Finite Group Databasebeta

← #14651376

Subgroups — #14651376

Order 2816.

400 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 97 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#13078997C211yesmaximal, characteristic
2#13077717C211yesmaximal, characteristic
3#13067353C211yesmaximal, characteristic
4#13067302C211yesmaximal, characteristic
5#13067300C211yesmaximal, characteristic
6#13066506C211yesmaximal, characteristic
7C11×#1299C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13#10622733—22no—
14#10622538C2211yescharacteristic
15#10622537C2211yescharacteristic
16#10622444—21no—
17#10622443—21no—
18#10622333—22no—
19#10622316C414yes—
20#10622294—21no—
21#10622294—21no—
22#10622292—21no—
23C8×Dic22—21no—
24#10622124—21no—
25#10622124—21no—
26#10622124—21no—
27#10622120—21no—
28#10622120—21no—
29#10622120—21no—
30C22×Dic22—21no—
31C2×C11×M16—21no—
32C2×C11×M16—21no—
33C2×C42×C11C2311yescharacteristic
34#66979D412yes—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37#66977—21no—
38#66977—21no—
39C2×#4318—21no—
40#66923C2×C412yes—
41#66922—21no—
42#66922—21no—
43#66922—21no—
44#66922C2×C412yes—
45#66922D411yescharacteristic
46#66922D411yescharacteristic
47C4×Dic22—21no—
48C4×Dic22—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8D411yescharacteristic
52C11×C4⋊C8D411yescharacteristic
53C11×C22⋊C8—21no—
54C11×#97C2×C412yes—
55C4×C8×C11—21no—
56C4×C8×C11—21no—
57C22⋊(C11⋊C8)—21no—
58#66880—24no—
59#66880—24no—
60#66879—22no—
61Dic11⋊C8—22no—
62Dic11⋊C8—22no—
63C8×Dic11—22no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)D411yescharacteristic
67C4⋊(C11⋊C8)D411yescharacteristic
68C4×C11⋊C8—21no—
69#9436—111nomaximal, Sylow
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×Dic11—41no—
74C2×Dic22—22no—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—42no—
78C2×Dic22—42no—
79C2×Dic22—41no—
80C11×M16—41no—
81C11×M16—41no—
82C11×M16—81no—
83C2×C8×C11—22no—
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C2×C8×C11—41no—
87C42×C11C22×C411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C22⋊Dic11—22no—
92C4⋊Dic11—22no—
93C4⋊Dic11—22no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11C22⋊C412yes—
99C4⋊Dic11C22⋊C412yes—
100Dic11⋊C4—22no—
101Dic11⋊C4—22no—
102C4×Dic11—22no—
103#4318—81no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—41no—
107#3139—111no—
108#2986—111no—
109#1561—111no—
110#1549—111no—
111#1549—111no—
112#1299—111no—
113#1299D1111yescharacteristic
114C23×C11#12311yescharacteristic
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11C2×C22⋊C411yescharacteristic
122C2×C4×C11C4×D411yescharacteristic
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×Dic11—22no—
128C2×Dic11—22no—
129C2×Dic11—42no—
130C2×Dic11—82no—
131Dic22—41no—
132Dic22—41no—
133Dic22—41no—
134Dic22—41no—
135Dic22—44no—
136Dic22—81no—
137Dic22—81no—
138C8×C11—42no—
139C8×C11—41no—
140C8×C11—41no—
141C8×C11—81no—
142C11⋊C8—41no—
143C11⋊C8—41no—
144C11⋊C8—81no—
145#533—111no—
146C2×C4⋊Q8—111no—
147#491—114no—
148#487—221no—
149#487—221no—
150#446—221no—
151#446—221no—
152C8×Q8—221no—
153C8×Q8—221no—
154#433—222no—
155#431—111no—
156#431C2×D1111yescharacteristic
157#423—111no—
158#423C2×D1111yescharacteristic
159#419—222no—
160C4×M16C2×D1111yescharacteristic
161#332—221no—
162#332—221no—
163#332—221no—
164#332—221no—
165#332—221no—
166#332—221no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11#38611yescharacteristic
