Finite Group Databasebeta

← #14666548

Subgroups — #14666548

Order 2816.

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

normal subgroups only

This group has 460 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#13069777C211yesmaximal, characteristic, complemented
2#13067555C212yesmaximal, complemented
3#13066619C212yesmaximal, complemented
4#13066550C211yesmaximal, characteristic, complemented
5C11×#2733C211yesmaximal, characteristic
6C2×C11×#124—21no—
7#10623031C2211yescharacteristic
8C11×#394C2212yes—
9C11×#392—22no—
10C11×#391C2211yescharacteristic
11C11×#390—21no—
12C11×#388—22no—
13#10622838—21no—
14#10622831—22no—
15#10622168C2211yescharacteristic
16#10622166C2212yes—
17#10622161—21no—
18#10622090—22no—
19C22×Q8×C11D411yescharacteristic
20C22×D4×C11—21no—
21C22×D4×C11—21no—
22C22×D4×C11D412yes—
23C11×#124—42no—
24C11×#124—42no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4C2311yescharacteristic
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4—22no—
31C2×C42×C11—21no—
32C2×C42×C11D411yescharacteristic
33C2×#4324—42no—
34#66979—21no—
35#66977—22no—
36C2×#4318—21no—
37#66943—41no—
38#66941—41no—
39C11×#95—22no—
40C11×#95D412yes—
41#66899—41no—
42#66899—41no—
43#66896—42no—
44C22⋊(C11⋊C8)—22no—
45#12212—111nomaximal, Sylow
46C24×C11—22no—
47C2×Q8×C11—21no—
48C2×Q8×C11—41no—
49C2×Q8×C11—41no—
50C2×Q8×C11SD1612yescomplemented
51C2×D4×C11—42no—
52C2×D4×C11—42no—
53C2×D4×C11—42no—
54C2×D4×C11—82no—
55C2×D4×C11—81no—
56C2×D4×C11—81no—
57C2×D4×C11—81no—
58C2×D4×C11—81no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—22no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D412yes—
64C2×Dic22—22no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—81no—
67C11×C22⋊C4—44no—
68C11×C22⋊C4—44no—
69C11×C22⋊C4—42no—
70C11×C22⋊C4—42no—
71C11×C22⋊C4—82no—
72C42×C11—42no—
73C42×C11—41no—
74C22⋊Dic11—41no—
75#4324—84no—
76C4⋊Dic11—22no—
77C4⋊Dic11—21no—
78C4⋊Dic11—21no—
79Dic11⋊C4—42no—
80C4×Dic11—41no—
81#4318—41no—
82#4318—41no—
83C2×C11⋊C8—42no—
84C2×C11⋊C8—41no—
85#2733D1111yescharacteristic
86#2028—111no—
87#1599—112no—
88#1345—112no—
89#1319—111no—
90C23×C11—42no—
91C23×C11—42no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11—42no—
95C23×C11—42no—
96C23×C11—42no—
97C23×C11#12011yescharacteristic
98Q8×C11—42no—
99Q8×C11—81no—
100D4×C11—44no—
101D4×C11—82no—
102D4×C11—84no—
103D4×C11—84no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11C2×SD1611yescharacteristic
118C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
119C2×Dic11—41no—
120C2×Dic11—41no—
121Dic22—82no—
122C11⋊C8—81no—
123C11⋊C8—82no—
124#544—111no—
125C2×#124—21no—
126#450—222no—
127#419—221no—
128#394C2×D1112yes—
129#392—22no—
130#391C2×D1111yescharacteristic
131#390—21no—
132#388—22no—
133#343—111no—
134#339—221no—
135#328—222no—
136#324—112no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—82no—
140C22×C11—82no—
141C22×C11—82no—
142C22×C11—82no—
143C22×C11—82no—
144C22×C11—82no—
145C22×C11—82no—
146C22×C11#45011yescharacteristic
