Finite Group Databasebeta

← #16830967

Subgroups — #16830967

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
2C2×D8×D29C211yesmaximal, characteristic, complemented
3#14271808C211yesmaximal, characteristic, complemented
4#14271798C211yesmaximal, characteristic, complemented
5#14271550C211yesmaximal, characteristic, complemented
6#14271415C211yesmaximal, characteristic, complemented
7#14271391C211yesmaximal, characteristic, complemented
8#14271379C211yesmaximal, characteristic, complemented
9#14271315C211yesmaximal, characteristic, complemented
10#14271305C211yesmaximal, characteristic, complemented
11#14271298C211yesmaximal, characteristic, complemented
12#14271295C211yesmaximal, characteristic, complemented
13#14271273C211yesmaximal, characteristic, complemented
14#14271233C211yesmaximal, characteristic, complemented
15C29×#459C211yesmaximal, characteristic, complemented
16C2×#90807C2211yescharacteristic, complemented
17C2×D4×D29—21no—
18C2×D4×D29C2211yescharacteristic
19C2×D4×D29C2211yescharacteristic, complemented
20C2×D4×D29C2211yescharacteristic, complemented
21C2×D8×C29C2211yescharacteristic, complemented
22C2×D8×C29C2211yescharacteristic, complemented
23C29×#127C2211yescharacteristic, complemented
24C4×D4×C29C2211yescharacteristic, complemented
25#11745300—21no—
26#11745300C2211yescharacteristic
27#11745300C2211yescharacteristic, complemented
28#11745299—21no—
29#11745299—21no—
30C2×#90783C2211yescharacteristic, complemented
31C2×#90783C2211yescharacteristic, complemented
32C2×#90782C2211yescharacteristic
33C2×#90782C2211yescharacteristic, complemented
34C2×#90782C2211yescharacteristic, complemented
35#11745292—21no—
36C2×#90781—21no—
37#11745273—24no—
38D8×D29—24no—
39C2×D232C2211yescharacteristic
40C2×#90773C2211yescharacteristic, complemented
41C2×#90772C2211yescharacteristic, complemented
42C2×C8×D29C2211yescharacteristic, complemented
43#11745259C2211yescharacteristic, complemented
44#11745257C2211yescharacteristic, complemented
45#11745248—21no—
46#11745244—21no—
47#11745237C2211yescharacteristic, complemented
48C4×D116C2211yescharacteristic
49C4×D116C2211yescharacteristic, complemented
50C29×C4⋊C8C2211yescharacteristic, complemented
51C29×#102C2211yescharacteristic, complemented
52C29×#102C2211yescharacteristic, complemented
53#11745180C2211yescharacteristic, complemented
54#11745169C2211yescharacteristic, complemented
55#11745168C2211yescharacteristic, complemented
56#11745168C2211yescharacteristic, complemented
57#11745164C2211yescharacteristic, complemented
58#11745157C2211yescharacteristic, complemented
59#11745156C2211yescharacteristic, complemented
60#11745151C2211yescharacteristic, complemented
61C23×D29—21no—
62C23×D29—21no—
63C23×D29—21no—
64C2×D4×C29—21no—
65C2×D4×C29—21no—
66C2×D4×C29C2311yescharacteristic
67C2×D4×C29C2311yescharacteristic
68C2×D4×C29C2311yescharacteristic
69C22×C4×C29—21no—
70C2×C22⋊D29—21no—
71C2×C22⋊D29—21no—
72C2×C22⋊D29—21no—
73C2×C22⋊D29—21no—
74C2×C22⋊D29—21no—
75C2×C22⋊D29—21no—
76C22×Dic29—21no—
77#90807—22no—
78#90807—41no—
79D4×D29—22no—
80D4×D29—22no—
81D4×D29—22no—
82D4×D29—41no—
83D4×D29—41no—
84D4×D29—41no—
85D4×D29—44no—
86C2×D116—21no—
87C2×D116D411yescharacteristic
88C2×D116C2311yescharacteristic
89C2×D116C2311yescharacteristic
90C2×C4×D29—21no—
91C2×C4×D29C2311yescharacteristic
92C2×C4×D29C2311yescharacteristic
93C2×Dic58C2311yescharacteristic
94D8×C29—22no—
95D8×C29—22no—
