Finite Group Databasebeta

← #14674170

Subgroups — #14674170

Order 2816.

332 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 67 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#13079688C211yesmaximal, characteristic
2#13070285C211yesmaximal, characteristic
3#13066792C212yesmaximal, complemented
4#13066777C212yesmaximal, complemented
5C11×#2134C211yesmaximal, characteristic
6C11×#535C2211yescharacteristic
7#10623049C411yescharacteristic, complemented
8C11×#413—21no—
9#10622852—21no—
10C2×#66898—21no—
11#10622831—21no—
12#10622689C411yescharacteristic, complemented
13#10622688—21no—
14#10622684C411yescharacteristic, complemented
15#10622673C2211yescharacteristic
16#10622669C2211yescharacteristic
17#10622667—21no—
18#10622613C411yescharacteristic, complemented
19C11×#355—21no—
20C11×#355C2212yes—
21#10622183—21no—
22#10622179C2212yes—
23C2×C11×#41D411yescharacteristic
24C22×D4×C11D411yescharacteristic
25C2×C11×M16—41no—
26C11×#127C2×C411yescharacteristic
27C11×#127D411yescharacteristic
28C11×#124D411yescharacteristic
29C11×#124C2311yescharacteristic
30C11×#121—41no—
31C11×#120—41no—
32C11×#117C2×C411yescharacteristic
33C2×C22⋊Dic11—41no—
34C2×#4326—21no—
35C2×#4324—21no—
36C2×#4324—21no—
37C2×#4324—21no—
38#66977—21no—
39#66942—41no—
40#66932—41no—
41#66923C2×C411yescharacteristic, complemented
42#66922C2×C411yescharacteristic, complemented
43C4×Dic22—21no—
44C11×#101—22no—
45C11×#100—41no—
46#66899—21no—
47#66898—22no—
48#66898—41no—
49#66896—21no—
50#66896—21no—
51#66896—21no—
52C22⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54#66867C2×C411yescharacteristic, complemented
55C4×C11⋊C8C2×C411yescharacteristic, complemented
56#13607—111nomaximal, Sylow
57C24×C11—21no—
58C11×#41—81no—
59C2×Q8×C11C2×D411yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11—81no—
65C2×D4×C11C22⋊C411yescharacteristic
66C2×D4×C11C22⋊C411yescharacteristic
67C2×D4×C11C2×D411yescharacteristic
68C22×C4×C11—21no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×Dic11—81no—
71C2×Dic22—21no—
72C11×M16—42no—
73C11×M16—81no—
74C2×C8×C11—81no—
75C11×C4⋊C4—21no—
76C11×C22⋊C4—21no—
77C11×C22⋊C4—41no—
78C11×C22⋊C4—41no—
79C42×C11C22⋊C411yescharacteristic
80C42×C11C22×C411yescharacteristic
81C22⋊Dic11—42no—
82C22⋊Dic11—41no—
83C22⋊Dic11—81no—
84#4326—81no—
85#4324—81no—
86#4324—81no—
87#4324—81no—
88C4⋊Dic11—21no—
89C4⋊Dic11—41no—
90Dic11⋊C4—41no—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93C4×Dic11—41no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—21no—
96#3222—111no—
97#2134D1111yescharacteristic
98#2127—111no—
99#1414—112no—
100#1407—112no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11—161no—
107C23×C11#9911yescharacteristic
108Q8×C11—41no—
109D4×C11—41no—
110D4×C11—41no—
111D4×C11—41no—
112D4×C11—81no—
113D4×C11—81no—
114D4×C11—161no—
115D4×C11—161no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11#9911yescharacteristic
123C2×C4×C11C2×C22⋊C411yescharacteristic
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—82no—
127C2×Dic11—162no—
128Dic22—41no—
129Dic22—41no—
130C8×C11—82no—
131C11⋊C8—41no—
132C11⋊C8—41no—
133#541—111no—
134#535C2×D1111yescharacteristic
135#497—111no—
136#492—111no—
137#490—111no—
138#488—111no—
139#464—221no—
140#460—221no—
141#452—221no—
142#450—221no—
143#433—111no—
144#413—21no—
145C2×#99—221no—
146#355—21no—
147#355C2×D1112yes—
148#354—112no—
149#353—221no—
