Finite Group Databasebeta

← #16829416

Subgroups — #16829416

Order 3712.

458 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#14271676C211yesmaximal, characteristic
2C2×C4⋊C4×D29C211yesmaximal, characteristic, complemented
3#14271497C212yesmaximal, complemented
4#14271491C211yesmaximal, characteristic, complemented
5#14271483C212yesmaximal, complemented
6#14271477C211yesmaximal, characteristic, complemented
7#14271476C211yesmaximal, characteristic, complemented
8#14271202C212yesmaximal, complemented
9#14271163C212yesmaximal, complemented
10#14271125C211yesmaximal, characteristic, complemented
11C29×#483C211yesmaximal, characteristic, complemented
12C2×#90809C2211yescharacteristic
13C22×C4×D29—21no—
14C22×C4×D29C2211yescharacteristic
15C29×C22⋊Q8C2211yescharacteristic
16C2×C4⋊C4×C29C2211yescharacteristic
17#11745308C2211yescharacteristic
18#11745292C2211yescharacteristic
19C2×C4⋊Dic29C2211yescharacteristic
20C2×#90779—21no—
21C2×#90772C2212yes—
22#11745257C2211yescharacteristic
23#11745256—21no—
24#11745255—21no—
25#11745254C2211yescharacteristic
26C4⋊C4×D29—21no—
27C4⋊C4×D29—21no—
28C4⋊C4×D29C2212yes—
29C4⋊C4×D29C2212yes—
30#11745244—21no—
31#11745243—21no—
32C29×#106C2212yescomplemented
33C29×#103C2212yescomplemented
34C29×C22⋊C8C2211yescharacteristic
35#11745183C2212yescomplemented
36C22⋊#6597C2211yescharacteristic
37#11745169C2212yescomplemented
38#11745168C2212yes—
39#11745166C2212yescomplemented
40#11745157C2212yescomplemented
41#11745156C2212yescomplemented
42#11745155C2212yescomplemented
43C23×D29D411yescharacteristic
44C2×Q8×C29C2311yescharacteristic
45C22×C4×C29—21no—
46C22×C4×C29C2311yescharacteristic
47C2×C22⋊D29—21no—
48C22×Dic29—21no—
49C22×Dic29D411yescharacteristic
50#90809—24no—
51C2×D116—21no—
52C2×D116—21no—
53C2×D116C2311yescharacteristic
54C2×C4×D29—24no—
55C2×C4×D29—22no—
56C2×C4×D29—22no—
57C2×C4×D29—21no—
58C2×C4×D29—44no—
59C2×C4×D29D411yescharacteristic
60C2×C4×D29D411yescharacteristic
61C2×C4×D29C2311yescharacteristic
62C2×C4×D29C2311yescharacteristic
63C2×C8×C29C2312yes—
64C4⋊C4×C29—21no—
65C4⋊C4×C29—21no—
66C4⋊C4×C29C2312yes—
67C4⋊C4×C29C2311yescharacteristic
68C22⋊C4×C29—21no—
69#90781—21no—
70#90781—21no—
71#90781—21no—
72#90781—21no—
73C4⋊Dic29—21no—
74C4⋊Dic29C2312yes—
75C4⋊Dic29C2311yescharacteristic
76#90779—22no—
77#90779—22no—
78#90779—21no—
79C4×Dic29—21no—
80C2×#6597C2312yes—
81#90772—24no—
82C23×C29C2×D411yescharacteristic
83C22×D29—22no—
84C22×D29—22no—
85C22×D29—22no—
86C22×D29—21no—
87C22×D29C2×D411yescharacteristic
88C22×D29C2×D411yescharacteristic
89Q8×C29—22no—
90C2×C4×C29—22no—
91C2×C4×C29—21no—
92C2×C4×C29—22no—
93C2×C4×C29—21no—
94C2×C4×C29—42no—
95C2×C4×C29C2×D411yescharacteristic
96C2×C4×C29C2411yescharacteristic
97C22⋊D29—42no—
98C2×Dic29—22no—
99C2×Dic29—21no—
100C2×Dic29—22no—
101C2×Dic29—42no—
102C2×Dic29C2×D411yescharacteristic
103C2×Dic29C2×D411yescharacteristic
104D116—22no—
105D116—42no—
106D116—42no—
107C4×D29—22no—
108C4×D29—22no—
109C4×D29—22no—
110C4×D29—44no—
111C4×D29—44no—
112C4×D29—42no—
113C4×D29#4114yes—
114C8×C29—22no—
115#6597—22no—
116#3092—291nomaximal, Sylow
117C22×C29—21no—
118C22×C29—21no—
119C22×C29AGL(1,ℤ/8)12yes—
120C22×C29C22×D411yescharacteristic
121C2×D29—28no—
122C2×D29—21no—
123C2×D29—21no—
124C2×D29—21no—
125C2×D29—21no—
126C2×D29—41no—
127C2×D29—41no—
128C2×D29—41no—
129C2×D29#12312yes—
130C2×D29#13712yes—
131C4×C29—21no—
132C4×C29—41no—
133C4×C29—42no—
134C4×C29—41no—
135C4×C29C2×#4112yes—
136Dic29—21no—
137Dic29—42no—
138Dic29—41no—
139Dic29#12312yes—
140#525—291no—
141C22×C4⋊C4—291no—
142#484—292no—
143#483—291no—
144#483D2911yescharacteristic, complemented
145#481—292no—
