Finite Group Databasebeta

← #14656269

Subgroups — #14656269

Order 2816.

526 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079961C211yesmaximal, characteristic, complemented
2#13078413C212yesmaximal
3#13067072C212yesmaximal, complemented
4#13066491C211yesmaximal, characteristic, complemented
5C11×#1954C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7#10623001C2212yes—
8C2×C11×C4⋊C8C2211yescharacteristic
9C2×C11×C22⋊C8—22no—
10C2×C4×C8×C11C2211yescharacteristic
11#10622828—22no—
12#10622729—22no—
13#10622622—24no—
14#10622621—22no—
15#10622620—22no—
16#10622577—22no—
17#10622537C2212yes—
18#10622463—22no—
19#10622462—22no—
20#10622094—24no—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11—21no—
23C22×C8×C11—21no—
24C22×C8×C11D412yes—
25C4×D4×C11—22no—
26C4×D4×C11—22no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C22⋊C4—21no—
29C2×C42×C11C2311yescharacteristic
30#66979—22no—
31#66977—22no—
32#66977—22no—
33C2×#4318—22no—
34C2×Dic44—22no—
35#66923—22no—
36#66922D412yes—
37#66922D412yes—
38C4×Dic22—22no—
39C4×Dic22—22no—
40C11×C4⋊C8—22no—
41C11×C22⋊C8—44no—
42C4×C8×C11—22no—
43#66896—24no—
44#66896—24no—
45#66882—22no—
46#66880—24no—
47#66872—24no—
48#66871—24no—
49C4⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)D414yes—
51#10258—111nomaximal, Sylow
52C24×C11—21no—
53C2×D4×C11—22no—
54C2×D4×C11—21no—
55C2×D4×C11—22no—
56C2×D4×C11Q1612yescomplemented
57C22×C4×C11—21no—
58C22×C4×C11—42no—
59C22×C4×C11—42no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11#4111yescharacteristic
65C2×Dic22—22no—
66C2×Dic22—22no—
67C2×C8×C11—22no—
68C2×C8×C11—22no—
69C2×C8×C11—42no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C11×C4⋊C4—22no—
73C11×C22⋊C4—42no—
74C42×C11C2×D412yes—
75C42×C11C2×D412yes—
76C22⋊Dic11—42no—
77C4⋊Dic11—22no—
78C4⋊Dic11—22no—
79C4⋊Dic11—22no—
80C4⋊Dic11—22no—
81Dic11⋊C4—42no—
82Dic11⋊C4—42no—
83C4×Dic11—42no—
84#4318—42no—
85#4318—42no—
86C2×C11⋊C8—24no—
87Dic44—82no—
88#3249—111no—
89#3077—112no—
90#1954D1111yescharacteristic
91#1493—112no—
92#1292—111no—
93C23×C11—22no—
94C23×C11—42no—
95C23×C11—42no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11#12111yescharacteristic
99D4×C11—24no—
100D4×C11—42no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—41no—
104C2×C4×C11—42no—
105C2×C4×C11—41no—
106C2×C4×C11—82no—
107C2×C4×C11—81no—
108C2×C4×C11—81no—
109C2×C4×C11#12012yes—
110C2×C4×C11#12011yescharacteristic
111C2×C4×C11#12112yes—
112C2×C4×C11#12711yescharacteristic
113C2×C4×C11C2×Q1611yescharacteristic
114C2×C4×C11#13511yescharacteristic
115C2×C4×C11#13712yes—
116C2×Dic11—42no—
117C2×Dic11—42no—
118Dic22—44no—
119Dic22—42no—
120Dic22—42no—
121C8×C11—42no—
122C8×C11—42no—
123C11⋊C8—44no—
124#533—112no—
125C2×C4×D4C2×D1111yescharacteristic
126#478—224no—
127#477—222no—
128#476—222no—
129#474—222no—
130#467—222no—
131#462—222no—
132#428—222no—
133#423—112no—
134C2×C4⋊C8C2×D1111yescharacteristic
135#418—222no—
136C2×C22⋊C8—22no—
137C2×C4×C8C2×D1111yescharacteristic
138Q8⋊C8—224no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—44no—
142C22×C11—42no—
143C22×C11—82no—
144C22×C11—81no—
145C22×C11—81no—
146C22×C11#39211yescharacteristic
