Finite Group Databasebeta

← #14647915

Subgroups — #14647915

Order 2816.

364 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 109 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#13077556C211yesmaximal, characteristic
2#13069339C211yesmaximal, characteristic
3#13067391C211yesmaximal, characteristic
4#13067116C211yesmaximal, characteristic
5#13067020C211yesmaximal, characteristic
6#13066518C211yesmaximal, characteristic
7C11×#1281C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C2×C11×#97C2211yescharacteristic
12#10622715—21no—
13#10622714—21no—
14C2×Dic11⋊C8—21no—
15C4×C4⋊Dic11C2211yescharacteristic
16#10622537C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18#10622314—22no—
19#10622314—22no—
20#10622188—21no—
21#10622105C412yes—
22#10622105C412yes—
23#10622096—22no—
24#10622094—22no—
25C22×C8×C11D411yescharacteristic
26C22×C8×C11D411yescharacteristic
27C2×C42×C11C2311yescharacteristic
28#66979—21no—
29C2×C4⋊Dic11—21no—
30#66977—21no—
31#66977C2×C412yes—
32C2×C4×Dic11—21no—
33C2×#4318—21no—
34C22×C11⋊C8—21no—
35#66923—21no—
36#66922Q811yescharacteristic
37#66922Q811yescharacteristic
38C4×Dic22—21no—
39C4×Dic22D412yes—
40C11×C4⋊C8—21no—
41C11×C4⋊C8—21no—
42C11×C22⋊C8—21no—
43C11×C22⋊C8C2×C412yes—
44C11×#97—21no—
45C11×#97—21no—
46C4×C8×C11—21no—
47C4×C8×C11—21no—
48C11⋊#95C2×C411yescharacteristic
49C11⋊#95C2×C411yescharacteristic
50#66879—22no—
51Dic11⋊C8—24no—
52Dic11⋊C8—42no—
53C8×Dic11—22no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)D412yes—
58#8879—111nomaximal, Sylow
59C22×C4×C11C22×C411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11#4111yescharacteristic
62C22×Dic11—21no—
63C22×Dic11—21no—
64C2×Dic22—21no—
65C2×Dic22C4⋊C412yes—
66C2×C8×C11—22no—
67C2×C8×C11—21no—
68C2×C8×C11—21no—
69C2×C8×C11—21no—
70C2×C8×C11—21no—
71C2×C8×C11—21no—
72C2×C8×C11—41no—
73C2×C8×C11Q1612yes—
74C42×C11C2×D411yescharacteristic
75C42×C11C2×D411yescharacteristic
76C42×C11C2×Q811yescharacteristic
77C42×C11#4111yescharacteristic
78C22⋊Dic11—22no—
79C4⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—42no—
83C4⋊Dic11C4⋊C412yes—
84Dic11⋊C4—22no—
85Dic11⋊C4—22no—
86C4×Dic11—22no—
87C4×Dic11—41no—
88C4×Dic11—41no—
89#4318—41no—
90#4318—41no—
91C2×C11⋊C8—22no—
92C2×C11⋊C8—41no—
93C2×C11⋊C8—41no—
94C2×C11⋊C8—41no—
95#2961—111no—
96#1940—111no—
97#1571—111no—
98#1503—111no—
99#1481—111no—
100#1303—111no—
101#1281D1111yescharacteristic
102C23×C11C4×D411yescharacteristic
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11C2×C4⋊C411yescharacteristic
106C2×C4×C11C4×D411yescharacteristic
107C2×C4×C11#12011yescharacteristic
108C2×C4×C11C22⋊Q811yescharacteristic
109C2×C4×C11C22⋊Q811yescharacteristic
110C2×C4×C11#12311yescharacteristic
111C2×C4×C11C2×Q1611yescharacteristic
112C2×C4×C11#13511yescharacteristic
113C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C11#13711yescharacteristic
115C2×Dic11—22no—
116C2×Dic11—22no—
117C2×Dic11—22no—
118C2×Dic11—41no—
119C2×Dic11—41no—
120C2×Dic11—41no—
121C2×Dic11—41no—
122C2×Dic11—41no—
123Dic22—42no—
124Dic22—81no—
125C8×C11—22no—
126C8×C11—42no—
127C8×C11—41no—
128C8×C11—81no—
129C11⋊C8—42no—
130C11⋊C8—81no—
131#533—111no—
132#446—222no—
133#446—222no—
134#431C2×D1111yescharacteristic
135#431C2×D1111yescharacteristic
136#424—221no—
137#423—111no—
138C2×C4⋊C8—111no—
139C2×C4⋊C8—221no—
140#405—221no—
141C2×#97C2×D1111yescharacteristic
142C4×C4⋊C4—111no—
143#336—221no—
144#335—222no—
145#328—112no—
146#328—112no—
