Finite Group Databasebeta

← #14656864

Subgroups — #14656864

Order 2816.

416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 95 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#13069594C211yesmaximal, characteristic
3#13067180C211yesmaximal, characteristic
4#13066475C211yesmaximal, characteristic
5#13066474C211yesmaximal, characteristic
6#13066448C211yesmaximal, characteristic
7C11×#1518C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×#66941—21no—
10C11×#431C2211yescharacteristic
11C11×#382C2211yescharacteristic
12#10622590—21no—
13#10622549C2211yescharacteristic
14C42×Dic11C2211yescharacteristic
15#10622538C2211yescharacteristic
16#10622537C2211yescharacteristic
17#10622259—22no—
18#10622259—22no—
19C11×#328—22no—
20#10622176—22no—
21#10622170—21no—
22#10622170—21no—
23C22×Dic22—22no—
24C11×C4⋊Q8Q811yescharacteristic, complemented
25C11×C4⋊Q8Q811yescharacteristic, complemented
26C11×#125—21no—
27C11×C22⋊Q8—21no—
28C11×C22⋊Q8—21no—
29C4×Q8×C11—21no—
30C4×Q8×C11—21no—
31C11×#117—21no—
32C2×C11×C4⋊C4—21no—
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11—21no—
35C2×Dic11⋊C4—22no—
36C2×C4×Dic11—21no—
37C2×C4×Dic11—21no—
38C2×C4×Dic11D411yescharacteristic
39C2×C4×Dic11D411yescharacteristic
40C2×#4318—21no—
41#66941—42no—
42#66941—42no—
43C11×C4⋊C8—21no—
44C11×C22⋊C8—21no—
45C4×C8×C11—21no—
46C11×#95—21no—
47C11×#95D412yes—
48C11⋊#95—24no—
49C11⋊#95—21no—
50C11⋊#95D412yes—
51C22⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4×C11⋊C8—21no—
56#10363—111nomaximal, Sylow
57C2×Q8×C11—21no—
58C2×Q8×C11—21no—
59C22×C4×C11—22no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—21no—
64C22×Dic11—21no—
65C22×Dic11—22no—
66C2×Dic22—44no—
67C2×Dic22—44no—
68C2×Dic22—44no—
69C2×C8×C11—41no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C22⋊C4—41no—
79C42×C11—41no—
80C42×C11C2×Q811yescharacteristic
81C42×C11#4111yescharacteristic
82C42×C11#4111yescharacteristic
83C42×C11#4111yescharacteristic
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86Dic11⋊C4—44no—
87C4×Dic11—21no—
88C4×Dic11—21no—
89C4×Dic11—42no—
90C4×Dic11—42no—
91C4×Dic11SD1612yes—
92C4×Dic11Q1612yes—
93#4318—41no—
94#4318—41no—
95C2×C11⋊C8—41no—
96C2×C11⋊C8—41no—
97#2862—111no—
98#1994—111no—
99#1518—111no—
100#1518D1111yescharacteristic
101#1286—111no—
102#1286—111no—
103#1276—111no—
104C23×C11#12011yescharacteristic
105Q8×C11—81no—
106Q8×C11—81no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—42no—
114C2×C4×C11C22⋊Q811yescharacteristic
115C2×C4×C11C22⋊Q811yescharacteristic
116C2×C4×C11C22⋊Q811yescharacteristic
117C2×C4×C11#12411yescharacteristic
118C2×C4×C11#12411yescharacteristic
119C2×C4×C11#12411yescharacteristic
120C2×C4×C11C2×SD1611yescharacteristic
121C2×C4×C11C2×Q1611yescharacteristic
122C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C11#13711yescharacteristic
124C2×Dic11—22no—
125C2×Dic11—22no—
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133Dic22—88no—
134C8×C11—81no—
135C11⋊C8—81no—
136C11⋊C8—81no—
137#533C2×D1111yescharacteristic
138C2×C4⋊Q8—221no—
139#431—111no—
140#431C2×D1111yescharacteristic
141#423—111no—
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—22no—
