Finite Group Databasebeta

← #14745259

Subgroups — #14745259

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081602C211yesmaximal, characteristic, complemented
2#13080847C212yesmaximal, complemented
3#13068221C211yesmaximal, characteristic, complemented
4#13068175C212yesmaximal, complemented
5#13067981C211yesmaximal, characteristic, complemented
6#13067973C211yesmaximal, characteristic, complemented
7#13067795C212yesmaximal, complemented
8#13067724C212yesmaximal, complemented
9#13067501C211yesmaximal, characteristic, complemented
10C8×#4324C211yesmaximal, characteristic, complemented
11D4×C11×D8C211yesmaximal, characteristic
12C22×C11×D8—21no—
13D42×C11C2212yes—
14#10623073C2212yescomplemented
15C11×#493C2211yescharacteristic
16C11×#466—21no—
17C11×#459C2212yes—
18C11×#447—22no—
19C4×C11×D8C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622831—22no—
22#10622828—22no—
23#10622768—21no—
24#10622688C2212yescomplemented
25#10622683C2212yescomplemented
26#10622683C2212yescomplemented
27#10622655—22no—
28#10622648—22no—
29#10622632C2212yescomplemented
30C4×#4324C2211yescharacteristic
31#10622625C2212yescomplemented
32#10622620C2212yes—
33#10622486—21no—
34#10622380—22no—
35#10622312C2211yescharacteristic, complemented
36C8×Dic22C2211yescharacteristic, complemented
37#10622182C2212yescomplemented
38D4⋊(C11⋊C8)C2211yescharacteristic
39D4⋊(C11⋊C8)C2212yescomplemented
40#10622122C2211yescharacteristic, complemented
41#10622120C2212yescomplemented
42#10622118C2211yescharacteristic, complemented
43#10622096C2211yescharacteristic, complemented
44C8×C11⋊C8C2211yescharacteristic, complemented
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C2×C11×D8—22no—
48C2×C11×D8—21no—
49C2×C11×D8—21no—
50C2×C11×D8—44no—
51C2×C11×D8D411yescharacteristic
52C22×C8×C11—21no—
53C11×#127C2312yes—
54C11×#121—22no—
55C11×#121—22no—
56C11×#120—42no—
57C4×D4×C11C2312yes—
58C4×D4×C11C2311yescharacteristic
59#66989—22no—
60C2×#4324—22no—
61C2×#4324—22no—
62C2×#4324D411yescharacteristic
63#66979—22no—
64#66977—22no—
65C2×#4318—22no—
66C2×Dic44—21no—
67C2×Dic44—21no—
68#66940—22no—
69#66932—42no—
70#66922C2312yes—
71C4×Dic22C2311yescharacteristic
72C11×#107D411yescharacteristic
73C11×C4⋊C8C2311yescharacteristic
74C11×#102—22no—
75C11×#102D412yes—
76C11×C22⋊C8—21no—
77C4×C8×C11C2311yescharacteristic
78#66896—22no—
79#66896—22no—
80#66896—22no—
81#66896—22no—
82#66896—42no—
83#66896D411yescharacteristic
84C22⋊(C11⋊C8)—22no—
85Dic11⋊C8—21no—
86C8×Dic11—21no—
87#66874—22no—
88#66874D411yescharacteristic
89#66872D411yescharacteristic
90#66871—22no—
91C4⋊(C11⋊C8)C2311yescharacteristic
92C4⋊(C11⋊C8)C2312yes—
93C4×C11⋊C8C2311yescharacteristic
94C4×C11⋊C8C2311yescharacteristic
95#19900—111nomaximal, Sylow
96C24×C11—42no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—42no—
101C2×D4×C11—42no—
102C2×D4×C11—44no—
103C2×D4×C11—44no—
104C2×D4×C11—82no—
105C2×D4×C11—82no—
106C2×D4×C11C2×D412yes—
107C2×D4×C11C2×D411yescharacteristic
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C2×Dic22—22no—
111C2×Dic22C2×D411yescharacteristic
112C11×D8—22no—
113C11×D8—44no—
114C11×D8—42no—
115C11×D8—81no—
116C2×C8×C11—21no—
117C2×C8×C11—42no—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C11×C4⋊C4C2×D411yescharacteristic