147Q8⋊C8—222no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11#38511yescharacteristic
151C22×C11C4×Q1611yescharacteristic
152C22×C11#44011yescharacteristic
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—21no—
156C4×C11—21no—
157C4×C11#44911yescharacteristic
158C4×C11#45111yescharacteristic
159C4×C11#47711yescharacteristic
160C4×C11#47911yescharacteristic
161Dic11—42no—
162Dic11—42no—
163Dic11—42no—
164Dic11—81no—
165C2×M16—221no—
166C22×C8—221no—
167C22×C8D4411yescharacteristic
168C22×C8D4411yescharacteristic
169C4⋊Q8—111no—
170C4⋊Q8—111no—
171#125—221no—
172C22⋊Q8—112no—
173C22⋊Q8—221no—
174C4×Q8—112no—
175C4×Q8—221no—
176#117—221no—
177C2×C4⋊C4—221no—
178C2×C42—221no—
179C2×C42C22×D1111yescharacteristic
180C4⋊C8—21no—
181C4⋊C8—21no—
182C4⋊C8—112no—
183C4⋊C8—224no—
184C4⋊C8—221no—
185C4⋊C8—221no—
186C4⋊C8—221no—
187C4⋊C8—442no—
188C22⋊C8—21no—
189C22⋊C8C4×D1112yes—
190#97—21no—
191#97—21no—
192#97—222no—
193C4×C8—21no—
194C4×C8—21no—
195C4×C8—222no—
196#95—111no—
197#95—111no—
198C2×C11—21no—
199C2×C11—21no—
200C2×C11#186111yescharacteristic
201C2×C11#186311yescharacteristic
202C2×C11#186811yescharacteristic
203C2×Q8—112no—
204C2×Q8—221no—
205C22×C4—221no—
206C22×C4—221no—
207C22×C4C2×C4×D1111yescharacteristic
208C22×C4C2×D4411yescharacteristic
209C22×C4#433911yescharacteristic
210M16—441no—
211M16—441no—
212C2×C8—21no—
213C2×C8—21no—
214C2×C8—22no—
215C2×C8—21no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—41no—
219C2×C8—222no—
220C2×C8—441no—
221C2×C8—441no—
222C2×C8—441no—
223C2×C8Dic4412yes—
224C4⋊C4—112no—
225C4⋊C4—222no—
226C4⋊C4—222no—
227C4⋊C4—221no—
228C4⋊C4—221no—
229C4⋊C4—221no—
230C4⋊C4—442no—
231C22⋊C4—222no—
232C42—222no—
233C42—441no—
234C42—441no—
235C42D4×D1111yescharacteristic
236C42D4×D1111yescharacteristic
237C42#434111yescharacteristic
238C42Q8×D1111yescharacteristic
239C11#887911yescharacteristic, complemented, Sylow
240C23C4×D4411yescharacteristic
241Q8—442no—
242Q8—881no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—222no—
246C2×C4—222no—
247C2×C4—222no—
248C2×C4—441no—
249C2×C4—441no—
250C2×C4—441no—
251C2×C4—441no—
252C2×C4—441no—
253C2×C4(C22⋊D11)⋊C411yescharacteristic
254C2×C4#6693511yescharacteristic
255C2×C4#6693611yescharacteristic
256C2×C4C4⋊C4×D1111yescharacteristic
257C2×C4#6694911yescharacteristic
258C2×C4#6695011yescharacteristic
259C2×C4#6695711yescharacteristic
260C2×C4C2×Dic4411yescharacteristic
261C2×C4#6696111yescharacteristic
262C2×C4#6696211yescharacteristic
263C8—22no—
264C8—42no—
265C8—41no—
266C8—81no—
267C8—442no—
268C8—881no—
269C22—21no—
270C22—21no—
271C22#1062228111yescharacteristic
272C22C4×Dic4411yescharacteristic
273C22#1062232311yescharacteristic
274C4—21no—
275C4—21no—
276C4—21no—
277C4—21no—
278C4—442no—
279C4—442no—
280C4—442no—
281C4—881no—
282C4#1062234711yescharacteristic
283C4#1062235211yescharacteristic
284C4#1062244211yescharacteristic
285C4#1062246311yescharacteristic
286C2—21no—
287C2—21no—
288C2#1306885911yescharacteristic
289C2#1306887311yescharacteristic
290C2#1306890311yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1281C2
socleC22×C11#385
prime radicalC23×C11C4×D4
cosocleC2×C42×C11C23
hypercenter#1281D11
hypocenterC11#8879
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1281

Complements

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

NH ≅ G/Ntype
239. C11#8879semidirect

Maximal subgroups

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

subgroupindex
#130775562
#130693392
#130673912
#130671162
#130670202
#130665182
C11×#12812
#887911