Finite Group Databasebeta

← #14674166

Subgroups — #14674166

Order 2816.

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

normal subgroups only

This group has 332 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#13079683C211yesmaximal, characteristic
2#13070306C211yesmaximal, characteristic
3#13070284C211yesmaximal, characteristic
4#13066792C211yesmaximal, characteristic, complemented
5#13066790C211yesmaximal, characteristic, complemented
6#13066776C211yesmaximal, characteristic, complemented
7C11×#1407C211yesmaximal, characteristic, complemented
8#10623262C411yescharacteristic, complemented
9#10623205C2211yescharacteristic
10C11×#497C2211yescharacteristic
11#10622800—21no—
12#10622798—21no—
13#10622782—21no—
14#10622776—21no—
15#10622698C411yescharacteristic, complemented
16#10622669C2211yescharacteristic
17#10622364—21no—
18D11×#99—21no—
19#10622326C411yescharacteristic, complemented
20#10622322C411yescharacteristic, complemented
21C11×#355C2211yescharacteristic
22C11×#354C2211yescharacteristic
23#10622180C2211yescharacteristic
24#10622179C2211yescharacteristic
25#10622115—21no—
26#10622112—21no—
27C2×#4343D411yescharacteristic
28C2×D4×D11D411yescharacteristic
29C2×C11×Q16—21no—
30C2×C11×SD16—21no—
31C11×C4⋊Q8C2×C411yescharacteristic, complemented
32C11×#124C2311yescharacteristic
33#67000D411yescharacteristic
34#66999—21no—
35Q8×Dic11—21no—
36C2×#4325—21no—
37C2×#4325—21no—
38#66993D411yescharacteristic
39M16×D11—41no—
40#66951—41no—
41#66942—41no—
42#66937—41no—
43#66935—41no—
44C22⋊C4×D11—41no—
45#66927C2×C411yescharacteristic
46#66925C2×C411yescharacteristic
47#66923C2×C411yescharacteristic, complemented
48C11×#101—21no—
49C11×#99—21no—
50C11×#97C2×C411yescharacteristic, complemented
51#66900—21no—
52#66899—21no—
53#66898—21no—
54#66896—21no—
55#66887—41no—
56#66885—21no—
57#66885—21no—
58(C2×D11)⋊C8—21no—
59Dic11⋊C8—21no—
60#66870—41no—
61C4×C11⋊C8C2×C411yescharacteristic, complemented
62#13607—111nomaximal, Sylow
63C23×D11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11C2×D411yescharacteristic
66C2×D4×C11C2×D411yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11—41no—
69#4343—81no—
70D4×D11—81no—
71C2×D44—21no—
72C2×D44—41no—
73C2×D44C22⋊C411yescharacteristic
74C2×D44C22⋊C411yescharacteristic
75C2×C4×D11—21no—
76C2×C4×D11—81no—
77C2×C4×D11C22⋊C411yescharacteristic
78C11×Q16—81no—
79C11×SD16—81no—
80C11×M16—41no—
81C2×C8×C11—21no—
82C11×C4⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C42×C11C22×C411yescharacteristic
86C22⋊Dic11—41no—
87#4325—81no—
88#4325—81no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—41no—
92(C2×D11)⋊C4—81no—
93C4⋊Dic11—21no—
94C4⋊Dic11—41no—
95Dic11⋊C4—21no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98C4×Dic11—41no—
99C4×Dic11C22⋊C411yescharacteristic
100#4318—41no—
101C2×C11⋊C8—21no—
102#4313—81no—
103C8×D11—81no—
104#3222—111no—
105#2134—111no—
106#2127—111no—
107#1414—111no—
108#1414—111no—
109#1407—111no—
110#1407D1111yescharacteristic, complemented
111C23×C11—21no—
112C22×D11—21no—
113C22×D11—21no—
114C22×D11—41no—
115C22×D11—41no—
116C22×D11—161no—
117C22×D11#9911yescharacteristic
118Q8×C11—41no—
119Q8×C11—41no—
120Q8×C11—41no—
121D4×C11—41no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—41no—
125C2×C4×C11—81no—
126C2×C4×C11C2×C22⋊C411yescharacteristic
127C22⋊D11—81no—
128C22⋊D11—161no—
129C2×Dic11—21no—
130C2×Dic11—41no—
131C2×Dic11—81no—
132C2×Dic11#9911yescharacteristic
133D44—41no—
134D44—41no—
135D44—81no—
136D44—161no—
137C4×D11—41no—
138C4×D11—41no—
139C4×D11—41no—
140C4×D11—162no—
141C8×C11—41no—
142C8×C11—81no—
143C11⋊C8—41no—
144C11⋊C8—81no—
145#541—111no—
146#535—111no—
147#497C2×D1111yescharacteristic
148#492—111no—
149#490—111no—
150#488—111no—
151#464—221no—
152#460—221no—
