Finite Group Databasebeta

← #14664721

Subgroups — #14664721

Order 2816.

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

normal subgroups only

This group has 358 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#13068745C211yesmaximal, characteristic, complemented
4#13066626C211yesmaximal, characteristic, complemented
5#13066625C211yesmaximal, characteristic, complemented
6#13066624C211yesmaximal, characteristic, complemented
7C11×#1347C211yesmaximal, characteristic, complemented
8#10623127—21no—
9C11×#466C2211yescharacteristic
10#10622764C411yescharacteristic, complemented
11D8×Dic11C411yescharacteristic, complemented
12#10622728C2211yescharacteristic
13C2×C8×Dic11C2211yescharacteristic
14#10622651—21no—
15#10622590—21no—
16#10622487C411yescharacteristic, complemented
17#10622485C411yescharacteristic, complemented
18#10622373—21no—
19#10622369—21no—
20C11×C22⋊C16C2211yescharacteristic
21C11×#340C2211yescharacteristic
22#10622189C2211yescharacteristic
23C22⋊(C11⋊C16)C2211yescharacteristic
24#10622167—21no—
25#10622140—21no—
26Dic11⋊C16—21no—
27C2×#4341—41no—
28C2×C11×D8C2×C411yescharacteristic
29C22×C8×C11C2311yescharacteristic
30C11×#121—21no—
31C2×C11×C4⋊C4—21no—
32#66993—21no—
33#66992—41no—
34D4×Dic11—21no—
35C2×#4323—21no—
36#66983—21no—
37C2×C4⋊Dic11—21no—
38C2×C4×Dic11D411yescharacteristic
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—
49C11⋊#95—41no—
50C11⋊#95—41no—
51#66885—21no—
52#66882C2×C411yescharacteristic
53C8×Dic11C2×C411yescharacteristic
54C8×Dic11C2×C411yescharacteristic
55C8×Dic11D411yescharacteristic
56C8×Dic11D411yescharacteristic
57C2×C11⋊C16—21no—
58#66873—21no—
59#66871—21no—
60#11858—111nomaximal, Sylow
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C2×C22⋊D11—41no—
66C2×C22⋊D11—41no—
67C2×C22⋊D11—41no—
68C22×Dic11—41no—
69C22×Dic11—41no—
70C22×Dic11D811yescharacteristic
71C22×Dic11D811yescharacteristic
72#4341—82no—
73#4341—82no—
74C2×D44—21no—
75C2×C4×D11—41no—
76C2×Dic22—41no—
77C11×D8—41no—
78C2×C8×C11—41no—
79C2×C8×C11C22×C411yescharacteristic
80C2×C8×C11C2×D411yescharacteristic
81C11×C4⋊C4—21no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C22⋊C4—41no—
85C22⋊Dic11—41no—
86#4323—42no—
87(C2×D11)⋊C4—41no—
88(C2×D11)⋊C4—41no—
89C4⋊Dic11—21no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92Dic11⋊C4—41no—
93C4×Dic11C22⋊C411yescharacteristic
94C4×Dic11C22⋊C411yescharacteristic
95C4×Dic11SD1611yescharacteristic
96C4×Dic11SD1611yescharacteristic
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—
105#1835—111no—
106#1347—111no—
107#1347—111no—
108#1347—111no—
109#1347D1111yescharacteristic, complemented
110C23×C11—41no—
111C23×C11C2×D811yescharacteristic
112C22×D11—41no—
113D4×C11—41no—
114D4×C11—41no—
115D4×C11—81no—
116D4×C11—81no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—41no—
120C2×C4×C11—81no—
121C2×C4×C11—81no—
122C2×C4×C11—81no—
123C2×C4×C11C2×C22⋊C411yescharacteristic
124C2×C4×C11C2×SD1611yescharacteristic
125C22⋊D11—82no—
126C22⋊D11—82no—
127C22⋊D11—81no—
128C22⋊D11—81no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—82no—
134C2×Dic11—81no—
135C2×Dic11—81no—
136C2×Dic11—81no—
137C2×Dic11#10211yescharacteristic
138C2×Dic11#10211yescharacteristic
139C2×Dic11#10211yescharacteristic
140C2×Dic11#10211yescharacteristic
141D44—41no—
142D44—41no—
143C4×D11—82no—
144Dic22—82no—
145C8×C11—21no—
146C8×C11—21no—
147C11⋊C8—21no—
148C11⋊C8—21no—
149#532—221no—
150#500—111no—
151#493—111no—
152#486—221no—
153#466—111no—
154#466—221no—
155#466C2×D1111yescharacteristic
156C4×D8—111no—
157C4×D8—111no—
158C4×D8—221no—
159C2×C4×C8—111no—
160#382—221no—
161C4⋊C16—221no—
162C22⋊C16—111no—
163C22⋊C16C2×D1111yescharacteristic
164#346—221no—
165#340—111no—
166#340—221no—
167#340C2×D1111yescharacteristic
