Finite Group Databasebeta

← #14664747

Subgroups — #14664747

Order 2816.

344 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 77 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#13079190C211yesmaximal, characteristic
2#13070416C211yesmaximal, characteristic, complemented
3#13068752C211yesmaximal, characteristic, complemented
4#13066632C211yesmaximal, characteristic, complemented
5#13066631C211yesmaximal, characteristic, complemented
6#13066630C211yesmaximal, characteristic, complemented
7C11×#1349C211yesmaximal, characteristic, complemented
8#10623127—21no—
9C11×#466C2211yescharacteristic
10#10622764C411yescharacteristic
11D8×Dic11C411yescharacteristic
12#10622731—21no—
13#10622728C2211yescharacteristic
14C2×C8×Dic11C2211yescharacteristic
15#10622651—21no—
16#10622487C411yescharacteristic
17#10622485C411yescharacteristic
18#10622373—21no—
19#10622369—21no—
20C11×C22⋊C16C2211yescharacteristic
21C11×#341C2211yescharacteristic
22#10622196—21no—
23#10622190C2211yescharacteristic
24C22⋊(C11⋊C16)C2211yescharacteristic
25#10622140—21no—
26Dic11⋊C16—21no—
27C2×#4341—41no—
28C2×C11×D8C2×C411yescharacteristic
29C2×C11×M16—21no—
30C22×C8×C11C2311yescharacteristic
31C11×#121—21no—
32#66993—21no—
33#66992—41no—
34D4×Dic11—21no—
35C2×#4323—21no—
36#66983—21no—
37C2×C4×Dic11D411yescharacteristic
38C2×#4318—21no—
39C22×C11⋊C8D411yescharacteristic
40C2×D88C2×C411yescharacteristic
41#66946—21no—
42#66941—21no—
43#66938—41no—
44(C22⋊D11)⋊C4—41no—
45C2×C11×C16—21no—
46C11×#107C2×C411yescharacteristic
47C11×#102—21no—
48#66896—21no—
49#66885—21no—
50#66882C2×C411yescharacteristic
51Dic11⋊C8—41no—
52Dic11⋊C8—41no—
53C8×Dic11C2×C411yescharacteristic
54C8×Dic11C2×C411yescharacteristic
55C8×Dic11D411yescharacteristic
56C8×Dic11D411yescharacteristic
57C2×C11⋊C16—21no—
58#66873—21no—
59#66871—21no—
60#11864—111nomaximal, Sylow
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C2×C22⋊D11—41no—
65C2×C22⋊D11—41no—
66C2×C22⋊D11—41no—
67C22×Dic11—41no—
68C22×Dic11SD1611yescharacteristic
69C22×Dic11SD1611yescharacteristic
70#4341—84no—
71C2×D44—21no—
72C2×C4×D11—41no—
73C2×Dic22—41no—
74C11×D8—41no—
75C11×M16—41no—
76C11×M16—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11C22×C411yescharacteristic
80C2×C8×C11C2×D411yescharacteristic
81C11×C4⋊C4—21no—
82C11×C22⋊C4—41no—
83C22⋊Dic11—41no—
84#4323—42no—
85(C2×D11)⋊C4—41no—
86(C2×D11)⋊C4—41no—
87C4⋊Dic11—21no—
88Dic11⋊C4—41no—
89C4×Dic11C22⋊C411yescharacteristic
90C4×Dic11C22⋊C411yescharacteristic
91C4×Dic11D811yescharacteristic
92C4×Dic11D811yescharacteristic
93#4318—41no—
94#4318—41no—
95C2×C11⋊C8—41no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8C22⋊C411yescharacteristic
98C2×C11⋊C8C22⋊C411yescharacteristic
99D88—41no—
100C11×C16—41no—
101C11⋊C16—41no—
102#3169—111no—
103#2163—111no—
104#1837—111no—
105#1349—111no—
106#1349—111no—
107#1349—111no—
108#1349D1111yescharacteristic, complemented
109C23×C11—41no—
110C23×C11C2×SD1611yescharacteristic
111C22×D11—41no—
112D4×C11—41no—
113D4×C11—41no—
114D4×C11—82no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—41no—
118C2×C4×C11C2×C22⋊C411yescharacteristic
119C2×C4×C11C2×D811yescharacteristic
120C22⋊D11—82no—
121C22⋊D11—82no—
122C22⋊D11—82no—
123C2×Dic11—22no—
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—82no—
127C2×Dic11#10211yescharacteristic
128C2×Dic11#10211yescharacteristic
129C2×Dic11#10211yescharacteristic
130C2×Dic11#10211yescharacteristic
131D44—41no—
132D44—41no—
133C4×D11—82no—
134Dic22—82no—
135C8×C11—21no—
136C8×C11—21no—
137C8×C11—81no—
138C11⋊C8—21no—
139C11⋊C8—21no—
140C11⋊C8—81no—
141#532—221no—
142#500—111no—
143#493—111no—
144#486—221no—
145#466—111no—
146#466—221no—
147#466C2×D1111yescharacteristic
