Finite Group Databasebeta

← #16829975

Subgroups — #16829975

Order 3712.

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

normal subgroups only

This group has 596 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×#11745294C211yesmaximal, characteristic, complemented
2C2×#11745311C211yesmaximal, characteristic, complemented
3C2×#11745312C211yesmaximal, characteristic, complemented
4C22×#90782C211yesmaximal, characteristic, complemented
5#14271732C211yesmaximal, characteristic, complemented
6#14271553C212yesmaximal, complemented
7#14271550C212yesmaximal, complemented
8#14271545C212yesmaximal, complemented
9#14271539C212yesmaximal, complemented
10#14271119C211yesmaximal, characteristic, complemented
11C29×#535C211yesmaximal, characteristic, complemented
12C2×#41×C29C2211yescharacteristic
13C22×D4×C29C2211yescharacteristic
14C2×#90805C2211yescharacteristic
15C22×D116C2211yescharacteristic
16C29×#127C2212yescomplemented
17C29×#124C2212yescomplemented
18C29×#121—22no—
19C29×#120—22no—
20C29×#117C2211yescharacteristic
21#11745312—24no—
22#11745311—24no—
23C2×#90785C2211yescharacteristic, complemented
24C2×#90784C2212yescomplemented
25C2×#90784C2211yescharacteristic, complemented
26C2×#90783C2212yescomplemented
27C2×#90783C2211yescharacteristic, complemented
28#11745294—24no—
29C2×#90782—24no—
30C2×#90782C2212yes—
31C2×#90782C2212yes—
32C2×#90782C2211yescharacteristic, complemented
33C2×#90782C2212yescomplemented
34C2×#90782C2212yescomplemented
35C2×#90777C2211yescharacteristic
36C22×#6597C2211yescharacteristic
37#11745257—22no—
38#11745244—22no—
39#11745237C2212yescomplemented
40#11745236C2212yescomplemented
41#11745151C2212yescomplemented
42C4×#6597C2212yescomplemented
43C24×C29—21no—
44C23×D29—21no—
45#41×C29—22no—
46#41×C29—22no—
47C2×Q8×C29C2311yescharacteristic
48C2×D4×C29—21no—
49C2×D4×C29—22no—
50C2×D4×C29—22no—
51C2×D4×C29—21no—
52C2×D4×C29—24no—
53C2×D4×C29C2312yes—
54C2×D4×C29C2311yescharacteristic
55C22×C4×C29—21no—
56C22×C4×C29C2311yescharacteristic
57C2×C22⋊D29—21no—
58#90805—22no—
59#90805—22no—
60C2×D116—22no—
61C2×D116—22no—
62C2×D116—21no—
63C2×D116—24no—
64C2×D116C2312yes—
65C2×D116C2311yescharacteristic
66C2×C4×D29—21no—
67C2×Dic58C2311yescharacteristic
68C4⋊C4×C29D412yes—
69C22⋊C4×C29—24no—
70C22⋊C4×C29D412yes—
71C42×C29C2312yes—
72#90785—22no—
73#90784—24no—
74#90784—22no—
75#90783—24no—
76#90783—22no—
77#90782—24no—
78#90782—24no—
79#90782—24no—
80#90782—24no—
81#90782—22no—
82#90781—24no—
83#90777D414yescomplemented
84C2×#6597D414yescomplemented
85C2×#6597C2311yescharacteristic
86C2×#6597C2311yescharacteristic
87C2×#6597C2312yes—
88C23×C29—22no—
89C23×C29—21no—
90C23×C29—42no—
91C23×C29—82no—
92C23×C29C2×D411yescharacteristic
93C22×D29—22no—
94C22×D29—21no—
95C22×D29—42no—
96C22×D29—82no—
97Q8×C29—21no—
98Q8×C29—21no—
99D4×C29—22no—
100D4×C29—21no—
101D4×C29—22no—
102D4×C29—21no—
103D4×C29—42no—
104D4×C29—42no—
105D4×C29—84no—
106C2×C4×C29—21no—
107C2×C4×C29—42no—
108C2×C4×C29C2×D412yes—
109C2×C4×C29C2×D412yes—
110C2×C4×C29C2×D414yes—
111C2×C4×C29C2×D411yescharacteristic
112C2×C4×C29C2411yescharacteristic
113C22⋊D29—42no—
114C2×Dic29—21no—
115D116—22no—
116D116—21no—
117D116—22no—
118D116—21no—
119D116—42no—
120D116—84no—
121C4×D29—42no—
122Dic58—21no—
123Dic58—21no—
124#6597C2×D412yes—
125#6597C2×D412yes—
126#6597C2×D414yes—
127#3155—291nomaximal, Sylow
128C22×C29—22no—
129C22×C29—41no—
130C22×C29—42no—
131C22×C29—42no—
132C22×C29—44no—
133C22×C29—84no—
134C22×C29#12712yes—
135C22×C29C22×D411yescharacteristic
136C2×D29—41no—
137C2×D29—42no—
138C2×D29—42no—
139C2×D29—44no—
140C2×D29—84no—
141C4×C29—24no—
142C4×C29—41no—
143C4×C29#12712yes—
144C4×C29C22×D411yescharacteristic
145C4×C29C22×D411yescharacteristic
146Dic29—41no—
147C2×AGL(1,ℤ/8)—291no—
148C2×AGL(1,ℤ/8)—291no—
149C2×#135—291no—
150C22×D8—291no—
151#535—291no—
152#535D2911yescharacteristic, complemented
153#496—292no—