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11#45411yescharacteristic
175C4×C11#45411yescharacteristic
176C4×C11#47111yescharacteristic
177C4×C11#47111yescharacteristic
178C4×C11#47311yescharacteristic
179C4×C11#47311yescharacteristic
180Dic11—42no—
181Dic11—42no—
182Dic11—82no—
183C22×Q8—221no—
184C2×M16—21no—
185C2×M16—21no—
186C2×M16—221no—
187C4⋊Q8—112no—
188C4⋊Q8—111no—
189C4⋊Q8—111no—
190C4⋊Q8—221no—
191C4⋊Q8—221no—
192C4⋊Q8—221no—
193#125—112no—
194C22⋊Q8—221no—
195C22⋊Q8—221no—
196C4×Q8—221no—
197C4×Q8—221no—
198#117—112no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C42C22×D1111yescharacteristic
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—111no—
205C4⋊C8—111no—
206C4⋊C8—222no—
207C4⋊C8—222no—
208C4⋊C8—221no—
209C4⋊C8—221no—
210C4⋊C8D4411yescharacteristic
211C4⋊C8D4411yescharacteristic
212#103—224no—
213#103—224no—
214C22⋊C8—21no—
215C22⋊C8—221no—
216#97—222no—
217#97C4×D1112yes—
218C4×C8—21no—
219C4×C8—21no—
220C4×C8—222no—
221C4×C8—221no—
222C2×C11—41no—
223C2×C11#188811yescharacteristic
224C2×C11#190811yescharacteristic
225C2×C11#190811yescharacteristic
226C2×Q8—221no—
227C2×Q8—221no—
228C2×Q8—222no—
229C2×Q8—442no—
230C2×Q8—442no—
231C2×Q8—441no—
232C22×C4—441no—
233C22×C4#433911yescharacteristic
234C22×C4D4×D1111yescharacteristic
235C22×C4#434311yescharacteristic
236M16—41no—
237M16—41no—
238M16—81no—
239M16—881no—
240C2×C8—22no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—41no—
244C2×C8—221no—
245C2×C8—221no—
246C2×C8—441no—
247C4⋊C4—112no—
248C4⋊C4—112no—
249C4⋊C4—222no—
250C4⋊C4—221no—
251C4⋊C4—222no—
252C4⋊C4—221no—
253C4⋊C4—222no—
254C4⋊C4—222no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C22⋊C4—222no—
258C42—222no—
259C42C2×C4×D1111yescharacteristic
260C42C2×D4411yescharacteristic
261C42D4×D1111yescharacteristic
262C42D4×D1111yescharacteristic
263C11#943611yescharacteristic, complemented, Sylow
264C23#6694711yescharacteristic
265Q8—444no—
266Q8—441no—
267Q8—441no—
268Q8—441no—
269Q8—441no—
270Q8—881no—
271Q8—881no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—222no—
279C2×C4—222no—
280C2×C4—442no—
281C2×C4—882no—
282C2×C4C4×D4411yescharacteristic
283C2×C4C22⋊C4×D1111yescharacteristic
284C2×C4#6693511yescharacteristic
285C2×C4#6693711yescharacteristic
286C2×C4#6694611yescharacteristic
287C2×C4#6694811yescharacteristic
288C8—42no—
289C8—41no—
290C8—41no—
291C8—81no—
292C8—441no—
293C8—441no—
294C8—881no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22#1062227811yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—442no—
303C4—442no—
304C4—882no—
305C4#1062236111yescharacteristic
306C4#1062236811yescharacteristic
307C4#1062244011yescharacteristic
308C4#1062244011yescharacteristic
309C4#1062250911yescharacteristic
310C4#1062251111yescharacteristic
311C2—41no—
312C2#1306901811yescharacteristic
313C2#1306913011yescharacteristic
314C2#1306913211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1299C2
socleC22×C11#386
prime radicalC23×C11#123
cosocleC2×C42×C11C23
hypercenter#1299D11
hypocenterC11#9436
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1299

Complements

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

NH ≅ G/Ntype
263. C11#9436semidirect

Maximal subgroups

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

subgroupindex
#130789972
#130777172
#130673532
#130673022
#130673002
#130665062
C11×#12992
#943611