Finite Group Databasebeta

← #14647171

Subgroups — #14647171

Order 2816.

554 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 111 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×#382C211yesmaximal, characteristic
2#13068379C212yesmaximal
3#13066498C212yesmaximal, complemented
4#13066497C211yesmaximal, characteristic, complemented
5C11×#1295C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D11C411yescharacteristic
7C2×C4⋊C4×D11C411yescharacteristic
8C2×C42×D11C2211yescharacteristic
9C2×C11×#97C2212yes—
10C11×#382C2211yescharacteristic
11C2×(C2×D11)⋊C8—22no—
12#10622590C411yescharacteristic
13#10622590C411yescharacteristic
14#10622549C2211yescharacteristic
15C2×#66867C2212yes—
16D11×#95—22no—
17#10622263—22no—
18#10622188—22no—
19C22×C4×D11—21no—
20C22×C4×D11—21no—
21C22×C4×D11C2×C411yescharacteristic
22C22×C4×D11D412yes—
23C22×C8×C11—22no—
24C2×C11×C4⋊C4C2×C411yescharacteristic
25C2×C11×C4⋊C4C2×C411yescharacteristic
26C2×C42×C11C2311yescharacteristic
27C2×C4⋊Dic11C2×C411yescharacteristic
28C2×C4⋊Dic11C2×C411yescharacteristic
29C2×Dic11⋊C4—21no—
30C2×Dic11⋊C4—21no—
31C2×C4×Dic11C2×C411yescharacteristic
32C2×C4×Dic11D412yes—
33C22×C11⋊C8—22no—
34C4⋊C4×D11—42no—
35C4⋊C4×D11—42no—
36C42×D11—22no—
37C42×D11—21no—
38C42×D11—21no—
39C11×#97—22no—
40C11×#97—22no—
41C11×#95—22no—
42C11⋊#95—22no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45(C2×D11)⋊C8—28no—
46#66867—22no—
47#66867—22no—
48#8718—111nomaximal, Sylow
49C23×D11C22⋊C411yescharacteristic
50C22×C4×C11—21no—
51C22×C4×C11—21no—
52C22×C4×C11C22×C411yescharacteristic
53C22×C4×C11C2×D412yes—
54C22×Dic11—21no—
55C22×Dic11—21no—
56C22×Dic11C22⋊C412yes—
57C22×Dic11C22⋊C411yescharacteristic
58C2×C4×D11—22no—
59C2×C4×D11—22no—
60C2×C4×D11—24no—
61C2×C4×D11—21no—
62C2×C4×D11—21no—
63C2×C4×D11—22no—
64C2×C4×D11—22no—
65C2×C4×D11—42no—
66C2×C4×D11—44no—
67C2×C4×D11—42no—
68C2×C4×D11—42no—
69C2×C4×D11—44no—
70C2×C8×C11—24no—
71C2×C8×C11—42no—
72C2×C8×C11—42no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C42×C11#4112yes—
76C42×C11#4111yescharacteristic
77C42×C11#4111yescharacteristic
78C4⋊Dic11—41no—
79C4⋊Dic11—41no—
80Dic11⋊C4—42no—
81Dic11⋊C4—42no—
82C4×Dic11—21no—
83C4×Dic11—21no—
84C4×Dic11—22no—
85C4×Dic11—22no—
86C2×C11⋊C8—24no—
87C2×C11⋊C8—42no—
88C2×C11⋊C8—42no—
89C2×#382—111no—
90#1749—112no—
91#1295—112no—
92#1295—111no—
93#1295D1111yescharacteristic, complemented
94C23×C11C2×C22⋊C411yescharacteristic
95C22×D11—21no—
96C22×D11—21no—
97C22×D11—22no—
98C22×D11#10012yes—
99C22×D11#10414yes—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11#11711yescharacteristic
109C2×C4×C11#11711yescharacteristic
110C2×C4×C11#12312yes—
111C2×C4×C11#12312yes—
112C2×Dic11—21no—
113C2×Dic11—21no—
114C2×Dic11—22no—
115C2×Dic11—22no—
116C2×Dic11—22no—
117C2×Dic11—41no—
118C2×Dic11—41no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11#10112yes—
122C4×D11—24no—
123C4×D11—24no—
124C4×D11—44no—
125C4×D11—44no—
126C4×D11—84no—
127C4×D11—84no—
128C8×C11—44no—
129C11⋊C8—44no—
130C22×C4⋊C4—111no—
131C22×C4⋊C4—111no—
132C22×C42—111no—
133C2×C22⋊C8—222no—
134C2×#97—112no—
135C2×#97C2×D1112yes—
136#382—111no—
137#382—111no—
138#382—111no—
139#382—222no—
140#382C2×D1111yescharacteristic
141C2×#95—222no—
142#336—222no—
143C22×C11#38111yescharacteristic
