Finite Group Databasebeta

← #14651015

Subgroups — #14651015

Order 2816.

420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 89 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#13079623C211yesmaximal, characteristic
2#13077694C211yesmaximal, characteristic
3#13067312C211yesmaximal, characteristic
4#13067019C211yesmaximal, characteristic, complemented
5#13066485C211yesmaximal, characteristic, complemented
6#13066479C211yesmaximal, characteristic, complemented
7C11×#1537C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9#10623008C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12#10622702C412yes—
13#10622699C412yes—
14#10622660—22no—
15#10622644—21no—
16#10622640—21no—
17#10622539C2211yescharacteristic
18#10622538C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20#10622451—21no—
21#10622447—21no—
22#10622340—22no—
23#10622319—22no—
24C11×#330—22no—
25Q8⋊(C11⋊C8)—21no—
26Q8⋊(C11⋊C8)—21no—
27#10622123—21no—
28#10622119—21no—
29C2×#4339D412yes—
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×#125—21no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C11×#117—21no—
38C2×C42×C11C2311yescharacteristic
39C2×#4326—22no—
40C2×#4325—22no—
41#66983—21no—
42#66983—21no—
43C22×C11⋊C8—21no—
44C2×#4313—22no—
45C2×C8×D11—22no—
46#66928C2×C412yes—
47#66927D411yescharacteristic
48C4×D44—21no—
49C4×D44—21no—
50#66922D411yescharacteristic
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×#97—21no—
56C11×#97D412yes—
57C22⋊(C11⋊C8)—21no—
58C22⋊(C11⋊C8)—21no—
59(C2×D11)⋊C8—22no—
60(C2×D11)⋊C8—22no—
61#66874—22no—
62#66873—22no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67#66867C2×C412yes—
68C4×C11⋊C8D411yescharacteristic
69C4×C11⋊C8D411yescharacteristic
70#9373—111nomaximal, Sylow
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C2×C22⋊D11—22no—
77#4339—82no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44C22⋊C412yes—
81C2×C4×D11—22no—
82C2×Dic22C22⋊C412yes—
83C2×C8×C11—22no—
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×C11C2×D411yescharacteristic
97#4326—82no—
98#4325—82no—
99(C2×D11)⋊C4—22no—
100(C2×D11)⋊C4—22no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—81no—
108#4313—82no—
109C8×D11—82no—
110#3216—111no—
111#2981—111no—
112#1551—111no—
113#1537D1111yescharacteristic, complemented
114#1481—111no—
115#1290—111no—
116#1287—111no—
117C23×C11#12311yescharacteristic
118C22×D11—22no—
119Q8×C11—41no—
120Q8×C11—41no—
121Q8×C11—42no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11C2×C22⋊C411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C22⋊D11—82no—
135C2×Dic11—22no—
136D44—42no—
137D44—41no—
138D44—41no—
139D44—81no—
140C4×D11—42no—
141C4×D11—42no—
142Dic22—42no—
143C8×C11—42no—
144C8×C11—81no—
145C11⋊C8—41no—
146C11⋊C8—41no—
147C11⋊C8—42no—
148C11⋊C8—81no—
149#533C2×D1111yescharacteristic
150#532—111no—
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#432C2×D1111yescharacteristic
161#432C2×D1111yescharacteristic
162#431—111no—
163C2×C4⋊C8—111no—
164#408—222no—
165#333—221no—
166#331—221no—
167#330—22no—
168Q8⋊C8—221no—
169Q8⋊C8—221no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11#38611yescharacteristic
174C2×D11—42no—
175C2×D11—42no—
176C2×D11—42no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—81no—
183C4×C11—81no—
184C4×C11#47111yescharacteristic
185C4×C11#47311yescharacteristic
186Dic11—42no—
187C2×#41—112no—
188C2×Q16—222no—
189C2×SD16—222no—
190C2×M16—222no—
191C22×C8—222no—
192C22×C8—221no—
193C4⋊Q8—111no—
194C4⋊Q8C4×D1111yescharacteristic
195C4⋊Q8C4×D1111yescharacteristic
196#127—111no—
197#125—21no—
198#124—112no—
199C22⋊Q8—21no—
200C22⋊Q8—21no—
201#121—221no—
202#121—221no—
203C4×Q8—21no—
204C4×Q8—21no—
205C4×D4—221no—
206C4×D4—221no—
207#117—21no—
208C2×C42C22×D1111yescharacteristic
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—221no—
212C4⋊C8—221no—
213C4⋊C8—221no—
214C4⋊C8—221no—
215#103—222no—
216#102—222no—
217C22⋊C8—21no—
218C22⋊C8—21no—
219C22⋊C8—222no—
220C22⋊C8—222no—
221C22⋊C8—221no—
222C22⋊C8—221no—
223#97—21no—
224#97—112no—
225#97C22⋊D1112yes—
226C4×C8—111no—
227C4×C8—111no—
228C2×C11—41no—
229C2×C11#188111yescharacteristic
230C2×C11#190811yescharacteristic
231C2×C11#191111yescharacteristic
232D11—82no—
233#41—882no—
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8—112no—
237C2×D4—112no—
238C2×D4—222no—
239C2×D4—221no—
240C2×D4—221no—
241C22×C4—222no—
242C22×C4#433911yescharacteristic
243C22×C4D4×D1111yescharacteristic
244C22×C4#434111yescharacteristic
245Q16—882no—
246SD16—882no—
247M16—882no—
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—222no—
251C2×C8—221no—
252C2×C8—221no—
253C2×C8—441no—
254C2×C8—882no—
255C2×C8—881no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C22⋊C4—41no—
265C22⋊C4—222no—
266C22⋊C4—222no—
267C42—41no—
268C42C2×C4×D1111yescharacteristic
269C42D4×D1111yescharacteristic
270C42D4×D1111yescharacteristic
271C42C2×C22⋊D1111yescharacteristic
272C11#937311yescharacteristic, complemented, Sylow
273C23—222no—
274C23#6693611yescharacteristic
275Q8—41no—
276Q8—41no—
277Q8—42no—
278Q8—442no—
279D4—442no—
280D4—441no—
281D4—441no—
282D4—881no—
283D4—882no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—222no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4C22⋊C4×D1111yescharacteristic
294C2×C4(C22⋊D11)⋊C411yescharacteristic
295C2×C4#6693711yescharacteristic
296C2×C4C4×C22⋊D1111yescharacteristic
297C2×C4#6699011yescharacteristic
298C2×C4#6699111yescharacteristic
299C8—42no—
300C8—81no—
301C8—441no—
302C8—441no—
303C8—442no—
304C8—881no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—442no—
309C22—442no—
310C22—442no—
311C22#1062256911yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—81no—
318C4—81no—
319C4—442no—
320C4#1062236711yescharacteristic
321C4#1062236811yescharacteristic
322C2—41no—
323C2—882no—
324C2#1306897511yescharacteristic
325C2#1306912811yescharacteristic
326C2#1306914511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1537C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1537D11
hypocenterC11#9373
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1537

Complements

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

NH ≅ G/Ntype
4. #13067019C2semidirect
5. #13066485C2semidirect
6. #13066479C2semidirect
7. C11×#1537C2semidirect
113. #1537D11semidirect
272. C11#9373semidirect

Maximal subgroups

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

subgroupindex
#130796232
#130776942
#130673122
#130670192
#130664852
#130664792
C11×#15372
#937311