Finite Group Databasebeta

← #16819937

Subgroups — #16819937

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#14271670C211yesmaximal, characteristic
2C2×#11745234C211yesmaximal, characteristic, complemented
3C2×#11745185C211yesmaximal, characteristic, complemented
4#14271126C211yesmaximal, characteristic, complemented
5#14270924C211yesmaximal, characteristic, complemented
6#14270923C211yesmaximal, characteristic, complemented
7C2×C29×#104C211yesmaximal, characteristic, complemented
8C2×#41×C29C2211yescharacteristic
9C22×C4×D29C2211yescharacteristic
10C2×M16×C29C2211yescharacteristic
11C2×C42×C29C2211yescharacteristic
12#11745308C412yescomplemented
13#11745300C412yescomplemented
14#11745299—21no—
15#11745297—21no—
16C4×C22⋊D29—22no—
17C2×#90781—21no—
18#11745288C2211yescharacteristic
19C2×#90779—21no—
20C2×C4×Dic29C2211yescharacteristic
21C2×#90777C2211yescharacteristic
22#11745234—22no—
23#11745234—22no—
24C29×#104—22no—
25#11745185—22no—
26#11745168—22no—
27C23×D29D411yescharacteristic
28#41×C29—21no—
29#41×C29—21no—
30#41×C29—21no—
31#41×C29—21no—
32C2×Q8×C29C2×C411yescharacteristic
33C2×D4×C29—21no—
34C2×D4×C29C2×C411yescharacteristic
35C22×C4×C29—21no—
36C22×C4×C29—21no—
37C22×C4×C29C2311yescharacteristic
38C2×C22⋊D29—22no—
39C22×Dic29—21no—
40C22×Dic29D411yescharacteristic
41C2×C4×D29—21no—
42C2×C4×D29—21no—
43C2×C4×D29—21no—
44C2×C4×D29—21no—
45C2×C4×D29C2×C412yes—
46C2×C4×D29D412yes—
47M16×C29—21no—
48M16×C29—21no—
49C2×C8×C29—21no—
50C42×C29—21no—
51C42×C29D412yescomplemented
52C22⋊Dic29—21no—
53C22⋊Dic29—22no—
54#90781—24no—
55#90781—22no—
56C4⋊Dic29C2×C412yes—
57#90779—24no—
58#90779—22no—
59C4×Dic29—21no—
60C4×Dic29—21no—
61C4×Dic29D412yescomplemented
62#90777—21no—
63#90777—21no—
64C2×#6597—21no—
65C23×C29—21no—
66C23×C29C2×D411yescharacteristic
67C22×D29—21no—
68C22×D29—21no—
69C22×D29—42no—
70C22×D29C22⋊C412yes—
71Q8×C29—21no—
72Q8×C29—21no—
73D4×C29—21no—
74D4×C29—21no—
75D4×C29—41no—
76D4×C29—41no—
77C2×C4×C29—21no—
78C2×C4×C29—22no—
79C2×C4×C29—42no—
80C2×C4×C29—41no—
81C2×C4×C29—41no—
82C2×C4×C29C22×C411yescharacteristic
83C2×C4×C29C2×D411yescharacteristic
84C2×C4×C29C2×D411yescharacteristic
85C2×C4×C29C2×D411yescharacteristic
86C2×C4×C29#4111yescharacteristic
87C2×C4×C29#4111yescharacteristic
88C22⋊D29—44no—
89C2×Dic29—21no—
90C2×Dic29—21no—
91C2×Dic29—22no—
92C2×Dic29—22no—
93C2×Dic29—42no—
94C2×Dic29C22⋊C412yes—
95C4×D29—22no—
96C4×D29—22no—
97C4×D29—22no—
98C4×D29—22no—
99C8×C29—41no—
100#6597—41no—
101#1897—291nomaximal, Sylow
102C22×C29—22no—
103C22×C29—41no—
104C22×C29—42no—
105C22×C29C2×C22⋊C411yescharacteristic
106C22×C29#12011yescharacteristic
107C22×C29#12311yescharacteristic
108C2×D29—22no—
109C2×D29—22no—
110C2×D29—22no—
111C2×D29—42no—
112C2×D29—42no—
113C4×C29—42no—
114C4×C29—41no—
115C4×C29C4×D411yescharacteristic
116C4×C29C4×D411yescharacteristic
117C4×C29#12111yescharacteristic
118C4×C29#12111yescharacteristic
119Dic29—22no—
120Dic29—42no—
