Finite Group Databasebeta

← #14658758

Subgroups — #14658758

Order 2816.

320 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 93 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#13068790C211yesmaximal, characteristic
3#13067390C211yesmaximal, characteristic
4#13067046C211yesmaximal, characteristic
5#13067044C211yesmaximal, characteristic
6#13066446C211yesmaximal, characteristic
7C11×#1571C211yesmaximal, characteristic
8C2×C4×Dic22C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×#66886—22no—
13#10622538C2211yescharacteristic
14#10622537C2211yescharacteristic
15C2×#66867C2211yescharacteristic
16C11×#335—22no—
17#10622188—22no—
18#10622122—22no—
19#10622117—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—
42#66886—44no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46#66867—21no—
47#66867—21no—
48C4×C11⋊C8D412yes—
49#10662—111nomaximal, Sylow
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11C2×Q811yescharacteristic
52C22×C4×C11#4111yescharacteristic
53C22×Dic11—21no—
54C22×Dic11—21no—
55C2×Dic22—21no—
56C2×Dic22—21no—
57C2×Dic22—42no—
58C11×M16—42no—
59C2×C8×C11—22no—
60C2×C8×C11—41no—
61C2×C8×C11—41no—
62C2×C8×C11—42no—
63C42×C11C2×D411yescharacteristic
64C42×C11C2×D411yescharacteristic
65C42×C11#4111yescharacteristic
66C42×C11#4111yescharacteristic
67C4⋊Dic11—21no—
68C4⋊Dic11—21no—
69Dic11⋊C4—41no—
70Dic11⋊C4—41no—
71C4×Dic11—41no—
72C4×Dic11—41no—
73#4318—42no—
74C2×C11⋊C8—22no—
75C2×C11⋊C8—22no—
76C2×C11⋊C8—22no—
77C2×C11⋊C8—41no—
78C2×C11⋊C8Q1614yes—
79#1985—111no—
80#1849—111no—
81#1571—111no—
82#1571D1111yescharacteristic
83#1487—111no—
84#1487—111no—
85#1275—111no—
86C23×C11C22⋊Q811yescharacteristic
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11C22⋊Q811yescharacteristic
90C2×C4×C11C22⋊Q811yescharacteristic
91C2×C4×C11#12311yescharacteristic
92C2×C4×C11#12311yescharacteristic
93C2×C4×C11#12311yescharacteristic
94C2×C4×C11#12711yescharacteristic
95C2×C4×C11C2×Q1612yes—
96C2×C4×C11AGL(1,ℤ/8)12yes—
97C2×Dic11—22no—
98C2×Dic11—41no—
99C2×Dic11—41no—
100C2×Dic11—42no—
101C2×Dic11—41no—
102Dic22—22no—
103Dic22—22no—
104Dic22—41no—
105Dic22—41no—
106C8×C11—42no—
107C8×C11—81no—
108C8×C11—81no—
109C11⋊C8—24no—
110C11⋊C8—42no—
111C11⋊C8—81no—
112C2×C4×Q8—111no—
113#431—111no—
114#431C2×D1111yescharacteristic
115C2×#108—222no—
116#423—111no—
117#423C2×D1111yescharacteristic
118C2×C4⋊C8C2×D1111yescharacteristic
119C2×#97—111no—
120#336—222no—
121#335—22no—
122#335—222no—
123Q8⋊C8—222no—
124Q8⋊C8—222no—
125C22×C11—21no—
126C22×C11—21no—
127C22×C11#39911yescharacteristic
128C22×C11#47712yes—
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—21no—
132C4×C11—21no—
133C4×C11#48412yes—
134C4×C11#49411yescharacteristic
135C4×C11#49611yescharacteristic
136Dic11—42no—
137Dic11—81no—
138C22×Q8—111no—
139C2×M16—21no—
140C2×M16—221no—
141C22×C8—21no—
142C22×C8—112no—
143C4×Q8—221no—
144C4×Q8—221no—
145C4×Q8—221no—
146C4×Q8—221no—
147C2×C4⋊C4—111no—
148C2×C4⋊C4—221no—
149C2×C42—221no—
150C2×C42C22×D1111yescharacteristic
151#108—444no—
152C4⋊C8—21no—
153C4⋊C8—21no—
154C4⋊C8—21no—
155C4⋊C8—21no—
156C4⋊C8—21no—
157C4⋊C8—221no—
158C4⋊C8—221no—
159C4⋊C8—221no—
160C22⋊C8—21no—
161C22⋊C8—221no—
162#97—221no—
163#97—221no—
164C4×C8—112no—
165C4×C8C22⋊D1112yes—
166C2×C11—22no—
167C2×C11#209111yescharacteristic
168C2×C11#209511yescharacteristic
169C2×C11#209811yescharacteristic
170C2×Q8—221no—
171C2×Q8—221no—
172C2×Q8—442no—
173C22×C4—221no—
174C22×C4—221no—
175C22×C4#433911yescharacteristic
176C22×C4D4×D1111yescharacteristic
177C22×C4Q8×D1111yescharacteristic
178M16—42no—
179M16—442no—
180C2×C8—22no—
181C2×C8—42no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—114no—
185C2×C8—222no—
186C2×C8—222no—
187C2×C8—222no—
188C2×C8—441no—
189C4⋊C4—221no—
190C4⋊C4—221no—
191C4⋊C4—441no—
192C4⋊C4—441no—
193C42—441no—
194C42—441no—
195C42#433911yescharacteristic
196C42D4×D1111yescharacteristic
197C42#434311yescharacteristic
198C42C2×C22⋊D1111yescharacteristic
199C11#1066211yescharacteristic, complemented, Sylow
200C23#6694911yescharacteristic
201Q8—222no—
202Q8—222no—
203Q8—441no—
204Q8—441no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—222no—
208C2×C4—441no—
209C2×C4—441no—
210C2×C4—442no—
211C2×C4—441no—
212C2×C4#6694711yescharacteristic
213C2×C4#6694711yescharacteristic
214C2×C4#6694911yescharacteristic
215C2×C4#6696412yes—
216C2×C4Q16×D1112yes—
217C2×C4#6698211yescharacteristic
218C2×C4#6699311yescharacteristic
219C2×C4#6699911yescharacteristic
220C8—42no—
221C8—81no—
222C8—81no—
223C8—224no—
224C8—442no—
225C8—881no—
226C22—21no—
227C22—21no—
228C22#1062248812yes—
229C22#1062260511yescharacteristic
230C4—21no—
231C4—21no—
232C4—21no—
233C4—21no—
234C4—442no—
235C4—881no—
236C4#1062249712yes—
237C4#1062276711yescharacteristic
238C4#1062279411yescharacteristic
239C2—22no—
240C2#1307013111yescharacteristic
241C2#1307015111yescharacteristic
242C2#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#10662
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
199. C11#10662semidirect

Maximal subgroups

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

subgroupindex
#130695552
#130687902
#130673902
#130670462
#130670442
#130664462
C11×#15712
#1066211