Finite Group Databasebeta

← #16819939

Subgroups — #16819939

Order 3712.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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#14271675C211yesmaximal, characteristic
2C2×#11745234C211yesmaximal, characteristic, complemented
3C2×#11745153C211yesmaximal, characteristic, complemented
4C2×#11745173C211yesmaximal, characteristic, complemented
5#14271126C211yesmaximal, characteristic, complemented
6#14270922C211yesmaximal, characteristic, complemented
7C29×#339C211yesmaximal, characteristic, complemented
8C2×#90805C2211yescharacteristic
9C22×C4×D29C2211yescharacteristic
10C2×M16×C29C2211yescharacteristic
11C29×#117C2211yescharacteristic
12C2×C42×C29C2211yescharacteristic
13C2×#90781—21no—
14C2×#90779—21no—
15C2×C4×Dic29C2211yescharacteristic
16C2×#90777C2211yescharacteristic
17#11745259C412yescomplemented
18#11745257C412yescomplemented
19#11745248—21no—
20#11745244—21no—
21C4×D116—22no—
22#11745234—22no—
23#11745234—22no—
24#11745173—22no—
25#11745168—22no—
26#11745153—22no—
27C23×D29D411yescharacteristic
28C22×C4×C29—21no—
29C22×C4×C29C2311yescharacteristic
30C2×C22⋊D29—21no—
31C22×Dic29—21no—
32C22×Dic29D411yescharacteristic
33#90805—21no—
34#90805—21no—
35#90805—21no—
36#90805—21no—
37C2×D116—22no—
38C2×D116C2×C411yescharacteristic
39C2×C4×D29—21no—
40C2×C4×D29—21no—
41C2×C4×D29—21no—
42C2×C4×D29—21no—
43C2×C4×D29—21no—
44C2×C4×D29C2×C412yes—
45C2×C4×D29D412yes—
46C2×Dic58C2×C411yescharacteristic
47M16×C29—21no—
48M16×C29—21no—
49C2×C8×C29—21no—
50C4⋊C4×C29C2×C412yes—
51C22⋊C4×C29—21no—
52C42×C29—21no—
53C42×C29—21no—
54C42×C29D412yescomplemented
55#90781—24no—
56#90781—22no—
57#90781—22no—
58C4⋊Dic29—22no—
59#90779—24no—
60C4×Dic29—21no—
61C4×Dic29D412yescomplemented
62#90777—21no—
63#90777—21no—
64C2×#6597—21no—
65C23×C29C2×D411yescharacteristic
66C22×D29—21no—
67C22×D29—21no—
68C22×D29—21no—
69C22×D29—42no—
70C22×D29C22⋊C412yes—
71C2×C4×C29—22no—
72C2×C4×C29—22no—
73C2×C4×C29—42no—
74C2×C4×C29C22×C411yescharacteristic
75C2×C4×C29C2×D411yescharacteristic
76C2×C4×C29C2×D411yescharacteristic
77C2×C4×C29C2×D411yescharacteristic
78C2×C4×C29#4111yescharacteristic
79C2×C4×C29#4111yescharacteristic
80C22⋊D29—41no—
81C22⋊D29—41no—
82C2×Dic29—21no—
83C2×Dic29—21no—
84C2×Dic29—21no—
85C2×Dic29—22no—
86C2×Dic29—42no—
87C2×Dic29C22⋊C412yes—
88D116—21no—
89D116—21no—
90D116—44no—
91C4×D29—22no—
92C4×D29—22no—
93C4×D29—22no—
94C4×D29—22no—
95C4×D29—41no—
96C4×D29—41no—
97Dic58—21no—
98Dic58—21no—
99C8×C29—41no—
100#6597—41no—
101#1897—291nomaximal, Sylow
102C22×C29—22no—
103C22×C29C2×C22⋊C411yescharacteristic
104C22×C29#12011yescharacteristic
105C22×C29#12311yescharacteristic
106C2×D29—22no—
107C2×D29—22no—
108C2×D29—22no—
109C2×D29—42no—
110C2×D29—42no—
111C2×D29—41no—
112C2×D29—42no—
113C4×C29—42no—
114C4×C29—42no—
115C4×C29C4×D411yescharacteristic
116C4×C29C4×D411yescharacteristic
117C4×C29#12111yescharacteristic
118C4×C29#12111yescharacteristic
119Dic29—22no—
120Dic29—42no—
121Dic29—41no—
122#525—291no—
123C2×#117—291no—
124C2×#104—291no—
125C2×#104—291no—
126#407—291no—
127#339—291no—
128#339D2911yescharacteristic, complemented
