Finite Group Databasebeta

← #14739117

Subgroups — #14739117

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#13079746C211yesmaximal, characteristic
2C2×#10622463C211yesmaximal, characteristic, complemented
3#13078090C211yesmaximal, characteristic
4#13077696C211yesmaximal, characteristic, complemented
5#13068033C214yesmaximal, complemented
6#13067999C214yesmaximal, complemented
7#13067298C211yesmaximal, characteristic, complemented
8#13067266C211yesmaximal, characteristic
9C11×#1570C211yesmaximal, characteristic, complemented
10C2×#66962—21no—
11#10623008C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C2×C4×Dic22C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17#10622746—21no—
18C2×#66882—21no—
19C2×#66880—21no—
20#10622538C2211yescharacteristic
21#10622463—22no—
22#10622463C2214yes—
23#10622462C2212yes—
24#10622461C2212yes—
25#10622458—22no—
26#10622455—22no—
27#10622443—22no—
28#10622348—22no—
29#10622331—22no—
30#10622307C2212yes—
31#10622293C2212yes—
32C8×Dic22C2214yes—
33C11×#334C2214yes—
34#10622123C2212yes—
35#10622120C2212yes—
36#10622119C2214yes—
37C2×#4339—21no—
38C22×Dic22—21no—
39C22×Dic22D411yescharacteristic
40C2×C11×M16—21no—
41C22×C8×C11—21no—
42C2×C42×C11C2311yescharacteristic
43#66983—21no—
44#66983—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11D411yescharacteristic
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11—21no—
50#66962—44no—
51C2×Dic44—22no—
52C2×#4314—22no—
53#66928—21no—
54#66927C2311yescharacteristic
55C4×D44—21no—
56C4×D44—21no—
57#66922—21no—
58#66922—21no—
59#66922—21no—
60#66922C2312yes—
61#66922C2311yescharacteristic
62C4×Dic22—21no—
63C4×Dic22—21no—
64C4×Dic22D412yes—
65C4×Dic22C2312yes—
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8D412yes—
69C11×C4⋊C8C2312yes—
70C11×C4⋊C8C2312yes—
71C11×C22⋊C8D412yes—
72C4×C8×C11C2312yes—
73C22⋊(C11⋊C8)—21no—
74#66885—24no—
75#66885—22no—
76#66882—24no—
77#66881—24no—
78#66880—24no—
79#66880—22no—
80Dic11⋊C8—24no—
81C8×Dic11—24no—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8—21no—
84#19403—111nomaximal, Sylow
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C2×C22⋊D11—41no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—41no—
92#4339—42no—
93#4339—42no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×C4×D11—41no—
98C2×Dic22—21no—
99C2×Dic22—22no—
100C2×Dic22—21no—
101C2×Dic22—22no—
102C2×Dic22—41no—
103C2×Dic22—82no—
104C2×Dic22SD1614yes—
105C2×Dic22C2×D412yes—
106C11×M16—42no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—42no—
110C2×C8×C11C2×D414yes—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114C42×C11C2411yescharacteristic
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117C4⋊Dic11—21no—
118C4⋊Dic11—22no—
119C4⋊Dic11—21no—
120C4⋊Dic11—22no—
121C4⋊Dic11—21no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124C4⋊Dic11C2×D412yes—
125Dic11⋊C4—22no—
126Dic11⋊C4—22no—
127C4×Dic11—22no—
128C4×Dic11—22no—
129C2×C11⋊C8—22no—
130Dic44—44no—
131#4314—44no—
132#3227—111no—
133C2×#477—111no—
134#3037—111no—
135#2982—111no—
136#1678—114no—
137#1672—114no—
138#1570D1111yescharacteristic, complemented
139#1548—111no—
140#1540—111no—
141C23×C11#12111yescharacteristic
142C22×D11—41no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11C2×SD1612yes—
149C2×C4×C11#13512yes—
150C2×C4×C11C22×D411yescharacteristic
151C2×C4×C11C22×D411yescharacteristic
152C2×C4×C11C2×#4111yescharacteristic
153C22⋊D11—82no—
154C2×Dic11—22no—
155C2×Dic11—24no—
156C2×Dic11—22no—
157C2×Dic11—42no—
158C2×Dic11—41no—
159C2×Dic11—81no—
160C2×Dic11—82no—
161D44—41no—
162D44—41no—
163D44—42no—
164D44—81no—
165C4×D11—82no—
166Dic22—22no—
167Dic22—24no—
168Dic22—41no—
169Dic22—41no—
170Dic22—82no—
171Dic22—82no—
172Dic22C2×SD1614yes—
173C8×C11—24no—
174C8×C11—42no—
175C8×C11—42no—
176C11⋊C8—42no—
177C2×#137—221no—
178#532—111no—
179C2×C4⋊Q8—111no—
