Finite Group Databasebeta

← #14673452

Subgroups — #14673452

Order 2816.

484 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 81 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#13068896C212yesmaximal
2#13068825C211yesmaximal, characteristic
3#13066741C211yesmaximal, characteristic
4#13066734C212yesmaximal
5C11×#2804C211yesmaximal, characteristic
6#10623329C2211yescharacteristic
7C11×#400—21no—
8C11×#393—22no—
9C11×#391—21no—
10C11×#390C2211yescharacteristic
11C11×#386C2212yes—
12C11×#385—22no—
13C2×#66898C2212yes—
14C2×#66897C2211yescharacteristic
15#10622823—22no—
16#10622577—21no—
17#10622165—22no—
18#10622161—21no—
19C22×Q8×C11—21no—
20C22×D4×C11C2311yescharacteristic
21C23×C4×C11D412yes—
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C11×C22⋊C4—22no—
26C2×C11×C22⋊C4—22no—
27C2×C11×C22⋊C4D412yes—
28C2×C42×C11D411yescharacteristic
29C2×C22⋊Dic11—22no—
30C2×C22⋊Dic11—22no—
31D4×Dic11—41no—
32D4×Dic11—41no—
33#66979—21no—
34C2×Dic11⋊C4—42no—
35C2×#4318—21no—
36C11×#95—22no—
37C11×#95—22no—
38C11×#95—21no—
39C11×#95—22no—
40#66898—22no—
41#66898Q814yescomplemented
42#66897—21no—
43#66897Q812yescomplemented
44C11⋊#95—42no—
45#66872—41no—
46#66871—41no—
47#13463—111nomaximal, Sylow
48C24×C11C2×D412yes—
49C2×Q8×C11—42no—
50C2×Q8×C11—81no—
51C2×Q8×C11—81no—
52C2×D4×C11—41no—
53C2×D4×C11—41no—
54C2×D4×C11C2×Q811yescharacteristic
55C2×D4×C11C2×Q812yes—
56C2×D4×C11#4111yescharacteristic
57C22×C4×C11—21no—
58C22×C4×C11—22no—
59C22×C4×C11—21no—
60C22×C4×C11—22no—
61C22×C4×C11—42no—
62C22×C4×C11—82no—
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—22no—
65C22×Dic11—22no—
66C22×Dic11—42no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—81no—
69C11×C4⋊C4—81no—
70C11×C22⋊C4—44no—
71C11×C22⋊C4—42no—
72C11×C22⋊C4—82no—
73C42×C11—41no—
74C22⋊Dic11—24no—
75C22⋊Dic11—42no—
76C22⋊Dic11—42no—
77C22⋊Dic11—41no—
78C4⋊Dic11—21no—
79C4⋊Dic11—21no—
80Dic11⋊C4—84no—
81C4×Dic11—41no—
82#4318—22no—
83#4318—41no—
84C2×C11⋊C8—41no—
85#2804D1111yescharacteristic
86#1867—112no—
87#1856—111no—
88#1393—111no—
89#1390—112no—
90C23×C11—22no—
91C23×C11—22no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11#12011yescharacteristic
95C23×C11C22⋊Q812yes—
96C23×C11C4⋊Q812yes—
97Q8×C11—84no—
98D4×C11—41no—
99D4×C11—42no—
100D4×C11—41no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—44no—
112C2×C4×C11—41no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—82no—
116C2×C4×C11C22⋊Q811yescharacteristic
117C2×C4×C11C4⋊Q811yescharacteristic
118C2×Dic11—44no—
119C2×Dic11—41no—
120C2×Dic11—41no—
121C2×Dic11—82no—
122C2×Dic11—82no—
123C2×Dic11—82no—
124C2×Dic11—82no—
125C11⋊C8—42no—
126#518—111no—
127#428—221no—
128C2×#100—111no—
129C2×#99—112no—
130#400—21no—
131#393—22no—
132#391—21no—
133#390C2×D1111yescharacteristic
134#386C2×D1112yes—
135#385—22no—
136#385—222no—
137#342—222no—
138#339—221no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—22no—
142C22×C11—22no—
143C22×C11—42no—
144C22×C11—42no—
145C22×C11—42no—
146C22×C11—42no—
147C22×C11—82no—
148C22×C11#39511yescharacteristic
149C22×C11B(4,𝔽2)11yescharacteristic
150C22×C11#45811yescharacteristic
