Finite Group Databasebeta

← #16829112

Subgroups — #16829112

Order 3712.

548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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×#11745270C211yesmaximal, characteristic, complemented
2C2×M16×D29C211yesmaximal, characteristic, complemented
3#14271675C211yesmaximal, characteristic, complemented
4C2×#11745257C211yesmaximal, characteristic, complemented
5#14271417C212yesmaximal, complemented
6#14271410C212yesmaximal, complemented
7#14271400C212yesmaximal, complemented
8#14271393C212yesmaximal, complemented
9#14271167C211yesmaximal, characteristic, complemented
10#14271162C211yesmaximal, characteristic, complemented
11C29×#428C211yesmaximal, characteristic, complemented
12C2×#90805C2211yescharacteristic
13C22×D116—21no—
14C22×D116C2211yescharacteristic
15C22×C4×D29C2211yescharacteristic
16C2×M16×C29C2211yescharacteristic
17C29×#117C2211yescharacteristic
18C2×C4⋊C4×C29C2211yescharacteristic
19C2×#90781—21no—
20C2×#90777C2211yescharacteristic
21#11745270—24no—
22M16×D29—24no—
23C2×D232C2212yescomplemented
24C2×#90773C2212yescomplemented
25C2×#90772C2212yescomplemented
26C2×C8×D29C2212yescomplemented
27#11745259C2211yescharacteristic, complemented
28#11745259C2211yescharacteristic, complemented
29#11745257—21no—
30#11745257—21no—
31#11745257C2212yes—
32#11745257C2212yes—
33#11745257C2211yescharacteristic, complemented
34#11745257C2211yescharacteristic, complemented
35#11745248—21no—
36#11745244—21no—
37C4×D116—21no—
38C4×D116—21no—
39C29×#107C2212yescomplemented
40C29×#106C2212yescomplemented
41#11745158C2212yescomplemented
42#11745157C2212yescomplemented
43#11745157C2212yescomplemented
44#11745157C2212yescomplemented
45C23×D29—21no—
46C23×D29D411yescharacteristic
47C22×C4×C29—21no—
48C22×C4×C29C2311yescharacteristic
49C2×C22⋊D29—21no—
50C22×Dic29D411yescharacteristic
51#90805—22no—
52#90805—22no—
53C2×D116—22no—
54C2×D116—22no—
55C2×D116—22no—
56C2×D116—22no—
57C2×D116—21no—
58C2×D116—21no—
59C2×D116—21no—
60C2×D116—44no—
61C2×D116C2312yes—
62C2×D116C2311yescharacteristic
63C2×C4×D29—22no—
64C2×C4×D29—22no—
65C2×C4×D29—21no—
66C2×C4×D29D411yescharacteristic
67C2×C4×D29D411yescharacteristic
68C2×C4×D29C2311yescharacteristic
69C2×C4×D29C2311yescharacteristic
70C2×Dic58C2311yescharacteristic
71M16×C29D414yescomplemented
72C2×C8×C29C2312yes—
73C4⋊C4×C29—21no—
74C4⋊C4×C29C2312yes—
75C4⋊C4×C29C2311yescharacteristic
76C4⋊C4×C29C2311yescharacteristic
77C22⋊C4×C29—21no—
78C42×C29—21no—
79#90781—21no—
80#90781—21no—
81#90781—22no—
82#90781—22no—
83#90781—21no—
84#90781—21no—
85C4⋊Dic29—21no—
86C4⋊Dic29—21no—
87#90777—22no—
88C2×#6597C2312yes—
89D232—24no—
90#90773—24no—
91#90772—24no—
92C8×D29—24no—
93C23×C29C2×D411yescharacteristic
94C22×D29—22no—
95C22×D29—22no—
96C22×D29—21no—
97C22×D29—22no—
98C22×D29—41no—
99C22×D29—42no—
100C22×D29—42no—
101C22×D29—42no—
102C22×D29C2×D411yescharacteristic
