Finite Group Databasebeta

← #14674183

Subgroups — #14674183

Order 2816.

336 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 57 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#13079689C211yesmaximal, characteristic
2#13070286C211yesmaximal, characteristic
3#13070282C211yesmaximal, characteristic
4#13066787C211yesmaximal, characteristic, complemented
5#13066780C211yesmaximal, characteristic, complemented
6#13066780C211yesmaximal, characteristic, complemented
7C11×#1412C211yesmaximal, characteristic, complemented
8#10623246C2211yescharacteristic
9#10623228C411yescharacteristic, complemented
10C11×#490C2211yescharacteristic
11#10622689C2211yescharacteristic
12#10622681C411yescharacteristic, complemented
13#10622396—21no—
14#10622389—21no—
15#10622380—21no—
16#10622375—21no—
17D11×#99—21no—
18#10622353—21no—
19#10622328C411yescharacteristic, complemented
20#10622322C411yescharacteristic, complemented
21C11×#353C2211yescharacteristic
22C11×#353C2211yescharacteristic
23#10622183C2211yescharacteristic
24#10622183C2211yescharacteristic
25#10622112—21no—
26#10622111—21no—
27C2×#4341D411yescharacteristic
28C2×D4×D11D411yescharacteristic
29C11×#127C2311yescharacteristic
30C11×#125C2×C411yescharacteristic, complemented
31#66993D411yescharacteristic
32#66992—41no—
33#66990—41no—
34#66989D411yescharacteristic
35C2×#4324—21no—
36C2×#4324—21no—
37C2×Dic44—21no—
38C2×#4314—21no—
39#66951—41no—
40#66950—21no—
41#66943—41no—
42#66940—21no—
43C22⋊C4×D11—41no—
44#66930—41no—
45#66928C2×C411yescharacteristic
46#66925C2×C411yescharacteristic
47#66922C2×C411yescharacteristic, complemented
48C11×#102—21no—
49C11×#102—21no—
50C11×#99—21no—
51C11×#99—21no—
52C11×#97C2×C411yescharacteristic, complemented
53#66898—21no—
54#66898—21no—
55(C2×D11)⋊C8—21no—
56Dic11⋊C8—21no—
57#66874—21no—
58#66873—21no—
59#66870—41no—
60#66870—41no—
61C4×C11⋊C8C2×C411yescharacteristic, complemented
62#13610—111nomaximal, Sylow
63C23×D11—21no—
64C2×D4×C11—41no—
65C2×D4×C11C2×D411yescharacteristic
66C2×D4×C11C2×D411yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—41no—
70C22×Dic11—21no—
71#4341—81no—
72D4×D11—81no—
73C2×D44C22⋊C411yescharacteristic
74C2×C4×D11—81no—
75C2×C4×D11C22⋊C411yescharacteristic
76C2×Dic22—21no—
77C2×Dic22C22⋊C411yescharacteristic
78C2×C8×C11—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C42×C11C22×C411yescharacteristic
84C22⋊Dic11—41no—
85C22⋊Dic11—41no—
86C22⋊Dic11—41no—
87#4324—81no—
88#4324—81no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—41no—
92(C2×D11)⋊C4—81no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95Dic11⋊C4—21no—
96Dic11⋊C4—41no—
97Dic11⋊C4—81no—
98C4×Dic11—41no—
99C4×Dic11—81no—
100C4×Dic11C22⋊C411yescharacteristic
101C2×C11⋊C8—21no—
102Dic44—81no—
103#4314—81no—
104#3222—111no—
105#2128—111no—
106#2127—111no—
107#1412—111no—
108#1412D1111yescharacteristic, complemented
109#1409—111no—
110#1409—111no—
111C23×C11—21no—
112C23×C11—21no—
113C22×D11—21no—
114C22×D11—41no—
115C22×D11—41no—
116C22×D11—161no—
117C22×D11#9911yescharacteristic
118D4×C11—41no—
119D4×C11—41no—
120D4×C11—161no—
121C2×C4×C11—21no—
122C2×C4×C11—41no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11C2×C22⋊C411yescharacteristic
126C22⋊D11—81no—
127C22⋊D11—81no—
128C22⋊D11—161no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—81no—
135C2×Dic11—81no—
136C2×Dic11#9911yescharacteristic
137D44—41no—
138C4×D11—41no—
139C4×D11—162no—
140Dic22—41no—
141Dic22—41no—
142Dic22—41no—
143C8×C11—41no—
144C11⋊C8—41no—
145#541—111no—
146#535—111no—
147#497—111no—
148#492—111no—
149#490C2×D1111yescharacteristic
150#488—111no—
151#464—221no—
152#460—221no—
153#452—221no—
154#450—221no—
155#433—111no—
156#410—221no—
157C2×#99—221no—
158#354—221no—
159#353—111no—
160#353—111no—