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—42no—
154C4×C11—82no—
155C4×C11—81no—
156C4×C11—82no—
157Dic11—84no—
158Dic11—81no—
159Dic11—81no—
160C22×Q8—21no—
161C22×D4C22×D1111yescharacteristic
162C23×C4C22⋊D1112yes—
163C2×M16—221no—
164C4×D4—441no—
165C4×D4—441no—
166#117—221no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—442no—
170C2×C4⋊C4C22⋊D1111yescharacteristic
171C2×C22⋊C4—22no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—222no—
174C2×C22⋊C4—222no—
175C2×C22⋊C4C22⋊D1112yes—
176C2×C42C22⋊D1111yescharacteristic
177#107—441no—
178#106—441no—
179#100—112no—
180#100—221no—
181#99—114no—
182#99—222no—
183#95—22no—
184#95—22no—
185#95—21no—
186#95—22no—
187#95—442no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11—42no—
191C2×C11—42no—
192C2×C11#206211yescharacteristic
193C2×C11#219811yescharacteristic
194C2×C11#219911yescharacteristic
195C24C2×C22⋊D1112yes—
196C2×Q8—42no—
197C2×Q8—81no—
198C2×Q8—81no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4Q8×D1112yes—
202C2×D4Q8×D1111yescharacteristic
203C2×D4#434311yescharacteristic
204C22×C4—21no—
205C22×C4—22no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—42no—
209C22×C4—82no—
210C22×C4—222no—
211C22×C4—222no—
212C22×C4—442no—
213C22×C4C2×C22⋊D1111yescharacteristic
214M16—222no—
215M16—441no—
216C2×C8—441no—
217C4⋊C4—41no—
218C4⋊C4—81no—
219C4⋊C4—81no—
220C4⋊C4—221no—
221C4⋊C4—221no—
222C4⋊C4—884no—
223C22⋊C4—44no—
224C22⋊C4—42no—
225C22⋊C4—82no—
226C22⋊C4—224no—
227C22⋊C4—442no—
228C22⋊C4—442no—
229C22⋊C4—441no—
230C42—41no—
231C42—441no—
232C11#1346311yescharacteristic, complemented, Sylow
233C23—22no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23#6699712yes—
238C23#6699912yes—
239C23#6700611yescharacteristic
240Q8—84no—
241D4—41no—
242D4—42no—
243D4—41no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—44no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—82no—
259C2×C4—444no—
260C2×C4—441no—
261C2×C4—441no—
262C2×C4—882no—
263C2×C4—882no—
264C2×C4—882no—
265C2×C4—882no—
266C2×C4#6699711yescharacteristic
267C2×C4#6699911yescharacteristic
268C8—442no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—82no—
278C22#1062284211yescharacteristic
279C22#1062285611yescharacteristic
280C22#1062285711yescharacteristic
281C4—21no—
282C4—21no—
283C4—42no—
284C4—82no—
285C4—81no—
286C4—82no—
287C4—884no—
288C4—881no—
289C4—881no—
290C2—21no—
291C2—21no—
292C2—42no—
293C2—42no—
294C2#1306996811yescharacteristic
295C2#1307061211yescharacteristic
296C2#1307061711yescharacteristic
subgroupG/H
centerC22#10622857
commutator, prime radical, cosocleC22×D4×C11C23
FrattiniC22×D4C22×D11
FittingC11×#2804C2
socleC22×C11B(4,𝔽2)
hypercenter#2804D11
hypocenterC11#13463
LCSG ▷ C22×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #2804

Complements

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

NH ≅ G/Ntype
41. #66898Q8semidirect
43. #66897Q8semidirect
232. C11#13463semidirect

Maximal subgroups

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

subgroupindex
#130688962
#130688252
#130667412
#130667342
C11×#28042
#1346311