Finite Group Databasebeta

← #14739115

Subgroups — #14739115

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079744C211yesmaximal, characteristic
2C2×#10622704C211yesmaximal, characteristic, complemented
3#13078090C211yesmaximal, characteristic
4#13077696C211yesmaximal, characteristic, complemented
5#13068035C214yesmaximal, complemented
6#13068001C214yesmaximal, complemented
7#13067388C211yesmaximal, characteristic, complemented
8#13067263C211yesmaximal, characteristic
9C11×#1548C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66962—21no—
12#10623008C2211yescharacteristic
13C2×C4×Dic22C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16#10622746—21no—
17#10622704—22no—
18#10622704C2214yes—
19#10622701C2212yes—
20#10622697—22no—
21#10622692C2212yes—
22C2×#66874—21no—
23#10622581—22no—
24C2×#66871—21no—
25#10622538C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622462C2212yes—
28#10622461C2212yes—
29#10622458—22no—
30#10622443C2214yes—
31#10622331—22no—
32C8×Dic22—22no—
33C11×#333C2214yes—
34#10622124C2212yes—
35#10622123C2212yes—
36#10622118C2214yes—
37C22×Q8×C11—21no—
38C2×#4339—21no—
39C22×Dic22D411yescharacteristic
40C2×C11×M16—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8C2312yes—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48#66983—21no—
49#66983—21no—
50C2×C4⋊Dic11D411yescharacteristic
51C2×Dic11⋊C4—21no—
52C2×C4×Dic11—21no—
53C22×C11⋊C8—21no—
54#66962—44no—
55C2×Dic44—22no—
56C2×#4314—22no—
57#66928—21no—
58#66927C2311yescharacteristic
59C4×D44—21no—
60C4×D44—21no—
61#66922C2311yescharacteristic
62C4×Dic22—21no—
63C4×Dic22—21no—
64C4×Dic22D412yes—
65C4×Dic22C2312yes—
66C11×C4⋊C8—21no—
67C11×C4⋊C8C2312yes—
68C11×C4⋊C8C2312yes—
69C11×C22⋊C8—21no—
70C4×C8×C11—21no—
71C22⋊(C11⋊C8)D412yes—
72#66885—22no—
73#66880—22no—
74Dic11⋊C8—24no—
75C8×Dic11—24no—
76#66874—24no—
77#66873—24no—
78#66872—24no—
79#66871—24no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)D412yes—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8C2312yes—
84#19403—111nomaximal, Sylow
85C2×Q8×C11—22no—
86C2×Q8×C11—41no—
87C2×Q8×C11—82no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C2×C22⋊D11—41no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95#4339—42no—
96#4339—42no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×C4×D11—41no—
101C2×Dic22—21no—
102C2×Dic22—22no—
103C2×Dic22—21no—
104C2×Dic22SD1614yes—
105C2×Dic22C2×D412yes—
106C11×M16—42no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C42×C11C2411yescharacteristic
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11C2×D412yes—
123Dic11⋊C4—22no—
124Dic11⋊C4—22no—
125C4×Dic11—22no—
126C4×Dic11—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—42no—
129C2×C11⋊C8C2×D414yes—
130Dic44—44no—
131#4314—44no—
132#3227—111no—
133C2×#477—111no—
134#3037—111no—
135#2982—111no—
136#1678—114no—
137#1672—114no—
138#1570—111no—
139#1548D1111yescharacteristic, complemented
140#1540—111no—
141C23×C11#12111yescharacteristic
142C22×D11—41no—
143Q8×C11—82no—
144Q8×C11—82no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—82no—
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11C2×SD1612yes—
153C2×C4×C11#13512yes—
154C2×C4×C11C22×D411yescharacteristic
155C2×C4×C11C22×D411yescharacteristic
156C2×C4×C11C2×#4111yescharacteristic
157C22⋊D11—82no—
158C2×Dic11—22no—
159C2×Dic11—24no—
160C2×Dic11—22no—
161C2×Dic11—41no—
162C2×Dic11—81no—
163D44—41no—
164D44—41no—
165D44—42no—
166D44—81no—
167C4×D11—82no—
168Dic22—22no—
169Dic22—24no—
170Dic22—41no—
171Dic22—41no—
172Dic22C2×SD1614yes—
173C8×C11—42no—
174C8×C11—42no—
175C11⋊C8—24no—
176C11⋊C8—42no—
177C2×#137—221no—
178#532—111no—
179C2×C4⋊Q8C2×D1111yescharacteristic
180C2×C4×Q8—111no—
181#498—112no—
182#486—112no—
183#481—222no—
184#477—114no—
185#477—222no—
186#476—222no—
187#464—222no—
188#462—112no—
189#460—112no—
190C8×Q8—114no—
191C8×Q8—222no—
192#431—111no—
193#431—222no—
194#431C2×D1111yescharacteristic
195C2×#107—221no—
196#423C2×D1111yescharacteristic
