Finite Group Databasebeta

← #14657269

Subgroups — #14657269

Order 2816.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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#13069586C212yesmaximal
2#13068785C211yesmaximal, characteristic
3C2×#10622181C212yesmaximal
4#13066497C211yesmaximal, characteristic
5C11×#2822C211yesmaximal, characteristic
6C2×C11×#125C2212yes—
7C11×#400—22no—
8C11×#398—21no—
9C11×#398—21no—
10C11×#398—22no—
11C11×#382C2211yescharacteristic
12C2×#66872—21no—
13C2×#66871—21no—
14#10622548C2211yescharacteristic
15C2×#66867C2212yes—
16C2×#66867C2211yescharacteristic
17#10622181—24no—
18#10622167—22no—
19#10622167—22no—
20C11×#125—22no—
21C11×#125—22no—
22C11×#125—22no—
23C11×#125—22no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4D412yes—
29C2×C11×C4⋊C4D412yes—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—22no—
35C22×C11⋊C8—21no—
36C22×C11⋊C8—22no—
37C11×#95—22no—
38C11×#95—22no—
39C11×#95—21no—
40C11×#95—21no—
41C11×#95—22no—
42#66872—42no—
43#66871—42no—
44#66867—21no—
45#66867—22no—
46#66867—22no—
47#66867D412yes—
48#10429—111nomaximal, Sylow
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11C2×D412yes—
54C22×C4×C11C2×D411yescharacteristic
55C22×Dic11—41no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—22no—
59C11×C4⋊C4—22no—
60C11×C4⋊C4—41no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—42no—
63C11×C4⋊C4—42no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—81no—
67C11×C4⋊C4—81no—
68C42×C11C2×D411yescharacteristic
69C42×C11#4111yescharacteristic
70C42×C11#4112yes—
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73C4⋊Dic11—44no—
74C2×C11⋊C8—22no—
75C2×C11⋊C8—22no—
76C2×C11⋊C8—24no—
77C2×C11⋊C8—22no—
78C2×C11⋊C8—42no—
79C2×C11⋊C8—42no—
80#2822D1111yescharacteristic
81#1992—112no—
82#1847—111no—
83C2×#330—112no—
84#1295—111no—
85C23×C11#12011yescharacteristic
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11—42no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11#12111yescharacteristic
101C2×C4×C11#12112yes—
102C2×C4×C11#12312yes—
103C2×C4×C11#12411yescharacteristic
104C2×Dic11—81no—
105C2×Dic11—82no—
106C11⋊C8—24no—
107C11⋊C8—44no—
108C2×#125C2×D1112yes—
109C2×#107—221no—
110C2×#106—221no—
111C2×#97—111no—
112C2×#97—112no—
113#400—22no—
114#398—21no—
115#398—21no—
116#398—22no—
117#384—111no—
118#382C2×D1111yescharacteristic
119#340—222no—
120#340—222no—
121#330—224no—
122C22×C11#39411yescharacteristic
123C22×C11#45311yescharacteristic
124C22×C11#45412yes—
125C22×C11#45612yes—
126C22×C11#45611yescharacteristic
127C4×C11—22no—
128C4×C11—22no—
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—81no—
132C4×C11—81no—
133C4×C11—82no—
134C4×C11—82no—
135Dic11—161no—
136C22×C8—221no—
137C22×C8—222no—
138#125—22no—
139#125—22no—
140#125—22no—
141#125—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—222no—
147C2×C4⋊C4—221no—
148C2×C4⋊C4C22⋊D1112yes—
149C2×C4⋊C4C22⋊D1112yes—
150C2×C4⋊C4C22⋊D1111yescharacteristic
151C2×C4⋊C4C22⋊D1111yescharacteristic
152C2×C42C22×D1111yescharacteristic
153#107—442no—
154#106—442no—
155#97—112no—
156#97—222no—
157#97—221no—
158#97—222no—
159#95—22no—
160#95—22no—
161#95—21no—
162#95—21no—
163#95—22no—
164C2×C11#165711yescharacteristic
165C2×C11#166011yescharacteristic
166C2×C11#166312yes—
167C2×C11#203812yes—
168C2×C11#203911yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—441no—
174C22×C4C2×C22⋊D1112yes—
175C22×C4C2×C22⋊D1111yescharacteristic
176C2×C8—222no—
177C2×C8—222no—
178C2×C8—222no—
179C2×C8—224no—
180C2×C8—442no—
181C2×C8—442no—
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—81no—
193C4⋊C4—81no—
194C4⋊C4—441no—
195C4⋊C4—441no—
196C4⋊C4—444no—
197C42D4×D1111yescharacteristic
198C42#434111yescharacteristic
199C42#434112yes—
200C11#1042911yescharacteristic, complemented, Sylow
201C23#6700611yescharacteristic
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—881no—
217C2×C4—882no—
218C2×C4#6698812yes—
219C2×C4#6698911yescharacteristic
220C2×C4#6699111yescharacteristic
221C2×C4#6699212yes—
222C8—224no—
223C8—444no—
224C22#1062283511yescharacteristic
225C22#1062285411yescharacteristic
226C22#1062285812yes—
227C22#1062285912yes—
228C22#1062285911yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—82no—
234C4—82no—
235C4—81no—
236C4—81no—
237C4—1761no—
238C2#1306791411yescharacteristic
239C2#1306792711yescharacteristic
240C2#1306794412yes—
241C2#1306983012yes—
242C2#1306983711yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2822C2
socle, prime radicalC23×C11#120
hypercenter#2822D11
hypocenterC11#10429
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

Complements

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

NH ≅ G/Ntype
200. C11#10429semidirect

Maximal subgroups

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

subgroupindex
#130695862
#130687852
C2×#106221812
#130664972
C11×#28222
#1042911