Finite Group Databasebeta

← #14674123

Subgroups — #14674123

Order 2816.

388 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 71 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#13078990C211yesmaximal, characteristic
2C2×#10622183C211yesmaximal, characteristic
3#13066786C214yesmaximal, complemented
4C2×C11×#353C211yesmaximal, characteristic
5C2×C11×#127C2211yescharacteristic
6#10623001C411yescharacteristic, complemented
7C2×C11×#99—21no—
8C2×#66898—21no—
9#10622828—21no—
10#10622828—21no—
11#10622684C412yescomplemented
12#10622684C2212yes—
13#10622683—21no—
14#10622683—21no—
15C4×#4318C411yescharacteristic, complemented
16C11×#353—21no—
17C11×#353C2212yes—
18#10622183—21no—
19#10622183C2212yes—
20C22×D4×C11—41no—
21C22×D4×C11D411yescharacteristic
22C22×D4×C11D411yescharacteristic
23C11×#127—41no—
24C11×#127C2×C411yescharacteristic
25C11×#127D411yescharacteristic
26C11×#127D411yescharacteristic
27C11×#127C2311yescharacteristic
28C2×C11×C22⋊C4—41no—
29C2×C42×C11C2×C411yescharacteristic
30C2×C22⋊Dic11—41no—
31#66979—21no—
32#66977—41no—
33C2×#4318—21no—
34#66923C2×C412yescomplemented
35#66922—21no—
36C4×Dic22—41no—
37C11×#99—22no—
38C11×#99—41no—
39#66898—22no—
40#66898—41no—
41#66896—22no—
42#66896—22no—
43#66896—22no—
44#66896—22no—
45#66867C2×C412yescomplemented
46C4×C11⋊C8—21no—
47#13595—111nomaximal, Sylow
48C24×C11—21no—
49C24×C11—21no—
50C2×D4×C11—21no—
51C2×D4×C11—21no—
52C2×D4×C11—41no—
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C2×D4×C11—41no—
60C2×D4×C11—84no—
61C2×D4×C11C22⋊C411yescharacteristic
62C2×D4×C11C22⋊C411yescharacteristic
63C2×D4×C11C2×D411yescharacteristic
64C2×D4×C11C2×D411yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—81no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×Dic11—81no—
69C2×Dic22—41no—
70C11×C22⋊C4—42no—
71C11×C22⋊C4—81no—
72C42×C11—21no—
73C42×C11C22⋊C411yescharacteristic
74C42×C11C22×C411yescharacteristic
75C22⋊Dic11—42no—
76C22⋊Dic11—41no—
77C22⋊Dic11—81no—
78C4⋊Dic11—22no—
79C4⋊Dic11—41no—
80Dic11⋊C4—42no—
81C4×Dic11—41no—
82#4318—41no—
83#4318—41no—
84C2×C11⋊C8—22no—
85#3138—111no—
86C2×#353—111no—
87C2×#353D1111yescharacteristic
88#1412—114no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—41no—
94C23×C11—41no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11—82no—
98C23×C11—82no—
99C23×C11#9911yescharacteristic
100D4×C11—41no—
101D4×C11—41no—
102D4×C11—41no—
103D4×C11—41no—
104D4×C11—81no—
105D4×C11—81no—
106D4×C11—82no—
107D4×C11—82no—
108D4×C11—82no—
109D4×C11—82no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—42no—
115C2×C4×C11—82no—
116C2×C4×C11—162no—
117C2×C4×C11#9911yescharacteristic
118C2×C4×C11C2×C22⋊C411yescharacteristic
119C2×Dic11—42no—
120C2×Dic11—82no—
121C2×Dic11—162no—
122Dic22—82no—
123C11⋊C8—42no—
124#533—111no—
125C2×#127C2×D1111yescharacteristic
126#490—112no—
127#490—112no—
128#486—221no—
129#486—221no—
130#418—221no—
131#418—221no—
132C2×#99—21no—
133C2×#99—221no—
134C4×M16—111no—
135#353—21no—
136#353—112no—
137#353—221no—
138#353C2×D1112yes—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11—41no—
142C22×C11—41no—
143C22×C11—41no—
144C22×C11—81no—
145C22×C11—81no—
146C22×C11—81no—
147C22×C11—81no—
148C22×C11—82no—
149C22×C11—82no—
150C22×C11—161no—
151C22×C11—161no—
152C22×C11#35411yescharacteristic
