Finite Group Databasebeta

← #14665978

Subgroups — #14665978

Order 2816.

470 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 59 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#13074281C211yesmaximal, characteristic, complemented
2#13067568C212yesmaximal
3#13066636C212yesmaximal, complemented
4#13066546C211yesmaximal, characteristic, complemented
5C11×#2022C211yesmaximal, characteristic
6C11×#534C2211yescharacteristic
7C2×C11×#123—21no—
8C2×C11×#99—21no—
9C11×#381C2211yescharacteristic
10C4×C22⋊Dic11—21no—
11#10622653—22no—
12#10622562—21no—
13#10622560C2212yes—
14#10622268—22no—
15#10622259—22no—
16C11×#342C2211yescharacteristic
17#10622175—22no—
18#10622163C2212yes—
19C22×D4×C11—21no—
20C23×C4×C11D411yescharacteristic
21C22×Dic22D412yes—
22C11×#123—42no—
23C11×#123—41no—
24C11×#123—42no—
25C11×#121—22no—
26C11×#120—41no—
27C2×C11×C4⋊C4—41no—
28C2×C11×C22⋊C4—21no—
29C2×C11×C22⋊C4—41no—
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C11×C22⋊C4C2311yescharacteristic
32C2×C22⋊Dic11—22no—
33C2×#4324—42no—
34C2×C4⋊Dic11—21no—
35C2×Dic11⋊C4—22no—
36C2×C4×Dic11—21no—
37C2×C4×Dic11—21no—
38C11×#99—42no—
39C11×#95—22no—
40C11⋊#95—21no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43C11⋊#95D412yes—
44C22⋊(C11⋊C8)—22no—
45#66874—42no—
46#12121—111nomaximal, Sylow
47C24×C11—21no—
48C24×C11C2×D411yescharacteristic
49C2×D4×C11—22no—
50C2×D4×C11—41no—
51C2×D4×C11—41no—
52C2×D4×C11—41no—
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11—41no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11SD1612yescomplemented
64C22×C4×C11C2×D412yes—
65C22×Dic11—22no—
66C22×Dic11—22no—
67C2×Dic22—42no—
68C2×Dic22—44no—
69C11×C4⋊C4—22no—
70C11×C4⋊C4—44no—
71C11×C22⋊C4—22no—
72C11×C22⋊C4—41no—
73C11×C22⋊C4—42no—
74C11×C22⋊C4—44no—
75C11×C22⋊C4—41no—
76C11×C22⋊C4—41no—
77C22⋊Dic11—44no—
78#4324—84no—
79C4⋊Dic11—81no—
80Dic11⋊C4—44no—
81C4×Dic11—81no—
82C4×Dic11—81no—
83C2×C11⋊C8—42no—
84#2607—111no—
85#2022D1111yescharacteristic
86#1601—112no—
87#1351—112no—
88#1317—111no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—42no—
92C23×C11—41no—
93C23×C11—41no—
94C23×C11—41no—
95C23×C11—82no—
96C23×C11#12011yescharacteristic
97C23×C11C2×SD1611yescharacteristic
98C23×C11#13711yescharacteristic
99D4×C11—82no—
100D4×C11—81no—
101D4×C11—81no—
102D4×C11—81no—
103D4×C11—81no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—81no—
117C2×C4×C11—82no—
118C2×Dic11—24no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124Dic22—44no—
125Dic22—82no—
126C11⋊C8—82no—
127#534C2×D1111yescharacteristic
128C2×#123—21no—
129#448—222no—
130C2×#99—21no—
131#399—221no—
132#393—112no—
133#391—222no—
134#387—222no—
135#381C2×D1111yescharacteristic
136C4×C22⋊C4—221no—
137#342C2×D1111yescharacteristic
138#327—222no—
139#323—112no—
140C22×C11—22no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—41no—
144C22×C11—41no—
145C22×C11—42no—
146C22×C11—81no—
147C22×C11—82no—
148C22×C11—81no—
149C22×C11—82no—
150C22×C11—161no—
151C22×C11#44811yescharacteristic
