Finite Group Databasebeta

← #14739316

Subgroups — #14739316

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079554C211yesmaximal, characteristic, complemented
2#13078409C211yesmaximal, characteristic, complemented
3C2×#10622456C211yesmaximal, characteristic
4#13077656C211yesmaximal, characteristic, complemented
5#13068152C214yesmaximal, complemented
6#13068084C214yesmaximal, complemented
7#13067390C211yesmaximal, characteristic, complemented
8#13067283C211yesmaximal, characteristic, complemented
9C11×#1542C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C22×D88—21no—
12C2×#66927C2211yescharacteristic
13C2×C4×D44C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×#66885—21no—
17#10622701C2212yescomplemented
18#10622700C2212yescomplemented
19#10622698C2212yescomplemented
20#10622697C2212yescomplemented
21#10622679—22no—
22#10622659—22no—
23#10622640—22no—
24#10622614—21no—
25#10622608—21no—
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622456—22no—
29#10622456C2214yes—
30#10622451C2214yescomplemented
31#10622339—22no—
32#10622301—22no—
33C11×#333C2212yescomplemented
34C11×#332C2212yescomplemented
35#10622123C2214yescomplemented
36#10622117C2214yescomplemented
37C22×D44—21no—
38C22×D44—21no—
39C22×D44—21no—
40C22×D44D411yescharacteristic
41C22×C4×D11—21no—
42C22×C8×C11—21no—
43C11×C4⋊Q8C2311yescharacteristic
44C11×C4⋊Q8C2311yescharacteristic
45C11×#125—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C11×#117—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4325—24no—
53C2×(C2×D11)⋊C4—21no—
54C2×C4⋊Dic11D411yescharacteristic
55C2×#4318—21no—
56C2×D88—24no—
57C2×D88—44no—
58C2×#4313—24no—
59#66927—21no—
60#66927—21no—
61#66927—21no—
62#66927C2312yes—
63C4×D44—21no—
64C4×D44—21no—
65C4×D44D412yes—
66C4×D44C2312yes—
67C11×C4⋊C8—21no—
68C11×C4⋊C8C2312yes—
69C11×C4⋊C8C2312yes—
70C11×C22⋊C8—21no—
71C4×C8×C11—21no—
72C22⋊(C11⋊C8)D412yes—
73#66885—24no—
74(C2×D11)⋊C8—24no—
75#66873—22no—
76#66873—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#19420—111nomaximal, Sylow
85C23×D11—21no—
86C23×D11—41no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×Dic11—21no—
93C2×D44—21no—
94C2×D44—22no—
95C2×D44—22no—
96C2×D44—22no—
97C2×D44—22no—
98C2×D44—22no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—42no—
103C2×D44—42no—
104C2×D44—82no—
105C2×D44—82no—
106C2×D44C2×D412yes—
107C2×C4×D11—22no—
108C2×C4×D11—22no—
109C2×C4×D11—82no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—42no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—41no—
120C42×C11—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11#4111yescharacteristic
124C42×C11C2411yescharacteristic
125#4325—84no—
126(C2×D11)⋊C4—22no—
127(C2×D11)⋊C4—22no—
128C4⋊Dic11—21no—
129C4⋊Dic11C2×D412yes—
130#4318—42no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8C2×D414yes—
133D88—48no—
134#4313—84no—
135#3208—111no—
136#3077—111no—
137C2×#459—111no—
138#2975—111no—
139#1697—114no—
140#1685—114no—
141#1571—111no—
142#1545—111no—
143#1542D1111yescharacteristic, complemented
144C23×C11#12111yescharacteristic
145C22×D11—22no—
146C22×D11—42no—
147C22×D11—42no—
148C22×D11—81no—
149C22×D11—81no—
150C22×D11—82no—
151C22×D11—82no—
152C22×D11—82no—
153Q8×C11—42no—
154Q8×C11—81no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11AGL(1,ℤ/8)12yes—
163C2×C4×C11#13712yes—
164C2×C4×C11C22×D411yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C2×#4111yescharacteristic
167C2×Dic11—22no—
168C2×Dic11—81no—
169D44—22no—
170D44—22no—
171D44—42no—
172D44—42no—
173D44—44no—
174D44—42no—
175D44—82no—
176D44—82no—
177D44—82no—
178D44—82no—
179C4×D11—44no—
180C4×D11—82no—
181C8×C11—42no—
182C8×C11—42no—
183C11⋊C8—24no—
184C11⋊C8—42no—
185C22×D8—221no—
186#533C2×D1111yescharacteristic
187C2×#127—111no—
188C2×C4×D4—111no—
189#492—112no—
190#486—112no—
191#478—222no—
192#476—112no—
193#474—112no—
194#460—222no—
195#459—114no—
196#459—222no—
197#450—222no—
198#436—114no—
199#436—222no—
200#431—111no—
201#431C2×D1111yescharacteristic
202#428—221no—
203#423—111no—
204C2×C4⋊C8C2×D1111yescharacteristic
205#418—221no—
206C2×#102—221no—
207#407—222no—
208#335—114no—
209#333C2×D1112yescomplemented
210#332C2×D1112yescomplemented
211#331—114no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11#46812yes—
215C22×C11C2×#12111yescharacteristic
216C2×D11—42no—
217C2×D11—42no—
218C2×D11—42no—
