Finite Group Databasebeta

← #14651016

Subgroups — #14651016

Order 2816.

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

normal subgroups only

This group has 420 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#13079627C211yesmaximal, characteristic
2#13077692C211yesmaximal, characteristic
3#13067253C211yesmaximal, characteristic, complemented
4#13067018C211yesmaximal, characteristic, complemented
5#13066486C211yesmaximal, characteristic, complemented
6#13066479C211yesmaximal, characteristic, complemented
7C11×#1551C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12#10622852—22no—
13#10622847—22no—
14#10622703—21no—
15#10622688—21no—
16#10622673C412yes—
17#10622668C412yes—
18#10622625—21no—
19#10622624—22no—
20D4×C11⋊C8—21no—
21#10622539C2211yescharacteristic
22#10622539C2211yescharacteristic
23#10622538C2211yescharacteristic
24C11×#333—21no—
25C11×#331—21no—
26#10622122—21no—
27#10622122—21no—
28#10622103—22no—
29C2×C11×#41D412yes—
30C22×C8×C11—21no—
31C11×C4⋊Q8D411yescharacteristic
32C11×#127D411yescharacteristic
33C11×#124C2×C412yes—
34C11×#121—21no—
35C11×#121—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C2×C42×C11C2311yescharacteristic
39C2×#4326—22no—
40C2×#4324—22no—
41#66979—21no—
42#66977—21no—
43#66977—21no—
44C2×#4318—22no—
45C22×C11⋊C8—22no—
46#66923—21no—
47#66922C2×C411yescharacteristic
48#66922C2×C411yescharacteristic
49C4×Dic22—21no—
50C4×Dic22—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×#97—21no—
56#66899—22no—
57#66896—22no—
58C22⋊(C11⋊C8)—22no—
59C22⋊(C11⋊C8)—22no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62C22⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#66867C2×C412yes—
67#66867D412yes—
68C4×C11⋊C8D411yescharacteristic
69C4×C11⋊C8D411yescharacteristic
70#9373—111nomaximal, Sylow
71C11×#41—82no—
72C2×Q8×C11C22⋊C412yes—
73C2×D4×C11—22no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11C22⋊C412yes—
77C22×C4×C11—22no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C2×Dic22—21no—
82C2×Dic22—21no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11—81no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C22⋊C4—22no—
89C11×C22⋊C4—22no—
90C42×C11C22×C411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C22⋊Dic11—41no—
95#4326—82no—
96#4324—82no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101Dic11⋊C4—41no—
102Dic11⋊C4—41no—
103C4×Dic11—41no—
104#4318—82no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—82no—
110#3216—111no—
111#2981—111no—
112#1551D1111yescharacteristic
113#1537—111no—
114#1481—111no—
115#1290—111no—
116#1287—111no—
117C23×C11—22no—
118C23×C11#12311yescharacteristic
119Q8×C11—42no—
120D4×C11—42no—
121D4×C11—41no—
122D4×C11—41no—
123D4×C11—81no—
124D4×C11—82no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—22no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11C2×C22⋊C411yescharacteristic
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11C4×D411yescharacteristic
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×Dic11—41no—
139C2×Dic11—41no—
140Dic22—41no—
141Dic22—41no—
142Dic22—42no—
143C8×C11—81no—
144C8×C11—81no—
145C11⋊C8—41no—
146C11⋊C8—42no—
147C11⋊C8—41no—
148C11⋊C8—42no—
149#533—111no—
150#532C2×D1111yescharacteristic
151#497—112no—
152#489—112no—
153#462—221no—
154#460—221no—
155#452—222no—
156#436—221no—
157#435—222no—
158C8×D4—221no—
159#432—111no—
160#432—111no—
161#432C2×D1111yescharacteristic
162#431—111no—
