Finite Group Databasebeta

← #14737068

Subgroups — #14737068

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079566C211yesmaximal, characteristic, complemented
2#13079559C211yesmaximal, characteristic
3C2×#10622307C211yesmaximal, characteristic
4#13077550C211yesmaximal, characteristic, complemented
5#13068185C214yesmaximal, complemented
6#13068061C214yesmaximal, complemented
7#13067300C211yesmaximal, characteristic, complemented
8#13067283C211yesmaximal, characteristic
9C11×#1564C211yesmaximal, characteristic, complemented
10C2×#66927C2211yescharacteristic
11#10623001C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C2×C4×C8×C11C2211yescharacteristic
16C2×#66885—21no—
17C2×#66885—21no—
18#10622715—21no—
19#10622714—21no—
20#10622537C2211yescharacteristic
21#10622462C2214yescomplemented
22#10622461C2214yes—
23#10622352—22no—
24#10622344—22no—
25#10622312—21no—
26#10622307—21no—
27#10622307—21no—
28#10622307—21no—
29#10622307C2212yes—
30#10622307C2212yes—
31#10622306—21no—
32#10622294—21no—
33#10622292—21no—
34#10622292C2212yescomplemented
35C8×Dic22—21no—
36C8×Dic22C2212yescomplemented
37C11×#335C2212yescomplemented
38C11×#334C2212yescomplemented
39#10622123C2214yes—
40#10622120C2214yescomplemented
41C22×D44—21no—
42C22×D44—21no—
43C22×D44—21no—
44C22×Dic22—21no—
45C22×C8×C11D411yescharacteristic
46C22×C8×C11D411yescharacteristic
47C2×C42×C11C2311yescharacteristic
48#66979—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51#66977—21no—
52#66977D412yes—
53C2×#4318—21no—
54C2×Dic44—24no—
55C2×#4314—24no—
56#66927—21no—
57#66927—21no—
58#66927—21no—
59#66927C2312yes—
60#66923—21no—
61#66922—21no—
62#66922—21no—
63#66922—21no—
64#66922D411yescharacteristic
65#66922D411yescharacteristic
66#66922C2312yes—
67C4×Dic22—21no—
68C4×Dic22C2312yes—
69C11×C4⋊C8C2312yes—
70C11×C4⋊C8C2312yes—
71C11×C22⋊C8—21no—
72C11×C22⋊C8—21no—
73C4×C8×C11—21no—
74C4×C8×C11—21no—
75C4×C8×C11D411yescharacteristic
76C4×C8×C11D411yescharacteristic
77C4×C8×C11C2311yescharacteristic
78C4×C8×C11C2311yescharacteristic
79#66885—22no—
80#66885—22no—
81#66885—22no—
82#66885—22no—
83#66885—24no—
84#66880—24no—
85#66879—22no—
86Dic11⋊C8—22no—
87Dic11⋊C8—22no—
88C8×Dic11—22no—
89C4⋊(C11⋊C8)—21no—
90C4⋊(C11⋊C8)C2312yes—
91#19214—111nomaximal, Sylow
92C23×D11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C22×Dic11—41no—
97C2×D44—22no—
98C2×D44—22no—
99C2×D44—22no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—42no—
104C2×D44—42no—
105C2×D44—82no—
106C2×D44—82no—
107C2×Dic22—21no—
108C2×Dic22—22no—
109C2×Dic22—41no—
110C2×Dic22—82no—
111C2×Dic22C2×D412yes—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11#4111yescharacteristic
123C42×C11C2411yescharacteristic
124C22⋊Dic11—22no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—41no—
131C4⋊Dic11—41no—
132C4⋊Dic11C2×D412yes—
133Dic11⋊C4—22no—
134Dic11⋊C4—22no—
135C4×Dic11—22no—
136#4318—42no—
137C2×C11⋊C8—22no—