197C2×C4⋊C8—111no—
198#417—221no—
199C2×#103—221no—
200#334—114no—
201#333C2×D1114yes—
202#332—112no—
203#331—112no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11#46512yes—
207C22×C11C2×#12111yescharacteristic
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—82no—
215C4×C11#46512yes—
216C4×C11C22×SD1611yescharacteristic
217C4×C11C2×#13511yescharacteristic
218C4×C11#57812yes—
219Dic11—24no—
220Dic11—42no—
221Dic11—81no—
222C2×#41—221no—
223C22×Q8—21no—
224C22×Q8—111no—
225#137—444no—
226C2×Q16—222no—
227C2×SD16—222no—
228C2×M16—21no—
229C22×C8—221no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—111no—
234C4⋊Q8C22×D1112yes—
235#127—111no—
236#124—221no—
237#121—221no—
238#121—221no—
239C4×Q8—112no—
240C4×Q8—112no—
241C4×Q8—221no—
242C4×Q8—221no—
243C4×D4—221no—
244C4×D4—221no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4—221no—
249C2×C42—221no—
250C2×C42C22×D1111yescharacteristic
251#107—224no—
252#106—224no—
253C4⋊C8—21no—
254C4⋊C8—112no—
255C4⋊C8—112no—
256C4⋊C8—224no—
257C4⋊C8—221no—
258C4⋊C8C22×D1112yes—
259C4⋊C8C22×D1112yes—
260#103—224no—
261#103—222no—
262#102—224no—
263#102—222no—
264C22⋊C8—21no—
265C22⋊C8—112no—
266C4×C8—21no—
267C4×C8—112no—
268C4×C8—224no—
269C2×C11—22no—
270C2×C11#304411yescharacteristic
271C2×C11C2×#46511yescharacteristic
272C2×C11#306811yescharacteristic
273D11—161no—
274#41—442no—
275#41—442no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—82no—
279C2×Q8—114no—
280C2×Q8—112no—
281C2×Q8—221no—
282C2×Q8—222no—
283C2×Q8—221no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—441no—
288C22×C4—41no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—441no—
292C22×C4#433911yescharacteristic
293C22×C4D4×D1111yescharacteristic
294C22×C4D4×D1111yescharacteristic
295Q16—444no—
296SD16—444no—
297M16—42no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—114no—
301C2×C8—222no—
302C2×C8—442no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—112no—
308C4⋊C4—221no—
309C4⋊C4—222no—
310C4⋊C4—222no—
311C4⋊C4—221no—
312C4⋊C4—221no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C42—222no—
316C42—222no—
317C42#433911yescharacteristic
318C42D4×D1111yescharacteristic
319C42D4×D1111yescharacteristic
320C42C23×D1111yescharacteristic
321C11#1940311yescharacteristic, complemented, Sylow
322C23—441no—
323C23#6693711yescharacteristic
324Q8—82no—
325Q8—82no—
326Q8—114no—
327Q8—222no—
328Q8—224no—
329Q8—441no—
330Q8—441no—
331D4—441no—
332D4—441no—
333D4—442no—
334D4—881no—
335D4—882no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—82no—
340C2×C4—222no—
341C2×C4—224no—
342C2×C4—222no—
343C2×C4—441no—
344C2×C4—881no—
345C2×C4—882no—
346C2×C4#6693711yescharacteristic
347C2×C4#6693711yescharacteristic
348C2×C4#6693711yescharacteristic
349C2×C4SD16×D1112yes—
350C2×C4#6697212yes—
351C2×C4C2×#433911yescharacteristic
352C2×C4C2×D4×D1111yescharacteristic
353C2×C4C2×D4×D1111yescharacteristic
354C8—42no—
355C8—42no—
356C8—224no—
357C8—442no—
358C22—21no—
359C22—21no—
360C22—881no—
361C22—881no—
362C22—881no—
363C22#1062242012yes—
364C22C2×#6693711yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—82no—
369C4—224no—
370C4—442no—
371C4—881no—
372C4#1062242012yes—
373C4C2×SD16×D1111yescharacteristic
374C4C2×#6697211yescharacteristic
375C4#1062331012yes—
376C2—22no—
377C2—1761no—
378C2#1307814511yescharacteristic
379C2C2×#1062242011yescharacteristic
380C2#1307834311yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1548C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#1548D11
hypocenterC11#19403
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
2. C2×#10622704C2semidirect
4. #13077696C2semidirect
5. #13068035C2semidirect
6. #13068001C2semidirect
7. #13067388C2semidirect
9. C11×#1548C2semidirect
139. #1548D11semidirect
321. C11#19403semidirect

Maximal subgroups

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

subgroupindex
#130797442
C2×#106227042
#130780902
#130776962
#130680352
#130680012
#130673882
#130672632
C11×#15482
#1940311