Finite Group Databasebeta

← #14739052

Subgroups — #14739052

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079554C211yesmaximal, characteristic
2#13078417C211yesmaximal, characteristic, complemented
3C2×#10622461C211yesmaximal, characteristic
4#13077696C211yesmaximal, characteristic, complemented
5#13068035C214yesmaximal, complemented
6#13067967C214yesmaximal, complemented
7#13067386C211yesmaximal, characteristic, complemented
8#13067283C211yesmaximal, characteristic
9C11×#1542C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C22×#4314—21no—
12C2×#66927C2211yescharacteristic
13C2×C4×Dic22C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×#66885—21no—
17#10622707C2212yescomplemented
18#10622704C2212yescomplemented
19#10622701C2212yes—
20#10622698C2212yes—
21#10622676—22no—
22#10622659—22no—
23#10622640—22no—
24#10622617—21no—
25#10622608—21no—
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622461—22no—
29#10622461C2214yes—
30#10622443C2214yescomplemented
31#10622331—22no—
32C8×Dic22—22no—
33C11×#333C2212yescomplemented
34C11×#332C2212yescomplemented
35#10622123C2214yes—
36#10622118C2214yescomplemented
37C22×D44—21no—
38C22×D44—21no—
39C22×D44—21no—
40C22×Dic22D411yescharacteristic
41C22×C8×C11—21no—
42C11×C4⋊Q8C2311yescharacteristic
43C11×C4⋊Q8C2311yescharacteristic
44C11×#125—21no—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C11×#117—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4325—24no—
52C2×C4⋊Dic11D411yescharacteristic
53C2×Dic11⋊C4—21no—
54C2×C4×Dic11—21no—
55C2×#4318—21no—
56C2×#4314—24no—
57C2×#4314—44no—
58#66927—21no—
59#66927—21no—
60#66927—21no—
61#66927C2312yes—
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—24no—
73Dic11⋊C8—24no—
74C8×Dic11—24no—
75#66874—22no—
76#66874—22no—
77#66873—24no—
78#66872—22no—
79#66871—22no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)D412yes—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8C2312yes—
84#19396—111nomaximal, Sylow
85C23×D11—41no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×Dic11—21no—
92C22×Dic11—21no—
93C2×D44—22no—
94C2×D44—22no—
95C2×D44—22no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44—42no—
100C2×D44—42no—
101C2×D44—82no—
102C2×D44—82no—
103C2×Dic22—21no—
104C2×Dic22—22no—
105C2×Dic22SD1614yescomplemented
106C2×Dic22C2×D412yes—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—42no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C22⋊C4—41no—
117C42×C11—41no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11#4111yescharacteristic
121C42×C11C2411yescharacteristic
122#4325—84no—
123C4⋊Dic11—21no—
124C4⋊Dic11C2×D412yes—
125Dic11⋊C4—22no—
126Dic11⋊C4—22no—
127C4×Dic11—22no—
128C4×Dic11—22no—
129#4318—42no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8C2×D414yes—
132#4314—48no—
133#3208—111no—
134#3078—111no—
135C2×#460—111no—
136#2982—111no—
137#1678—114no—
138#1666—114no—
139#1570—111no—
140#1545—111no—
141#1542D1111yescharacteristic, complemented
142C23×C11#12111yescharacteristic
143C22×D11—42no—
144C22×D11—82no—
145C22×D11—82no—
146C22×D11—82no—
147Q8×C11—42no—
148Q8×C11—81no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11C2×SD1612yes—
157C2×C4×C11#13512yes—
158C2×C4×C11C22×D411yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C2×C4×C11C2×#4111yescharacteristic
161C2×Dic11—22no—
162C2×Dic11—24no—
163C2×Dic11—22no—
164C2×Dic11—81no—
165D44—42no—
166D44—42no—
167D44—44no—
168D44—82no—
169D44—82no—
170D44—82no—
171D44—82no—
172Dic22—22no—
173Dic22—24no—
174Dic22C2×SD1614yes—
175C8×C11—42no—
176C8×C11—42no—
177C11⋊C8—24no—
178C11⋊C8—42no—
179C22×SD16—221no—
180#533C2×D1111yescharacteristic
181C2×#127—111no—
182C2×C4×Q8—111no—
183#492—112no—
184#486—112no—
185#479—222no—
186#477—112no—
187#475—112no—
188#460—114no—
189#460—222no—
190#460—222no—
191#450—222no—
192C8×Q8—114no—
193C8×Q8—222no—
194#431—111no—
195#431—222no—
196#431C2×D1111yescharacteristic
197#428—221no—
198#423—111no—
199C2×C4⋊C8C2×D1111yescharacteristic
200#419—221no—
201C2×#102—221no—
202#334—114no—
203#333C2×D1112yescomplemented
204#332C2×D1112yescomplemented
205#331—114no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11#46512yes—
