Finite Group Databasebeta

← #16830983

Subgroups — #16830983

Order 3712.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745294C211yesmaximal, characteristic, complemented
2C22×#90783C211yesmaximal, characteristic, complemented
3#14271822C211yesmaximal, characteristic, complemented
4#14271550C211yesmaximal, characteristic, complemented
5#14271407C211yesmaximal, characteristic, complemented
6#14271397C211yesmaximal, characteristic, complemented
7#14271378C211yesmaximal, characteristic, complemented
8#14271360C211yesmaximal, characteristic, complemented
9#14271314C211yesmaximal, characteristic, complemented
10#14271306C211yesmaximal, characteristic, complemented
11#14271301C211yesmaximal, characteristic, complemented
12#14271297C211yesmaximal, characteristic, complemented
13#14271263C211yesmaximal, characteristic, complemented
14#14271235C211yesmaximal, characteristic, complemented
15D42×C29C211yesmaximal, characteristic, complemented
16C22×D4×C29—21no—
17C22×D4×C29C2211yescharacteristic
18C22×D4×C29C2211yescharacteristic
19C2×#90805C2211yescharacteristic, complemented
20C22×Dic58C2211yescharacteristic, complemented
21C29×#127C2211yescharacteristic
22C29×#121—21no—
23C29×#121C2211yescharacteristic
24C29×#121C2211yescharacteristic
25C29×#120—21no—
26C29×#120—21no—
27C4×D4×C29C2211yescharacteristic
28C4×D4×C29C2211yescharacteristic
29#11745301—21no—
30C2×#90783—24no—
31C2×#90783C2211yescharacteristic
32C2×#90783C2211yescharacteristic
33C2×#90783C2211yescharacteristic, complemented
34C2×#90783C2211yescharacteristic, complemented
35C2×#90783C2211yescharacteristic, complemented
36C2×#90783C2211yescharacteristic, complemented
37#11745294—24no—
38C2×#90782C2211yescharacteristic
39C2×#90782C2211yescharacteristic, complemented
40C2×#90782C2211yescharacteristic, complemented
41#11745292C2211yescharacteristic, complemented
42#11745286C2211yescharacteristic, complemented
43C2×#90777C2211yescharacteristic, complemented
44C22×#6597C2211yescharacteristic, complemented
45#11745258—21no—
46#11745247—21no—
47#11745243—21no—
48#11745237C2211yescharacteristic, complemented
49C4×Dic58C2211yescharacteristic, complemented
50#11745180C2211yescharacteristic
51#11745180C2211yescharacteristic, complemented
52#11745180C2211yescharacteristic, complemented
53C22⋊#6597C2211yescharacteristic, complemented
54C22⋊#6597C2211yescharacteristic, complemented
55#11745158C2211yescharacteristic, complemented
56#11745158C2211yescharacteristic, complemented
57#11745157C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C4⋊#6597C2211yescharacteristic, complemented
60#11745151C2211yescharacteristic, complemented
61C24×C29—21no—
62C24×C29—21no—
63C2×D4×C29—22no—
64C2×D4×C29—22no—
65C2×D4×C29—21no—
66C2×D4×C29—21no—
67C2×D4×C29—21no—
68C2×D4×C29—21no—
69C2×D4×C29—21no—
70C2×D4×C29—21no—
71C2×D4×C29—41no—
72C2×D4×C29—41no—
73C2×D4×C29—44no—
74C2×D4×C29D411yescharacteristic
75C2×D4×C29C2311yescharacteristic
76C2×D4×C29C2311yescharacteristic
77C2×D4×C29C2311yescharacteristic
78C22×C4×C29—21no—
79C22×C4×C29C2311yescharacteristic
80C22×C4×C29C2311yescharacteristic
81C2×C22⋊D29—21no—
82C2×C22⋊D29—21no—
83C22×Dic29—21no—
84#90805—22no—
85#90805—41no—
86C2×D116C2311yescharacteristic
87C2×C4×D29—21no—
88C2×Dic58—22no—
89C2×Dic58—21no—
90C2×Dic58—41no—
91C2×Dic58C2311yescharacteristic
92C2×Dic58C2311yescharacteristic
93C4⋊C4×C29D411yescharacteristic
94C4⋊C4×C29C2311yescharacteristic
95C22⋊C4×C29—21no—
96C22⋊C4×C29—21no—
97C22⋊C4×C29—21no—
98C22⋊C4×C29D411yescharacteristic
99C22⋊C4×C29D411yescharacteristic
100C42×C29C2311yescharacteristic
101C22⋊Dic29—21no—
102#90783—22no—
103#90783—22no—
104#90783—22no—
105#90783—22no—
106#90783—41no—
107#90783D414yescomplemented
108#90782—22no—
