Finite Group Databasebeta

← #14654335

Subgroups — #14654335

Order 2816.

804 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#10622352C212yesmaximal
2#13074730C211yesmaximal, characteristic
3C2×#10622105C212yesmaximal
4#13066886C211yesmaximal, characteristic
5C11×#1280C211yesmaximal, characteristic
6C23×Dic22C2211yescharacteristic
7C2×#66977C2212yes—
8C22×Dic44—22no—
9C2×C11×C22⋊C8C2212yes—
10C2×C11×#95C2211yescharacteristic
11#10622825—22no—
12C2×C11⋊#95—22no—
13C2×C11⋊#95C2211yescharacteristic
14C2×#66880—22no—
15#10622352—24no—
16#10622352—24no—
17#10622274—22no—
18#10622269—22no—
19#10622105—24no—
20C23×C4×C11D412yes—
21C23×C4×C11C2311yescharacteristic
22C23×Dic11—21no—
23C23×Dic11—21no—
24C22×Dic22—22no—
25C22×Dic22—22no—
26C22×Dic22—21no—
27C22×Dic22—44no—
28C22×Dic22D412yes—
29C22×Dic22D412yes—
30C22×C8×C11—22no—
31C2×C22⋊Dic11—22no—
32C2×C4⋊Dic11—22no—
33C2×C4⋊Dic11—22no—
34C2×C4⋊Dic11D412yes—
35#66977—22no—
36#66977—22no—
37#66977—22no—
38#66977—22no—
39C2×Dic11⋊C4—22no—
40C2×Dic44—28no—
41C2×Dic44—48no—
42C11×C22⋊C8—22no—
43C11×C22⋊C8D414yes—
44C11×#95—22no—
45C11⋊#95—24no—
46C11⋊#95—22no—
47C11⋊#95—44no—
48#66880—28no—
49#9967—111nomaximal, Sylow
50C24×C11C2×D411yescharacteristic
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—42no—
54C22×C4×C11—42no—
55C22×C4×C11—42no—
56C22×C4×C11Q1614yescomplemented
57C22×C4×C11C2×D412yes—
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D412yes—
60C22×C4×C11#4111yescharacteristic
61C22×Dic11—24no—
62C22×Dic11—22no—
63C22×Dic11—22no—
64C22×Dic11—22no—
65C22×Dic11—22no—
66C22×Dic11—42no—
67C22×Dic11—42no—
68C22×Dic11—41no—
69C22×Dic11—41no—
70C22×Dic11—41no—
71C22×Dic11—41no—
72C22×Dic11—42no—
73C2×Dic22—28no—
74C2×Dic22—24no—
75C2×Dic22—22no—
76C2×Dic22—22no—
77C2×Dic22—44no—
78C2×Dic22—44no—
79C2×Dic22—44no—
80C2×Dic22—48no—
81C2×Dic22—44no—
82C2×Dic22—42no—
83C2×C8×C11—24no—
84C2×C8×C11—44no—
85C22⋊Dic11—42no—
86C22⋊Dic11—42no—
87C4⋊Dic11—22no—
88C4⋊Dic11—22no—
89C4⋊Dic11—82no—
90C4⋊Dic11—82no—
91Dic11⋊C4—42no—
92Dic11⋊C4—42no—
93Dic44—416no—
94C2×#451—112no—
95#2659—111no—
96C2×#328—112no—
97#1446—111no—
98#1280D1111yescharacteristic
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—22no—
102C23×C11#12011yescharacteristic
103C23×C11#12111yescharacteristic
104C23×C11#12711yescharacteristic
105C23×C11C2×Q1612yes—
106C23×C11#13712yes—
107C2×C4×C11—24no—
108C2×C4×C11—24no—
109C2×C4×C11—42no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—44no—
115C2×C4×C11—82no—
116C2×C4×C11#12012yes—
117C2×C4×C11#12112yes—
118C2×Dic11—24no—
119C2×Dic11—42no—
120C2×Dic11—44no—
121C2×Dic11—42no—
122C2×Dic11—44no—
123C2×Dic11—44no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—44no—
130C2×Dic11—82no—
131C2×Dic11—81no—
132C2×Dic11—81no—
133Dic22—28no—
134Dic22—44no—
135Dic22—48no—
136Dic22—44no—
137Dic22—82no—
138C8×C11—44no—
139C23×Q8—111no—
140C22×Q16—222no—
141C2×C22⋊Q8—112no—
142#451—224no—
143#451—224no—
144C2×#103—222no—
145C2×C22⋊C8C2×D1112yes—
146#398—222no—
147#395—222no—
148#380—222no—
149C2×#95—111no—
150C2×#95—222no—
151C2×#95C2×D1111yescharacteristic
152#328—224no—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11#39211yescharacteristic
162C22×C11#45112yes—
163C22×C11#45511yescharacteristic
164C22×C11#45611yescharacteristic
165C22×C11B(4,𝔽2)12yes—
166C22×C11#46212yes—
