Finite Group Databasebeta

← #14650379

Subgroups — #14650379

Order 2816.

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

normal subgroups only

This group has 416 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#13079568C211yesmaximal, characteristic
2#13077711C211yesmaximal, characteristic, complemented
3#13067123C211yesmaximal, characteristic
4#13067084C211yesmaximal, characteristic
5#13066477C211yesmaximal, characteristic, complemented
6#13066445C211yesmaximal, characteristic, complemented
7C11×#1506C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9#10623008C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#376C2211yescharacteristic
12#10622706C411yescharacteristic, complemented
13#10622705C411yescharacteristic, complemented
14#10622701C411yescharacteristic, complemented
15#10622698C411yescharacteristic, complemented
16#10622660—22no—
17#10622641—22no—
18#10622637—22no—
19#10622637—21no—
20Q8×C11⋊C8—21no—
21#10622613—22no—
22#10622539C2211yescharacteristic
23#10622538C2211yescharacteristic
24#10622538C2211yescharacteristic
25C11×#328—22no—
26#10622121—21no—
27#10622121—21no—
28#10622089—22no—
29C2×#4339—21no—
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×#125—21no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8D412yes—
35C4×Q8×C11—21no—
36C4×Q8×C11D412yes—
37C11×#117—21no—
38C2×C42×C11—21no—
39C2×C42×C11C2311yescharacteristic
40C2×#4326—22no—
41C2×#4325—22no—
42#66983—21no—
43#66983—21no—
44#66928—21no—
45#66927C2×C411yescharacteristic
46C4×D44—21no—
47C4×D44—21no—
48#66922C2×C411yescharacteristic
49C11×C4⋊C8—21no—
50C11×C22⋊C8—21no—
51C11×#97—21no—
52C11×#95—21no—
53C11×#95—21no—
54C22⋊(C11⋊C8)—21no—
55C22⋊(C11⋊C8)—21no—
56C22⋊(C11⋊C8)D412yes—
57#66874—22no—
58#66873—22no—
59C4⋊(C11⋊C8)—22no—
60C4⋊(C11⋊C8)—22no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64#66867—22no—
65#66867—21no—
66C4×C11⋊C8—22no—
67C4×C11⋊C8C2×C411yescharacteristic
68C4×C11⋊C8C2×C411yescharacteristic
69C4×C11⋊C8D411yescharacteristic
70C4×C11⋊C8D411yescharacteristic
71#9282—111nomaximal, Sylow
72C2×Q8×C11—21no—
73C2×Q8×C11C22⋊C412yes—
74C22×C4×C11—41no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C2×C22⋊D11—41no—
79#4339—82no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—21no—
83C2×C4×D11—41no—
84C2×Dic22—21no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4C22⋊C412yes—
92C11×C22⋊C4—22no—
93C42×C11—22no—
94C42×C11—22no—
95C42×C11—41no—
96C42×C11C22×C411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100#4326—82no—
101#4325—82no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—21no—
111#3210—111no—
112#2985—111no—
113#1506D1111yescharacteristic, complemented
114#1505—111no—
115#1496—111no—
116#1287—111no—
117#1274—111no—
118C23×C11#12111yescharacteristic
119C22×D11—41no—
120Q8×C11—42no—
121Q8×C11—41no—
122Q8×C11—41no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—42no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11C2×C22⋊C411yescharacteristic
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11C4×D411yescharacteristic
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12311yescharacteristic
138C22⋊D11—82no—
139C2×Dic11—41no—
140D44—42no—
141D44—41no—
142D44—41no—
143D44—81no—
144C4×D11—82no—
145Dic22—42no—
146C8×C11—81no—
147C11⋊C8—41no—
148C11⋊C8—42no—
149C11⋊C8—41no—
150C11⋊C8—41no—
151C11⋊C8—41no—
152#533C2×D1111yescharacteristic
153#532—111no—
154#494—111no—
155#492—111no—
156#487—111no—
157#486—111no—
158#464—222no—
159#452—222no—
160#446—221no—
161#446—222no—
162C8×Q8—221no—
163#433—222no—
164#432—111no—
165#432C2×D1111yescharacteristic
