Finite Group Databasebeta

← #14656874

Subgroups — #14656874

Order 2816.

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

normal subgroups only

This group has 400 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#13076978C211yesmaximal, characteristic
2#13069594C211yesmaximal, characteristic
3#13067180C211yesmaximal, characteristic
4#13066475C211yesmaximal, characteristic
5#13066474C211yesmaximal, characteristic
6#13066448C211yesmaximal, characteristic
7C11×#1518C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×#66943—21no—
10C11×#431C2211yescharacteristic
11C11×#382C2211yescharacteristic
12#10622589—21no—
13#10622549C2211yescharacteristic
14C42×Dic11C2211yescharacteristic
15#10622538C2211yescharacteristic
16#10622537C2211yescharacteristic
17#10622260—22no—
18#10622260—22no—
19C11×#328—22no—
20#10622176—22no—
21#10622170—21no—
22#10622170—21no—
23C11×C4⋊Q8Q811yescharacteristic
24C11×C4⋊Q8Q811yescharacteristic
25C11×#125—21no—
26C11×C22⋊Q8—21no—
27C11×C22⋊Q8—21no—
28C4×Q8×C11—21no—
29C4×Q8×C11—21no—
30C11×#117—21no—
31C2×C11×C4⋊C4—21no—
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—22no—
34C2×C4⋊Dic11—21no—
35C2×Dic11⋊C4—22no—
36C2×Dic11⋊C4—22no—
37C2×Dic11⋊C4—22no—
38C2×C4×Dic11—21no—
39C2×C4×Dic11—21no—
40C2×C4×Dic11D411yescharacteristic
41C2×C4×Dic11D411yescharacteristic
42C2×#4318—21no—
43#66943—42no—
44#66943—42no—
45C11×C4⋊C8—21no—
46C11×C22⋊C8—21no—
47C4×C8×C11—21no—
48C11×#95—21no—
49C11×#95D412yes—
50C11⋊#95—21no—
51C11⋊#95D412yes—
52C22⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4×C11⋊C8—21no—
57#10365—111nomaximal, Sylow
58C2×Q8×C11—21no—
59C2×Q8×C11—21no—
60C22×C4×C11—22no—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—21no—
65C22×Dic11—21no—
66C22×Dic11—22no—
67C2×C8×C11—41no—
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C22⋊C4—41no—
77C42×C11—41no—
78C42×C11C2×Q811yescharacteristic
79C42×C11#4111yescharacteristic
80C42×C11#4111yescharacteristic
81C42×C11#4111yescharacteristic
82C4⋊Dic11—44no—
83C4⋊Dic11—41no—
84C4⋊Dic11—41no—
85Dic11⋊C4—44no—
86Dic11⋊C4—44no—
87Dic11⋊C4—44no—
88C4×Dic11—21no—
89C4×Dic11—21no—
90C4×Dic11—42no—
91C4×Dic11—42no—
92C4×Dic11SD1612yes—
93C4×Dic11Q1612yes—
94#4318—41no—
95#4318—41no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8—41no—
98#2859—111no—
99#1994—111no—
100#1518—111no—
101#1518D1111yescharacteristic
102#1286—111no—
103#1286—111no—
104#1276—111no—
105C23×C11#12011yescharacteristic
106Q8×C11—81no—
107Q8×C11—81no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—42no—
115C2×C4×C11C22⋊Q811yescharacteristic
116C2×C4×C11C22⋊Q811yescharacteristic
117C2×C4×C11C22⋊Q811yescharacteristic
118C2×C4×C11#12411yescharacteristic
119C2×C4×C11#12411yescharacteristic
120C2×C4×C11#12411yescharacteristic
121C2×C4×C11C2×SD1611yescharacteristic
122C2×C4×C11C2×Q1611yescharacteristic
123C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C11#13711yescharacteristic
125C2×Dic11—22no—
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—22no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C8×C11—81no—
135C11⋊C8—81no—
136C11⋊C8—81no—
137#533C2×D1111yescharacteristic
138C2×#125—221no—
139#431—111no—
140#431C2×D1111yescharacteristic
141#423—111no—
142#389—222no—
143#389—222no—
144#384—221no—
145#382—111no—
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—
171C2×M16—221no—
172C4⋊Q8Dic2211yescharacteristic
173C4⋊Q8Dic2211yescharacteristic
174#125—21no—
175#125—442no—
176#125—442no—
177C22⋊Q8—21no—
178C22⋊Q8—21no—
179C4×Q8—21no—
180C4×Q8—21no—
181#117—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—222no—
184C2×C4⋊C4—222no—
185C2×C4⋊C4—222no—
186C2×C4⋊C4—222no—
187C2×C4⋊C4—221no—
188C2×C42—111no—
189C2×C42—111no—
190C2×C42—221no—
191C2×C42—221no—
192C2×C42C22×D1111yescharacteristic
193C4⋊C8—21no—
194C4⋊C8—221no—
195C4⋊C8—221no—
196C4⋊C8—221no—
197C22⋊C8—21no—
198C22⋊C8—221no—
199C4×C8—21no—
200C4×C8—221no—
201#95—21no—
202#95—112no—
203#95—221no—
204#95C22⋊D1112yes—
205C2×C11—21no—
206C2×C11—21no—
207C2×C11#202411yescharacteristic
208C2×C11#203111yescharacteristic
209C2×C11#203111yescharacteristic
210C2×Q8—21no—
211C2×Q8—21no—
212C22×C4—22no—
213C22×C4—221no—
214C22×C4—221no—
215C22×C4—222no—
216C22×C4D4×D1111yescharacteristic
217C22×C4D4×D1111yescharacteristic
218C22×C4C2×C22⋊D1111yescharacteristic
219M16—441no—
220M16—441no—
221C2×C8—41no—
222C2×C8—441no—
223C2×C8—441no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—444no—
233C4⋊C4—444no—
234C4⋊C4—444no—
235C4⋊C4—444no—
236C4⋊C4—441no—
237C4⋊C4—441no—
238C22⋊C4—41no—
239C42—41no—
240C42—112no—
241C42—112no—
242C42—221no—
243C42—221no—
244C42—442no—
245C42—442no—
246C42C2×Dic2211yescharacteristic
247C42#433911yescharacteristic
248C42#434111yescharacteristic
249C42#434111yescharacteristic
250C11#1036511yescharacteristic, complemented, Sylow
251C23#6699011yescharacteristic
252Q8—81no—
253Q8—81no—
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#10365
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
250. C11#10365semidirect

Maximal subgroups

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

subgroupindex
#130769782
#130695942
#130671802
#130664752
#130664742
#130664482
C11×#15182
#1036511