146#480—291no—
147#480—291no—
148#428—292no—
149#417—292no—
150#407—291no—
151C2×C29—22no—
152C2×C29C2×#12311yescharacteristic
153C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
154C2×C29C2×#13711yescharacteristic
155D29—22no—
156D29—22no—
157D29—81no—
158C2×#41—291no—
159C23×C4—291no—
160C23×C4—581no—
161C2×M16—292no—
162#123—581no—
163C22⋊Q8—291no—
164C22⋊Q8C2×D2911yescharacteristic
165#121—291no—
166#121—291no—
167#120—581no—
168C4×D4—581no—
169C4×D4—581no—
170#117—291no—
171C2×C4⋊C4—291no—
172C2×C4⋊C4—292no—
173C2×C4⋊C4—292no—
174C2×C4⋊C4—581no—
175C2×C4⋊C4—581no—
176C2×C4⋊C4—581no—
177C2×C4⋊C4C2×D2911yescharacteristic
178#107—292no—
179#107—292no—
180#106—292no—
181#106C2×D2912yescomplemented
182#103—292no—
183#103C2×D2912yescomplemented
184#102—292no—
185#102—292no—
186C22⋊C8—291no—
187C22⋊C8—292no—
188C22⋊C8C2×D2911yescharacteristic
189C29#309211yescharacteristic, complemented, Sylow
190C24—291no—
191#41—584no—
192C2×Q8C22×D2911yescharacteristic
193C2×D4—291no—
194C2×D4—581no—
195C2×D4—581no—
196C2×D4—581no—
197C22×C4—21no—
198C22×C4—291no—
199C22×C4—291no—
200C22×C4—291no—
201C22×C4—291no—
202C22×C4—291no—
203C22×C4—584no—
204C22×C4—581no—
205C22×C4—582no—
206C22×C4—582no—
207C22×C4—581no—
208C22×C4—1164no—
209C22×C4C22×D2911yescharacteristic
210M16—584no—
211C2×C8—292no—
212C2×C8C22×D2912yes—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—292no—
216C4⋊C4—291no—
217C4⋊C4—582no—
218C4⋊C4—582no—
219C4⋊C4—581no—
220C4⋊C4—581no—
221C4⋊C4C22×D2912yes—
222C4⋊C4C22×D2911yescharacteristic
223C22⋊C4—21no—
224C22⋊C4—581no—
225C22⋊C4—581no—
226C22⋊C4—581no—
227C22⋊C4—581no—
228C42—581no—
229C23—291no—
230C23—291no—
231C23—582no—
232C23—582no—
233C23—582no—
234C23—581no—
235C23D4×D2911yescharacteristic
236Q8—22no—
237D4—582no—
238D4—1162no—
239D4—1162no—
240D4—1162no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—42no—
246C2×C4—291no—
247C2×C4—294no—
248C2×C4—291no—
249C2×C4—582no—
250C2×C4—582no—
251C2×C4—582no—
252C2×C4—582no—
253C2×C4—581no—
254C2×C4—582no—
255C2×C4—1162no—
256C2×C4—1164no—
257C2×C4—1164no—
258C2×C4—1162no—
259C2×C4D4×D2911yescharacteristic
260C2×C4C23×D2911yescharacteristic
261C8—22no—
262C8—582no—
263C22—21no—
264C22—21no—
265C22—292no—
266C22—292no—
267C22—588no—
268C22—581no—
269C22—581no—
270C22—581no—
271C22—581no—
272C22—1161no—
273C22—1161no—
274C22—1161no—
275C22#1174527612yes—
276C22C2×D4×D2911yescharacteristic
277C4—21no—
278C4—41no—
279C4—42no—
280C4—41no—
281C4—292no—
282C4—581no—
283C4—1162no—
284C4—1161no—
285C4#41×D2912yes—
286C2—22no—
287C2—582no—
288C2—582no—
289C2—2321no—
290C2#123×D2911yescharacteristic
291C2C2×#1174527611yescharacteristic
292C2#137×D2911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#483C2
socleC22×C29C22×D4
prime radical#14271676C2
hypercenter#483D29
hypocenterC29#3092
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D29C2semidirect
3. #14271497C2semidirect
4. #14271491C2semidirect
5. #14271483C2semidirect
6. #14271477C2semidirect
7. #14271476C2semidirect
8. #14271202C2semidirect
9. #14271163C2semidirect
10. #14271125C2semidirect
11. C29×#483C2semidirect
32. C29×#106C22semidirect
33. C29×#103C22semidirect
35. #11745183C22semidirect
37. #11745169C22semidirect
39. #11745166C22semidirect
40. #11745157C22semidirect
41. #11745156C22semidirect
42. #11745155C22semidirect
144. #483D29semidirect
181. #106C2×D29semidirect
183. #103C2×D29semidirect
189. C29#3092semidirect

Maximal subgroups

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

subgroupindex
#142716762
C2×C4⋊C4×D292
#142714972
#142714912
#142714832
#142714772
#142714762
#142712022
#142711632
#142711252
C29×#4832
#309229