Finite Group Databasebeta

← #13077909

Subgroups — #13077909

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
2C11×#536C211yesmaximal, characteristic, complemented
3C22×#4326C211yesmaximal, characteristic, complemented
4C2×#66995C211yesmaximal, characteristic, complemented
5#10622847C211yesmaximal, characteristic, complemented
6#10622663C214yesmaximal, complemented
7#10622660C214yesmaximal, complemented
8#10622617C211yesmaximal, characteristic, complemented
9#10622615C211yesmaximal, characteristic, complemented
10C2×C11×#41C2211yescharacteristic
11C22×Q8×C11C2211yescharacteristic
12#67043—24no—
13#67043—24no—
14C2×Q8×D11—21no—
15C2×#4341—22no—
16C2×#4341—21no—
17C2×#4339C2212yes—
18C2×#4339C2211yescharacteristic
19C22×Dic22C2212yes—
20C22×Dic22C2211yescharacteristic
21C11×C4⋊Q8—21no—
22C11×#124—21no—
23C11×#123—22no—
24C11×C22⋊Q8C2214yes—
25C11×#117C2211yescharacteristic
26C2×#4326—24no—
27C2×#4326C2212yes—
28C2×#4326C2214yes—
29#66995—24no—
30C2×#4325C2212yes—
31C2×#4318C2211yescharacteristic
32C22×C11⋊C8C2211yescharacteristic
33C22⋊(C11⋊C8)C2214yes—
34#66874C2212yes—
35#66874C2214yes—
36#66873C2212yes—
37C11×#41—22no—
38C11×#41—22no—
39C2×Q8×C11—21no—
40C2×Q8×C11—22no—
41C2×Q8×C11—22no—
42C2×Q8×C11D411yescharacteristic
43C2×Q8×C11C2312yes—
44C2×D4×C11D412yes—
45C2×D4×C11D411yescharacteristic
46C22×C4×C11—21no—
47C22×C4×C11C2312yes—
48C22×C4×C11C2311yescharacteristic
49C2×C22⋊D11—22no—
50C2×C22⋊D11—21no—
51C22×Dic11—22no—
52C22×Dic11—21no—
53Q8×D11—28no—
54#4341—216no—
55#4341—28no—
56#4339—24no—
57#4339—24no—
58#4339—22no—
59#4339D414yes—
60C2×D44C2311yescharacteristic
61C2×C4×D11—22no—
62C2×C4×D11—21no—
63C2×Dic22—24no—
64C2×Dic22—24no—
65C2×Dic22—22no—
66C2×Dic22—21no—
67C2×Dic22—22no—
68C2×Dic22D414yes—
69C2×Dic22C2311yescharacteristic
70C2×Dic22C2312yes—
71C11×C4⋊C4—24no—
72C11×C4⋊C4C2312yes—
73C11×C22⋊C4—21no—
74C11×C22⋊C4—24no—
75C42×C11—21no—
76#4326—24no—
77#4326—28no—
78#4325—24no—
79#4318—22no—
80C2×C11⋊C8—22no—
81C2×C11⋊C8C2312yes—
82C2×C11⋊C8C2312yes—
83#3011—111nomaximal, Sylow
84C23×C11C2×D412yes—
85C23×C11C2×D411yescharacteristic
86C22×D11—21no—
87Q8×C11—22no—
88Q8×C11—22no—
89Q8×C11—22no—
90Q8×C11—42no—
91D4×C11—24no—
92D4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—42no—
98C2×C4×C11C2×D412yes—
99C2×C4×C11C2×D412yes—
100C2×C4×C11C2×D412yes—
101C2×C4×C11C2×D411yescharacteristic
102C2×C4×C11C2411yescharacteristic
103C22⋊D11—28no—
104C22⋊D11—24no—
105C2×Dic11—28no—
106C2×Dic11—24no—
107C2×Dic11—21no—
108C2×Dic11—22no—
109D44—21no—
110D44C2×D412yes—
111C4×D11—28no—
112C4×D11—24no—
113Dic22—28no—
114Dic22—24no—
115Dic22—22no—
116Dic22—21no—
117Dic22C2×D412yes—
118Dic22C2×D414yes—
119C11⋊C8—22no—
120C11⋊C8—22no—
121C2×2−1+4—111no—
122C2×#137—111no—
123C22×Q16—111no—
