Finite Group Databasebeta

← #16830972

Subgroups — #16830972

Order 3712.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745273C211yesmaximal, characteristic, complemented
2#14271807C211yesmaximal, characteristic, complemented
3D4×C22⋊D29C211yesmaximal, characteristic, complemented
4#14271551C211yesmaximal, characteristic, complemented
5#14271413C211yesmaximal, characteristic, complemented
6#14271392C211yesmaximal, characteristic, complemented
7#14271376C211yesmaximal, characteristic, complemented
8#14271356C211yesmaximal, characteristic, complemented
9#14271314C211yesmaximal, characteristic, complemented
10#14271305C211yesmaximal, characteristic, complemented
11#14271297C211yesmaximal, characteristic, complemented
12#14271295C211yesmaximal, characteristic, complemented
13#14271275C211yesmaximal, characteristic, complemented
14#14271234C211yesmaximal, characteristic, complemented
15C22×D8×C29C211yesmaximal, characteristic, complemented
16C22×D4×C29C2211yescharacteristic
17C22×D4×C29C2211yescharacteristic, complemented
18C22×C22⋊D29—21no—
19C2×#90807C2211yescharacteristic, complemented
20C2×D4×D29C2211yescharacteristic, complemented
21C2×D8×C29—24no—
22C2×D8×C29C2211yescharacteristic
23C2×D8×C29C2211yescharacteristic
24C2×D8×C29C2211yescharacteristic, complemented
25C2×D8×C29C2211yescharacteristic, complemented
26C22×C8×C29C2211yescharacteristic, complemented
27#11745315—21no—
28#11745315—21no—
29C2×C22⋊Dic29—21no—
30#11745302C2211yescharacteristic, complemented
31#11745301—21no—
32#11745301—21no—
33#11745300C2211yescharacteristic, complemented
34#11745300C2211yescharacteristic, complemented
35#11745299—21no—
36#11745298C2211yescharacteristic, complemented
37#11745297—21no—
38D4×Dic29C2211yescharacteristic, complemented
39D4×Dic29C2211yescharacteristic, complemented
40C2×#90783C2211yescharacteristic, complemented
41C2×#90783C2211yescharacteristic, complemented
42C2×#90782C2211yescharacteristic, complemented
43C2×#90782C2211yescharacteristic, complemented
44#11745292C2211yescharacteristic
45C4×C22⋊D29C2211yescharacteristic
46#11745286C2211yescharacteristic, complemented
47#11745273—24no—
48C2×#90773C2211yescharacteristic, complemented
49C2×#90772C2211yescharacteristic, complemented
50#11745180C2211yescharacteristic, complemented
51#11745180C2211yescharacteristic, complemented
52#11745180C2211yescharacteristic, complemented
53#11745180C2211yescharacteristic, complemented
54C22⋊#6597C2211yescharacteristic, complemented
55#11745169C2211yescharacteristic, complemented
56#11745168C2211yescharacteristic, complemented
57#11745165C2211yescharacteristic, complemented
58#11745164C2211yescharacteristic, complemented
59#11745163C2211yescharacteristic, complemented
60#11745162C2211yescharacteristic, complemented
61C24×C29—21no—
62C24×C29—21no—
63C23×D29—21no—
64C2×D4×C29—22no—
65C2×D4×C29—22no—
66C2×D4×C29—21no—
67C2×D4×C29—21no—
68C2×D4×C29—41no—
69C2×D4×C29—41no—
70C2×D4×C29C2311yescharacteristic
71C2×D4×C29C2311yescharacteristic