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⋊C8C2×D1111yescharacteristic
198#417—221no—
199C2×#103—221no—
200#334C2×D1114yes—
201#333—114no—
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#46512yes—
215C4×C11C22×SD1611yescharacteristic
216C4×C11C2×#13511yescharacteristic
217C4×C11#57812yes—
218Dic11—24no—
219Dic11—42no—
220Dic11—81no—
221Dic11—82no—
222C2×#41—221no—
223C22×Q8—111no—
224C22×Q8—221no—
225#137—444no—
226C2×Q16—222no—
227C2×SD16—222no—
228C2×M16—21no—
229C22×C8—21no—
230C4⋊Q8—112no—
231C4⋊Q8—111no—
232C4⋊Q8—221no—
233C4⋊Q8—221no—
234C4⋊Q8—221no—
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—111no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C42—221no—
250C2×C42C22×D1111yescharacteristic
251#107—224no—
252#106—224no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—112no—
256C4⋊C8—224no—
257C4⋊C8D4412yes—
258C4⋊C8C22×D1112yes—
259C4⋊C8C22×D1112yes—
260#103—222no—
261#103—224no—
262#102—222no—
263#102—224no—
264C22⋊C8—221no—
265C22⋊C8D4412yes—
266C4×C8—224no—
267C4×C8—221no—
268C4×C8C22×D1112yes—
269C2×C11—22no—
270C2×C11#304411yescharacteristic
271C2×C11C2×#46511yescharacteristic
272C2×C11#306811yescharacteristic
273D11—161no—
274#41—442no—
275#41—442no—
276C2×Q8—114no—
277C2×Q8—112no—
278C2×Q8—221no—
279C2×Q8—222no—
280C2×Q8—221no—
281C2×Q8—222no—
282C2×Q8—441no—
283C2×Q8—882no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—441no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—441no—
291C22×C4—441no—
292C22×C4C2×D4411yescharacteristic
293C22×C4D4×D1111yescharacteristic
294C22×C4#434311yescharacteristic
295Q16—444no—
296SD16—444no—
297M16—42no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—42no—
301C2×C8—222no—
302C2×C8C2×D4414yes—
303C4⋊C4—112no—
304C4⋊C4—221no—
305C4⋊C4—222no—
306C4⋊C4—222no—
307C4⋊C4—222no—
308C4⋊C4—221no—
309C4⋊C4—222no—
310C4⋊C4—221no—
311C4⋊C4—441no—
312C4⋊C4—441no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C42—222no—
316C42—222no—
317C42C2×D4411yescharacteristic
318C42D4×D1111yescharacteristic
319C42#434311yescharacteristic
320C42C23×D1111yescharacteristic
321C11#1940311yescharacteristic, complemented, Sylow
322C23—441no—
323C23#6694811yescharacteristic
324Q8—114no—
325Q8—224no—
326Q8—222no—
327Q8—441no—
328Q8—441no—
329Q8—882no—
330Q8—882no—
331D4—442no—
332D4—441no—
333D4—441no—
334D4—881no—
335D4—882no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—224no—
339C2×C4—222no—
340C2×C4—222no—
341C2×C4—441no—
342C2×C4—442no—
343C2×C4—881no—
344C2×C4—882no—
345C2×C4—882no—
346C2×C4#6694811yescharacteristic
347C2×C4#6694811yescharacteristic
348C2×C4#6694811yescharacteristic
349C2×C4SD16×D1112yes—
350C2×C4#6696912yes—
351C2×C4C22×D4411yescharacteristic
352C2×C4C2×D4×D1111yescharacteristic
353C2×C4C2×#434311yescharacteristic
354C8—24no—
355C8—42no—
356C8—42no—
357C8—442no—
358C22—21no—
359C22—21no—
360C22—881no—
361C22—881no—
362C22—881no—
363C22#1062247712yes—
364C22C2×#6694811yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—224no—
369C4—442no—
370C4—882no—
371C4—881no—
372C4#1062247712yes—
373C4#1062328412yes—
374C4C2×SD16×D1111yescharacteristic
375C4C2×#6696911yescharacteristic
376C2—22no—
377C2—1761no—
378C2#1307814711yescharacteristic
379C2C2×#1062247711yescharacteristic
380C2#1307834511yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1570C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#1570D11
hypocenterC11#19403
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
2. C2×#10622463C2semidirect
4. #13077696C2semidirect
5. #13068033C2semidirect
6. #13067999C2semidirect
7. #13067298C2semidirect
9. C11×#1570C2semidirect
138. #1570D11semidirect
321. C11#19403semidirect

Maximal subgroups

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

subgroupindex
#130797462
C2×#106224632
#130780902
#130776962
#130680332
#130679992
#130672982
#130672662
C11×#15702
#1940311