154#496—292no—
155#495—292no—
156#493—292no—
157#405—291no—
158C2×C29—22no—
159C2×C29—81no—
160C2×C29—82no—
161C2×C29C2×#12711yescharacteristic
162C2×C29#57612yes—
163D29—81no—
164D29—82no—
165C2×#41—291no—
166C2×#41C2×D2911yescharacteristic
167C22×D4—291no—
168C22×D4C2×D2911yescharacteristic
169AGL(1,ℤ/8)—584no—
170AGL(1,ℤ/8)—584no—
171#135—584no—
172C2×Q16—291no—
173C2×SD16—291no—
174C2×SD16—292no—
175C2×SD16—291no—
176C2×SD16—292no—
177C2×D8—292no—
178C2×D8—292no—
179C2×D8—291no—
180C2×D8—292no—
181C2×D8—292no—
182C2×D8—584no—
183C2×M16—291no—
184C22×C8—291no—
185#127—292no—
186#127C2×D2912yescomplemented
187#124—292no—
188#124C2×D2912yescomplemented
189#121—22no—
190#121—582no—
191#120—22no—
192#120—582no—
193#117C2×D2911yescharacteristic
194#97—292no—
195C4×C8—292no—
196C29#315511yescharacteristic, complemented, Sylow
197C24—21no—
198C24—581no—
199#41—22no—
200#41—22no—
201#41—582no—
202#41—582no—
203C2×Q8—291no—
204C2×Q8C22×D2911yescharacteristic
205C2×D4—21no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—24no—
210C2×D4—292no—
211C2×D4—291no—
212C2×D4—581no—
213C2×D4—582no—
214C2×D4—582no—
215C2×D4—581no—
216C2×D4—584no—
217C2×D4C22×D2912yes—
218C2×D4C22×D2911yescharacteristic
219C22×C4—21no—
220C22×C4—581no—
221C22×C4C22×D2911yescharacteristic
222Q16—582no—
223SD16—582no—
224SD16—584no—
225SD16—582no—
226SD16—584no—
227D8—584no—
228D8—584no—
229D8—582no—
230D8—584no—
231D8—584no—
232M16—294no—
233C2×C8—294no—
234C2×C8—291no—
235C2×C8—292no—
236C2×C8—291no—
237C4⋊C4C22⋊D2912yes—
238C22⋊C4—24no—
239C22⋊C4—584no—
240C22⋊C4C22⋊D2912yes—
241C42C22×D2912yes—
242C23—22no—
243C23—21no—
244C23—42no—
245C23—82no—
246C23—582no—
247C23—581no—
248C23—1162no—
249C23—2322no—
250C23C2×C22⋊D2911yescharacteristic
251Q8—21no—
252Q8—21no—
253Q8—581no—
254Q8—581no—
255D4—22no—
256D4—21no—
257D4—22no—
258D4—21no—
259D4—42no—
260D4—42no—
261D4—84no—
262D4—582no—
263D4—581no—
264D4—582no—
265D4—581no—
266D4—1162no—
267D4—1162no—
268D4—2324no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—581no—
272C2×C4—1162no—
273C2×C4D4×D2912yes—
274C2×C4D4×D2912yes—
275C2×C4C2×C22⋊D2914yes—
276C2×C4C2×C22⋊D2911yescharacteristic
277C2×C4C23×D2911yescharacteristic
278C8—292no—
279C8—292no—
280C8—294no—
281C22—22no—
282C22—41no—
283C22—42no—
284C22—42no—
285C22—44no—
286C22—84no—
287C22—1161no—
288C22—1162no—
289C22—1162no—
290C22—1164no—
291C22—2324no—
292C22#1174530212yes—
293C22C22×C22⋊D2911yescharacteristic
294C4—24no—
295C4—41no—
296C4—1161no—
297C4#1174530212yes—
298C4C2×D4×D2911yescharacteristic
299C4C2×D4×D2911yescharacteristic
300C2—22no—
301C2—82no—
302C2—81no—
303C2—2322no—
304C2—2321no—
305C2C2×#1174530211yescharacteristic
306C2#1427196612yes—
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#535C2
socleC22×C29C22×D4
hypercenter#535D29
hypocenterC29#3155
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#11745294C2semidirect
2. C2×#11745311C2semidirect
3. C2×#11745312C2semidirect
4. C22×#90782C2semidirect
5. #14271732C2semidirect
6. #14271553C2semidirect
7. #14271550C2semidirect
8. #14271545C2semidirect
9. #14271539C2semidirect
10. #14271119C2semidirect
11. C29×#535C2semidirect
16. C29×#127C22semidirect
17. C29×#124C22semidirect
23. C2×#90785C22semidirect
24. C2×#90784C22semidirect
25. C2×#90784C22semidirect
26. C2×#90783C22semidirect
27. C2×#90783C22semidirect
32. C2×#90782C22semidirect
33. C2×#90782C22semidirect
34. C2×#90782C22semidirect
39. #11745237C22semidirect
40. #11745236C22semidirect
41. #11745151C22semidirect
42. C4×#6597C22semidirect
83. #90777D4semidirect
84. C2×#6597D4semidirect
152. #535D29semidirect
186. #127C2×D29semidirect
188. #124C2×D29semidirect
196. C29#3155semidirect

Maximal subgroups

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

subgroupindex
C2×#117452942
C2×#117453112
C2×#117453122
C22×#907822
#142717322
#142715532
#142715502
#142715452
#142715392
#142711192
C29×#5352
#315529