Finite Group Databasebeta

← #13077911

Subgroups — #13077911

Order 1408.

700 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 165 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×C11×2−1+4C211yesmaximal, characteristic
2#10623356C211yesmaximal, characteristic, complemented
3C2×#67004C211yesmaximal, characteristic, complemented
4C22×#4326C211yesmaximal, characteristic, complemented
5#10622852C214yesmaximal, complemented
6#10622847C211yesmaximal, characteristic, complemented
7#10622846C211yesmaximal, characteristic, complemented
8#10622841C214yesmaximal, complemented
9#10622838C211yesmaximal, characteristic, complemented
10C11×2−1+4—24no—
11C11×2−1+4—24no—
12C2×C11×#41—22no—
13C2×C11×#41—21no—
14C2×C11×#41C2212yes—
15C2×C11×#41C2211yescharacteristic
16C2×C11×#41C2211yescharacteristic
17C22×Q8×C11—21no—
18C22×Q8×C11C2212yes—
19C22×Q8×C11C2211yescharacteristic
20C22×Dic22C2211yescharacteristic
21#67004—24no—
22#66997—21no—
23C2×#4326—24no—
24C2×#4326C2214yes—
25C2×#4326C2212yes—
26#66989—21no—
27#66988—22no—
28C2×#4324C2212yes—
29#66979C2211yescharacteristic
30#66977C2214yes—
31C2×#4318C2211yescharacteristic
32C22×C11⋊C8C2211yescharacteristic
33#66899C2214yes—
34#66899C2212yes—
35#66896C2212yes—
36C22⋊(C11⋊C8)C2214yes—
37C11×#41—216no—
38C11×#41—28no—
39C11×#41—24no—
40C11×#41—24no—
41C11×#41—22no—
42C11×#41—22no—
43C11×#41—22no—
44C11×#41D414yes—
45C2×Q8×C11—28no—
46C2×Q8×C11—24no—
47C2×Q8×C11—24no—
48C2×Q8×C11—22no—
49C2×Q8×C11—21no—
50C2×Q8×C11—22no—
51C2×Q8×C11D414yes—
52C2×Q8×C11D411yescharacteristic
53C2×Q8×C11C2311yescharacteristic
54C2×Q8×C11C2312yes—
55C2×D4×C11—22no—
56C2×D4×C11—21no—
57C2×D4×C11D412yes—
58C2×D4×C11D411yescharacteristic
59C2×D4×C11C2311yescharacteristic
60C22×C4×C11—22no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—21no—
64C22×C4×C11C2312yes—
65C22×C4×C11C2311yescharacteristic
66C22×Dic11—21no—
67C2×Dic22—22no—
68C2×Dic22—22no—
69C2×Dic22—21no—
70C2×Dic22C2312yes—
71C22⋊Dic11—24no—
72C22⋊Dic11—21no—
73#4326—28no—
74#4326—24no—
75#4324—24no—
76C4⋊Dic11C2312yes—
77Dic11⋊C4—24no—
78C4×Dic11—21no—
79#4318—22no—
80C2×C11⋊C8—22no—
81C2×C11⋊C8C2312yes—
82C2×C11⋊C8C2312yes—
83#3011—111nomaximal, Sylow
84C23×C11—21no—
85C23×C11C2×D412yes—
86C23×C11C2×D411yescharacteristic
87Q8×C11—28no—
88Q8×C11—24no—
89Q8×C11—22no—
90Q8×C11—21no—
91Q8×C11—22no—
92Q8×C11C2×D412yes—
93Q8×C11C2×D414yes—
94D4×C11—28no—
95D4×C11—24no—
96D4×C11—24no—
97D4×C11—22no—
98D4×C11—21no—
99D4×C11C2×D412yes—
100C2×C4×C11—28no—
101C2×C4×C11—28no—
102C2×C4×C11—24no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C2×C4×C11—24no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11C2×D412yes—
109C2×C4×C11C2×D411yescharacteristic
110C2×C4×C11C2×D412yes—
111C2×C4×C11C2×D412yes—
112C2×C4×C11C2411yescharacteristic
113C2×Dic11—22no—
114C2×Dic11—22no—
115C2×Dic11—42no—
116Dic22—22no—
117Dic22—22no—
118Dic22—42no—
119C11⋊C8—22no—
120C11⋊C8—22no—
121C2×2−1+4D1111yescharacteristic
122C2×#137—111no—
123C22×Q16—111no—
124#536—111no—
125#452—114no—
126#451—114no—
127#419—111no—
128#416—111no—
129#408—111no—
130C22×C11—22no—
131C22×C11—22no—
132C22×C11—22no—
133C22×C11—24no—
134C22×C11—42no—
135C22×C11#12012yes—
136C22×C11C22×D411yescharacteristic
