Finite Group Databasebeta

← #14658768

Subgroups — #14658768

Order 2816.

304 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 89 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#13069555C211yesmaximal, characteristic
2#13068756C211yesmaximal, characteristic
3#13067386C211yesmaximal, characteristic
4#13067046C211yesmaximal, characteristic
5#13067044C211yesmaximal, characteristic
6#13066446C211yesmaximal, characteristic
7C11×#1571C211yesmaximal, characteristic
8C2×C4×Dic22C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12#10622538C2211yescharacteristic
13#10622537C2211yescharacteristic
14C2×#66867C2211yescharacteristic
15C11×#335—22no—
16#10622196—22no—
17#10622188—22no—
18#10622122—22no—
19#10622118—22no—
20#10622094—22no—
21C22×Dic22Q811yescharacteristic
22C2×C11×M16—21no—
23C22×C8×C11—21no—
24C2×C42×C11C2311yescharacteristic
25C2×C4⋊Dic11Q811yescharacteristic
26C2×Dic11⋊C4—21no—
27C2×C4×Dic11—21no—
28C2×#4318—21no—
29C22×C11⋊C8D412yes—
30C4×Dic22—21no—
31C4×Dic22—21no—
32C4×Dic22—21no—
33C4×Dic22—21no—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C4⋊C8—21no—
37C11×C4⋊C8—21no—
38C11×C4⋊C8—21no—
39C11×C22⋊C8—21no—
40C4×C8×C11D412yes—
41C22⋊(C11⋊C8)—21no—
42C4⋊(C11⋊C8)—21no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45#66867—21no—
46#66867—21no—
47C4×C11⋊C8D412yes—
48#10664—111nomaximal, Sylow
49C22×C4×C11C2×D411yescharacteristic
50C22×C4×C11C2×Q811yescharacteristic
51C22×C4×C11#4111yescharacteristic
52C22×Dic11—21no—
53C22×Dic11—21no—
54C2×Dic22—21no—
55C2×Dic22—21no—
56C2×Dic22—42no—
57C11×M16—42no—
58C2×C8×C11—22no—
59C2×C8×C11—41no—
60C2×C8×C11—41no—
61C2×C8×C11—42no—
62C42×C11C2×D411yescharacteristic
63C42×C11C2×D411yescharacteristic
64C42×C11#4111yescharacteristic
65C42×C11#4111yescharacteristic
66C4⋊Dic11—21no—
67C4⋊Dic11—21no—
68Dic11⋊C4—41no—
69Dic11⋊C4—41no—
70C4×Dic11—41no—
71C4×Dic11—41no—
72#4318—42no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8—22no—
75C2×C11⋊C8—22no—
76C2×C11⋊C8—22no—
77C2×C11⋊C8—41no—
78#1985—111no—
79#1838—111no—
80#1571D1111yescharacteristic
81#1570—111no—
82#1487—111no—
83#1487—111no—
84#1275—111no—
85C23×C11C22⋊Q811yescharacteristic
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11C22⋊Q811yescharacteristic
89C2×C4×C11C22⋊Q811yescharacteristic
90C2×C4×C11#12311yescharacteristic
91C2×C4×C11#12311yescharacteristic
92C2×C4×C11#12311yescharacteristic
93C2×C4×C11#12711yescharacteristic
94C2×C4×C11#13512yes—
95C2×C4×C11#13712yes—
96C2×Dic11—22no—
97C2×Dic11—41no—
98C2×Dic11—41no—
99C2×Dic11—42no—
100C2×Dic11—41no—
101Dic22—22no—
102Dic22—22no—
103Dic22—41no—
104Dic22—41no—
105C8×C11—42no—
106C8×C11—81no—
107C8×C11—81no—
108C11⋊C8—42no—
109C11⋊C8—42no—
110C11⋊C8—81no—
111C2×C4×Q8—111no—
112#431—111no—
113#431C2×D1111yescharacteristic
114#423—111no—
115#423C2×D1111yescharacteristic
116C2×C4⋊C8C2×D1111yescharacteristic
117C2×#97—111no—
