Finite Group Databasebeta

← #13078783

Subgroups — #13078783

Order 1408.

386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C11×#529C211yesmaximal, characteristic
2C2×C4×Dic22C211yesmaximal, characteristic, complemented
3#10622676C212yesmaximal, complemented
4#10622667C212yesmaximal, complemented
5#10622663C211yesmaximal, characteristic, complemented
6#10622657C211yesmaximal, characteristic, complemented
7#10622653C211yesmaximal, characteristic
8#10622647C211yesmaximal, characteristic
9#10622643C212yesmaximal, complemented
10#10622631C212yesmaximal, complemented
11#10622539C211yesmaximal, characteristic, complemented
12C22×Dic22C2211yescharacteristic
13C11×#126—21no—
14C11×#125C2211yescharacteristic
15C11×#124C2211yescharacteristic
16C11×#123—21no—
17C11×C22⋊Q8C2211yescharacteristic
18C11×#121C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20C4×D4×C11—21no—
21C4×D4×C11C2211yescharacteristic
22C11×#117—21no—
23C2×C42×C11C2211yescharacteristic
24C2×#4326C2212yes—
25C2×#4324C2212yes—
26C2×C4⋊Dic11C2211yescharacteristic
27C2×Dic11⋊C4—21no—
28C2×C4×Dic11—21no—
29C4×Dic22—21no—
30C4×Dic22—21no—
31C4×Dic22C2212yes—
32C4×Dic22C2212yes—
33#66899C2212yes—
34#66896C2212yes—
35C22⋊(C11⋊C8)C2211yescharacteristic
36C22⋊(C11⋊C8)C2211yescharacteristic
37#66874C2212yes—
38#66874C2212yes—
39#66872C2212yes—
40#66871C2212yes—
41C4⋊(C11⋊C8)C2212yes—
42#66867C2212yes—
43C2×Q8×C11C2311yescharacteristic
44C2×D4×C11—21no—
45C2×D4×C11C2311yescharacteristic
46C22×C4×C11—21no—
47C22×C4×C11D411yescharacteristic
48C22×C4×C11D411yescharacteristic
49C22×C4×C11C2311yescharacteristic
50C22×Dic11—21no—
51C22×Dic11—21no—
52C2×Dic22—24no—
53C2×Dic22—21no—
54C2×Dic22C2312yes—
55C11×C4⋊C4—21no—
56C11×C4⋊C4—21no—
57C11×C4⋊C4—21no—
58C11×C4⋊C4—21no—
59C11×C4⋊C4C2311yescharacteristic
60C11×C4⋊C4C2311yescharacteristic
61C11×C22⋊C4—21no—
62C11×C22⋊C4—21no—
63C11×C22⋊C4—21no—
64C11×C22⋊C4—21no—
65C11×C22⋊C4—21no—
66C42×C11—21no—
67C42×C11D411yescharacteristic
68C42×C11D411yescharacteristic
69C42×C11C2311yescharacteristic
70C42×C11C2311yescharacteristic
71#4326—24no—
72#4324—24no—
73C4⋊Dic11—21no—
74C4⋊Dic11C2312yes—
75Dic11⋊C4—22no—
76Dic11⋊C4—22no—
77C4×Dic11—22no—
78C4×Dic11—22no—
79C2×C11⋊C8C2312yes—
80C2×C11⋊C8C2312yes—
81#3117—111nomaximal, Sylow
82C23×C11—21no—
83C23×C11C2×D411yescharacteristic
84Q8×C11—22no—
85D4×C11—22no—
86D4×C11—42no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—41no—
93C2×C4×C11—42no—
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11C2×D411yescharacteristic
96C2×C4×C11C2×D411yescharacteristic
97C2×C4×C11C2×D411yescharacteristic
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11C2411yescharacteristic
100C2×Dic11—24no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—42no—
104Dic22—24no—
105Dic22—22no—
106Dic22#4114yes—
107C11⋊C8—22no—
108C11⋊C8—22no—
109#529D1111yescharacteristic
110C2×C4×Q8—111no—
111#484—111no—
112#481—111no—
113#479—112no—
114#464—112no—
115#451—111no—
116#448—111no—
117#441—112no—
118#440—112no—
119#432—111no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11—41no—
123C22×C11—41no—
124C22×C11—41no—
125C22×C11#13712yes—
126C22×C11C22×D411yescharacteristic
127C4×C11—21no—
128C4×C11—21no—
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—21no—