137C4×C11—24no—
138C4×C11—22no—
139C4×C11—22no—
140C4×C11#12012yes—
141C4×C11C22×D411yescharacteristic
142C4×C11C22×D411yescharacteristic
143Dic11—42no—
144Dic11—42no—
1452−1+4—24no—
1462−1+4—24no—
147C2×#41—22no—
148C2×#41—21no—
149C2×#41C2×D1112yes—
150C2×#41C2×D1111yescharacteristic
151C2×#41C2×D1111yescharacteristic
152C22×Q8—21no—
153C22×Q8—111no—
154C22×Q8C2×D1112yes—
155C22×Q8C2×D1111yescharacteristic
156#137—224no—
157C2×Q16—114no—
158C2×Q16—112no—
159C2×Q16—224no—
160C2×SD16—112no—
161C2×M16—111no—
162C22×C8—111no—
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⋊C8—114no—
172C2×C11—22no—
173C2×C11—42no—
174C2×C11—42no—
175C2×C11C2×#12011yescharacteristic
176C2×C11#57812yes—
177#41—216no—
178#41—28no—
179#41—24no—
180#41—24no—
181#41—22no—
182#41—22no—
183#41—22no—
184#41C22⋊D1114yes—
185C2×Q8—28no—
186C2×Q8—24no—
187C2×Q8—24no—
188C2×Q8—22no—
189C2×Q8—21no—
190C2×Q8—22no—
191C2×Q8—112no—
192C2×Q8—221no—
193C2×Q8—222no—
194C2×Q8—222no—
195C2×Q8C22⋊D1114yes—
196C2×Q8C22⋊D1111yescharacteristic
197C2×Q8C22×D1111yescharacteristic
198C2×Q8C22×D1112yes—
199C2×D4—22no—
200C2×D4—21no—
201C2×D4C22⋊D1112yes—
202C2×D4C22⋊D1111yescharacteristic
203C2×D4C22×D1111yescharacteristic
204C22×C4—22no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—221no—
209C22×C4C22×D1112yes—
210C22×C4C22×D1111yescharacteristic
211Q16—228no—
212Q16—224no—
213SD16—224no—
214M16—222no—
215C2×C8—112no—
216C2×C8—112no—
217C2×C8—222no—
218C4⋊C4—112no—
219C4⋊C4—224no—
220C22⋊C4—221no—
221C22⋊C4—224no—
222C42—221no—
223C11#301111yescharacteristic, complemented, Sylow
224C23—21no—
225C23C2×C22⋊D1112yes—
226C23C2×C22⋊D1111yescharacteristic
227Q8—28no—
228Q8—24no—
229Q8—22no—
230Q8—21no—
231Q8—22no—
232Q8—222no—
233Q8—222no—
234Q8—442no—
235Q8C2×C22⋊D1112yes—
236Q8C2×C22⋊D1114yes—
237D4—28no—
238D4—24no—
239D4—24no—
240D4—22no—
241D4—21no—
242D4C2×C22⋊D1112yes—
243C2×C4—28no—
244C2×C4—28no—
245C2×C4—24no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—24no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—222no—
252C2×C4—222no—
253C2×C4—442no—
254C2×C4C2×C22⋊D1112yes—
255C2×C4C2×C22⋊D1111yescharacteristic
256C2×C4C2×C22⋊D1112yes—
257C2×C4C2×C22⋊D1112yes—
258C2×C4C23×D1111yescharacteristic
259C8—222no—
260C8—222no—
261C22—22no—
262C22—24no—
263C22—22no—
264C22—22no—
265C22—42no—
266C22#6700612yes—
267C22C22×C22⋊D1111yescharacteristic
268C4—24no—
269C4—22no—
270C4—22no—
271C4—442no—
272C4—442no—
273C4#6700612yes—
274C4C22×C22⋊D1111yescharacteristic
275C4C22×C22⋊D1111yescharacteristic
276C2—22no—
277C2—42no—
278C2—42no—
279C2#1062336912yes—
280C2C2×#6700611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC2×C11×2−1+4C2
socleC22×C11C22×D4
hypercenterC2×2−1+4D11
hypocenterC11#3011
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
2. #10623356C2semidirect
3. C2×#67004C2semidirect
4. C22×#4326C2semidirect
5. #10622852C2semidirect
6. #10622847C2semidirect
7. #10622846C2semidirect
8. #10622841C2semidirect
9. #10622838C2semidirect
223. C11#3011semidirect

Maximal subgroups

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

subgroupindex
C2×C11×2−1+42
#106233562
C2×#670042
C22×#43262
#106228522
#106228472
#106228462
#106228412
#106228382
#301111