Finite Group Databasebeta

← #14745233

Subgroups — #14745233

Order 2816.

724 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081040C211yesmaximal, characteristic, complemented
2#13080858C212yesmaximal, complemented
3#13068205C211yesmaximal, characteristic, complemented
4#13068147C212yesmaximal, complemented
5#13068015C211yesmaximal, characteristic, complemented
6#13067968C211yesmaximal, characteristic, complemented
7#13067732C212yesmaximal, complemented
8#13067698C212yesmaximal, complemented
9#13067501C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11D4×C11×D8C211yesmaximal, characteristic, complemented
12C22×C11×D8—21no—
13D42×C11C2212yes—
14#10623094C2212yescomplemented
15C11×#493C2211yescharacteristic
16C11×#466—21no—
17C11×#459C2212yes—
18C11×#447—22no—
19C4×C11×D8C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622830—22no—
22#10622828—22no—
23#10622770—21no—
24#10622689C2212yescomplemented
25#10622685C2212yescomplemented
26#10622683C2212yescomplemented
27#10622652—22no—
28#10622648—22no—
29C4×#4323C2211yescharacteristic
30#10622625C2212yescomplemented
31#10622621C2212yes—
32#10622621C2212yescomplemented
33#10622493—21no—
34#10622397—22no—
35C8×D44C2211yescharacteristic, complemented
36#10622295C2211yescharacteristic, complemented
37#10622182C2212yescomplemented
38D4⋊(C11⋊C8)C2211yescharacteristic
39D4⋊(C11⋊C8)C2212yescomplemented
40#10622121C2211yescharacteristic, complemented
41#10622119C2212yescomplemented
42#10622117C2211yescharacteristic, 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#66991—22no—
60C2×#4324—42no—
61C2×#4323—22no—
62C2×#4323D411yescharacteristic
63#66983—22no—
64#66979—22no—
65C2×#4318—22no—
66C2×C8×D11—21no—
67#66945—22no—
68#66938—42no—
69C4×D44C2311yescharacteristic
70#66922C2312yes—
71C11×#107D411yescharacteristic
72C11×C4⋊C8C2311yescharacteristic
73C11×#102—22no—
74C11×#102D412yes—
75C11×C22⋊C8—21no—
76C4×C8×C11C2311yescharacteristic
77#66896—22no—
78#66896—22no—
79#66896—22no—
80#66896—22no—
81#66896—22no—
82#66896D411yescharacteristic
83C22⋊(C11⋊C8)—22no—
84(C2×D11)⋊C8—21no—
85#66882—21no—
86#66882—21no—
87#66873D411yescharacteristic
88#66872—22no—
89#66872—22no—
90#66871D411yescharacteristic
91C4⋊(C11⋊C8)C2311yescharacteristic
92C4⋊(C11⋊C8)C2312yes—
93C4×C11⋊C8C2311yescharacteristic
94C4×C11⋊C8C2311yescharacteristic
95#19898—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×C22⋊D11—42no—
111C2×D44C2×D411yescharacteristic
112C2×C4×D11—21no—
113C2×Dic22—22no—
114C11×D8—22no—
115C11×D8—44no—
116C11×D8—42no—
117C11×D8—81no—
118C2×C8×C11—21no—
119C2×C8×C11—42no—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C11×C4⋊C4C2×D411yescharacteristic
123C11×C4⋊C4C2×D412yes—
124C11×C22⋊C4—22no—
125C11×C22⋊C4—21no—
126C11×C22⋊C4—42no—
127C42×C11C2411yescharacteristic
128C22⋊Dic11—42no—
129#4324—84no—
130#4323—22no—
131#4323—82no—
132(C2×D11)⋊C4—21no—
133(C2×D11)⋊C4—42no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11C2×D411yescharacteristic
137C4×Dic11—42no—