152C22×C11#45311yescharacteristic
153C22×C11B(4,𝔽2)11yescharacteristic
154C4×C11—42no—
155C4×C11—42no—
156C4×C11—81no—
157C4×C11—82no—
158C4×C11—81no—
159Dic11—44no—
160Dic11—82no—
161C22×Q8—112no—
162C22×D4—21no—
163C23×C4C22⋊D1111yescharacteristic
164C2×SD16—442no—
165#123—42no—
166#123—41no—
167#123—42no—
168#121—22no—
169#120—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—222no—
172C2×C4⋊C4—221no—
173C2×C22⋊C4—21no—
174C2×C22⋊C4—41no—
175C2×C22⋊C4—222no—
176C2×C22⋊C4C22⋊D1111yescharacteristic
177C2×C22⋊C4C22×D1111yescharacteristic
178C2×C42—221no—
179C2×C42—221no—
180#103—442no—
181#99—42no—
182C22⋊C8—222no—
183#95—22no—
184#95—112no—
185#95—222no—
186#95—221no—
187#95—222no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11—41no—
191C2×C11—41no—
192C2×C11—161no—
193C2×C11#159611yescharacteristic
194C2×C11#219712yes—
195C24—21no—
196C24C2×C22⋊D1111yescharacteristic
197C2×Q8—442no—
198C2×Q8—444no—
199C2×D4—22no—
200C2×D4—41no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4—41no—
205C2×D4—41no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—222no—
214C22×C4—222no—
215C22×C4#432412yescomplemented
216C22×C4D4×D1112yes—
217SD16—884no—
218C2×C8—442no—
219C4⋊C4—22no—
220C4⋊C4—44no—
221C4⋊C4—444no—
222C4⋊C4—881no—
223C22⋊C4—22no—
224C22⋊C4—41no—
225C22⋊C4—42no—
226C22⋊C4—44no—
227C22⋊C4—41no—
228C22⋊C4—41no—
229C22⋊C4—444no—
230C42—881no—
231C42—881no—
232C11#1212111yescharacteristic, complemented, Sylow
233C23—21no—
234C23—21no—
235C23—42no—
236C23—41no—
237C23—41no—
238C23—41no—
239C23—82no—
240C23C2×#432411yescharacteristic
241C23#6699011yescharacteristic
242C23#6700411yescharacteristic
243Q8—444no—
244Q8—882no—
245D4—82no—
246D4—81no—
247D4—81no—
248D4—81no—
249D4—81no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—81no—
263C2×C4—82no—
264C2×C4—224no—
265C2×C4—442no—
266C2×C4—442no—
267C2×C4—442no—
268C2×C4—442no—
269C2×C4—442no—
270C8—882no—
271C22—22no—
272C22—21no—
273C22—21no—
274C22—41no—
275C22—41no—
276C22—42no—
277C22—81no—
278C22—82no—
279C22—82no—
280C22—81no—
281C22—161no—
282C22#1062264511yescharacteristic
283C22#1062265311yescharacteristic
284C22#1062269011yescharacteristic
285C4—42no—
286C4—42no—
287C4—81no—
288C4—82no—
289C4—81no—
290C4—444no—
291C4—882no—
292C2—21no—
293C2—21no—
294C2—41no—
295C2—41no—
296C2—161no—
297C2#1306753811yescharacteristic
298C2#1307060312yes—
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2022C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#534C22
hypercenter#2022D11
hypocenterC11#12121
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2022

Complements

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

NH ≅ G/Ntype
1. #13074281C2semidirect
3. #13066636C2semidirect
4. #13066546C2semidirect
63. C22×C4×C11SD16semidirect
215. C22×C4#4324semidirect
232. C11#12121semidirect

Maximal subgroups

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

subgroupindex
#130742812
#130675682
#130666362
#130665462
C11×#20222
#1212111