Finite Group Databasebeta

← #14664708

Subgroups — #14664708

Order 2816.

324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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#13079181C211yesmaximal, characteristic
2#13070412C211yesmaximal, characteristic, complemented
3#13068745C211yesmaximal, characteristic, complemented
4#13066629C211yesmaximal, characteristic, complemented
5#13066627C211yesmaximal, characteristic, complemented
6#13066625C211yesmaximal, characteristic
7C11×#1347C211yesmaximal, characteristic
8#10623131—21no—
9C11×#466C2211yescharacteristic
10#10622768C411yescharacteristic, complemented
11D8×Dic11C411yescharacteristic, complemented
12#10622729C2211yescharacteristic
13C2×C8×Dic11C2211yescharacteristic
14#10622654—21no—
15#10622590—21no—
16#10622491C411yescharacteristic, complemented
17#10622486C411yescharacteristic, complemented
18#10622381—21no—
19#10622371—21no—
20C11×C22⋊C16C2211yescharacteristic
21C11×#340C2211yescharacteristic
22#10622189C2211yescharacteristic
23C22⋊(C11⋊C16)C2211yescharacteristic
24#10622167—21no—
25Dic11⋊C16—21no—
26C16×Dic11—21no—
27C2×C11×D8C2×C411yescharacteristic
28C22×C8×C11C2311yescharacteristic
29C11×#121—21no—
30C2×C11×C4⋊C4—21no—
31#66989—21no—
32#66988—41no—
33D4×Dic11—21no—
34D4×Dic11—41no—
35C2×#4324—21no—
36C2×C4⋊Dic11—21no—
37#66977—21no—
38C2×C4×Dic11D411yescharacteristic
39C22×C11⋊C8D411yescharacteristic
40C2×Dic44C2×C411yescharacteristic
41#66943—21no—
42#66940—21no—
43#66932—41no—
44#66930—41no—
45C2×C11×C16—21no—
46C11×#107C2×C411yescharacteristic
47C11×#102—21no—
48#66896—21no—
49C11⋊#95—41no—
50C11⋊#95—41no—
51#66882C2×C411yescharacteristic
52#66880—21no—
53C8×Dic11C2×C411yescharacteristic
54C8×Dic11C2×C411yescharacteristic
55C8×Dic11D411yescharacteristic
56C8×Dic11D411yescharacteristic
57C2×C11⋊C16—21no—
58#66874—21no—
59#66872—21no—
60#11855—111nomaximal, Sylow
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×Dic11—41no—
66C22×Dic11—41no—
67C22×Dic11D811yescharacteristic
68C22×Dic11D811yescharacteristic
69C2×Dic22—21no—
70C11×D8—41no—
71C2×C8×C11—41no—
72C2×C8×C11C22×C411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C22⋊C4—41no—
78C22⋊Dic11—41no—
79C22⋊Dic11—41no—
80C22⋊Dic11—41no—
81C22⋊Dic11—41no—
82#4324—42no—
83C4⋊Dic11—21no—
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90C4×Dic11—41no—
91C4×Dic11C22⋊C411yescharacteristic
92C4×Dic11C22⋊C411yescharacteristic
93C4×Dic11SD1611yescharacteristic
94C4×Dic11SD1611yescharacteristic
95C2×C11⋊C8—41no—
96C2×C11⋊C8C22⋊C411yescharacteristic
97C2×C11⋊C8C22⋊C411yescharacteristic
98Dic44—41no—
99C11×C16—41no—
100C11⋊C16—41no—
101#3168—111no—
102#2162—111no—
103#1835—111no—
104#1348—111no—
105#1348—111no—
106#1347—111no—
107#1347D1111yescharacteristic
108C23×C11—41no—
109C23×C11C2×D811yescharacteristic
110D4×C11—41no—
111D4×C11—41no—
112D4×C11—81no—
113D4×C11—81no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—41no—
117C2×C4×C11—81no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11C2×C22⋊C411yescharacteristic
121C2×C4×C11C2×SD1611yescharacteristic
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—82no—
128C2×Dic11—81no—
129C2×Dic11—81no—
130C2×Dic11—81no—
131C2×Dic11#10211yescharacteristic
132C2×Dic11#10211yescharacteristic
133C2×Dic11#10211yescharacteristic
134C2×Dic11#10211yescharacteristic
135Dic22—41no—
136Dic22—41no—
137C8×C11—21no—
138C8×C11—21no—
139C11⋊C8—21no—
140C11⋊C8—21no—
141#529—221no—
142#499—111no—
143#495—111no—
144#488—221no—
145#467—111no—
146#466C2×D1111yescharacteristic
147#465—221no—
148C4×Q16—111no—
149C4×SD16—221no—
150C4×D8—111no—
151C2×C4×C8—111no—
152#382—221no—
153C4⋊C16—221no—
154C22⋊C16—111no—
155C22⋊C16C2×D1111yescharacteristic