118#341—222no—
119#336—222no—
120#335—22no—
121#334—222no—
122Q8⋊C8—222no—
123Q8⋊C8—222no—
124C22×C11—21no—
125C22×C11—21no—
126C22×C11#39911yescharacteristic
127C22×C11#47912yes—
128C4×C11—21no—
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—21no—
132C4×C11#48512yes—
133C4×C11#49511yescharacteristic
134C4×C11#49711yescharacteristic
135Dic11—42no—
136Dic11—81no—
137C22×Q8—111no—
138C2×M16—21no—
139C2×M16—221no—
140C22×C8—21no—
141C22×C8—112no—
142C4×Q8—221no—
143C4×Q8—221no—
144C4×Q8—221no—
145C4×Q8—221no—
146C2×C4⋊C4—111no—
147C2×C4⋊C4—221no—
148C2×C42—221no—
149C2×C42C22×D1111yescharacteristic
150C4⋊C8—21no—
151C4⋊C8—21no—
152C4⋊C8—21no—
153C4⋊C8—21no—
154C4⋊C8—21no—
155C4⋊C8—221no—
156C4⋊C8—221no—
157C4⋊C8—221no—
158C22⋊C8—21no—
159C22⋊C8—221no—
160#97—221no—
161#97—221no—
162C4×C8—112no—
163C4×C8C22⋊D1112yes—
164C2×C11—22no—
165C2×C11#209111yescharacteristic
166C2×C11#209711yescharacteristic
167C2×C11#209811yescharacteristic
168C2×Q8—221no—
169C2×Q8—221no—
170C2×Q8—442no—
171C22×C4—221no—
172C22×C4—221no—
173C22×C4#433911yescharacteristic
174C22×C4D4×D1111yescharacteristic
175C22×C4Q8×D1111yescharacteristic
176M16—42no—
177M16—442no—
178C2×C8—22no—
179C2×C8—42no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—222no—
183C2×C8—222no—
184C2×C8—222no—
185C2×C8—222no—
186C2×C8—441no—
187C4⋊C4—221no—
188C4⋊C4—221no—
189C4⋊C4—441no—
190C4⋊C4—441no—
191C42—441no—
192C42—441no—
193C42#433911yescharacteristic
194C42D4×D1111yescharacteristic
195C42#434311yescharacteristic
196C42C2×C22⋊D1111yescharacteristic
197C11#1066411yescharacteristic, complemented, Sylow
198C23#6694911yescharacteristic
199Q8—222no—
200Q8—222no—
201Q8—441no—
202Q8—441no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—222no—
206C2×C4—441no—
207C2×C4—441no—
208C2×C4—442no—
209C2×C4—441no—
210C2×C4#6694711yescharacteristic
211C2×C4#6694711yescharacteristic
212C2×C4#6694911yescharacteristic
213C2×C4#6696512yes—
214C2×C4#6697112yes—
215C2×C4#6698211yescharacteristic
216C2×C4#6699311yescharacteristic
217C2×C4#6699911yescharacteristic
218C8—42no—
219C8—81no—
220C8—81no—
221C8—442no—
222C8—442no—
223C8—881no—
224C22—21no—
225C22—21no—
226C22#1062249012yes—
227C22#1062260511yescharacteristic
228C4—21no—
229C4—21no—
230C4—21no—
231C4—21no—
232C4—442no—
233C4—881no—
234C4#1062250112yes—
235C4#1062276811yescharacteristic
236C4#1062280311yescharacteristic
237C2—22no—
238C2#1307013111yescharacteristic
239C2#1307016111yescharacteristic
240C2#1307017211yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1571C2
socleC22×C11#399
prime radicalC23×C11C22⋊Q8
hypercenter#1571D11
hypocenterC11#10664
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
197. C11#10664semidirect

Maximal subgroups

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

subgroupindex
#130695552
#130687562
#130673862
#130670462
#130670442
#130664462
C11×#15712
#1066411