Finite Group Databasebeta

← #14670522

Subgroups — #14670522

Order 2816.

396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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×#10622329C211yesmaximal, characteristic
2C2×#10622151C211yesmaximal, characteristic
3C2×#10622155C211yesmaximal, characteristic
4#13070337C211yesmaximal, characteristic
5#13069369C211yesmaximal, characteristic
6#13066722C211yesmaximal, characteristic
7C11×#1375C211yesmaximal, characteristic
8C22×Dic44C2211yescharacteristic
9C2×C4×Dic22—21no—
10C2×C11×M32C2211yescharacteristic
11C2×C11×M32C2211yescharacteristic
12C2×C11×#97C2211yescharacteristic
13C2×#66883C2211yescharacteristic
14#10622719C2211yescharacteristic
15C2×#66881C2211yescharacteristic
16C2×#66880—21no—
17#10622715—21no—
18#10622329—22no—
19#10622329—22no—
20#10622161—21no—
21#10622155—22no—
22#10622151—22no—
23#10622141C414yescomplemented
24C22×Dic22—21no—
25C22×C8×C11D411yescharacteristic
26C22×C8×C11C2311yescharacteristic
27C2×C42×C11D411yescharacteristic
28#66979—21no—
29C2×C4⋊Dic11—21no—
30C2×Dic11⋊C4—41no—
31C2×C4×Dic11—41no—
32C2×#4318—21no—
33C2×Dic44—21no—
34C2×Dic44—21no—
35C2×Dic44—21no—
36C2×Dic44C2×C412yes—
37C2×Dic44D412yes—
38C2×Dic44Q812yes—
39C4×Dic22—24no—
40C4×Dic22—42no—
41C11×M32—21no—
42C11×M32—21no—
43C11×M32—21no—
44C11×M32—21no—
45C2×C11×C16—21no—
46C2×C11×C16C2×C412yes—
47C11×#97—21no—
48C11×#97—21no—
49#66883—21no—
50#66883—21no—
51#66882C2×C412yes—
52#66881—21no—
53#66881—21no—
54#66881D412yes—
55#66880—24no—
56Dic11⋊C8—42no—
57#12957—111nomaximal, Sylow
58C22×C4×C11—21no—
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—41no—
61C22×Dic11—41no—
62C2×Dic22—22no—
63C2×Dic22—22no—
64C2×Dic22—22no—
65C2×Dic22—41no—
66C2×Dic22—41no—
67C2×Dic22—41no—
68C2×C8×C11—21no—
69C2×C8×C11—21no—
70C2×C8×C11—21no—
71C2×C8×C11C22×C411yescharacteristic
72C2×C8×C11C2×D411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C2×C8×C11C2×Q811yescharacteristic
75C2×C8×C11#4111yescharacteristic
76C2×C8×C11#4111yescharacteristic
77C42×C11—21no—
78C42×C11SD1612yes—
79C22⋊Dic11—41no—
80C4⋊Dic11—22no—
81C4⋊Dic11—22no—
82C4⋊Dic11—41no—
83Dic11⋊C4—44no—
84C4×Dic11—44no—
85C4×Dic11—41no—
86#4318—41no—
87#4318—41no—
88C2×C11⋊C8—41no—
89Dic44—22no—
90Dic44—22no—
91Dic44—22no—
92Dic44C4⋊C414yes—
93C11×C16—22no—
94C11×C16—41no—
95C2×#441—111no—
96C2×#365—111no—
97C2×#362—111no—
98#2141—111no—
99#1946—111no—
100#1386—111no—
101#1375D1111yescharacteristic
102C23×C11AGL(1,ℤ/8)11yescharacteristic
103C2×C4×C11—22no—
104C2×C4×C11—42no—
105C2×C4×C11C4×D411yescharacteristic
106C2×C4×C11#12011yescharacteristic
107C2×C4×C11C22⋊Q811yescharacteristic
108C2×C4×C11C2×SD1611yescharacteristic
109C2×C4×C11#13511yescharacteristic
110C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116C2×Dic11—82no—
117Dic22—24no—
118Dic22—42no—
119Dic22—42no—
120Dic22—42no—
121C8×C11—41no—
122C8×C11C2×C4⋊C411yescharacteristic
123C8×C11C4×D411yescharacteristic
124C8×C11C22⋊Q811yescharacteristic
125C8×C11#12311yescharacteristic
126C11⋊C8—81no—
127C22×Q16—111no—
128C2×C4×Q8—221no—
129C2×M32C2×D1111yescharacteristic
130C2×M32C2×D1111yescharacteristic
131#441—222no—
132#441—222no—
133C2×#108—111no—
134#427—111no—
135C2×#106—111no—
136#424—221no—
137C2×#103—221no—
138C2×#97C2×D1111yescharacteristic
139#365—222no—
140#362—222no—