96C2×C8×C29C2311yescharacteristic
97C2×C8×C29C2311yescharacteristic
98C4⋊C4×C29C2311yescharacteristic
99C22⋊C4×C29—21no—
100C42×C29C2311yescharacteristic
101C22⋊Dic29—21no—
102C22⋊Dic29—21no—
103#90783—22no—
104#90783—41no—
105#90782—22no—
106#90782—41no—
107#90782D414yescomplemented
108#90781—21no—
109#90781—21no—
110#90781—21no—
111#90781—21no—
112#90781—21no—
113#90781D411yescharacteristic
114#90781D411yescharacteristic
115C4⋊Dic29—21no—
116C4⋊Dic29D411yescharacteristic
117C4⋊Dic29C2311yescharacteristic
118C2×#6597C2311yescharacteristic
119C2×#6597C2311yescharacteristic
120D232—22no—
121#90773—22no—
122#90772—22no—
123C8×D29—22no—
124C23×C29—21no—
125C23×C29—21no—
126C23×C29—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
140D4×C29—21no—
141D4×C29—21no—
142D4×C29—21no—
143D4×C29—21no—
144D4×C29—21no—
145D4×C29—42no—
146D4×C29—81no—
147D4×C29C2×D412yescomplemented
148C2×C4×C29—21no—
149C2×C4×C29—81no—
150C2×C4×C29C2×D411yescharacteristic
151C2×C4×C29C2×D411yescharacteristic
152C2×C4×C29C2411yescharacteristic
153C22⋊D29—42no—
154C22⋊D29—42no—
155C22⋊D29—42no—
156C22⋊D29—42no—
157C22⋊D29—42no—
158C22⋊D29—42no—
159C2×Dic29—21no—
160C2×Dic29—21no—
161C2×Dic29—42no—
162C2×Dic29C2×D411yescharacteristic
163C2×Dic29C2×D411yescharacteristic
164D116—22no—
165D116—21no—
166D116—21no—
167D116—21no—
168D116—81no—
169D116C2×D412yes—
170C4×D29—21no—
171C4×D29—21no—
172C4×D29—21no—
173C4×D29—21no—
174C4×D29—42no—
175Dic58—21no—
176Dic58—21no—
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×C29—41no—
189C22×C29—41no—
190C22×C29—41no—
191C22×C29C22×D411yescharacteristic
192C2×D29—21no—
193C2×D29—21no—
194C2×D29—21no—
195C2×D29—22no—
196C2×D29—21no—
197C2×D29—21no—
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×C29C22×D411yescharacteristic
211C4×C29H(5,𝔽2)11yescharacteristic
212Dic29—21no—
213Dic29—21no—
214Dic29—41no—
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#463—291no—
224#459D2911yescharacteristic, complemented
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×C29—81no—
234C2×C29D4211yescharacteristic
235C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
236C2×C29#57611yescharacteristic
237D29—22no—
238D29—41no—
239D29—42no—
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×SD16—291no—
250C2×D8—291no—
251C2×D8—291no—
252C2×D8—291no—
253C2×D8—291no—
254C2×D8—584no—
255C2×D8C2×D2911yescharacteristic, complemented
256C2×D8C2×D2911yescharacteristic, complemented
257C2×M16—291no—
258C22×C8—291no—
259#127C2×D2911yescharacteristic, complemented
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×D4C2×D2911yescharacteristic, complemented
274C2×C22⋊C4—581no—
275#106—291no—
276C4⋊C8C2×D2911yescharacteristic, complemented
277#103—291no—
278#102—291no—
279#102—291no—
280#102—291no—
281#102C2×D2911yescharacteristic, complemented
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×Q8—291no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—291no—
296C2×D4—291no—
297C2×D4—291no—
298C2×D4—581no—
299C2×D4—581no—
300C2×D4—581no—
301C2×D4—581no—
302C2×D4—582no—
303C2×D4—582no—
304C2×D4—582no—
305C2×D4—581no—
306C2×D4—581no—
307C2×D4—581no—
308C2×D4—1161no—
309C2×D4—1161no—
310C2×D4—1161no—
311C2×D4—1164no—
312C2×D4C22×D2911yescharacteristic
313C2×D4C22×D2911yescharacteristic
314C2×D4C22×D2911yescharacteristic
315C22×C4—21no—
316C22×C4—291no—
317C22×C4—291no—
318C22×C4—581no—
319C22×C4—581no—
320SD16—582no—
321SD16—582no—
322SD16—1161no—
323D8—22no—
324D8—22no—
