Finite Group Databasebeta

← #14656881

Subgroups — #14656881

Order 2816.

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

normal subgroups only

This group has 402 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#13077003C211yesmaximal, characteristic, complemented
2#13067176C212yesmaximal
3#13066476C212yesmaximal, complemented
4#13066449C211yesmaximal, characteristic, complemented
5C11×#1962C211yesmaximal, characteristic
6C11×#532C2211yescharacteristic
7C11×#423C2211yescharacteristic
8C2×C11×#104—22no—
9C43×C11C2211yescharacteristic
10#10622549C2212yes—
11#10622546—24no—
12#10622541—22no—
13#10622538C2212yes—
14#10622175—24no—
15C2×C11×#41—21no—
16C2×C11×M16—21no—
17C11×C4⋊Q8Q811yescharacteristic
18C11×#127Q811yescharacteristic
19C11×#124—21no—
20C11×#121—22no—
21C4×D4×C11—22no—
22C2×C42×C11—22no—
23C2×C42×C11D412yes—
24C2×C42×C11C2311yescharacteristic
25C2×C4⋊Dic11—22no—
26C2×Dic11⋊C4—24no—
27C11×C4⋊C8—22no—
28C11×#104—44no—
29C11⋊#95—24no—
30C11⋊#95—22no—
31C11⋊#95D414yes—
32C22⋊(C11⋊C8)—22no—
33C4⋊(C11⋊C8)—22no—
34C4×C11⋊C8—22no—
35#10366—111nomaximal, Sylow
36C11×#41—42no—
37C11×#41—42no—
38C2×Q8×C11—21no—
39C2×D4×C11—21no—
40C2×D4×C11—22no—
41C2×D4×C11—41no—
42C22×C4×C11—22no—
43C22×C4×C11—41no—
44C22×C4×C11C2×D412yes—
45C22×C4×C11C2×D411yescharacteristic
46C22×Dic11—24no—
47C11×M16—42no—
48C2×C8×C11—41no—
49C11×C4⋊C4—22no—
50C11×C22⋊C4—42no—
51C42×C11—22no—
52C42×C11—22no—
53C42×C11—44no—
54C42×C11C2×Q811yescharacteristic
55C42×C11#4111yescharacteristic
56C42×C11#4112yes—
57C4⋊Dic11—42no—
58C4⋊Dic11—42no—
59Dic11⋊C4—48no—
60C2×C11⋊C8—42no—
61#2864—111no—
62#1962D1111yescharacteristic
63#1517—112no—
64#1286—112no—
65#1276—111no—
66C23×C11—41no—
67C23×C11#12011yescharacteristic
68Q8×C11—42no—
69D4×C11—42no—
70D4×C11—82no—
71D4×C11—82no—
72C2×C4×C11—24no—
73C2×C4×C11—42no—
74C2×C4×C11—42no—
75C2×C4×C11—42no—
76C2×C4×C11—41no—
77C2×C4×C11—81no—
78C2×C4×C11—81no—
79C2×C4×C11C22⋊Q812yes—
80C2×C4×C11C22⋊Q811yescharacteristic
81C2×C4×C11#12412yes—
82C2×C4×C11#12411yescharacteristic
83C2×C4×C11#13512yes—
84C2×C4×C11AGL(1,ℤ/8)12yes—
85C2×Dic11—48no—
86C2×Dic11—44no—
87C8×C11—81no—
88C11⋊C8—82no—
89#532C2×D1111yescharacteristic
90#431—112no—
91#423C2×D1111yescharacteristic
92C2×#104—22no—
93#389—222no—
94#387—224no—
95#382—112no—
96C43C2×D1111yescharacteristic
97#327—224no—
98C22×C11—22no—
99C22×C11—81no—
100C22×C11—82no—
101C22×C11#39311yescharacteristic
102C22×C11#44912yes—
103C4×C11—22no—
104C4×C11—22no—
105C4×C11—44no—
106C4×C11—81no—
107C4×C11#47812yes—
108C4×C11#48811yescharacteristic
109C4×C11#49011yescharacteristic
110Dic11—84no—
111C2×#41—21no—
112C2×M16—21no—
113C4⋊Q8Dic2211yescharacteristic
114#127Dic2211yescharacteristic
115#124—21no—
116#121—22no—
117C4×D4—22no—
118C2×C4⋊C4—224no—
119C2×C4⋊C4—222no—
120C2×C42—22no—
121C2×C42C22⋊D1112yes—
122C2×C42C22×D1111yescharacteristic
123C4⋊C8—22no—
124C4⋊C8—222no—
125#104—44no—
126C22⋊C8—222no—
127C4×C8—222no—
128#95—114no—
129#95—224no—
130#95—222no—
131C2×C11—22no—
132C2×C11—161no—
133C2×C11#202511yescharacteristic
134C2×C11#203112yes—
135#41—42no—
136#41—42no—
137C2×Q8—21no—
138C2×D4—22no—
139C2×D4—21no—
140C2×D4—41no—
141C22×C4—22no—
142C22×C4—41no—
143C22×C4—224no—
144C22×C4D4×D1112yes—
145C22×C4C2×C22⋊D1111yescharacteristic
146M16—42no—
147C2×C8—41no—
148C2×C8—442no—
149C4⋊C4—22no—
150C4⋊C4—448no—
151C4⋊C4—442no—
152C4⋊C4—442no—
153C22⋊C4—42no—
154C42—22no—
155C42—22no—
156C42—44no—
157C42C2×Dic2211yescharacteristic
158C42#433911yescharacteristic
159C42#434112yes—
160C11#1036611yescharacteristic, complemented, Sylow
161C23—41no—
162C23#6699011yescharacteristic
163Q8—42no—
164D4—42no—
165D4—82no—
166D4—82no—
167C2×C4—24no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—81no—
173C2×C4—81no—
174C2×C4—448no—
175C2×C4—444no—
176C2×C4#6693112yes—
177C2×C4#6693812yes—
178C2×C4#6697711yescharacteristic
179C2×C4#6698512yes—
180C2×C4#6698911yescharacteristic
181C2×C4#6700312yes—
182C8—81no—
183C8—882no—
184C22—22no—
185C22—81no—
186C22—82no—
187C22#1062256011yescharacteristic
188C22#1062265012yes—
189C4—22no—
190C4—22no—
191C4—44no—
192C4—81no—
193C4—884no—
194C4#1062262212yes—
195C4#1062266911yescharacteristic
196C4#1062268411yescharacteristic
197C2—22no—
198C2—161no—
199C2#1306976211yescharacteristic
200C2#1306978812yes—
subgroupG/H
centerC22#10622560
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1962C2
socleC22×C11#393
prime radicalC11×#532C22
hypercenter#1962D11
hypocenterC11#10366
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1962

Complements

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

NH ≅ G/Ntype
1. #13077003C2semidirect
3. #13066476C2semidirect
4. #13066449C2semidirect
160. C11#10366semidirect

Maximal subgroups

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

subgroupindex
#130770032
#130671762
#130664762
#130664492
C11×#19622
#1036611