Finite Group Databasebeta

← #14656802

Subgroups — #14656802

Order 2816.

416 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 125 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#13069564C212yesmaximal
2#13069417C211yesmaximal, characteristic
3#13066499C211yesmaximal, characteristic
4#13066457C212yesmaximal
5C11×#2571C211yesmaximal, characteristic
6C2×#66922C2211yescharacteristic
7C11×#400—22no—
8C11×#389—22no—
9C11×#384C2211yescharacteristic
10C11×#382—22no—
11C4×C11×C4⋊C4C2212yes—
12C2×#66874—22no—
13C2×C4⋊(C11⋊C8)C2212yes—
14C2×C4×C11⋊C8C2211yescharacteristic
15#10622167—22no—
16#10622167—22no—
17C22×Dic22—21no—
18C2×C11×C4⋊C4—22no—
19C2×C11×C4⋊C4—22no—
20C2×C11×C4⋊C4D412yes—
21C2×C11×C4⋊C4D412yes—
22C2×C11×C4⋊C4D412yes—
23C2×C42×C11—22no—
24C2×C42×C11C2311yescharacteristic
25C2×C4⋊Dic11—22no—
26C22×C11⋊C8—21no—
27C22×C11⋊C8—22no—
28#66922—22no—
29#66922—21no—
30#66922Q812yes—
31C11×#95—22no—
32C11×#95—24no—
33C11×#95—22no—
34#66874—44no—
35C4⋊(C11⋊C8)—22no—
36C4⋊(C11⋊C8)—22no—
37C4×C11⋊C8—22no—
38#10352—111nomaximal, Sylow
39C22×C4×C11—22no—
40C22×C4×C11—22no—
41C22×C4×C11—22no—
42C22×C4×C11C2×D411yescharacteristic
43C22×C4×C11C2×D412yes—
44C22×Dic11—41no—
45C2×Dic22—22no—
46C2×Dic22—42no—
47C2×Dic22—42no—
48C2×Dic22—41no—
49C11×C4⋊C4—22no—
50C11×C4⋊C4—22no—
51C11×C4⋊C4—22no—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—42no—
54C11×C4⋊C4—42no—
55C11×C4⋊C4—42no—
56C11×C4⋊C4—82no—
57C42×C11—42no—
58C42×C11—42no—
59C42×C11C2×Q811yescharacteristic
60C42×C11#4112yes—
61C42×C11#4111yescharacteristic
62C4⋊Dic11—24no—
63C4⋊Dic11—42no—
64C2×C11⋊C8—22no—
65C2×C11⋊C8—41no—
66C2×C11⋊C8—41no—
67C2×C11⋊C8—42no—
68C2×C11⋊C8—42no—
69C2×C11⋊C8—42no—
70#2571D1111yescharacteristic
71#1987—112no—
72#1956—111no—
73#1296—111no—
74#1279—112no—
75C23×C11#12011yescharacteristic
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—42no—
79C2×C4×C11—42no—
80C2×C4×C11—42no—
81C2×C4×C11—42no—
82C2×C4×C11—44no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11—42no—
86C2×C4×C11C22⋊Q811yescharacteristic
87C2×C4×C11C22⋊Q812yes—
88C2×C4×C11#12411yescharacteristic
89C2×C4×C11#12412yes—
90C2×C4×C11#13512yes—
91C2×C4×C11#13512yes—
92C2×C4×C11#13712yes—
93C2×C4×C11#13712yes—
94C2×Dic11—42no—
95C2×Dic11—81no—
96C2×Dic11—81no—
97Dic22—44no—
98Dic22—82no—
99C11⋊C8—42no—
100C11⋊C8—82no—
101C2×C4⋊Q8—111no—
102C2×C4⋊C8—112no—
103C2×#103—222no—
104C2×C4×C8—111no—
105#400—22no—
106#389—22no—
107#384C2×D1111yescharacteristic
108#382—22no—
109C4×C4⋊C4C2×D1112yes—
110#340—222no—
111#340—222no—
112C22×C11#39311yescharacteristic
113C22×C11#45212yes—
114C22×C11#45212yes—
115C22×C11#45311yescharacteristic
116C22×C11#45411yescharacteristic
117C4×C11—21no—
118C4×C11—21no—
119C4×C11—82no—
120C4×C11—82no—
121C4×C11—82no—
122C4×C11#47912yes—
123C4×C11#47912yes—
124C4×C11#48812yes—
125C4×C11#49112yes—
126Dic11—82no—
127C22×Q8—221no—
128C22×C8—221no—
129C22×C8—222no—
130C4⋊Q8—112no—
131C4⋊Q8—222no—
132C4⋊Q8—221no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—222no—
136C2×C4⋊C4C22⋊D1112yes—
137C2×C4⋊C4C22⋊D1112yes—
138C2×C4⋊C4C22⋊D1112yes—
139C2×C42—22no—
140C2×C42C22×D1111yescharacteristic
141C4⋊C8—222no—
142C4⋊C8—222no—
143#103—444no—
144C4×C8—222no—
145#95—22no—
146#95—24no—
147#95—22no—
148C2×C11#163011yescharacteristic
149C2×C11#163411yescharacteristic
150C2×C11#163812yes—
151C2×C11#202612yes—
152C2×C11#202711yescharacteristic
153C2×Q8—222no—
154C2×Q8—442no—
155C2×Q8—442no—
156C2×Q8—441no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—441no—
161C22×C4C2×C22⋊D1111yescharacteristic
162C22×C4C2×C22⋊D1112yes—
163C2×C8—222no—
164C2×C8—441no—
165C2×C8—441no—
166C2×C8—442no—
167C2×C8—442no—
168C2×C8—442no—
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—42no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—82no—
177C4⋊C4—224no—
178C4⋊C4—442no—
179C42—42no—
180C42—42no—
181C42Q8×D1111yescharacteristic
182C42#434312yes—
183C42#434311yescharacteristic
184C11#1035211yescharacteristic, complemented, Sylow
185C23#6700611yescharacteristic
186Q8—444no—
187Q8—882no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—44no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—442no—
199C2×C4—881no—
200C2×C4—881no—
201C2×C4#6699911yescharacteristic
202C2×C4#6699912yes—
203C2×C4#6700011yescharacteristic
204C2×C4#6700012yes—
205C2×C4#6700312yes—
206C2×C4#6700312yes—
207C2×C4#6700412yes—
208C2×C4#6700412yes—
209C8—442no—
210C8—882no—
211C22#1062284411yescharacteristic
212C22#1062285212yes—
213C22#1062285212yes—
214C22#1062285411yescharacteristic
215C22#1062285811yescharacteristic
216C4—21no—
217C4—21no—
218C4—82no—
219C4—82no—
220C4—82no—
221C4—882no—
222C4#1062267612yes—
223C4#1062267612yes—
224C4#1062268112yes—
225C4#1062268212yes—
226C2#1306773711yescharacteristic
227C2#1306776111yescharacteristic
228C2#1306778812yes—
229C2#1306976412yes—
230C2#1306976911yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2571C2
socle, prime radicalC23×C11#120
hypercenter#2571D11
hypocenterC11#10352
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2571

Complements

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

NH ≅ G/Ntype
184. C11#10352semidirect

Maximal subgroups

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

subgroupindex
#130695642
#130694172
#130664992
#130664572
C11×#25712
#1035211