Finite Group Databasebeta

← #14650435

Subgroups — #14650435

Order 2816.

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

normal subgroups only

This group has 422 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#13079561C211yesmaximal, characteristic
2#13077557C211yesmaximal, characteristic
3#13069588C211yesmaximal, characteristic
4#13067300C211yesmaximal, characteristic
5#13066474C211yesmaximal, characteristic
6#13066446C211yesmaximal, characteristic
7C11×#1518C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#382C2211yescharacteristic
12#10622706C412yescomplemented
13#10622705C412yescomplemented
14#10622663—22no—
15#10622644—22no—
16#10622637—22no—
17#10622637—22no—
18#10622612—21no—
19#10622610—21no—
20#10622538C2211yescharacteristic
21#10622537C2211yescharacteristic
22C2×#66867C2211yescharacteristic
23C11×#328—22no—
24#10622167—21no—
25#10622167—21no—
26#10622120—22no—
27C22×Dic22—21no—
28C11×C4⋊Q8C2×C411yescharacteristic
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×#125—21no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8D412yes—
33C4×Q8×C11—21no—
34C4×Q8×C11D412yes—
35C11×#117—21no—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×#4326—24no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×#4318—21no—
42C22×C11⋊C8D411yescharacteristic
43C22×C11⋊C8D411yescharacteristic
44#66922—21no—
45#66922—21no—
46#66922—21no—
47#66922C2×C412yes—
48C11×C4⋊C8—21no—
49C11×C22⋊C8—21no—
50C4×C8×C11—21no—
51C11×#95—21no—
52C11×#95—21no—
53C22⋊(C11⋊C8)—21no—
54#66874—24no—
55C4⋊(C11⋊C8)—24no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)D412yes—
59#66867—22no—
60#66867—21no—
61#66867—21no—
62C4×C11⋊C8—22no—
63C4×C11⋊C8C2×C412yes—
64#9290—111nomaximal, Sylow
65C2×Q8×C11—21no—
66C2×Q8×C11C22⋊C412yes—
67C22×C4×C11—41no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×Dic11—41no—
72C2×Dic22—22no—
73C2×Dic22—41no—
74C2×Dic22—82no—
75C2×C8×C11—41no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4C22⋊C412yes—
84C11×C22⋊C4—22no—
85C42×C11—22no—
86C42×C11C22×C411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11#4111yescharacteristic
90#4326—84no—
91C4⋊Dic11—22no—
92C4⋊Dic11—22no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95#4318—41no—
96#4318—41no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8Q1612yescomplemented
105#3209—111no—
106#2961—111no—
107#1993—111no—
108#1549—111no—
109#1518D1111yescharacteristic
110#1286—111no—
111#1275—111no—
112C23×C11#12111yescharacteristic
113Q8×C11—42no—
114Q8×C11—81no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11—81no—
122C2×C4×C11C2×C22⋊C411yescharacteristic
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12311yescharacteristic
128C2×C4×C11C2×Q1611yescharacteristic
129C2×C4×C11#13511yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×Dic11—42no—
133C2×Dic11—82no—
134Dic22—44no—
135Dic22—82no—
136C8×C11—81no—
137C11⋊C8—22no—
138C11⋊C8—42no—
139C11⋊C8—41no—
140C11⋊C8—42no—
141#533C2×D1111yescharacteristic
142C2×C4⋊Q8—111no—
143#494—112no—
144#487—112no—
145#462—222no—
146#451—222no—
147#446—222no—
148#446—222no—
149#431—111no—
150#431C2×D1111yescharacteristic
151#424—221no—
152#423—111no—
153#405—221no—
154C2×#97—111no—
155#382C2×D1111yescharacteristic
156#340—221no—
157#340—221no—
158#332—222no—
159#328—22no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11#38611yescharacteristic
