Finite Group Databasebeta

← #14673443

Subgroups — #14673443

Order 2816.

540 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 79 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#13074988C211yesmaximal, characteristic
2#13068897C212yesmaximal
3#13066741C211yesmaximal, characteristic
4#13066735C212yesmaximal
5C11×#1856C211yesmaximal, characteristic
6C11×#518C2211yescharacteristic
7C2×#66931—22no—
8C11×#428—21no—
9C2×C11×#100C2211yescharacteristic
10C11×#390C2211yescharacteristic
11#10622833C2212yes—
12C2×#66898C2212yes—
13#10622592—21no—
14#10622561—22no—
15#10622559—22no—
16#10622541—21no—
17C11×#339—21no—
18#10622164—22no—
19C22×D4×C11C2311yescharacteristic
20C23×Dic11D412yes—
21C22×Dic22—21no—
22C2×C11×M16—21no—
23C4×D4×C11—41no—
24C4×D4×C11—41no—
25C11×#117—21no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4—22no—
29C2×C42×C11D411yescharacteristic
30C2×C22⋊Dic11—22no—
31C2×C22⋊Dic11—22no—
32C2×C22⋊Dic11D412yes—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×Dic11⋊C4—22no—
36C2×Dic11⋊C4—22no—
37C2×Dic11⋊C4—42no—
38#66931—48no—
39C11×#107—41no—
40C11×#106—41no—
41C11×#100—21no—
42C11×#100Q812yescomplemented
43#66898—22no—
44#66898Q814yescomplemented
45C11⋊#95—21no—
46C11⋊#95—22no—
47C11⋊#95—42no—
48#13461—111nomaximal, Sylow
49C24×C11C2×D412yes—
50C2×D4×C11—41no—
51C2×D4×C11—41no—
52C2×D4×C11C2×Q811yescharacteristic
53C2×D4×C11C2×Q812yes—
54C2×D4×C11#4111yescharacteristic
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—22no—
61C22×Dic11—22no—
62C22×Dic11—42no—
63C22×Dic11—42no—
64C22×Dic11—44no—
65C2×Dic22—44no—
66C2×Dic22—81no—
67C11×M16—22no—
68C11×M16—41no—
69C2×C8×C11—41no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—41no—
73C11×C22⋊C4—44no—
74C11×C22⋊C4—42no—
75C11×C22⋊C4—41no—
76C42×C11—41no—
77C42×C11—41no—
78C22⋊Dic11—24no—
79C22⋊Dic11—42no—
80C22⋊Dic11—42no—
81C22⋊Dic11—44no—
82C4⋊Dic11—24no—
83C4⋊Dic11—81no—
84Dic11⋊C4—44no—
85Dic11⋊C4—44no—
86Dic11⋊C4—84no—
87#2683—111no—
88#1867—112no—
89#1856D1111yescharacteristic
90#1393—111no—
91#1390—112no—
92C23×C11—22no—
93C23×C11—22no—
94C23×C11—42no—
95C23×C11—42no—
96C23×C11#12011yescharacteristic
97C23×C11C22⋊Q812yes—
98C23×C11C4⋊Q812yes—
99D4×C11—41no—
100D4×C11—42no—
101D4×C11—41no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—22no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—42no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—82no—
112C2×C4×C11—82no—
113C2×C4×C11C22⋊Q811yescharacteristic
114C2×C4×C11C4⋊Q811yescharacteristic
115C2×Dic11—24no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—44no—
119C2×Dic11—42no—
120C2×Dic11—44no—
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—82no—
124C2×Dic11—82no—
125C2×Dic11—82no—
126Dic22—84no—
127C8×C11—42no—
128C2×C22⋊Q8—222no—
129#518C2×D1111yescharacteristic
130#428—21no—
131C2×#100C2×D1111yescharacteristic
132C2×#99—112no—
133#396—222no—
134#395—221no—
135#390C2×D1111yescharacteristic
136#389—221no—
137#386—112no—
138#385—222no—
139#342—222no—
140#339—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—22no—
144C22×C11—22no—
145C22×C11—42no—
146C22×C11—42no—
147C22×C11—42no—
148C22×C11—42no—
149C22×C11—82no—
150C22×C11#39511yescharacteristic
151C22×C11B(4,𝔽2)11yescharacteristic
