Finite Group Databasebeta

← #14664218

Subgroups — #14664218

Order 2816.

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

normal subgroups only

This group has 364 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#13079190C211yesmaximal, characteristic
2#13070416C211yesmaximal, characteristic, complemented
3#13068517C211yesmaximal, 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
12C2×#66886—21no—
13M16×Dic11—21no—
14#10622728C2211yescharacteristic
15C2×C8×Dic11C2211yescharacteristic
16#10622651—21no—
17#10622487C411yescharacteristic
18#10622485C411yescharacteristic
19#10622373—21no—
20#10622369—21no—
21C11×C22⋊C16C2211yescharacteristic
22C11×#341C2211yescharacteristic
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#66886—24no—
50#66885—21no—
51#66882C2×C411yescharacteristic
52#66879—41no—
53C8×Dic11—41no—
54C8×Dic11C2×C411yescharacteristic
55C8×Dic11C2×C411yescharacteristic
56C8×Dic11D411yescharacteristic
57C8×Dic11D411yescharacteristic
58C2×C11⋊C16—21no—
59#66873—21no—
60#66871—21no—
61#11751—111nomaximal, Sylow
62C2×D4×C11—21no—
63C2×D4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C2×C22⋊D11—41no—
66C2×C22⋊D11—41no—
67C2×C22⋊D11—41no—
68C22×Dic11—41no—
69C22×Dic11SD1611yescharacteristic
70C22×Dic11SD1611yescharacteristic
71#4341—84no—
72C2×D44—21no—
73C2×C4×D11—41no—
74C2×Dic22—41no—
75C11×D8—41no—
76C11×M16—22no—
77C11×M16—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11C22×C411yescharacteristic
81C2×C8×C11C2×D411yescharacteristic
82C11×C4⋊C4—21no—
83C11×C22⋊C4—41no—
84C22⋊Dic11—41no—
85#4323—42no—
86(C2×D11)⋊C4—41no—
87(C2×D11)⋊C4—41no—
88C4⋊Dic11—21no—
89Dic11⋊C4—41no—
90C4×Dic11C22⋊C411yescharacteristic
91C4×Dic11C22⋊C411yescharacteristic
92C4×Dic11D811yescharacteristic
93C4×Dic11D811yescharacteristic
94#4318—22no—
95#4318—41no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8C22⋊C411yescharacteristic
99C2×C11⋊C8C22⋊C411yescharacteristic
100D88—41no—
101C11×C16—41no—
102C11⋊C16—41no—
103#3169—111no—
104#2163—111no—
105C4×#108—111no—
106#1349—111no—
107#1349—111no—
108#1349—111no—
109#1349D1111yescharacteristic, complemented
110C23×C11—41no—
111C23×C11C2×SD1611yescharacteristic
112C22×D11—41no—
113D4×C11—41no—
114D4×C11—41no—
115D4×C11—82no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11C2×C22⋊C411yescharacteristic
120C2×C4×C11C2×D811yescharacteristic
121C22⋊D11—82no—
122C22⋊D11—82no—
123C22⋊D11—82no—
124C2×Dic11—22no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—82no—
128C2×Dic11#10211yescharacteristic
129C2×Dic11#10211yescharacteristic
130C2×Dic11#10211yescharacteristic
131C2×Dic11#10211yescharacteristic
132D44—41no—
133D44—41no—
134C4×D11—82no—
135Dic22—82no—
136C8×C11—21no—
137C8×C11—21no—
138C8×C11—42no—
139C11⋊C8—21no—
140C11⋊C8—42no—
141C11⋊C8#10412yes—
142#532—221no—
143#500—111no—
144#493—111no—
145#486—221no—
146#466—111no—
147#466—221no—
148#466C2×D1111yescharacteristic
149C4×D8—111no—
150C4×D8—111no—
151C4×D8—221no—
152C2×#108—221no—
153C4×M16—221no—
154C2×C4×C8—111no—
155C4⋊C16—221no—
156C22⋊C16—111no—
157C22⋊C16C2×D1111yescharacteristic
158#346—221no—
159#341—111no—
160#341C2×D1111yescharacteristic
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—81no—
165C22×C11—81no—
