Finite Group Databasebeta

← #14735814

Subgroups — #14735814

Order 2816.

944 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 179 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#13079163C212yesmaximal, complemented
2#13079076C211yesmaximal, characteristic
3#13067927C218yesmaximal, complemented
4#13067211C212yesmaximal, complemented
5#13067208C211yesmaximal, characteristic
6C11×#3550C211yesmaximal, characteristic
7C11×#563C2214yes—
8C11×#559—21no—
9Q82×C11—21no—
10C11×#556—22no—
11D4×Q8×C11—22no—
12C11×#542—24no—
13C11×#536—22no—
14C11×#533C2212yes—
15C11×#532C2211yescharacteristic
16C2×#67004—22no—
17C2×#66922C2211yescharacteristic
18#10622705—21no—
19#10622692—22no—
20#10622691—22no—
21#10622689—21no—
22#10622678C2218yes—
23#10622673C2214yes—
24#10622608—24no—
25C4×#4318C2211yescharacteristic
26C4×#4318C2212yes—
27#10622181C2218yes—
28#10622178C2214yes—
29C2×C11×#41D412yes—
30C22×Q8×C11—22no—
31C22×Dic22—21no—
32C11×C4⋊Q8—24no—
33C11×C4⋊Q8—24no—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D412yes—
36C11×C4⋊Q8D412yes—
37C11×#127D411yescharacteristic
38C11×#126—28no—
39C11×#125C2314yes—
40C11×#124—24no—
41C11×#124—24no—
42C11×#124C2312yes—
43C11×#123—24no—
44C11×#123—24no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—22no—
48C11×C22⋊Q8—28no—
49C11×#121—22no—
50C4×Q8×C11—24no—
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C4×D4×C11—24no—
54C4×D4×C11—22no—
55C11×#117—22no—
56C11×#117D414yes—
57C2×C42×C11C2311yescharacteristic
58#67004—48no—
59C2×#4326—24no—
60C2×#4324—24no—
61C2×C4⋊Dic11—22no—
62C2×#4318—21no—
63C2×#4318—22no—
64#66922—22no—
65#66922—21no—
66#66922C2312yes—
67#66872—28no—
68#66871—28no—
69#66867C2312yes—
70#66867C2314yes—
71C4×C11⋊C8—21no—
72C4×C11⋊C8—22no—
73#19078—111nomaximal, Sylow
74C11×#41—44no—
75C2×Q8×C11—24no—
76C2×Q8×C11—22no—
77C2×Q8×C11—22no—
78C2×Q8×C11—84no—
79C2×Q8×C11C2×D412yes—
80C2×D4×C11—22no—
81C2×D4×C11—22no—
82C2×D4×C11C2×D412yes—
83C22×C4×C11—24no—
84C22×C4×C11—22no—
85C22×C4×C11C2×D412yes—
86C22×C4×C11C2×D411yescharacteristic
87C22×Dic11—41no—
88C2×Dic22—22no—
89C2×Dic22—44no—
90C2×Dic22—41no—
91C11×C4⋊C4—28no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—24no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4C2×D414yes—
98C11×C4⋊C4C2×D414yes—
99C11×C22⋊C4—24no—
100C11×C22⋊C4—28no—
101C11×C22⋊C4—24no—
102C11×C22⋊C4—24no—
103C42×C11—24no—
104C42×C11—24no—
105C42×C11C2×D412yes—
106C42×C11C2×D411yescharacteristic
107C42×C11C2411yescharacteristic
108#4326—48no—
109#4324—48no—
110C4⋊Dic11—24no—
111C4⋊Dic11—42no—
112#4318—28no—
113#4318—24no—
114C2×C11⋊C8—24no—
115C2×C11⋊C8—22no—
116#3550D1111yescharacteristic
117#3165—112no—
118#3152—111no—
119#1660—118no—
120#1526—112no—
121#1525—111no—
122C23×C11—22no—
123C23×C11#12011yescharacteristic
124Q8×C11—42no—
125Q8×C11—44no—
126Q8×C11—44no—
127Q8×C11—84no—
128D4×C11—42no—
129D4×C11—44no—
130D4×C11—82no—
131C2×C4×C11—22no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—22no—
135C2×C4×C11—24no—
136C2×C4×C11—44no—
137C2×C4×C11—84no—
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12012yes—
140C2×C4×C11C22×D412yes—
141C2×C4×C11C22×D411yescharacteristic
142C2×Dic11—42no—
143C2×Dic11—82no—
144Dic22—44no—
145Dic22—82no—
146C11⋊C8—28no—
147C11⋊C8—24no—
148C2×#137—222no—
149#563C2×D1114yes—
150#559—21no—
151Q82—21no—
152#556—22no—
153D4×Q8—22no—
154#542—24no—
155#536—22no—