138Dic44—84no—
139#4314—84no—
140#3209—111no—
141#3208—111no—
142C2×#486—111no—
143#2960—111no—
144#1702—114no—
145#1682—114no—
146#1564D1111yescharacteristic, complemented
147#1549—111no—
148#1545—111no—
149C23×C11#12111yescharacteristic
150C22×D11—42no—
151C22×D11—82no—
152C22×D11—82no—
153C22×D11—82no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#13512yes—
160C2×C4×C11#13712yes—
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C2×#4111yescharacteristic
164C2×Dic11—22no—
165C2×Dic11—22no—
166C2×Dic11—42no—
167C2×Dic11—82no—
168D44—42no—
169D44—42no—
170D44—44no—
171D44—82no—
172D44—82no—
173D44—82no—
174D44—82no—
175Dic22—24no—
176Dic22—42no—
177Dic22—44no—
178Dic22—82no—
179C8×C11—21no—
180C8×C11—21no—
181C8×C11—21no—
182C8×C11—21no—
183C8×C11—42no—
184C8×C11—42no—
185C11⋊C8—42no—
186#533—111no—
187C2×C4⋊Q8—111no—
188C2×#127—111no—
189#494—221no—
190#492—221no—
191#487—221no—
192#486—112no—
193#486—112no—
194#486—221no—
195#486—221no—
196#486—221no—
197#462—114no—
198#460—114no—
199#451—222no—
200#450—222no—
201#446—112no—
202#446—221no—
203C8×Q8—112no—
204C8×Q8—221no—
205#431C2×D1111yescharacteristic
206#431C2×D1111yescharacteristic
207#424—221no—
208#423—111no—
209C2×#102—221no—
210C2×#102—221no—
211#405—221no—
212C2×C4×C8C2×D1111yescharacteristic
213#335C2×D1112yescomplemented
214#334C2×D1112yescomplemented
215#332—114no—
216#331—114no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11#46412yes—
220C22×C11C2×#12111yescharacteristic
221C2×D11—82no—
222C2×D11—82no—
223C2×D11—82no—
224C2×D11—164no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11#46412yes—
228C4×C11#47112yes—
229C4×C11C2×#13511yescharacteristic
230C4×C11C2×#13711yescharacteristic
231C4×C11#57612yes—
232Dic11—42no—
233Dic11—42no—
234Dic11—82no—
235C22×Q8—221no—
236C22×D4—221no—
237C22×D4—221no—
238C22×D4—221no—
239C2×Q16—224no—
240C2×SD16—224no—
241C2×M16—221no—
242C22×C8D4411yescharacteristic
243C22×C8D4411yescharacteristic
244C4⋊Q8—111no—
245C4⋊Q8—111no—
246C4⋊Q8—112no—
247C4⋊Q8—221no—
248C4⋊Q8—221no—
249C4⋊Q8—221no—
250#127—112no—
251#127—221no—
252#127—221no—
253#127—221no—
254#125—221no—
255C22⋊Q8—112no—
256C22⋊Q8—221no—
257C4×Q8—112no—
258C4×Q8—221no—
259#117—221no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C42C22×D1111yescharacteristic
263C4⋊C8—112no—
264C4⋊C8—222no—
265C4⋊C8—222no—
266C4⋊C8—221no—
267C4⋊C8C22×D1112yes—
268C4⋊C8C22×D1112yes—
269#103—224no—
270#102—224no—
271#102—222no—
272#102—222no—
273#102—222no—
274#102—222no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277#97—222no—
278C4×C8—21no—
279C4×C8—21no—
280C4×C8—222no—
281C4×C8D4411yescharacteristic
282C4×C8D4411yescharacteristic
283C4×C8C22×D1111yescharacteristic
284C4×C8C22×D1111yescharacteristic
285C2×C11—22no—
286C2×C11C2×#46411yescharacteristic
287C2×C11#305811yescharacteristic
288C2×C11C2×#47111yescharacteristic
289D11—162no—
290C24—441no—
291C2×Q8—112no—
292C2×Q8—221no—
