Finite Group Databasebeta

← #13078782

Subgroups — #13078782

Order 1408.

386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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×Q8×Dic11C211yesmaximal, characteristic, complemented
2#10623131C211yesmaximal, characteristic
3C11×#448C211yesmaximal, characteristic
4#10622841C211yesmaximal, characteristic, complemented
5#10622779C212yesmaximal, complemented
6#10622777C212yesmaximal, complemented
7#10622647C211yesmaximal, characteristic
8#10622409C212yesmaximal, complemented
9#10622402C212yesmaximal, complemented
10#10622335C211yesmaximal, characteristic, complemented
11#10622332C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C2×C11×SD16C2212yes—
14C11×#121C2211yescharacteristic
15Q8×Dic11—21no—
16Q8×Dic11—21no—
17Q8×Dic11C2212yes—
18Q8×Dic11C2212yes—
19C2×#4326C2212yes—
20#66989C2211yescharacteristic
21#66988—21no—
22D4×Dic11—21no—
23D4×Dic11C2211yescharacteristic
24C2×C4⋊Dic11—21no—
25C2×C4⋊Dic11C2211yescharacteristic
26#66977C2211yescharacteristic
27C2×C4×Dic11—21no—
28C2×C4×Dic11C2211yescharacteristic
29#66943C2211yescharacteristic
30#66940C2211yescharacteristic
31#66932—21no—
32#66930—21no—
33C11×#103C2212yes—
34C11×C22⋊C8C2211yescharacteristic
35#66899C2212yes—
36#66896C2212yes—
37C22⋊(C11⋊C8)C2211yescharacteristic
38#66882C2212yes—
39#66880C2212yes—
40#66879C2212yes—
41Dic11⋊C8C2212yes—
42#66872C2212yes—
43C2×Q8×C11—24no—
44C2×Q8×C11—21no—
45C2×Q8×C11C2312yes—
46C2×D4×C11—21no—
47C2×D4×C11C2311yescharacteristic
48C22×C4×C11—21no—
49C22×C4×C11C2311yescharacteristic
50C22×Dic11—21no—
51C22×Dic11—21no—
52C22×Dic11D411yescharacteristic
53C22×Dic11D411yescharacteristic
54C2×Dic22C2311yescharacteristic
55C11×SD16—24no—
56C2×C8×C11C2312yes—
57C11×C4⋊C4C2311yescharacteristic
58C11×C22⋊C4—21no—
59C22⋊Dic11—21no—
60C22⋊Dic11—21no—
61C22⋊Dic11—21no—
62C22⋊Dic11—21no—
63#4326—24no—
64C4⋊Dic11—21no—
65C4⋊Dic11—22no—
66C4⋊Dic11—22no—
67C4⋊Dic11—21no—
68C4⋊Dic11C2312yes—
69C4⋊Dic11C2311yescharacteristic
70Dic11⋊C4—21no—
71Dic11⋊C4—21no—
72Dic11⋊C4—21no—
73C4×Dic11—21no—
74C4×Dic11—22no—
75C4×Dic11—22no—
76C4×Dic11D411yescharacteristic
77C4×Dic11D411yescharacteristic
78C4×Dic11C2311yescharacteristic
79C4×Dic11C2311yescharacteristic
80C2×C11⋊C8C2312yes—
81#3117—111nomaximal, Sylow
82C23×C11—21no—
83C23×C11C2×D411yescharacteristic
84Q8×C11—24no—
85Q8×C11—22no—
86Q8×C11#4114yes—
87D4×C11—22no—
88D4×C11—42no—
89C2×C4×C11—24no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—21no—
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2411yescharacteristic
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—21no—
98C2×Dic11—21no—
99C2×Dic11—41no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11C2×D411yescharacteristic
103C2×Dic11C2×D411yescharacteristic
104C2×Dic11C2×D411yescharacteristic
105C2×Dic11C2×D411yescharacteristic
106Dic22—22no—
107C8×C11—22no—
108C11⋊C8—22no—
109#529—111no—
110C2×C4×Q8—111no—
111#484—111no—
112#481—111no—
113#479—112no—
114#464—112no—
115#451—111no—
116#448D1111yescharacteristic