144C22×C11C2×#10011yescharacteristic
145C22×C11C2×#10111yescharacteristic
146C22×C11C2×#10412yes—
147C22×C11#42112yes—
148C2×D11—22no—
149C2×D11—24no—
150C2×D11—24no—
151C2×D11—22no—
152C2×D11#32914yes—
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—22no—
156C4×C11—22no—
157C4×C11—81no—
158C4×C11—81no—
159Dic11—22no—
160Dic11—42no—
161Dic11—81no—
162Dic11—81no—
163C23×C4—111no—
164C23×C4—112no—
165C23×C4—221no—
166C23×C4—221no—
167C22×C8—22no—
168C22×C8—222no—
169C2×C4⋊C4—111no—
170C2×C4⋊C4—111no—
171C2×C4⋊C4—221no—
172C2×C4⋊C4—221no—
173C2×C4⋊C4—442no—
174C2×C4⋊C4—442no—
175C2×C4⋊C4C4×D1111yescharacteristic
176C2×C4⋊C4C4×D1111yescharacteristic
177C2×C42—111no—
178C2×C42—112no—
179C2×C42—222no—
180C2×C42—221no—
181C2×C42—221no—
182C2×C42C22×D1111yescharacteristic
183C22⋊C8—228no—
184#97—22no—
185#97—22no—
186#97—222no—
187#97—222no—
188#95—22no—
189#95—222no—
190#95—222no—
191#95—222no—
192C2×C11C2×#32911yescharacteristic
193C2×C11#152812yes—
194C2×C11#153311yescharacteristic
195C2×C11#182111yescharacteristic
196C2×C11#182612yes—
197D11—24no—
198C24—111no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—111no—
202C22×C4—112no—
203C22×C4—222no—
204C22×C4—222no—
205C22×C4—224no—
206C22×C4—221no—
207C22×C4—221no—
208C22×C4—222no—
209C22×C4—222no—
210C22×C4—221no—
211C22×C4—221no—
212C22×C4—442no—
213C22×C4—442no—
214C22×C4—442no—
215C22×C4—444no—
216C22×C4—444no—
217C22×C4C2×C4×D1111yescharacteristic
218C22×C4D4×D1112yes—
219C2×C8—24no—
220C2×C8—42no—
221C2×C8—42no—
222C2×C8—224no—
223C2×C8—442no—
224C2×C8—442no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—441no—
228C4⋊C4—441no—
229C4⋊C4—442no—
230C4⋊C4—442no—
231C42—221no—
232C42—222no—
233C42—221no—
234C42—222no—
235C42#433912yes—
236C42#434111yescharacteristic
237C42#434311yescharacteristic
238C11#871811yescharacteristic, complemented, Sylow
239C23—112no—
240C23—114no—
241C23—221no—
242C23—221no—
243C23—222no—
244C23C22⋊C4×D1111yescharacteristic
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—112no—
254C2×C4—224no—
255C2×C4—224no—
256C2×C4—221no—
257C2×C4—221no—
258C2×C4—222no—
259C2×C4—222no—
260C2×C4—222no—
261C2×C4—444no—
262C2×C4—444no—
263C2×C4—441no—
264C2×C4—441no—
265C2×C4—442no—
266C2×C4—442no—
267C2×C4—884no—
268C2×C4—884no—
269C2×C4#6692511yescharacteristic
270C2×C4#6693612yes—
271C2×C4#6694511yescharacteristic
272C2×C4#6694712yes—
273C8—44no—
274C8—444no—
275C22—114no—
276C22—222no—
277C22—224no—
278C22—224no—
279C22—222no—
280C22#1062227711yescharacteristic
281C22D11×#10011yescharacteristic
282C22D11×#10111yescharacteristic
283C22D11×#10412yes—
284C22#1062243412yes—
285C4—21no—
286C4—21no—
287C4—22no—
288C4—22no—
289C4—81no—
290C4—81no—
291C4—222no—
292C4—442no—
293C4—881no—
294C4—881no—
295C2—224no—
296C2D11×#32911yescharacteristic
297C2#1306721612yes—
298C2#1306723811yescharacteristic
299C2#1306869511yescharacteristic
300C2#1306871412yes—
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1295D11
hypocenterC11#8718
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
3. #13066498C2semidirect
4. #13066497C2semidirect
5. C11×#1295C2semidirect
93. #1295D11semidirect
238. C11#8718semidirect

Maximal subgroups

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

subgroupindex
D11×#3822
#130683792
#130664982
#130664972
C11×#12952
#871811