Finite Group Databasebeta

← #16830978

Subgroups — #16830978

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×#11745276C211yesmaximal, characteristic, complemented
2C2×D8×D29C211yesmaximal, characteristic, complemented
3#14271806C211yesmaximal, characteristic, complemented
4D4×D116C211yesmaximal, characteristic, complemented
5#14271553C211yesmaximal, characteristic, complemented
6#14271415C211yesmaximal, characteristic, complemented
7#14271395C211yesmaximal, characteristic, complemented
8#14271359C211yesmaximal, characteristic, complemented
9#14271312C211yesmaximal, characteristic, complemented
10#14271311C211yesmaximal, characteristic, complemented
11#14271298C211yesmaximal, characteristic, complemented
12#14271295C211yesmaximal, characteristic, complemented
13#14271273C211yesmaximal, characteristic, complemented
14#14271233C211yesmaximal, characteristic, complemented
15C29×#463C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic, complemented
17C2×D4×D29C2211yescharacteristic
18C2×D4×D29C2211yescharacteristic, complemented
19C2×D4×D29C2211yescharacteristic, complemented
20C22×D116—21no—
21C2×SD16×C29C2211yescharacteristic, complemented
22C2×D8×C29C2211yescharacteristic
23C29×#124C2211yescharacteristic, complemented
24C4×D4×C29C2211yescharacteristic, complemented
25#11745308C2211yescharacteristic, complemented
26C2×#90784C2211yescharacteristic, complemented
27C2×#90784C2211yescharacteristic, complemented
28#11745300C2211yescharacteristic, complemented
29C2×#90782C2211yescharacteristic
30C2×#90782C2211yescharacteristic, complemented
31C2×#90782C2211yescharacteristic, complemented
32#11745292—21no—
33#11745276—24no—
34D8×D29—24no—
35C2×D232C2211yescharacteristic, complemented
36C2×D232C2211yescharacteristic, complemented
37C2×#90772C2211yescharacteristic, complemented
38C2×C8×D29C2211yescharacteristic, complemented
39#11745257C2211yescharacteristic
40#11745257C2211yescharacteristic, complemented
41#11745246—21no—
42#11745245—21no—
43#11745244—21no—
44#11745244—21no—
45#11745244—21no—
46C22⋊C4×D29—21no—
47#11745236C2211yescharacteristic, complemented
48C4×D116C2211yescharacteristic
49C4×D116C2211yescharacteristic, complemented
50C29×C4⋊C8C2211yescharacteristic, complemented
51C29×#103C2211yescharacteristic, complemented
52C29×#102C2211yescharacteristic, complemented
53#11745180C2211yescharacteristic, complemented
54#11745169C2211yescharacteristic, complemented
55#11745169C2211yescharacteristic, complemented
56#11745168C2211yescharacteristic, complemented
57#11745168C2211yescharacteristic, complemented
58#11745157C2211yescharacteristic, complemented
59#11745156C2211yescharacteristic, complemented
60#11745151C2211yescharacteristic, complemented
61C23×D29—21no—
62C23×D29—21no—
63C23×D29—21no—
64C2×Q8×C29C2311yescharacteristic
65C2×D4×C29C2311yescharacteristic
66C2×D4×C29C2311yescharacteristic
67C22×C4×C29—21no—
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29—21no—
