Finite Group Databasebeta

← #16828801

Subgroups — #16828801

Order 3712.

764 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745359C211yesmaximal, characteristic, complemented
2C2×#11745294C211yesmaximal, characteristic, complemented
3C2×#11745266C211yesmaximal, characteristic, complemented
4#14271744C211yesmaximal, characteristic, complemented
5#14271326C212yesmaximal, complemented
6#14271315C212yesmaximal, complemented
7#14271309C212yesmaximal, complemented
8#14271298C212yesmaximal, complemented
9#14271162C211yesmaximal, characteristic, complemented
10#14271129C211yesmaximal, characteristic, complemented
11C2×C29×#102C211yesmaximal, characteristic, complemented
12C22×D4×C29C2211yescharacteristic
13C22×C22⋊D29—22no—
14#11745359—24no—
15#11745359—24no—
16C2×#90807—21no—
17C2×#90807C2212yes—
18C2×D4×D29—21no—
19C2×D4×D29C2212yes—
20C2×#90805C2211yescharacteristic
21C2×#90805C2211yescharacteristic
22C2×#90805C2211yescharacteristic, complemented
23C22×C8×C29C2211yescharacteristic, complemented
24C2×C4⋊C4×C29C2211yescharacteristic, complemented
25C2×#90783C2212yescomplemented
26#11745294—24no—
27C2×#90782C2212yescomplemented
28#11745292—22no—
29C2×#90777C2211yescharacteristic, complemented
30C2×Dic116C2211yescharacteristic, complemented
31#11745266—24no—
32C2×D232C2211yescharacteristic, complemented
33C2×#90773C2211yescharacteristic, complemented
34C2×#90773C2211yescharacteristic, complemented
35#11745259—21no—
36#11745259C2212yescomplemented
37#11745257—21no—
38#11745257C2212yescomplemented
39C29×#102C2212yescomplemented
40C29×#102C2212yescomplemented
41#11745168C2212yescomplemented
42#11745168C2212yescomplemented
43#11745158C2212yescomplemented
44#11745157C2212yescomplemented
45C24×C29—21no—
46C23×D29—22no—
47C2×D4×C29—21no—
48C2×D4×C29—22no—
49C2×D4×C29D414yescomplemented
50C2×D4×C29C2312yes—
51C22×C4×C29—21no—
52C22×C4×C29C2311yescharacteristic
53C2×C22⋊D29—216no—
54C2×C22⋊D29—21no—
55C2×C22⋊D29—22no—
56C2×C22⋊D29—21no—
57C2×C22⋊D29—22no—
58C2×C22⋊D29D412yes—
59C22×Dic29—22no—
60#90807—28no—
61#90807—24no—
62#90807—24no—
63D4×D29—28no—
64D4×D29—24no—
65D4×D29—24no—
66#90805—22no—
67#90805—22no—
68#90805—22no—
69#90805—22no—
70#90805—22no—
71#90805D414yescomplemented
72C2×D116—22no—
73C2×D116D411yescharacteristic
74C2×D116C2311yescharacteristic
75C2×D116C2311yescharacteristic
76C2×C4×D29—21no—
77C2×C4×D29—21no—
78C2×C4×D29C2312yes—
79C2×Dic58D411yescharacteristic
80C2×Dic58C2311yescharacteristic
81C2×Dic58C2311yescharacteristic
82C2×C8×C29—22no—
83C2×C8×C29C2311yescharacteristic
84C2×C8×C29C2311yescharacteristic
85C4⋊C4×C29—21no—
86C4⋊C4×C29C2312yes—
87#90783—24no—
88#90782—24no—
89#90781—22no—
90#90781—22no—
91C4⋊Dic29—22no—
92#90777—22no—
93C2×#6597C2312yes—
94Dic116—22no—
95D232—22no—
96#90773—22no—
97#90773—22no—
98C23×C29—22no—
99C23×C29—24no—
100C23×C29—81no—
101C23×C29—81no—
102C23×C29C2×D411yescharacteristic
103C22×D29—21no—
104C22×D29—28no—
105C22×D29—21no—
106C22×D29—82no—
107C22×D29—82no—
