Finite Group Databasebeta

← #14735658

Subgroups — #14735658

Order 2816.

942 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 171 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#13079611C212yesmaximal, complemented
2#13078964C211yesmaximal, characteristic, complemented
3#13067939C214yesmaximal, complemented
4#13067909C214yesmaximal, complemented
5#13067254C211yesmaximal, characteristic, complemented
6#13067227C212yesmaximal, complemented
7C11×#3548C211yesmaximal, characteristic, complemented
8C11×#562C2214yes—
9C11×#554—22no—
10C11×#550—22no—
11C11×#547—22no—
12C11×#540—22no—
13C11×#537—24no—
14C11×#533C2211yescharacteristic
15C11×#532C2212yes—
16#10623008C2211yescharacteristic
17#10622851—24no—
18#10622702—22no—
19#10622696—22no—
20#10622685—22no—
21#10622682C2212yes—
22#10622680C2212yes—
23#10622671C2214yes—
24#10622668C2214yes—
25#10622615—22no—
26#10622539C2212yes—
27C2×#66867C2211yescharacteristic
28#10622181C2214yes—
29#10622178C2218yes—
30C2×C11×#41—24no—
31C2×C11×#41D414yes—
32C2×#4339—21no—
33C11×C4⋊Q8D412yes—
34C11×C4⋊Q8D412yes—
35C11×#127—22no—
36C11×#127D412yes—
37C11×#125—22no—
38C11×#125C2312yes—
39C11×#124C2314yes—
40C11×#123—28no—
41C11×C22⋊Q8—24no—
42C11×C22⋊Q8—28no—
43C11×C22⋊Q8—22no—
44C11×#121—28no—
45C11×#121—24no—
46C11×#121—28no—
47C11×#121—22no—
48C11×#121—22no—
49C4×Q8×C11—22no—
50C4×D4×C11—24no—
51C4×D4×C11—22no—
52C4×D4×C11—22no—
53C11×#117D412yes—
54C2×C11×C4⋊C4—24no—
55C2×C42×C11C2311yescharacteristic
56C2×#4325—24no—
57C2×#4323—24no—
58#66983—22no—
59C22×C11⋊C8—21no—
60#66928—21no—
61#66927C2311yescharacteristic
62C4×D44—22no—
63#66922C2311yescharacteristic
64#66899—24no—
65#66896—24no—
66C22⋊(C11⋊C8)—22no—
67#66874—24no—
68#66873—24no—
69C4⋊(C11⋊C8)—22no—
70#66867—21no—
71#66867C2312yes—
72#66867C2314yes—
73#19061—111nomaximal, Sylow
74C11×#41—84no—
75C11×#41—88no—
76C2×Q8×C11—22no—
77C2×Q8×C11C2×D414yes—
78C2×D4×C11—28no—
79C2×D4×C11—24no—
80C2×D4×C11—22no—
81C2×D4×C11—22no—
82C2×D4×C11C2×D414yes—
83C22×C4×C11—28no—
84C22×C4×C11—24no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D412yes—
87C2×C22⋊D11—41no—
88#4339—44no—
89C2×D44—21no—
90C2×D44—22no—
91C2×C4×D11—41no—
92C2×Dic22—21no—
93C11×C4⋊C4—28no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4C2×D414yes—
99C11×C22⋊C4—28no—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—24no—
102C11×C22⋊C4—24no—
103C42×C11—22no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D412yes—
106C42×C11C2411yescharacteristic
107#4325—84no—
108#4323—84no—
109(C2×D11)⋊C4—42no—
110C4⋊Dic11—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—24no—
113C2×C11⋊C8—42no—
114#3548D1111yescharacteristic, complemented
115#3214—112no—
116#3135—111no—
117#1662—114no—
118#1656—114no—
119#1537—111no—
120#1530—112no—
121C23×C11—24no—
122C23×C11#12011yescharacteristic
123C22×D11—41no—
124Q8×C11—44no—
125Q8×C11—44no—
126D4×C11—44no—
127D4×C11—44no—
128D4×C11—44no—
129D4×C11—84no—
130D4×C11—88no—
131C2×C4×C11—22no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—42no—
135C2×C4×C11—48no—
136C2×C4×C11—88no—
137C2×C4×C11#12012yes—
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11C22×D412yes—
140C2×C4×C11C22×D411yescharacteristic
141C22⋊D11—82no—
142C2×Dic11—41no—
143D44—42no—
144D44—42no—
145D44—42no—
146C4×D11—82no—
147Dic22—42no—
148C11⋊C8—42no—
149C11⋊C8—44no—
150#562C2×D1114yes—
151#554—22no—
152#550—22no—
153#547—22no—
154#540—22no—
155#537—24no—
156#533C2×D1111yescharacteristic
157#532—111no—