71C2×C22⋊D29—21no—
72#90809—22no—
73#90809—41no—
74D4×D29—22no—
75D4×D29—22no—
76D4×D29—22no—
77D4×D29—41no—
78D4×D29—41no—
79D4×D29—41no—
80C2×D116—21no—
81C2×D116—21no—
82C2×D116—21no—
83C2×D116—21no—
84C2×D116—21no—
85C2×D116—44no—
86C2×D116D411yescharacteristic
87C2×D116C2311yescharacteristic
88C2×D116C2311yescharacteristic
89C2×D116C2311yescharacteristic
90C2×C4×D29—21no—
91C2×C4×D29—21no—
92C2×C4×D29C2311yescharacteristic
93C2×C4×D29C2311yescharacteristic
94SD16×C29—22no—
95D8×C29—22no—
96C2×C8×C29C2311yescharacteristic
97C2×C8×C29C2311yescharacteristic
98C4⋊C4×C29C2311yescharacteristic
99C22⋊C4×C29—21no—
100C22⋊C4×C29—21no—
101C22⋊C4×C29—21no—
102C42×C29C2311yescharacteristic
103C22⋊Dic29—21no—
104#90784—22no—
105#90784—41no—
106#90782—22no—
107#90782—41no—
108#90782D414yescomplemented
109#90781—21no—
110#90781—21no—
111#90781—21no—
112#90781—21no—
113#90781D411yescharacteristic
114#90781D411yescharacteristic
115C4⋊Dic29D411yescharacteristic
116C4⋊Dic29C2311yescharacteristic
117#90779—21no—
118C2×#6597C2311yescharacteristic
119C2×#6597C2311yescharacteristic
120D232—22no—
121D232—22no—
122#90772—22no—
123C8×D29—22no—
124C23×C29—21no—
125C23×C29—21no—
126C22×D29—21no—
127C22×D29—21no—
128C22×D29—21no—
129C22×D29—42no—
130C22×D29—42no—
131C22×D29—42no—
132C22×D29—42no—
133C22×D29—42no—
134C22×D29—42no—
135C22×D29—81no—
136C22×D29—81no—
137C22×D29—81no—
138C22×D29C2×D411yescharacteristic
139C22×D29C2×D411yescharacteristic
140Q8×C29—21no—
141Q8×C29—21no—
142D4×C29—21no—
143D4×C29—21no—
144D4×C29—21no—
145D4×C29C2×D412yes—
146C2×C4×C29—21no—
147C2×C4×C29—21no—
148C2×C4×C29—42no—
149C2×C4×C29C2×D411yescharacteristic
150C2×C4×C29C2×D411yescharacteristic
151C2×C4×C29C2411yescharacteristic
152C22⋊D29—42no—
153C22⋊D29—42no—
154C22⋊D29—42no—
155C22⋊D29—81no—
156C2×Dic29—21no—
157C2×Dic29C2×D411yescharacteristic
158C2×Dic29C2×D411yescharacteristic
159D116—22no—
160D116—21no—
161D116—21no—
162D116—21no—
163D116—21no—
164D116—21no—
165D116—42no—
166D116—42no—
167D116—42no—
168D116—42no—
169D116—81no—
170D116C2×D412yescomplemented
171C4×D29—21no—
172C4×D29—21no—
173C4×D29—21no—
174C4×D29—21no—
175C4×D29—42no—
176C4×D29—81no—
177C8×C29—21no—
178C8×C29—21no—
179#6597—21no—
180#6597C2×D412yescomplemented
181#3264—291nomaximal, Sylow
182C22×C29—22no—
183C22×C29—41no—
184C22×C29—41no—
185C22×C29—41no—
186C22×C29—41no—
187C22×C29—41no—
188C22×C29C22×D411yescharacteristic
189C2×D29—21no—
190C2×D29—21no—
191C2×D29—21no—
192C2×D29—22no—
193C2×D29—21no—
194C2×D29—21no—
195C2×D29—41no—
196C2×D29—41no—
197C2×D29—41no—
198C2×D29—41no—
199C2×D29—41no—
200C2×D29—41no—
201C2×D29—41no—
202C2×D29—41no—
203C2×D29—84no—
204C2×D29—84no—
205C2×D29—84no—
206C2×D29AGL(1,ℤ/8)12yescomplemented
207C4×C29—21no—
208C4×C29—21no—
209C4×C29—41no—
210C4×C29—41no—
211C4×C29C22×D411yescharacteristic
212C4×C29H(5,𝔽2)11yescharacteristic
213Dic29—21no—
214Dic29—21no—
215Dic29—41no—
