Finite Group Databasebeta

← #14650538

Subgroups — #14650538

Order 2816.

436 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 113 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#13078417C211yesmaximal, characteristic
2#13077696C211yesmaximal, characteristic
3#13068632C211yesmaximal, characteristic
4#13067180C211yesmaximal, characteristic
5#13066513C211yesmaximal, characteristic
6#13066475C211yesmaximal, characteristic
7C11×#1481C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×#66880—21no—
13#10622707C412yescomplemented
14#10622704C412yescomplemented
15#10622676—22no—
16#10622617—21no—
17#10622608—21no—
18#10622549C2211yescharacteristic
19#10622538C2211yescharacteristic
20#10622537C2211yescharacteristic
21#10622443—22no—
22#10622331—22no—
23C8×Dic22—22no—
24C11×Q8⋊C8—22no—
25#10622189—21no—
26#10622176—22no—
27C22×Dic22D411yescharacteristic
28C22×C8×C11—21no—
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×#125—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C11×#117—21no—
37C2×C42×C11C2311yescharacteristic
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11D411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11—21no—
42C2×#4318—21no—
43C4×Dic22—21no—
44C4×Dic22—21no—
45C4×Dic22C2×C412yes—
46C4×Dic22D412yes—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C22⋊C8—21no—
51C4×C8×C11D412yes—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C22⋊(C11⋊C8)D412yes—
55#66880—42no—
56Dic11⋊C8—24no—
57C8×Dic11—24no—
58#66874—22no—
59#66874—22no—
60#66872—22no—
61#66871—22no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)C2×C412yes—
65C4×C11⋊C8—21no—
66#9304—111nomaximal, Sylow
67C2×Q8×C11—21no—
68C2×Q8×C11—21no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—41no—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×Dic22C22⋊C412yes—
79C2×Dic22SD1612yes—
80C2×Dic22Q1612yes—
81C2×C8×C11—22no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C22⋊C4—41no—
92C42×C11—41no—
93C42×C11C22×C411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11#4111yescharacteristic
97C4⋊Dic11—21no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11C22⋊C412yes—
101Dic11⋊C4—22no—
102Dic11⋊C4—22no—
103C4×Dic11—22no—
104C4×Dic11—22no—
105#4318—41no—
106#4318—41no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—22no—
109#3078—111no—
110#2982—111no—
111#1805—111no—
112#1518—111no—
113#1481D1111yescharacteristic
114#1301—111no—
115#1286—111no—
116C23×C11#12111yescharacteristic
117Q8×C11—42no—
118Q8×C11—81no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11C2×C22⋊C411yescharacteristic
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11C4×D411yescharacteristic
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12311yescharacteristic
129C2×C4×C11C2×SD1611yescharacteristic
130C2×C4×C11C2×Q1611yescharacteristic
131C2×C4×C11#13511yescharacteristic
132C2×C4×C11#13511yescharacteristic
133C2×Dic11—22no—
134C2×Dic11—22no—
135C2×Dic11—22no—
136C2×Dic11—22no—
137C2×Dic11—81no—
138C2×Dic11—81no—
139C2×Dic11—81no—
140C2×Dic11—81no—
141Dic22—22no—
142Dic22—22no—
143Dic22—22no—
144Dic22#10314yes—
145C8×C11—42no—
146C8×C11—81no—
147C11⋊C8—42no—
148C11⋊C8—42no—
149#533C2×D1111yescharacteristic
150C2×C4×Q8—111no—
151#479—222no—
152#477—112no—
153#475—112no—
154C8×Q8—222no—
155C8×Q8—222no—
156#431—111no—
157#431—222no—
158#431C2×D1111yescharacteristic
159#428—221no—
160#423—111no—
161C2×C4⋊C8C2×D1111yescharacteristic
162#419—221no—
163C2×#103—221no—
164#382—111no—
165#340—221no—
166#328—222no—
167Q8⋊C8—22no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11#38611yescharacteristic
