Finite Group Databasebeta

← #13081330

Subgroups — #13081330

Order 1408.

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

normal subgroups only

This group has 372 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, complemented
2Q8×D44C211yesmaximal, characteristic, complemented
3#10622696C211yesmaximal, characteristic, complemented
4#10622694C211yesmaximal, characteristic, complemented
5#10622670C212yesmaximal
6#10622668C212yesmaximal, complemented
7#10622639C212yesmaximal, complemented
8#10622637C211yesmaximal, characteristic, complemented
9#10622634C212yesmaximal, complemented
10C4×#4323C211yesmaximal, characteristic
11#10622620C211yesmaximal, characteristic, complemented
12C2×Q8×D11—21no—
13C11×C4⋊Q8C2211yescharacteristic
14C11×#126—22no—
15C11×#124C2212yes—
16C11×C22⋊Q8—21no—
17C4×Q8×C11C2212yes—
18C4×Q8×C11C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20C11×#117—21no—
21C2×#4325C2212yes—
22C2×#4323C2211yescharacteristic
23#66950—21no—
24#66950—22no—
25C4×D44C2211yescharacteristic
26C4×D44C2212yes—
27#66922C2211yescharacteristic
28#66922C2212yes—
29#66899C2212yes—
30#66899C2212yes—
31#66899C2212yes—
32#66896C2212yes—
33#66896C2211yescharacteristic
34#66873C2211yescharacteristic
35#66871C2212yes—
36#66871C2211yescharacteristic
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—
45Q8×D11—44no—
46C2×D44C2311yescharacteristic
47C2×C4×D11—22no—
48C2×C4×D11—21no—
49C2×Dic22—22no—
50C2×Dic22—21no—
51C11×C4⋊C4—21no—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—21no—
54C11×C4⋊C4D411yescharacteristic
55C11×C4⋊C4D412yes—
56C11×C4⋊C4C2311yescharacteristic
57C11×C22⋊C4—22no—
58C11×C22⋊C4—21no—
59C11×C22⋊C4—22no—
60C42×C11—22no—
61C42×C11C2311yescharacteristic
62C42×C11C2312yes—
63#4325—24no—
64#4323—22no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4—21no—
67C4⋊Dic11—22no—
68C4⋊Dic11—21no—
69C4⋊Dic11C2312yes—
70C4⋊Dic11C2311yescharacteristic
71C2×C11⋊C8C2311yescharacteristic
72C2×C11⋊C8C2311yescharacteristic
73C2×C11⋊C8C2312yes—
74#3367—111nomaximal, Sylow
75C23×C11—21no—
76C22×D11—21no—
77Q8×C11—22no—
78Q8×C11—22no—
79Q8×C11—22no—
80D4×C11—21no—
81D4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—22no—
84C2×C4×C11—42no—
85C2×C4×C11C2×D412yes—
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2×D412yes—
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2411yescharacteristic
90C2×Dic11—21no—
91C2×Dic11—22no—
92D44—21no—
93D44#4112yes—
94C4×D11—44no—
95C4×D11—42no—
96Dic22—44no—
97Dic22—42no—
98C11⋊C8—21no—
99C11⋊C8—22no—
100C11⋊C8—21no—
101#556D1111yescharacteristic, complemented
102D4×Q8—111no—
103#489—112no—
104#487—111no—
105#477—112no—
106#474—111no—
107#463—112no—
108#461—111no—
109#446—111no—
110#440—112no—
111C4×D8—111no—
112C22×C11—41no—
113C22×C11—41no—
114C22×C11—41no—
115C22×C11C22×D411yescharacteristic
116C2×D11—22no—
117C2×D11—41no—
118C2×D11—41no—
119C4×C11—22no—
120C4×C11—22no—
121C4×C11—21no—
122C4×C11—42no—
123C4×C11—41no—
124C4×C11AGL(1,ℤ/8)12yes—
