Finite Group Databasebeta

← #13081669

Subgroups — #13081669

Order 1408.

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

normal subgroups only

This group has 362 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×#559C211yesmaximal, characteristic
2#10623101C211yesmaximal, characteristic, complemented
3#10622689C211yesmaximal, characteristic
4#10622688C211yesmaximal, characteristic
5#10622673C212yesmaximal, complemented
6#10622667C212yesmaximal, complemented
7#10622644C211yesmaximal, characteristic, complemented
8C4×#4326C211yesmaximal, characteristic, complemented
9#10622637C211yesmaximal, characteristic, complemented
10#10622632C212yesmaximal, complemented
11#10622631C212yesmaximal, complemented
12C11×#127C2211yescharacteristic
13C11×#124—21no—
14C11×#124C2212yes—
15C11×#123—22no—
16C4×Q8×C11C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18C4×D4×C11—21no—
19C4×D4×C11C2212yes—
20Q8×Dic11—21no—
21C2×#4326C2211yescharacteristic
22C2×#4326C2212yes—
23C2×#4324C2212yes—
24C2×#4324C2212yes—
25C2×#4324C2212yes—
26#66943—21no—
27#66943—22no—
28#66922C2212yes—
29#66922C2211yescharacteristic
30C4×Dic22C2212yes—
31C4×Dic22C2211yescharacteristic
32#66899C2211yescharacteristic
33#66896C2212yes—
34#66874C2212yes—
35#66874C2211yescharacteristic
36#66871C2211yescharacteristic
37C4⋊(C11⋊C8)C2212yes—
38C4⋊(C11⋊C8)C2211yescharacteristic
39#66867C2212yes—
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11D411yescharacteristic
42C2×Q8×C11C2311yescharacteristic
43C2×D4×C11—21no—
44C2×D4×C11—21no—
45C2×D4×C11C2312yes—
46C22×C4×C11—22no—
47C2×Dic22C2312yes—
48C2×Dic22C2311yescharacteristic
49C11×C4⋊C4—21no—
50C11×C4⋊C4D411yescharacteristic
51C11×C4⋊C4D412yes—
52C11×C4⋊C4C2311yescharacteristic
53C11×C22⋊C4—22no—
54C11×C22⋊C4—22no—
55C11×C22⋊C4—22no—
56C42×C11—21no—
57C42×C11C2311yescharacteristic
58C42×C11C2312yes—
59#4326—22no—
60#4326—42no—
61#4324—24no—
62#4324—42no—
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#3400—111nomaximal, Sylow
77C23×C11—22no—
78Q8×C11—22no—
79Q8×C11—21no—
80Q8×C11—21no—
81D4×C11—22no—
82D4×C11—22no—
83D4×C11—42no—
84D4×C11—81no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—82no—
88C2×C4×C11C2×D412yes—
89C2×C4×C11C2×D412yes—
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2411yescharacteristic
93C2×Dic11—21no—
94C2×Dic11—22no—
95C2×Dic11—21no—
96Dic22—22no—
97Dic22—21no—
98Dic22—21no—
99Dic22—22no—
100C11⋊C8—21no—
101C11⋊C8—22no—
102C11⋊C8#4112yes—
103#559D1111yescharacteristic
104#557—111no—
105#497—112no—
106#492—111no—
107#464—112no—
108#462—111no—
109#461—112no—
110#460—111no—
111#446—111no—
112#440—112no—
113C4×Q16—111no—
114C22×C11—42no—
115C22×C11—42no—
116C22×C11—42no—
117C22×C11C22×D411yescharacteristic
118C4×C11—22no—
119C4×C11—22no—
120C4×C11—21no—
121C4×C11—41no—
122C4×C11—41no—
123C4×C11#13712yes—
124C4×C11C2×#4111yescharacteristic