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—24no—
128C4×C11—21no—
129C4×C11—41no—
130C4×C11C2×#4112yes—
131Dic11—21no—
132Dic11—21no—
133Dic11—21no—
134Dic11—21no—
135Dic11—41no—
136Dic11—42no—
137Dic11—41no—
138C22×Q8C2×D1111yescharacteristic
139C2×Q16—112no—
140C2×SD16C2×D1112yes—
141#126—221no—
142#125—111no—
143#124—111no—
144#123—221no—
145C22⋊Q8—111no—
146#121C2×D1111yescharacteristic
147C4×Q8—112no—
148C4×Q8—112no—
149C4×Q8—111no—
150C4×Q8—221no—
151C4×Q8—221no—
152C4×D4—111no—
153C4×D4—221no—
154#117—221no—
155C2×C4⋊C4—111no—
156C2×C4⋊C4—221no—
157C2×C42—111no—
158C2×C42—221no—
159#107—112no—
160#106—112no—
161C4⋊C8—112no—
162#103—112no—
163#103—112no—
164#103C2×D1112yes—
165#102—112no—
166C22⋊C8—111no—
167C22⋊C8C2×D1111yescharacteristic
168#97—112no—
169C2×C11—22no—
170C2×C11—81no—
171C2×C11#52511yescharacteristic
172C2×C11C2×#13711yescharacteristic
173C2×C11#57511yescharacteristic
174C2×Q8—24no—
175C2×Q8—21no—
176C2×Q8—111no—
177C2×Q8C22×D1112yes—
178C2×D4—21no—
179C2×D4C22×D1111yescharacteristic
180C22×C4—21no—
181C22×C4—111no—
182C22×C4—111no—
183C22×C4—221no—
184C22×C4—221no—
185C22×C4C22×D1111yescharacteristic
186Q16—224no—
187SD16—24no—
188C2×C8—112no—
189C2×C8C22×D1112yes—
190C4⋊C4—112no—
191C4⋊C4—111no—
192C4⋊C4—222no—
193C4⋊C4—222no—
194C4⋊C4—221no—
195C4⋊C4—221no—
196C4⋊C4—221no—
197C4⋊C4—221no—
198C4⋊C4—221no—
199C4⋊C4C22×D1111yescharacteristic
200C22⋊C4—21no—
201C22⋊C4—221no—
202C22⋊C4—221no—
203C22⋊C4—221no—
204C22⋊C4—221no—
205C42—111no—
206C42—111no—
207C42—111no—
208C42—111no—
209C42—222no—
210C42—222no—
211C42—221no—
212C11#311711yescharacteristic, complemented, Sylow
213C23—21no—
214C23D4×D1111yescharacteristic
215Q8—24no—
216Q8—22no—
217Q8—222no—
218Q8#434114yes—
219D4—22no—
220D4—42no—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—111no—
226C2×C4—111no—
227C2×C4—111no—
228C2×C4—111no—
229C2×C4—222no—
230C2×C4—222no—
231C2×C4—221no—
232C2×C4—221no—
233C2×C4—441no—
234C2×C4—442no—
235C2×C4—442no—
236C2×C4D4×D1111yescharacteristic
237C2×C4C23×D1111yescharacteristic
238C8—22no—
239C8—222no—
240C22—21no—
241C22—21no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22#6696812yes—
246C22C2×D4×D1111yescharacteristic
247C4—24no—
248C4—21no—
249C4—41no—
250C4—221no—
251C4—221no—
252C4—221no—
253C4—221no—
254C4—442no—
255C4—441no—
256C4—441no—
257C4C2×#434112yes—
258C2—22no—
259C2—81no—
260C2#1062311711yescharacteristic
261C2C2×#6696811yescharacteristic
262C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#448C2
socleC22×C11C22×D4
prime radicalC11×#121C22
hypercenter#448D11
hypocenterC11#3117
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic11C2semidirect
4. #10622841C2semidirect
5. #10622779C2semidirect
6. #10622777C2semidirect
8. #10622409C2semidirect
9. #10622402C2semidirect
10. #10622335C2semidirect
11. #10622332C2semidirect
212. C11#3117semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic112
#106231312
C11×#4482
#106228412
#106227792
#106227772
#106226472
#106224092
#106224022
#106223352
#106223322
#311711