124#536D1111yescharacteristic, complemented
125#452—114no—
126#451—114no—
127#419—111no—
128#416—111no—
129#408—111no—
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—42no—
139C4×C11—42no—
140C4×C11#12012yes—
141C4×C11C22×D411yescharacteristic
142C4×C11C22×D411yescharacteristic
143Dic11—22no—
144Dic11—24no—
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—112no—
154C22×Q8—221no—
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—21no—
164#124—21no—
165#123—22no—
166C22⋊Q8C2×D1114yes—
167#117C2×D1111yescharacteristic
168#103—112no—
169#103—114no—
170#102—112no—
171C22⋊C8—114no—
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—21no—
186C2×Q8—22no—
187C2×Q8—22no—
188C2×Q8—114no—
189C2×Q8—112no—
190C2×Q8—111no—
191C2×Q8—224no—
192C2×Q8—224no—
193C2×Q8—228no—
194C2×Q8—222no—
195C2×Q8—222no—
196C2×Q8—221no—
197C2×Q8C22⋊D1111yescharacteristic
198C2×Q8C22×D1112yes—
199C2×D4—111no—
200C2×D4—222no—
201C2×D4—221no—
202C2×D4C22⋊D1112yes—
203C2×D4C22⋊D1111yescharacteristic
204C22×C4—21no—
205C22×C4—222no—
206C22×C4—221no—
207C22×C4—222no—
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—24no—
219C4⋊C4C22×D1112yes—
220C22⋊C4—21no—
221C22⋊C4—24no—
222C42—21no—
223C11#301111yescharacteristic, complemented, Sylow
224C23—221no—
225C23C2×C22⋊D1112yes—
226C23C2×C22⋊D1111yescharacteristic
227Q8—22no—
228Q8—22no—
229Q8—22no—
230Q8—42no—
231Q8—114no—
232Q8—112no—
233Q8—228no—
234Q8—224no—
235Q8—222no—
236Q8—221no—
237D4—24no—
238D4—22no—
239D4—112no—
240D4—228no—
241D4—224no—
242D4—221no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—42no—
248C2×C4—228no—
249C2×C4—228no—
250C2×C4—224no—
251C2×C4—222no—
252C2×C4—221no—
253C2×C4—224no—
254C2×C4D4×D1112yes—
255C2×C4D4×D1112yes—
256C2×C4C2×C22⋊D1112yes—
257C2×C4C2×C22⋊D1111yescharacteristic
258C2×C4C23×D1111yescharacteristic
259C8—222no—
260C8—222no—
261C22—22no—
262C22—22no—
263C22—24no—
264C22—222no—
265C22—442no—
266C22#6699012yes—
267C22C22×C22⋊D1111yescharacteristic
268C4—22no—
269C4—42no—
270C4—42no—
271C4—224no—
272C4—222no—
273C4#6699012yes—
274C4C2×D4×D1111yescharacteristic
275C4C2×D4×D1111yescharacteristic
276C2—22no—
277C2—42no—
278C2—442no—
279C2C2×#6699011yescharacteristic
280C2#1062336912yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#536C2
socleC22×C11C22×D4
prime radicalC2×#67043C2
hypercenter#536D11
hypocenterC11#3011
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C11×#536C2semidirect
3. C22×#4326C2semidirect
4. C2×#66995C2semidirect
5. #10622847C2semidirect
6. #10622663C2semidirect
7. #10622660C2semidirect
8. #10622617C2semidirect
9. #10622615C2semidirect
124. #536D11semidirect
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
C11×#5362
C22×#43262
C2×#669952
#106228472
#106226632
#106226602
#106226172
#106226152
#301111