Finite Group Databasebeta

← #14650397

Subgroups — #14650397

Order 2816.

396 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 103 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#13077711C211yesmaximal, characteristic, complemented
2#13067231C211yesmaximal, characteristic, complemented
3#13067227C211yesmaximal, characteristic
4#13067085C211yesmaximal, characteristic
5#13066478C211yesmaximal, characteristic, complemented
6#13066446C211yesmaximal, characteristic, complemented
7C11×#3228C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#532C2211yescharacteristic
10C11×#500C411yescharacteristic
11C11×#498C411yescharacteristic
12C11×#486C411yescharacteristic
13C11×#486C411yescharacteristic
14C11×#482—22no—
15C11×#478—22no—
16C11×#431C2211yescharacteristic
17#10622637—22no—
18#10622637—21no—
19Q8×C11⋊C8—21no—
20#10622613—22no—
21#10622539C2211yescharacteristic
22#10622539C2211yescharacteristic
23#10622538C2211yescharacteristic
24C2×#66867C2211yescharacteristic
25#10622181—22no—
26#10622178—22no—
27D4⋊(C11⋊C8)—21no—
28D4⋊(C11⋊C8)—21no—
29C2×C11×#41—21no—
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#127C2×C411yescharacteristic
34C11×#125D412yes—
35C11×#124—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C11×#121—21no—
39C11×#121—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C11×#117D412yes—
45C2×C42×C11C2311yescharacteristic
46C22×C11⋊C8—21no—
47C11×#107—22no—
48C11×#106—22no—
49C11×C4⋊C8—21no—
50C11×#102—22no—
51C11×#102—22no—
52C11×C22⋊C8—21no—
53C4×C8×C11C2×C411yescharacteristic
54C4×C8×C11C2×C411yescharacteristic
55C22⋊(C11⋊C8)—21no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—22no—
59C4⋊(C11⋊C8)—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63#66867—22no—
64#66867—21no—
65#66867—21no—
66#66867—21no—
67#66867D412yes—
68C4×C11⋊C8—22no—
69C4×C11⋊C8D411yescharacteristic
70C4×C11⋊C8D411yescharacteristic
71#9284—111nomaximal, Sylow
72C11×#41—82no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4C22⋊C412yes—
93C11×C4⋊C4C22⋊C412yes—
94C11×C22⋊C4—22no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C42×C11—22no—
98C42×C11C22×C411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C2×C11⋊C8—22no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#3228D1111yescharacteristic
110#2985—111no—
111#1531—111no—
112#1530—111no—
113#1496—111no—
114#1287—111no—
115#1275—111no—
116C23×C11—41no—
117C23×C11#12311yescharacteristic
118Q8×C11—41no—
119Q8×C11—41no—
120Q8×C11—81no—
121Q8×C11—81no—
122D4×C11—42no—
123D4×C11—41no—
124D4×C11—41no—
125D4×C11—81no—
126D4×C11—82no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—82no—
135C2×C4×C11C2×C22⋊C411yescharacteristic
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C8×C11—41no—
142C8×C11—41no—
143C11⋊C8—41no—
144C11⋊C8—42no—
145C11⋊C8—41no—
146C11⋊C8—42no—
147C11⋊C8—81no—
148#533C2×D1111yescharacteristic
149#532C2×D1111yescharacteristic
150#500Dic1111yescharacteristic
151#498Dic1111yescharacteristic
152#486Dic1111yescharacteristic
153#486Dic1111yescharacteristic
154#482—22no—
155#478—22no—
156#446—221no—
157#446—222no—
158C8×Q8—221no—
159#433—222no—
160#432—111no—
161#432—111no—
162#431—111no—
163#431C2×D1111yescharacteristic
164C2×#97—111no—
165#330—222no—
166#329—222no—
167D4⋊C8—221no—
168D4⋊C8—221no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—81no—
173C22×C11—81no—