109#90782—22no—
110#90782—41no—
111#90781—21no—
112#90781—21no—
113#90781—21no—
114C4⋊Dic29C2311yescharacteristic
115#90779—21no—
116#90779—21no—
117C4×Dic29—21no—
118#90777—22no—
119C2×#6597—22no—
120C2×#6597C2311yescharacteristic
121C2×#6597C2311yescharacteristic
122C2×#6597C2311yescharacteristic
123C2×#6597C2311yescharacteristic
124C23×C29—21no—
125C23×C29—21no—
126C23×C29—21no—
127C23×C29—42no—
128C23×C29—42no—
129C23×C29—42no—
130C23×C29—42no—
131C23×C29—81no—
132C23×C29—81no—
133C23×C29C2×D411yescharacteristic
134C23×C29C2×D411yescharacteristic
135C22×D29—21no—
136D4×C29—22no—
137D4×C29—21no—
138D4×C29—21no—
139D4×C29—21no—
140D4×C29—21no—
141D4×C29—21no—
142D4×C29—42no—
143D4×C29—42no—
144D4×C29—42no—
145D4×C29—42no—
146D4×C29—42no—
147D4×C29—81no—
148D4×C29C2×D412yes—
149C2×C4×C29—21no—
150C2×C4×C29—21no—
151C2×C4×C29—21no—
152C2×C4×C29—21no—
153C2×C4×C29—21no—
154C2×C4×C29—42no—
155C2×C4×C29C2×D411yescharacteristic
156C2×C4×C29C2×D411yescharacteristic
157C2×C4×C29C2×D411yescharacteristic
158C2×C4×C29C2×D411yescharacteristic
159C2×C4×C29C2411yescharacteristic
160C22⋊D29—42no—
161C22⋊D29—42no—
162C2×Dic29—21no—
163C2×Dic29—21no—
164C2×Dic29—21no—
165C2×Dic29—42no—
166D116—21no—
167D116—21no—
168C4×D29—42no—
169Dic58—21no—
170Dic58—21no—
171Dic58—21no—
172Dic58—42no—
173Dic58C2×D412yescomplemented
174#6597—21no—
175#6597—21no—
176#6597—21no—
177#6597C2×D412yescomplemented
178#3265—291nomaximal, Sylow
179C22×C29—21no—
180C22×C29—21no—
181C22×C29—21no—
182C22×C29—22no—
183C22×C29—21no—
184C22×C29—21no—
185C22×C29—41no—
186C22×C29—41no—
187C22×C29—41no—
188C22×C29—41no—
189C22×C29—41no—
190C22×C29—41no—
191C22×C29—41no—
192C22×C29—41no—
193C22×C29—84no—
194C22×C29—84no—
195C22×C29AGL(1,ℤ/8)12yescomplemented
196C22×C29C22×D411yescharacteristic
197C2×D29—41no—
198C2×D29—41no—
199C2×D29—41no—
200C4×C29—21no—
201C4×C29—21no—
202C4×C29—21no—
203C4×C29—21no—
204C4×C29—41no—
205C4×C29C22×D411yescharacteristic
206C4×C29H(5,𝔽2)11yescharacteristic
207Dic29—22no—
208Dic29—41no—
209Dic29—41no—
210C2×AGL(1,ℤ/8)—291no—
211C22×SD16—291no—
212#548—291no—
213D42D2911yescharacteristic, complemented
214#496—291no—
215#468—291no—
216#466—291no—
217#463—291no—
218#460—291no—
219#450—291no—
220#449—291no—
221#448—291no—
222#447—291no—
223#440—291no—
224#435—291no—
225C2×C29—22no—
226C2×C29—41no—
227C2×C29—42no—
228C2×C29—81no—
229C2×C29—81no—
230C2×C29D4211yescharacteristic
231C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
232C2×C29#57711yescharacteristic
233D29—81no—
234C2×#41—291no—
235C22×Q8—291no—
236C22×D4—21no—
237C22×D4C2×D2911yescharacteristic
238C22×D4C2×D2911yescharacteristic
239AGL(1,ℤ/8)—584no—
240C2×SD16—291no—
241C2×SD16—291no—
242C2×SD16—291no—
243C2×SD16—291no—
244C2×SD16—291no—
245C2×SD16—291no—
246C2×SD16—584no—
247C2×D8—291no—
248C2×D8—291no—
249C2×D8—291no—
250C2×M16—291no—
251C22×C8—291no—
252#127C2×D2911yescharacteristic
253#124—291no—
254#124—581no—
255C22⋊Q8—291no—
256C22⋊Q8—581no—
257#121—21no—
258#121—291no—
259#121—581no—
260#121C2×D2911yescharacteristic
261#121C2×D2911yescharacteristic
262#120—21no—
263#120—21no—
264C4×Q8—291no—
265C4×D4—581no—
266C4×D4C2×D2911yescharacteristic
267C4×D4C2×D2911yescharacteristic
268#107—291no—
269C4⋊C8—291no—
270#103—291no—
271#103—291no—
272#102—291no—
273#102—291no—
274#102—291no—
275#102—291no—
276C22⋊C8—291no—
277C22⋊C8—291no—
278#97—291no—
279C29#326511yescharacteristic, complemented, Sylow
280C24—21no—
281C24—21no—
282#41—582no—
283#41—1161no—
284C2×Q8—291no—
285C2×Q8—291no—
286C2×Q8—582no—
287C2×Q8—581no—
288C2×Q8—1161no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—44no—
300C2×D4—291no—
301C2×D4—581no—
302C2×D4—581no—
303C2×D4C22⋊D2911yescharacteristic
304C2×D4C22×D2911yescharacteristic