103C22×D29C2×D411yescharacteristic
104C2×C4×C29—21no—
105C2×C4×C29—21no—
106C2×C4×C29—22no—
107C2×C4×C29—42no—
108C2×C4×C29C2×D412yes—
109C2×C4×C29C2×D411yescharacteristic
110C2×C4×C29#4112yes—
111C2×C4×C29C2411yescharacteristic
112C22⋊D29—42no—
113C2×Dic29—22no—
114C2×Dic29—21no—
115C2×Dic29C2×D411yescharacteristic
116C2×Dic29C2×D411yescharacteristic
117D116—22no—
118D116—21no—
119D116—22no—
120D116—21no—
121D116—42no—
122D116—44no—
123D116—42no—
124D116—44no—
125D116—42no—
126C4×D29—22no—
127C4×D29—22no—
128C4×D29—21no—
129C4×D29—21no—
130C4×D29—21no—
131C4×D29—21no—
132C4×D29—42no—
133Dic58—21no—
134Dic58—21no—
135C8×C29C2×D414yescomplemented
136#6597—22no—
137#3055—291nomaximal, Sylow
138C22×C29—21no—
139C22×C29—21no—
140C22×C29#12112yes—
141C22×C29C22×D411yescharacteristic
142C2×D29—21no—
143C2×D29—21no—
144C2×D29—21no—
145C2×D29—21no—
146C2×D29—21no—
147C2×D29—44no—
148C2×D29—41no—
149C2×D29—42no—
150C2×D29—42no—
151C2×D29—41no—
152C2×D29—41no—
153C2×D29—42no—
154C2×D29—84no—
155C2×D29AGL(1,ℤ/8)12yescomplemented
156C4×C29—42no—
157C4×C29—41no—
158C4×C29—41no—
159C4×C29#12112yes—
160C4×C29C22×D411yescharacteristic
161C4×C29C2×#4111yescharacteristic
162Dic29—21no—
163Dic29—21no—
164Dic29—41no—
165C2×AGL(1,ℤ/8)—291no—
166C22×M16—291no—
167#525—291no—
168C2×#121—291no—
169#469—292no—
170#468—292no—
171#466—292no—
172#465—292no—
173#428D2911yescharacteristic, complemented
174#418—291no—
175#417—291no—
176C2×C29—22no—
177C2×C29C2×#12111yescharacteristic
178C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
179C2×C29#57511yescharacteristic
180D29—22no—
181D29—41no—
182D29—81no—
183D29—82no—
184C2×#41—291no—
185C22×D4—291no—
186C22×D4—581no—
187C23×C4—291no—
188AGL(1,ℤ/8)—584no—
189C2×SD16—292no—
190C2×D8—292no—
191C2×M16—291no—
192C2×M16—292no—
193C2×M16—584no—
194C2×M16C2×D2911yescharacteristic
195C22×C8—292no—
196#123—581no—
197C22⋊Q8—291no—
198C22⋊Q8—291no—
199#121—292no—
200#121—292no—
201#121—291no—
202#121—291no—
203#121—581no—
204#121—581no—
205#120—581no—
206C4×D4—581no—
207C4×D4—581no—
208#117C2×D2911yescharacteristic
209C2×C4⋊C4C2×D2911yescharacteristic
210C2×C22⋊C4—581no—
211#107C2×D2912yescomplemented
212#106C2×D2912yescomplemented
213#103—292no—
214#102—292no—
215#102—292no—
216#102—292no—
217C29#305511yescharacteristic, complemented, Sylow
218C24—291no—
219C24—581no—
220#41—582no—
221#41—582no—
222C2×Q8—291no—
223C2×D4—291no—
224C2×D4—292no—
225C2×D4—581no—
226C2×D4—581no—
227C2×D4—582no—
228C2×D4—582no—
229C2×D4—581no—
230C2×D4—582no—
231C2×D4—581no—
232C2×D4—582no—
233C2×D4—1164no—
234C22×C4—21no—
235C22×C4—291no—
236C22×C4—291no—
237C22×C4—291no—
238C22×C4—291no—
239C22×C4—291no—
240C22×C4—582no—
241C22×C4—582no—
242C22×C4—581no—
243C22×C4C22×D2911yescharacteristic
244SD16—584no—
245D8—584no—
246M16—582no—
247M16—584no—
248M16D11614yescomplemented
249C2×C8—292no—
250C2×C8—584no—
251C2×C8C22×D2912yes—