153#452—221no—
154#450—221no—
155#433—111no—
156#413—221no—
157C2×#99—221no—
158#355—111no—
159#355—221no—
160#355C2×D1111yescharacteristic
161#354—111no—
162#354C2×D1111yescharacteristic
163#353—221no—
164C22×C11—41no—
165C22×C11—81no—
166C22×C11C2×#9911yescharacteristic
167C2×D11—21no—
168C2×D11—41no—
169C2×D11—41no—
170C2×D11—41no—
171C2×D11—82no—
172C2×D11—81no—
173C2×D11—81no—
174C2×D11—161no—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—81no—
179C4×C11—161no—
180Dic11—21no—
181Dic11—41no—
182Dic11—81no—
183Dic11—161no—
184C2×#41—111no—
185C22×D4—111no—
186C2×Q16—21no—
187C2×SD16—21no—
188C2×SD16—221no—
189C2×SD16—221no—
190C2×M16—441no—
191C4⋊Q8C4×D1111yescharacteristic, complemented
192#127—111no—
193#127—111no—
194#126—441no—
195#125—111no—
196#125—441no—
197#124—111no—
198#124C22×D1111yescharacteristic
199C22⋊Q8—221no—
200#121—441no—
201#120—441no—
202C4×Q8—221no—
203#117—111no—
204C2×C22⋊C4—441no—
205C4⋊C8—221no—
206#103—221no—
207#102—221no—
208#102—221no—
209#102—221no—
210#101—21no—
211#101—221no—
212#100—441no—
213#99—21no—
214#99—221no—
215#99—441no—
216C22⋊C8—221no—
217#97C4×D1111yescharacteristic, complemented
218C4×C8—111no—
219C2×C11—21no—
220C2×C11—81no—
221C2×C11#212711yescharacteristic
222D11—41no—
223D11—81no—
224D11—81no—
225C24—221no—
226#41—881no—
227C2×Q8—21no—
228C2×Q8D4×D1111yescharacteristic
229C2×D4—111no—
230C2×D4—111no—
231C2×D4—221no—
232C2×D4—221no—
233C2×D4—441no—
234C2×D4—441no—
235C2×D4—881no—
236C2×D4D4×D1111yescharacteristic
237C22×C4—111no—
238C22×C4—221no—
239C22×C4—881no—
240Q16—81no—
241SD16—81no—
242SD16—881no—
243SD16—881no—
244M16—41no—
245M16—441no—
246M16—881no—
247C2×C8—21no—
248C2×C8—221no—
249C2×C8—881no—
250C4⋊C4—41no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—221no—
259C22⋊C4—441no—
260C22⋊C4—441no—
261C22⋊C4—441no—
262C22⋊C4—881no—
263C42—111no—
264C42—441no—
265C42C2×C4×D1111yescharacteristic
266C11#1360711yescharacteristic, complemented, Sylow
267C23—21no—
268C23—111no—
269C23—221no—
270C23—221no—
271C23—441no—
272C23—441no—
273C23—1761no—
274Q8—41no—
275Q8—41no—
276Q8—41no—
277D4—41no—
278D4—441no—
279D4—441no—
280D4—881no—
281D4—881no—
282D4—1761no—
283D4—1761no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—81no—
288C2×C4—111no—
289C2×C4—221no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—881no—
295C2×C4—1762no—
296C2×C4C22⋊C4×D1111yescharacteristic
297C8—41no—
298C8—81no—
299C8—441no—
300C8—881no—
301C22—41no—
302C22—81no—
303C22—221no—
304C22—441no—
305C22—441no—
306C22—441no—
307C22—881no—
308C22—881no—
309C22—882no—
310C22—1761no—
311C22D11×#9911yescharacteristic
312C4—21no—
313C4—41no—
314C4—41no—
315C4—81no—
316C4—161no—
317C4—221no—
318C4—441no—
319C4—881no—
320C4—1761no—
321C2—21no—
322C2—81no—
323C2—441no—
324C2—881no—
325C2—881no—
326C2#1307028211yescharacteristic
subgroupG/H
centerC2#13070282
commutatorC42×C11C22×C4
Frattini#124C22×D11
FittingC11×#1407C2
socleC2×C11#2127
prime radical#10623205C22
cosocleC11×#124C23
hypercenter#1407D11
hypocenterC11#13607
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #1407

Complements

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

NH ≅ G/Ntype
4. #13066792C2semidirect
5. #13066790C2semidirect
6. #13066776C2semidirect
7. C11×#1407C2semidirect
8. #10623262C4semidirect
15. #10622698C4semidirect
19. #10622326C4semidirect
20. #10622322C4semidirect
31. C11×C4⋊Q8C2×C4semidirect
47. #66923C2×C4semidirect
50. C11×#97C2×C4semidirect
61. C4×C11⋊C8C2×C4semidirect
110. #1407D11semidirect
191. C4⋊Q8C4×D11semidirect
217. #97C4×D11semidirect
266. C11#13607semidirect

Maximal subgroups

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

subgroupindex
#130796832
#130703062
#130702842
#130667922
#130667902
#130667762
C11×#14072
#1360711