Finite Group Databasebeta

← #14674173

Subgroups — #14674173

Order 2816.

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

normal subgroups only

This group has 308 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#13079702C211yesmaximal, characteristic
2#13070302C211yesmaximal, characteristic
3#13070289C211yesmaximal, characteristic
4#13066791C211yesmaximal, characteristic, complemented
5#13066777C211yesmaximal, characteristic, complemented
6#13066775C211yesmaximal, characteristic, complemented
7C11×#1414C211yesmaximal, characteristic, complemented
8#10623228C411yescharacteristic, complemented
9#10623206C2211yescharacteristic
10C11×#488C2211yescharacteristic
11#10622682C411yescharacteristic, complemented
12#10622673C2211yescharacteristic
13#10622421—21no—
14#10622406—21no—
15#10622396—21no—
16#10622380—21no—
17D11×#101—21no—
18#10622353—21no—
19#10622312C411yescharacteristic, complemented
20#10622303C411yescharacteristic, complemented
21C11×#355C2211yescharacteristic
22C11×#354C2211yescharacteristic
23#10622180C2211yescharacteristic
24#10622179C2211yescharacteristic
25#10622116—21no—
26#10622111—21no—
27C2×Q8×D11D411yescharacteristic
28C2×#4341D411yescharacteristic
29C11×#125C2×C411yescharacteristic
30C11×#124C2311yescharacteristic
31#66997D411yescharacteristic
32C2×#4326—21no—
33#66989D411yescharacteristic
34C2×#4324—21no—
35M16×D11—41no—
36C2×Dic44—21no—
37C2×Dic44—21no—
38#66951—41no—
39#66950—21no—
40#66943—41no—
41#66940—21no—
42#66936—41no—
43#66931—41no—
44#66930—41no—
45#66925C2×C411yescharacteristic
46#66922C2×C411yescharacteristic
47#66922C2×C411yescharacteristic
48C11×#103—21no—
49C11×#102—21no—
50C11×#101—21no—
51C11×#99—21no—
52C4×C8×C11C2×C411yescharacteristic
53#66900—21no—
54#66898—21no—
55#66888—41no—
56(C2×D11)⋊C8—21no—
57Dic11⋊C8—21no—
58#66874—21no—
59#66874—21no—
60#66870—41no—
61#66867C2×C411yescharacteristic
62#13608—111nomaximal, Sylow
63C2×Q8×C11C2×D411yescharacteristic
64C2×D4×C11C2×D411yescharacteristic
65C2×C22⋊D11—21no—
66C22×Dic11—21no—
67Q8×D11—81no—
68#4341—81no—
69C2×C4×D11—21no—
70C2×C4×D11C22⋊C411yescharacteristic
71C2×Dic22—21no—
72C2×Dic22—21no—
73C2×Dic22C22⋊C411yescharacteristic
74C2×Dic22C22⋊C411yescharacteristic
75C11×M16—41no—
76C2×C8×C11—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—41no—
79C11×C22⋊C4—41no—
80C11×C22⋊C4—41no—
81C42×C11C22×C411yescharacteristic
82C22⋊Dic11—41no—
83C22⋊Dic11—41no—
84#4326—81no—
85#4324—81no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—41no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91Dic11⋊C4—21no—
92Dic11⋊C4—41no—
93Dic11⋊C4—41no—
94Dic11⋊C4—81no—
95C4×Dic11—41no—
96C4×Dic11—81no—
97C4×Dic11C22⋊C411yescharacteristic
98#4318—41no—
99C2×C11⋊C8—21no—
100Dic44—81no—
101Dic44—81no—
102#4313—81no—
103C8×D11—81no—
104#3223—111no—
105#2133—111no—
106#2129—111no—
107#1414—111no—
108#1414D1111yescharacteristic, complemented
109#1407—111no—
110#1407—111no—
111C23×C11—21no—
112C22×D11#9911yescharacteristic
113Q8×C11—41no—
114D4×C11—41no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—41no—
118C2×C4×C11—81no—
119C2×C4×C11C2×C22⋊C411yescharacteristic
120C22⋊D11—81no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—81no—
128C2×Dic11#9911yescharacteristic
129C4×D11—41no—
130C4×D11—41no—
131C4×D11—41no—
132Dic22—41no—
133Dic22—41no—
134Dic22—41no—
135Dic22—41no—
136Dic22—81no—
137C8×C11—41no—
138C8×C11—81no—
139C11⋊C8—41no—
140C11⋊C8—81no—
141#541—111no—
142#536—111no—
143#497—111no—
