Finite Group Databasebeta

← #14656865

Subgroups — #14656865

Order 2816.

416 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 93 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#13076992C211yesmaximal, characteristic
2#13069592C211yesmaximal, characteristic
3#13067181C211yesmaximal, characteristic
4#13067179C211yesmaximal, characteristic
5#13066476C211yesmaximal, characteristic
6#13066448C211yesmaximal, characteristic
7C11×#1286C211yesmaximal, characteristic
8C2×#66941—21no—
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#382C2211yescharacteristic
13#10622590—21no—
14#10622549C2211yescharacteristic
15C42×Dic11C2211yescharacteristic
16#10622538C2211yescharacteristic
17#10622259—22no—
18#10622259—22no—
19#10622193—21no—
20#10622193—21no—
21#10622105—22no—
22#10622090—22no—
23C22×Dic22—22no—
24C2×C11×M16—21no—
25C2×C11×C4⋊C4—21no—
26C2×C42×C11C2311yescharacteristic
27#66979—21no—
28C2×C4⋊Dic11—21no—
29#66977—21no—
30#66977—21no—
31C2×Dic11⋊C4—22no—
32C2×C4×Dic11—21no—
33C2×C4×Dic11—21no—
34C2×C4×Dic11D411yescharacteristic
35C2×C4×Dic11D411yescharacteristic
36#66941—42no—
37#66941—42no—
38#66923—21no—
39#66922Q811yescharacteristic, complemented
40#66922Q811yescharacteristic, complemented
41C4×Dic22—21no—
42C4×Dic22—21no—
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C22⋊C8—21no—
47C4×C8×C11—21no—
48C11×#95—21no—
49C11×#95D412yes—
50C11⋊#95—24no—
51C11⋊#95—21no—
52C11⋊#95D412yes—
53C22⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4×C11⋊C8—21no—
56#10363—111nomaximal, Sylow
57C22×C4×C11—22no—
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×Dic11—21no—
62C22×Dic11—21no—
63C22×Dic11—22no—
64C2×Dic22—21no—
65C2×Dic22—21no—
66C2×Dic22—44no—
67C2×Dic22—44no—
68C2×Dic22—44no—
69C11×M16—41no—
70C11×M16—41no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C42×C11C2×Q811yescharacteristic
76C42×C11#4111yescharacteristic
77C42×C11#4111yescharacteristic
78C42×C11#4111yescharacteristic
79C22⋊Dic11—41no—
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86Dic11⋊C4—44no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89C4×Dic11—21no—
90C4×Dic11—21no—
91C4×Dic11—42no—
92C4×Dic11—42no—
93C4×Dic11—41no—
94C4×Dic11SD1612yes—
95C4×Dic11Q1612yes—
96C2×C11⋊C8—41no—
97#2862—111no—
98#1994—111no—
99#1518—111no—
100#1518—111no—
101#1286—111no—
102#1286D1111yescharacteristic
103#1276—111no—
104C23×C11#12011yescharacteristic
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11C22⋊Q811yescharacteristic
111C2×C4×C11C22⋊Q811yescharacteristic
112C2×C4×C11C22⋊Q811yescharacteristic
113C2×C4×C11#12411yescharacteristic
114C2×C4×C11#12411yescharacteristic
115C2×C4×C11#12411yescharacteristic
116C2×C4×C11C2×SD1611yescharacteristic
117C2×C4×C11C2×Q1611yescharacteristic
118C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C11#13711yescharacteristic
120C2×Dic11—22no—
121C2×Dic11—22no—
122C2×Dic11—22no—
123C2×Dic11—22no—
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—42no—
131Dic22—88no—
132Dic22—81no—
133Dic22—81no—
134C8×C11—81no—
135C8×C11—81no—
136C11⋊C8—81no—
137#533—111no—
138C2×C4⋊Q8—221no—
139#431—111no—
140#431C2×D1111yescharacteristic
141#423C2×D1111yescharacteristic
142#391—222no—
143#391—222no—
144#382—111no—
145#382—221no—
146#382C2×D1111yescharacteristic
147C43—111no—
148#339—221no—
149#339—221no—
150#328—222no—
151#328—222no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11#39311yescharacteristic
155C22×C11#45011yescharacteristic