171C22×C11#46511yescharacteristic
172C22×C11#46711yescharacteristic
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—81no—
178C4×C11—81no—
179C4×C11C2×#10311yescharacteristic
180C4×C11#41611yescharacteristic
181C4×C11#46511yescharacteristic
182C4×C11#46711yescharacteristic
183Dic11—24no—
184Dic11—42no—
185Dic11—161no—
186C22×Q8—111no—
187C2×M16—221no—
188C22×C8—21no—
189C4⋊Q8C4×D1111yescharacteristic
190C4⋊Q8C4×D1111yescharacteristic
191#125—21no—
192C22⋊Q8—21no—
193C22⋊Q8—21no—
194C4×Q8—21no—
195C4×Q8—21no—
196C4×Q8—112no—
197C4×Q8—112no—
198C4×Q8—221no—
199C4×Q8—221no—
200#117—21no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C42—221no—
205C2×C42C22×D1111yescharacteristic
206#107—222no—
207#106—222no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—112no—
212C4⋊C8—224no—
213C4⋊C8—221no—
214C4⋊C8—221no—
215#103—222no—
216#103—222no—
217#103—442no—
218C22⋊C8—21no—
219C22⋊C8—112no—
220C4×C8—224no—
221C4×C8—221no—
222C4×C8C22⋊D1112yes—
223#95—221no—
224#95—221no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11#188111yescharacteristic
228C2×C11#189211yescharacteristic
229C2×C11#190511yescharacteristic
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—112no—
233C2×Q8—112no—
234C2×Q8—112no—
235C2×Q8—221no—
236C2×Q8—221no—
237C2×Q8—221no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4—441no—
241C22×C4#433911yescharacteristic
242C22×C4D4×D1111yescharacteristic
243C22×C4D4×D1111yescharacteristic
244M16—441no—
245M16—441no—
246C2×C8—22no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—222no—
251C2×C8—222no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—112no—
259C4⋊C4—222no—
260C4⋊C4—222no—
261C4⋊C4—221no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C22⋊C4—41no—
265C42—41no—
266C42—222no—
267C42—222no—
268C42C2×C4×D1111yescharacteristic
269C42D4×D1111yescharacteristic
270C42#434111yescharacteristic
271C42C2×C22⋊D1111yescharacteristic
272C11#930411yescharacteristic, complemented, Sylow
273C23#6693711yescharacteristic
274Q8—42no—
275Q8—81no—
276Q8—114no—
277Q8—222no—
278Q8—222no—
279Q8—222no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—222no—
285C2×C4—222no—
286C2×C4—222no—
287C2×C4—222no—
288C2×C4—881no—
289C2×C4—881no—
290C2×C4—881no—
291C2×C4—881no—
292C2×C4C22⋊C4×D1111yescharacteristic
293C2×C4(C22⋊D11)⋊C411yescharacteristic
294C2×C4#6693611yescharacteristic
295C2×C4SD16×D1111yescharacteristic
296C2×C4#6696911yescharacteristic
297C2×C4Q16×D1111yescharacteristic
298C2×C4#6697211yescharacteristic
299C2×C4C4×C22⋊D1111yescharacteristic
300C2×C4#6699011yescharacteristic
301C2×C4#6699111yescharacteristic
302C8—42no—
303C8—81no—
304C8—442no—
305C8—442no—
306C22—21no—
307C22—21no—
308C22#1062242011yescharacteristic
309C22#1062242611yescharacteristic
310C22#1062256911yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—81no—
316C4—81no—
317C4—224no—
318C4—442no—
319C4—1761no—
320C4D11×#10311yescharacteristic
321C4#1062241711yescharacteristic
322C4#1062278411yescharacteristic
323C4#1062280111yescharacteristic
324C2—21no—
325C2—21no—
326C2#1306898111yescharacteristic
327C2#1306903611yescharacteristic
328C2#1306910711yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1481C2
socleC22×C11#386
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1481D11
hypocenterC11#9304
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
13. #10622707C4semidirect
14. #10622704C4semidirect
272. C11#9304semidirect

Maximal subgroups

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

subgroupindex
#130784172
#130776962
#130686322
#130671802
#130665132
#130664752
C11×#14812
#930411