—
236Q8—442no—
237D4—24no—
238D4—22no—
239D4—112no—
240D4—228no—
241D4—224no—
242D4—221no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—228no—
246C2×C4—228no—
247C2×C4—224no—
248C2×C4—222no—
249C2×C4—221no—
250C2×C4—224no—
251C2×C4—222no—
252C2×C4—222no—
253C2×C4—442no—
254C2×C4C2×D4412yes—
255C2×C4C2×D4411yescharacteristic
256C2×C4D4×D1112yes—
257C2×C4D4×D1112yes—
258C2×C4C23×D1111yescharacteristic
259C8—22no—
260C8—22no—
261C22—22no—
262C22—22no—
263C22—24no—
264C22—222no—
265C22—442no—
266C22#6693512yes—
267C22C22×D4411yescharacteristic
268C4—22no—
269C4—224no—
270C4—222no—
271C4—442no—
272C4—442no—
273C4#6693512yes—
274C4C2×D4×D1111yescharacteristic
275C4C2×D4×D1111yescharacteristic
276C2—22no—
277C2—42no—
278C2—442no—
279C2C2×#6693511yescharacteristic
280C2#1062328412yes—
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#408C2
socleC22×C11C22×D4
prime radicalC2×#67043C2
hypercenter#408D11
hypocenterC11#3011
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #10623356C2semidirect
3. C2×#66962C2semidirect
4. C22×Dic44C2semidirect
5. C11×#408C2semidirect
6. #10622733C2semidirect
7. #10622726C2semidirect
8. #10622352C2semidirect
9. #10622346C2semidirect
129. #408D11semidirect
223. C11#3011semidirect

Maximal subgroups

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

subgroupindex
C2×#670432
#106233562
C2×#669622
C22×Dic442
C11×#4082
#106227332
#106227262
#106223522
#106223462
#301111