132C4×C11—41no—
133C4×C11—41no—
134C4×C11—41no—
135C4×C11C2×#4112yes—
136Dic11—24no—
137Dic11—42no—
138C22×Q8—111no—
139C2×Q16—112no—
140C2×SD16—112no—
141#126—21no—
142#125C2×D1111yescharacteristic
143#124C2×D1111yescharacteristic
144#123—21no—
145C22⋊Q8C2×D1111yescharacteristic
146#121C2×D1111yescharacteristic
147C4×Q8—112no—
148C4×Q8—112no—
149C4×Q8—221no—
150C4×Q8—221no—
151C4×Q8C2×D1111yescharacteristic
152C4×D4—21no—
153C4×D4C2×D1111yescharacteristic
154#117—21no—
155C2×C4⋊C4—111no—
156C2×C4⋊C4—221no—
157C2×C42—221no—
158C2×C42C2×D1111yescharacteristic
159#107—112no—
160#106—112no—
161C4⋊C8—112no—
162#103—112no—
163#103—112no—
164#103—112no—
165#102—112no—
166C22⋊C8—111no—
167C22⋊C8—111no—
168#97—112no—
169C2×C11—22no—
170C2×C11—81no—
171C2×C11#52511yescharacteristic
172C2×C11C2×#13711yescharacteristic
173C2×C11#57511yescharacteristic
174C2×Q8—112no—
175C2×Q8—224no—
176C2×Q8—221no—
177C2×Q8C22×D1111yescharacteristic
178C2×D4—21no—
179C2×D4C22×D1111yescharacteristic
180C22×C4—21no—
181C22×C4—221no—
182C22×C4—221no—
183C22×C4C22⋊D1111yescharacteristic
184C22×C4C22⋊D1111yescharacteristic
185C22×C4C22×D1111yescharacteristic
186Q16—224no—
187SD16—224no—
188C2×C8—112no—
189C2×C8—112no—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—112no—
195C4⋊C4—221no—
196C4⋊C4—222no—
197C4⋊C4—222no—
198C4⋊C4C22×D1111yescharacteristic
199C4⋊C4C22×D1111yescharacteristic
200C22⋊C4—21no—
201C22⋊C4—21no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—21no—
205C42—21no—
206C42—222no—
207C42—222no—
208C42C22⋊D1111yescharacteristic
209C42C22⋊D1111yescharacteristic
210C42C22×D1111yescharacteristic
211C42C22×D1111yescharacteristic
212C11#311711yescharacteristic, complemented, Sylow
213C23—21no—
214C23C2×C22⋊D1111yescharacteristic
215Q8—22no—
216Q8—114no—
217Q8—224no—
218Q8—222no—
219D4—22no—
220D4—42no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—224no—
229C2×C4—222no—
230C2×C4—222no—
231C2×C4—442no—
232C2×C4C2×C22⋊D1111yescharacteristic
233C2×C4C2×C22⋊D1111yescharacteristic
234C2×C4C2×C22⋊D1111yescharacteristic
235C2×C4C2×C22⋊D1111yescharacteristic
236C2×C4C2×C22⋊D1111yescharacteristic
237C2×C4C23×D1111yescharacteristic
238C8—222no—
239C8—222no—
240C22—21no—
241C22—21no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22#6700412yes—
246C22C22×C22⋊D1111yescharacteristic
247C4—21no—
248C4—21no—
249C4—21no—
250C4—21no—
251C4—21no—
252C4—41no—
253C4—41no—
254C4—41no—
255C4—224no—
256C4—442no—
257C4#41×D1112yes—
258C2—22no—
259C2—81no—
260C2#1062335311yescharacteristic
261C2C2×#6700411yescharacteristic
262C2#1062335911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#529C2
socleC22×C11C22×D4
prime radicalC11×#121C22
hypercenter#529D11
hypocenterC11#3117
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic22C2semidirect
3. #10622676C2semidirect
4. #10622667C2semidirect
5. #10622663C2semidirect
6. #10622657C2semidirect
9. #10622643C2semidirect
10. #10622631C2semidirect
11. #10622539C2semidirect
212. C11#3117semidirect

Maximal subgroups

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

subgroupindex
C11×#5292
C2×C4×Dic222
#106226762
#106226672
#106226632
#106226572
#106226532
#106226472
#106226432
#106226312
#106225392
#311711