Finite Group Databasebeta

← #13081647

Subgroups — #13081647

Order 1408.

350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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×#556C211yesmaximal, characteristic
2#10623101C211yesmaximal, characteristic, complemented
3#10622705C211yesmaximal, characteristic, complemented
4#10622703C211yesmaximal, characteristic, complemented
5#10622673C212yesmaximal
6#10622667C212yesmaximal
7#10622644C212yesmaximal, complemented
8#10622643C212yesmaximal, complemented
9#10622637C211yesmaximal, characteristic, complemented
10#10622632C211yesmaximal, characteristic
11C4×#4324C211yesmaximal, characteristic
12C11×C4⋊Q8C2211yescharacteristic
13C11×#126—22no—
14C11×#124C2212yes—
15C11×C22⋊Q8—21no—
16C4×Q8×C11C2212yes—
17C4×Q8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19C11×#117—21no—
20Q8×Dic11—21no—
21C2×#4326C2212yes—
22C2×#4326C2212yes—
23C2×#4326C2212yes—
24C2×#4324C2211yescharacteristic
25C2×#4324C2212yes—
26#66943—21no—
27#66943—22no—
28#66922C2211yescharacteristic
29#66922C2212yes—
30C4×Dic22C2211yescharacteristic
31C4×Dic22C2212yes—
32#66899C2212yes—
33#66896C2211yescharacteristic
34#66874C2211yescharacteristic
35#66874C2212yes—
36#66872C2211yescharacteristic
37C4⋊(C11⋊C8)C2211yescharacteristic
38C4⋊(C11⋊C8)C2212yes—
39#66867C2212yes—
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11D411yescharacteristic
42C2×Q8×C11C2312yes—
43C2×D4×C11C2311yescharacteristic
44C22×C4×C11—21no—
45C2×Dic22C2311yescharacteristic
46C2×Dic22C2312yes—
47C11×C4⋊C4—21no—
48C11×C4⋊C4—22no—
49C11×C4⋊C4—21no—
50C11×C4⋊C4D411yescharacteristic
51C11×C4⋊C4D412yes—
52C11×C4⋊C4C2311yescharacteristic
53C11×C22⋊C4—22no—
54C11×C22⋊C4—21no—
55C11×C22⋊C4—22no—
56C42×C11—22no—
57C42×C11C2311yescharacteristic
58C42×C11C2312yes—
59#4326—24no—
60#4326—42no—
61#4326—42no—
62#4324—22no—
63#4324—42no—
64C4⋊Dic11—22no—
65C4⋊Dic11—21no—
66C4⋊Dic11—22no—
67C4⋊Dic11—21no—
68C4⋊Dic11C2311yescharacteristic
69Dic11⋊C4—22no—
70Dic11⋊C4—21no—
71C4×Dic11—22no—
72C4×Dic11—21no—
73C2×C11⋊C8C2311yescharacteristic
74C2×C11⋊C8C2312yes—
75C2×C11⋊C8C2311yescharacteristic
76#3398—111nomaximal, Sylow
77C23×C11—21no—
78Q8×C11—22no—
79Q8×C11—22no—
80Q8×C11—22no—
81D4×C11—21no—
82D4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—42no—
86C2×C4×C11C2×D412yes—
87C2×C4×C11C2×D412yes—
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11C2411yescharacteristic
91C2×Dic11—21no—
92C2×Dic11—21no—
93C2×Dic11—22no—
94Dic22—21no—
95Dic22—22no—
96Dic22—22no—
97Dic22—21no—
98C11⋊C8—22no—
99C11⋊C8—21no—
100C11⋊C8#4112yes—
101#557—111no—
102#556D1111yescharacteristic
103#497—112no—
104#494—111no—
105#464—112no—
106#462—111no—
107#462—112no—
108#461—111no—
109#446—111no—
110#441—112no—
111C4×SD16—111no—
112C22×C11—41no—
113C22×C11—41no—
114C22×C11—41no—
115C22×C11C22×D411yescharacteristic
116C4×C11—22no—
117C4×C11—22no—