129C2×C29—21no—
130C2×C29—21no—
131C2×C29#38611yescharacteristic
132C2×C29#42112yes—
133D29—42no—
134D29—81no—
135C2×#41—291no—
136C23×C4—291no—
137C2×M16—291no—
138C2×M16C2×D2911yescharacteristic
139#123—581no—
140C22⋊Q8—292no—
141#121—292no—
142#120—581no—
143C4×D4—582no—
144#117—582no—
145#117—582no—
146#117C2×D2911yescharacteristic
147C2×C4⋊C4—581no—
148C2×C22⋊C4—581no—
149C2×C42—291no—
150C2×C42C2×D2911yescharacteristic
151#104—582no—
152#104—582no—
153C22⋊C8—582no—
154C29#189711yescharacteristic, complemented, Sylow
155C24—291no—
156#41—581no—
157#41—581no—
158#41—581no—
159#41—581no—
160C2×Q8—291no—
161C2×D4—291no—
162C2×D4—582no—
163C2×D4—581no—
164C22×C4—21no—
165C22×C4—291no—
166C22×C4—292no—
167C22×C4—292no—
168C22×C4—581no—
169C22×C4—581no—
170C22×C4—581no—
171C22×C4—581no—
172C22×C4—581no—
173C22×C4—581no—
174C22×C4C22×D2911yescharacteristic
175M16—21no—
176M16—21no—
177M16—581no—
178M16—581no—
179C2×C8—21no—
180C2×C8—581no—
181C4⋊C4—582no—
182C4⋊C4—584no—
183C4⋊C4C4×D2912yes—
184C22⋊C4—21no—
185C22⋊C4—582no—
186C22⋊C4—582no—
187C22⋊C4—584no—
188C42—21no—
189C42—21no—
190C42—292no—
191C42—581no—
192C42D11612yescomplemented
193C23—292no—
194C23—581no—
195C23—581no—
196C23—581no—
197C23—1162no—
198C23D4×D2911yescharacteristic
199Q8—581no—
200Q8—581no—
201D4—581no—
202D4—581no—
203D4—1164no—
204D4—1161no—
205D4—1161no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—292no—
210C2×C4—581no—
211C2×C4—581no—
212C2×C4—582no—
213C2×C4—582no—
214C2×C4—582no—
215C2×C4—582no—
216C2×C4—581no—
217C2×C4—582no—
218C2×C4—1162no—
219C2×C4—1161no—
220C2×C4—1161no—
221C2×C4C2×C4×D2911yescharacteristic
222C2×C4C2×D11611yescharacteristic
223C2×C4#9080511yescharacteristic
224C2×C4D4×D2911yescharacteristic
225C2×C4D4×D2911yescharacteristic
226C2×C4#9080911yescharacteristic
227C8—41no—
228C8—1161no—
229C22—22no—
230C22—582no—
231C22—582no—
232C22—582no—
233C22—1162no—
234C22—1162no—
235C22—1161no—
236C22—1162no—
237C22C22⋊C4×D2911yescharacteristic
238C22#1174524411yescharacteristic
239C22#1174525611yescharacteristic
240C4—42no—
241C4—42no—
242C4—582no—
243C4—1162no—
244C4—1161no—
245C4C4×D11611yescharacteristic
246C4#1174524611yescharacteristic
247C4#1174525511yescharacteristic
248C4#1174525711yescharacteristic
249C2—21no—
250C2—21no—
251C2—1162no—
252C2—2321no—
253C2#1427104111yescharacteristic
254C2#1427117812yes—
subgroupG/H
centerC2×C4D4×D29
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#339C2
socleC22×C29C2×C22⋊C4
prime radical#14271675C2
cosocleC22×C4×C29C23
hypercenter#339D29
hypocenterC29#1897
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C2×#11745234C2semidirect
3. C2×#11745153C2semidirect
4. C2×#11745173C2semidirect
5. #14271126C2semidirect
6. #14270922C2semidirect
7. C29×#339C2semidirect
17. #11745259C4semidirect
18. #11745257C4semidirect
54. C42×C29D4semidirect
61. C4×Dic29D4semidirect
128. #339D29semidirect
154. C29#1897semidirect
192. C42D116semidirect

Maximal subgroups

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

subgroupindex
#142716752
C2×#117452342
C2×#117451532
C2×#117451732
#142711262
#142709222
C29×#3392
#189729