Finite Group Databasebeta

← #16828891

Subgroups — #16828891

Order 3712.

800 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 145 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
2#14271725C212yesmaximal, complemented
3#14271722C211yesmaximal, characteristic, complemented
4#14271354C214yesmaximal, complemented
5#14271351C214yesmaximal, complemented
6C2×#11745154C212yesmaximal, complemented
7C2×C29×#99C211yesmaximal, characteristic, complemented
8C22×D4×C29C2211yescharacteristic
9C22×C22⋊D29—21no—
10C22×C22⋊D29C2212yes—
11C22×C22⋊D29C2211yescharacteristic, complemented
12#11745359—22no—
13#11745359—24no—
14#11745359C2214yes—
15C2×#90807—22no—
16C2×D4×D29—22no—
17C2×#90805—21no—
18C2×C22⋊C4×C29C2212yescomplemented
19#11745315—21no—
20C2×C22⋊Dic29C2211yescharacteristic, complemented
21#11745301—22no—
22#11745299C2212yescomplemented
23#11745297C2212yescomplemented
24#11745292—24no—
25#11745291—21no—
26#11745248—22no—
27#11745248C2214yescomplemented
28#11745244—22no—
29#11745244C2214yescomplemented
30C29×#99C2214yescomplemented
31#11745154C2218yescomplemented
32C24×C29D411yescharacteristic, complemented
33C24×C29C2311yescharacteristic
34C23×D29—21no—
35C23×D29D412yescomplemented
36C23×D29C2311yescharacteristic, complemented
37C2×D4×C29—22no—
38C2×D4×C29—22no—
39C2×D4×C29D412yescomplemented
40C2×D4×C29C2312yes—
41C22×C4×C29—22no—
42C22×C4×C29D411yescharacteristic, complemented
43C2×C22⋊D29—22no—
44C2×C22⋊D29—24no—
45C2×C22⋊D29—22no—
46C2×C22⋊D29—22no—
47C2×C22⋊D29—22no—
48C2×C22⋊D29—22no—
49C2×C22⋊D29—24no—
50C2×C22⋊D29—21no—
51C2×C22⋊D29—22no—
52C2×C22⋊D29—21no—
53C2×C22⋊D29—22no—
54C2×C22⋊D29—22no—
55C2×C22⋊D29D414yescomplemented
56C2×C22⋊D29C2314yes—
57C22×Dic29—21no—
58C22×Dic29—21no—
59C22×Dic29D412yescomplemented
60C22×Dic29C2311yescharacteristic, complemented
61#90807—28no—
62#90807—28no—
63D4×D29—28no—
64D4×D29—28no—
65#90805—24no—
66#90805—24no—
67C2×D116—21no—
68C2×D116—24no—
69C2×C4×D29—22no—
70C2×Dic58—21no—
71C22⋊C4×C29—22no—
72C22⋊C4×C29C2314yescomplemented
73C22⋊Dic29—21no—
74C22⋊Dic29—22no—
75C22⋊Dic29C2312yescomplemented
76#90781—24no—
77#90781—22no—
78#90781—24no—
79C4⋊Dic29—24no—
80#90779—22no—
81C23×C29—21no—
82C23×C29—21no—
83C23×C29—81no—
84C23×C29—81no—
85C23×C29C2×D412yes—
86C23×C29C2×D411yescharacteristic
87C23×C29C2×D411yescharacteristic
88C23×C29C2×D412yes—
89C23×C29C2×D412yes—
90C23×C29C2411yescharacteristic
91C22×D29—22no—
92C22×D29—24no—
93C22×D29—22no—
94C22×D29—22no—
95C22×D29—21no—
96C22×D29—81no—
97C22×D29—82no—
98C22×D29—82no—
99C22×D29C2×D414yes—
100D4×C29—24no—
101D4×C29—24no—
102C2×C4×C29—21no—
103C2×C4×C29—21no—
104C2×C4×C29—24no—
