Finite Group Databasebeta

← #14656866

Subgroups — #14656866

Order 2816.

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

normal subgroups only

This group has 416 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#13076994C211yesmaximal, characteristic
2#13067180C212yesmaximal
3#13066476C212yesmaximal
4#13066449C211yesmaximal, characteristic
5C11×#1994C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C2×#66922—21no—
8C11×#423C2211yescharacteristic
9C43×C11C2211yescharacteristic
10#10622549—21no—
11#10622549C2212yes—
12#10622542—24no—
13#10622538C2212yes—
14C11×#339—21no—
15C11×#339—21no—
16#10622176—24no—
17C22×Dic22—22no—
18C2×C11×M16—21no—
19C11×C4⋊Q8Q812yescomplemented
20C11×#125—21no—
21C11×C22⋊Q8—22no—
22C4×Q8×C11—22no—
23C11×#117—21no—
24C2×C42×C11—22no—
25C2×C42×C11D411yescharacteristic
26C2×C42×C11D411yescharacteristic
27C2×C42×C11C2311yescharacteristic
28C2×C4⋊Dic11—22no—
29C2×C4⋊Dic11—22no—
30#66922—42no—
31#66922—42no—
32C11×C4⋊C8—22no—
33C11⋊#95—24no—
34C11⋊#95—22no—
35C11⋊#95D414yes—
36C22⋊(C11⋊C8)—22no—
37C4⋊(C11⋊C8)—22no—
38C4×C11⋊C8—22no—
39#10363—111nomaximal, Sylow
40C2×Q8×C11—22no—
41C22×C4×C11—21no—
42C22×C4×C11—21no—
43C22×C4×C11C2×D412yes—
44C22×C4×C11C2×D411yescharacteristic
45C22×Dic11—24no—
46C2×Dic22—44no—
47C2×Dic22—48no—
48C11×M16—41no—
49C11×M16—41no—
50C2×C8×C11—41no—
51C11×C4⋊C4—22no—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—42no—
54C11×C22⋊C4—41no—
55C42×C11—21no—
56C42×C11—21no—
57C42×C11—44no—
58C42×C11—41no—
59C42×C11SD1612yes—
60C42×C11Q1612yes—
61C42×C11C2×Q811yescharacteristic
62C42×C11#4111yescharacteristic
63C42×C11#4112yes—
64C4⋊Dic11—44no—
65C4⋊Dic11—42no—
66C4⋊Dic11—42no—
67C2×C11⋊C8—42no—
68#2862—111no—
69#1994D1111yescharacteristic
70#1518—112no—
71#1286—112no—
72#1276—111no—
73C23×C11#12011yescharacteristic
74Q8×C11—82no—
75C2×C4×C11—24no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—42no—
79C2×C4×C11—42no—
80C2×C4×C11—42no—
81C2×C4×C11C22⋊Q812yes—
82C2×C4×C11C22⋊Q811yescharacteristic
83C2×C4×C11#12412yes—
84C2×C4×C11#12411yescharacteristic
85C2×C4×C11C2×SD1611yescharacteristic
86C2×C4×C11C2×Q1611yescharacteristic
87C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
88C2×C4×C11#13711yescharacteristic
89C2×Dic11—48no—
90C2×Dic11—44no—
91Dic22—88no—
92C8×C11—81no—
93C11⋊C8—82no—
94#533C2×D1111yescharacteristic
95C2×C4⋊Q8—221no—
96#431—112no—
97#423C2×D1111yescharacteristic
98#391—224no—
99#382—112no—
100#382—221no—
101C43C2×D1111yescharacteristic
102#339—21no—
103#339—21no—
104#328—224no—
105C22×C11—22no—
106C22×C11#39311yescharacteristic
107C22×C11#45011yescharacteristic
108C22×C11#45111yescharacteristic
109C4×C11—24no—
110C4×C11—22no—
111C4×C11—22no—
112C4×C11—42no—
113C4×C11—82no—
114C4×C11#47511yescharacteristic
115C4×C11#47711yescharacteristic
116C4×C11#48711yescharacteristic
117C4×C11#48911yescharacteristic
118Dic11—84no—
119C22×Q8—222no—
120C2×M16—21no—
121C4⋊Q8—442no—
122C4⋊Q8—442no—
123C4⋊Q8Dic2212yescomplemented
124#125—21no—
125C22⋊Q8—22no—
126C4×Q8—22no—
127#117—21no—
128C2×C4⋊C4—222no—
129C2×C4⋊C4—222no—
130C2×C42—22no—
131C2×C42C22⋊D1111yescharacteristic
132C2×C42C22⋊D1111yescharacteristic
133C2×C42C22×D1111yescharacteristic
134C4⋊C8—22no—
135C4⋊C8—222no—
136C22⋊C8—222no—
137C4×C8—222no—
138#95—114no—
139#95—224no—
140#95—222no—
141C2×C11—21no—
142C2×C11—21no—
143C2×C11#202411yescharacteristic
144C2×C11#203112yes—
145C2×Q8—22no—
146C2×Q8—444no—
147C2×Q8—448no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—224no—
151C22×C4D4×D1112yes—
152C22×C4C2×C22⋊D1111yescharacteristic
153M16—41no—
154M16—41no—
155C2×C8—41no—
156C2×C8—442no—
157C4⋊C4—22no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—444no—
161C4⋊C4—442no—
162C4⋊C4—442no—
163C22⋊C4—41no—
164C42—21no—
165C42—21no—
166C42—44no—
167C42—41no—
168C42#432512yes—
169C42#432612yes—
170C42C2×Dic2211yescharacteristic
171C42#433911yescharacteristic
172C42#434112yes—
173C11#1036311yescharacteristic, complemented, Sylow
174C23#6699011yescharacteristic
175Q8—82no—
176Q8—888no—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—448no—
184C2×C4—444no—
185C2×C4#6693112yes—
186C2×C4#6693812yes—
187C2×C4#6697711yescharacteristic
188C2×C4#6698911yescharacteristic
189C2×C4C2×#432511yescharacteristic
190C2×C4C2×#432611yescharacteristic
191C2×C4#6700211yescharacteristic
192C2×C4#6700411yescharacteristic
193C8—81no—
194C8—882no—
195C22—22no—
196C22#1062256011yescharacteristic
197C22#1062265911yescharacteristic
198C22#1062266311yescharacteristic
199C4—24no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—82no—
204C4—884no—
205C4#1062263311yescharacteristic
206C4#1062263411yescharacteristic
207C4#1062266811yescharacteristic
208C4#1062269411yescharacteristic
209C2—21no—
210C2—21no—
211C2#1306975711yescharacteristic
212C2#1306978812yes—
subgroupG/H
centerC22#10622560
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1994C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1994D11
hypocenterC11#10363
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
19. C11×C4⋊Q8Q8semidirect
123. C4⋊Q8Dic22semidirect
173. C11#10363semidirect

Maximal subgroups

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

subgroupindex
#130769942
#130671802
#130664762
#130664492
C11×#19942
#1036311