141#358—114no—
142#339—221no—
143C22×C11—22no—
144C22×C11#44211yescharacteristic
145C22×C11#45011yescharacteristic
146C22×C11#47811yescharacteristic
147C4×C11—42no—
148C4×C11#38511yescharacteristic
149C4×C11C4×SD1611yescharacteristic
150C4×C11#44911yescharacteristic
151C4×C11#47611yescharacteristic
152Dic11—44no—
153Dic11—82no—
154Dic11—82no—
155C22×Q8—221no—
156C2×Q16—112no—
157C2×Q16—112no—
158C2×Q16—112no—
159C2×Q16—221no—
160C2×Q16—221no—
161C2×Q16—221no—
162C2×M16—221no—
163C22×C8D4411yescharacteristic
164C22×C8C22×D1111yescharacteristic
165C4×Q8—224no—
166C4×Q8—442no—
167#117—221no—
168C2×C4⋊C4—221no—
169C2×C4⋊C4—441no—
170C2×C42—441no—
171C2×C42D4411yescharacteristic
172M32—21no—
173M32—21no—
174M32—21no—
175M32—21no—
176C2×C16—21no—
177C2×C16C4×D1112yes—
178#108—221no—
179#108—221no—
180#107—112no—
181#106—112no—
182#106—221no—
183#106—221no—
184C4⋊C8—442no—
185#103—224no—
186#97—21no—
187#97—21no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11#186411yescharacteristic
191C2×C11#218012yes—
192C2×Q8—222no—
193C2×Q8—222no—
194C2×Q8—222no—
195C2×Q8—441no—
196C2×Q8—441no—
197C2×Q8—441no—
198C22×C4—21no—
199C22×C4—441no—
200C22×C4—441no—
201C22×C4C2×D4411yescharacteristic
202Q16—114no—
203Q16—222no—
204Q16—222no—
205Q16—222no—
206M16—441no—
207M16—441no—
208C2×C8—21no—
209C2×C8—21no—
210C2×C8—21no—
211C2×C8—441no—
212C2×C8C2×C4×D1111yescharacteristic
213C2×C8#433911yescharacteristic
214C2×C8D4×D1111yescharacteristic
215C2×C8D4×D1111yescharacteristic
216C2×C8#434111yescharacteristic
217C2×C8Q8×D1111yescharacteristic
218C4⋊C4—222no—
219C4⋊C4—222no—
220C4⋊C4—444no—
221C4⋊C4—441no—
222C22⋊C4—441no—
223C42—21no—
224C42—444no—
225C42—441no—
226C42#431412yes—
227C16—22no—
228C16—41no—
229C11#1295711yescharacteristic, complemented, Sylow
230C23#6696111yescharacteristic
231Q8—224no—
232Q8—442no—
233Q8—442no—
234Q8—442no—
235C2×C4—22no—
236C2×C4—42no—
237C2×C4—442no—
238C2×C4—442no—
239C2×C4—442no—
240C2×C4—442no—
241C2×C4—442no—
242C2×C4—882no—
243C2×C4C4×D4411yescharacteristic
244C2×C4#6693511yescharacteristic
245C2×C4#6695011yescharacteristic
246C2×C4C2×#431411yescharacteristic
247C2×C4#6695711yescharacteristic
248C2×C4#6696111yescharacteristic
249C8—41no—
250C8—881no—
251C8(C22⋊D11)⋊C411yescharacteristic
252C8#6693611yescharacteristic
253C8C4⋊C4×D1111yescharacteristic
254C8#6694911yescharacteristic
255C22—22no—
256C22#1062232411yescharacteristic
257C22#1062234411yescharacteristic
258C22#1062246011yescharacteristic
259C4—42no—
260C4—444no—
261C4—882no—
262C4—882no—
263C4#1062228111yescharacteristic
264C4C4×#431411yescharacteristic
265C4#1062234711yescharacteristic
266C4#1062245511yescharacteristic
267C2—21no—
268C2—21no—
269C2#1306888011yescharacteristic
270C2#1307050912yes—
subgroupG/H
centerC22#10622324
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1375C2
socleC22×C11#442
prime radicalC23×C11AGL(1,ℤ/8)
cosocleC22×C8×C11C23
hypercenter#1375D11
hypocenterC11#12957
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #1375

Complements

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

NH ≅ G/Ntype
23. #10622141C4semidirect
229. C11#12957semidirect

Maximal subgroups

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

subgroupindex
C2×#106223292
C2×#106221512
C2×#106221552
#130703372
#130693692
#130667222
C11×#13752
#1295711