Finite Group Databasebeta

← #14737799

Subgroups — #14737799

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079202C211yesmaximal, characteristic, complemented
2#13078415C212yesmaximal
3C2×#10622301C211yesmaximal, characteristic
4#13068192C214yesmaximal, complemented
5#13068140C212yesmaximal, complemented
6#13068106C212yesmaximal, complemented
7#13067307C212yesmaximal, complemented
8C11×#1566C211yesmaximal, characteristic, complemented
9C22×#4313—21no—
10C2×C4×D44C2211yescharacteristic
11#10623001C2212yes—
12C11×#423C2212yes—
13C2×C4×C8×C11C2211yescharacteristic
14#10622744—22no—
15#10622734—22no—
16#10622729—21no—
17#10622729—21no—
18C2×(C2×D11)⋊C8—21no—
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20#10622460—24no—
21#10622459C2214yes—
22#10622455C2214yes—
23#10622312C2211yescharacteristic, complemented
24C4×Dic44—21no—
25C4×Dic44—21no—
26#10622301—21no—
27#10622301—21no—
28#10622301C2212yes—
29#10622301C2212yes—
30#10622295C2211yescharacteristic, complemented
31#10622294C2212yescomplemented
32C11×#334C2212yescomplemented
33C11×#334C2212yescomplemented
34#10622124C2214yescomplemented
35#10622119C2214yescomplemented
36C22×D44D411yescharacteristic
37C22×C4×D11—21no—
38C2×C11×M16—22no—
39C22×C8×C11D411yescharacteristic
40C22×C8×C11D411yescharacteristic
41C2×C42×C11C2311yescharacteristic
42C2×(C2×D11)⋊C4—21no—
43#66979—22no—
44C2×C4⋊Dic11D411yescharacteristic
45#66977—22no—
46#66977—22no—
47C22×C11⋊C8—21no—
48C2×Dic44—21no—
49C2×Dic44—21no—
50C2×#4313—22no—
51C2×#4313—22no—
52C2×#4313—44no—
53C4×D44—21no—
54C4×D44—21no—
55C4×D44D412yes—
56C4×D44C2312yes—
57#66923—22no—
58#66922C2312yes—
59#66922C2312yes—
60C4×Dic22—22no—
61C4×Dic22—22no—
62C11×C4⋊C8—22no—
63C11×C4⋊C8C2314yes—
64C4×C8×C11D411yescharacteristic
65C4×C8×C11D411yescharacteristic
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2311yescharacteristic
68#66885—24no—
69#66885—24no—
70(C2×D11)⋊C8—22no—
71(C2×D11)⋊C8—22no—
72#66882—21no—
73#66882—21no—
74#66882—24no—
75#66881—24no—
76#66880—22no—
77#66880—22no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)C2312yes—
80#19281—111nomaximal, Sylow
81C23×D11—21no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—21no—
86C2×D44—21no—
87C2×D44—24no—
88C2×D44C2×D412yes—
89C2×C4×D11—22no—
90C2×C4×D11—22no—
91C2×C4×D11—42no—
92C2×C4×D11—42no—
93C2×Dic22—22no—
94C2×Dic22—22no—
95C11×M16—44no—
96C2×C8×C11—22no—
97C2×C8×C11—24no—
98C2×C8×C11—41no—
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C42×C11C2411yescharacteristic
107C22⋊Dic11—42no—
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—22no—
110C4⋊Dic11—21no—
111C4⋊Dic11—22no—
112C4⋊Dic11—22no—
113C4⋊Dic11—22no—
114C4⋊Dic11—22no—
115C4⋊Dic11C2×D412yes—
116Dic11⋊C4—42no—
117Dic11⋊C4—42no—
118C4×Dic11—42no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—42no—
121Dic44—42no—
122Dic44—42no—
123#4313—44no—
124#4313—44no—
125#3170—111no—
126#3077—112no—
127C2×#436—111no—
128#1703—114no—
129#1695—112no—
130#1689—112no—
131#1566D1111yescharacteristic, complemented
132#1550—112no—
133C23×C11#12111yescharacteristic
134C22×D11—22no—
135C22×D11—42no—
136C22×D11—42no—
137C22×D11—42no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—41no—
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#13714yes—
145C2×C4×C11C22×D411yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C2×#4111yescharacteristic
148C2×Dic11—22no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152D44—24no—
153D44—42no—
154C4×D11—44no—
155C4×D11—42no—
156C4×D11—42no—
157Dic22—42no—
158Dic22—42no—
159Dic22—82no—
160C8×C11—21no—
161C8×C11—21no—
162C8×C11—21no—
163C8×C11—44no—
164C8×C11AGL(1,ℤ/8)12yes—
165C11⋊C8—42no—
166C22×M16—221no—
167#533—112no—
168C2×C4×D4—111no—
169#500—111no—
170#494—111no—
171#487—112no—
172#478—224no—
173#476—114no—
174#474—114no—
175#467—221no—
176#467—221no—
177C4×Q16—221no—
178C4×Q16—221no—
179#436—112no—
180#436—112no—
181#436—221no—
182#436—221no—
183#428—222no—
184#423C2×D1112yes—
185C2×C4⋊C8—111no—
186#418—222no—
187C2×C22⋊C8—221no—
188C2×C4×C8C2×D1111yescharacteristic
189#334C2×D1112yescomplemented
190#334C2×D1112yescomplemented
191#333—114no—
192#332—114no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11#47012yes—
