Finite Group Databasebeta

← #14739076

Subgroups — #14739076

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079566C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic
3C2×#10622633C211yesmaximal, characteristic
4#13068074C214yesmaximal, complemented
5#13067986C214yesmaximal, complemented
6#13067391C211yesmaximal, characteristic
7#13067300C211yesmaximal, characteristic
8#13067271C211yesmaximal, characteristic
9C11×#2982C211yesmaximal, characteristic
10C2×C4×Q8×C11C2211yescharacteristic
11#10623001C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C8×Q8×C11—22no—
14C8×Q8×C11C2214yes—
15C11×#431—22no—
16C11×#431C2211yescharacteristic
17C11×#431C2211yescharacteristic
18#10622838—21no—
19C2×#66899—21no—
20#10622635—22no—
21#10622634C2212yes—
22#10622633—22no—
23#10622633C2214yes—
24#10622633C2212yes—
25#10622577—21no—
26C2×#66872—21no—
27#10622537C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29#10622462—22no—
30#10622352—22no—
31#10622312C2212yes—
32#10622294C2212yes—
33#10622120C2212yes—
34#10622120C2214yes—
35#10622119C2212yes—
36#10622096C2214yes—
37C22×Q8×C11D411yescharacteristic
38C22×Dic22—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11D412yes—
42C4×Q8×C11C2312yes—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C42×C11—21no—
46C2×C42×C11C2311yescharacteristic
47#66979—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50#66977—21no—
51#66977—21no—
52C2×#4318—21no—
53C22×C11⋊C8—21no—
54C2×Dic44—24no—
55#66923—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922C2312yes—
60#66922C2311yescharacteristic
61#66922C2311yescharacteristic
62C4×Dic22—21no—
63C4×Dic22—21no—
64C11×C4⋊C8—24no—
65C11×C4⋊C8D412yes—
66C11×C4⋊C8C2312yes—
67C11×C22⋊C8—21no—
68C11×C22⋊C8D412yes—
69C4×C8×C11—24no—
70C4×C8×C11—21no—
71C4×C8×C11C2312yes—
72#66899—24no—
73#66899—22no—
74#66899—22no—
75#66880—24no—
76#66872—24no—
77#66872—22no—
78#66871—22no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)C2312yes—
82C4⋊(C11⋊C8)C2312yes—
83#19399—111nomaximal, Sylow
84C2×Q8×C11—21no—
85C2×Q8×C11—22no—
86C2×Q8×C11Q1614yescomplemented
87C2×Q8×C11C2×D412yes—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×Dic11—41no—
94C2×Dic22—22no—
95C2×Dic22—21no—
96C2×Dic22—21no—
97C2×Dic22—41no—
98C2×Dic22—82no—
99C2×C8×C11—22no—
100C2×C8×C11C2×D414yes—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4C2×D412yes—
105C42×C11—22no—
106C42×C11—22no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11#4111yescharacteristic
110C42×C11C2411yescharacteristic
111C22⋊Dic11—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—22no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122C4×Dic11—41no—
123#4318—42no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—42no—
127Dic44—84no—
128#3209—111no—
129#3078—111no—
130C2×#475—111no—
131#2982D1111yescharacteristic
132#1684—114no—
133#1670—114no—
134#1571—111no—
135#1549—111no—
136#1542—111no—
137C23×C11#12111yescharacteristic
138Q8×C11—22no—
139Q8×C11—24no—
140Q8×C11C2×Q1614yes—
141C2×C4×C11—22no—
142C2×C4×C11—24no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—41no—
146C2×C4×C11—81no—
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11C2×Q1612yes—
151C2×C4×C11#13512yes—
152C2×C4×C11C22×D411yescharacteristic
153C2×C4×C11C22×D411yescharacteristic
154C2×C4×C11C2×#4111yescharacteristic
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—42no—
158C2×Dic11—82no—
159Dic22—42no—
160Dic22—44no—
161Dic22—82no—
162Dic22—81no—
163C8×C11—24no—
164C8×C11—42no—
165C11⋊C8—42no—
166C11⋊C8—42no—
167#533—111no—
168C2×C4⋊Q8—111no—
169C2×C4×Q8C2×D1111yescharacteristic
170#494—112no—
171#487—112no—
172#479—222no—
173#477—112no—
174#475—114no—
175#475—112no—
176#475—222no—
177#462—222no—
178#451—222no—
179C8×Q8—22no—
180C8×Q8C2×D1114yes—
181#431—22no—
182#431C2×D1111yescharacteristic
