Finite Group Databasebeta

← #14658208

Subgroups — #14658208

Order 2816.

494 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 135 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#13073645C211yesmaximal, characteristic
2#13069372C212yesmaximal
3#13066499C211yesmaximal, characteristic
4#13066456C212yesmaximal
5C11×#1845C211yesmaximal, characteristic
6C2×#66941—22no—
7C2×C11×#107—22no—
8C2×C4×C8×C11C2211yescharacteristic
9C11×#384C2211yescharacteristic
10C11×#384C2211yescharacteristic
11#10622592—22no—
12#10622586—22no—
13C2×#66871—22no—
14C4×C4⋊Dic11C2212yes—
15C2×C4⋊(C11⋊C8)C2212yes—
16#10622167—22no—
17C22×Dic22—22no—
18C22×C8×C11—21no—
19C2×C11×C4⋊C4—22no—
20C2×C11×C4⋊C4—22no—
21C2×C11×C4⋊C4—21no—
22C2×C11×C4⋊C4D412yes—
23C2×C42×C11C2311yescharacteristic
24C2×C4⋊Dic11D412yes—
25C2×C4⋊Dic11D412yes—
26C2×Dic11⋊C4—24no—
27C2×C4×Dic11—22no—
28C22×C11⋊C8—22no—
29#66941—44no—
30#66941—44no—
31C11×#107—44no—
32C4×C8×C11—21no—
33C4×C8×C11Q812yescomplemented
34C11⋊#95—22no—
35C11⋊#95—22no—
36#66871—44no—
37C4⋊(C11⋊C8)—22no—
38C4⋊(C11⋊C8)Q814yescomplemented
39#10573—111nomaximal, Sylow
40C22×C4×C11—22no—
41C22×C4×C11—41no—
42C22×C4×C11C2×D411yescharacteristic
43C22×C4×C11C2×D412yes—
44C22×Dic11—22no—
45C22×Dic11—22no—
46C2×Dic22—48no—
47C2×Dic22—82no—
48C2×C8×C11—22no—
49C2×C8×C11—22no—
50C2×C8×C11—22no—
51C11×C4⋊C4—42no—
52C11×C4⋊C4—42no—
53C11×C4⋊C4—42no—
54C11×C4⋊C4—42no—
55C11×C4⋊C4—42no—
56C11×C4⋊C4—42no—
57C42×C11C2×Q811yescharacteristic
58C42×C11C2×Q812yes—
59C42×C11#4111yescharacteristic
60C4⋊Dic11—22no—
61C4⋊Dic11—22no—
62C4⋊Dic11D814yes—
63C4⋊Dic11Q1614yes—
64Dic11⋊C4—48no—
65C4×Dic11—42no—
66C4×Dic11—42no—
67C2×C11⋊C8—24no—
68C2×C11⋊C8—42no—
69C2×C11⋊C8—42no—
70#2551—111no—
71#1947—112no—
72#1845D1111yescharacteristic
73#1296—111no—
74#1279—112no—
75C23×C11#12011yescharacteristic
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—44no—
79C2×C4×C11—42no—
80C2×C4×C11—82no—
81C2×C4×C11—81no—
82C2×C4×C11C22⋊Q812yes—
83C2×C4×C11C22⋊Q811yescharacteristic
84C2×C4×C11C4⋊Q812yes—
85C2×C4×C11C4⋊Q811yescharacteristic
86C2×C4×C11C2×D812yes—
87C2×C4×C11C2×Q1612yes—
88C2×C4×C11AGL(1,ℤ/8)12yes—
89C2×C4×C11#13712yes—
90C2×Dic11—24no—
91C2×Dic11—24no—
92C2×Dic11—42no—
93C2×Dic11—42no—
94C2×Dic11—42no—
95C2×Dic11—42no—
96Dic22—88no—
97C8×C11—24no—
98C11⋊C8—44no—
99C2×C4⋊Q8—222no—
100C2×#107—22no—
101C2×#107—222no—
102C2×C4⋊C8—112no—
103C2×C4×C8C2×D1111yescharacteristic
104#395—222no—
105#389—222no—
106#384C2×D1111yescharacteristic
107#384C2×D1111yescharacteristic
108C4×C4⋊C4—112no—
109#340—222no—
110C22×C11#39511yescharacteristic
111C22×C11#44712yes—
112C22×C11#45112yes—
113C22×C11#45311yescharacteristic
114C22×C11#45611yescharacteristic
115C4×C11—21no—