156C4×C16—221no—
157#340—111no—
158#340—221no—
159#340C2×D1111yescharacteristic
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—81no—
163C22×C11—81no—
164C22×C11—81no—
165C22×C11C2×#10211yescharacteristic
166C22×C11#50811yescharacteristic
167C22×C11#50811yescharacteristic
168C4×C11—21no—
169C4×C11—81no—
170C4×C11—161no—
171C4×C11#41011yescharacteristic
172C4×C11#42111yescharacteristic
173Dic11—21no—
174Dic11—21no—
175Dic11—21no—
176Dic11—21no—
177Dic11—81no—
178Dic11—81no—
179Dic11—161no—
180C2×Q16—111no—
181C2×SD16—221no—
182C2×D8C4×D1111yescharacteristic
183C22×C8—111no—
184C22×C8C22×D1111yescharacteristic
185#126—441no—
186#125—221no—
187#124—221no—
188#123—441no—
189C22⋊Q8—221no—
190#121—21no—
191C4×Q8—221no—
192C4×D4—221no—
193C4×D4—441no—
194#117—441no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—221no—
197C2×C42—111no—
198C2×C16—21no—
199C2×C16—221no—
200#107—111no—
201#107C4×D1111yescharacteristic
202#106—221no—
203#103—221no—
204#103—221no—
205#102—21no—
206#102—221no—
207C4×C8—111no—
208C4×C8—111no—
209C4×C8—111no—
210C4×C8—111no—
211#95—441no—
212#95—441no—
213C2×C11—21no—
214C2×C11—21no—
215C2×C11—161no—
216C2×C11#151711yescharacteristic
217C2×C11#213811yescharacteristic
218C2×C11#214511yescharacteristic
219C2×Q8—221no—
220C2×D4—21no—
221C2×D4—41no—
222C22×C4—41no—
223C22×C4—111no—
224C22×C4—111no—
225C22×C4—441no—
226C22×C4—441no—
227C22×C4D4×D1111yescharacteristic
228Q16—441no—
229SD16—442no—
230D8—41no—
231C2×C8—41no—
232C2×C8—111no—
233C2×C8—111no—
234C2×C8—441no—
235C2×C8C2×C4×D1111yescharacteristic
236C2×C8D4×D1111yescharacteristic
237C4⋊C4—21no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—221no—
241C4⋊C4—441no—
242C4⋊C4—441no—
243C4⋊C4—441no—
244C4⋊C4—441no—
245C4⋊C4—441no—
246C4⋊C4—441no—
247C22⋊C4—41no—
248C22⋊C4—441no—
249C22⋊C4—441no—
250C22⋊C4—441no—
251C22⋊C4—441no—
252C42—111no—
253C42—111no—
254C42—111no—
255C42—111no—
256C42—441no—
257C16—41no—
258C16—441no—
259C11#1185511yescharacteristic, complemented, Sylow
260C23—41no—
261C23D8×D1111yescharacteristic
262Q8—441no—
263Q8—441no—
264D4—41no—
265D4—41no—
266D4—81no—
267D4—81no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—111no—
275C2×C4—111no—
276C2×C4—111no—
277C2×C4—111no—
278C2×C4—221no—
279C2×C4—221no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—882no—
284C2×C4—881no—
285C2×C4—881no—
286C2×C4—881no—
287C2×C4C22⋊C4×D1111yescharacteristic
288C2×C4SD16×D1111yescharacteristic
289C8—21no—
290C8—21no—
291C8—221no—
292C8—221no—
293C22—21no—
294C22—21no—
295C22—81no—
296C22—81no—
297C22—81no—
298C22D11×#10211yescharacteristic
299C22#1062252511yescharacteristic
300C22#1062252911yescharacteristic
301C4—21no—
302C4—81no—
303C4—161no—
304C4—221no—
305C4—221no—
306C4—221no—
307C4—221no—
308C4—881no—
309C4—881no—
310C4—1761no—
311C4#1062235311yescharacteristic
312C4#1062243411yescharacteristic
313C2—21no—
314C2—21no—
315C2—161no—
316C2#1306717411yescharacteristic
317C2#1307032011yescharacteristic
318C2#1307035011yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1347C2
socleC22×C11C2×#102
prime radicalC11×#466C22
cosocleC22×C8×C11C23
hypercenter#1347D11
hypocenterC11#11855
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1347

Complements

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

NH ≅ G/Ntype
2. #13070412C2semidirect
3. #13068745C2semidirect
4. #13066629C2semidirect
5. #13066627C2semidirect
10. #10622768C4semidirect
11. D8×Dic11C4semidirect
16. #10622491C4semidirect
17. #10622486C4semidirect
259. C11#11855semidirect

Maximal subgroups

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

subgroupindex
#130791812
#130704122
#130687452
#130666292
#130666272
#130666252
C11×#13472
#1185511