Finite Group Databasebeta

← #14666597

Subgroups — #14666597

Order 2816.

392 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 63 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#13069772C211yesmaximal, characteristic
2#13067657C212yesmaximal, complemented
3#13066643C212yesmaximal, complemented
4#13066548C211yesmaximal, characteristic
5C11×#2804C211yesmaximal, characteristic
6#10623031C2211yescharacteristic
7C11×#400C2212yes—
8C11×#393—22no—
9C11×#391—21no—
10C11×#390C2211yescharacteristic
11C11×#386—21no—
12C11×#385—22no—
13#10622828—21no—
14#10622583—22no—
15#10622168C2211yescharacteristic
16#10622166C2212yes—
17#10622161—21no—
18#10622090—22no—
19C22×Q8×C11—21no—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11—21no—
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4D412yes—
24C2×C11×C4⋊C4C2311yescharacteristic
25C2×C11×C22⋊C4—22no—
26C2×C11×C22⋊C4—22no—
27C2×C11×C22⋊C4—21no—
28C2×C42×C11D411yescharacteristic
29#66979—21no—
30#66977—22no—
31C2×#4318—21no—
32#66943—41no—
33#66941—41no—
34C11×#95—22no—
35C11×#95—22no—
36C11×#95—22no—
37C11×#95D412yes—
38#66896—41no—
39#66896—41no—
40C22⋊(C11⋊C8)—22no—
41#66874—42no—
42#66871—42no—
43#12221—111nomaximal, Sylow
44C24×C11—21no—
45C2×Q8×C11—42no—
46C2×Q8×C11—81no—
47C2×Q8×C11—81no—
48C2×D4×C11—21no—
49C2×D4×C11—41no—
50C2×D4×C11—41no—
51C2×D4×C11Q1612yes—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—82no—
56C22×C4×C11—81no—
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D412yes—
59C2×Dic22—22no—
60C11×C4⋊C4—41no—
61C11×C4⋊C4—42no—
62C11×C4⋊C4—81no—
63C11×C22⋊C4—44no—
64C11×C22⋊C4—82no—
65C11×C22⋊C4—81no—
66C42×C11—41no—
67C22⋊Dic11—41no—
68C4⋊Dic11—22no—
69C4⋊Dic11—21no—
70C4⋊Dic11—21no—
71Dic11⋊C4—42no—
72C4×Dic11—41no—
73#4318—41no—
74#4318—41no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—41no—
77#2804D1111yescharacteristic
78#2027—111no—
79#1617—112no—
80#1353—112no—
81#1318—111no—
82C23×C11—22no—
83C23×C11—42no—
84C23×C11—42no—
85C23×C11—41no—
86C23×C11—41no—
87C23×C11#12011yescharacteristic
88Q8×C11—84no—
89D4×C11—42no—
90D4×C11—81no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—41no—
96C2×C4×C11—41no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—84no—
105C2×C4×C11C2×Q1611yescharacteristic
106C2×C4×C11#13711yescharacteristic
107C2×Dic11—41no—
108C2×Dic11—41no—
109Dic22—82no—
110C11⋊C8—81no—
111C11⋊C8—82no—
112#544—111no—
113#484—222no—
114#418—221no—
115#400C2×D1112yes—
116#393—22no—
117#391—21no—
118#390C2×D1111yescharacteristic
119#386—21no—
120#385—22no—
121#343—111no—
122#339—221no—
123#328—222no—
124#324—112no—
125C22×C11—21no—
126C22×C11—21no—
127C22×C11—44no—
128C22×C11—42no—
129C22×C11—82no—
130C22×C11—81no—
131C22×C11—81no—
132C22×C11#45111yescharacteristic
133C22×C11#45511yescharacteristic
134C22×C11B(4,𝔽2)11yescharacteristic
135C4×C11—21no—
136C4×C11—21no—
137C4×C11—42no—
138C4×C11—42no—
139C4×C11—82no—
140C4×C11—82no—
141Dic11—81no—
142Dic11—81no—
143C22×Q8—21no—
144C22×D4C22⋊D1111yescharacteristic
145C23×C4—21no—
146C2×M16—221no—
147C4⋊Q8—441no—
148#125—441no—
149C22⋊Q8—222no—
150#117—221no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4C22⋊D1112yes—
153C2×C4⋊C4C22×D1111yescharacteristic
154C2×C22⋊C4—22no—
155C2×C22⋊C4—22no—
156C2×C22⋊C4—21no—
157C2×C42C22⋊D1111yescharacteristic
158#107—442no—
159#103—442no—
160#102—441no—
161#102—441no—
162C22⋊C8—222no—
163#95—22no—
164#95—22no—
165#95—22no—
166#95C22⋊D1112yes—
167C2×C11—21no—
168C2×C11—21no—
169C2×C11—82no—
170C2×C11#160211yescharacteristic
171C2×C11#219811yescharacteristic
172C2×C11#220211yescharacteristic
173C24—21no—
174C2×Q8—42no—
175C2×Q8—81no—
176C2×Q8—81no—
177C2×Q8—222no—
178C2×D4—21no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4#432612yes—
182C22×C4—21no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—82no—
186C22×C4—81no—
187C22×C4C2×C22⋊D1111yescharacteristic
188C22×C4C2×C22⋊D1112yes—
189M16—441no—
190M16—441no—
191C2×C8—442no—
192C2×C8—441no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—81no—
196C4⋊C4—221no—
197C4⋊C4—221no—
198C4⋊C4—222no—
199C4⋊C4—442no—
200C22⋊C4—44no—
201C22⋊C4—82no—
202C22⋊C4—81no—
203C22⋊C4—441no—
204C42—41no—
205C42—441no—
206C11#1222111yescharacteristic, complemented, Sylow
207C23—22no—
208C23—42no—
209C23—42no—
210C23—41no—
211C23—41no—
212C23#6700611yescharacteristic
213Q8—84no—
214Q8—882no—
215D4—42no—
216D4—81no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—84no—
231C2×C4—441no—
232C2×C4—441no—
233C2×C4#6699511yescharacteristic
234C2×C4C2×#432611yescharacteristic
235C8—881no—
236C8—882no—
237C22—21no—
238C22—21no—
239C22—44no—
240C22—42no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22#1062284111yescharacteristic
245C22#1062285511yescharacteristic
246C22#1062285711yescharacteristic
247C4—21no—
248C4—21no—
249C4—42no—
250C4—42no—
251C4—82no—
252C4—82no—
253C4—881no—
254C4—881no—
255C2—21no—
256C2—21no—
257C2—82no—
258C2#1306757311yescharacteristic
259C2#1307061211yescharacteristic
260C2#1307063311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2804C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D4×C11D4
hypercenter#2804D11
hypocenterC11#12221
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2804

Complements

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

NH ≅ G/Ntype
2. #13067657C2semidirect
3. #13066643C2semidirect
206. C11#12221semidirect

Maximal subgroups

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

subgroupindex
#130697722
#130676572
#130666432
#130665482
C11×#28042
#1222111