163C2×C4⋊C8C2×D1111yescharacteristic
164#408—222no—
165#333—21no—
166#331—21no—
167#330—222no—
168Q8⋊C8—221no—
169Q8⋊C8—221no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—42no—
174C22×C11—42no—
175C22×C11—42no—
176C22×C11#38611yescharacteristic
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—42no—
183C4×C11#47111yescharacteristic
184C4×C11#47311yescharacteristic
185Dic11—81no—
186Dic11—81no—
187C2×#41D4412yes—
188C2×Q16—222no—
189C2×SD16—222no—
190C2×M16—222no—
191C22×C8—21no—
192C22×C8—222no—
193C4⋊Q8—111no—
194C4⋊Q8—111no—
195C4⋊Q8C22⋊D1111yescharacteristic
196#127C22⋊D1111yescharacteristic
197#125—221no—
198#124C4×D1112yes—
199C22⋊Q8—221no—
200C22⋊Q8—221no—
201#121—21no—
202#121—21no—
203C4×Q8—221no—
204C4×Q8—221no—
205C4×D4—21no—
206C4×D4—21no—
207#117—221no—
208C2×C42C22×D1111yescharacteristic
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—221no—
213C4⋊C8—221no—
214C4⋊C8—221no—
215#103—222no—
216#102—222no—
217C22⋊C8—21no—
218C22⋊C8—222no—
219C22⋊C8—222no—
220C22⋊C8—221no—
221C22⋊C8—221no—
222C22⋊C8—221no—
223#97—21no—
224#97—112no—
225#97—112no—
226C4×C8—111no—
227C4×C8—111no—
228C2×C11—41no—
229C2×C11—82no—
230C2×C11#188111yescharacteristic
231C2×C11#190811yescharacteristic
232C2×C11#191111yescharacteristic
233#41—82no—
234C2×Q8—221no—
235C2×Q8—221no—
236C2×Q8(C2×D11)⋊C412yes—
237C2×D4—22no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4(C2×D11)⋊C412yes—
241C22×C4—22no—
242C22×C4C2×D4411yescharacteristic
243C22×C4#434111yescharacteristic
244C22×C4#434111yescharacteristic
245Q16—882no—
246SD16—882no—
247M16—882no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—81no—
251C2×C8—221no—
252C2×C8—221no—
253C2×C8—222no—
254C2×C8—222no—
255C2×C8—882no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—441no—
267C42—441no—
268C42C2×C4×D1111yescharacteristic
269C42D4×D1111yescharacteristic
270C42D4×D1111yescharacteristic
271C42C2×C22⋊D1111yescharacteristic
272C11#937311yescharacteristic, complemented, Sylow
273C23—22no—
274C23#6693911yescharacteristic
275Q8—42no—
276Q8—441no—
277Q8—441no—
278Q8—442no—
279D4—42no—
280D4—41no—
281D4—41no—
282D4—81no—
283D4—82no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4(C22⋊D11)⋊C411yescharacteristic
294C2×C4(C22⋊D11)⋊C411yescharacteristic
295C2×C4#6693511yescharacteristic
296C2×C4C2×(C2×D11)⋊C411yescharacteristic
297C2×C4#6699211yescharacteristic
298C2×C4#6699211yescharacteristic
299C8—81no—
300C8—81no—
301C8—441no—
302C8—442no—
303C8—441no—
304C8—442no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—42no—
309C22—42no—
310C22—42no—
311C22#1062257111yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—42no—
318C4—881no—
319C4—881no—
320C4#1062281311yescharacteristic
321C4#1062281711yescharacteristic
322C2—41no—
323C2—82no—
324C2#1306897611yescharacteristic
325C2#1306912911yescharacteristic
326C2#1306914611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1551C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1551D11
hypocenterC11#9373
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1551

Complements

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

NH ≅ G/Ntype
3. #13067253C2semidirect
4. #13067018C2semidirect
5. #13066486C2semidirect
6. #13066479C2semidirect
272. C11#9373semidirect

Maximal subgroups

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

subgroupindex
#130796272
#130776922
#130672532
#130670182
#130664862
#130664792
C11×#15512
#937311