Finite Group Databasebeta

← #13068813

Subgroups — #13068813

Order 1408.

316 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 105 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×#66979C211yesmaximal, characteristic
2C11×#380C211yesmaximal, characteristic
3C2×C22⋊(C11⋊C8)C211yesmaximal, characteristic
4C2×#66872C211yesmaximal, characteristic, complemented
5C2×#66871C211yesmaximal, characteristic, complemented
6#10622167C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C23×C4×C11C2211yescharacteristic
9C2×C11×C4⋊C4C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C11×C22⋊C4—21no—
12C2×C22⋊Dic11—21no—
13#66979—22no—
14#66979—22no—
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2211yescharacteristic
17C2×C4×Dic11—21no—
18C22×C11⋊C8C2211yescharacteristic
19C22×C11⋊C8C2211yescharacteristic
20C11×#95—21no—
21C22⋊(C11⋊C8)C414yescomplemented
22#66872—22no—
23#66871—22no—
24C24×C11D411yescharacteristic
25C22×C4×C11—21no—
26C22×C4×C11—21no—
27C22×C4×C11—21no—
28C22×C4×C11—21no—
29C22×C4×C11—21no—
30C22×C4×C11—21no—
31C22×C4×C11C2×C412yes—
32C22×C4×C11D411yescharacteristic
33C22×C4×C11Q812yes—
34C22×C4×C11C2311yescharacteristic
35C22×Dic11—21no—
36C22×Dic11—21no—
37C11×C4⋊C4—21no—
38C11×C4⋊C4—21no—
39C11×C4⋊C4—21no—
40C11×C4⋊C4—21no—
41C11×C22⋊C4—42no—
42C22⋊Dic11—24no—
43C4⋊Dic11—21no—
44C4⋊Dic11—21no—
45C4⋊Dic11D412yes—
46C4⋊Dic11D412yes—
47C4×Dic11—24no—
48C2×C11⋊C8—21no—
49C2×C11⋊C8—21no—
50C2×C11⋊C8—21no—
51C2×C11⋊C8—21no—
52C2×C11⋊C8C2×C412yes—
53C2×C11⋊C8C2×C412yes—
54#1854—111nomaximal, Sylow
55C23×C11—21no—
56C23×C11—21no—
57C23×C11—21no—
58C23×C11—21no—
59C23×C11—21no—
60C23×C11—21no—
61C23×C11C4⋊C412yes—
62C23×C11C2×D411yescharacteristic
63C2×C4×C11—21no—
64C2×C4×C11—21no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—41no—
70C2×C4×C11—41no—
71C2×C4×C11—41no—
72C2×C4×C11—41no—
73C2×C4×C11—41no—
74C2×C4×C11—41no—
75C2×C4×C11C4⋊C412yes—
76C2×C4×C11C22×C411yescharacteristic
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2×Q811yescharacteristic
80C2×C4×C11#4111yescharacteristic
81C2×C4×C11#4111yescharacteristic
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—41no—
85C2×Dic11—41no—
86C2×Dic11—41no—
87C2×Dic11—41no—
88C11⋊C8—22no—
89C11⋊C8—22no—
90C2×#117—111no—
91C2×#107—111no—
92C2×#106—111no—
93C2×C22⋊C8—111no—
94#380D1111yescharacteristic
95#340—111no—
96#340—111no—
97C22×C11—22no—
98C22×C11—22no—
99C22×C11—22no—
100C22×C11—41no—
101C22×C11—41no—
102C22×C11—41no—
103C22×C11—41no—
104C22×C11C2×C4⋊C411yescharacteristic
105C22×C11#12011yescharacteristic
106C22×C11#12311yescharacteristic
107C22×C11#13511yescharacteristic
108C22×C11#13511yescharacteristic
109C22×C11AGL(1,ℤ/8)11yescharacteristic
110C22×C11#13711yescharacteristic
111C4×C11—22no—
112C4×C11—81no—
113C4×C11—81no—
114C4×C11C4×D411yescharacteristic
115C4×C11C4×D411yescharacteristic
116C4×C11C22⋊Q811yescharacteristic
117C4×C11C22⋊Q811yescharacteristic