144#494—111no—
145#491—111no—
146#488C2×D1111yescharacteristic
147#464—221no—
148#462—221no—
149#452—221no—
150#451—221no—
151#433—111no—
152C2×#101—221no—
153#410—221no—
154#356—221no—
155#355—111no—
156#355C2×D1111yescharacteristic
157#354—111no—
158#354—221no—
159#354C2×D1111yescharacteristic
160C22×C11—41no—
161C22×C11—81no—
162C22×C11C2×#9911yescharacteristic
163C2×D11—21no—
164C2×D11—41no—
165C4×C11—21no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—81no—
169C4×C11—161no—
170Dic11—21no—
171Dic11—41no—
172Dic11—41no—
173Dic11—41no—
174Dic11—81no—
175Dic11—161no—
176C2×#41—111no—
177C22×Q8—111no—
178C2×Q16—221no—
179C2×Q16—221no—
180C2×Q16—221no—
181C2×SD16—221no—
182C2×M16—441no—
183C4⋊Q8—111no—
184C4⋊Q8—111no—
185C4⋊Q8—111no—
186#126—441no—
187#125—441no—
188#125C4×D1111yescharacteristic
189#124—111no—
190#124C22×D1111yescharacteristic
191#123—441no—
192C22⋊Q8—221no—
193C22⋊Q8—441no—
194C4×Q8—221no—
195#117—111no—
196#117—441no—
197C4⋊C8—221no—
198#103—21no—
199#103—221no—
200#103—221no—
201#102—21no—
202#101—21no—
203#101—221no—
204#101—441no—
205#99—21no—
206#99—221no—
207#99—441no—
208C22⋊C8—221no—
209#97—111no—
210C4×C8C4×D1111yescharacteristic
211C2×C11—21no—
212C2×C11—81no—
213C2×C11#212711yescharacteristic
214D11—41no—
215#41—881no—
216C2×Q8—111no—
217C2×Q8—111no—
218C2×Q8—221no—
219C2×Q8—221no—
220C2×Q8—881no—
221C2×Q8D4×D1111yescharacteristic
222C2×D4—221no—
223C2×D4D4×D1111yescharacteristic
224C22×C4—111no—
225C22×C4—221no—
226C22×C4—221no—
227Q16—881no—
228Q16—881no—
229Q16—881no—
230SD16—881no—
231M16—41no—
232M16—441no—
233M16—881no—
234C2×C8—21no—
235C2×C8—221no—
236C2×C8—881no—
237C4⋊C4—21no—
238C4⋊C4—41no—
239C4⋊C4—221no—
240C4⋊C4—441no—
241C4⋊C4—441no—
242C4⋊C4—441no—
243C4⋊C4—441no—
244C4⋊C4—441no—
245C4⋊C4—881no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—221no—
249C22⋊C4—441no—
250C22⋊C4—441no—
251C22⋊C4—441no—
252C42—111no—
253C42—441no—
254C42—881no—
255C42C2×C4×D1111yescharacteristic
256C11#1360811yescharacteristic, complemented, Sylow
257C23—21no—
258C23—111no—
259Q8—41no—
260Q8—441no—
261Q8—441no—
262Q8—441no—
263Q8—441no—
264Q8—881no—
265D4—41no—
266D4—881no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—81no—
271C2×C4—111no—
272C2×C4—221no—
273C2×C4—221no—
274C2×C4—221no—
275C2×C4—441no—
276C2×C4—441no—
277C2×C4—441no—
278C2×C4—441no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—881no—
282C2×C4C22⋊C4×D1111yescharacteristic
283C8—41no—
284C8—81no—
285C8—441no—
286C8—881no—
287C22—41no—
288C22—81no—
289C22—221no—
290C22—441no—
291C22D11×#9911yescharacteristic
292C4—21no—
293C4—41no—
294C4—41no—
295C4—81no—
296C4—161no—
297C4—221no—
298C4—441no—
299C4—441no—
300C4—441no—
301C4—881no—
302C4—1761no—
303C2—21no—
304C2—81no—
305C2—441no—
306C2#1307028411yescharacteristic
subgroupG/H
centerC2#13070284
commutatorC42×C11C22×C4
Frattini#124C22×D11
FittingC11×#1414C2
socleC2×C11#2127
prime radicalC2×#4341D4
cosocleC11×#124C23
hypercenter#1414D11
hypocenterC11#13608
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. #13066791C2semidirect
5. #13066777C2semidirect
6. #13066775C2semidirect
7. C11×#1414C2semidirect
8. #10623228C4semidirect
11. #10622682C4semidirect
19. #10622312C4semidirect
20. #10622303C4semidirect
108. #1414D11semidirect
256. C11#13608semidirect

Maximal subgroups

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

subgroupindex
#130797022
#130703022
#130702892
#130667912
#130667772
#130667752
C11×#14142
#1360811