196C22×C11C2×#12111yescharacteristic
197C2×D11—42no—
198C2×D11—42no—
199C2×D11—42no—
200C2×D11—84no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11#47012yes—
205C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
206C4×C11C2×#13712yes—
207C4×C11#57511yescharacteristic
208Dic11—42no—
209Dic11—82no—
210Dic11—82no—
211C22×D4—111no—
212C23×C4—221no—
213C2×Q16—221no—
214C2×Q16—221no—
215C2×M16—22no—
216C2×M16—222no—
217C2×M16—222no—
218C2×M16—444no—
219C22×C8—221no—
220C22×C8D4411yescharacteristic
221C22×C8D4411yescharacteristic
222C4⋊Q8—112no—
223C4⋊Q8—112no—
224#125—222no—
225C22⋊Q8—222no—
226C22⋊Q8—222no—
227C4×Q8—222no—
228C4×Q8—222no—
229C4×D4—112no—
230C4×D4—112no—
231C4×D4—221no—
232C4×D4—221no—
233#117—222no—
234C2×C4⋊C4—111no—
235C2×C22⋊C4—221no—
236C2×C42C22×D1111yescharacteristic
237#107—224no—
238#107—221no—
239#107—221no—
240#106—224no—
241C4⋊C8—22no—
242C4⋊C8—112no—
243C4⋊C8—221no—
244C4⋊C8C22×D1114yes—
245#103—222no—
246#103—222no—
247#102—224no—
248#102—224no—
249C22⋊C8—222no—
250C22⋊C8—222no—
251C4×C8D4411yescharacteristic
252C4×C8D4411yescharacteristic
253C4×C8C22×D1111yescharacteristic
254C4×C8C22×D1111yescharacteristic
255C2×C11—22no—
256C2×C11#303611yescharacteristic
257C2×C11C2×#47011yescharacteristic
258C2×C11#306711yescharacteristic
259D11—82no—
260C24—221no—
261C2×Q8—222no—
262C2×Q8—222no—
263C2×D4—112no—
264C2×D4—221no—
265C2×D4—224no—
266C22×C4—221no—
267C22×C4—222no—
268C22×C4—222no—
269C22×C4—442no—
270C22×C4—442no—
271C22×C4C2×D4411yescharacteristic
272C22×C4D4×D1111yescharacteristic
273C22×C4#434311yescharacteristic
274Q16—442no—
275Q16—442no—
276M16—44no—
277M16—444no—
278M16—444no—
279C2×C8—22no—
280C2×C8—24no—
281C2×C8—41no—
282C2×C8—222no—
283C2×C8—442no—
284C2×C8C2×D4411yescharacteristic
285C2×C8C2×D4411yescharacteristic
286C2×C8C2×D4411yescharacteristic
287C2×C8C2×D4411yescharacteristic
288C4⋊C4—112no—
289C4⋊C4—221no—
290C4⋊C4—222no—
291C4⋊C4—222no—
292C4⋊C4—222no—
293C4⋊C4—222no—
294C4⋊C4—442no—
295C4⋊C4—442no—
296C22⋊C4—222no—
297C22⋊C4—222no—
298C22⋊C4—442no—
299C42—442no—
300C42C2×D4411yescharacteristic
301C42D4×D1111yescharacteristic
302C42#434311yescharacteristic
303C42C23×D1111yescharacteristic
304C11#1928111yescharacteristic, complemented, Sylow
305C23—222no—
306C23—442no—
307C23—442no—
308C23—442no—
309C23#6694811yescharacteristic
310Q8—442no—
311Q8—442no—
312Q8—882no—
313D4—224no—
314D4—442no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—222no—
319C2×C4—444no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4—442no—
325C2×C4#6694811yescharacteristic
326C2×C4#6694811yescharacteristic
327C2×C4#6694811yescharacteristic
328C2×C4#6696814yes—
329C2×C4C22×D4411yescharacteristic
330C2×C4C2×D4×D1111yescharacteristic
331C2×C4C2×#434311yescharacteristic
332C8—21no—
333C8—21no—
334C8—21no—
335C8—44no—
336C8—442no—
337C8#6696112yes—
338C22—21no—
339C22—21no—
340C22—442no—
341C22—442no—
342C22—442no—
343C22—884no—
344C22#1062248112yes—
345C22C2×#6694811yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—442no—
350C4—882no—
351C4—882no—
352C4#1062248112yes—
353C4C2×#6696111yescharacteristic
354C4#1062327911yescharacteristic
355C4C2×#6696812yes—
356C2—22no—
357C2—882no—
358C2#1307808211yescharacteristic
359C2C2×#1062248111yescharacteristic
360C2#1307833711yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1566C2
socleC22×C11C2×#121
prime radicalC22×D44D4
hypercenter#1566D11
hypocenterC11#19281
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1566

Complements

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

NH ≅ G/Ntype
1. #13079202C2semidirect
4. #13068192C2semidirect
5. #13068140C2semidirect
6. #13068106C2semidirect
7. #13067307C2semidirect
8. C11×#1566C2semidirect
23. #10622312C22semidirect
30. #10622295C22semidirect
31. #10622294C22semidirect
32. C11×#334C22semidirect
33. C11×#334C22semidirect
34. #10622124C22semidirect
35. #10622119C22semidirect
131. #1566D11semidirect
189. #334C2×D11semidirect
190. #334C2×D11semidirect
304. C11#19281semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130784152
C2×#106223012
#130681922
#130681402
#130681062
#130673072
C11×#15662
#1928111