Finite Group Databasebeta

← D11×#1327 #14662956

Subgroups — D11×#1327 #14662956

Order 2816.

410 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 91 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
1D11×#423C211yesmaximal, characteristic
2D11×#349C212yesmaximal
3#13066567C211yesmaximal, characteristic, complemented
4#13066566C212yesmaximal, complemented
5C11×#1327C211yesmaximal, characteristic, complemented
6C2×M16×D11C411yescharacteristic
7C2×M16×D11C2211yescharacteristic
8C2×C42×D11C411yescharacteristic
9C11×#423C2211yescharacteristic
10#10622731C411yescharacteristic
11#10622731C2211yescharacteristic
12#10622537C411yescharacteristic
13D11×M32—22no—
14#10622450—22no—
15D11×C4⋊C8—22no—
16C11×#349C2212yes—
17#10622191C2212yes—
18#10622152—22no—
19C22×C4×D11—21no—
20C22×C4×D11C2×C411yescharacteristic
21C2×C11×M16C2×C411yescharacteristic
22C2×C11×M16C2311yescharacteristic
23C2×C42×C11C2×C411yescharacteristic
24C2×C4×Dic11—21no—
25C2×C4×Dic11C2×C411yescharacteristic
26C2×#4318C2×C411yescharacteristic
27C2×#4318C2×C411yescharacteristic
28M16×D11—41no—
29M16×D11—41no—
30M16×D11—41no—
31M16×D11—41no—
32C2×#4313—21no—
33C2×#4313D412yes—
34C2×C8×D11—21no—
35C2×C8×D11D412yes—
36C42×D11—21no—
37C42×D11—21no—
38C42×D11C811yescharacteristic
39C42×D11C811yescharacteristic
40C42×D11C811yescharacteristic
41C42×D11C811yescharacteristic
42C11×M32—22no—
43C11×C4⋊C8—22no—
44Dic11⋊C8—22no—
45Dic11⋊C8—22no—
46#66876—22no—
47C4⋊(C11⋊C8)—22no—
48#66862—42no—
49C16×D11—42no—
50C2×#1327—111nomaximal, Sylow
51C23×D11M1611yescharacteristic
52C22×C4×C11—21no—
53C22×C4×C11C22×C411yescharacteristic
54C22×Dic11—21no—
55C22×Dic11M1611yescharacteristic
56C2×C4×D11—21no—
57C2×C4×D11—21no—
58C2×C4×D11—21no—
59C2×C4×D11—21no—
60C2×C4×D11—21no—
61C2×C4×D11—21no—
62C2×C4×D11—21no—
63C2×C4×D11—21no—
64C2×C4×D11—44no—
65C2×C4×D11C22⋊C411yescharacteristic
66C2×C4×D11C22⋊C411yescharacteristic
67C2×C4×D11C2×C811yescharacteristic
68C2×C4×D11C2×C811yescharacteristic
69C11×M16—41no—
70C11×M16—41no—
71C2×C8×C11—21no—
72C2×C8×C11C2×D412yes—
73C42×C11—21no—
74C42×C11C2×C811yescharacteristic
75C42×C11C2×C811yescharacteristic
76C4×Dic11—21no—
77C4×Dic11—21no—
78C4×Dic11—21no—
79C4×Dic11—21no—
80C4×Dic11—21no—
81C4×Dic11C2×C811yescharacteristic
82C4×Dic11C2×C811yescharacteristic
83#4318—41no—
84#4318—41no—
85C2×C11⋊C8—21no—
86C2×C11⋊C8C22⋊C412yes—
87#4313—42no—
88#4313—42no—
89C8×D11—22no—
90C8×D11—22no—
91C8×D11—41no—
92C8×D11—41no—
93C11×C16—42no—
94C11⋊C16—42no—
95C2×#423—111no—
96C2×#349—112no—
97#1327—111no—
98#1327—112no—
99#1327D1111yescharacteristic, direct product factor
100C23×C11C2×M1611yescharacteristic
101C22×D11—21no—
102C22×D11—21no—
103C22×D11—42no—
104C22×D11C22⋊C811yescharacteristic
105C22×D11C22⋊C811yescharacteristic
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—42no—
111C2×C4×C11C2×C22⋊C411yescharacteristic
112C2×C4×C11C22×C811yescharacteristic
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—42no—
118C2×Dic11C22⋊C811yescharacteristic
119C2×Dic11C22⋊C811yescharacteristic
120C4×D11—24no—
121C4×D11—21no—
122C4×D11—21no—
123C4×D11—21no—
124C4×D11—21no—
125C4×D11—21no—
126C4×D11—21no—
127C4×D11—42no—
128C4×D11—42no—
129C4×D11—42no—
130C4×D11#9911yescharacteristic
131C4×D11#9911yescharacteristic
132C4×D11#10111yescharacteristic
133C4×D11#10111yescharacteristic
134C8×C11—22no—
135C8×C11—41no—
136C11⋊C8—22no—
137C11⋊C8—41no—
138C22×M16—111no—
139C22×M16—111no—
140C22×C42—111no—
141C2×M32—222no—
142#423—111no—
143#423—111no—
144#423—111no—
145#423—222no—
146#423C2×D1111yescharacteristic
147C2×C4⋊C8—222no—
148#349—112no—