147C22×C11#45511yescharacteristic
148C22×C11B(4,𝔽2)11yescharacteristic
149C4×C11—21no—
150C4×C11—21no—
151C4×C11—42no—
152C4×C11—42no—
153C4×C11—42no—
154C4×C11—82no—
155Dic11—81no—
156Dic11—81no—
157C22×Q8C22⋊D1111yescharacteristic
158C22×D4—21no—
159C22×D4—21no—
160C22×D4C22⋊D1112yes—
161C2×SD16—442no—
162C2×M16—221no—
163C4⋊Q8—441no—
164#125—441no—
165#124—42no—
166#124—42no—
167C22⋊Q8—222no—
168#117—221no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4C22×D1111yescharacteristic
171C2×C22⋊C4—22no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C42—21no—
176C2×C42C22⋊D1111yescharacteristic
177#103—441no—
178#103—441no—
179#102—442no—
180C22⋊C8—222no—
181#95—22no—
182#95C22⋊D1112yes—
183C2×C11—21no—
184C2×C11—21no—
185C2×C11—162no—
186C2×C11#160111yescharacteristic
187C2×C11#219911yescharacteristic
188C2×C11#220411yescharacteristic
189C24—22no—
190C2×Q8—21no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8—222no—
194C2×Q8#432412yescomplemented
195C2×D4—42no—
196C2×D4—42no—
197C2×D4—42no—
198C2×D4—82no—
199C2×D4—81no—
200C2×D4—81no—
201C2×D4—81no—
202C2×D4—81no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4C2×C22⋊D1111yescharacteristic
207C22×C4C2×C22⋊D1112yes—
208SD16—884no—
209M16—441no—
210M16—441no—
211C2×C8—442no—
212C2×C8—441no—
213C4⋊C4—41no—
214C4⋊C4—81no—
215C4⋊C4—222no—
216C4⋊C4—221no—
217C4⋊C4—221no—
218C4⋊C4—442no—
219C22⋊C4—44no—
220C22⋊C4—44no—
221C22⋊C4—42no—
222C22⋊C4—42no—
223C22⋊C4—82no—
224C22⋊C4—441no—
225C42—41no—
226C42—42no—
227C42—441no—
228C11#1221211yescharacteristic, complemented, Sylow
229C23—42no—
230C23—42no—
231C23—42no—
232C23—42no—
233C23—42no—
234C23—42no—
235C23—42no—
236C23#6700611yescharacteristic
237Q8—42no—
238Q8—81no—
239Q8—882no—
240D4—44no—
241D4—82no—
242D4—84no—
243D4—84no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—441no—
258C2×C4—441no—
259C2×C4#6698511yescharacteristic
260C2×C4C2×#432411yescharacteristic
261C8—881no—
262C8—882no—
263C22—21no—
264C22—21no—
265C22—82no—
266C22—82no—
267C22—82no—
268C22—82no—
269C22—82no—
270C22—82no—
271C22—82no—
272C22#1062283111yescharacteristic
273C22#1062285511yescharacteristic
274C22#1062285711yescharacteristic
275C4—21no—
276C4—21no—
277C4—42no—
278C4—42no—
279C4—42no—
280C4—82no—
281C4—881no—
282C4—881no—
283C2—21no—
284C2—21no—
285C2—162no—
286C2#1306756811yescharacteristic
287C2#1307061711yescharacteristic
288C2#1307064211yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
Fitting, prime radicalC11×#2733C2
socleC22×C11B(4,𝔽2)
hypercenter#2733D11
hypocenterC11#12212
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2733

Complements

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

NH ≅ G/Ntype
1. #13069777C2semidirect
2. #13067555C2semidirect
3. #13066619C2semidirect
4. #13066550C2semidirect
50. C2×Q8×C11SD16semidirect
194. C2×Q8#4324semidirect
228. C11#12212semidirect

Maximal subgroups

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

subgroupindex
#130697772
#130675552
#130666192
#130665502
C11×#27332
#1221211