325D8—294no—
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—291no—
341C22⋊C4—291no—
342C22⋊C4—581no—
343C22⋊C4—581no—
344C22⋊C4—581no—
345C22⋊C4—581no—
346C22⋊C4—581no—
347C22⋊C4—581no—
348C22⋊C4—581no—
349C42C22×D2911yescharacteristic
350C23—21no—
351C23—21no—
352C23—21no—
353C23—291no—
354C23—291no—
355C23—581no—
356C23—581no—
357C23—1162no—
358C23—1162no—
359C23—1162no—
360C23—1162no—
361C23—1162no—
362C23—1162no—
363C23—2321no—
364C23—2321no—
365C23—2321no—
366Q8—581no—
367Q8—581no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—42no—
374D4—81no—
375D4—292no—
376D4—582no—
377D4—581no—
378D4—581no—
379D4—581no—
380D4—1162no—
381D4—1162no—
382D4—1162no—
383D4—1162no—
384D4—1162no—
385D4—1162no—
386D4—2321no—
387D4D4×D2912yescomplemented
388C2×C4—21no—
389C2×C4—81no—
390C2×C4—291no—
391C2×C4—291no—
392C2×C4—581no—
393C2×C4—581no—
394C2×C4—581no—
395C2×C4—581no—
396C2×C4—581no—
397C2×C4—581no—
398C2×C4—1162no—
399C2×C4—1162no—
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—41no—
414C22—41no—
415C22—41no—
416C22—292no—
417C22—581no—
418C22—581no—
419C22—581no—
420C22—582no—
421C22—581no—
422C22—581no—
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—581no—
436C4—581no—
437C4—1161no—
438C4—1161no—
439C4C2×D4×D2911yescharacteristic
440C4#1174536411yescharacteristic
441C2—42no—
442C2—81no—
443C2—81no—
444C2—582no—
445C2—1161no—
446C2—1162no—
447C2—2321no—
448C2#1427179711yescharacteristic
449C2AGL(1,ℤ/8)×D2911yescharacteristic
450C2#1427196411yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#459C2
socleC22×C29C22×D4
hypercenter#459D29
hypocenterC29#3264
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#11745273C2semidirect
2. C2×D8×D29C2semidirect
3. #14271808C2semidirect
4. #14271798C2semidirect
5. #14271550C2semidirect
6. #14271415C2semidirect
7. #14271391C2semidirect
8. #14271379C2semidirect
9. #14271315C2semidirect
10. #14271305C2semidirect
11. #14271298C2semidirect
12. #14271295C2semidirect
13. #14271273C2semidirect
14. #14271233C2semidirect
15. C29×#459C2semidirect
16. C2×#90807C22semidirect
19. C2×D4×D29C22semidirect
20. C2×D4×D29C22semidirect
21. C2×D8×C29C22semidirect
22. C2×D8×C29C22semidirect
23. C29×#127C22semidirect
24. C4×D4×C29C22semidirect
27. #11745300C22semidirect
30. C2×#90783C22semidirect
31. C2×#90783C22semidirect
33. C2×#90782C22semidirect
34. C2×#90782C22semidirect
40. C2×#90773C22semidirect
41. C2×#90772C22semidirect
42. C2×C8×D29C22semidirect
43. #11745259C22semidirect
44. #11745257C22semidirect
47. #11745237C22semidirect
49. C4×D116C22semidirect
50. C29×C4⋊C8C22semidirect
51. C29×#102C22semidirect
52. C29×#102C22semidirect
53. #11745180C22semidirect
54. #11745169C22semidirect
55. #11745168C22semidirect
56. #11745168C22semidirect
57. #11745164C22semidirect
58. #11745157C22semidirect
59. #11745156C22semidirect
60. #11745151C22semidirect
107. #90782D4semidirect
147. D4×C29C2×D4semidirect
180. #6597C2×D4semidirect
206. C2×D29AGL(1,ℤ/8)semidirect
224. #459D29semidirect
255. C2×D8C2×D29semidirect
256. C2×D8C2×D29semidirect
259. #127C2×D29semidirect
273. C4×D4C2×D29semidirect
276. C4⋊C8C2×D29semidirect
281. #102C2×D29semidirect
282. #102C2×D29semidirect
286. C29#3264semidirect
387. D4D4×D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117452732
C2×D8×D292
#142718082
#142717982
#142715502
#142714152
#142713912
#142713792
#142713152
#142713052
#142712982
#142712952
#142712732
#142712332
C29×#4592
#326429