Finite Group Databasebeta

← #14658793

Subgroups — #14658793

Order 2816.

316 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 95 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#13068769C211yesmaximal, characteristic
3#13067391C211yesmaximal, characteristic
4#13067390C211yesmaximal, characteristic
5#13067019C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic
7C11×#1481C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×Dic11⋊C8—22no—
12#10622545C2211yescharacteristic
13#10622538C2211yescharacteristic
14#10622537C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C11×Q8⋊C8—22no—
17Q8⋊(C11⋊C8)—22no—
18#10622170—22no—
19#10622117—22no—
20#10622096—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—
42Dic11⋊C8—44no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4×C11⋊C8D412yes—
49#10668—111nomaximal, Sylow
50C2×Q8×C11—21no—
51C2×Q8×C11—21no—
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11#4111yescharacteristic
54C22×C4×C11#4111yescharacteristic
55C22×Dic11—22no—
56C2×C8×C11—22no—
57C2×C8×C11—41no—
58C2×C8×C11—42no—
59C11×C4⋊C4—21no—
60C11×C4⋊C4—21no—
61C11×C4⋊C4—21no—
62C11×C4⋊C4—21no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C11×C22⋊C4—41no—
66C42×C11—41no—
67C42×C11C2×D411yescharacteristic
68C42×C11C2×D411yescharacteristic
69C42×C11C2×Q811yescharacteristic
70C42×C11#4111yescharacteristic
71C4×Dic11—22no—
72C4×Dic11Q1614yes—
73#4318—42no—
74C2×C11⋊C8—22no—
75C2×C11⋊C8—41no—
76C2×C11⋊C8—41no—
77C2×C11⋊C8—42no—
78#1995—111no—
79#1843—111no—
80#1571—111no—
81#1571—111no—
82#1481—111no—
83#1481D1111yescharacteristic
84#1274—111no—
85C23×C11#12311yescharacteristic
86Q8×C11—42no—
87Q8×C11—42no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11—41no—
92C2×C4×C11C22⋊Q811yescharacteristic
93C2×C4×C11C22⋊Q811yescharacteristic
94C2×C4×C11C22⋊Q811yescharacteristic
95C2×C4×C11#12311yescharacteristic
96C2×C4×C11#12311yescharacteristic
97C2×C4×C11#12711yescharacteristic
98C2×C4×C11C2×Q1612yes—
99C2×C4×C11AGL(1,ℤ/8)12yes—
100C2×Dic11—24no—
101C2×Dic11—42no—
102C2×Dic11—42no—
103C8×C11—42no—
104C8×C11—81no—
105C11⋊C8—42no—
106C11⋊C8—81no—
107C11⋊C8—81no—
108#533C2×D1111yescharacteristic
109#431—111no—
110#431C2×D1111yescharacteristic
111#423—111no—
112C2×C4⋊C8—111no—
113C2×C4⋊C8—222no—
114C2×C4⋊C8C2×D1111yescharacteristic
115#376—111no—
116#339—222no—
117#335—222no—
118#335—222no—
119Q8⋊C8—22no—
120Q8⋊C8—222no—
121C22×C11—21no—
122C22×C11—21no—
123C22×C11#39911yescharacteristic
124C22×C11#48412yes—
125C4×C11—21no—
126C4×C11—21no—
127C4×C11—21no—
128C4×C11—21no—
129C4×C11—81no—
130C4×C11—81no—
131C4×C11#47712yes—
132C4×C11#49411yescharacteristic
133C4×C11#49611yescharacteristic
134Dic11—44no—
135C2×M16—221no—
136C22×C8—21no—
137C22×C8—221no—
138C4⋊Q8Dic2211yescharacteristic
139C4⋊Q8Dic2211yescharacteristic
140#125—21no—
141C22⋊Q8—21no—
142C22⋊Q8—21no—
143C4×Q8—21no—
144C4×Q8—21no—
145#117—21no—
146C2×C42—112no—
147C2×C42C22×D1111yescharacteristic
148C4⋊C8—21no—
149C4⋊C8—21no—
150C4⋊C8—21no—
151C4⋊C8—221no—
152C4⋊C8—221no—
153C4⋊C8—221no—
154C4⋊C8—221no—
155C4⋊C8—221no—
156C4⋊C8—444no—
157C22⋊C8—21no—
158C22⋊C8—221no—
159C4×C8—112no—
160C4×C8C22⋊D1112yes—
161#95—221no—
162#95—221no—
163C2×C11—22no—
164C2×C11#209511yescharacteristic
165C2×C11#209811yescharacteristic
166C2×C11#209811yescharacteristic
167C2×Q8—21no—
168C2×Q8—21no—
169C22×C4—222no—
170C22×C4#433911yescharacteristic
171C22×C4D4×D1111yescharacteristic
172C22×C4#434111yescharacteristic
173M16—442no—
174C2×C8—22no—
175C2×C8—42no—
176C2×C8—41no—
177C2×C8—222no—
178C2×C8—442no—
179C2×C8—441no—
180C2×C8—441no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—21no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C22⋊C4—41no—
188C42—41no—
189C42—114no—
190C42—222no—
191C42C2×Dic2211yescharacteristic
192C42D4×D1111yescharacteristic
193C42#434111yescharacteristic
194C42C2×C22⋊D1111yescharacteristic
195C11#1066811yescharacteristic, complemented, Sylow
196C23#6693611yescharacteristic
197Q8—42no—
198Q8—42no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—224no—
204C2×C4—442no—
205C2×C4—442no—
206C2×C4#6693111yescharacteristic
207C2×C4#6693111yescharacteristic
208C2×C4#6693611yescharacteristic
209C2×C4#6696712yes—
210C2×C4Q16×D1112yes—
211C2×C4#6697711yescharacteristic
212C2×C4#6698811yescharacteristic
213C2×C4#6699311yescharacteristic
214C8—42no—
215C8—81no—
216C8—442no—
217C8—881no—
218C8—881no—
219C22—21no—
220C22—21no—
221C22#1062242212yes—
222C22#1062256211yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—81no—
228C4—81no—
229C4—444no—
230C4#1062240712yes—
231C4#1062278911yescharacteristic
232C4#1062279411yescharacteristic
233C2—22no—
234C2#1307015211yescharacteristic
235C2#1307016911yescharacteristic
236C2#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#10668
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
195. C11#10668semidirect

Maximal subgroups

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

subgroupindex
#130695982
#130687692
#130673912
#130673902
#130670192
#130664442
C11×#14812
#1066811