Finite Group Databasebeta

← #14673444

Subgroups — #14673444

Order 2816.

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

normal subgroups only

This group has 540 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#13074988C211yesmaximal, characteristic
2#13068899C212yesmaximal
3#13068825C211yesmaximal, characteristic
4#13066733C212yesmaximal
5C11×#1393C211yesmaximal, characteristic
6#10623329C2211yescharacteristic
7C2×#66931—22no—
8C2×C11×#99C2212yes—
9C11×#390C2211yescharacteristic
10#10622833C2212yes—
11C2×#66897C2211yescharacteristic
12#10622592—21no—
13#10622577—21no—
14#10622563—22no—
15#10622561—22no—
16#10622541—21no—
17#10622165—22no—
18#10622161—21no—
19C22×D4×C11C2311yescharacteristic
20C23×Dic11D412yes—
21C22×Dic22—21no—
22C2×C11×C4⋊C4D411yescharacteristic
23C2×C11×C22⋊C4—22no—
24C2×C11×C22⋊C4—22no—
25C2×C42×C11D411yescharacteristic
26C2×C22⋊Dic11—22no—
27C2×C22⋊Dic11—22no—
28C2×C22⋊Dic11D412yes—
29D4×Dic11—41no—
30D4×Dic11—41no—
31#66979—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—42no—
35C2×Dic11⋊C4—22no—
36C2×Dic11⋊C4—22no—
37C2×#4318—21no—
38#66931—48no—
39C11×#99—22no—
40C11×#99Q814yescomplemented
41#66897—21no—
42#66897Q812yescomplemented
43C11⋊#95—21no—
44C11⋊#95—22no—
45C11⋊#95—42no—
46#66872—41no—
47#66871—41no—
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—42no—
58C22×C4×C11C2×D411yescharacteristic
59C22×Dic11—22no—
60C22×Dic11—22no—
61C22×Dic11—22no—
62C22×Dic11—22no—
63C22×Dic11—42no—
64C22×Dic11—44no—
65C2×Dic22—44no—
66C2×Dic22—81no—
67C11×C4⋊C4—41no—
68C11×C22⋊C4—24no—
69C11×C22⋊C4—44no—
70C11×C22⋊C4—42no—
71C42×C11—41no—
72C22⋊Dic11—42no—
73C22⋊Dic11—42no—
74C22⋊Dic11—44no—
75C22⋊Dic11—41no—
76C4⋊Dic11—24no—
77C4⋊Dic11—21no—
78C4⋊Dic11—21no—
79C4⋊Dic11—81no—
80C4⋊Dic11—84no—
81Dic11⋊C4—44no—
82Dic11⋊C4—44no—
83C4×Dic11—41no—
84#4318—22no—
85#4318—41no—
86C2×C11⋊C8—41no—
87#2683—111no—
88#1867—112no—
89#1856—111no—
90#1393D1111yescharacteristic
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—42no—
100D4×C11—41no—
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—44no—
109C2×C4×C11—41no—
110C2×C4×C11—82no—
111C2×C4×C11—82no—
112C2×C4×C11C22⋊Q811yescharacteristic
113C2×C4×C11C4⋊Q811yescharacteristic
114C2×Dic11—24no—
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—44no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—41no—
121C2×Dic11—41no—
122C2×Dic11—42no—
123C2×Dic11—82no—
124C2×Dic11—82no—
125C2×Dic11—82no—
126Dic22—84no—
127C11⋊C8—42no—
128C2×C22⋊Q8—222no—
129#518—111no—
130#428—221no—
131C2×#100—111no—
132C2×#99C2×D1112yes—
133#396—222no—
134#395—221no—
135#390C2×D1111yescharacteristic
136#389—221no—
137#386—112no—
138#385—222no—
139#342—222no—
140#339—221no—
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—84no—
157C4×C11—81no—
158Dic11—44no—
159Dic11—82no—
160Dic11—81no—
161Dic11—81no—
162C22×Q8—221no—
163C22×D4C22×D1111yescharacteristic
164C23×C4—112no—
165C2×M16—221no—
166C22⋊Q8—448no—
167C4×D4—441no—
168C4×D4—441no—
169#117—221no—
170C2×C4⋊C4—221no—
171C2×C4⋊C4—222no—
172C2×C4⋊C4—222no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4—442no—
175C2×C4⋊C4D4411yescharacteristic
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—112no—
179C2×C22⋊C4—222no—
180C2×C22⋊C4—222no—
181C2×C42D4411yescharacteristic
182#107—441no—
183#106—441no—
184#100—112no—
185#100—221no—
186#99—22no—
187#99Dic2214yescomplemented
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×Dic2212yes—
204C2×D4#434111yescharacteristic
205C2×D4Q8×D1111yescharacteristic
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—42no—
209C22×C4—222no—
210C22×C4—222no—
211C22×C4—222no—
212C22×C4—222no—
213C22×C4—444no—
214C22×C4—442no—
215C22×C4C2×D4411yescharacteristic
216M16—222no—
217M16—441no—
218C2×C8—441no—
219C4⋊C4—41no—
220C4⋊C4—224no—
221C4⋊C4—221no—
222C4⋊C4—221no—
223C4⋊C4—444no—
224C4⋊C4—444no—
225C4⋊C4—881no—
226C4⋊C4—884no—
227C22⋊C4—24no—
228C22⋊C4—44no—
229C22⋊C4—42no—
230C22⋊C4—444no—
231C22⋊C4—442no—
232C22⋊C4—441no—
233C22⋊C4—442no—
234C42—41no—
235C42—441no—
236C11#1346111yescharacteristic, complemented, Sylow
237C23—22no—
238C23—22no—
239C23—42no—
240C23—42no—
241C23#6693112yes—
242C23#6693511yescharacteristic
243C23#6694112yes—
244Q8—884no—
245D4—42no—
246D4—41no—
247D4—41no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—44no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—224no—
259C2×C4—442no—
260C2×C4—442no—
261C2×C4—444no—
262C2×C4—442no—
263C2×C4—442no—
264C2×C4—441no—
265C2×C4—441no—
266C2×C4—442no—
267C2×C4—882no—
268C2×C4—882no—
269C2×C4—882no—
270C2×C4#6692211yescharacteristic
271C2×C4#6695011yescharacteristic
272C8—442no—
273C22—21no—
274C22—21no—
275C22—22no—
276C22—22no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—82no—
282C22#1062226911yescharacteristic
283C22#1062235411yescharacteristic
284C22#1062235511yescharacteristic
285C4—21no—
286C4—21no—
287C4—42no—
288C4—84no—
289C4—81no—
290C4—444no—
291C4—882no—
292C4—881no—
293C4—881no—
294C2—21no—
295C2—21no—
296C2—42no—
297C2—42no—
298C2#1306997011yescharacteristic
299C2#1307060211yescharacteristic
300C2#1307063111yescharacteristic
subgroupG/H
centerC22#10622354
commutator, prime radical, cosocleC22×D4×C11C23
FrattiniC22×D4C22×D11
FittingC11×#1393C2
socleC22×C11B(4,𝔽2)
hypercenter#1393D11
hypocenterC11#13461
LCSG ▷ C22×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
40. C11×#99Q8semidirect
42. #66897Q8semidirect
187. #99Dic22semidirect
236. C11#13461semidirect

Maximal subgroups

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

subgroupindex
#130749882
#130688992
#130688252
#130667332
C11×#13932
#1346111