72C2×D4×C29C2311yescharacteristic
73C2×D4×C29C2311yescharacteristic
74C22×C4×C29C2311yescharacteristic
75C2×C22⋊D29—21no—
76C2×C22⋊D29—21no—
77C2×C22⋊D29—21no—
78C2×C22⋊D29—21no—
79C2×C22⋊D29—21no—
80C2×C22⋊D29—21no—
81C2×C22⋊D29—21no—
82C2×C22⋊D29—44no—
83C2×C22⋊D29D411yescharacteristic
84C22×Dic29—21no—
85C22×Dic29—21no—
86C22×Dic29—21no—
87#90807—22no—
88#90807—41no—
89D4×D29—22no—
90D4×D29—41no—
91C2×D116C2311yescharacteristic
92C2×C4×D29C2311yescharacteristic
93C2×Dic58C2311yescharacteristic
94D8×C29—22no—
95D8×C29—22no—
96D8×C29—22no—
97D8×C29D414yescomplemented
98C2×C8×C29—22no—
99C2×C8×C29C2311yescharacteristic
100C2×C8×C29C2311yescharacteristic
101C22⋊Dic29—21no—
102C22⋊Dic29—21no—
103C22⋊Dic29—21no—
104C22⋊Dic29—21no—
105C22⋊Dic29—21no—
106C22⋊Dic29—21no—
107C22⋊Dic29—21no—
108C22⋊Dic29D411yescharacteristic
109#90783—22no—
110#90783—41no—
111#90782—22no—
112#90782—41no—
113#90781—21no—
114#90781D411yescharacteristic
115C4⋊Dic29C2311yescharacteristic
116C4⋊Dic29C2311yescharacteristic
117#90779—21no—
118#90779D411yescharacteristic
119C4×Dic29C2311yescharacteristic
120C2×#6597C2311yescharacteristic
121C2×#6597C2311yescharacteristic
122#90773—22no—
123#90772—22no—
124C23×C29—21no—
125C23×C29—21no—
126C23×C29—21no—
127C23×C29—21no—
128C23×C29—42no—
129C23×C29—42no—
130C23×C29—42no—
131C23×C29—42no—
132C23×C29—81no—
133C23×C29—81no—
134C23×C29C2×D411yescharacteristic
135C22×D29—21no—
136C22×D29—42no—
137C22×D29—42no—
138C22×D29—81no—
139C22×D29C2×D411yescharacteristic
140D4×C29—21no—
141D4×C29—21no—
142D4×C29—21no—
143D4×C29—21no—
144D4×C29—21no—
145D4×C29—21no—
146D4×C29—42no—
147D4×C29—42no—
148D4×C29C2×D412yes—
149D4×C29C2×D412yescomplemented
150C2×C4×C29—21no—
151C2×C4×C29—21no—
152C2×C4×C29C2×D411yescharacteristic
153C2×C4×C29C2411yescharacteristic
154C22⋊D29—22no—
155C22⋊D29—42no—
156C22⋊D29—42no—
157C22⋊D29—42no—
158C22⋊D29—42no—
159C22⋊D29—42no—
160C22⋊D29—81no—
161C22⋊D29—81no—
162C2×Dic29—21no—
163C2×Dic29—21no—
164C2×Dic29—21no—
165C2×Dic29—42no—
166C2×Dic29—42no—
167C2×Dic29—81no—
168C2×Dic29C2×D411yescharacteristic
169C2×Dic29C2×D411yescharacteristic
170C2×Dic29C2×D411yescharacteristic
171D116—21no—
172D116—21no—
173C4×D29—21no—
174C4×D29—21no—
175Dic58—21no—
176Dic58—21no—
177C8×C29—21no—
178C8×C29C2×D412yescomplemented
179#6597—21no—
180#6597—21no—
181#3264—291nomaximal, Sylow
182C22×C29—21no—
183C22×C29—21no—
184C22×C29—22no—
185C22×C29—22no—
186C22×C29—41no—
187C22×C29—41no—
188C22×C29—41no—
189C22×C29—41no—
190C22×C29—41no—
191C22×C29—41no—
192C22×C29—41no—
193C22×C29—41no—
194C22×C29—41no—
195C22×C29—41no—
196C22×C29—84no—
197C22×C29—84no—
198C22×C29AGL(1,ℤ/8)12yescomplemented
199C22×C29C22×D411yescharacteristic
200C2×D29—21no—
201C2×D29—21no—
202C2×D29—21no—
203C2×D29—41no—
204C2×D29—41no—
205C2×D29—41no—
206C2×D29—84no—
207C4×C29—21no—
208C4×C29C22×D411yescharacteristic
209C4×C29H(5,𝔽2)11yescharacteristic
210Dic29—21no—
211Dic29—21no—
212Dic29—21no—
213Dic29—41no—
214Dic29—41no—
215Dic29—41no—
216C2×AGL(1,ℤ/8)—291no—
