Finite Group Databasebeta

← #14650485

Subgroups — #14650485

Order 2816.

454 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079566C211yesmaximal, characteristic
2#13071364C211yesmaximal, characteristic
3#13069597C211yesmaximal, characteristic
4#13067296C211yesmaximal, characteristic
5#13067181C211yesmaximal, characteristic
6#13066475C211yesmaximal, characteristic
7C11×#1274C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#376C2211yescharacteristic
13#10622549C2211yescharacteristic
14C4×C4⋊Dic11—21no—
15#10622541—21no—
16#10622537C2211yescharacteristic
17#10622462—22no—
18#10622352—22no—
19#10622312C412yescomplemented
20#10622294C412yescomplemented
21#10622267—22no—
22#10622259—22no—
23#10622161—21no—
24#10622161—21no—
25#10622119—22no—
26#10622105—22no—
27C22×Dic22D412yes—
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11C2311yescharacteristic
31#66979—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35#66977—21no—
36#66977—21no—
37C2×Dic11⋊C4—22no—
38C2×C4×Dic11—22no—
39C2×#4318—21no—
40C2×Dic44—24no—
41#66923—21no—
42#66922—21no—
43#66922—21no—
44#66922C2×C411yescharacteristic
45#66922C2×C411yescharacteristic
46#66922C2×C412yes—
47#66922D412yes—
48C4×Dic22—21no—
49C4×Dic22—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×C22⋊C8—21no—
54C4×C8×C11—21no—
55C4×C8×C11C2×C412yes—
56C11×#95—21no—
57C11×#95—21no—
58C11⋊#95—22no—
59C11⋊#95—22no—
60C11⋊#95—21no—
61C11⋊#95D412yes—
62#66880—24no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65#9297—111nomaximal, Sylow
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—22no—
72C22×Dic11—22no—
73C2×Dic22—21no—
74C2×Dic22—21no—
75C2×Dic22—22no—
76C2×Dic22—82no—
77C2×Dic22C22⋊C414yes—
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11Q1612yescomplemented
84C42×C11C22×C411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11#4111yescharacteristic
87C42×C11#4111yescharacteristic
88C22⋊Dic11—41no—
89C4⋊Dic11—21no—
90C4⋊Dic11—22no—
91C4⋊Dic11—22no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—22no—
96C4⋊Dic11—22no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101Dic11⋊C4—82no—
102C4×Dic11—41no—
103C4×Dic11—82no—
104#4318—41no—
105#4318—41no—
106C2×C11⋊C8—41no—
107Dic44—84no—
108#3209—111no—
109#2331—111no—
110#1995—111no—
111#1548—111no—
112#1518—111no—
113#1286—111no—
114#1274D1111yescharacteristic
115C23×C11#12011yescharacteristic
116C2×C4×C11—22no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11C2×C22⋊C411yescharacteristic
125C2×C4×C11C4×D411yescharacteristic
126C2×C4×C11C4×D411yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11#12311yescharacteristic
130C2×C4×C11C2×Q1611yescharacteristic
131C2×C4×C11#13511yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×C4×C11#13711yescharacteristic
134C2×Dic11—24no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—42no—
142Dic22—44no—
143Dic22—42no—
144Dic22—82no—
145Dic22—81no—
146C8×C11—42no—
147C8×C11—81no—
148C11⋊C8—81no—
149#533—111no—
150C2×C4⋊Q8—111no—
151#494—112no—
152#487—112no—
153#462—222no—
154#451—222no—
155#431C2×D1111yescharacteristic
156#431C2×D1111yescharacteristic
157#423—111no—
158#391—222no—
159#389—221no—
160#387—222no—
161#382—111no—
162C4×C4⋊C4—221no—
163#376C2×D1111yescharacteristic
164#339—221no—
165#339—221no—
166#333—222no—
167#328—222no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11#38611yescharacteristic
171C22×C11#45111yescharacteristic
172C22×C11#45211yescharacteristic
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—42no—
