Finite Group Databasebeta

← #14656876

Subgroups — #14656876

Order 2816.

400 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 99 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#13076979C211yesmaximal, characteristic
2#13067180C212yesmaximal
3#13066476C212yesmaximal
4#13066449C211yesmaximal, characteristic
5C11×#1994C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C2×#66923—21no—
8C11×#423C2211yescharacteristic
9C43×C11C2211yescharacteristic
10#10622549C2212yes—
11#10622548—21no—
12#10622541—24no—
13#10622538C2212yes—
14C11×#339—21no—
15C11×#339—21no—
16#10622176—24no—
17C2×C11×M16—21no—
18C11×C4⋊Q8Q812yes—
19C11×#125—21no—
20C11×C22⋊Q8—22no—
21C4×Q8×C11—22no—
22C11×#117—21no—
23C2×C42×C11—22no—
24C2×C42×C11D411yescharacteristic
25C2×C42×C11D411yescharacteristic
26C2×C42×C11C2311yescharacteristic
27C2×C4⋊Dic11—24no—
28C2×C4⋊Dic11—22no—
29C2×Dic11⋊C4—24no—
30#66923—42no—
31#66923—42no—
32C11×C4⋊C8—22no—
33C11⋊#95—22no—
34C11⋊#95D414yes—
35C22⋊(C11⋊C8)—22no—
36C4⋊(C11⋊C8)—22no—
37C4×C11⋊C8—22no—
38#10365—111nomaximal, Sylow
39C2×Q8×C11—22no—
40C22×C4×C11—21no—
41C22×C4×C11—21no—
42C22×C4×C11C2×D412yes—
43C22×C4×C11C2×D411yescharacteristic
44C22×Dic11—24no—
45C11×M16—41no—
46C11×M16—41no—
47C2×C8×C11—41no—
48C11×C4⋊C4—22no—
49C11×C4⋊C4—22no—
50C11×C4⋊C4—42no—
51C11×C22⋊C4—41no—
52C42×C11—21no—
53C42×C11—21no—
54C42×C11—44no—
55C42×C11—41no—
56C42×C11SD1612yes—
57C42×C11Q1612yes—
58C42×C11C2×Q811yescharacteristic
59C42×C11#4111yescharacteristic
60C42×C11#4112yes—
61C4⋊Dic11—48no—
62C4⋊Dic11—42no—
63C4⋊Dic11—42no—
64Dic11⋊C4—48no—
65C2×C11⋊C8—42no—
66#2859—111no—
67#1994D1111yescharacteristic
68#1518—112no—
69#1286—112no—
70#1276—111no—
71C23×C11#12011yescharacteristic
72Q8×C11—82no—
73C2×C4×C11—24no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—42no—
77C2×C4×C11—42no—
78C2×C4×C11—42no—
79C2×C4×C11C22⋊Q812yes—
80C2×C4×C11C22⋊Q811yescharacteristic
81C2×C4×C11#12412yes—
82C2×C4×C11#12411yescharacteristic
83C2×C4×C11C2×SD1611yescharacteristic
84C2×C4×C11C2×Q1611yescharacteristic
85C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
86C2×C4×C11#13711yescharacteristic
87C2×Dic11—48no—
88C2×Dic11—44no—
89C8×C11—81no—
90C11⋊C8—82no—
91#533C2×D1111yescharacteristic
92C2×#125—221no—
93#431—112no—
94#423C2×D1111yescharacteristic
95#389—224no—
96#384—221no—
97#382—112no—
98C43C2×D1111yescharacteristic
99#339—21no—
100#339—21no—
101#328—224no—
102C22×C11—22no—
103C22×C11#39311yescharacteristic
104C22×C11#45011yescharacteristic
105C22×C11#45111yescharacteristic
106C4×C11—24no—
107C4×C11—22no—
108C4×C11—22no—
109C4×C11—42no—
110C4×C11—82no—
111C4×C11#47511yescharacteristic
112C4×C11#47711yescharacteristic
113C4×C11#48711yescharacteristic
114C4×C11#48911yescharacteristic
115Dic11—84no—
116C2×M16—21no—
117C4⋊Q8Dic2212yes—
118#125—21no—
119#125—442no—
120#125—442no—
121C22⋊Q8—22no—
122C4×Q8—22no—
123#117—21no—
124C2×C4⋊C4—224no—
125C2×C4⋊C4—224no—
126C2×C4⋊C4—222no—
127C2×C42—22no—
128C2×C42C22⋊D1111yescharacteristic
129C2×C42C22⋊D1111yescharacteristic
130C2×C42C22×D1111yescharacteristic
131C4⋊C8—22no—
132C4⋊C8—222no—
133C22⋊C8—222no—
134C4×C8—222no—
135#95—114no—
136#95—222no—
137C2×C11—21no—
138C2×C11—21no—
139C2×C11#202411yescharacteristic
140C2×C11#203112yes—
141C2×Q8—22no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—224no—
145C22×C4D4×D1112yes—
146C22×C4C2×C22⋊D1111yescharacteristic
147M16—41no—
148M16—41no—
149C2×C8—41no—
150C2×C8—442no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—42no—
154C4⋊C4—448no—
155C4⋊C4—448no—
156C4⋊C4—442no—
157C4⋊C4—442no—
158C22⋊C4—41no—
159C42—21no—
160C42—21no—
161C42—44no—
162C42—41no—
163C42#432512yes—
164C42#432612yes—
165C42C2×Dic2211yescharacteristic
166C42#433911yescharacteristic
167C42#434112yes—
168C11#1036511yescharacteristic, complemented, Sylow
169C23#6699011yescharacteristic
170Q8—82no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—448no—
178C2×C4—444no—
179C2×C4#6693112yes—
180C2×C4#6693812yes—
181C2×C4#6697711yescharacteristic
182C2×C4#6698911yescharacteristic
183C2×C4C2×#432511yescharacteristic
184C2×C4C2×#432611yescharacteristic
185C2×C4#6700211yescharacteristic
186C2×C4#6700411yescharacteristic
187C8—81no—
188C8—882no—
189C22—22no—
190C22#1062256011yescharacteristic
191C22#1062265911yescharacteristic
192C22#1062266311yescharacteristic
193C4—24no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—82no—
198C4—884no—
199C4#1062263311yescharacteristic
200C4#1062263411yescharacteristic
201C4#1062266811yescharacteristic
202C4#1062269411yescharacteristic
203C2—21no—
204C2—21no—
205C2#1306975711yescharacteristic
206C2#1306978812yes—
subgroupG/H
centerC22#10622560
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1994C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1994D11
hypocenterC11#10365
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
168. C11#10365semidirect

Maximal subgroups

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

subgroupindex
#130769792
#130671802
#130664762
#130664492
C11×#19942
#1036511