167C22×C11#49411yescharacteristic
168C22×C11#49711yescharacteristic
169C4×C11—22no—
170C4×C11—22no—
171C4×C11—44no—
172Dic11—44no—
173Dic11—82no—
174Dic11—82no—
175Dic11—82no—
176C22×Q8—112no—
177C22×Q8—112no—
178C22×Q8—221no—
179C22×Q8—222no—
180C22×Q8—222no—
181C22×Q8—444no—
182C23×C4—221no—
183C23×C4—221no—
184C23×C4D4412yes—
185C23×C4C22×D1111yescharacteristic
186C2×Q16—228no—
187C2×Q16—448no—
188C22×C8—22no—
189C22⋊Q8—222no—
190C22⋊Q8—222no—
191C22⋊Q8—222no—
192C22⋊Q8—222no—
193C2×C4⋊C4—112no—
194C2×C4⋊C4—222no—
195C2×C4⋊C4—222no—
196C2×C4⋊C4—222no—
197C2×C22⋊C4—222no—
198#103—228no—
199C22⋊C8—22no—
200C22⋊C8D4414yes—
201#95—22no—
202#95—224no—
203#95—222no—
204#95—444no—
205C2×C11—21no—
206C2×C11—22no—
207C2×C11—21no—
208C2×C11#160212yes—
209C2×C11#160512yes—
210C2×C11#200711yescharacteristic
211C2×C11#201611yescharacteristic
212C2×C11#202111yescharacteristic
213C24C2×D4411yescharacteristic
214C2×Q8—228no—
215C2×Q8—224no—
216C2×Q8—222no—
217C2×Q8—222no—
218C2×Q8—444no—
219C2×Q8—444no—
220C2×Q8—444no—
221C2×Q8—444no—
222C2×Q8—448no—
223C2×Q8—442no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—224no—
230C22×C4—222no—
231C22×C4—222no—
232C22×C4—222no—
233C22×C4—222no—
234C22×C4—442no—
235C22×C4—441no—
236C22×C4—441no—
237C22×C4—442no—
238C22×C4—441no—
239C22×C4—441no—
240C22×C4—442no—
241C22×C4Dic4414yescomplemented
242C22×C4C2×D4412yes—
243C22×C4D4×D1112yes—
244C22×C4D4×D1111yescharacteristic
245C22×C4#434311yescharacteristic
246Q16—4416no—
247C2×C8—24no—
248C2×C8—44no—
249C4⋊C4—222no—
250C4⋊C4—222no—
251C4⋊C4—442no—
252C4⋊C4—442no—
253C4⋊C4—882no—
254C4⋊C4—882no—
255C22⋊C4—442no—
256C22⋊C4—442no—
257C11#996711yescharacteristic, complemented, Sylow
258C23—22no—
259C23—21no—
260C23—21no—
261C23#6692711yescharacteristic
262C23#6693511yescharacteristic
263C23#6694811yescharacteristic
264C23C2×Dic4412yes—
265C23#6696212yes—
266Q8—228no—
267Q8—444no—
268Q8—448no—
269Q8—444no—
270Q8—882no—
271C2×C4—24no—
272C2×C4—24no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—44no—
279C2×C4—82no—
280C2×C4—224no—
281C2×C4—442no—
282C2×C4—444no—
283C2×C4—442no—
284C2×C4—444no—
285C2×C4—444no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—444no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4—882no—
293C2×C4—881no—
294C2×C4—881no—
295C2×C4#6693512yes—
296C2×C4#6694812yes—
297C8—44no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22#1062228411yescharacteristic
307C22#1062231211yescharacteristic
308C22#1062232811yescharacteristic
309C22#1062235212yes—
310C22#1062235412yes—
311C22#1062235911yescharacteristic
312C22#1062236511yescharacteristic
313C22#1062246212yes—
314C4—22no—
315C4—22no—
316C4—44no—
317C4—444no—
318C4—882no—
319C4—882no—
320C4—882no—
321C2—21no—
322C2—21no—
323C2—22no—
324C2#1306757512yes—
325C2#1306759212yes—
326C2#1306966511yescharacteristic
327C2#1306971811yescharacteristic
328C2#1306974311yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1280C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1280D11
hypocenterC11#9967
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
56. C22×C4×C11Q16semidirect
241. C22×C4Dic44semidirect
257. C11#9967semidirect

Maximal subgroups

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

subgroupindex
C2×#106223522
#130747302
C2×#106221052
#130668862
C11×#12802
#996711