209C22×C11C2×#12111yescharacteristic
210C2×D11—82no—
211C2×D11—82no—
212C2×D11—82no—
213C2×D11—164no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—81no—
218C4×C11—81no—
219C4×C11#46512yes—
220C4×C11C22×SD1611yescharacteristic
221C4×C11C2×#13511yescharacteristic
222C4×C11#57712yes—
223Dic11—24no—
224Dic11—42no—
225C22×Q8—111no—
226C22×D4—221no—
227C22×D4—221no—
228C22×D4—221no—
229C2×SD16—224no—
230C2×SD16—224no—
231C2×SD16—444no—
232C2×M16—221no—
233C22×C8—21no—
234C4⋊Q8C22×D1111yescharacteristic
235C4⋊Q8C22×D1111yescharacteristic
236#127—112no—
237#127—221no—
238#127—221no—
239#127—221no—
240#125—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—112no—
246C4×Q8—112no—
247C4×Q8—221no—
248C4×Q8—221no—
249#117—21no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—221no—
252C2×C42—221no—
253C2×C42C22×D1111yescharacteristic
254#107—222no—
255#106—222no—
256C4⋊C8—21no—
257C4⋊C8—112no—
258C4⋊C8—112no—
259C4⋊C8—224no—
260C4⋊C8—221no—
261C4⋊C8C22×D1112yes—
262C4⋊C8C22×D1112yes—
263#103—222no—
264#103—222no—
265#102—224no—
266#102—224no—
267C22⋊C8—21no—
268C22⋊C8—112no—
269C4×C8—21no—
270C4×C8—112no—
271C4×C8—224no—
272C2×C11—22no—
273C2×C11#304311yescharacteristic
274C2×C11C2×#46511yescharacteristic
275C2×C11#306811yescharacteristic
276D11—162no—
277C24—441no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—114no—
281C2×Q8—112no—
282C2×Q8—221no—
283C2×Q8—222no—
284C2×D4—222no—
285C2×D4—222no—
286C2×D4—222no—
287C2×D4—441no—
288C2×D4—441no—
289C2×D4—441no—
290C2×D4—442no—
291C2×D4—442no—
292C2×D4—882no—
293C2×D4—882no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4#433911yescharacteristic
297C22×C4D4×D1111yescharacteristic
298C22×C4D4×D1111yescharacteristic
299SD16—448no—
300SD16—884no—
301M16—442no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—42no—
305C2×C8—114no—
306C2×C8—222no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—112no—
314C4⋊C4—221no—
315C4⋊C4—222no—
316C4⋊C4—222no—
317C22⋊C4—41no—
318C42—41no—
319C42—222no—
320C42—222no—
321C42#433911yescharacteristic
322C42D4×D1111yescharacteristic
323C42D4×D1111yescharacteristic
324C42C23×D1111yescharacteristic
325C11#1939611yescharacteristic, complemented, Sylow
326C23—442no—
327C23—882no—
328C23—882no—
329C23—882no—
330C23#6693711yescharacteristic
331Q8—42no—
332Q8—81no—
333Q8—114no—
334Q8—222no—
335Q8—224no—
336D4—442no—
337D4—442no—
338D4—444no—
339D4—882no—
340D4—882no—
341D4—882no—
342D4—882no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—222no—
348C2×C4—224no—
349C2×C4—222no—
350C2×C4—881no—
351C2×C4#6693711yescharacteristic
352C2×C4#6693711yescharacteristic
353C2×C4#6693711yescharacteristic
354C2×C4SD16×D1112yes—
355C2×C4#6697212yes—
356C2×C4C2×#433911yescharacteristic
357C2×C4C2×D4×D1111yescharacteristic
358C2×C4C2×D4×D1111yescharacteristic
359C8—42no—
360C8—42no—
361C8—224no—
362C8—442no—
363C22—21no—
364C22—21no—
365C22—882no—
366C22—882no—
367C22—882no—
368C22—1764no—
369C22#1062242012yes—
370C22C2×#6693711yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—81no—
375C4—81no—
376C4—224no—
377C4—442no—
378C4#1062242012yes—
379C4C2×SD16×D1111yescharacteristic
380C4C2×#6697211yescharacteristic
381C4#1062330112yes—
382C2—22no—
383C2—1762no—
384C2#1307814011yescharacteristic
385C2C2×#1062242011yescharacteristic
386C2#1307834711yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1542C2
socleC22×C11C2×#121
prime radicalC2×#66927C22
hypercenter#1542D11
hypocenterC11#19396
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
2. #13078417C2semidirect
4. #13077696C2semidirect
5. #13068035C2semidirect
6. #13067967C2semidirect
7. #13067386C2semidirect
9. C11×#1542C2semidirect
17. #10622707C22semidirect
18. #10622704C22semidirect
30. #10622443C22semidirect
33. C11×#333C22semidirect
34. C11×#332C22semidirect
36. #10622118C22semidirect
105. C2×Dic22SD16semidirect
141. #1542D11semidirect
203. #333C2×D11semidirect
204. #332C2×D11semidirect
325. C11#19396semidirect

Maximal subgroups

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

subgroupindex
#130795542
#130784172
C2×#106224612
#130776962
#130680352
#130679672
#130673862
#130672832
C11×#15422
#1939611