Finite Group Databasebeta

← #14647635

Subgroups — #14647635

Order 2816.

482 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 143 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
1#13069411C211yesmaximal, characteristic
2C4×#66897C211yesmaximal, characteristic
3#13067369C212yesmaximal, complemented
4#13066452C212yesmaximal, complemented
5C11×#2972C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C8×D4×C11—22no—
8C8×D4×C11—22no—
9C11×#431C2212yes—
10C2×C11×C22⋊C8—22no—
11C2×#66897C411yescharacteristic
12C2×#66897C411yescharacteristic
13C2×C22⋊(C11⋊C8)—22no—
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C4×#4318C2212yes—
16C2×C4×C11⋊C8C2211yescharacteristic
17#10622168C412yes—
18#10622118—22no—
19#10622117—22no—
20C22×D4×C11C2×C411yescharacteristic
21C23×C4×C11D412yes—
22C22×C8×C11—22no—
23C22×C8×C11—22no—
24C4×D4×C11—22no—
25C4×D4×C11—22no—
26C2×C11×C4⋊C4C2×C411yescharacteristic
27C2×C11×C22⋊C4Q812yes—
28C2×C42×C11C2311yescharacteristic
29C2×#4318C2×C412yes—
30C2×#4318C2×C412yes—
31C22×C11⋊C8—21no—
32C22×C11⋊C8—21no—
33C11×C4⋊C8D412yes—
34C11×C4⋊C8D412yes—
35C11×C22⋊C8—24no—
36C11×C22⋊C8—22no—
37C4×C8×C11—22no—
38#66897—22no—
39#66897C814yescomplemented
40C22⋊(C11⋊C8)—44no—
41C4⋊(C11⋊C8)—22no—
42#66867—22no—
43C4×C11⋊C8—22no—
44C4×C11⋊C8—22no—
45#8835—111nomaximal, Sylow
46C24×C11C4⋊C412yes—
47C2×D4×C11—22no—
48C2×D4×C11—22no—
49C2×D4×C11C2×C812yes—
50C2×D4×C11M1612yes—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—42no—
54C22×C4×C11—42no—
55C22×C4×C11C4⋊C412yes—
56C22×C4×C11C22×C411yescharacteristic
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×Q811yescharacteristic
59C2×C8×C11—22no—
60C2×C8×C11—22no—
61C2×C8×C11—82no—
62C2×C8×C11—82no—
63C11×C4⋊C4—22no—
64C11×C22⋊C4—24no—
65C42×C11C2×D412yes—
66C42×C11#4112yes—
67#4318—22no—
68#4318—22no—
69#4318—22no—
70#4318C2×C814yescomplemented
71C2×C11⋊C8—22no—
72C2×C11⋊C8—22no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8—41no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—41no—
77C2×C11⋊C8—41no—
78#2972D1111yescharacteristic
79#1954—111no—
80C4×#100—111no—
81#1565—112no—
82#1278—112no—
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—42no—
86C23×C11—42no—
87C23×C11C4⋊C814yes—
88C23×C11C2×C4⋊C411yescharacteristic
89D4×C11—24no—
90D4×C11—24no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—41no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—82no—
99C2×C4×C11C4×D412yes—
100C2×C4×C11#12011yescharacteristic
101C2×C4×C11C22⋊Q812yes—
102C2×C4×C11#12311yescharacteristic
103C2×C4×C11C22×C811yescharacteristic
104C2×C4×C11C2×M1611yescharacteristic
105C2×C4×C11#13112yes—
106C8×C11—42no—
107C8×C11—42no—
108C11⋊C8—24no—
109C11⋊C8—42no—
110C11⋊C8—42no—
111C11⋊C8—81no—
112C2×C4×D4C2×D1111yescharacteristic
113C8×D4—22no—
114C8×D4—22no—
115#431C2×D1112yes—
116C2×C4⋊C8—111no—
117C2×#100—111no—
118C2×#100—111no—
119C2×C22⋊C8—22no—
120C2×C22⋊C8—222no—
121C4×M16—112no—
122C2×C4×C8—111no—
123#343—112no—
124#335—222no—
125#334—222no—
126C22×C11—21no—
127C22×C11—21no—
128C22×C11—24no—
129C22×C11—44no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11—82no—