166#431—111no—
167#431—111no—
168#376C2×D1111yescharacteristic
169#328—22no—
170#327—222no—
171D4⋊C8—221no—
172D4⋊C8—221no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11#38611yescharacteristic
177C2×D11—81no—
178C2×D11—81no—
179C2×D11—81no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—42no—
186C4×C11—42no—
187C4×C11—82no—
188C4×C11#44311yescharacteristic
189C4×C11#44411yescharacteristic
190Dic11—81no—
191C2×#41—221no—
192C2×Q16—222no—
193C2×SD16—222no—
194C4⋊Q8—111no—
195C4⋊Q8C4×D1111yescharacteristic
196C4⋊Q8C4×D1111yescharacteristic
197#127—111no—
198#125—21no—
199#124—221no—
200C22⋊Q8—21no—
201C22⋊Q8C22⋊D1112yes—
202#121—221no—
203#121—221no—
204C4×Q8—21no—
205C4×Q8D4412yes—
206C4×D4—221no—
207C4×D4—221no—
208#117—21no—
209C2×C42—21no—
210C2×C42C22×D1111yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—222no—
213C4⋊C8—222no—
214C4⋊C8—221no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217#103—222no—
218#102—222no—
219C22⋊C8—21no—
220C22⋊C8—112no—
221C22⋊C8—221no—
222C22⋊C8—221no—
223#97—21no—
224#97—222no—
225#97—221no—
226C4×C8—111no—
227C4×C8—111no—
228C4×C8—111no—
229C4×C8—111no—
230C4×C8—222no—
231#95—21no—
232#95—21no—
233C2×C11—41no—
234C2×C11#187611yescharacteristic
235C2×C11#190511yescharacteristic
236C2×C11#191011yescharacteristic
237D11—161no—
238#41—882no—
239C2×Q8—21no—
240C2×Q8—221no—
241C2×Q8(C2×D11)⋊C412yes—
242C2×D4—221no—
243C2×D4—221no—
244C2×D4—221no—
245C2×D4—441no—
246C22×C4—41no—
247C22×C4—441no—
248C22×C4D4×D1111yescharacteristic
249C22×C4#434111yescharacteristic
250C22×C4C2×C22⋊D1111yescharacteristic
251Q16—882no—
252SD16—882no—
253C2×C8—41no—
254C2×C8—221no—
255C2×C8—221no—
256C2×C8—222no—
257C2×C8—221no—
258C2×C8—221no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4(C2×D11)⋊C412yes—
267C22⋊C4—22no—
268C22⋊C4—441no—
269C22⋊C4—441no—
270C42—22no—
271C42—22no—
272C42—41no—
273C42C2×C4×D1111yescharacteristic
274C42C2×D4411yescharacteristic
275C42D4×D1111yescharacteristic
276C42#434111yescharacteristic
277C11#928211yescharacteristic, complemented, Sylow
278C23—441no—
279C23#6699211yescharacteristic
280Q8—42no—
281Q8—41no—
282Q8—41no—
283Q8—442no—
284D4—442no—
285D4—441no—
286D4—441no—
287D4—881no—
288D4—882no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—441no—
299C2×C4—882no—
300C2×C4(C22⋊D11)⋊C411yescharacteristic
301C2×C4(C22⋊D11)⋊C411yescharacteristic
302C2×C4#6693511yescharacteristic
303C2×C4#6693911yescharacteristic
304C2×C4C2×(C2×D11)⋊C411yescharacteristic
305C2×C4#6699211yescharacteristic
306C8—81no—
307C8—441no—
308C8—441no—
309C8—441no—
310C8—441no—
311C8—442no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—881no—
316C22—881no—
317C22—881no—
318C22#1062257111yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—42no—
325C4—42no—
326C4—82no—
327C4—881no—
328C4#1062243611yescharacteristic
329C4#1062243711yescharacteristic
330C2—41no—
331C2—1761no—
332C2#1306894111yescharacteristic
333C2#1306910811yescharacteristic
334C2#1306914111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1506C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1506D11
hypocenterC11#9282
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
2. #13077711C2semidirect
5. #13066477C2semidirect
6. #13066445C2semidirect
7. C11×#1506C2semidirect
12. #10622706C4semidirect
13. #10622705C4semidirect
14. #10622701C4semidirect
15. #10622698C4semidirect
113. #1506D11semidirect
277. C11#9282semidirect

Maximal subgroups

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

subgroupindex
#130795682
#130777112
#130671232
#130670842
#130664772
#130664452
C11×#15062
#928211