153C22×C11#35411yescharacteristic
154C22×C11C2×#9911yescharacteristic
155C4×C11—22no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—41no—
159C4×C11—162no—
160Dic11—82no—
161Dic11—162no—
162C22×D4—41no—
163C22×D4D4411yescharacteristic
164C22×D4C22⋊D1111yescharacteristic
165C2×M16—221no—
166C4⋊Q8—221no—
167#127—41no—
168#127C4×D1111yescharacteristic
169#127D4411yescharacteristic
170#127C22⋊D1111yescharacteristic
171#127C22×D1111yescharacteristic
172#125—112no—
173C22⋊Q8—441no—
174C4×Q8—441no—
175#117—221no—
176C2×C22⋊C4—41no—
177C2×C22⋊C4—441no—
178C2×C42C4×D1111yescharacteristic
179#102—222no—
180#102—222no—
181#102—222no—
182#102—222no—
183#99—22no—
184#99—41no—
185#99—222no—
186#99—441no—
187#97—112no—
188C4×C8—221no—
189C2×C11—21no—
190C2×C11—21no—
191C2×C11—21no—
192C2×C11—81no—
193C2×C11—81no—
194C2×C11—81no—
195C2×C11—81no—
196C2×C11C2×#35411yescharacteristic
197C24—21no—
198C24—21no—
199C2×Q8—441no—
200C2×D4—21no—
201C2×D4—21no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4—41no—
205C2×D4—41no—
206C2×D4—41no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—84no—
211C2×D4(C2×D11)⋊C411yescharacteristic
212C2×D4(C2×D11)⋊C411yescharacteristic
213C2×D4C2×D4411yescharacteristic
214C2×D4C2×C22⋊D1111yescharacteristic
215C22×C4—21no—
216C22×C4—81no—
217C22×C4—881no—
218C22×C4(C2×D11)⋊C411yescharacteristic
219M16—441no—
220M16—441no—
221C2×C8—222no—
222C4⋊C4—222no—
223C4⋊C4—442no—
224C4⋊C4—441no—
225C22⋊C4—42no—
226C22⋊C4—81no—
227C22⋊C4—441no—
228C22⋊C4—442no—
229C22⋊C4—881no—
230C42—21no—
231C42—441no—
232C42(C2×D11)⋊C411yescharacteristic
233C42C2×C4×D1111yescharacteristic
234C11#1359511yescharacteristic, complemented, Sylow
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23—82no—
244C23—82no—
245C23#6687011yescharacteristic
246Q8—882no—
247D4—41no—
248D4—41no—
249D4—41no—
250D4—41no—
251D4—81no—
252D4—81no—
253D4—82no—
254D4—82no—
255D4—82no—
256D4—82no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—82no—
263C2×C4—162no—
264C2×C4—442no—
265C2×C4—882no—
266C2×C4—1762no—
267C2×C4#6687011yescharacteristic
268C2×C4C2×(C2×D11)⋊C411yescharacteristic
269C8—442no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—41no—
275C22—81no—
276C22—81no—
277C22—81no—
278C22—81no—
279C22—82no—
280C22—82no—
281C22—161no—
282C22—161no—
283C22#1062211111yescharacteristic
284C22#1062211111yescharacteristic
285C22C2×#6687011yescharacteristic
286C4—22no—
287C4—21no—
288C4—21no—
289C4—41no—
290C4—162no—
291C4—882no—
292C4—1762no—
293C2—21no—
294C2—21no—
295C2—21no—
296C2—81no—
297C2—81no—
298C2—81no—
299C2—81no—
300C2C2×#1062211111yescharacteristic
subgroupG/H
centerC2C2×#10622111
commutatorC42×C11C22×C4
Frattini#127C22×D11
FittingC2×C11×#353C2
socleC2×C11C2×#354
prime radicalC2×C11×#127C22
cosocleC11×#127C23
hypercenterC2×#353D11
hypocenterC11#13595
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×#127 ◁ C2×#353

Complements

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

NH ≅ G/Ntype
3. #13066786C2semidirect
6. #10623001C4semidirect
11. #10622684C4semidirect
15. C4×#4318C4semidirect
34. #66923C2×C4semidirect
45. #66867C2×C4semidirect
234. C11#13595semidirect

Maximal subgroups

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

subgroupindex
#130789902
C2×#106221832
#130667862
C2×C11×#3532
#1359511