Finite Group Databasebeta

← #14654419

Subgroups — #14654419

Order 2816.

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

normal subgroups only

This group has 722 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#13077876C212yesmaximal
2#13076653C211yesmaximal, characteristic, complemented
3#13067148C212yesmaximal, complemented
4#13066524C211yesmaximal, characteristic, complemented
5C11×#1782C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C2×#67004—22no—
8C2×#66977C2212yes—
9C2×C11×#99—22no—
10C11×#381C2211yescharacteristic
11C11×#381C2211yescharacteristic
12#10622852—24no—
13#10622845—22no—
14#10622841—22no—
15#10622831—22no—
16#10622820C2212yes—
17#10622566—22no—
18#10622272—22no—
19#10622269—22no—
20#10622090—24no—
21C2×C11×#41—22no—
22C2×C11×#41—22no—
23C2×C11×#41—44no—
24C22×Q8×C11D411yescharacteristic
25C22×D4×C11—21no—
26C22×D4×C11D411yescharacteristic
27C23×C4×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C22×Dic22D412yes—
30C2×C11×C22⋊C4—21no—
31C2×C11×C22⋊C4D412yes—
32C2×C22⋊Dic11—22no—
33#67004—48no—
34C2×#4326—24no—
35C2×#4324—24no—
36C2×C4⋊Dic11—22no—
37C2×C4⋊Dic11D412yes—
38#66977—22no—
39#66977—22no—
40#66977—22no—
41#66977—22no—
42C2×Dic11⋊C4—22no—
43C2×#4318—22no—
44C11×#99—44no—
45C11×#95—22no—
46C11×#95—22no—
47#66899—24no—
48#66896—24no—
49C11⋊#95—24no—
50C11⋊#95—22no—
51C22⋊(C11⋊C8)—22no—
52C22⋊(C11⋊C8)D414yes—
53#9982—111nomaximal, Sylow
54C24×C11—21no—
55C24×C11C2×D411yescharacteristic
56C11×#41—28no—
57C11×#41—44no—
58C11×#41—44no—
59C11×#41—44no—
60C2×Q8×C11—22no—
61C2×Q8×C11—42no—
62C2×D4×C11—24no—
63C2×D4×C11—22no—
64C2×D4×C11—42no—
65C2×D4×C11—42no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C22×C4×C11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—42no—
71C22×C4×C11—42no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11—41no—
75C22×C4×C11C2×D412yes—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D412yes—
78C22×C4×C11#4111yescharacteristic
79C22×Dic11—22no—
80C22×Dic11—22no—
81C2×Dic22—22no—
82C2×Dic22—22no—
83C2×Dic22—44no—
84C11×C22⋊C4—42no—
85C11×C22⋊C4—42no—
86C22⋊Dic11—42no—
87C22⋊Dic11—42no—
88#4326—48no—
89#4324—48no—
90C4⋊Dic11—22no—
91C4⋊Dic11—22no—
92C4⋊Dic11—82no—
93Dic11⋊C4—42no—
94Dic11⋊C4—42no—
95#4318—44no—
96C2×C11⋊C8—24no—
97#3007—112no—
98#2817—111no—
99#1782D1111yescharacteristic
100#1511—112no—
101#1306—111no—
102C23×C11—22no—
103C23×C11—22no—
104C23×C11—42no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11—82no—
108C23×C11#12011yescharacteristic
109C23×C11#12111yescharacteristic
110C23×C11#12711yescharacteristic
111Q8×C11—24no—
112Q8×C11—42no—
113D4×C11—24no—
114D4×C11—42no—
115D4×C11—44no—
116D4×C11—44no—
117C2×C4×C11—24no—
118C2×C4×C11—22no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11—48no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—44no—
126C2×C4×C11—42no—
127C2×C4×C11—81no—
128C2×C4×C11—82no—
129C2×C4×C11#12012yes—
130C2×C4×C11#12112yes—
131C2×Dic11—44no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—44no—
135Dic22—44no—
136Dic22—82no—
137C11⋊C8—44no—
138C22×#41C2×D1111yescharacteristic
139C2×#137—222no—
140C2×C22⋊Q8—112no—
141#452—224no—
142#451—222no—
143#450—222no—
144#417—222no—
145C2×#99—22no—
146#407—112no—
147#400—222no—
148#397—222no—
149#395—222no—
150#381C2×D1111yescharacteristic