161#353—221no—
162#353C2×D1111yescharacteristic
163#353C2×D1111yescharacteristic
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—81no—
167C22×C11—81no—
168C22×C11C2×#9911yescharacteristic
169C2×D11—21no—
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—82no—
173C2×D11—81no—
174C2×D11—161no—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11—81no—
178C4×C11—161no—
179C4×C11—161no—
180Dic11—21no—
181Dic11—41no—
182Dic11—41no—
183Dic11—81no—
184Dic11—161no—
185Dic11—161no—
186C2×#41—111no—
187C22×D4—111no—
188C2×Q16—221no—
189C2×SD16—221no—
190C2×SD16—221no—
191C2×SD16—221no—
192C4⋊Q8—111no—
193#127—111no—
194#127C22×D1111yescharacteristic
195#126—441no—
196#125—441no—
197#125C4×D1111yescharacteristic, complemented
198#124—111no—
199#124—111no—
200C22⋊Q8—221no—
201#121—441no—
202#120—441no—
203C4×Q8—221no—
204#117—111no—
205#117—441no—
206C2×C22⋊C4—441no—
207C4⋊C8—221no—
208#103—221no—
209#102—21no—
210#102—21no—
211#102—221no—
212#99—21no—
213#99—21no—
214#99—221no—
215#99—221no—
216#99—441no—
217#99—441no—
218C22⋊C8—221no—
219#97C4×D1111yescharacteristic, complemented
220C4×C8—111no—
221C2×C11—21no—
222C2×C11—81no—
223C2×C11—81no—
224C2×C11#212711yescharacteristic
225D11—41no—
226D11—81no—
227C24—221no—
228#41—881no—
229C2×Q8—111no—
230C2×Q8—221no—
231C2×D4—41no—
232C2×D4—111no—
233C2×D4—221no—
234C2×D4—221no—
235C2×D4—441no—
236C2×D4—881no—
237C2×D4D4×D1111yescharacteristic
238C2×D4D4×D1111yescharacteristic
239C22×C4—111no—
240C22×C4—221no—
241C22×C4—881no—
242Q16—881no—
243SD16—881no—
244SD16—881no—
245SD16—881no—
246C2×C8—21no—
247C2×C8—221no—
248C4⋊C4—21no—
249C4⋊C4—41no—
250C4⋊C4—221no—
251C4⋊C4—441no—
252C4⋊C4—441no—
253C4⋊C4—441no—
254C4⋊C4—881no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—221no—
258C22⋊C4—441no—
259C22⋊C4—441no—
260C22⋊C4—441no—
261C22⋊C4—441no—
262C22⋊C4—441no—
263C22⋊C4—881no—
264C42—111no—
265C42—441no—
266C42—881no—
267C42C2×C4×D1111yescharacteristic
268C11#1361011yescharacteristic, complemented, Sylow
269C23—21no—
270C23—21no—
271C23—111no—
272C23—221no—
273C23—441no—
274C23—441no—
275C23—1761no—
276Q8—441no—
277Q8—441no—
278Q8—441no—
279D4—41no—
280D4—41no—
281D4—161no—
282D4—441no—
283D4—881no—
284D4—881no—
285D4—1761no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—111no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—881no—
298C2×C4—881no—
299C2×C4—1762no—
300C2×C4C22⋊C4×D1111yescharacteristic
301C8—41no—
302C8—441no—
303C22—41no—
304C22—41no—
305C22—81no—
306C22—81no—
307C22—221no—
308C22—441no—
309C22—441no—
310C22—881no—
311C22—882no—
312C22—1761no—
313C22D11×#9911yescharacteristic
314C4—21no—
315C4—41no—
316C4—81no—
317C4—161no—
318C4—161no—
319C4—221no—
320C4—441no—
321C4—441no—
322C4—881no—
323C4—1761no—
324C4—1761no—
325C2—21no—
326C2—81no—
327C2—81no—
328C2—441no—
329C2—881no—
330C2#1307028411yescharacteristic
subgroupG/H
centerC2#13070284
commutatorC42×C11C22×C4
Frattini#127C22×D11
FittingC11×#1412C2
socleC2×C11#2127
prime radical#10623246C22
cosocleC11×#127C23
hypercenter#1412D11
hypocenterC11#13610
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #1412

Complements

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

NH ≅ G/Ntype
4. #13066787C2semidirect
5. #13066780C2semidirect
6. #13066780C2semidirect
7. C11×#1412C2semidirect
9. #10623228C4semidirect
12. #10622681C4semidirect
19. #10622328C4semidirect
20. #10622322C4semidirect
30. C11×#125C2×C4semidirect
47. #66922C2×C4semidirect
52. C11×#97C2×C4semidirect
61. C4×C11⋊C8C2×C4semidirect
108. #1412D11semidirect
197. #125C4×D11semidirect
219. #97C4×D11semidirect
268. C11#13610semidirect

Maximal subgroups

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

subgroupindex
#130796892
#130702862
#130702822
#130667872
#130667802
C11×#14122
#1361011