Finite Group Databasebeta

← #14657240

Subgroups — #14657240

Order 2816.

534 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 93 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#13069433C212yesmaximal, complemented
2#13068785C211yesmaximal, characteristic, complemented
3C2×#10622178C212yesmaximal, complemented
4#13066497C211yesmaximal, characteristic, complemented
5C11×#2819C211yesmaximal, characteristic
6C2×C11×#124C2212yes—
7C11×#394—21no—
8C11×#394—21no—
9C11×#393—22no—
10C11×#392—22no—
11C11×#382C2211yescharacteristic
12C2×#66899—22no—
13C2×#66896—22no—
14C2×#66872—21no—
15C2×#66871—21no—
16#10622548C2211yescharacteristic
17C2×#66867C2212yes—
18C2×#66867C2211yescharacteristic
19#10622178—24no—
20C22×Q8×C11D412yes—
21C22×D4×C11—21no—
22C22×D4×C11—21no—
23C22×D4×C11D412yes—
24C11×#124—22no—
25C11×#124—22no—
26C11×#124—22no—
27C11×#124—22no—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11—22no—
36C2×C4⋊Dic11—21no—
37C22×C11⋊C8—21no—
38C22×C11⋊C8—22no—
39C11×#95—21no—
40C11×#95—21no—
41C11×#95—22no—
42#66899—44no—
43#66896—44no—
44#66872—42no—
45#66871—42no—
46#66867—21no—
47#66867—22no—
48#66867—22no—
49#66867D412yescomplemented
50#10424—111nomaximal, Sylow
51C24×C11—22no—
52C2×Q8×C11—22no—
53C2×Q8×C11—22no—
54C2×Q8×C11—42no—
55C2×Q8×C11—42no—
56C2×D4×C11—22no—
57C2×D4×C11—22no—
58C2×D4×C11—42no—
59C2×D4×C11—42no—
60C2×D4×C11—82no—
61C2×D4×C11—81no—
62C2×D4×C11—81no—
63C2×D4×C11—82no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—22no—
67C22×C4×C11C2×D412yes—
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—41no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C22⋊C4—42no—
73C11×C22⋊C4—42no—
74C11×C22⋊C4—42no—
75C11×C22⋊C4—42no—
76C11×C22⋊C4—82no—
77C11×C22⋊C4—82no—
78C42×C11C2×D411yescharacteristic
79C42×C11#4111yescharacteristic
80C42×C11#4112yes—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83C4⋊Dic11—42no—
84C4⋊Dic11—42no—
85C2×C11⋊C8—22no—
86C2×C11⋊C8—22no—
87C2×C11⋊C8—24no—
88C2×C11⋊C8—22no—
89C2×C11⋊C8—42no—
90C2×C11⋊C8—42no—
91#2819D1111yescharacteristic
92#1959—112no—
93#1847—111no—
94C2×#329—112no—
95#1295—111no—
96C23×C11—42no—
97C23×C11—42no—
98C23×C11—42no—
99C23×C11—42no—
100C23×C11—42no—
101C23×C11—42no—
102C23×C11—42no—
103C23×C11#12011yescharacteristic
104Q8×C11—44no—
105Q8×C11—82no—
106D4×C11—44no—
107D4×C11—82no—
108D4×C11—84no—
109D4×C11—84no—
110C2×C4×C11—21no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12112yes—
123C2×C4×C11#12312yes—
124C2×C4×C11#12411yescharacteristic
125C2×Dic11—81no—
126C2×Dic11—82no—
127C11⋊C8—24no—
128C11⋊C8—44no—
129C2×#124C2×D1112yes—
130C2×#107—221no—
131C2×#106—221no—
132C2×#103—222no—
133C2×#102—222no—
134C2×#97—111no—
135C2×#97—112no—
136#394—21no—
137#394—21no—
138#393—22no—
139#392—22no—
140#384—111no—
141#382C2×D1111yescharacteristic
142#329—224no—
143C22×C11—82no—
144C22×C11—82no—
145C22×C11—82no—
146C22×C11—82no—
147C22×C11—82no—
148C22×C11—82no—
149C22×C11—82no—
150C22×C11#39411yescharacteristic
151C22×C11#45311yescharacteristic
152C22×C11#45312yes—
153C22×C11#45512yes—
154C22×C11#45611yescharacteristic
