Finite Group Databasebeta

← #14674152

Subgroups — #14674152

Order 2816.

322 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 59 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#13079013C211yesmaximal, characteristic
2#13070298C211yesmaximal, characteristic
3#13070280C211yesmaximal, characteristic
4#13066792C211yesmaximal, characteristic, complemented
5#13066791C211yesmaximal, characteristic, complemented
6#13066790C211yesmaximal, characteristic, complemented
7C11×#1414C211yesmaximal, characteristic, complemented
8D11×#125C411yescharacteristic, complemented
9#10623199C2211yescharacteristic
10C11×#488C2211yescharacteristic
11#10622681C411yescharacteristic, complemented
12#10622669C2211yescharacteristic
13#10622416—21no—
14#10622410—21no—
15#10622384—21no—
16#10622377—21no—
17#10622364—21no—
18#10622353—21no—
19#10622310C411yescharacteristic, complemented
20C4×#4313C411yescharacteristic, complemented
21C11×#355C2211yescharacteristic
22C11×#354C2211yescharacteristic
23#10622180C2211yescharacteristic
24#10622179C2211yescharacteristic
25#10622116—21no—
26#10622112—21no—
27C2×#4343D411yescharacteristic
28C2×#4341D411yescharacteristic
29C11×#125C2×C411yescharacteristic
30C11×#124C2311yescharacteristic
31#66997D411yescharacteristic
32#66993D411yescharacteristic
33M16×D11—41no—
34C2×#4313—21no—
35C4⋊C4×D11—21no—
36C4⋊C4×D11—41no—
37#66943—21no—
38#66942—41no—
39#66937—41no—
40(C22⋊D11)⋊C4—41no—
41#66930—41no—
42#66928C2×C411yescharacteristic
43C42×D11C2×C411yescharacteristic
44#66923C2×C411yescharacteristic
45C11×#103—21no—
46C11×#102—21no—
47C11×#101—21no—
48C11×#99—21no—
49C4×C8×C11C2×C411yescharacteristic
50#66900—21no—
51#66899—21no—
52#66898—21no—
53#66896—21no—
54#66887—41no—
55#66885—21no—
56#66880—21no—
57#66879—21no—
58#66874—21no—
59#66873—21no—
60#66870—41no—
61C4×C11⋊C8C2×C411yescharacteristic
62#13604—111nomaximal, Sylow
63C2×Q8×C11C2×D411yescharacteristic
64C2×D4×C11C2×D411yescharacteristic
65C2×C22⋊D11—21no—
66C2×C22⋊D11—41no—
67C22×Dic11—21no—
68#4343—41no—
69#4343—41no—
70#4341—41no—
71#4341—41no—
72C2×D44—21no—
73C2×D44C22⋊C411yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—41no—
77C2×C4×D11C22⋊C411yescharacteristic
78C2×Dic22C22⋊C411yescharacteristic
79C11×M16—41no—
80C2×C8×C11—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C42×C11C22×C411yescharacteristic
86C22⋊Dic11—41no—
87(C2×D11)⋊C4—41no—
88C4⋊Dic11—21no—
89C4⋊Dic11—41no—
90Dic11⋊C4—41no—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93Dic11⋊C4—41no—
94Dic11⋊C4—81no—
95C4×Dic11—21no—
96C4×Dic11—81no—
97C4×Dic11C22⋊C411yescharacteristic
98#4318—41no—
99C2×C11⋊C8—21no—
100#4313—41no—
101#4313—41no—
102#4313—81no—
103C8×D11—81no—
104#3142—111no—
105#2132—111no—
106#2126—111no—
107#1414—111no—
108#1414—111no—
109#1414—111no—
110#1414D1111yescharacteristic, complemented
111C23×C11—21no—
112C22×D11—21no—
113C22×D11#9911yescharacteristic
114Q8×C11—41no—
115D4×C11—41no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11—81no—
120C2×C4×C11C2×C22⋊C411yescharacteristic
121C22⋊D11—81no—
122C22⋊D11—82no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—81no—
129C2×Dic11#9911yescharacteristic
130D44—41no—
131D44—81no—
132C4×D11—21no—
133C4×D11—21no—
134C4×D11—41no—
135C4×D11—41no—
136C4×D11—81no—
137C4×D11—82no—
138Dic22—41no—
139C8×C11—41no—
140C8×C11—81no—
141C11⋊C8—41no—
142C11⋊C8—81no—
143#532—111no—
144C2×#125—111no—
145#491—221no—
146#490—221no—
147#488—111no—
148#488—111no—
149#488—111no—
150#488C2×D1111yescharacteristic
151#417—221no—