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—81no—
163C4×C11—81no—
164C4×C11#47511yescharacteristic
165C4×C11#47711yescharacteristic
166C4×C11#48711yescharacteristic
167C4×C11#48911yescharacteristic
168Dic11—24no—
169Dic11—42no—
170Dic11—82no—
171C22×Q8—222no—
172C2×M16—221no—
173C4⋊Q8—442no—
174C4⋊Q8—442no—
175C4⋊Q8Dic2211yescharacteristic, complemented
176C4⋊Q8Dic2211yescharacteristic, complemented
177#125—21no—
178C22⋊Q8—21no—
179C22⋊Q8—21no—
180C4×Q8—21no—
181C4×Q8—21no—
182#117—21no—
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—221no—
193C4⋊C8—221no—
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#95C22⋊D1112yes—
204C2×C11—21no—
205C2×C11—21no—
206C2×C11#202411yescharacteristic
207C2×C11#203111yescharacteristic
208C2×C11#203111yescharacteristic
209C2×Q8—21no—
210C2×Q8—21no—
211C2×Q8—444no—
212C2×Q8—444no—
213C2×Q8—444no—
214C22×C4—22no—
215C22×C4—221no—
216C22×C4—221no—
217C22×C4—222no—
218C22×C4D4×D1111yescharacteristic
219C22×C4D4×D1111yescharacteristic
220C22×C4C2×C22⋊D1111yescharacteristic
221M16—441no—
222M16—441no—
223C2×C8—41no—
224C2×C8—441no—
225C2×C8—441no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—444no—
235C4⋊C4—441no—
236C4⋊C4—441no—
237C22⋊C4—41no—
238C42—41no—
239C42—112no—
240C42—112no—
241C42—221no—
242C42—221no—
243C42—442no—
244C42—442no—
245C42C2×Dic2211yescharacteristic
246C42#433911yescharacteristic
247C42#434111yescharacteristic
248C42#434111yescharacteristic
249C11#1036311yescharacteristic, complemented, Sylow
250C23#6699011yescharacteristic
251Q8—81no—
252Q8—81no—
253Q8—888no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—222no—
262C2×C4—222no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4—441no—
266C2×C4—441no—
267C2×C4—442no—
268C2×C4—442no—
269C2×C4—442no—
270C2×C4#6693111yescharacteristic
271C2×C4#6693111yescharacteristic
272C2×C4#6693811yescharacteristic
273C2×C4#6693811yescharacteristic
274C2×C4SD16×D1111yescharacteristic
275C2×C4#6696711yescharacteristic
276C2×C4Q16×D1111yescharacteristic
277C2×C4#6697111yescharacteristic
278C2×C4#6697711yescharacteristic
279C2×C4#6698911yescharacteristic
280C8—81no—
281C8—881no—
282C8—881no—
283C22—21no—
284C22—21no—
285C22#1062256011yescharacteristic
286C22#1062278211yescharacteristic
287C22#1062279911yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—82no—
293C4—81no—
294C4—81no—
295C4—224no—
296C4—442no—
297C4—882no—
298C4#1062240411yescharacteristic
299C4#1062240511yescharacteristic
300C4#1062240711yescharacteristic
301C4#1062240811yescharacteristic
302C2—21no—
303C2—21no—
304C2#1306975511yescharacteristic
305C2#1306978611yescharacteristic
306C2#1306979011yescharacteristic
subgroupG/H
centerC22#10622560
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1518C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1518D11
hypocenterC11#10363
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
24. C11×C4⋊Q8Q8semidirect
25. C11×C4⋊Q8Q8semidirect
175. C4⋊Q8Dic22semidirect
176. C4⋊Q8Dic22semidirect
249. C11#10363semidirect

Maximal subgroups

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

subgroupindex
#130769922
#130695942
#130671802
#130664752
#130664742
#130664482
C11×#15182
#1036311