217C22×D8D2911yescharacteristic, complemented
218#546—291no—
219D42—291no—
220#496—291no—
221#469—291no—
222#465—291no—
223#463—291no—
224#459—291no—
225#450—291no—
226#449—291no—
227#447—291no—
228#447—291no—
229#442—291no—
230#435—291no—
231C2×C29—22no—
232C2×C29—42no—
233C2×C29—42no—
234C2×C29—81no—
235C2×C29—81no—
236C2×C29D4211yescharacteristic
237C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
238C2×C29#57611yescharacteristic
239D29—41no—
240D29—81no—
241C2×#41—291no—
242C22×D4—291no—
243C22×D4—581no—
244C22×D4C2×D2911yescharacteristic
245C22×D4C2×D2911yescharacteristic, complemented
246AGL(1,ℤ/8)—584no—
247C2×SD16—291no—
248C2×SD16—291no—
249C2×SD16—291no—
250C2×D8—24no—
251C2×D8—291no—
252C2×D8—291no—
253C2×D8C2×D2911yescharacteristic
254C2×D8C2×D2911yescharacteristic
255C2×D8C2×D2911yescharacteristic, complemented
256C2×D8C2×D2911yescharacteristic, complemented
257C2×M16—291no—
258C22×C8C2×D2911yescharacteristic, complemented
259#127—291no—
260#124—291no—
261#123—581no—
262C22⋊Q8—291no—
263#121—291no—
264#121—291no—
265#121—291no—
266#121—581no—
267#121—581no—
268#120—581no—
269#120—581no—
270#120—581no—
271C4×D4—291no—
272C4×D4—291no—
273C4×D4—291no—
274C2×C22⋊C4—581no—
275#106—291no—
276C4⋊C8—291no—
277#103—291no—
278#102—291no—
279#102—291no—
280#102—291no—
281#102—291no—
282#102—291no—
283C22⋊C8—291no—
284C22⋊C8—291no—
285#97—291no—
286C29#326411yescharacteristic, complemented, Sylow
287C24—21no—
288C24—21no—
289C24—581no—
290#41—582no—
291#41—1161no—
292C2×Q8—291no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—291no—
300C2×D4—291no—
301C2×D4—581no—
302C2×D4—581no—
303C2×D4—581no—
304C2×D4—582no—
305C2×D4—581no—
306C2×D4—581no—
307C2×D4—581no—
308C2×D4—581no—
309C2×D4—1161no—
310C2×D4—1164no—
311C2×D4C22×D2911yescharacteristic
312C2×D4C22×D2911yescharacteristic
313C2×D4C22×D2911yescharacteristic
314C2×D4C22×D2911yescharacteristic
315C22×C4—291no—
316C22×C4—581no—
317C22×C4—581no—
318C22×C4—581no—
319C22×C4C22×D2911yescharacteristic
320SD16—582no—
321SD16—582no—
322SD16—1161no—
323D8—22no—
324D8—22no—
325D8—22no—
326D8—582no—
327D8—1161no—
328D8C22⋊D2914yescomplemented
329M16—582no—
330C2×C8—22no—
331C2×C8—291no—
332C2×C8—291no—
333C2×C8C22×D2911yescharacteristic
334C2×C8C22×D2911yescharacteristic
335C4⋊C4—291no—
336C4⋊C4—291no—
337C4⋊C4—291no—
338C4⋊C4—581no—
339C22⋊C4—291no—
340C22⋊C4—291no—
341C22⋊C4—581no—
342C22⋊C4—581no—
343C22⋊C4—581no—
344C22⋊C4—581no—
345C22⋊C4—581no—
346C22⋊C4—581no—
347C22⋊C4—581no—
348C22⋊C4—581no—
349C42—291no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—81no—
359C23—81no—
360C23—291no—
361C23—581no—
362C23—1162no—
363C23—1162no—
364C23—2321no—
365C23D4×D2911yescharacteristic
366Q8—581no—
367Q8—581no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—21no—
374D4—42no—
375D4—42no—
376D4—582no—
377D4—581no—
378D4—581no—
379D4—1162no—
380D4—1162no—
381D4—1162no—
382D4—1162no—
383D4—1162no—
384D4—2321no—
385D4—2321no—
386D4C2×C22⋊D2912yes—