105C2×C4×C29—82no—
106C2×C4×C29C2×D412yes—
107C22⋊D29—28no—
108C22⋊D29—24no—
109C22⋊D29—24no—
110C22⋊D29—24no—
111C22⋊D29—24no—
112C22⋊D29—41no—
113C22⋊D29—42no—
114C22⋊D29—41no—
115C22⋊D29—82no—
116C2×Dic29—24no—
117C2×Dic29—22no—
118C2×Dic29—22no—
119C2×Dic29—21no—
120C2×Dic29—22no—
121C2×Dic29—22no—
122C2×Dic29—81no—
123C2×Dic29C2×D414yes—
124D116—24no—
125D116—84no—
126C4×D29—28no—
127Dic58—24no—
128#3026—291nomaximal, Sylow
129C22×C29—22no—
130C22×C29—41no—
131C22×C29—42no—
132C22×C29—42no—
133C22×C29—41no—
134C22×C29—41no—
135C22×C29—42no—
136C22×C29—42no—
137C22×C29—81no—
138C22×C29#12011yescharacteristic
139C22×C29#12012yes—
140C22×C29#12011yescharacteristic
141C22×C29C22×D411yescharacteristic
142C22×C29C22×D412yes—
143C2×D29—24no—
144C2×D29—44no—
145C2×D29—44no—
146C2×D29—44no—
147C2×D29—42no—
148C2×D29—41no—
149C2×D29—82no—
150C2×D29—84no—
151C4×C29—22no—
152C4×C29—44no—
153Dic29—24no—
154Dic29—42no—
155Dic29—41no—
156C2×H(5,𝔽2)—291no—
157#534—291no—
158#534—292no—
159#458—294no—
160B(4,𝔽2)—294no—
161C2×#99—292no—
162C2×#99D2911yescharacteristic, complemented
163C2×C29—21no—
164C2×C29—22no—
165C2×C29—21no—
166C2×C29—22no—
167C2×C29—21no—
168C2×C29—42no—
169C2×C29C2×#12011yescharacteristic
170D29—44no—
171D29—81no—
172H(5,𝔽2)—294no—
173H(5,𝔽2)—584no—
174H(5,𝔽2)—582no—
175C2×#41—582no—
176C2×#41—581no—
177C22×D4—292no—
178C22×D4—291no—
179C22×D4—582no—
180C22×D4—581no—
181C22×D4C2×D2911yescharacteristic
182#123—292no—
183#123—294no—
184#123—582no—
185#123—581no—
186#121—584no—
187#121—582no—
188#120—292no—
189#120—294no—
190#120—582no—
191#120—581no—
192C2×C22⋊C4—291no—
193C2×C22⋊C4C2×D2912yescomplemented
194#99—298no—
195#99C2×D2914yescomplemented
196C29#302611yescharacteristic, complemented, Sylow
197C24—292no—
198C24—291no—
199C24—581no—
200C24D11611yescharacteristic, complemented
201C24C22×D2911yescharacteristic
202#41—584no—
203#41—588no—
204#41—588no—
205#41—584no—
206C2×Q8—581no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—294no—
210C2×D4—294no—
211C2×D4—581no—
212C2×D4—584no—
213C2×D4—588no—
214C2×D4—588no—
215C2×D4—582no—
216C2×D4—584no—
217C2×D4—582no—
218C2×D4—582no—
219C2×D4—584no—
220C2×D4—582no—
221C2×D4—582no—
222C2×D4—581no—
223C2×D4—581no—
224C2×D4—582no—
225C2×D4—582no—
226C2×D4—582no—
227C2×D4D11612yescomplemented
228C2×D4C22×D2912yes—
229C22×C4—22no—
230C22×C4—292no—
231C22×C4—291no—
232C22×C4—582no—
233C22×C4—581no—
234C22×C4—581no—
235C22×C4D11611yescharacteristic, complemented
236C4⋊C4—584no—
237C4⋊C4—582no—
238C22⋊C4—22no—
239C22⋊C4—292no—
240C22⋊C4—584no—
241C22⋊C4—584no—
242C22⋊C4—581no—
243C22⋊C4—582no—
244C22⋊C4—582no—
