Finite Group Databasebeta

← #16830097

Subgroups — #16830097

Order 3712.

364 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 115 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#14271718C211yesmaximal, characteristic, complemented
2#14271698C211yesmaximal, characteristic
3#14271573C211yesmaximal, characteristic, complemented
4#14271555C211yesmaximal, characteristic, complemented
5#14271523C211yesmaximal, characteristic, complemented
6#14271420C212yesmaximal, complemented
7#14271412C212yesmaximal
8#14271255C212yesmaximal, complemented
9#14271248C212yesmaximal, complemented
10#14271115C211yesmaximal, characteristic, complemented
11C29×#491C211yesmaximal, characteristic, complemented
12C29×C4⋊Q8C2211yescharacteristic
13C29×#125C2211yescharacteristic
14#11745308C2212yes—
15Q8×Dic29C2212yes—
16C2×#90785C2212yes—
17C2×#90784C2212yes—
18C2×#90772C2212yes—
19#11745260—21no—
20#11745259—21no—
21#11745259C2211yescharacteristic
22#11745257C2211yescharacteristic
23#11745256—21no—
24#11745255—21no—
25#11745255C2211yescharacteristic
26#11745254—21no—
27#11745254—21no—
28#11745252—21no—
29#11745249—21no—
30#11745249C2211yescharacteristic
31#11745237C2211yescharacteristic
32C42×D29C2211yescharacteristic
33#11745231C2211yescharacteristic
34C29×#103C2212yes—
35C29×#103C2212yes—
36C29×#97C2211yescharacteristic
37#11745169C2212yes—
38#11745164C2212yes—
39C8×Dic29C2212yes—
40#11745156C2212yes—
41#11745155C2212yes—
42#11745151C2211yescharacteristic
43C2×Q8×C29C2312yes—
44C2×D116—21no—
45C2×D116C2311yescharacteristic
46C2×C4×D29—21no—
47C2×C4×D29D411yescharacteristic
48C2×C4×D29D411yescharacteristic
49C2×C4×D29C2311yescharacteristic
50C2×Dic58—21no—
51C2×Dic58C2311yescharacteristic
52C2×C8×C29C2312yes—
53C4⋊C4×C29—21no—
54C4⋊C4×C29—21no—
55C4⋊C4×C29—21no—
56C4⋊C4×C29—21no—
57C4⋊C4×C29C2311yescharacteristic
58C4⋊C4×C29C2311yescharacteristic
59C42×C29C2311yescharacteristic
60#90785—24no—
61#90784—24no—
62#90781—22no—
63#90781—21no—
64#90781—21no—
65#90781—21no—
66#90781—21no—
67#90781—21no—
68C4⋊Dic29—21no—
69C4⋊Dic29—22no—
70C4⋊Dic29—21no—
71C4⋊Dic29C2312yes—
72#90779—22no—
73#90779—21no—
74C4×Dic29—22no—
75C4×Dic29—21no—
76C4×Dic29D411yescharacteristic
77C4×Dic29D411yescharacteristic
78C4×Dic29C2311yescharacteristic
79C2×#6597C2312yes—
80#90772—24no—
81C22×D29—21no—
82C22×D29C2×D411yescharacteristic
83Q8×C29—22no—
84Q8×C29—22no—
85C2×C4×C29—22no—
86C2×C4×C29—21no—
87C2×C4×C29—21no—
88C2×C4×C29C2×D411yescharacteristic
89C2×C4×C29C2×D411yescharacteristic
90C2×C4×C29C2411yescharacteristic
91C2×Dic29—22no—
92C2×Dic29—21no—
93C2×Dic29C2×D411yescharacteristic
94C2×Dic29C2×D411yescharacteristic
95C2×Dic29C2×D411yescharacteristic
96D116—22no—
97D116—42no—
98C4×D29—22no—
99C4×D29—22no—
100C4×D29—41no—
101C4×D29—42no—
102Dic58—22no—
103Dic58—42no—
104C8×C29—22no—
105#6597#4114yes—
106#3172—291nomaximal, Sylow
107C22×C29C22×D411yescharacteristic
108C2×D29—21no—
109C2×D29—21no—
110C2×D29—21no—
111C2×D29—41no—
112C2×D29—41no—
113C2×D29—41no—
114C4×C29—21no—
115C4×C29—21no—
116C4×C29—42no—
117C4×C29—41no—
118C4×C29—41no—
119C4×C29C2×#4112yes—
120Dic29—21no—
121Dic29—21no—