152#417—221no—
153#413—221no—
154#410—221no—
155C4×M16—111no—
156#356—221no—
157#355—111no—
158#355C2×D1111yescharacteristic
159#354—111no—
160#354C2×D1111yescharacteristic
161#353—221no—
162C22×C11—41no—
163C22×C11—81no—
164C22×C11C2×#9911yescharacteristic
165C2×D11—21no—
166C2×D11—41no—
167C2×D11—41no—
168C2×D11—81no—
169C4×C11—21no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—81no—
173C4×C11—161no—
174Dic11—41no—
175Dic11—41no—
176Dic11—81no—
177Dic11—161no—
178Dic11#35411yescharacteristic
179Dic11#35411yescharacteristic
180C2×#41—111no—
181C2×#41—111no—
182C2×M16—221no—
183C2×M16—441no—
184C4⋊Q8—111no—
185#127—111no—
186#125—111no—
187#125—221no—
188#125—441no—
189#125C4×D1111yescharacteristic
190#124—111no—
191#124C22×D1111yescharacteristic
192#121—441no—
193C4×D4—441no—
194#117—441no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—441no—
197C2×C42—111no—
198#103—21no—
199#103—221no—
200#103—221no—
201#103—221no—
202#102—21no—
203#102—221no—
204#102—221no—
205#102—221no—
206#101—21no—
207#101—221no—
208#100—441no—
209#99—21no—
210#99—221no—
211#99—441no—
212#97—221no—
213C4×C8—111no—
214C4×C8C4×D1111yescharacteristic
215C2×C11—21no—
216C2×C11—81no—
217C2×C11C2×#35411yescharacteristic
218D11—41no—
219D11—81no—
220#41—441no—
221#41—441no—
222#41—441no—
223#41—441no—
224C2×Q8—111no—
225C2×Q8D4×D1111yescharacteristic
226C2×D4—111no—
227C2×D4—221no—
228C2×D4—221no—
229C2×D4—441no—
230C2×D4D4×D1111yescharacteristic
231C22×C4—111no—
232C22×C4—221no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4—441no—
236M16—41no—
237M16—441no—
238M16—441no—
239M16—441no—
240M16—881no—
241C2×C8—21no—
242C2×C8—221no—
243C2×C8—881no—
244C4⋊C4—21no—
245C4⋊C4—41no—
246C4⋊C4—221no—
247C4⋊C4—441no—
248C4⋊C4—441no—
249C4⋊C4—441no—
250C4⋊C4—441no—
251C4⋊C4—441no—
252C4⋊C4—881no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—441no—
256C22⋊C4—441no—
257C42—111no—
258C42—221no—
259C42—881no—
260C42C2×C4×D1111yescharacteristic
261C11#1360411yescharacteristic, complemented, Sylow
262C23—21no—
263C23—111no—
264C23—221no—
265Q8—41no—
266Q8—441no—
267D4—41no—
268D4—441no—
269D4—881no—
270D4—881no—
271D4—882no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—111no—
277C2×C4—221no—
278C2×C4—221no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—881no—
287C2×C4—882no—
288C2×C4—881no—
289C2×C4C22⋊C4×D1111yescharacteristic
290C8—41no—
291C8—81no—
292C8—441no—
293C8—881no—
294C22—41no—
295C22—81no—
296C22—221no—
297C22—441no—
298C22—441no—
299C22—881no—
300C22D11×#9911yescharacteristic
301C4—21no—
302C4—41no—
303C4—41no—
304C4—81no—
305C4—111no—
306C4—111no—
307C4—161no—
308C4—441no—
309C4—441no—
310C4—881no—
311C4—1761no—
312C2—21no—
313C2—81no—
314C2—441no—
315C2—881no—
316C2D11×#35411yescharacteristic
subgroupG/H
centerC2D11×#354
commutatorC42×C11C22×C4
Frattini#124C22×D11
FittingC11×#1414C2
socleC2×C11C2×#354
prime radical#10623199C22
cosocleC11×#124C23
hypercenter#1414D11
hypocenterC11#13604
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #1414

Complements

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

NH ≅ G/Ntype
4. #13066792C2semidirect
5. #13066791C2semidirect
6. #13066790C2semidirect
7. C11×#1414C2semidirect
8. D11×#125C4semidirect
11. #10622681C4semidirect
19. #10622310C4semidirect
20. C4×#4313C4semidirect
110. #1414D11semidirect
261. C11#13604semidirect

Maximal subgroups

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

subgroupindex
#130790132
#130702982
#130702802
#130667922
#130667912
#130667902
C11×#14142
#1360411