156C22×C11#45111yescharacteristic
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—82no—
162C4×C11#47511yescharacteristic
163C4×C11#47711yescharacteristic
164C4×C11#48711yescharacteristic
165C4×C11#48911yescharacteristic
166Dic11—24no—
167Dic11—42no—
168Dic11—82no—
169Dic11—81no—
170Dic11—81no—
171C22×Q8—222no—
172C2×M16—21no—
173C4⋊Q8—111no—
174C4⋊Q8—111no—
175C4⋊Q8—442no—
176C4⋊Q8—442no—
177#125—221no—
178C22⋊Q8—221no—
179C22⋊Q8—221no—
180C4×Q8—221no—
181C4×Q8—221no—
182#117—221no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—222no—
185C2×C4⋊C4—221no—
186C2×C42—111no—
187C2×C42—111no—
188C2×C42—221no—
189C2×C42—221no—
190C2×C42C22×D1111yescharacteristic
191C4⋊C8—21no—
192C4⋊C8—21no—
193C4⋊C8—21no—
194C4⋊C8—221no—
195C22⋊C8—21no—
196C22⋊C8—221no—
197C4×C8—21no—
198C4×C8—221no—
199#95—21no—
200#95—112no—
201#95—224no—
202#95—221no—
203#95D4412yes—
204C2×C11—21no—
205C2×C11—21no—
206C2×C11#202411yescharacteristic
207C2×C11#203111yescharacteristic
208C2×C11#203111yescharacteristic
209C2×Q8—221no—
210C2×Q8—221no—
211C2×Q8—444no—
212C2×Q8—444no—
213C2×Q8—444no—
214C22×C4—22no—
215C22×C4—221no—
216C22×C4—221no—
217C22×C4—222no—
218C22×C4C2×D4411yescharacteristic
219C22×C4D4×D1111yescharacteristic
220C22×C4D4×D1111yescharacteristic
221M16—41no—
222M16—41no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—441no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—221no—
229C4⋊C4—221no—
230C4⋊C4—221no—
231C4⋊C4—221no—
232C4⋊C4—444no—
233C4⋊C4—441no—
234C4⋊C4—441no—
235C4⋊C4—441no—
236C4⋊C4—441no—
237C22⋊C4—441no—
238C42—112no—
239C42—112no—
240C42—221no—
241C42—221no—
242C42—442no—
243C42—442no—
244C42—441no—
245C42#433911yescharacteristic
246C42#433911yescharacteristic
247C42#434111yescharacteristic
248C42Q8×D1111yescharacteristic
249C11#1036311yescharacteristic, complemented, Sylow
250C23#6693511yescharacteristic
251Q8—881no—
252Q8—881no—
253Q8—888no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—222no—
260C2×C4—222no—
261C2×C4—222no—
262C2×C4—222no—
263C2×C4—441no—
264C2×C4—441no—
265C2×C4—442no—
266C2×C4—442no—
267C2×C4—441no—
268C2×C4—441no—
269C2×C4—442no—
270C2×C4#6692811yescharacteristic
271C2×C4#6693811yescharacteristic
272C2×C4#6693811yescharacteristic
273C2×C4#6694911yescharacteristic
274C2×C4#6694911yescharacteristic
275C2×C4#6695011yescharacteristic
276C2×C4#6696411yescharacteristic
277C2×C4SD16×D1111yescharacteristic
278C2×C4#6696811yescharacteristic
279C2×C4Q16×D1111yescharacteristic
280C8—81no—
281C8—81no—
282C8—881no—
283C22—21no—
284C22—21no—
285C22#1062228611yescharacteristic
286C22#1062238911yescharacteristic
287C22#1062242111yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—82no—
293C4—224no—
294C4—442no—
295C4—882no—
296C4—881no—
297C4—881no—
298C4#1062237811yescharacteristic
299C4#1062240511yescharacteristic
300C4#1062246711yescharacteristic
301C4#1062248811yescharacteristic
302C2—21no—
303C2—21no—
304C2#1306975611yescharacteristic
305C2#1306978711yescharacteristic
306C2#1306979111yescharacteristic
subgroupG/H
centerC22#10622286
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1286D11
hypocenterC11#10363
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
39. #66922Q8semidirect
40. #66922Q8semidirect
249. C11#10363semidirect

Maximal subgroups

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

subgroupindex
#130769922
#130695922
#130671812
#130671792
#130664762
#130664482
C11×#12862
#1036311