152C22×C11#45811yescharacteristic
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—42no—
156C4×C11—81no—
157C4×C11—81no—
158C4×C11—81no—
159Dic11—44no—
160Dic11—82no—
161Dic11—84no—
162C22×Q8—221no—
163C22×D4C22×D1111yescharacteristic
164C23×C4—112no—
165C2×M16—21no—
166C22⋊Q8—448no—
167C4×D4—41no—
168C4×D4—41no—
169#117—21no—
170C2×C4⋊C4—221no—
171C2×C4⋊C4—222no—
172C2×C4⋊C4—222no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4—442no—
175C2×C4⋊C4C22⋊D1111yescharacteristic
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—112no—
179C2×C22⋊C4—222no—
180C2×C22⋊C4—222no—
181C2×C42C22⋊D1111yescharacteristic
182#107—41no—
183#106—41no—
184#100—21no—
185#100Dic2212yescomplemented
186#99—114no—
187#99—222no—
188#95—221no—
189#95—222no—
190#95—442no—
191C2×C11—21no—
192C2×C11—21no—
193C2×C11—42no—
194C2×C11—42no—
195C2×C11#206211yescharacteristic
196C2×C11#219611yescharacteristic
197C2×C11#220111yescharacteristic
198C24D4×D1112yes—
199C2×Q8—444no—
200C2×Q8—881no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4C2×Dic2211yescharacteristic
204C2×D4#433911yescharacteristic
205C2×D4Q8×D1112yes—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—222no—
211C22×C4—222no—
212C22×C4—444no—
213C22×C4—442no—
214C22×C4—442no—
215C22×C4C2×C22⋊D1111yescharacteristic
216M16—22no—
217M16—41no—
218C2×C8—41no—
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—41no—
222C4⋊C4—224no—
223C4⋊C4—444no—
224C4⋊C4—444no—
225C4⋊C4—881no—
226C4⋊C4—884no—
227C22⋊C4—44no—
228C22⋊C4—42no—
229C22⋊C4—41no—
230C22⋊C4—224no—
231C22⋊C4—444no—
232C22⋊C4—442no—
233C22⋊C4—442no—
234C42—41no—
235C42—41no—
236C11#1346111yescharacteristic, complemented, Sylow
237C23—22no—
238C23—22no—
239C23—42no—
240C23—42no—
241C23#6694112yes—
242C23#6694912yes—
243C23#6699011yescharacteristic
244Q8—884no—
245D4—41no—
246D4—41no—
247D4—42no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4—224no—
260C2×C4—442no—
261C2×C4—442no—
262C2×C4—444no—
263C2×C4—444no—
264C2×C4—442no—
265C2×C4—442no—
266C2×C4—442no—
267C2×C4—882no—
268C2×C4—882no—
269C2×C4—882no—
270C2×C4#6697711yescharacteristic
271C2×C4#6699711yescharacteristic
272C8—42no—
273C22—21no—
274C22—21no—
275C22—22no—
276C22—22no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—82no—
282C22#1062259211yescharacteristic
283C22#1062264511yescharacteristic
284C22#1062266611yescharacteristic
285C4—21no—
286C4—21no—
287C4—42no—
288C4—81no—
289C4—81no—
290C4—81no—
291C4—444no—
292C4—882no—
293C4—884no—
294C2—21no—
295C2—21no—
296C2—42no—
297C2—42no—
298C2#1306996911yescharacteristic
299C2#1307059911yescharacteristic
300C2#1307062811yescharacteristic
subgroupG/H
centerC22#10622645
commutator, prime radical, cosocleC22×D4×C11C23
FrattiniC22×D4C22×D11
FittingC11×#1856C2
socleC22×C11B(4,𝔽2)
hypercenter#1856D11
hypocenterC11#13461
LCSG ▷ C22×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1856

Complements

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

NH ≅ G/Ntype
42. C11×#100Q8semidirect
44. #66898Q8semidirect
185. #100Dic22semidirect
236. C11#13461semidirect

Maximal subgroups

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

subgroupindex
#130749882
#130688972
#130667412
#130667352
C11×#18562
#1346111