108C22×D29C2×D412yes—
109D4×C29—24no—
110D4×C29—22no—
111D4×C29C2×D414yes—
112C2×C4×C29—22no—
113C2×C4×C29—81no—
114C2×C4×C29C2×D412yes—
115C2×C4×C29C2×D411yescharacteristic
116C2×C4×C29C2×D412yes—
117C2×C4×C29C2411yescharacteristic
118C22⋊D29—28no—
119C22⋊D29—28no—
120C22⋊D29—24no—
121C22⋊D29—24no—
122C22⋊D29—42no—
123C2×Dic29—28no—
124C2×Dic29—21no—
125C2×Dic29—21no—
126C2×Dic29C2×D412yes—
127D116—22no—
128D116—21no—
129D116—21no—
130D116—21no—
131D116—82no—
132D116C2×D412yes—
133C4×D29—24no—
134C4×D29—22no—
135C4×D29—22no—
136C4×D29—42no—
137Dic58—22no—
138Dic58—21no—
139Dic58—21no—
140Dic58—21no—
141Dic58C2×D412yes—
142C8×C29—21no—
143C8×C29—21no—
144#6597—22no—
145#3012—291nomaximal, Sylow
146C22×C29—21no—
147C22×C29—21no—
148C22×C29—24no—
149C22×C29—42no—
150C22×C29—42no—
151C22×C29—84no—
152C22×C29#12012yes—
153C22×C29C22×D411yescharacteristic
154C2×D29—22no—
155C2×D29—22no—
156C2×D29—22no—
157C2×D29—22no—
158C2×D29—41no—
159C2×D29—41no—
160C2×D29—41no—
161C2×D29—41no—
162C2×D29—41no—
163C2×D29—88no—
164C4×C29—42no—
165C4×C29#12012yes—
166C4×C29C22×D411yescharacteristic
167C4×C29C22×D411yescharacteristic
168Dic29—22no—
169Dic29—22no—
170Dic29—41no—
171C2×H(5,𝔽2)—291no—
172C2×AGL(1,ℤ/8)—291no—
173C2×#135—291no—
174#537—291no—
175#452—292no—
176#450—292no—
177#449—292no—
178#447—292no—
179#417—291no—
180C2×#102D2911yescharacteristic, complemented
181#408—291no—
182C2×C29—22no—
183C2×C29—44no—
184C2×C29C2×#12011yescharacteristic
185C2×C29#57611yescharacteristic
186C2×C29#57711yescharacteristic
187D29—42no—
188D29—42no—
189D29—81no—
190H(5,𝔽2)—584no—
191H(5,𝔽2)—584no—
192C2×#41—291no—
193C2×#41—292no—
194C2×#41—291no—
195C2×#41—291no—
196C2×#41—581no—
197C22×D4—292no—
198C22×D4—581no—
199C22×D4—582no—
200C22×D4C2×D2911yescharacteristic
201AGL(1,ℤ/8)—584no—
202#135—584no—
203C2×Q16—291no—
204C2×SD16—292no—
205C2×SD16—291no—
206C2×SD16—291no—
207C2×D8—292no—
208C2×D8—291no—
209C2×M16—291no—
210C22×C8C2×D2911yescharacteristic, complemented
211C22⋊Q8—292no—
212C22⋊Q8—581no—
213#121—292no—
214#121—581no—
215#121—582no—
216C2×C4⋊C4C2×D2911yescharacteristic, complemented
217#103—292no—
218#102—292no—
219#102C2×D2912yescomplemented
220#102C2×D2912yescomplemented
221C22⋊C8—292no—
222C22⋊C8—292no—
223C29#301211yescharacteristic, complemented, Sylow
224C24—21no—
225C24—582no—
226#41—294no—
227#41—584no—
228#41—588no—
229#41—584no—
230#41—582no—
231#41—582no—
232#41—582no—
233#41—582no—
234#41—582no—
235C2×Q8—291no—
236C2×Q8—291no—
237C2×Q8—291no—
238C2×D4—21no—
239C2×D4—22no—
240C2×D4—292no—
241C2×D4—291no—
242C2×D4—291no—
243C2×D4—291no—
244C2×D4—582no—
245C2×D4—582no—
246C2×D4—584no—
247C2×D4—588no—
248C2×D4—582no—
249C2×D4—5816no—
250C2×D4—581no—
251C2×D4—584no—
252C2×D4—581no—
253C2×D4D11614yescomplemented
254C2×D4C22×D2912yes—
255C22×C4—21no—
256C22×C4—292no—
257C22×C4—582no—
258C22×C4—581no—
259C22×C4—581no—
260C22×C4C22×D2911yescharacteristic
261Q16—582no—
262SD16—582no—
263SD16—582no—
264SD16—584no—
