Finite Group Databasebeta

← #14666832

Subgroups — #14666832

Order 2816.

342 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 59 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#13073858C211yesmaximal, characteristic
2#13067658C212yesmaximal
3#13066642C212yesmaximal
4#13066562C211yesmaximal, characteristic
5C11×#2060C211yesmaximal, characteristic
6C11×#544C2211yescharacteristic
7C11×#428—21no—
8C11×#384C2211yescharacteristic
9#10622657—22no—
10#10622599—21no—
11#10622599C2212yes—
12#10622598—22no—
13#10622590—22no—
14C4×C4⋊Dic11—21no—
15C11×#343C2211yescharacteristic
16C11×#339—21no—
17#10622176—22no—
18#10622166C2212yes—
19C2×C11×M16—21no—
20C11×C4⋊Q8—41no—
21C11×#125—41no—
22C11×C22⋊Q8—22no—
23C11×#117—21no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C11×C4⋊C4C2311yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11D412yes—
32C2×C4×Dic11—22no—
33C11×#107—41no—
34C11×#106—41no—
35#66899—42no—
36C11⋊#95—21no—
37C11⋊#95—22no—
38C11⋊#95—22no—
39C11⋊#95—22no—
40C11⋊#95D412yes—
41C22⋊(C11⋊C8)—22no—
42#66871—42no—
43#12257—111nomaximal, Sylow
44C2×Q8×C11—22no—
45C22×C4×C11—21no—
46C22×C4×C11—21no—
47C22×C4×C11C2×D411yescharacteristic
48C22×C4×C11C2×D412yes—
49C22×Dic11—22no—
50C22×Dic11—22no—
51C11×M16—22no—
52C11×M16—41no—
53C2×C8×C11—41no—
54C11×C4⋊C4—22no—
55C11×C4⋊C4—21no—
56C11×C4⋊C4—21no—
57C11×C4⋊C4—41no—
58C11×C4⋊C4—44no—
59C11×C4⋊C4—42no—
60C11×C4⋊C4—41no—
61C11×C22⋊C4—41no—
62C42×C11—21no—
63C42×C11—41no—
64C42×C11Q1612yes—
65C4⋊Dic11—42no—
66C4⋊Dic11—42no—
67C4⋊Dic11—42no—
68C4⋊Dic11—81no—
69C4×Dic11—44no—
70C2×C11⋊C8—42no—
71#2571—111no—
72#2060D1111yescharacteristic
73#1617—112no—
74#1353—112no—
75#1325—111no—
76C23×C11#12011yescharacteristic
77Q8×C11—82no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—22no—
84C2×C4×C11—42no—
85C2×C4×C11—42no—
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11C2×Q1611yescharacteristic
90C2×C4×C11#13711yescharacteristic
91C2×Dic11—42no—
92C2×Dic11—42no—
93C2×Dic11—42no—
94C2×Dic11—42no—
95C2×Dic11—42no—
96C2×Dic11—42no—
97C8×C11—42no—
98C11⋊C8—82no—
99#544C2×D1111yescharacteristic
100#484—222no—
101#428—21no—
102#400—112no—
103#400—221no—
104#389—222no—
105#384C2×D1111yescharacteristic
106#382—222no—
107C4×C4⋊C4—221no—
108#343C2×D1111yescharacteristic
109#339—21no—
110#328—222no—
111#324—112no—
112C22×C11—21no—
113C22×C11—21no—
114C22×C11#45111yescharacteristic
115C22×C11#45611yescharacteristic
116C22×C11B(4,𝔽2)11yescharacteristic
117C4×C11—24no—
118C4×C11—21no—
119C4×C11—21no—
120C4×C11—42no—
121C4×C11—81no—
122C4×C11—81no—
123C4×C11—81no—
124Dic11—82no—
125Dic11—82no—
126C2×M16—21no—
127C4⋊Q8—41no—
128#125—41no—
129C22⋊Q8—22no—
130#117—21no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—112no—
133C2×C4⋊C4—221no—
134C2×C4⋊C4—221no—
135C2×C4⋊C4—221no—
136C2×C4⋊C4C22⋊D1111yescharacteristic
137C2×C4⋊C4C22×D1111yescharacteristic
138C2×C42—222no—
139C2×C42C22⋊D1111yescharacteristic
140#107—41no—
141#107—442no—
142#106—41no—
143#103—442no—
144C22⋊C8—222no—
145#95—112no—
146#95—221no—
147#95—222no—
148#95—222no—
149#95—222no—
150C2×C11—21no—
151C2×C11—21no—
152C2×C11#160511yescharacteristic
153C2×C11#219811yescharacteristic
154C2×C11#220411yescharacteristic
155C2×Q8—22no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—222no—
159C22×C4—222no—
160C22×C4D4×D1112yes—
161C22×C4C2×C22⋊D1111yescharacteristic
162M16—22no—
163M16—41no—
164C2×C8—41no—
165C2×C8—442no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—22no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—44no—
172C4⋊C4—42no—
173C4⋊C4—442no—
174C4⋊C4—442no—
175C4⋊C4—442no—
176C4⋊C4—881no—
177C22⋊C4—41no—
178C42—21no—
179C42—41no—
180C42—444no—
181C42#432612yes—
182C11#1225711yescharacteristic, complemented, Sylow
183C23#6699011yescharacteristic
184Q8—82no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—442no—
197C2×C4—442no—
198C2×C4—442no—
199C2×C4—442no—
200C2×C4—442no—
201C2×C4—442no—
202C2×C4C2×#432611yescharacteristic
203C2×C4#6700411yescharacteristic
204C8—42no—
205C8—882no—
206C22—21no—
207C22—21no—
208C22#1062264511yescharacteristic
209C22#1062266311yescharacteristic
210C22#1062270811yescharacteristic
211C4—24no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—81no—
216C4—81no—
217C4—81no—
218C4—882no—
219C4—882no—
220C2—21no—
221C2—21no—
222C2#1306758911yescharacteristic
223C2#1307061111yescharacteristic
224C2#1307064111yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2060C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2060D11
hypocenterC11#12257
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2060

Complements

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

NH ≅ G/Ntype
182. C11#12257semidirect

Maximal subgroups

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

subgroupindex
#130738582
#130676582
#130666422
#130665622
C11×#20602
#1225711