163C22×C11#46211yescharacteristic
164C22×C11#46411yescharacteristic
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—42no—
170C4×C11—42no—
171C4×C11—161no—
172C4×C11C4×Q1611yescharacteristic
173C4×C11#44111yescharacteristic
174C4×C11#45111yescharacteristic
175C4×C11#45211yescharacteristic
176Dic11—82no—
177C22×Q8—221no—
178C2×Q16—224no—
179C2×M16—221no—
180C22×C8—111no—
181C22×C8—111no—
182C4⋊Q8—112no—
183C4⋊Q8—221no—
184C4⋊Q8—221no—
185C4⋊Q8—221no—
186C4⋊Q8C4×D1111yescharacteristic
187C4⋊Q8C4×D1111yescharacteristic
188#125—21no—
189C22⋊Q8—21no—
190C22⋊Q8C22⋊D1112yes—
191C4×Q8—21no—
192C4×Q8D4412yes—
193#117—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C42C22×D1111yescharacteristic
198C4⋊C8—21no—
199C4⋊C8—112no—
200C4⋊C8—224no—
201C4⋊C8—221no—
202C4⋊C8—221no—
203#103—224no—
204C22⋊C8—21no—
205C22⋊C8—221no—
206#97—222no—
207#97—221no—
208#97—221no—
209C4×C8—21no—
210C4×C8—112no—
211C4×C8—222no—
212#95—21no—
213#95—21no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11#187811yescharacteristic
217C2×C11#190211yescharacteristic
218C2×C11#191011yescharacteristic
219C2×Q8—21no—
220C2×Q8—222no—
221C2×Q8—441no—
222C2×Q8—882no—
223C2×Q8(C2×D11)⋊C412yes—
224C22×C4—41no—
225C22×C4—441no—
226C22×C4D4×D1111yescharacteristic
227C22×C4#434111yescharacteristic
228C22×C4C2×C22⋊D1111yescharacteristic
229Q16—884no—
230M16—441no—
231M16—441no—
232C2×C8—41no—
233C2×C8—112no—
234C2×C8—221no—
235C2×C8—221no—
236C2×C8—222no—
237C2×C8—221no—
238C2×C8—221no—
239C2×C8—221no—
240C2×C8—222no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—222no—
249C4⋊C4—222no—
250C4⋊C4—441no—
251C4⋊C4—441no—
252C4⋊C4(C2×D11)⋊C412yes—
253C22⋊C4—22no—
254C42—22no—
255C42C2×C4×D1111yescharacteristic
256C42C2×D4411yescharacteristic
257C42D4×D1111yescharacteristic
258C42#434111yescharacteristic
259C11#929011yescharacteristic, complemented, Sylow
260C23#6699211yescharacteristic
261Q8—42no—
262Q8—81no—
263Q8—444no—
264Q8—882no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—442no—
273C2×C4—882no—
274C2×C4(C22⋊D11)⋊C411yescharacteristic
275C2×C4(C22⋊D11)⋊C411yescharacteristic
276C2×C4#6693511yescharacteristic
277C2×C4#6693911yescharacteristic
278C2×C4#6696811yescharacteristic
279C2×C4#6696911yescharacteristic
280C2×C4Q16×D1111yescharacteristic
281C2×C4#6697111yescharacteristic
282C2×C4C2×(C2×D11)⋊C411yescharacteristic
283C2×C4#6699211yescharacteristic
284C8—81no—
285C8—222no—
286C8—442no—
287C8—441no—
288C8—442no—
289C22—21no—
290C22—21no—
291C22#1062257111yescharacteristic
292C22#1062277911yescharacteristic
293C22#1062279511yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—42no—
299C4—42no—
300C4—161no—
301C4—882no—
302C4#1062240211yescharacteristic
303C4#1062240311yescharacteristic
304C4#1062242111yescharacteristic
305C4#1062242311yescharacteristic
306C2—21no—
307C2—21no—
308C2#1306895511yescharacteristic
309C2#1306908711yescharacteristic
310C2#1306914111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1518C2
socleC22×C11#386
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1518D11
hypocenterC11#9290
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
12. #10622706C4semidirect
13. #10622705C4semidirect
104. C2×C11⋊C8Q16semidirect
259. C11#9290semidirect

Maximal subgroups

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

subgroupindex
#130795612
#130775572
#130695882
#130673002
#130664742
#130664462
C11×#15182
#929011