118C4×C11—21no—
119C4×C11—42no—
120C4×C11—41no—
121C4×C11#13712yes—
122C4×C11C2×#4111yescharacteristic
123C4×C11H(5,𝔽2)11yescharacteristic
124Dic11—41no—
125Dic11—42no—
126Dic11—41no—
127C2×Q16—112no—
128C2×Q16—112no—
129C2×Q16—112no—
130C2×SD16—111no—
131C2×SD16—112no—
132C4⋊Q8—111no—
133C4⋊Q8—112no—
134C4⋊Q8C2×D1111yescharacteristic
135#126—22no—
136#125—221no—
137#125—222no—
138#124C2×D1112yes—
139C22⋊Q8—21no—
140C4×Q8—111no—
141C4×Q8—112no—
142C4×Q8—221no—
143C4×Q8C2×D1112yes—
144C4×Q8C2×D1111yescharacteristic
145C4×D4C2×D1111yescharacteristic
146#117—21no—
147#106—111no—
148C4⋊C8—111no—
149C4⋊C8—112no—
150#103—112no—
151#103—111no—
152#103—112no—
153#102—111no—
154#97—112no—
155C4×C8—111no—
156C2×C11—81no—
157C2×C11#55011yescharacteristic
158C2×C11C2×#13711yescharacteristic
159C2×C11#57811yescharacteristic
160C2×Q8—111no—
161C2×Q8—112no—
162C2×Q8C22⋊D1111yescharacteristic
163C2×Q8C22×D1112yes—
164C2×D4C22×D1111yescharacteristic
165C22×C4—21no—
166Q16—224no—
167Q16—442no—
168Q16—442no—
169SD16—222no—
170SD16—442no—
171C2×C8—111no—
172C2×C8—111no—
173C2×C8—112no—
174C4⋊C4—21no—
175C4⋊C4—22no—
176C4⋊C4—21no—
177C4⋊C4—111no—
178C4⋊C4—222no—
179C4⋊C4—221no—
180C4⋊C4—222no—
181C4⋊C4—221no—
182C4⋊C4—222no—
183C4⋊C4—221no—
184C4⋊C4C22⋊D1111yescharacteristic
185C4⋊C4C22⋊D1112yes—
186C4⋊C4C22×D1111yescharacteristic
187C22⋊C4—22no—
188C22⋊C4—21no—
189C22⋊C4—22no—
190C42—22no—
191C42—222no—
192C42—221no—
193C42C22×D1111yescharacteristic
194C42C22×D1112yes—
195C11#339811yescharacteristic, complemented, Sylow
196C23—21no—
197Q8—22no—
198Q8—22no—
199Q8—22no—
200Q8—221no—
201Q8—222no—
202Q8—222no—
203Q8—221no—
204D4—21no—
205D4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—221no—
210C2×C4—221no—
211C2×C4—222no—
212C2×C4C2×C22⋊D1112yes—
213C2×C4C2×C22⋊D1112yes—
214C2×C4C2×C22⋊D1111yescharacteristic
215C2×C4C2×C22⋊D1111yescharacteristic
216C2×C4C23×D1111yescharacteristic
217C8—112no—
218C8—222no—
219C8—221no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22C22×C22⋊D1111yescharacteristic
224C4—22no—
225C4—22no—
226C4—21no—
227C4—41no—
228C4—42no—
229C4—441no—
230C4—442no—
231C4—441no—
232C4#6700412yes—
233C4#41×D1111yescharacteristic
234C4#6704211yescharacteristic
235C2—81no—
236C2C2×#6700411yescharacteristic
237C2#1062336511yescharacteristic
238C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#556C2
socleC22×C11C22×D4
prime radicalC2×D4×C11C23
hypercenter#556D11
hypocenterC11#3398
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
2. #10623101C2semidirect
3. #10622705C2semidirect
4. #10622703C2semidirect
7. #10622644C2semidirect
8. #10622643C2semidirect
9. #10622637C2semidirect
195. C11#3398semidirect

Maximal subgroups

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

subgroupindex
C11×#5562
#106231012
#106227052
#106227032
#106226732
#106226672
#106226442
#106226432
#106226372
#106226322
C4×#43242
#339811