219C2×D11—84no—
220C2×D11—82no—
221C2×D11—82no—
222C2×D11—82no—
223C2×D11—164no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—81no—
228C4×C11—81no—
229C4×C11#46812yes—
230C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
231C4×C11C2×#13711yescharacteristic
232C4×C11#57612yes—
233Dic11—42no—
234C22×D4—111no—
235C22×D4—221no—
236C22×D4—221no—
237C22×D4—221no—
238C23×C4—221no—
239C2×SD16—224no—
240C2×D8—224no—
241C2×D8—444no—
242C2×M16—224no—
243C2×M16—221no—
244C22×C8—21no—
245C4⋊Q8C22×D1111yescharacteristic
246C4⋊Q8C22×D1111yescharacteristic
247#127—112no—
248#127—221no—
249#127—221no—
250#127—221no—
251#125—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×D4—112no—
257C4×D4—112no—
258C4×D4—221no—
259C4×D4—221no—
260#117—21no—
261C2×C4⋊C4—111no—
262C2×C22⋊C4—221no—
263C2×C42C22×D1111yescharacteristic
264#107—222no—
265#106—222no—
266C4⋊C8—21no—
267C4⋊C8—112no—
268C4⋊C8—112no—
269C4⋊C8—221no—
270C4⋊C8C22×D1112yes—
271C4⋊C8C22×D1112yes—
272#102—224no—
273#102—222no—
274#102—222no—
275#102—224no—
276C22⋊C8—21no—
277C22⋊C8—112no—
278C22⋊C8—224no—
279C4×C8—21no—
280C4×C8—112no—
281C2×C11—22no—
282C2×C11#304111yescharacteristic
283C2×C11C2×#46811yescharacteristic
284C2×C11#306811yescharacteristic
285D11—82no—
286D11—162no—
287C24—221no—
288C24—441no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×D4—112no—
292C2×D4—221no—
293C2×D4—222no—
294C2×D4—222no—
295C2×D4—222no—
296C2×D4—222no—
297C2×D4—222no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—442no—
302C2×D4—442no—
303C2×D4—882no—
304C2×D4—882no—
305C22×C4—221no—
306C22×C4—222no—
307C22×C4—222no—
308C22×C4—882no—
309C22×C4#433911yescharacteristic
310C22×C4D4×D1111yescharacteristic
311C22×C4D4×D1111yescharacteristic
312SD16—884no—
313D8—448no—
314M16—442no—
315M16—884no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—42no—
319C2×C8—114no—
320C2×C8—222no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—112no—
328C4⋊C4—221no—
329C22⋊C4—41no—
330C22⋊C4—222no—
331C22⋊C4—222no—
332C42—41no—
333C42#433911yescharacteristic
334C42D4×D1111yescharacteristic
335C42D4×D1111yescharacteristic
336C42C23×D1111yescharacteristic
337C11#1942011yescharacteristic, complemented, Sylow
338C23—222no—
339C23—442no—
340C23—442no—
341C23—881no—
342C23—881no—
343C23—882no—
344C23—882no—
345C23—882no—
346C23#6693711yescharacteristic
347Q8—42no—
348Q8—81no—
349D4—222no—
350D4—222no—
351D4—442no—
352D4—442no—
353D4—444no—
354D4—442no—
355D4—882no—
356D4—882no—
357D4—882no—
358D4—882no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—222no—
364C2×C4—444no—
365C2×C4—882no—
366C2×C4—881no—
367C2×C4#6693711yescharacteristic
368C2×C4#6693711yescharacteristic
369C2×C4#6693711yescharacteristic
370C2×C4#6696712yes—
371C2×C4#6697112yes—
372C2×C4C2×#433911yescharacteristic
373C2×C4C2×D4×D1111yescharacteristic
374C2×C4C2×D4×D1111yescharacteristic
375C8—42no—
376C8—42no—
377C8—224no—
378C8—442no—
379C22—21no—
380C22—21no—
381C22—442no—
382C22—442no—
383C22—442no—
384C22—884no—
385C22—882no—
386C22—882no—
387C22—882no—
388C22—1764no—
389C22#1062242512yes—
390C22C2×#6693711yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—81no—
395C4—81no—
396C4—442no—
397C4#1062242512yes—
398C4C2×#6696711yescharacteristic
399C4C2×#6697111yescharacteristic
400C4#1062330012yes—
401C2—22no—
402C2—882no—
403C2—1762no—
404C2#1307812211yescharacteristic
405C2C2×#1062242511yescharacteristic
406C2#1307834711yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1542C2
socleC22×C11C2×#121
prime radicalC2×#10622456C2
hypercenter#1542D11
hypocenterC11#19420
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
1. #13079554C2semidirect
2. #13078409C2semidirect
4. #13077656C2semidirect
5. #13068152C2semidirect
6. #13068084C2semidirect
7. #13067390C2semidirect
8. #13067283C2semidirect
9. C11×#1542C2semidirect
17. #10622701C22semidirect
18. #10622700C22semidirect
19. #10622698C22semidirect
20. #10622697C22semidirect
30. #10622451C22semidirect
33. C11×#333C22semidirect
34. C11×#332C22semidirect
35. #10622123C22semidirect
36. #10622117C22semidirect
143. #1542D11semidirect
209. #333C2×D11semidirect
210. #332C2×D11semidirect
337. C11#19420semidirect

Maximal subgroups

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

subgroupindex
#130795542
#130784092
C2×#106224562
#130776562
#130681522
#130680842
#130673902
#130672832
C11×#15422
#1942011