216C2×AGL(1,ℤ/8)—291no—
217C22×D8—291no—
218#546—291no—
219D42—291no—
220#496—291no—
221#469—291no—
222#465—291no—
223#463D2911yescharacteristic, complemented
224#459—291no—
225#450—291no—
226#449—291no—
227#447—291no—
228#447—291no—
229#442—291no—
230#435—291no—
231C2×C29—42no—
232C2×C29—81no—
233C2×C29D4211yescharacteristic
234C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
235C2×C29#57611yescharacteristic
236D29—22no—
237D29—41no—
238D29—42no—
239D29—81no—
240D29—81no—
241C2×#41—291no—
242C22×D4—291no—
243C22×D4—291no—
244C22×D4—291no—
245C22×D4—581no—
246AGL(1,ℤ/8)—584no—
247C2×SD16—291no—
248C2×SD16—291no—
249C2×SD16C2×D2911yescharacteristic, complemented
250C2×D8—291no—
251C2×D8—291no—
252C2×D8—291no—
253C2×D8—291no—
254C2×D8—291no—
255C2×D8—584no—
256C2×D8C2×D2911yescharacteristic
257C2×M16—291no—
258C22×C8—291no—
259#127—291no—
260#124C2×D2911yescharacteristic, complemented
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×D4C2×D2911yescharacteristic, complemented
274C2×C22⋊C4—581no—
275#106—291no—
276C4⋊C8C2×D2911yescharacteristic, complemented
277#103C2×D2911yescharacteristic, complemented
278#102—291no—
279#102—291no—
280#102—291no—
281#102—291no—
282#102C2×D2911yescharacteristic, complemented
283C22⋊C8—291no—
284C22⋊C8—291no—
285#97—291no—
286C29#326411yescharacteristic, complemented, Sylow
287C24—581no—
288C24—581no—
289C24—581no—
290#41—582no—
291#41—1161no—
292C2×Q8C22×D2911yescharacteristic
293C2×D4—291no—
294C2×D4—291no—
295C2×D4—291no—
296C2×D4—291no—
297C2×D4—581no—
298C2×D4—581no—
299C2×D4—581no—
300C2×D4—581no—
301C2×D4—581no—
302C2×D4—581no—
303C2×D4—582no—
304C2×D4—582no—
305C2×D4—582no—
306C2×D4—581no—
307C2×D4—581no—
308C2×D4—581no—
309C2×D4—1164no—
310C2×D4—1161no—
311C2×D4—1161no—
312C2×D4—1161no—
313C2×D4C22×D2911yescharacteristic
314C2×D4C22×D2911yescharacteristic
315C22×C4—21no—
316C22×C4—291no—
317C22×C4—291no—
318C22×C4—581no—
319C22×C4—581no—
320SD16—22no—
321SD16—582no—
322SD16—1161no—
323D8—22no—
324D8—294no—
325D8—582no—
326D8—582no—
327D8—582no—
328D8—1161no—
329M16—582no—
330C2×C8—291no—
331C2×C8—291no—
332C2×C8—582no—
333C2×C8C22×D2911yescharacteristic
334C2×C8C22×D2911yescharacteristic
335C4⋊C4—291no—
336C4⋊C4—291no—
337C4⋊C4—581no—
338C4⋊C4C22×D2911yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—291no—
343C22⋊C4—291no—
344C22⋊C4—581no—
345C22⋊C4—581no—
346C22⋊C4—581no—
347C22⋊C4—581no—
348C22⋊C4—581no—
349C42C22×D2911yescharacteristic
350C23—21no—
351C23—21no—
352C23—291no—
353C23—291no—
354C23—581no—
355C23—581no—
356C23—581no—
357C23—1162no—
358C23—1162no—
359C23—1162no—
360C23—1162no—
361C23—1162no—
362C23—1162no—
363C23—2321no—
364C23—2321no—
365C23—2321no—
366Q8—21no—
367Q8—21no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—292no—
372D4—582no—
373D4—581no—
374D4—581no—
375D4—581no—
376D4—581no—
377D4—581no—
378D4—1162no—
379D4—1162no—
380D4—1162no—
381D4—1162no—
382D4—1162no—
383D4—1162no—
384D4—1162no—