121C11×C4⋊C4C2×D412yes—
122C11×C22⋊C4—22no—
123C11×C22⋊C4—21no—
124C11×C22⋊C4—42no—
125C42×C11C2411yescharacteristic
126C22⋊Dic11—42no—
127C22⋊Dic11—42no—
128#4324—22no—
129#4324—82no—
130#4324—82no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11C2×D411yescharacteristic
134Dic11⋊C4—21no—
135Dic11⋊C4—42no—
136C4×Dic11—21no—
137C4×Dic11—42no—
138#4318—82no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8C2×D411yescharacteristic
143C2×C11⋊C8C2×D411yescharacteristic
144Dic44—42no—
145Dic44—81no—
146#3393—111no—
147#3324—112no—
148D4×D8D1111yescharacteristic
149#1709—111no—
150#1701—112no—
151#1669—111no—
152#1668—111no—
153#1639—112no—
154#1628—112no—
155#1589—111no—
156C8×SD16—111no—
157C23×C11—21no—
158C23×C11—22no—
159C23×C11—42no—
160C23×C11—84no—
161C23×C11—84no—
162C23×C11—162no—
163D4×C11—22no—
164D4×C11—21no—
165D4×C11—22no—
166D4×C11—42no—
167D4×C11—42no—
168D4×C11—42no—
169D4×C11—42no—
170D4×C11—82no—
171D4×C11—84no—
172D4×C11—84no—
173D4×C11#13512yes—
174C2×C4×C11—22no—
175C2×C4×C11—21no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11H(5,𝔽2)11yescharacteristic
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—42no—
186Dic22—21no—
187Dic22—21no—
188Dic22—42no—
189Dic22—42no—
190C8×C11—21no—
191C8×C11—41no—
192C8×C11AGL(1,ℤ/8)12yes—
193C11⋊C8—21no—
194C11⋊C8—21no—
195C11⋊C8—41no—
196C11⋊C8—42no—
197C11⋊C8—41no—
198C22×D8—21no—
199#556—112no—
200D42C2×D1112yes—
201#495—221no—
202#494—111no—
203#493C2×D1111yescharacteristic
204#486—112no—
205#486—112no—
206#482—222no—
207#474—112no—
208#468—222no—
209#466—21no—
210#464—222no—
211#461—112no—
212#460—112no—
213#459C2×D1112yes—
214#450—222no—
215#447—22no—
216C8×Q8—111no—
217C4×Q16—221no—
218C4×SD16—111no—
219C4×D8C2×D1111yescharacteristic
220#436—112no—
221C8×D4C2×D1111yescharacteristic
222#418—222no—
223#335—111no—
224#334—111no—
225#332—112no—
226#331—112no—
227Q8⋊C8—111no—
228D4⋊C8—111no—
229D4⋊C8—112no—
230C82—111no—
231C22×C11—22no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11—168no—
241C22×C11D4211yescharacteristic
242C4×C11—21no—
243C4×C11—41no—
244C4×C11—42no—
245C4×C11C2×#13511yescharacteristic
246C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
247C4×C11#57611yescharacteristic
248C4×C11#57611yescharacteristic
249Dic11—41no—
250Dic11—41no—
251Dic11—82no—
252C22×D4—22no—
253C22×D4—22no—
254C2×Q16—221no—
255C2×Q16—221no—
256C2×SD16—111no—
257C2×SD16—222no—
258C2×SD16—222no—
259C2×D8—22no—
260C2×D8—21no—
261C2×D8—21no—
262C2×D8—44no—
263C2×D8C22⋊D1111yescharacteristic
264C2×M16—222no—
265C22×C8—21no—
266C4⋊Q8—112no—
267#127C22×D1112yes—
268#126—442no—
269#124—222no—
270C22⋊Q8—222no—
271#121—22no—
272#121—22no—
273#120—42no—
274C4×Q8—111no—
275C4×Q8—222no—
276C4×D4C22×D1111yescharacteristic
277C4×D4C22×D1112yes—
278#117—222no—
279#107—222no—
280#107C22⋊D1111yescharacteristic
281#106—111no—
282C4⋊C8—111no—
283C4⋊C8—112no—
284C4⋊C8—221no—
285C4⋊C8C22×D1111yescharacteristic
286#103—111no—
287#103—222no—
288#102—22no—
289#102—111no—
290#102—222no—
291#102—222no—
292#102—222no—
293#102—222no—
294#102—442no—
295#102C22⋊D1112yes—
296C22⋊C8—21no—
297C22⋊C8—222no—
298C4×C8—111no—
299C4×C8—111no—
300C4×C8—221no—
301C4×C8C22×D1111yescharacteristic
302C2×C11—42no—
303C2×C11—82no—