116C4×C11—21no—
117C4×C11—82no—
118C4×C11—161no—
119C4×C11#47412yes—
120C4×C11#47712yes—
121C4×C11#50012yes—
122C4×C11#50112yes—
123Dic11—44no—
124Dic11—44no—
125C22×Q8—222no—
126C22×C8—21no—
127C22×C8—222no—
128C4⋊Q8—444no—
129C4⋊Q8—444no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—112no—
134C2×C4⋊C4—112no—
135C2×C4⋊C4—224no—
136C2×C4⋊C4C22⋊D1112yes—
137C2×C42—222no—
138C2×C42C22×D1111yescharacteristic
139#107—44no—
140#107—444no—
141C4⋊C8—114no—
142C4⋊C8—222no—
143C4×C8—21no—
144C4×C8Dic2212yescomplemented
145#95—222no—
146#95—222no—
147C2×C11#161911yescharacteristic
148C2×C11#163311yescharacteristic
149C2×C11#164912yes—
150C2×C11#205712yes—
151C2×C11#206011yescharacteristic
152C2×Q8—448no—
153C2×Q8—882no—
154C22×C4—22no—
155C22×C4—41no—
156C22×C4—222no—
157C22×C4—222no—
158C22×C4D4×D1112yes—
159C22×C4C2×C22⋊D1111yescharacteristic
160C2×C8—22no—
161C2×C8—22no—
162C2×C8—22no—
163C2×C8—224no—
164C2×C8—442no—
165C2×C8—442no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C4⋊C4—42no—
171C4⋊C4—42no—
172C4⋊C4—114no—
173C4⋊C4—114no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4—448no—
177C42—442no—
178C42—442no—
179C42C2×Dic2211yescharacteristic
180C42#433911yescharacteristic
181C42Q8×D1112yes—
182C11#1057311yescharacteristic, complemented, Sylow
183C23#6699011yescharacteristic
184Q8—888no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—44no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4—224no—
192C2×C4—224no—
193C2×C4—442no—
194C2×C4—442no—
195C2×C4—442no—
196C2×C4—442no—
197C2×C4#6694112yes—
198C2×C4#6694912yes—
199C2×C4D8×D1112yes—
200C2×C4#6696412yes—
201C2×C4Q16×D1112yes—
202C2×C4#6697112yes—
203C2×C4#6697711yescharacteristic
204C2×C4#6699711yescharacteristic
205C8—24no—
206C8—444no—
207C22#1062259211yescharacteristic
208C22#1062269011yescharacteristic
209C22#1062270811yescharacteristic
210C22#1062276912yes—
211C22#1062279912yes—
212C4—21no—
213C4—21no—
214C4—82no—
215C4—161no—
216C4—444no—
217C4—444no—
218C4#1062248712yes—
219C4#1062248812yes—
220C4#1062248912yes—
221C4#1062250312yes—
222C2#1306766811yescharacteristic
223C2#1306775411yescharacteristic
224C2#1306786212yes—
225C2#1306994212yes—
226C2#1306996111yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1845C2
socle, prime radicalC23×C11#120
hypercenter#1845D11
hypocenterC11#10573
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1845

Complements

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

NH ≅ G/Ntype
33. C4×C8×C11Q8semidirect
38. C4⋊(C11⋊C8)Q8semidirect
144. C4×C8Dic22semidirect
182. C11#10573semidirect

Maximal subgroups

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

subgroupindex
#130736452
#130693722
#130664992
#130664562
C11×#18452
#1057311