121Dic29—42no—
122#525—291no—
123C2×#117—291no—
124C2×#104—291no—
125C2×#104D2911yescharacteristic, complemented
126#407—291no—
127#339—291no—
128#339—291no—
129C2×C29—21no—
130C2×C29—21no—
131C2×C29—81no—
132C2×C29#38611yescharacteristic
133C2×C29#42112yes—
134D29—42no—
135C2×#41C2×D2911yescharacteristic
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—291no—
145#117—582no—
146#117—582no—
147C2×C4⋊C4—581no—
148C2×C22⋊C4—581no—
149C2×C42—291no—
150C2×C42C2×D2911yescharacteristic
151#104—22no—
152#104—582no—
153C22⋊C8—582no—
154C29#189711yescharacteristic, complemented, Sylow
155C24—291no—
156#41—21no—
157#41—21no—
158#41—21no—
159#41—21no—
160C2×Q8C4×D2911yescharacteristic
161C2×D4—21no—
162C2×D4—582no—
163C2×D4C4×D2911yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—291no—
167C22×C4—292no—
168C22×C4—292no—
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—292no—
182C4⋊C4—582no—
183C4⋊C4—584no—
184C22⋊C4—582no—
185C22⋊C4—584no—
186C22⋊C4—582no—
187C22⋊C4—581no—
188C42—21no—
189C42—292no—
190C42—581no—
191C42—581no—
192C42C22⋊D2912yescomplemented
193C23—21no—
194C23—292no—
195C23—581no—
196C23—581no—
197C23—1162no—
198C23D4×D2911yescharacteristic
199Q8—21no—
200Q8—21no—
201D4—21no—
202D4—21no—
203D4—41no—
204D4—41no—
205D4—1164no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—292no—
212C2×C4—581no—
213C2×C4—581no—
214C2×C4—582no—
215C2×C4—582no—
216C2×C4—582no—
217C2×C4—582no—
218C2×C4—582no—
219C2×C4—582no—
220C2×C4—1162no—
221C2×C4C2×C4×D2911yescharacteristic
222C2×C4#9080511yescharacteristic
223C2×C4D4×D2911yescharacteristic
224C2×C4D4×D2911yescharacteristic
225C2×C4#9080711yescharacteristic
226C2×C4C2×C22⋊D2911yescharacteristic
227C8—41no—
228C8—1161no—
229C22—22no—
230C22—41no—
231C22—42no—
232C22—582no—
233C22—582no—
234C22—582no—
235C22—1162no—
236C22—1162no—
237C22C22⋊C4×D2911yescharacteristic
238C22#1174524511yescharacteristic
239C22#1174529911yescharacteristic
240C4—42no—
241C4—41no—
242C4—582no—
243C4—1162no—
244C4—1162no—
245C4#1174524311yescharacteristic
246C4#1174524611yescharacteristic
247C4C4×C22⋊D2911yescharacteristic
248C4#1174530011yescharacteristic
249C2—21no—
250C2—21no—
251C2—81no—
252C2—1162no—
253C2#1427103911yescharacteristic
254C2#1427117812yes—
subgroupG/H
centerC2×C4D4×D29
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC2×C29×#104C2
socleC22×C29C2×C22⋊C4
prime radical#14271670C2
cosocleC22×C4×C29C23
hypercenterC2×#104D29
hypocenterC29#1897
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#11745234C2semidirect
3. C2×#11745185C2semidirect
4. #14271126C2semidirect
5. #14270924C2semidirect
6. #14270923C2semidirect
7. C2×C29×#104C2semidirect
12. #11745308C4semidirect
13. #11745300C4semidirect
51. C42×C29D4semidirect
61. C4×Dic29D4semidirect
125. C2×#104D29semidirect
154. C29#1897semidirect
192. C42C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
#142716702
C2×#117452342
C2×#117451852
#142711262
#142709242
#142709232
C2×C29×#1042
#189729