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—81no—
171C22×C11—81no—
172C22×C11—81no—
173C22×C11C2×#10211yescharacteristic
174C22×C11#50911yescharacteristic
175C22×C11#50911yescharacteristic
176C2×D11—81no—
177C2×D11—81no—
178C2×D11—81no—
179C4×C11—21no—
180C4×C11—81no—
181C4×C11—161no—
182C4×C11#41011yescharacteristic
183C4×C11#42111yescharacteristic
184Dic11—21no—
185Dic11—21no—
186Dic11—21no—
187Dic11—21no—
188Dic11—81no—
189Dic11—161no—
190C2×#41—441no—
191C2×D8—111no—
192C2×D8—221no—
193C2×D8C4×D1111yescharacteristic
194C22×C8—111no—
195C22×C8C22×D1111yescharacteristic
196C4⋊Q8—221no—
197#127—221no—
198#124—441no—
199#121—21no—
200#121—221no—
201#121—441no—
202C4×D4—221no—
203C4×D4—221no—
204C4×D4—441no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—221no—
207C2×C42—111no—
208C2×C16—21no—
209C2×C16—221no—
210#107—111no—
211#107—221no—
212#107C4×D1111yescharacteristic
213#102—21no—
214#102—221no—
215#102—221no—
216#102—221no—
217C4×C8—111no—
218C4×C8—111no—
219C4×C8—111no—
220C4×C8—111no—
221#95—441no—
222#95—441no—
223C2×C11—21no—
224C2×C11—21no—
225C2×C11—161no—
226C2×C11#151711yescharacteristic
227C2×C11#214011yescharacteristic
228C2×C11#214511yescharacteristic
229D11—161no—
230#41—882no—
231#41—882no—
232C2×Q8—441no—
233C2×D4—21no—
234C2×D4—41no—
235C2×D4—221no—
236C2×D4—441no—
237C2×D4—441no—
238C2×D4—441no—
239C22×C4—41no—
240C22×C4—111no—
241C22×C4—111no—
242C22×C4—441no—
243C22×C4—441no—
244C22×C4—441no—
245C22×C4D4×D1111yescharacteristic
246D8—41no—
247D8—441no—
248D8—442no—
249C2×C8—41no—
250C2×C8—111no—
251C2×C8—111no—
252C2×C8—441no—
253C2×C8C2×C4×D1111yescharacteristic
254C2×C8D4×D1111yescharacteristic
255C4⋊C4—21no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—221no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C22⋊C4—41no—
263C22⋊C4—441no—
264C22⋊C4—441no—
265C22⋊C4—441no—
266C42—111no—
267C42—111no—
268C42—111no—
269C42—111no—
270C16—41no—
271C16—441no—
272C11#1185811yescharacteristic, complemented, Sylow
273C23—41no—
274C23—441no—
275C23D8×D1111yescharacteristic
276Q8—882no—
277D4—41no—
278D4—41no—
279D4—81no—
280D4—81no—
281D4—441no—
282D4—441no—
283D4—882no—
284D4—882no—
285D4—881no—
286D4—881no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—111no—
296C2×C4—111no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—882no—
302C2×C4—882no—
303C2×C4—881no—
304C2×C4—881no—
305C2×C4—881no—
306C2×C4C22⋊C4×D1111yescharacteristic
307C2×C4SD16×D1111yescharacteristic
308C8—21no—
309C8—21no—
310C8—221no—
311C8—221no—
312C22—21no—
313C22—21no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22—881no—
318C22—881no—
319C22—881no—
320C22D11×#10211yescharacteristic
321C22#1062252411yescharacteristic
322C22#1062252711yescharacteristic
323C4—21no—
324C4—81no—
325C4—161no—
326C4—221no—
327C4—221no—
328C4—221no—
329C4—221no—
330C4—881no—
331C4—1761no—
332C4#1062235311yescharacteristic
333C4#1062243411yescharacteristic
334C2—21no—
335C2—21no—
336C2—161no—
337C2—1761no—
338C2#1306717411yescharacteristic
339C2#1307033011yescharacteristic
340C2#1307035011yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1347C2
socleC22×C11C2×#102
prime radical#13079190C2
cosocleC22×C8×C11C23
hypercenter#1347D11
hypocenterC11#11858
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. #13070416C2semidirect
3. #13068745C2semidirect
4. #13066626C2semidirect
5. #13066625C2semidirect
6. #13066624C2semidirect
7. C11×#1347C2semidirect
10. #10622764C4semidirect
11. D8×Dic11C4semidirect
16. #10622487C4semidirect
17. #10622485C4semidirect
109. #1347D11semidirect
272. C11#11858semidirect

Maximal subgroups

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

subgroupindex
#130791902
#130704162
#130687452
#130666262
#130666252
#130666242
C11×#13472
#1185811