385D4—2321no—
386D4—2321no—
387D4D4×D2912yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
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—2321no—
400C2×C4D4×D2911yescharacteristic
401C2×C4D4×D2911yescharacteristic
402C2×C4C23×D2911yescharacteristic
403C8—21no—
404C8—21no—
405C8—292no—
406C8—581no—
407C22—22no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—292no—
414C22—581no—
415C22—581no—
416C22—581no—
417C22—582no—
418C22—581no—
419C22—581no—
420C22—1161no—
421C22—1161no—
422C22—1161no—
423C22—1161no—
424C22—1161no—
425C22—1161no—
426C22—1161no—
427C22—1161no—
428C22—2324no—
429C22—2324no—
430C22—2324no—
431C22C2×D4×D2911yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—581no—
437C4—581no—
438C4—1161no—
439C4C2×D4×D2911yescharacteristic
440C4#1174536411yescharacteristic
441C2—42no—
442C2—81no—
443C2—582no—
444C2—1161no—
445C2—1162no—
446C2—2321no—
447C2—2321no—
448C2#1427179711yescharacteristic
449C2AGL(1,ℤ/8)×D2911yescharacteristic
450C2#1427196511yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#463C2
socleC22×C29C22×D4
hypercenter#463D29
hypocenterC29#3264
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#11745276C2semidirect
2. C2×D8×D29C2semidirect
3. #14271806C2semidirect
4. D4×D116C2semidirect
5. #14271553C2semidirect
6. #14271415C2semidirect
7. #14271395C2semidirect
8. #14271359C2semidirect
9. #14271312C2semidirect
10. #14271311C2semidirect
11. #14271298C2semidirect
12. #14271295C2semidirect
13. #14271273C2semidirect
14. #14271233C2semidirect
15. C29×#463C2semidirect
16. C2×#90809C22semidirect
18. C2×D4×D29C22semidirect
19. C2×D4×D29C22semidirect
21. C2×SD16×C29C22semidirect
23. C29×#124C22semidirect
24. C4×D4×C29C22semidirect
25. #11745308C22semidirect
26. C2×#90784C22semidirect
27. C2×#90784C22semidirect
28. #11745300C22semidirect
30. C2×#90782C22semidirect
31. C2×#90782C22semidirect
35. C2×D232C22semidirect
36. C2×D232C22semidirect
37. C2×#90772C22semidirect
38. C2×C8×D29C22semidirect
40. #11745257C22semidirect
47. #11745236C22semidirect
49. C4×D116C22semidirect
50. C29×C4⋊C8C22semidirect
51. C29×#103C22semidirect
52. C29×#102C22semidirect
53. #11745180C22semidirect
54. #11745169C22semidirect
55. #11745169C22semidirect
56. #11745168C22semidirect
57. #11745168C22semidirect
58. #11745157C22semidirect
59. #11745156C22semidirect
60. #11745151C22semidirect
108. #90782D4semidirect
170. D116C2×D4semidirect
180. #6597C2×D4semidirect
206. C2×D29AGL(1,ℤ/8)semidirect
223. #463D29semidirect
249. C2×SD16C2×D29semidirect
260. #124C2×D29semidirect
273. C4×D4C2×D29semidirect
276. C4⋊C8C2×D29semidirect
277. #103C2×D29semidirect
282. #102C2×D29semidirect
286. C29#3264semidirect

Maximal subgroups

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

subgroupindex
C2×#117452762
C2×D8×D292
#142718062
D4×D1162
#142715532
#142714152
#142713952
#142713592
#142713122
#142713112
#142712982
#142712952
#142712732
#142712332
C29×#4632
#326429