148C4×D8—111no—
149C4×D8—111no—
150C4×D8—221no—
151#423—221no—
152C2×C4×C8—111no—
153C4⋊C16—221no—
154C22⋊C16—111no—
155C22⋊C16C2×D1111yescharacteristic
156#346—221no—
157#341—111no—
158#341—221no—
159#341C2×D1111yescharacteristic
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—81no—
164C22×C11—81no—
165C22×C11—81no—
166C22×C11C2×#10211yescharacteristic
167C2×D11—81no—
168C2×D11—81no—
169C2×D11—81no—
170C4×C11—21no—
171C4×C11—81no—
172C4×C11#41011yescharacteristic
173C4×C11#42111yescharacteristic
174Dic11—21no—
175Dic11—21no—
176Dic11—21no—
177Dic11—81no—
178Dic11#36112yes—
179C2×#41—441no—
180C2×D8—111no—
181C2×D8—221no—
182C2×D8C4×D1111yescharacteristic
183C2×M16—21no—
184C2×M16—221no—
185C22×C8—111no—
186C22×C8C22×D1111yescharacteristic
187C4⋊Q8—221no—
188#127—221no—
189#124—441no—
190#121—21no—
191#121—221no—
192#121—441no—
193C4×D4—221no—
194C4×D4—221no—
195C4×D4—441no—
196C2×C42—111no—
197C2×C16—21no—
198C2×C16—221no—
199#107—111no—
200#107—221no—
201#107C4×D1111yescharacteristic
202C4⋊C8—441no—
203C4⋊C8—441no—
204#102—21no—
205#102—221no—
206#102—221no—
207#102—221no—
208C4×C8—111no—
209C4×C8—111no—
210C4×C8—111no—
211C4×C8—111no—
212C2×C11—41no—
213C2×C11—161no—
214C2×C11#151711yescharacteristic
215C2×C11#214311yescharacteristic
216C2×C11C2×#36111yescharacteristic
217D11—161no—
218#41—884no—
219C2×Q8—441no—
220C2×D4—21no—
221C2×D4—41no—
222C2×D4—221no—
223C2×D4—441no—
224C2×D4—441no—
225C2×D4—441no—
226C22×C4—111no—
227C22×C4—111no—
228C22×C4—441no—
229C22×C4—441no—
230C22×C4D4×D1111yescharacteristic
231D8—41no—
232D8—441no—
233D8—442no—
234M16—41no—
235M16—41no—
236M16—441no—
237M16—441no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—111no—
241C2×C8—111no—
242C2×C8—441no—
243C2×C8—441no—
244C2×C8C2×C4×D1111yescharacteristic
245C2×C8D4×D1111yescharacteristic
246C4⋊C4—21no—
247C4⋊C4—221no—
248C4⋊C4—441no—
249C22⋊C4—41no—
250C22⋊C4—441no—
251C22⋊C4—441no—
252C22⋊C4—441no—
253C42—111no—
254C42—111no—
255C42—111no—
256C42—111no—
257C16—41no—
258C16—441no—
259C11#1186411yescharacteristic, complemented, Sylow
260C23—41no—
261C23—441no—
262C23SD16×D1111yescharacteristic
263Q8—882no—
264D4—41no—
265D4—41no—
266D4—82no—
267D4—441no—
268D4—441no—
269D4—882no—
270D4—882no—
271D4—882no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—111no—
276C2×C4—111no—
277C2×C4—111no—
278C2×C4—111no—
279C2×C4—222no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—882no—
283C2×C4—882no—
284C2×C4C22⋊C4×D1111yescharacteristic
285C2×C4D8×D1111yescharacteristic
286C8—21no—
287C8—21no—
288C8—81no—
289C8—221no—
290C8—221no—
291C8—881no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—81no—
296C22—81no—
297C22—81no—
298C22—881no—
299C22—881no—
300C22—881no—
301C22D11×#10211yescharacteristic
302C4—21no—
303C4—81no—
304C4—112no—
305C4—221no—
306C4—221no—
307C4—221no—
308C4—881no—
309C4#1062235311yescharacteristic
310C4#1062243411yescharacteristic
311C2—41no—
312C2—161no—
313C2—1761no—
314C2#1306717411yescharacteristic
315C2#1307034211yescharacteristic
316C2D11×#36111yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1349C2
socleC22×C11C2×#102
prime radical#13079190C2
cosocleC22×C8×C11C23
hypercenter#1349D11
hypocenterC11#11864
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1349

Complements

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

NH ≅ G/Ntype
2. #13070416C2semidirect
3. #13068752C2semidirect
4. #13066632C2semidirect
5. #13066631C2semidirect
6. #13066630C2semidirect
7. C11×#1349C2semidirect
108. #1349D11semidirect
259. C11#11864semidirect

Maximal subgroups

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

subgroupindex
#130791902
#130704162
#130687522
#130666322
#130666312
#130666302
C11×#13492
#1186411