166C22×C11—81no—
167C22×C11C2×#10211yescharacteristic
168C2×D11—81no—
169C2×D11—81no—
170C2×D11—81no—
171C4×C11—21no—
172C4×C11—81no—
173C4×C11#41011yescharacteristic
174C4×C11C2×#10411yescharacteristic
175Dic11—21no—
176Dic11—21no—
177Dic11—21no—
178Dic11—81no—
179Dic11#36112yes—
180C2×#41—441no—
181C2×D8—111no—
182C2×D8—221no—
183C2×D8C4×D1111yescharacteristic
184C2×M16—21no—
185C2×M16—221no—
186C22×C8—111no—
187C22×C8C22×D1111yescharacteristic
188C4⋊Q8—221no—
189#127—221no—
190#124—441no—
191#121—21no—
192#121—221no—
193#121—441no—
194C4×D4—221no—
195C4×D4—221no—
196C4×D4—441no—
197C2×C42—111no—
198C2×C16—21no—
199C2×C16—221no—
200#108—224no—
201#107—111no—
202#107—221no—
203#107C4×D1111yescharacteristic
204#102—21no—
205#102—221no—
206#102—221no—
207#102—221no—
208#97—441no—
209C4×C8—111no—
210C4×C8—111no—
211C4×C8—111no—
212C4×C8—111no—
213C4×C8—441no—
214C2×C11—41no—
215C2×C11—161no—
216C2×C11#150211yescharacteristic
217C2×C11#214311yescharacteristic
218C2×C11C2×#36111yescharacteristic
219D11—161no—
220#41—884no—
221C2×Q8—441no—
222C2×D4—21no—
223C2×D4—41no—
224C2×D4—221no—
225C2×D4—441no—
226C2×D4—441no—
227C2×D4—441no—
228C22×C4—111no—
229C22×C4—111no—
230C22×C4—441no—
231C22×C4—441no—
232C22×C4D4×D1111yescharacteristic
233D8—41no—
234D8—441no—
235D8—442no—
236M16—22no—
237M16—41no—
238M16—222no—
239M16—441no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—111no—
243C2×C8—111no—
244C2×C8—222no—
245C2×C8—441no—
246C2×C8C2×C4×D1111yescharacteristic
247C2×C8D4×D1111yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—221no—
250C4⋊C4—441no—
251C22⋊C4—41no—
252C22⋊C4—441no—
253C22⋊C4—441no—
254C22⋊C4—441no—
255C42—111no—
256C42—111no—
257C42—111no—
258C42—111no—
259C16—41no—
260C16—441no—
261C11#1175111yescharacteristic, complemented, Sylow
262C23—41no—
263C23—441no—
264C23SD16×D1111yescharacteristic
265Q8—882no—
266D4—41no—
267D4—41no—
268D4—82no—
269D4—441no—
270D4—441no—
271D4—882no—
272D4—882no—
273D4—882no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—111no—
278C2×C4—111no—
279C2×C4—111no—
280C2×C4—111no—
281C2×C4—222no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—882no—
285C2×C4—882no—
286C2×C4C22⋊C4×D1111yescharacteristic
287C2×C4D8×D1111yescharacteristic
288C8—21no—
289C8—21no—
290C8—42no—
291C8—112no—
292C8—221no—
293C8—442no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—81no—
298C22—81no—
299C22—81no—
300C22—881no—
301C22—881no—
302C22—881no—
303C22D11×#10211yescharacteristic
304C4—21no—
305C4—81no—
306C4—112no—
307C4—221no—
308C4—221no—
309C4—221no—
310C4—881no—
311C4#1062235311yescharacteristic
312C4D11×#10411yescharacteristic
313C2—41no—
314C2—161no—
315C2—1761no—
316C2#1306710911yescharacteristic
317C2#1307034211yescharacteristic
318C2D11×#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#11751
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. #13068517C2semidirect
4. #13066632C2semidirect
5. #13066631C2semidirect
6. #13066630C2semidirect
7. C11×#1349C2semidirect
109. #1349D11semidirect
261. C11#11751semidirect

Maximal subgroups

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

subgroupindex
#130791902
#130704162
#130685172
#130666322
#130666312
#130666302
C11×#13492
#1175111