Finite Group Databasebeta

← #14670521

Subgroups — #14670521

Order 2816.

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

normal subgroups only

This group has 396 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×#10622797C211yesmaximal, characteristic
2C2×#10622151C211yesmaximal, characteristic
3C2×#10622203C211yesmaximal, characteristic
4#13069370C211yesmaximal, characteristic
5#13066721C211yesmaximal, characteristic
6#13066695C211yesmaximal, characteristic
7C11×#2141C211yesmaximal, characteristic
8C22×C11×Q16C2211yescharacteristic
9C2×Q8×Dic11—21no—
10C2×C11×M32C2211yescharacteristic
11C11×#427C2211yescharacteristic
12C2×#66899—21no—
13#10622797—22no—
14#10622797—22no—
15C2×#66883C2211yescharacteristic
16C2×#66881C2211yescharacteristic
17C2×#66879C2211yescharacteristic
18C2×#66876C2211yescharacteristic
19#10622612—21no—
20C11×#358C414yescomplemented
21#10622203—22no—
22#10622170—21no—
23#10622151—22no—
24C22×Q8×C11—21no—
25C2×C11×Q16—21no—
26C2×C11×Q16—21no—
27C2×C11×Q16—21no—
28C2×C11×Q16C2×C412yes—
29C2×C11×Q16D412yes—
30C2×C11×Q16Q812yes—
31C22×C8×C11C2311yescharacteristic
32C11×#117—21no—
33Q8×Dic11—24no—
34Q8×Dic11—42no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—41no—
37C2×C4×Dic11—41no—
38C2×C4×Dic11D411yescharacteristic
39C2×#4318—21no—
40C22×C11⋊C8D411yescharacteristic
41C11×M32—21no—
42C11×M32—21no—
43C2×C11×C16C2×C412yes—
44C11×#107C2×C412yes—
45C11×#106—21no—
46#66899—24no—
47#66883—21no—
48#66883—21no—
49#66881—21no—
50#66881D412yes—
51#66879—21no—
52#66879—21no—
53#66876—21no—
54#66876—21no—
55C2×C11⋊C16—21no—
56C4⋊(C11⋊C8)—42no—
57#12957—111nomaximal, Sylow
58C2×Q8×C11—22no—
59C2×Q8×C11—22no—
60C2×Q8×C11—22no—
61C2×Q8×C11—41no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—21no—
67C22×Dic11—41no—
68C11×Q16—22no—
69C11×Q16—22no—
70C11×Q16—22no—
71C11×Q16C4⋊C414yes—
72C2×C8×C11C22×C411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C2×C8×C11C2×D411yescharacteristic
75C2×C8×C11C2×Q811yescharacteristic
76C2×C8×C11#4111yescharacteristic
77C2×C8×C11#4111yescharacteristic
78C11×C4⋊C4—22no—
79C11×C22⋊C4—41no—
80C42×C11—41no—
81C4⋊Dic11—22no—
82C4⋊Dic11—44no—
83C4⋊Dic11—41no—
84C4×Dic11—21no—
85C4×Dic11—44no—
86C4×Dic11SD1612yes—
87#4318—41no—
88#4318—41no—
89C2×C11⋊C8—21no—
90C2×C11⋊C8—21no—
91C2×C11⋊C8—21no—
92C2×C11⋊C8—41no—
93C11×C16—22no—
94C11⋊C16—41no—
95C2×#441—111no—
96C2×#365—111no—
97C2×#362—111no—
98#2141D1111yescharacteristic
99#1946—111no—
100#1386—111no—
101#1375—111no—
102C23×C11AGL(1,ℤ/8)11yescharacteristic
103Q8×C11—24no—
104Q8×C11—42no—
105Q8×C11—42no—
106Q8×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11C4×D411yescharacteristic
112C2×C4×C11#12011yescharacteristic
113C2×C4×C11C22⋊Q811yescharacteristic
114C2×C4×C11C2×SD1611yescharacteristic
115C2×C4×C11#13511yescharacteristic
116C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
117C2×Dic11—22no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—82no—
121C8×C11C2×C4⋊C411yescharacteristic
122C8×C11C4×D411yescharacteristic
123C8×C11C22⋊Q811yescharacteristic
124C8×C11#12311yescharacteristic
125C11⋊C8—41no—
126C11⋊C8—81no—
127C22×Q16C2×D1111yescharacteristic
128C2×C4×Q8—221no—
129C2×M32—111no—
130C2×M32C2×D1111yescharacteristic
131#441—222no—
132#441—222no—
133C2×#108—111no—
134#427C2×D1111yescharacteristic
135C2×#106—111no—
136#424—221no—
137C2×#103—221no—