252C4⋊C4—21no—
253C4⋊C4—581no—
254C4⋊C4—581no—
255C4⋊C4C22×D2911yescharacteristic
256C4⋊C4C22×D2911yescharacteristic
257C4⋊C4C22×D2912yes—
258C22⋊C4—21no—
259C22⋊C4—582no—
260C22⋊C4—582no—
261C22⋊C4—581no—
262C22⋊C4—581no—
263C22⋊C4—581no—
264C22⋊C4—581no—
265C42—21no—
266C23—291no—
267C23—291no—
268C23—582no—
269C23—582no—
270C23—581no—
271C23—582no—
272C23—1161no—
273C23—1162no—
274C23—1162no—
275C23—1162no—
276C23D4×D2911yescharacteristic
277Q8—581no—
278Q8—581no—
279D4—581no—
280D4—582no—
281D4—582no—
282D4—581no—
283D4—1164no—
284D4—1162no—
285D4—1164no—
286D4—1162no—
287D4—1162no—
288D4—1162no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—42no—
293C2×C4—291no—
294C2×C4—291no—
295C2×C4—582no—
296C2×C4—581no—
297C2×C4—581no—
298C2×C4—581no—
299C2×C4—581no—
300C2×C4—582no—
301C2×C4—582no—
302C2×C4—581no—
303C2×C4—1162no—
304C2×C4C2×D11612yes—
305C2×C4D4×D2911yescharacteristic
306C2×C4#9080912yes—
307C2×C4C23×D2911yescharacteristic
308C8—582no—
309C8C2×D11614yescomplemented
310C22—21no—
311C22—21no—
312C22—292no—
313C22—581no—
314C22—581no—
315C22—581no—
316C22—581no—
317C22—581no—
318C22—1164no—
319C22—1161no—
320C22—1162no—
321C22—1162no—
322C22—1161no—
323C22—1161no—
324C22—1162no—
325C22—2324no—
326C22#1174525712yes—
327C22C2×D4×D2911yescharacteristic
328C4—42no—
329C4—41no—
330C4—41no—
331C4—581no—
332C4—581no—
333C4—1161no—
334C4#1174525712yes—
335C4C22×D11611yescharacteristic
336C4C2×#9080911yescharacteristic
337C2—22no—
338C2—582no—
339C2—1161no—
340C2—2322no—
341C2—2321no—
342C2C2×#1174525711yescharacteristic
343C2AGL(1,ℤ/8)×D2911yescharacteristic
344C2#1427196211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#428C2
socleC22×C29C22×D4
hypercenter#428D29
hypocenterC29#3055
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#11745270C2semidirect
2. C2×M16×D29C2semidirect
3. #14271675C2semidirect
4. C2×#11745257C2semidirect
5. #14271417C2semidirect
6. #14271410C2semidirect
7. #14271400C2semidirect
8. #14271393C2semidirect
9. #14271167C2semidirect
10. #14271162C2semidirect
11. C29×#428C2semidirect
23. C2×D232C22semidirect
24. C2×#90773C22semidirect
25. C2×#90772C22semidirect
26. C2×C8×D29C22semidirect
27. #11745259C22semidirect
28. #11745259C22semidirect
33. #11745257C22semidirect
34. #11745257C22semidirect
39. C29×#107C22semidirect
40. C29×#106C22semidirect
41. #11745158C22semidirect
42. #11745157C22semidirect
43. #11745157C22semidirect
44. #11745157C22semidirect
71. M16×C29D4semidirect
135. C8×C29C2×D4semidirect
155. C2×D29AGL(1,ℤ/8)semidirect
173. #428D29semidirect
211. #107C2×D29semidirect
212. #106C2×D29semidirect
217. C29#3055semidirect
248. M16D116semidirect
309. C8C2×D116semidirect

Maximal subgroups

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

subgroupindex
C2×#117452702
C2×M16×D292
#142716752
C2×#117452572
#142714172
#142714102
#142714002
#142713932
#142711672
#142711622
C29×#4282
#305529