155C4×C11—22no—
156C4×C11—22no—
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—81no—
160C4×C11—81no—
161C4×C11—82no—
162Dic11—161no—
163C22×Q8C22⋊D1112yes—
164C22×D4—21no—
165C22×D4—21no—
166C22×D4C22⋊D1112yes—
167C22×C8—221no—
168C22×C8—222no—
169#124—22no—
170#124—22no—
171#124—22no—
172#124—22no—
173C2×C4⋊C4—222no—
174C2×C4⋊C4—221no—
175C2×C4⋊C4C22⋊D1111yescharacteristic
176C2×C4⋊C4C22⋊D1111yescharacteristic
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—22no—
180C2×C22⋊C4—22no—
181C2×C42C22×D1111yescharacteristic
182#107—442no—
183#106—442no—
184#103—444no—
185#102—444no—
186#97—112no—
187#97—222no—
188#97—221no—
189#97—222no—
190#95—21no—
191#95—21no—
192#95—22no—
193C2×C11—162no—
194C2×C11#165511yescharacteristic
195C2×C11#165911yescharacteristic
196C2×C11#166112yes—
197C2×C11#203712yes—
198C2×C11#203911yescharacteristic
199C24—22no—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—42no—
203C2×Q8—42no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—82no—
209C2×D4—81no—
210C2×D4—81no—
211C2×D4—82no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—22no—
215C22×C4—441no—
216C22×C4C2×C22⋊D1112yes—
217C22×C4C2×C22⋊D1111yescharacteristic
218C2×C8—222no—
219C2×C8—222no—
220C2×C8—222no—
221C2×C8—224no—
222C2×C8—442no—
223C2×C8—442no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—442no—
227C4⋊C4—442no—
228C4⋊C4—441no—
229C4⋊C4—441no—
230C22⋊C4—42no—
231C22⋊C4—42no—
232C22⋊C4—42no—
233C22⋊C4—42no—
234C22⋊C4—82no—
235C22⋊C4—82no—
236C42D4×D1111yescharacteristic
237C42#434111yescharacteristic
238C42#434112yes—
239C11#1042411yescharacteristic, complemented, Sylow
240C23—42no—
241C23—42no—
242C23—42no—
243C23—42no—
244C23—42no—
245C23—42no—
246C23—42no—
247C23#6700611yescharacteristic
248Q8—44no—
249Q8—82no—
250D4—44no—
251D4—82no—
252D4—84no—
253D4—84no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—881no—
266C2×C4—882no—
267C2×C4#6698812yes—
268C2×C4#6698911yescharacteristic
269C2×C4#6699111yescharacteristic
270C2×C4#6699212yes—
271C8—224no—
272C8—444no—
273C22—82no—
274C22—82no—
275C22—82no—
276C22—82no—
277C22—82no—
278C22—82no—
279C22—82no—
280C22#1062283511yescharacteristic
281C22#1062285411yescharacteristic
282C22#1062285412yes—
283C22#1062285512yes—
284C22#1062285911yescharacteristic
285C4—21no—
286C4—21no—
287C4—22no—
288C4—22no—
289C4—81no—
290C4—81no—
291C4—82no—
292C4—1761no—
293C2—162no—
294C2#1306790511yescharacteristic
295C2#1306792211yescharacteristic
296C2#1306793312yes—
297C2#1306982312yes—
298C2#1306983711yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#2819C2
socleC23×C11#120
hypercenter#2819D11
hypocenterC11#10424
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2819

Complements

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

NH ≅ G/Ntype
1. #13069433C2semidirect
2. #13068785C2semidirect
3. C2×#10622178C2semidirect
4. #13066497C2semidirect
49. #66867D4semidirect
239. C11#10424semidirect

Maximal subgroups

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

subgroupindex
#130694332
#130687852
C2×#106221782
#130664972
C11×#28192
#1042411