133C22×C11#38511yescharacteristic
134C22×C11C2×C4⋊C811yescharacteristic
135C22×C11#42411yescharacteristic
136C4×C11—21no—
137C4×C11—22no—
138C4×C11—42no—
139C4×C11C8×D412yes—
140C4×C11#43512yes—
141C4×C11#45311yescharacteristic
142C4×C11#45511yescharacteristic
143C22×D4C4×D1111yescharacteristic
144C23×C4C22⋊D1112yes—
145C2×M16—112no—
146C2×M16—112no—
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—221no—
150C22×C8—221no—
151C4×D4—22no—
152C4×D4—22no—
153C2×C4⋊C4C4×D1111yescharacteristic
154C2×C22⋊C4Dic2212yes—
155C2×C42C22×D1111yescharacteristic
156C4⋊C8—222no—
157C4⋊C8C22⋊D1112yes—
158C4⋊C8C22⋊D1112yes—
159#100—114no—
160#100—222no—
161C22⋊C8—24no—
162C22⋊C8—22no—
163C22⋊C8—444no—
164#97—222no—
165C4×C8—22no—
166C4×C8—222no—
167C4×C8—222no—
168C2×C11—21no—
169C2×C11—21no—
170C2×C11—44no—
171C2×C11#185011yescharacteristic
172C2×C11#185611yescharacteristic
173C2×C11#185811yescharacteristic
174C24Dic11⋊C412yes—
175C2×D4—22no—
176C2×D4—22no—
177C2×D4C8×D1112yes—
178C2×D4#431312yes—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—42no—
182C22×C4—42no—
183C22×C4Dic11⋊C412yes—
184C22×C4C2×Dic2211yescharacteristic
185C22×C4C2×C4×D1111yescharacteristic
186C22×C4C2×C22⋊D1111yescharacteristic
187M16—114no—
188M16—222no—
189M16—222no—
190M16—222no—
191C2×C8—22no—
192C2×C8—22no—
193C2×C8—82no—
194C2×C8—82no—
195C2×C8—222no—
196C2×C8—222no—
197C2×C8—222no—
198C2×C8—441no—
199C2×C8—441no—
200C2×C8—442no—
201C2×C8—441no—
202C4⋊C4—22no—
203C22⋊C4—24no—
204C42#433912yes—
205C42C2×C22⋊D1112yes—
206C11#883511yescharacteristic, complemented, Sylow
207C23—22no—
208C23—22no—
209C23—42no—
210C23—42no—
211C23Dic11⋊C814yes—
212C23C2×Dic11⋊C411yescharacteristic
213D4—24no—
214D4—24no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—82no—
223C2×C4C2×C8×D1111yescharacteristic
224C2×C4C2×#431311yescharacteristic
225C2×C4#6695412yes—
226C2×C4#6697712yes—
227C2×C4C4×C22⋊D1112yes—
228C2×C4#6698211yescharacteristic
229C2×C4#6700611yescharacteristic
230C8—42no—
231C8—42no—
232C8—224no—
233C8—442no—
234C8—442no—
235C8—881no—
236C22—21no—
237C22—21no—
238C22—24no—
239C22—44no—
240C22—42no—
241C22—42no—
242C22—82no—
243C22C2×Dic11⋊C811yescharacteristic
244C22#1062271511yescharacteristic
245C22#1062282311yescharacteristic
246C4—21no—
247C4—22no—
248C4—42no—
249C4C8×C22⋊D1112yes—
250C4#1062272412yes—
251C4#1062285411yescharacteristic
252C4#1062285511yescharacteristic
253C2—21no—
254C2—21no—
255C2—44no—
256C2#1306879411yescharacteristic
257C2#1306882611yescharacteristic
258C2#1306883611yescharacteristic
subgroupG/H
centerC2×C4#67006
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC11×#2972C2
socleC22×C11#385
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#2972D11
hypocenterC11#8835
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2972

Complements

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

NH ≅ G/Ntype
3. #13067369C2semidirect
4. #13066452C2semidirect
39. #66897C8semidirect
70. #4318C2×C8semidirect
206. C11#8835semidirect

Maximal subgroups

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

subgroupindex
#130694112
C4×#668972
#130673692
#130664522
C11×#29722
#883511