125C4×C11C2×#4111yescharacteristic
126C4×C112−1+411yescharacteristic
127Dic11—41no—
128Dic11—42no—
129C22×Q8—221no—
130C2×SD16—112no—
131C2×D8—111no—
132C4⋊Q8—111no—
133C4⋊Q8—112no—
134C4⋊Q8C2×D1111yescharacteristic
135#126—22no—
136#124C2×D1112yes—
137C22⋊Q8—21no—
138C22⋊Q8—221no—
139C22⋊Q8—222no—
140C4×Q8C2×D1112yes—
141C4×Q8C2×D1111yescharacteristic
142C4×D4—111no—
143C4×D4—112no—
144C4×D4C2×D1111yescharacteristic
145#117—21no—
146#107—111no—
147#107—112no—
148C4⋊C8—111no—
149C4⋊C8—112no—
150#103—112no—
151#103—112no—
152#103—112no—
153#102—111no—
154#102—112no—
155#102—111no—
156#97—112no—
157C4×C8—111no—
158C2×C11—81no—
159C2×C11#54811yescharacteristic
160C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
161C2×C11#57811yescharacteristic
162D11—42no—
163C2×Q8—222no—
164C2×Q8—221no—
165C2×Q8—444no—
166C2×Q8C22⋊D1111yescharacteristic
167C2×Q8C22×D1112yes—
168C2×D4—111no—
169C2×D4C22×D1111yescharacteristic
170C22×C4—21no—
171C22×C4—222no—
172C22×C4—221no—
173SD16—224no—
174D8—222no—
175C2×C8—111no—
176C2×C8—111no—
177C2×C8—112no—
178C4⋊C4—21no—
179C4⋊C4—22no—
180C4⋊C4—21no—
181C4⋊C4—111no—
182C4⋊C4—112no—
183C4⋊C4—222no—
184C4⋊C4—221no—
185C4⋊C4C22⋊D1111yescharacteristic
186C4⋊C4C22⋊D1112yes—
187C4⋊C4C22×D1111yescharacteristic
188C22⋊C4—22no—
189C22⋊C4—21no—
190C22⋊C4—22no—
191C22⋊C4—222no—
192C22⋊C4—221no—
193C42—22no—
194C42C22×D1111yescharacteristic
195C42C22×D1112yes—
196C11#336711yescharacteristic, complemented, Sylow
197C23—21no—
198C23—221no—
199Q8—22no—
200Q8—22no—
201Q8—22no—
202Q8—444no—
203Q8—442no—
204D4—21no—
205D4—21no—
206D4—112no—
207D4—221no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—222no—
212C2×C4—221no—
213C2×C4—444no—
214C2×C4—442no—
215C2×C4C2×C22⋊D1112yes—
216C2×C4C2×C22⋊D1111yescharacteristic
217C2×C4C2×C22⋊D1112yes—
218C2×C4C2×C22⋊D1111yescharacteristic
219C2×C4C23×D1111yescharacteristic
220C8—221no—
221C8—222no—
222C8—221no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—222no—
227C22—441no—
228C22—441no—
229C22C22×C22⋊D1111yescharacteristic
230C4—22no—
231C4—22no—
232C4—21no—
233C4—41no—
234C4—42no—
235C4—442no—
236C4—441no—
237C4#6700212yes—
238C4#41×D1111yescharacteristic
239C4#6704311yescharacteristic
240C2—81no—
241C2—442no—
242C2C2×#6700211yescharacteristic
243C2#1062336211yescharacteristic
244C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#556C2
socleC22×C11C22×D4
prime radicalC2×#4323C22
hypercenter#556D11
hypocenterC11#3367
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
1. C11×#556C2semidirect
2. Q8×D44C2semidirect
3. #10622696C2semidirect
4. #10622694C2semidirect
6. #10622668C2semidirect
7. #10622639C2semidirect
8. #10622637C2semidirect
9. #10622634C2semidirect
11. #10622620C2semidirect
101. #556D11semidirect
196. C11#3367semidirect

Maximal subgroups

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

subgroupindex
C11×#5562
Q8×D442
#106226962
#106226942
#106226702
#106226682
#106226392
#106226372
#106226342
C4×#43232
#106226202
#336711