147C22×C11#46711yescharacteristic
148C22×C11#47011yescharacteristic
149C4×C11—21no—
150C4×C11—22no—
151C4×C11—81no—
152C4×C11#45112yes—
153C4×C11#45212yes—
154C4×C11#45311yescharacteristic
155C4×C11#45411yescharacteristic
156Dic11—82no—
157Dic11—82no—
158C22×D4D4411yescharacteristic
159C23×C4—21no—
160C2×Q16—222no—
161C2×M16—222no—
162C22×C8—21no—
163C22×C8C22⋊D1112yes—
164C4⋊Q8—112no—
165C4⋊Q8—112no—
166#125—222no—
167C22⋊Q8—222no—
168C22⋊Q8—222no—
169C4×Q8—222no—
170C4×Q8—222no—
171C4×D4—22no—
172C4×D4—22no—
173#117—222no—
174C2×C4⋊C4D4411yescharacteristic
175C2×C22⋊C4—21no—
176C2×C42C22×D1111yescharacteristic
177#107—224no—
178#107—222no—
179#106—224no—
180C4⋊C8—22no—
181C4⋊C8—114no—
182C4⋊C8—222no—
183#103—224no—
184#102—224no—
185#102—224no—
186C22⋊C8—44no—
187C4×C8—22no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11—82no—
191C2×C11#200111yescharacteristic
192C2×C11#200611yescharacteristic
193C2×C11#201711yescharacteristic
194C24—21no—
195C2×Q8—222no—
196C2×Q8—222no—
197C2×D4—22no—
198C2×D4—21no—
199C2×D4—22no—
200C2×D4Dic4412yescomplemented
201C22×C4—21no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4C2×D4411yescharacteristic
207C22×C4#433911yescharacteristic
208C22×C4C2×C22⋊D1111yescharacteristic
209Q16—882no—
210M16—442no—
211M16—442no—
212C2×C8—22no—
213C2×C8—22no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—42no—
217C2×C8—224no—
218C4⋊C4—22no—
219C4⋊C4—222no—
220C4⋊C4—222no—
221C4⋊C4—222no—
222C4⋊C4—222no—
223C4⋊C4—442no—
224C4⋊C4—442no—
225C22⋊C4—42no—
226C22⋊C4—442no—
227C42—442no—
228C42D4×D1112yes—
229C42D4×D1112yes—
230C11#1025811yescharacteristic, complemented, Sylow
231C23—22no—
232C23—42no—
233C23—42no—
234C23—41no—
235C23—41no—
236C23#6698311yescharacteristic
237Q8—444no—
238Q8—442no—
239Q8—442no—
240D4—24no—
241D4—42no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—82no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—442no—
251C2×C4—442no—
252C2×C4#6693512yes—
253C2×C4#6693712yes—
254C2×C4#6695711yescharacteristic
255C2×C4C2×Dic4411yescharacteristic
256C2×C4#6696212yes—
257C2×C4#6699011yescharacteristic
258C2×C4#6699311yescharacteristic
259C8—42no—
260C8—42no—
261C8—444no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—42no—
266C22—82no—
267C22—81no—
268C22—81no—
269C22#1062257311yescharacteristic
270C22#1062272911yescharacteristic
271C22#1062275011yescharacteristic
272C4—21no—
273C4—22no—
274C4—81no—
275C4—882no—
276C4—882no—
277C4#1062234612yes—
278C4#1062235212yes—
279C4#1062267511yescharacteristic
280C4#1062269011yescharacteristic
281C2—21no—
282C2—21no—
283C2—82no—
284C2#1306962611yescharacteristic
285C2#1306965711yescharacteristic
286C2#1306972011yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1954C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#1954D11
hypocenterC11#10258
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. #13079961C2semidirect
3. #13067072C2semidirect
4. #13066491C2semidirect
56. C2×D4×C11Q16semidirect
200. C2×D4Dic44semidirect
230. C11#10258semidirect

Maximal subgroups

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

subgroupindex
#130799612
#130784132
#130670722
#130664912
C11×#19542
#1025811