293C2×Q8—222no—
294C2×Q8—441no—
295C2×Q8—882no—
296C2×D4—222no—
297C2×D4—222no—
298C2×D4—222no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—441no—
302C2×D4—442no—
303C2×D4—442no—
304C2×D4—882no—
305C2×D4—882no—
306C22×C4—441no—
307C22×C4C2×D4411yescharacteristic
308C22×C4D4×D1111yescharacteristic
309C22×C4#434311yescharacteristic
310Q16—884no—
311SD16—884no—
312M16—442no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—222no—
318C2×C8C2×D4411yescharacteristic
319C2×C8C2×D4411yescharacteristic
320C2×C8C2×D4411yescharacteristic
321C2×C8C2×D4411yescharacteristic
322C4⋊C4—112no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C4⋊C4—222no—
326C4⋊C4—221no—
327C4⋊C4—222no—
328C4⋊C4—222no—
329C4⋊C4—222no—
330C4⋊C4—441no—
331C4⋊C4—441no—
332C22⋊C4—222no—
333C42—222no—
334C42C2×D4411yescharacteristic
335C42D4×D1111yescharacteristic
336C42#434311yescharacteristic
337C42C23×D1111yescharacteristic
338C11#1921411yescharacteristic, complemented, Sylow
339C23—442no—
340C23—882no—
341C23—882no—
342C23—882no—
343C23#6694811yescharacteristic
344Q8—224no—
345Q8—442no—
346Q8—444no—
347Q8—882no—
348D4—442no—
349D4—442no—
350D4—444no—
351D4—882no—
352D4—882no—
353D4—882no—
354D4—882no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—222no—
358C2×C4—222no—
359C2×C4—442no—
360C2×C4—882no—
361C2×C4#6694811yescharacteristic
362C2×C4#6694811yescharacteristic
363C2×C4#6694811yescharacteristic
364C2×C4#6695712yes—
365C2×C4#6696212yes—
366C2×C4C22×D4411yescharacteristic
367C2×C4C2×D4×D1111yescharacteristic
368C2×C4C2×#434311yescharacteristic
369C8—21no—
370C8—21no—
371C8—21no—
372C8—21no—
373C8—42no—
374C8—42no—
375C8—442no—
376C22—21no—
377C22—21no—
378C22—882no—
379C22—882no—
380C22—882no—
381C22—1764no—
382C22#1062245812yes—
383C22C2×#6694811yescharacteristic
384C4—21no—
385C4—21no—
386C4—442no—
387C4—442no—
388C4—882no—
389C4#1062245812yes—
390C4#1062251112yes—
391C4C2×#6695711yescharacteristic
392C4C2×#6696211yescharacteristic
393C4#1062330012yes—
394C2—22no—
395C2—1762no—
396C2C2×#1062245811yescharacteristic
397C2#1307826511yescharacteristic
398C2C2×#1062251111yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1564C2
socleC22×C11C2×#121
prime radicalC2×#66927C22
hypercenter#1564D11
hypocenterC11#19214
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
1. #13079566C2semidirect
4. #13077550C2semidirect
5. #13068185C2semidirect
6. #13068061C2semidirect
7. #13067300C2semidirect
9. C11×#1564C2semidirect
21. #10622462C22semidirect
34. #10622292C22semidirect
36. C8×Dic22C22semidirect
37. C11×#335C22semidirect
38. C11×#334C22semidirect
40. #10622120C22semidirect
146. #1564D11semidirect
213. #335C2×D11semidirect
214. #334C2×D11semidirect
338. C11#19214semidirect

Maximal subgroups

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

subgroupindex
#130795662
#130795592
C2×#106223072
#130775502
#130681852
#130680612
#130673002
#130672832
C11×#15642
#1921411