158#532C2×D1112yes—
159#496—114no—
160#491—112no—
161#490—112no—
162#489—114no—
163#489—222no—
164#461—222no—
165#459—222no—
166#449—224no—
167#432—112no—
168#416—222no—
169C2×#97—111no—
170#330—114no—
171#329—118no—
172C22×C11—21no—
173C22×C11—22no—
174C22×C11—44no—
175C22×C11—44no—
176C22×C11—44no—
177C22×C11C2×#12011yescharacteristic
178C2×D11—81no—
179C2×D11—82no—
180C4×C11—21no—
181C4×C11—22no—
182C4×C11—22no—
183C4×C11—44no—
184C4×C11—44no—
185C4×C11#45412yes—
186Dic11—81no—
187C2×#41—24no—
188C2×#41—221no—
189C2×#41C22⋊D1114yes—
190C2×SD16—224no—
191C2×D8—224no—
192C22×C8—221no—
193C4⋊Q8—111no—
194C4⋊Q8C22⋊D1112yes—
195C4⋊Q8C22⋊D1112yes—
196#127—22no—
197#127—111no—
198#127C22⋊D1112yes—
199#125—22no—
200#125C22×D1112yes—
201#124—221no—
202#124C22×D1114yes—
203#123—28no—
204C22⋊Q8—24no—
205C22⋊Q8—28no—
206C22⋊Q8—22no—
207#121—28no—
208#121—24no—
209#121—28no—
210#121—22no—
211#121—22no—
212#121—222no—
213C4×Q8—22no—
214C4×D4—24no—
215C4×D4—22no—
216C4×D4—22no—
217C4×D4—222no—
218#117C22⋊D1112yes—
219C2×C4⋊C4—24no—
220C2×C42C22×D1111yescharacteristic
221C4⋊C8—222no—
222#103—224no—
223#103—224no—
224#102—224no—
225#102—224no—
226C22⋊C8—222no—
227#97—112no—
228#97—114no—
229#97—221no—
230C2×C11—41no—
231C2×C11—84no—
232C2×C11C2×#45411yescharacteristic
233C2×C11#301912yes—
234D11—161no—
235#41—84no—
236#41—88no—
237#41—444no—
238C2×Q8—22no—
239C2×Q8—221no—
240C2×Q8C2×C22⋊D1114yes—
241C2×D4—28no—
242C2×D4—24no—
243C2×D4—22no—
244C2×D4—22no—
245C2×D4—221no—
246C2×D4—222no—
247C2×D4—441no—
248C2×D4C2×C22⋊D1114yes—
249C22×C4—28no—
250C22×C4—24no—
251C22×C4—441no—
252C22×C4C2×C22⋊D1111yescharacteristic
253C22×C4C2×C22⋊D1112yes—
254SD16—884no—
255D8—884no—
256C2×C8—222no—
257C2×C8—224no—
258C2×C8—442no—
259C4⋊C4—28no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—24no—
264C4⋊C4—222no—
265C4⋊C4C2×C22⋊D1114yes—
266C22⋊C4—28no—
267C22⋊C4—22no—
268C22⋊C4—24no—
269C22⋊C4—24no—
270C22⋊C4—442no—
271C42—22no—
272C42C2×C22⋊D1111yescharacteristic
273C42C2×C22⋊D1112yes—
274C42C23×D1111yescharacteristic
275C11#1906111yescharacteristic, complemented, Sylow
276C23—24no—
277C23—441no—
278C23#6700611yescharacteristic
279Q8—44no—
280Q8—44no—
281Q8—442no—
282D4—44no—
283D4—44no—
284D4—44no—
285D4—84no—
286D4—88no—
287D4—442no—
288D4—442no—
289D4—442no—
290D4—882no—
291C2×C4—22no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—42no—
295C2×C4—48no—
296C2×C4—88no—
297C2×C4—441no—
298C2×C4—882no—
299C2×C4#6700612yes—
300C2×C4#6700611yescharacteristic
301C2×C4C22×C22⋊D1111yescharacteristic
302C2×C4C22×C22⋊D1112yes—
303C8—442no—
304C8—444no—
305C22—21no—
306C22—22no—
307C22—44no—
308C22—44no—
309C22—44no—
310C22—881no—
311C22—882no—
312C22C2×#6700611yescharacteristic
313C4—21no—
314C4—22no—
315C4—22no—
316C4—44no—
317C4—44no—
318C4—881no—
319C4#1062285812yes—
320C2—41no—
321C2—84no—
322C2—1761no—
323C2C2×#1062285811yescharacteristic
324C2#1307797312yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3548C2
socleC22×C11C2×#120
hypercenter#3548D11
hypocenterC11#19061
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #13079611C2semidirect
2. #13078964C2semidirect
3. #13067939C2semidirect
4. #13067909C2semidirect
5. #13067254C2semidirect
6. #13067227C2semidirect
7. C11×#3548C2semidirect
114. #3548D11semidirect
275. C11#19061semidirect

Maximal subgroups

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

subgroupindex
#130796112
#130789642
#130679392
#130679092
#130672542
#130672272
C11×#35482
#1906111