149#349—222no—
150#349C2×D1112yes—
151C22×C11—21no—
152C22×C11—41no—
153C22×C11C2×C22⋊C811yescharacteristic
154C2×D11—22no—
155C2×D11—21no—
156C2×D11—42no—
157C2×D11—42no—
158C2×D11—41no—
159C2×D11#32411yescharacteristic
160C2×D11#32411yescharacteristic
161C4×C11—22no—
162C4×C11—21no—
163C4×C11—41no—
164C4×C11C2×#9911yescharacteristic
165C4×C11C2×#10111yescharacteristic
166Dic11—22no—
167Dic11—21no—
168Dic11—41no—
169Dic11#32411yescharacteristic
170Dic11#32411yescharacteristic
171C23×C4—111no—
172C23×C4—221no—
173C2×M16—111no—
174C2×M16—112no—
175C2×M16—111no—
176C2×M16—221no—
177C2×M16—441no—
178C2×M16—441no—
179C2×M16—441no—
180C2×M16—441no—
181C2×M16C4×D1111yescharacteristic
182C2×M16C22×D1111yescharacteristic
183C22×C8—112no—
184C22×C8—221no—
185C2×C42—111no—
186C2×C42—111no—
187C2×C42—111no—
188C2×C42—111no—
189C2×C42—111no—
190C2×C42—221no—
191C2×C42—221no—
192C2×C42—221no—
193C2×C42C4×D1111yescharacteristic
194M32—22no—
195M32—222no—
196M32—442no—
197C2×C16—442no—
198C4⋊C8—22no—
199C4⋊C8—222no—
200C4⋊C8—222no—
201C4⋊C8—222no—
202C2×C11—21no—
203C2×C11—41no—
204C2×C11C2×#32411yescharacteristic
205D11—21no—
206D11—41no—
207D11#132712yesdirect product factor
208C24—111no—
209C22×C4—21no—
210C22×C4—111no—
211C22×C4—111no—
212C22×C4—111no—
213C22×C4—111no—
214C22×C4—111no—
215C22×C4—221no—
216C22×C4—221no—
217C22×C4—221no—
218C22×C4—221no—
219C22×C4—221no—
220C22×C4—221no—
221C22×C4—221no—
222C22×C4—221no—
223C22×C4—221no—
224C22×C4—444no—
225C22×C4C2×C4×D1111yescharacteristic
226M16—41no—
227M16—41no—
228M16—442no—
229M16—442no—
230M16—441no—
231M16—441no—
232C2×C8—21no—
233C2×C8—112no—
234C2×C8—222no—
235C2×C8—222no—
236C2×C8—221no—
237C2×C8—441no—
238C2×C8—441no—
239C2×C8D4×D1112yes—
240C42—21no—
241C42—111no—
242C42—111no—
243C42—221no—
244C42—221no—
245C42—221no—
246C42—221no—
247C42—221no—
248C42C8×D1111yescharacteristic
249C42C8×D1111yescharacteristic
250C16—42no—
251C16—442no—
252C11C2×#132711yescharacteristic, complemented, Sylow
253C23—111no—
254C23—111no—
255C23—221no—
256C23—221no—
257C23—442no—
258C23M16×D1111yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—111no—
265C2×C4—111no—
266C2×C4—111no—
267C2×C4—111no—
268C2×C4—111no—
269C2×C4—111no—
270C2×C4—221no—
271C2×C4—221no—
272C2×C4—221no—
273C2×C4—221no—
274C2×C4—224no—
275C2×C4—221no—
276C2×C4—221no—
277C2×C4—221no—
278C2×C4—221no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—442no—
282C2×C4—442no—
283C2×C4—442no—
284C2×C4—442no—
285C2×C4C22⋊C4×D1111yescharacteristic
286C2×C4C2×C8×D1111yescharacteristic
287C8—22no—
288C8—41no—
289C8—222no—
290C8—441no—
291C22—21no—
292C22—41no—
293C22—111no—
294C22—111no—
295C22—222no—
296C22—221no—
297C22—441no—
298C22—442no—
299C22—442no—
300C22D11×C22⋊C811yescharacteristic
301C4—22no—
302C4—21no—
303C4—41no—
304C4—111no—
305C4—111no—
306C4—222no—
307C4—221no—
308C4—441no—
309C4D11×#9911yescharacteristic
310C4D11×#10111yescharacteristic
311C2—21no—
312C2—41no—
313C2—112no—
314C2—221no—
315C2—441no—
316C2D11×#32411yescharacteristic
subgroupG/H
centerC4D11×#99
commutatorC2×C4×C11C22×C8
FrattiniC2×M16C22×D11
FittingC11×#1327C2
socleC2×C11C2×#324
prime radicalC23×D11M16
cosocleC2×C11×M16C23
hypercenter#1327D11
hypocenterC11C2×#1327
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
3. #13066567C2semidirect
4. #13066566C2semidirect
5. C11×#1327C2semidirect
99. #1327D11direct (N × H)
207. D11#1327direct (N × H)
252. C11C2×#1327semidirect

Maximal subgroups

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

subgroupindex
D11×#4232
D11×#3492
#130665672
#130665662
C11×#13272
C2×#132711