305C2×D4C22×D2911yescharacteristic
306C2×D4C22×D2911yescharacteristic
307C22×C4—21no—
308C22×C4—581no—
309C22×C4—581no—
310C22×C4C22×D2911yescharacteristic
311C22×C4C22×D2911yescharacteristic
312SD16—294no—
313SD16—582no—
314SD16—582no—
315SD16—582no—
316SD16—582no—
317SD16—1161no—
318D8—582no—
319D8—582no—
320D8—1161no—
321M16—582no—
322C2×C8—291no—
323C2×C8—291no—
324C2×C8—291no—
325C2×C8—291no—
326C2×C8—582no—
327C4⋊C4—291no—
328C4⋊C4—581no—
329C4⋊C4—581no—
330C4⋊C4C22⋊D2911yescharacteristic
331C4⋊C4C22×D2911yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—581no—
336C22⋊C4—581no—
337C22⋊C4—581no—
338C22⋊C4—581no—
339C22⋊C4C22⋊D2911yescharacteristic
340C22⋊C4C22⋊D2911yescharacteristic
341C42—581no—
342C42C22×D2911yescharacteristic
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—81no—
351C23—81no—
352C23—581no—
353C23C2×C22⋊D2911yescharacteristic
354C23C2×C22⋊D2911yescharacteristic
355Q8—292no—
356Q8—581no—
357Q8—581no—
358Q8—581no—
359Q8—1162no—
360D4—22no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—42no—
367D4—42no—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—81no—
372D4—581no—
373D4—581no—
374D4—1162no—
375D4—1162no—
376D4D4×D2912yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—581no—
384C2×C4—581no—
385C2×C4—581no—
386C2×C4—1162no—
387C2×C4—1162no—
388C2×C4C2×C22⋊D2911yescharacteristic
389C2×C4C2×C22⋊D2911yescharacteristic
390C2×C4C2×C22⋊D2911yescharacteristic
391C2×C4C2×C22⋊D2911yescharacteristic
392C2×C4C23×D2911yescharacteristic
393C8—292no—
394C8—581no—
395C8—581no—
396C8—581no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—84no—
412C22—84no—
413C22—1161no—
414C22—1161no—
415C22—1161no—
416C22#1174529412yescomplemented
417C22C22×C22⋊D2911yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—41no—
423C4—582no—
424C4—1161no—
425C4—1161no—
426C4C2×D4×D2911yescharacteristic
427C4#1174535911yescharacteristic
428C2—22no—
429C2—41no—
430C2—42no—
431C2—81no—
432C2—81no—
433C2—2321no—
434C2D4×C22⋊D2911yescharacteristic
435C2C2×#1174529411yescharacteristic
436C2#1427197411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingD42×C29C2
socleC22×C29C22×D4
hypercenterD42D29
hypocenterC29#3265
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#11745294C2semidirect
2. C22×#90783C2semidirect
3. #14271822C2semidirect
4. #14271550C2semidirect
5. #14271407C2semidirect
6. #14271397C2semidirect
7. #14271378C2semidirect
8. #14271360C2semidirect
9. #14271314C2semidirect
10. #14271306C2semidirect
11. #14271301C2semidirect
12. #14271297C2semidirect
13. #14271263C2semidirect
14. #14271235C2semidirect
15. D42×C29C2semidirect
19. C2×#90805C22semidirect
20. C22×Dic58C22semidirect
33. C2×#90783C22semidirect
34. C2×#90783C22semidirect
35. C2×#90783C22semidirect
36. C2×#90783C22semidirect
39. C2×#90782C22semidirect
40. C2×#90782C22semidirect
41. #11745292C22semidirect
42. #11745286C22semidirect
43. C2×#90777C22semidirect
44. C22×#6597C22semidirect
48. #11745237C22semidirect
49. C4×Dic58C22semidirect
51. #11745180C22semidirect
52. #11745180C22semidirect
53. C22⋊#6597C22semidirect
54. C22⋊#6597C22semidirect
55. #11745158C22semidirect
56. #11745158C22semidirect
57. #11745157C22semidirect
58. #11745155C22semidirect
59. C4⋊#6597C22semidirect
60. #11745151C22semidirect
107. #90783D4semidirect
173. Dic58C2×D4semidirect
177. #6597C2×D4semidirect
195. C22×C29AGL(1,ℤ/8)semidirect
213. D42D29semidirect
279. C29#3265semidirect
416. C22#11745294semidirect

Maximal subgroups

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

subgroupindex
C2×#117452942
C22×#907832
#142718222
#142715502
#142714072
#142713972
#142713782
#142713602
#142713142
#142713062
#142713012
#142712972
#142712632
#142712352
D42×C292
#326529