156#533C2×D1112yes—
157#532C2×D1111yescharacteristic
158C2×C4⋊Q8—111no—
159#501—118no—
160#500—222no—
161#498—222no—
162#497—114no—
163#494—221no—
164#492—221no—
165#428—224no—
166C4×M16—111no—
167C4×M16—112no—
168#330—118no—
169#329—114no—
170C22×C11—21no—
171C22×C11—22no—
172C22×C11—42no—
173C22×C11—44no—
174C22×C11C2×#12011yescharacteristic
175C4×C11—21no—
176C4×C11—22no—
177C4×C11—42no—
178C4×C11—44no—
179C4×C11—44no—
180C4×C11#45312yes—
181C4×C11#45614yes—
182Dic11—82no—
183C2×#41C22⋊D1112yes—
184C22×Q8—22no—
185C22×Q8—221no—
186#137—448no—
187C2×Q16—224no—
188C2×SD16—224no—
189C2×M16—221no—
190C2×M16—222no—
191C4⋊Q8—24no—
192C4⋊Q8—24no—
193C4⋊Q8—112no—
194C4⋊Q8—222no—
195C4⋊Q8—221no—
196C4⋊Q8C22⋊D1111yescharacteristic
197C4⋊Q8C22⋊D1112yes—
198C4⋊Q8C22⋊D1112yes—
199#127C22⋊D1111yescharacteristic
200#126—28no—
201#125C22×D1114yes—
202#124—24no—
203#124—24no—
204#124C22×D1112yes—
205#123—24no—
206#123—24no—
207C22⋊Q8—24no—
208C22⋊Q8—22no—
209C22⋊Q8—22no—
210C22⋊Q8—28no—
211#121—22no—
212C4×Q8—24no—
213C4×Q8—22no—
214C4×Q8—22no—
215C4×D4—24no—
216C4×D4—22no—
217#117—22no—
218#117C22⋊D1114yes—
219C2×C4⋊C4—222no—
220C2×C42C22×D1111yescharacteristic
221#107—228no—
222#106—228no—
223#97—114no—
224#97—112no—
225C4×C8—221no—
226C4×C8—222no—
227C2×C11—41no—
228C2×C11—82no—
229C2×C11C2×#45311yescharacteristic
230C2×C11C2×#45612yes—
231#41—44no—
232C2×Q8—24no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—84no—
236C2×Q8—222no—
237C2×Q8—444no—
238C2×Q8—441no—
239C2×Q8C2×C22⋊D1112yes—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4C2×C22⋊D1112yes—
243C22×C4—24no—
244C22×C4—22no—
245C22×C4—441no—
246C22×C4C2×C22⋊D1112yes—
247C22×C4C2×C22⋊D1111yescharacteristic
248Q16—448no—
249SD16—448no—
250M16—224no—
251M16—228no—
252C2×C8—224no—
253C2×C8—222no—
254C4⋊C4—28no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—24no—
259C4⋊C4—24no—
260C4⋊C4—224no—
261C4⋊C4—442no—
262C4⋊C4C2×C22⋊D1114yes—
263C4⋊C4C2×C22⋊D1114yes—
264C22⋊C4—24no—
265C22⋊C4—28no—
266C22⋊C4—24no—
267C22⋊C4—24no—
268C42—24no—
269C42—24no—
270C42C2×C22⋊D1112yes—
271C42C2×C22⋊D1111yescharacteristic
272C42C23×D1111yescharacteristic
273C11#1907811yescharacteristic, complemented, Sylow
274C23—22no—
275C23#6700611yescharacteristic
276Q8—42no—
277Q8—44no—
278Q8—44no—
279Q8—84no—
280Q8—444no—
281Q8—882no—
282D4—42no—
283D4—44no—
284D4—82no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—24no—
290C2×C4—44no—
291C2×C4—84no—
292C2×C4—442no—
293C2×C4—882no—
294C2×C4#6700611yescharacteristic
295C2×C4#6700612yes—
296C2×C4C22×C22⋊D1112yes—
297C2×C4C22×C22⋊D1111yescharacteristic
298C8—224no—
299C8—228no—
300C22—21no—
301C22—22no—
302C22—42no—
303C22—44no—
304C22C2×#6700611yescharacteristic
305C4—21no—
306C4—22no—
307C4—42no—
308C4—44no—
309C4—44no—
310C4—882no—
311C4#1062285412yes—
312C4#1062285914yes—
313C2—41no—
314C2—82no—
315C2C2×#1062285411yescharacteristic
316C2C2×#1062285912yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3550C2
socleC22×C11C2×#120
prime radicalC11×#532C22
hypercenter#3550D11
hypocenterC11#19078
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #13079163C2semidirect
3. #13067927C2semidirect
4. #13067211C2semidirect
273. C11#19078semidirect

Maximal subgroups

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

subgroupindex
#130791632
#130790762
#130679272
#130672112
#130672082
C11×#35502
#1907811