151#381C2×D1111yescharacteristic
152#328—224no—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11—22no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—42no—
159C22×C11—82no—
160C22×C11—82no—
161C22×C11—82no—
162C22×C11—82no—
163C22×C11#39211yescharacteristic
164C22×C11B(4,𝔽2)12yes—
165C4×C11—22no—
166C4×C11—22no—
167C4×C11—42no—
168C4×C11—82no—
169C4×C11—161no—
170Dic11—82no—
171Dic11—82no—
172C2×#41—22no—
173C2×#41—22no—
174C2×#41—44no—
175C22×Q8—112no—
176C22×Q8D4411yescharacteristic
177C22×D4—21no—
178C22×D4D4411yescharacteristic
179C23×C4—21no—
180C23×C4C22×D1111yescharacteristic
181#137—448no—
182C2×Q16—224no—
183C2×SD16—224no—
184C2×M16—222no—
185C22⋊Q8—222no—
186C22⋊Q8—222no—
187C22⋊Q8—222no—
188C22⋊Q8—222no—
189C2×C4⋊C4—112no—
190C2×C4⋊C4—222no—
191C2×C4⋊C4—222no—
192C2×C22⋊C4—21no—
193C2×C22⋊C4—222no—
194C2×C22⋊C4C22⋊D1112yes—
195#103—224no—
196#102—224no—
197#99—44no—
198C22⋊C8—114no—
199C22⋊C8—222no—
200#95—22no—
201#95—22no—
202#95—224no—
203#95—222no—
204C2×C11—22no—
205C2×C11—41no—
206C2×C11—41no—
207C2×C11—82no—
208C2×C11#200912yes—
209C2×C11#202111yescharacteristic
210C24—21no—
211C24C2×C22⋊D1111yescharacteristic
212#41—28no—
213#41—44no—
214#41—44no—
215#41—44no—
216C2×Q8—22no—
217C2×Q8—42no—
218C2×Q8—222no—
219C2×Q8—222no—
220C2×Q8—444no—
221C2×D4—24no—
222C2×D4—22no—
223C2×D4—42no—
224C2×D4—42no—
225C2×D4—41no—
226C2×D4—41no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—41no—
234C22×C4—222no—
235C22×C4—222no—
236C22×C4C2×D4411yescharacteristic
237C22×C4#433911yescharacteristic
238C22×C4D4×D1112yes—
239C22×C4D4×D1112yes—
240Q16—448no—
241SD16—448no—
242M16—444no—
243C2×C8—224no—
244C4⋊C4—222no—
245C4⋊C4—222no—
246C4⋊C4—442no—
247C4⋊C4—442no—
248C4⋊C4—882no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—442no—
252C22⋊C4—442no—
253C11#998211yescharacteristic, complemented, Sylow
254C23—22no—
255C23—22no—
256C23—42no—
257C23—41no—
258C23—41no—
259C23—82no—
260C23#6698311yescharacteristic
261C23#6699011yescharacteristic
262C23#6699311yescharacteristic
263Q8—24no—
264Q8—42no—
265Q8—444no—
266Q8—882no—
267D4—24no—
268D4—42no—
269D4—44no—
270D4—44no—
271C2×C4—24no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—48no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—44no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—82no—
283C2×C4—444no—
284C2×C4—442no—
285C2×C4—442no—
286C2×C4—444no—
287C2×C4#6693512yes—
288C2×C4#6693712yes—
289C8—444no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—21no—
294C22—21no—
295C22—42no—
296C22—82no—
297C22—82no—
298C22—82no—
299C22—82no—
300C22#1062257311yescharacteristic
301C22#1062264512yes—
302C4—22no—
303C4—22no—
304C4—42no—
305C4—82no—
306C4—161no—
307C4—882no—
308C4—882no—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—82no—
313C2#1306967512yes—
314C2#1306974211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1782C2
socleC22×C11#392
prime radicalC22×C11×#41C22
hypercenter#1782D11
hypocenterC11#9982
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
2. #13076653C2semidirect
3. #13067148C2semidirect
4. #13066524C2semidirect
253. C11#9982semidirect

Maximal subgroups

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

subgroupindex
#130778762
#130766532
#130671482
#130665242
C11×#17822
#998211