122Dic29—41no—
123Dic29—42no—
124Dic29#13712yes—
125#533—291no—
126#529—291no—
127#501—291no—
128#497—291no—
129#491D2911yescharacteristic, complemented
130#489—291no—
131#470—292no—
132#468—292no—
133C4×Q16—292no—
134C4×SD16—292no—
135C4×M16—291no—
136C2×C29#53211yescharacteristic
137C2×C29C2×#13711yescharacteristic
138C2×C29#57511yescharacteristic
139D29—41no—
140D29—81no—
141C2×Q16—292no—
142C2×SD16—292no—
143C2×M16—292no—
144C4⋊Q8—291no—
145C4⋊Q8C2×D2911yescharacteristic
146#126—581no—
147#125—581no—
148#125C2×D2911yescharacteristic
149#124—291no—
150#123—581no—
151C22⋊Q8—292no—
152C22⋊Q8—291no—
153C22⋊Q8—581no—
154#121—291no—
155C4×Q8—292no—
156C4×Q8—291no—
157C4×Q8—581no—
158C4×D4—291no—
159C4×D4—581no—
160#117—581no—
161#117—581no—
162C2×C42—291no—
163#107—292no—
164#106—292no—
165#103—292no—
166#103C2×D2912yes—
167#103C2×D2912yes—
168#102—292no—
169#97—291no—
170#97C2×D2911yescharacteristic
171C4×C8—292no—
172C29#317211yescharacteristic, complemented, Sylow
173C2×Q8—291no—
174C2×Q8—581no—
175C2×Q8C22×D2912yes—
176C2×D4—291no—
177C2×D4—581no—
178C22×C4—291no—
179C22×C4—291no—
180C22×C4—291no—
181C22×C4—581no—
182Q16—584no—
183SD16—584no—
184M16—584no—
185C2×C8—292no—
186C2×C8C22×D2912yes—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—292no—
192C4⋊C4—581no—
193C4⋊C4—582no—
194C4⋊C4—581no—
195C4⋊C4—582no—
196C4⋊C4—581no—
197C4⋊C4C22×D2911yescharacteristic
198C4⋊C4C22×D2911yescharacteristic
199C22⋊C4—581no—
200C22⋊C4—581no—
201C22⋊C4—582no—
202C22⋊C4—581no—
203C22⋊C4—581no—
204C22⋊C4—581no—
205C42—291no—
206C42—291no—
207C42—291no—
208C42—581no—
209C42—582no—
210C42C22×D2911yescharacteristic
211C23—291no—
212C23—581no—
213Q8—22no—
214Q8—22no—
215Q8—582no—
216Q8—1162no—
217D4—582no—
218D4—1162no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—291no—
223C2×C4—291no—
224C2×C4—291no—
225C2×C4—582no—
226C2×C4—582no—
227C2×C4—581no—
228C2×C4—582no—
229C2×C4—1161no—
230C2×C4—1162no—
231C2×C4D4×D2911yescharacteristic
232C2×C4D4×D2911yescharacteristic
233C2×C4C23×D2911yescharacteristic
234C8—22no—
235C8—294no—
236C22—581no—
237C22—581no—
238C22—581no—
239C22—1161no—
240C22—1161no—
241C22—1161no—
242C22C2×D4×D2911yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—42no—
248C4—292no—
249C4—581no—
250C4—581no—
251C4—1162no—
252C4—1161no—
253C4#41×D2912yes—
254C2—1161no—
255C2—2321no—
256C2#1427171211yescharacteristic
257C2#137×D2911yescharacteristic
258C2#1427196211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#491C2
socleC22×C29C22×D4
prime radical#11745257C22
hypercenter#491D29
hypocenterC29#3172
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #14271718C2semidirect
3. #14271573C2semidirect
4. #14271555C2semidirect
5. #14271523C2semidirect
6. #14271420C2semidirect
8. #14271255C2semidirect
9. #14271248C2semidirect
10. #14271115C2semidirect
11. C29×#491C2semidirect
129. #491D29semidirect
172. C29#3172semidirect

Maximal subgroups

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

subgroupindex
#142717182
#142716982
#142715732
#142715552
#142715232
#142714202
#142714122
#142712552
#142712482
#142711152
C29×#4912
#317229