387D4C2×C22⋊D2912yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—291no—
391C2×C4—291no—
392C2×C4—291no—
393C2×C4—581no—
394C2×C4—581no—
395C2×C4—581no—
396C2×C4—581no—
397C2×C4—581no—
398C2×C4—1162no—
399C2×C4—1162no—
400C2×C4—2321no—
401C2×C4D4×D2911yescharacteristic
402C2×C4C23×D2911yescharacteristic
403C8—21no—
404C8—581no—
405C8—581no—
406C8C2×C22⋊D2912yescomplemented
407C22—21no—
408C22—21no—
409C22—22no—
410C22—22no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—84no—
422C22—84no—
423C22—581no—
424C22—581no—
425C22—581no—
426C22—1161no—
427C22—1161no—
428C22—1161no—
429C22—2324no—
430C22#1174527312yescomplemented
431C22C2×D4×D2911yescharacteristic
432C4—21no—
433C4—581no—
434C4—581no—
435C4—581no—
436C4—1161no—
437C4—1161no—
438C4—1161no—
439C4#1174535911yescharacteristic
440C4C22×C22⋊D2911yescharacteristic
441C2—22no—
442C2—42no—
443C2—42no—
444C2—81no—
445C2—81no—
446C2—1161no—
447C2—2321no—
448C2D4×C22⋊D2911yescharacteristic
449C2C2×#1174527311yescharacteristic
450C2#1427196411yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC22×D8×C29C2
socleC22×C29C22×D4
hypercenterC22×D8D29
hypocenterC29#3264
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#11745273C2semidirect
2. #14271807C2semidirect
3. D4×C22⋊D29C2semidirect
4. #14271551C2semidirect
5. #14271413C2semidirect
6. #14271392C2semidirect
7. #14271376C2semidirect
8. #14271356C2semidirect
9. #14271314C2semidirect
10. #14271305C2semidirect
11. #14271297C2semidirect
12. #14271295C2semidirect
13. #14271275C2semidirect
14. #14271234C2semidirect
15. C22×D8×C29C2semidirect
17. C22×D4×C29C22semidirect
19. C2×#90807C22semidirect
20. C2×D4×D29C22semidirect
24. C2×D8×C29C22semidirect
25. C2×D8×C29C22semidirect
26. C22×C8×C29C22semidirect
30. #11745302C22semidirect
33. #11745300C22semidirect
34. #11745300C22semidirect
36. #11745298C22semidirect
38. D4×Dic29C22semidirect
39. D4×Dic29C22semidirect
40. C2×#90783C22semidirect
41. C2×#90783C22semidirect
42. C2×#90782C22semidirect
43. C2×#90782C22semidirect
46. #11745286C22semidirect
48. C2×#90773C22semidirect
49. C2×#90772C22semidirect
50. #11745180C22semidirect
51. #11745180C22semidirect
52. #11745180C22semidirect
53. #11745180C22semidirect
54. C22⋊#6597C22semidirect
55. #11745169C22semidirect
56. #11745168C22semidirect
57. #11745165C22semidirect
58. #11745164C22semidirect
59. #11745163C22semidirect
60. #11745162C22semidirect
97. D8×C29D4semidirect
149. D4×C29C2×D4semidirect
178. C8×C29C2×D4semidirect
198. C22×C29AGL(1,ℤ/8)semidirect
217. C22×D8D29semidirect
245. C22×D4C2×D29semidirect
255. C2×D8C2×D29semidirect
256. C2×D8C2×D29semidirect
258. C22×C8C2×D29semidirect
286. C29#3264semidirect
328. D8C22⋊D29semidirect
387. D4C2×C22⋊D29semidirect
406. C8C2×C22⋊D29semidirect
430. C22#11745273semidirect

Maximal subgroups

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

subgroupindex
C2×#117452732
#142718072
D4×C22⋊D292
#142715512
#142714132
#142713922
#142713762
#142713562
#142713142
#142713052
#142712972
#142712952
#142712752
#142712342
C22×D8×C292
#326429