118Dic11—42no—
119Dic11—42no—
120C23×C4C2×D1111yescharacteristic
121C22×C8—111no—
122C22×C8—111no—
123#117—222no—
124#117—222no—
125C2×C4⋊C4—111no—
126C2×C4⋊C4—111no—
127C2×C4⋊C4C2×D1111yescharacteristic
128C2×C4⋊C4C2×D1111yescharacteristic
129C2×C22⋊C4—21no—
130C2×C22⋊C4—221no—
131C2×C42—221no—
132#107—222no—
133#106—222no—
134C22⋊C8—114no—
135#95—21no—
136C2×C11—42no—
137C2×C11#38511yescharacteristic
138C2×C11#42711yescharacteristic
139C2×C11#42811yescharacteristic
140C2×C11#44911yescharacteristic
141C2×C11#45211yescharacteristic
142C2×C11#48211yescharacteristic
143C2×C11#48511yescharacteristic
144C24C22⋊D1111yescharacteristic
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—221no—
152C22×C4—221no—
153C22×C4Dic2212yes—
154C22×C4C4×D1112yes—
155C22×C4C22⋊D1111yescharacteristic
156C22×C4C22×D1111yescharacteristic
157C2×C8—112no—
158C2×C8—112no—
159C2×C8—221no—
160C2×C8—221no—
161C2×C8—221no—
162C2×C8—221no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—112no—
168C4⋊C4—112no—
169C4⋊C4—221no—
170C4⋊C4—221no—
171C22⋊C4—42no—
172C22⋊C4—224no—
173C42—224no—
174C11#185411yescharacteristic, complemented, Sylow
175C23—21no—
176C23—21no—
177C23—21no—
178C23—21no—
179C23—21no—
180C23—21no—
181C23Dic11⋊C412yes—
182C23C2×C22⋊D1111yescharacteristic
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—222no—
196C2×C4—222no—
197C2×C4—441no—
198C2×C4—441no—
199C2×C4—441no—
200C2×C4—441no—
201C2×C4Dic11⋊C412yes—
202C2×C4C2×Dic2211yescharacteristic
203C2×C4C2×C4×D1111yescharacteristic
204C2×C4D4×D1111yescharacteristic
205C2×C4D4×D1111yescharacteristic
206C2×C4#434111yescharacteristic
207C2×C4#434111yescharacteristic
208C8—222no—
209C8—222no—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22C2×Dic11⋊C411yescharacteristic
218C22#6698511yescharacteristic
219C22#6698811yescharacteristic
220C22#6699011yescharacteristic
221C22#6699511yescharacteristic
222C22#6700311yescharacteristic
223C22#6700311yescharacteristic
224C4—22no—
225C4—81no—
226C4—81no—
227C4—442no—
228C4—442no—
229C4#6693111yescharacteristic
230C4#6693111yescharacteristic
231C4(C22⋊D11)⋊C411yescharacteristic
232C4(C22⋊D11)⋊C411yescharacteristic
233C2—42no—
234C2#1062255911yescharacteristic
235C2#1062257711yescharacteristic
236C2#1062261111yescharacteristic
237C2#1062264811yescharacteristic
238C2#1062265011yescharacteristic
239C2#1062265811yescharacteristic
240C2#1062266011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC11×#380C2
socleC23×C11C2×D4
prime radicalC24×C11D4
cosocleC22×C4×C11C23
hypercenter#380D11
hypocenterC11#1854
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
4. C2×#66872C2semidirect
5. C2×#66871C2semidirect
6. #10622167C2semidirect
7. #10622167C2semidirect
21. C22⋊(C11⋊C8)C4semidirect
174. C11#1854semidirect

Maximal subgroups

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

subgroupindex
C2×#669792
C11×#3802
C2×C22⋊(C11⋊C8)2
C2×#668722
C2×#668712
#106221672
#185411