138C2×#97—111no—
139#365—222no—
140#362—222no—
141#358Dic1114yescomplemented
142#339—221no—
143C22×C11—22no—
144C22×C11#44211yescharacteristic
145C22×C11#45011yescharacteristic
146C22×C11#47811yescharacteristic
147C4×C11—44no—
148C4×C11—82no—
149C4×C11#38511yescharacteristic
150C4×C11C4×SD1611yescharacteristic
151C4×C11#44911yescharacteristic
152C4×C11#47611yescharacteristic
153Dic11—42no—
154Dic11—82no—
155C22×Q8—21no—
156C2×Q16—21no—
157C2×Q16—21no—
158C2×Q16—21no—
159C2×Q16Dic2212yes—
160C2×Q16D4412yes—
161C2×Q16C2×Dic1112yes—
162C2×M16—221no—
163C22×C8—111no—
164C22×C8C22×D1111yescharacteristic
165C4×Q8—224no—
166C4×Q8—442no—
167#117—21no—
168C2×C4⋊C4—221no—
169C2×C4⋊C4—441no—
170C2×C42—111no—
171C2×C42—441no—
172M32—21no—
173M32—21no—
174M32—221no—
175M32—221no—
176C2×C16—221no—
177C2×C16C2×Dic1112yes—
178#108—221no—
179#108—221no—
180#107C2×Dic1112yes—
181#106—21no—
182#106—112no—
183#106—221no—
184C4⋊C8—442no—
185#103—224no—
186#97—221no—
187#97—221no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11#186411yescharacteristic
191C2×C11#218012yes—
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×Q8—41no—
198C22×C4—41no—
199C22×C4—221no—
200C22×C4—441no—
201C22×C4D4×D1111yescharacteristic
202Q16—22no—
203Q16—22no—
204Q16—22no—
205Q16C4⋊Dic1114yes—
206M16—441no—
207M16—441no—
208C2×C8—221no—
209C2×C8—221no—
210C2×C8—221no—
211C2×C8—441no—
212C2×C8C2×Dic2211yescharacteristic
213C2×C8C2×D4411yescharacteristic
214C2×C8D4×D1111yescharacteristic
215C2×C8#434111yescharacteristic
216C2×C8#434111yescharacteristic
217C2×C8C22×Dic1111yescharacteristic
218C4⋊C4—22no—
219C4⋊C4—222no—
220C4⋊C4—444no—
221C4⋊C4—441no—
222C22⋊C4—41no—
223C42—41no—
224C42—112no—
225C42—221no—
226C42—444no—
227C16—22no—
228C16—441no—
229C11#1295711yescharacteristic, complemented, Sylow
230C23#6696411yescharacteristic
231Q8—24no—
232Q8—42no—
233Q8—42no—
234Q8—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—222no—
240C2×C4—442no—
241C2×C4—442no—
242C2×C4—882no—
243C2×C4#6693111yescharacteristic
244C2×C4#6693511yescharacteristic
245C2×C4#6696411yescharacteristic
246C2×C4SD16×D1111yescharacteristic
247C2×C4#6696911yescharacteristic
248C2×C4D4×Dic1111yescharacteristic
249C8—441no—
250C8—881no—
251C8#6693111yescharacteristic
252C8#6693911yescharacteristic
253C8C2×C4⋊Dic1111yescharacteristic
254C8D4×Dic1111yescharacteristic
255C22—22no—
256C22#1062237611yescharacteristic
257C22#1062238911yescharacteristic
258C22#1062276511yescharacteristic
259C4—44no—
260C4—82no—
261C4—442no—
262C4—882no—
263C4#1062237411yescharacteristic
264C4#1062239411yescharacteristic
265C4#1062256311yescharacteristic
266C4SD16×Dic1111yescharacteristic
267C2—21no—
268C2—21no—
269C2#1306887911yescharacteristic
270C2#1307050812yes—
subgroupG/H
centerC22#10622765
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#2141C2
socleC22×C11#442
prime radicalC23×C11AGL(1,ℤ/8)
cosocleC22×C8×C11C23
hypercenter#2141D11
hypocenterC11#12957
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2141

Complements

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

NH ≅ G/Ntype
20. C11×#358C4semidirect
141. #358Dic11semidirect
229. C11#12957semidirect

Maximal subgroups

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

subgroupindex
C2×#106227972
C2×#106221512
C2×#106222032
#130693702
#130667212
#130666952
C11×#21412
#1295711