Finite Group Databasebeta

← #14663447

Subgroups — #14663447

Order 2816.

554 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 87 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#13071981C211yesmaximal, characteristic
2#13066934C211yesmaximal, characteristic
3#13066565C214yesmaximal, complemented
4C11×#1466C211yesmaximal, characteristic
5C23×Dic22C411yescharacteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66977—21no—
8C11×#432—21no—
9#10622833C412yes—
10#10622825C411yescharacteristic
11C2×C22⋊(C11⋊C8)—21no—
12#10622592—21no—
13#10622560—21no—
14#10622559C2212yes—
15#10622542—21no—
16C11×#323—21no—
17C11×#323C2212yes—
18#10622166—21no—
19#10622163C2212yes—
20C22×D4×C11C2×C411yescharacteristic
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11C2×C412yes—
24C22×Dic22—21no—
25C22×Dic22—21no—
26C22×Dic22—44no—
27C22×Dic22—41no—
28C22×Dic22—41no—
29C4×D4×C11—41no—
30C4×D4×C11—41no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C11×C22⋊C4C2311yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—22no—
36C2×C22⋊Dic11C2×C412yes—
37C2×C4⋊Dic11—21no—
38#66977—44no—
39C2×Dic11⋊C4—22no—
40C22×C11⋊C8—41no—
41C11×C4⋊C8—41no—
42C11×C22⋊C8—22no—
43C11×#97—41no—
44C11⋊#95—22no—
45C11⋊#95—21no—
46C11⋊#95—22no—
47C22⋊(C11⋊C8)—22no—
48C22⋊(C11⋊C8)—41no—
49#11575—111nomaximal, Sylow
50C24×C11C22⋊C411yescharacteristic
51C24×C11C22×C411yescharacteristic
52C2×D4×C11—22no—
53C2×D4×C11—22no—
54C2×D4×C11—41no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—42no—
60C22×C4×C11—42no—
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—22no—
67C22×Dic11—22no—
68C22×Dic11—42no—
69C22×Dic11—44no—
70C2×Dic22—24no—
71C2×Dic22—42no—
72C2×Dic22—42no—
73C2×Dic22—44no—
74C2×Dic22—48no—
75C2×Dic22—44no—
76C2×Dic22—44no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×C8×C11—42no—
80C11×C4⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C42×C11—21no—
84C42×C11—21no—
85C22⋊Dic11—24no—
86C22⋊Dic11—44no—
87C4⋊Dic11—42no—
88Dic11⋊C4—44no—
89C2×C11⋊C8—42no—
90C2×C11⋊C8—82no—
91#2409—111no—
92#1466D1111yescharacteristic
93#1459—111no—
94#1326—114no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—41no—
100C23×C11—41no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11#10112yes—
104C23×C11C2×C22⋊C411yescharacteristic
105C23×C11#13112yes—
106D4×C11—44no—
107C2×C4×C11—22no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—81no—
121C2×C4×C11#9911yescharacteristic
122C2×C4×C11#9911yescharacteristic
123C2×Dic11—24no—
124C2×Dic11—42no—
125C2×Dic11—44no—
126C2×Dic11—42no—
127C2×Dic11—44no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131Dic22—44no—
132Dic22—48no—
133Dic22—44no—
134C8×C11—82no—
135C11⋊C8—82no—
136C23×Q8—111no—
137C2×C22⋊Q8—221no—
138C2×C4×D4C2×D1111yescharacteristic
139#432—21no—
140C2×C22⋊C8—221no—
141#395—221no—
142#393—221no—
143#391—221no—
144#386—112no—
145#385—112no—
146#380—111no—
147#324—221no—
148#323—21no—
149#323—112no—
150#323C2×D1112yes—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11—42no—
156C22×C11—42no—
157C22×C11—42no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—81no—
163C22×C11#40811yescharacteristic
164C22×C11C2×#9911yescharacteristic
165C22×C11C2×#10111yescharacteristic
166C4×C11—21no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11AΣL(1,𝔽16)12yes—
172Dic11—44no—
173Dic11—82no—
174C22×Q8—221no—
175C22×Q8—221no—
176C22×Q8—441no—
177C22×Q8—441no—
178C22×Q8—444no—
179C22×D4C4×D1111yescharacteristic
180C23×C4—112no—
181C23×C4C4×D1111yescharacteristic
182C23×C4D4411yescharacteristic
183C22×C8—441no—
184C22⋊Q8—444no—
185C4×D4—41no—
186C4×D4—41no—
187C2×C4⋊C4—221no—
188C2×C4⋊C4—222no—
189C2×C4⋊C4D4411yescharacteristic
190C2×C22⋊C4—112no—
191C2×C22⋊C4—222no—
192C2×C22⋊C4C22⋊D1111yescharacteristic
193C2×C22⋊C4C22×D1111yescharacteristic
194C2×C42C22⋊D1111yescharacteristic
195C4⋊C8—41no—
196C22⋊C8—22no—
197C22⋊C8—222no—
198C22⋊C8—441no—
199#97—41no—
200#95—221no—
201#95—222no—
202#95—222no—
203C2×C11—21no—
204C2×C11—21no—
205C2×C11—42no—
206C2×C11—42no—
207C2×C11#147211yescharacteristic
208C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
209C2×C11#212311yescharacteristic
210C24(C2×D11)⋊C411yescharacteristic
211C24C2×C4×D1111yescharacteristic
212C2×Q8—224no—
213C2×Q8—442no—
214C2×Q8—442no—
215C2×Q8—444no—
216C2×Q8—444no—
217C2×Q8—448no—
218C2×Q8—444no—
219C2×Q8—441no—
220C2×Q8—441no—
221C2×D4—22no—
222C2×D4—22no—
223C2×D4—41no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—222no—
231C22×C4—222no—
232C22×C4—444no—
233C22×C4—442no—
234C22×C4(C2×D11)⋊C411yescharacteristic
235C22×C4(C2×D11)⋊C411yescharacteristic
236C22×C4(C2×D11)⋊C411yescharacteristic
237C22×C4C2×D4411yescharacteristic
238C22×C4C2×C22⋊D1111yescharacteristic
239C2×C8—42no—
240C2×C8—442no—
241C2×C8—882no—
242C4⋊C4—41no—
243C4⋊C4—442no—
244C4⋊C4—444no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—224no—
248C22⋊C4—444no—
249C42—21no—
250C42—21no—
251C11#1157511yescharacteristic, complemented, Sylow
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23#6688812yes—
261C23#6696012yes—
262C23C2×(C2×D11)⋊C411yescharacteristic
263Q8—444no—
264Q8—448no—
265Q8—444no—
266D4—44no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—81no—
281C2×C4—224no—
282C2×C4—442no—
283C2×C4—444no—
284C2×C4—442no—
285C2×C4—444no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4#6687011yescharacteristic
290C2×C4#6687011yescharacteristic
291C8—82no—
292C8—882no—
293C22—21no—
294C22—21no—
295C22—22no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—81no—
305C22C2×#6687011yescharacteristic
306C22#1062274211yescharacteristic
307C22C2×#6688811yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—444no—
314C4—882no—
315C4#1062211312yes—
316C2—21no—
317C2—21no—
318C2—42no—
319C2—42no—
320C2#1306698111yescharacteristic
321C2C2×#1062211311yescharacteristic
322C2#1307026911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1466C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1466D11
hypocenterC11#11575
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #13066565C2semidirect
251. C11#11575semidirect

Maximal subgroups

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

subgroupindex
#130719812
#130669342
#130665652
C11×#14662
#1157511