178C4×C11—81no—
179C4×C11C4×Q1611yescharacteristic
180C4×C11#44111yescharacteristic
181C4×C11#46211yescharacteristic
182C4×C11#46411yescharacteristic
183Dic11—44no—
184Dic11—82no—
185Dic11—81no—
186Dic11—81no—
187C22×Q8—112no—
188C2×Q16—224no—
189C2×M16—221no—
190C4⋊Q8—112no—
191C4⋊Q8—111no—
192C4⋊Q8—111no—
193C4⋊Q8—112no—
194C4⋊Q8—221no—
195C4⋊Q8—221no—
196#125—221no—
197C22⋊Q8—221no—
198C22⋊Q8—221no—
199C4×Q8—221no—
200C4×Q8—221no—
201#117—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—222no—
206C2×C42—222no—
207C2×C42D4411yescharacteristic
208C2×C42D4411yescharacteristic
209C2×C42C22×D1111yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—221no—
213C4⋊C8—221no—
214#103—224no—
215C22⋊C8—21no—
216C22⋊C8—21no—
217C4×C8—21no—
218C4×C8C4×D1112yes—
219#95—21no—
220#95—21no—
221#95—112no—
222#95—222no—
223#95—222no—
224#95—221no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11#187811yescharacteristic
228C2×C11#190511yescharacteristic
229C2×C11#191111yescharacteristic
230C2×Q8—114no—
231C2×Q8—222no—
232C2×Q8—221no—
233C2×Q8—221no—
234C2×Q8—882no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—222no—
238C22×C4—222no—
239C22×C4C2×D4411yescharacteristic
240C22×C4D4×D1111yescharacteristic
241C22×C4D4×D1111yescharacteristic
242Q16—884no—
243M16—441no—
244M16—441no—
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—441no—
248C4⋊C4—222no—
249C4⋊C4—222no—
250C4⋊C4—222no—
251C4⋊C4—222no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—882no—
261C22⋊C4—441no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—441no—
266C42—882no—
267C42Dic4412yescomplemented
268C42C2×C4×D1111yescharacteristic
269C42#433911yescharacteristic
270C42D4×D1111yescharacteristic
271C42#434311yescharacteristic
272C11#929711yescharacteristic, complemented, Sylow
273C23#6693511yescharacteristic
274Q8—444no—
275Q8—442no—
276Q8—882no—
277Q8—881no—
278C2×C4—22no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—224no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—442no—
290C2×C4—442no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—442no—
294C2×C4C4×D4411yescharacteristic
295C2×C4C22⋊C4×D1111yescharacteristic
296C2×C4#6693711yescharacteristic
297C2×C4#6694611yescharacteristic
298C2×C4#6694711yescharacteristic
299C2×C4#6694811yescharacteristic
300C2×C4#6695711yescharacteristic
301C2×C4C2×Dic4411yescharacteristic
302C2×C4#6696211yescharacteristic
303C2×C4#6696211yescharacteristic
304C8—42no—
305C8—81no—
306C8—881no—
307C22—21no—
308C22—21no—
309C22#1062227811yescharacteristic
310C22#1062234611yescharacteristic
311C22#1062235211yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—42no—
317C4—81no—
318C4—444no—
319C4—882no—
320C4—881no—
321C4—881no—
322C4C4×Dic4411yescharacteristic
323C4#1062232911yescharacteristic
324C4#1062245811yescharacteristic
325C4#1062246211yescharacteristic
326C2—21no—
327C2—21no—
328C2#1306895611yescharacteristic
329C2#1306911111yescharacteristic
330C2#1306914711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1274C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1274D11
hypocenterC11#9297
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
19. #10622312C4semidirect
20. #10622294C4semidirect
83. C42×C11Q16semidirect
267. C42Dic44semidirect
272. C11#9297semidirect

Maximal subgroups

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

subgroupindex
#130795662
#130713642
#130695972
#130672962
#130671812
#130664752
C11×#12742
#929711