138#4318—82no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8C2×D411yescharacteristic
143C2×C11⋊C8C2×D411yescharacteristic
144C8×D11—42no—
145#3341—111no—
146#3325—112no—
147D4×D8D1111yescharacteristic, complemented
148#1706—111no—
149#1697—112no—
150#1675—111no—
151#1667—111no—
152#1629—112no—
153#1624—112no—
154#1589—111no—
155C8×D8—111no—
156C23×C11—21no—
157C23×C11—22no—
158C23×C11—42no—
159C23×C11—84no—
160C23×C11—84no—
161C23×C11—162no—
162C22×D11—21no—
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
183C22⋊D11—162no—
184C2×Dic11—21no—
185C2×Dic11—42no—
186D44—21no—
187D44—21no—
188C4×D11—41no—
189C4×D11—41no—
190Dic22—82no—
191C8×C11—21no—
192C8×C11—41no—
193C8×C11AGL(1,ℤ/8)12yes—
194C11⋊C8—22no—
195C11⋊C8—21no—
196C11⋊C8—21no—
197C11⋊C8—41no—
198C11⋊C8—42no—
199C22×D8—21no—
200#555—112no—
201D42C2×D1112yes—
202#500—111no—
203#493C2×D1111yescharacteristic
204#492—112no—
205#486—112no—
206#482—222no—
207#482—222no—
208#476—112no—
209#476—112no—
210#469—222no—
211#466—21no—
212#466—221no—
213#459—112no—
214#459C2×D1112yes—
215#447—22no—
216#447—222no—
217C4×D8—111no—
218C4×D8C2×D1111yescharacteristic
219#436—112no—
220C8×D4—111no—
221C8×D4C2×D1111yescharacteristic
222#427—221no—
223#418—222no—
224#335—111no—
225#335—111no—
226#333—112no—
227#331—112no—
228D4⋊C8—111no—
229D4⋊C8—112no—
230D4⋊C8—111no—
231C82—111no—
232C22×C11—22no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11—82no—
241C22×C11—168no—
242C22×C11D4211yescharacteristic
243C2×D11—41no—
244C2×D11—41no—
245C2×D11—41no—
246C4×C11—21no—
247C4×C11—41no—
248C4×C11—42no—
249C4×C11C2×#13511yescharacteristic
250C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
251C4×C11#57611yescharacteristic
252C4×C11#57711yescharacteristic
253Dic11—41no—
254Dic11—82no—
255C22×D4—22no—
256C22×D4—22no—
257C2×SD16—442no—
258C2×D8—22no—
259C2×D8—21no—
260C2×D8—21no—
261C2×D8—44no—
262C2×D8—111no—
263C2×D8—222no—
264C2×D8C22⋊D1111yescharacteristic
265C2×M16—222no—
266C22×C8—21no—
267C22×C8—221no—
268C4⋊Q8—112no—
269#127C22×D1112yes—
270#124—442no—
271#121—22no—
272#121—22no—
273#121—222no—
274#121—222no—
275#120—42no—
276C4×D4—111no—
277C4×D4C22×D1111yescharacteristic
278C4×D4C22×D1112yes—
279#117—222no—
280#117—222no—
281#107—111no—
282#107—221no—
283#107—221no—
284#107C22⋊D1111yescharacteristic
285#106—222no—
286#106—222no—
287C4⋊C8—111no—
288C4⋊C8—112no—
289C4⋊C8C22×D1111yescharacteristic
290#102—22no—
291#102—111no—
292#102—111no—
293#102—222no—
294#102—222no—
295#102—222no—
296#102—222no—
297#102—222no—
298#102C22⋊D1112yes—
299C22⋊C8—21no—
300C22⋊C8—222no—
301C22⋊C8—221no—
302C4×C8—111no—
303C4×C8—111no—
304C4×C8C22×D1111yescharacteristic
305C2×C11—42no—
306C2×C11—82no—
307C2×C11—162no—
308C2×C11#327211yescharacteristic
309C2×C11#328011yescharacteristic
310C2×C11#329211yescharacteristic
311D11—81no—
312C24—42no—
313C2×Q8—222no—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—42no—
318C2×D4—42no—
319C2×D4—44no—
320C2×D4—44no—
321C2×D4—82no—
322C2×D4—82no—
323C2×D4—111no—
324C2×D4—442no—
325C2×D4D4×D1111yescharacteristic