150C22×C11—21no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—81no—
156C22×C11—81no—
157C22×C11—81no—
158C22×C11—82no—
159C22×C11—161no—
160C22×C11C2×#9911yescharacteristic
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—41no—
166Dic11—81no—
167Dic11—81no—
168Dic11—162no—
169C2×#41C22⋊D1111yescharacteristic
170C22×D4D4411yescharacteristic
171C2×Q16—221no—
172C2×SD16—221no—
173C2×SD16—221no—
174C2×SD16—221no—
175C2×M16—41no—
176C4⋊Q8—111no—
177#127C4×D1111yescharacteristic
178#127D4411yescharacteristic
179#126—441no—
180#125—111no—
181#125—441no—
182#124C22⋊D1111yescharacteristic
183#124C22×D1111yescharacteristic
184C22⋊Q8—221no—
185#121—41no—
186#120—41no—
187C4×Q8—221no—
188#117C4×D1111yescharacteristic
189C2×C22⋊C4—441no—
190C4⋊C8—221no—
191#103—221no—
192#102—221no—
193#102—221no—
194#102—221no—
195#101—22no—
196#100—41no—
197#99—222no—
198#99—441no—
199C22⋊C8—221no—
200#97—111no—
201C4×C8—111no—
202C2×C11—21no—
203C2×C11—41no—
204C2×C11—81no—
205C2×C11—81no—
206C2×C11—81no—
207C2×C11#212711yescharacteristic
208C24—21no—
209#41—81no—
210C2×Q8—221no—
211C2×Q8C2×C22⋊D1111yescharacteristic
212C2×D4—21no—
213C2×D4—21no—
214C2×D4—41no—
215C2×D4—41no—
216C2×D4—81no—
217C2×D4(C2×D11)⋊C411yescharacteristic
218C2×D4(C2×D11)⋊C411yescharacteristic
219C2×D4C2×D4411yescharacteristic
220C22×C4—21no—
221C22×C4—881no—
222C22×C4(C2×D11)⋊C411yescharacteristic
223Q16—881no—
224SD16—881no—
225SD16—881no—
226SD16—881no—
227M16—42no—
228M16—81no—
229C2×C8—81no—
230C2×C8—221no—
231C2×C8—221no—
232C4⋊C4—21no—
233C4⋊C4—221no—
234C4⋊C4—441no—
235C4⋊C4—441no—
236C4⋊C4—441no—
237C4⋊C4—441no—
238C22⋊C4—21no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—441no—
242C22⋊C4—442no—
243C22⋊C4—881no—
244C42—441no—
245C42(C2×D11)⋊C411yescharacteristic
246C42C2×C4×D1111yescharacteristic
247C11#1360711yescharacteristic, complemented, Sylow
248C23—21no—
249C23—21no—
250C23—21no—
251C23—41no—
252C23—41no—
253C23—161no—
254C23#6687011yescharacteristic
255Q8—41no—
256Q8—441no—
257Q8—441no—
258D4—41no—
259D4—41no—
260D4—41no—
261D4—81no—
262D4—81no—
263D4—161no—
264D4—161no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—441no—
272C2×C4—441no—
273C2×C4—882no—
274C2×C4—1762no—
275C2×C4#6687011yescharacteristic
276C2×C4C2×(C2×D11)⋊C411yescharacteristic
277C8—82no—
278C8—441no—
279C8—441no—
280C22—21no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—81no—
286C22—81no—
287C22—81no—
288C22—82no—
289C22—161no—
290C22C2×#6687011yescharacteristic
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—881no—
297C4—881no—
298C4—1762no—
299C2—21no—
300C2—41no—
301C2—81no—
302C2—81no—
303C2—81no—
304C2#1307028311yescharacteristic
subgroupG/H
centerC2#13070283
commutatorC42×C11C22×C4
Frattini#124C22×D11
FittingC11×#2134C2
socleC2×C11#2127
prime radicalC11×#535C22
cosocleC11×#124C23
hypercenter#2134D11
hypocenterC11#13607
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ #535 ◁ #2134

Complements

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

NH ≅ G/Ntype
3. #13066792C2semidirect
4. #13066777C2semidirect
7. #10623049C4semidirect
12. #10622689C4semidirect
14. #10622684C4semidirect
18. #10622613C4semidirect
41. #66923C2×C4semidirect
42. #66922C2×C4semidirect
54. #66867C2×C4semidirect
55. C4×C11⋊C8C2×C4semidirect
247. C11#13607semidirect

Maximal subgroups

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

subgroupindex
#130796882
#130702852
#130667922
#130667772
C11×#21342
#1360711