183#431C2×D1111yescharacteristic
184#428—221no—
185C2×#106—221no—
186#423—111no—
187C2×C4⋊C8—111no—
188#419—221no—
189C2×#103—221no—
190#335—114no—
191#333—112no—
192#332—112no—
193#332—114no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11#46712yes—
197C22×C11C2×#12111yescharacteristic
198C4×C11—21no—
199C4×C11—24no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—42no—
203C4×C11#46712yes—
204C4×C11C22×Q1611yescharacteristic
205C4×C11C2×#13511yescharacteristic
206C4×C11#57712yes—
207Dic11—82no—
208Dic11—81no—
209Dic11—81no—
210C22×Q8—221no—
211C22×Q8D4411yescharacteristic
212C2×Q16—224no—
213C2×M16—221no—
214C22×C8—221no—
215C4⋊Q8—112no—
216C4⋊Q8—111no—
217C4⋊Q8—111no—
218C4⋊Q8—221no—
219C4⋊Q8—221no—
220C4⋊Q8—221no—
221#125—221no—
222C22⋊Q8—221no—
223C22⋊Q8—221no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8—221no—
227C4×Q8—221no—
228C4×Q8D4412yes—
229C4×Q8C22×D1112yes—
230#117—221no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4D4411yescharacteristic
235C2×C42—21no—
236C2×C42C22×D1111yescharacteristic
237#107—222no—
238#106—224no—
239#106—222no—
240C4⋊C8—24no—
241C4⋊C8—112no—
242C4⋊C8—112no—
243C4⋊C8—221no—
244C4⋊C8—221no—
245C4⋊C8C22⋊D1112yes—
246C4⋊C8C22×D1112yes—
247#103—224no—
248#103—222no—
249#103—222no—
250#103—224no—
251C22⋊C8—21no—
252C22⋊C8C22⋊D1112yes—
253C4×C8—24no—
254C4×C8—21no—
255C4×C8C22×D1112yes—
256C2×C11—22no—
257C2×C11#304311yescharacteristic
258C2×C11C2×#46711yescharacteristic
259C2×C11#306911yescharacteristic
260C2×Q8—22no—
261C2×Q8—21no—
262C2×Q8—221no—
263C2×Q8—222no—
264C2×Q8—221no—
265C2×Q8—441no—
266C2×Q8—882no—
267C2×Q8Dic4414yescomplemented
268C2×Q8C2×D4412yes—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—441no—
272C22×C4C2×D4411yescharacteristic
273C22×C4#433911yescharacteristic
274C22×C4C2×C22⋊D1111yescharacteristic
275Q16—884no—
276M16—442no—
277C2×C8—22no—
278C2×C8—222no—
279C2×C8—222no—
280C2×C8—442no—
281C2×C8C2×C22⋊D1114yes—
282C4⋊C4—22no—
283C4⋊C4—21no—
284C4⋊C4—22no—
285C4⋊C4—222no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4—222no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C4⋊C4C2×D4412yes—
296C22⋊C4—441no—
297C42—22no—
298C42—22no—
299C42—441no—
300C42C2×D4411yescharacteristic
301C42#433911yescharacteristic
302C42C2×C22⋊D1111yescharacteristic
303C42C23×D1111yescharacteristic
304C11#1939911yescharacteristic, complemented, Sylow
305C23#6698311yescharacteristic
306Q8—24no—
307Q8—22no—
308Q8—442no—
309Q8—444no—
310Q8—881no—
311Q8—882no—
312Q8C2×Dic4414yes—
313C2×C4—24no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—442no—
322C2×C4—882no—
323C2×C4#6695712yes—
324C2×C4C2×Dic4412yes—
325C2×C4#6698311yescharacteristic
326C2×C4#6698311yescharacteristic
327C2×C4#6698311yescharacteristic
328C2×C4C22×D4411yescharacteristic
329C2×C4C2×#433911yescharacteristic
330C2×C4C22×C22⋊D1111yescharacteristic
331C8—24no—
332C8—42no—
333C8—442no—
334C8—442no—
335C22—21no—
336C22—21no—
337C22#1062272912yes—
338C22C2×#6698311yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—24no—
343C4—42no—
344C4—881no—
345C4—882no—
346C4—881no—
347C4#1062272912yes—
348C4C2×#6695711yescharacteristic
349C4C22×Dic4411yescharacteristic
350C4#1062336812yes—
351C2—22no—
352C2#1307813711yescharacteristic
353C2C2×#1062272911yescharacteristic
354C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2982C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenter#2982D11
hypocenterC11#19399
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
4. #13068074C2semidirect
5. #13067986C2semidirect
86. C2×Q8×C11Q16semidirect
267. C2×Q8Dic44semidirect
304. C11#19399semidirect

Maximal subgroups

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

subgroupindex
#130795662
#130784212
C2×#106226332
#130680742
#130679862
#130673912
#130673002
#130672712
C11×#29822
#1939911