326C2×D4C2×C22⋊D1112yes—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—221no—
330SD16—884no—
331D8—22no—
332D8—44no—
333D8—42no—
334D8—81no—
335D8—222no—
336D8—882no—
337M16—882no—
338C2×C8—21no—
339C2×C8—42no—
340C2×C8—111no—
341C2×C8—111no—
342C2×C8—221no—
343C2×C8—222no—
344C2×C8—221no—
345C2×C8—442no—
346C2×C8C2×C22⋊D1111yescharacteristic
347C2×C8C2×C22⋊D1111yescharacteristic
348C4⋊C4—111no—
349C4⋊C4—222no—
350C4⋊C4—222no—
351C4⋊C4D4×D1111yescharacteristic
352C4⋊C4C2×C22⋊D1112yes—
353C22⋊C4—21no—
354C22⋊C4—22no—
355C22⋊C4—42no—
356C22⋊C4—221no—
357C22⋊C4—442no—
358C22⋊C4—442no—
359C42—442no—
360C42C23×D1111yescharacteristic
361C11#1989811yescharacteristic, complemented, Sylow
362C23—21no—
363C23—22no—
364C23—42no—
365C23—84no—
366C23—84no—
367C23—162no—
368C23—221no—
369Q8—882no—
370D4—21no—
371D4—22no—
372D4—22no—
373D4—42no—
374D4—42no—
375D4—42no—
376D4—42no—
377D4—82no—
378D4—84no—
379D4—84no—
380D4—221no—
381D4—221no—
382D4—1762no—
383D4#6696512yes—
384C2×C4—22no—
385C2×C4—21no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—221no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—442no—
394C2×C4C2×D4×D1111yescharacteristic
395C2×C4#6703711yescharacteristic
396C2×C4C22×C22⋊D1111yescharacteristic
397C8—21no—
398C8—41no—
399C8—222no—
400C8—221no—
401C8—221no—
402C8—442no—
403C8—441no—
404C8#6698512yes—
405C22—22no—
406C22—41no—
407C22—41no—
408C22—42no—
409C22—42no—
410C22—42no—
411C22—82no—
412C22—82no—
413C22—82no—
414C22—168no—
415C22—441no—
416C22—441no—
417C22—441no—
418C22D4×C22⋊D1111yescharacteristic
419C4—21no—
420C4—41no—
421C4—42no—
422C4—441no—
423C4—882no—
424C4C2×#6696511yescharacteristic
425C4#1062328811yescharacteristic
426C4C2×#6698511yescharacteristic
427C4#1062336711yescharacteristic
428C2—42no—
429C2—82no—
430C2—162no—
431C2—881no—
432C2#1308021211yescharacteristic
433C2#1308030111yescharacteristic
434C2#1308041311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingD4×C11×D8C2
socleC22×C11D42
hypercenterD4×D8D11
hypocenterC11#19898
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. #13081040C2semidirect
2. #13080858C2semidirect
3. #13068205C2semidirect
4. #13068147C2semidirect
5. #13068015C2semidirect
6. #13067968C2semidirect
7. #13067732C2semidirect
8. #13067698C2semidirect
9. #13067501C2semidirect
10. C8×#4323C2semidirect
11. D4×C11×D8C2semidirect
14. #10623094C22semidirect
24. #10622689C22semidirect
25. #10622685C22semidirect
26. #10622683C22semidirect
30. #10622625C22semidirect
32. #10622621C22semidirect
35. C8×D44C22semidirect
36. #10622295C22semidirect
37. #10622182C22semidirect
39. D4⋊(C11⋊C8)C22semidirect
40. #10622121C22semidirect
41. #10622119C22semidirect
42. #10622117C22semidirect
43. #10622096C22semidirect
44. C8×C11⋊C8C22semidirect
147. D4×D8D11semidirect
361. C11#19898semidirect

Maximal subgroups

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

subgroupindex
#130810402
#130808582
#130682052
#130681472
#130680152
#130679682
#130677322
#130676982
#130675012
C8×#43232
D4×C11×D82
#1989811