174C22×C11—81no—
175C22×C11#38611yescharacteristic
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—42no—
182C4×C11—42no—
183C4×C11—81no—
184C4×C11#44311yescharacteristic
185C4×C11#44411yescharacteristic
186C2×#41—21no—
187C22×C8—221no—
188C4⋊Q8C2×Dic1111yescharacteristic
189C4⋊Q8C2×Dic1111yescharacteristic
190C4⋊Q8C2×Dic1111yescharacteristic
191#127C2×Dic1111yescharacteristic
192#125C22⋊D1112yes—
193#124—21no—
194C22⋊Q8—21no—
195C22⋊Q8—21no—
196#121—21no—
197#121—21no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×D4—21no—
201C4×D4—21no—
202#117C22⋊D1112yes—
203C2×C42C22×D1111yescharacteristic
204#107—22no—
205#106—22no—
206C4⋊C8—21no—
207C4⋊C8—222no—
208C4⋊C8—222no—
209C4⋊C8—221no—
210C4⋊C8—221no—
211C4⋊C8—221no—
212#102—22no—
213#102—22no—
214C22⋊C8—21no—
215C22⋊C8—221no—
216C22⋊C8—221no—
217C22⋊C8—221no—
218#97—112no—
219#97—222no—
220#97—221no—
221#97—221no—
222#97—221no—
223C4×C8—111no—
224C4×C8—111no—
225C4×C8—222no—
226C4×C8C2×Dic1111yescharacteristic
227C4×C8C2×Dic1111yescharacteristic
228C2×C11—41no—
229C2×C11—161no—
230C2×C11#187611yescharacteristic
231C2×C11#190311yescharacteristic
232C2×C11#191211yescharacteristic
233#41—82no—
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8—21no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—41no—
241C22×C4—41no—
242C22×C4#434111yescharacteristic
243C22×C4#434111yescharacteristic
244C22×C4C2×C22⋊D1111yescharacteristic
245C2×C8—21no—
246C2×C8—21no—
247C2×C8—222no—
248C2×C8—221no—
249C2×C8—221no—
250C2×C8—222no—
251C2×C8—441no—
252C2×C8—441no—
253C2×C8—441no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4C22⋊Dic1112yes—
261C4⋊C4C22⋊Dic1112yes—
262C22⋊C4—22no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C42—22no—
266C42D4×D1111yescharacteristic
267C42D4×D1111yescharacteristic
268C42C22×Dic1111yescharacteristic
269C42C2×C22⋊D1111yescharacteristic
270C11#928411yescharacteristic, complemented, Sylow
271C23—41no—
272C23#6698811yescharacteristic
273Q8—41no—
274Q8—41no—
275Q8—81no—
276Q8—81no—
277D4—42no—
278D4—41no—
279D4—41no—
280D4—81no—
281D4—82no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—82no—
290C2×C4D4×Dic1111yescharacteristic
291C2×C4D4×Dic1111yescharacteristic
292C2×C4#6699011yescharacteristic
293C2×C4#6699211yescharacteristic
294C2×C4#6699211yescharacteristic
295C2×C4C2×C22⋊Dic1111yescharacteristic
296C8—41no—
297C8—41no—
298C8—442no—
299C8—441no—
300C8—441no—
301C8—442no—
302C8—881no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22#1062283311yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4—42no—
317C4—81no—
318C4#1062280911yescharacteristic
319C4#1062281011yescharacteristic
320C2—41no—
321C2—161no—
322C2#1306894511yescharacteristic
323C2#1306909811yescharacteristic
324C2#1306915411yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3228C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#3228D11
hypocenterC11#9284
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3228

Complements

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

NH ≅ G/Ntype
1. #13077711C2semidirect
2. #13067231C2semidirect
5. #13066478C2semidirect
6. #13066446C2semidirect
270. C11#9284semidirect

Maximal subgroups

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

subgroupindex
#130777112
#130672312
#130672272
#130670852
#130664782
#130664462
C11×#32282
#928411