Finite Group Databasebeta

← #14658798

Subgroups — #14658798

Order 2816.

296 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 91 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#13069598C211yesmaximal, characteristic
2#13068735C211yesmaximal, characteristic
3#13067390C211yesmaximal, characteristic
4#13067387C211yesmaximal, characteristic
5#13067019C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic
7C11×#1481C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11#10622545C2211yescharacteristic
12#10622538C2211yescharacteristic
13#10622537C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C11×Q8⋊C8—22no—
16#10622188—22no—
17Q8⋊(C11⋊C8)—22no—
18#10622170—22no—
19#10622117—22no—
20#10622095—22no—
21C22×C8×C11—21no—
22C11×C4⋊Q8Q811yescharacteristic
23C11×C4⋊Q8Q811yescharacteristic
24C11×#125—21no—
25C11×C22⋊Q8—21no—
26C11×C22⋊Q8—21no—
27C4×Q8×C11—21no—
28C4×Q8×C11—21no—
29C11×#117—21no—
30C2×C42×C11C2311yescharacteristic
31C2×C4×Dic11D412yes—
32C2×#4318—21no—
33C22×C11⋊C8—21no—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C4⋊C8—21no—
37C11×C22⋊C8—21no—
38C4×C8×C11D412yes—
39C11⋊#95—21no—
40C11⋊#95—21no—
41C22⋊(C11⋊C8)—21no—
42C4⋊(C11⋊C8)—21no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47C4×C11⋊C8D412yes—
48#10669—111nomaximal, Sylow
49C2×Q8×C11—21no—
50C2×Q8×C11—21no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11#4111yescharacteristic
53C22×C4×C11#4111yescharacteristic
54C22×Dic11—22no—
55C2×C8×C11—22no—
56C2×C8×C11—41no—
57C2×C8×C11—42no—
58C11×C4⋊C4—21no—
59C11×C4⋊C4—21no—
60C11×C4⋊C4—21no—
61C11×C4⋊C4—21no—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—41no—
64C11×C22⋊C4—41no—
65C42×C11—41no—
66C42×C11C2×D411yescharacteristic
67C42×C11C2×D411yescharacteristic
68C42×C11C2×Q811yescharacteristic
69C42×C11#4111yescharacteristic
70C4×Dic11—22no—
71C4×Dic11—22no—
72#4318—42no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8—41no—
75C2×C11⋊C8—41no—
76C2×C11⋊C8—42no—
77#1995—111no—
78#1832—111no—
79#1571—111no—
80#1570—111no—
81#1481—111no—
82#1481D1111yescharacteristic
83#1274—111no—
84C23×C11#12311yescharacteristic
85Q8×C11—42no—
86Q8×C11—42no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11C22⋊Q811yescharacteristic
92C2×C4×C11C22⋊Q811yescharacteristic
93C2×C4×C11C22⋊Q811yescharacteristic
94C2×C4×C11#12311yescharacteristic
95C2×C4×C11#12311yescharacteristic
96C2×C4×C11#12711yescharacteristic
97C2×C4×C11#13512yes—
98C2×C4×C11#13712yes—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C8×C11—42no—
103C8×C11—81no—
104C11⋊C8—42no—
105C11⋊C8—81no—
106C11⋊C8—81no—
107#533C2×D1111yescharacteristic
108#431—111no—
109#431C2×D1111yescharacteristic
110#423—111no—
111C2×C4⋊C8—111no—
112C2×C4⋊C8C2×D1111yescharacteristic
113#376—111no—
114#339—222no—
115#336—222no—
116#335—222no—
117#334—222no—
118Q8⋊C8—22no—
119Q8⋊C8—222no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11#39911yescharacteristic
123C22×C11#48512yes—
124C4×C11—21no—
125C4×C11—21no—
126C4×C11—21no—
127C4×C11—21no—
128C4×C11—81no—
129C4×C11—81no—
130C4×C11#47912yes—
131C4×C11#49511yescharacteristic
132C4×C11#49711yescharacteristic
133Dic11—82no—
134C2×M16—221no—
135C22×C8—21no—
136C22×C8—221no—
137C4⋊Q8Dic2211yescharacteristic
138C4⋊Q8Dic2211yescharacteristic
139#125—21no—
140C22⋊Q8—21no—
141C22⋊Q8—21no—
142C4×Q8—21no—
143C4×Q8—21no—
144#117—21no—
145C2×C42—112no—
146C2×C42C22×D1111yescharacteristic
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—21no—
150C4⋊C8—221no—
151C4⋊C8—221no—
152C4⋊C8—221no—
153C4⋊C8—221no—
154C4⋊C8—221no—
155C22⋊C8—21no—
156C22⋊C8—221no—
157C4×C8—112no—
158C4×C8C22⋊D1112yes—
159#95—221no—
160#95—221no—
161C2×C11—22no—
162C2×C11#209711yescharacteristic
163C2×C11#209811yescharacteristic
164C2×C11#209811yescharacteristic
165C2×Q8—21no—
166C2×Q8—21no—
167C22×C4—222no—
168C22×C4#433911yescharacteristic
169C22×C4D4×D1111yescharacteristic
170C22×C4#434111yescharacteristic
171M16—442no—
172C2×C8—22no—
173C2×C8—42no—
174C2×C8—41no—
175C2×C8—222no—
176C2×C8—442no—
177C2×C8—441no—
178C2×C8—441no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C22⋊C4—41no—
186C42—41no—
187C42—222no—
188C42—222no—
189C42C2×Dic2211yescharacteristic
190C42D4×D1111yescharacteristic
191C42#434111yescharacteristic
192C42C2×C22⋊D1111yescharacteristic
193C11#1066911yescharacteristic, complemented, Sylow
194C23#6693611yescharacteristic
195Q8—42no—
196Q8—42no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—442no—
202C2×C4—442no—
203C2×C4—442no—
204C2×C4#6693111yescharacteristic
205C2×C4#6693111yescharacteristic
206C2×C4#6693611yescharacteristic
207C2×C4#6696912yes—
208C2×C4#6697112yes—
209C2×C4#6697711yescharacteristic
210C2×C4#6698811yescharacteristic
211C2×C4#6699311yescharacteristic
212C8—42no—
213C8—81no—
214C8—442no—
215C8—881no—
216C8—881no—
217C22—21no—
218C22—21no—
219C22#1062242812yes—
220C22#1062256211yescharacteristic
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—81no—
226C4—81no—
227C4—882no—
228C4#1062241212yes—
229C4#1062278111yescharacteristic
230C4#1062280311yescharacteristic
231C2—22no—
232C2#1307016611yescharacteristic
233C2#1307016911yescharacteristic
234C2#1307017111yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1481C2
socleC22×C11#399
prime radicalC23×C11#123
hypercenter#1481D11
hypocenterC11#10669
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
193. C11#10669semidirect

Maximal subgroups

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

subgroupindex
#130695982
#130687352
#130673902
#130673872
#130670192
#130664442
C11×#14812
#1066911