125C4×C11H(5,𝔽2)11yescharacteristic
126Dic11—42no—
127Dic11—41no—
128Dic11—41no—
129C2×Q16—111no—
130C2×Q16—112no—
131C2×SD16—112no—
132C2×SD16—112no—
133C2×SD16—112no—
134C4⋊Q8—112no—
135C4⋊Q8—111no—
136#127C2×D1111yescharacteristic
137#125—221no—
138#125—222no—
139#124—21no—
140#124C2×D1112yes—
141#123—22no—
142C4×Q8—111no—
143C4×Q8—112no—
144C4×Q8—221no—
145C4×Q8C2×D1111yescharacteristic
146C4×Q8C2×D1111yescharacteristic
147C4×D4—21no—
148C4×D4C2×D1112yes—
149#107—111no—
150C4⋊C8—111no—
151C4⋊C8—112no—
152#103—111no—
153#103—111no—
154#103—112no—
155#102—112no—
156#97—112no—
157C4×C8—111no—
158C2×C11—82no—
159C2×C11#55011yescharacteristic
160C2×C11C2×#13711yescharacteristic
161C2×C11#57711yescharacteristic
162C2×Q8—112no—
163C2×Q8—111no—
164C2×Q8C22⋊D1111yescharacteristic
165C2×Q8C22×D1111yescharacteristic
166C2×D4—21no—
167C2×D4—21no—
168C2×D4C22×D1112yes—
169C22×C4—22no—
170Q16—222no—
171Q16—442no—
172SD16—224no—
173SD16—442no—
174SD16—442no—
175C2×C8—111no—
176C2×C8—111no—
177C2×C8—112no—
178C4⋊C4—21no—
179C4⋊C4—111no—
180C4⋊C4—222no—
181C4⋊C4—221no—
182C4⋊C4—222no—
183C4⋊C4—221no—
184C4⋊C4—222no—
185C4⋊C4—221no—
186C4⋊C4C22⋊D1111yescharacteristic
187C4⋊C4C22⋊D1112yes—
188C4⋊C4C22×D1111yescharacteristic
189C22⋊C4—22no—
190C22⋊C4—22no—
191C22⋊C4—22no—
192C42—21no—
193C42—222no—
194C42—221no—
195C42C22×D1111yescharacteristic
196C42C22×D1112yes—
197C11#340011yescharacteristic, complemented, Sylow
198C23—22no—
199Q8—22no—
200Q8—21no—
201Q8—21no—
202Q8—222no—
203Q8—221no—
204Q8—221no—
205Q8—222no—
206D4—22no—
207D4—22no—
208D4—42no—
209D4—81no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—82no—
213C2×C4—221no—
214C2×C4—222no—
215C2×C4—221no—
216C2×C4C2×C22⋊D1112yes—
217C2×C4C2×C22⋊D1112yes—
218C2×C4C2×C22⋊D1111yescharacteristic
219C2×C4C2×C22⋊D1111yescharacteristic
220C2×C4C23×D1111yescharacteristic
221C8—112no—
222C8—221no—
223C8—222no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22C22×C22⋊D1111yescharacteristic
228C4—22no—
229C4—22no—
230C4—21no—
231C4—41no—
232C4—41no—
233C4—442no—
234C4—441no—
235C4—441no—
236C4#6700412yes—
237C4#41×D1111yescharacteristic
238C4#6704211yescharacteristic
239C2—82no—
240C2C2×#6700411yescharacteristic
241C2#1062336511yescharacteristic
242C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#559C2
socleC22×C11C22×D4
prime radicalC11×#127C22
hypercenter#559D11
hypocenterC11#3400
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
2. #10623101C2semidirect
5. #10622673C2semidirect
6. #10622667C2semidirect
7. #10622644C2semidirect
8. C4×#4326C2semidirect
9. #10622637C2semidirect
10. #10622632C2semidirect
11. #10622631C2semidirect
197. C11#3400semidirect

Maximal subgroups

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

subgroupindex
C11×#5592
#106231012
#106226892
#106226882
#106226732
#106226672
#106226442
C4×#43262
#106226372
#106226322
#106226312
#340011