245C22⋊C4C22×D2914yescomplemented
246C23—21no—
247C23—21no—
248C23—81no—
249C23—81no—
250C23—294no—
251C23—584no—
252C23—582no—
253C23—582no—
254C23—581no—
255C23—582no—
256C23—2321no—
257C23—2322no—
258C23—2322no—
259C23C2×D11612yes—
260C23C2×D11611yescharacteristic
261C23C2×D11611yescharacteristic
262C23D4×D2912yes—
263C23D4×D2912yes—
264C23C23×D2911yescharacteristic
265Q8—584no—
266D4—24no—
267D4—24no—
268D4—584no—
269D4—588no—
270D4—584no—
271D4—584no—
272D4—584no—
273D4—584no—
274D4—1161no—
275D4—1161no—
276D4—1162no—
277D4—2324no—
278D4—2322no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—24no—
282C2×C4—82no—
283C2×C4—294no—
284C2×C4—588no—
285C2×C4—584no—
286C2×C4—582no—
287C2×C4—582no—
288C2×C4—582no—
289C2×C4—581no—
290C2×C4—582no—
291C2×C4—2321no—
292C2×C4C2×D11612yes—
293C22—22no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—41no—
299C22—42no—
300C22—42no—
301C22—81no—
302C22—584no—
303C22—1164no—
304C22—1164no—
305C22—1164no—
306C22—1162no—
307C22—1161no—
308C22—2322no—
309C22—2324no—
310C22#1174524411yescharacteristic
311C22#1174524411yescharacteristic
312C22#1174524412yes—
313C22C22×D11611yescharacteristic
314C22C2×D4×D2912yes—
315C4—22no—
316C4—44no—
317C4—584no—
318C4—1162no—
319C4—1161no—
320C2—22no—
321C2—21no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—42no—
326C2—1164no—
327C2—2321no—
328C2C2×#1174524411yescharacteristic
subgroupG/H
centerC2C2×#11745244
commutator, cosocleC23×C29C24
FrattiniC23C23×D29
FittingC2×C29×#99C2
socleC2×C29C2×#120
hypercenterC2×#99D29
hypocenterC29#3026
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. C2×#11745359C2semidirect
2. #14271725C2semidirect
3. #14271722C2semidirect
4. #14271354C2semidirect
5. #14271351C2semidirect
6. C2×#11745154C2semidirect
7. C2×C29×#99C2semidirect
11. C22×C22⋊D29C22semidirect
18. C2×C22⋊C4×C29C22semidirect
20. C2×C22⋊Dic29C22semidirect
22. #11745299C22semidirect
23. #11745297C22semidirect
27. #11745248C22semidirect
29. #11745244C22semidirect
30. C29×#99C22semidirect
31. #11745154C22semidirect
32. C24×C29D4semidirect
35. C23×D29D4semidirect
36. C23×D29C23semidirect
39. C2×D4×C29D4semidirect
42. C22×C4×C29D4semidirect
55. C2×C22⋊D29D4semidirect
59. C22×Dic29D4semidirect
60. C22×Dic29C23semidirect
72. C22⋊C4×C29C23semidirect
75. C22⋊Dic29C23semidirect
162. C2×#99D29semidirect
193. C2×C22⋊C4C2×D29semidirect
195. #99C2×D29semidirect
196. C29#3026semidirect
200. C24D116semidirect
227. C2×D4D116semidirect
235. C22×C4D116semidirect
245. C22⋊C4C22×D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117453592
#142717252
#142717222
#142713542
#142713512
C2×#117451542
C2×C29×#992
#302629