304C2×C11—162no—
305C2×C11#327411yescharacteristic
306C2×C11#328011yescharacteristic
307C2×C11#329011yescharacteristic
308C24—42no—
309C2×Q8—111no—
310C2×Q8—222no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—44no—
317C2×D4—44no—
318C2×D4—82no—
319C2×D4—82no—
320C2×D4D4×D1111yescharacteristic
321C2×D4C2×C22⋊D1112yes—
322C22×C4—22no—
323C22×C4—21no—
324Q16—442no—
325Q16—881no—
326SD16—222no—
327SD16—882no—
328SD16—882no—
329D8—22no—
330D8—44no—
331D8—42no—
332D8—81no—
333M16—882no—
334C2×C8—21no—
335C2×C8—42no—
336C2×C8—111no—
337C2×C8—111no—
338C2×C8—222no—
339C2×C8—221no—
340C2×C8—221no—
341C2×C8C2×C22⋊D1111yescharacteristic
342C2×C8C2×C22⋊D1111yescharacteristic
343C4⋊C4—111no—
344C4⋊C4—221no—
345C4⋊C4—222no—
346C4⋊C4—222no—
347C4⋊C4—442no—
348C4⋊C4D4×D1111yescharacteristic
349C4⋊C4C2×C22⋊D1112yes—
350C22⋊C4—21no—
351C22⋊C4—22no—
352C22⋊C4—42no—
353C22⋊C4—442no—
354C22⋊C4—442no—
355C42—221no—
356C42—442no—
357C42C23×D1111yescharacteristic
358C11#1990011yescharacteristic, complemented, Sylow
359C23—21no—
360C23—22no—
361C23—42no—
362C23—84no—
363C23—84no—
364C23—162no—
365Q8—221no—
366Q8—221no—
367Q8—442no—
368Q8—442no—
369D4—21no—
370D4—22no—
371D4—22no—
372D4—42no—
373D4—42no—
374D4—42no—
375D4—42no—
376D4—82no—
377D4—84no—
378D4—84no—
379D4#6696512yes—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—442no—
389C2×C4C2×D4×D1111yescharacteristic
390C2×C4#6703711yescharacteristic
391C2×C4C22×C22⋊D1111yescharacteristic
392C8—21no—
393C8—41no—
394C8—221no—
395C8—221no—
396C8—441no—
397C8—442no—
398C8—441no—
399C8#6698512yes—
400C22—22no—
401C22—41no—
402C22—41no—
403C22—42no—
404C22—42no—
405C22—42no—
406C22—82no—
407C22—82no—
408C22—82no—
409C22—168no—
410C22D4×C22⋊D1111yescharacteristic
411C4—21no—
412C4—41no—
413C4—42no—
414C4—441no—
415C4—441no—
416C4—882no—
417C4C2×#6696511yescharacteristic
418C4#1062328811yescharacteristic
419C4C2×#6698511yescharacteristic
420C4#1062336611yescharacteristic
421C2—42no—
422C2—82no—
423C2—162no—
424C2#1308023211yescharacteristic
425C2#1308030111yescharacteristic
426C2#1308039811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalD4×C11×D8C2
socleC22×C11D42
hypercenterD4×D8D11
hypocenterC11#19900
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ D4×D8

Complements

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

NH ≅ G/Ntype
1. #13081602C2semidirect
2. #13080847C2semidirect
3. #13068221C2semidirect
4. #13068175C2semidirect
5. #13067981C2semidirect
6. #13067973C2semidirect
7. #13067795C2semidirect
8. #13067724C2semidirect
9. #13067501C2semidirect
10. C8×#4324C2semidirect
14. #10623073C22semidirect
24. #10622688C22semidirect
25. #10622683C22semidirect
26. #10622683C22semidirect
29. #10622632C22semidirect
31. #10622625C22semidirect
35. #10622312C22semidirect
36. C8×Dic22C22semidirect
37. #10622182C22semidirect
39. D4⋊(C11⋊C8)C22semidirect
40. #10622122C22semidirect
41. #10622120C22semidirect
42. #10622118C22semidirect
43. #10622096C22semidirect
44. C8×C11⋊C8C22semidirect
358. C11#19900semidirect

Maximal subgroups

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

subgroupindex
#130816022
#130808472
#130682212
#130681752
#130679812
#130679732
#130677952
#130677242
#130675012
C8×#43242
D4×C11×D82
#1990011