265D8—582no—
266D8—584no—
267M16—582no—
268C2×C8—22no—
269C2×C8—292no—
270C2×C8C22×D2911yescharacteristic
271C2×C8C22×D2911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—582no—
274C4⋊C4C22×D2912yes—
275C22⋊C4—582no—
276C22⋊C4—582no—
277C23—22no—
278C23—24no—
279C23—81no—
280C23—81no—
281C23—292no—
282C23—588no—
283C23—581no—
284C23—581no—
285C23—2322no—
286C23—2322no—
287C23D4×D2911yescharacteristic
288Q8—292no—
289Q8—581no—
290Q8—582no—
291Q8—581no—
292Q8—581no—
293D4—22no—
294D4—24no—
295D4—292no—
296D4—588no—
297D4—588no—
298D4—584no—
299D4—584no—
300D4—581no—
301D4—581no—
302D4—581no—
303D4—582no—
304D4—1162no—
305D4—2322no—
306D4C2×D11614yes—
307C2×C4—22no—
308C2×C4—81no—
309C2×C4—292no—
310C2×C4—588no—
311C2×C4—581no—
312C2×C4—582no—
313C2×C4—582no—
314C2×C4—584no—
315C2×C4—581no—
316C2×C4—1162no—
317C2×C4C2×D11612yes—
318C2×C4D4×D2912yes—
319C2×C4D4×D2911yescharacteristic
320C2×C4C23×D2911yescharacteristic
321C8—21no—
322C8—21no—
323C8—582no—
324C22—21no—
325C22—21no—
326C22—24no—
327C22—42no—
328C22—42no—
329C22—84no—
330C22—582no—
331C22—582no—
332C22—582no—
333C22—582no—
334C22—1161no—
335C22—1161no—
336C22—1161no—
337C22—1161no—
338C22—1161no—
339C22—2328no—
340C22#1174524412yes—
341C22C2×D4×D2911yescharacteristic
342C4—42no—
343C4—582no—
344C4—582no—
345C4—1161no—
346C4#1174524412yes—
347C4C22×D11611yescharacteristic
348C4C2×D4×D2911yescharacteristic
349C2—22no—
350C2—44no—
351C2—1162no—
352C2—1162no—
353C2—2321no—
354C2C2×#1174524411yescharacteristic
355C2#1427196411yescharacteristic
356C2#1427196911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#102C2
socleC22×C29C22×D4
hypercenterC2×#102D29
hypocenterC29#3012
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#11745359C2semidirect
2. C2×#11745294C2semidirect
3. C2×#11745266C2semidirect
4. #14271744C2semidirect
5. #14271326C2semidirect
6. #14271315C2semidirect
7. #14271309C2semidirect
8. #14271298C2semidirect
9. #14271162C2semidirect
10. #14271129C2semidirect
11. C2×C29×#102C2semidirect
22. C2×#90805C22semidirect
23. C22×C8×C29C22semidirect
24. C2×C4⋊C4×C29C22semidirect
25. C2×#90783C22semidirect
27. C2×#90782C22semidirect
29. C2×#90777C22semidirect
30. C2×Dic116C22semidirect
32. C2×D232C22semidirect
33. C2×#90773C22semidirect
34. C2×#90773C22semidirect
36. #11745259C22semidirect
38. #11745257C22semidirect
39. C29×#102C22semidirect
40. C29×#102C22semidirect
41. #11745168C22semidirect
42. #11745168C22semidirect
43. #11745158C22semidirect
44. #11745157C22semidirect
49. C2×D4×C29D4semidirect
71. #90805D4semidirect
180. C2×#102D29semidirect
210. C22×C8C2×D29semidirect
216. C2×C4⋊C4C2×D29semidirect
219. #102C2×D29semidirect
220. #102C2×D29semidirect
223. C29#3012semidirect
253. C2×D4D116semidirect

Maximal subgroups

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

subgroupindex
C2×#117453592
C2×#117452942
C2×#117452662
#142717442
#142713262
#142713152
#142713092
#142712982
#142711622
#142711292
C2×C29×#1022
#301229