Finite Group Databasebeta

← #16835499

Subgroups — #16835499

Order 3712.

444 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 68 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#14272230C211yesmaximal, characteristic, complemented
2#14272155C212yesmaximal, complemented
3D29⋊#100C211yesmaximal, characteristic, complemented
4#14272034C212yesmaximal, complemented
5#127×D29C211yesmaximal, characteristic
6C2×D4×D29—22no—
7C2×D4×D29C2211yescharacteristic
8C2×D4×D29C2211yescharacteristic
9C2×C22⋊#1181—22no—
10D4×#1181—24no—
11#11745345C2212yes—
12D29⋊M16C2212yes—
13C29×#127C411yescharacteristic, complemented
14#11745302—22no—
15#11745302C411yescharacteristic, complemented
16#11745302C411yescharacteristic, complemented
17#11745236C411yescharacteristic, complemented
18C42×D29C2211yescharacteristic
19#11745229—22no—
20#11745223—24no—
21C23×D29—21no—
22C23×D29D412yes—
23C22×#1181—24no—
24C2×D4×C29—22no—
25C2×D4×C29C2×C411yescharacteristic
26C2×D4×C29C2×C411yescharacteristic, complemented
27C2×C22⋊D29—22no—
28C2×C22⋊D29—22no—
29C2×C22⋊D29—21no—
30C2×C22⋊D29D412yes—
31D4×D29—22no—
32D4×D29—22no—
33D4×D29—22no—
34D4×D29—22no—
35D4×D29—48no—
36C2×D116—22no—
37C2×D116C2×C411yescharacteristic
38C2×D116C2×C411yescharacteristic, complemented
39C2×C4×D29—21no—
40C2×C4×D29C2311yescharacteristic
41C22⋊#1181—24no—
42C22⋊#1181—22no—
43#90800—22no—
44C4⋊#1181D414yescomplemented
45C4×#1181—22no—
46#90796—22no—
47D29⋊C8—22no—
48C42×C29C2×C411yescharacteristic, complemented
49C4×Dic29—21no—
50C4×Dic29C2×C411yescharacteristic, complemented
51C23×C29—21no—
52C23×C29C22⋊C412yes—
53C22×D29—22no—
54C22×D29—22no—
55C22×D29—21no—
56C22×D29—44no—
57C22×D29—44no—
58C22×D29—41no—
59C22×D29—41no—
60C22×D29C22⋊C412yes—
61C22×D29C2×D411yescharacteristic
62C2×#1181—24no—
63C2×#1181—84no—
64D4×C29—22no—
65D4×C29—22no—
66D4×C29—44no—
67C2×C4×C29—21no—
68C2×C4×C29C22×C411yescharacteristic
69C22⋊D29—24no—
70C22⋊D29—44no—
71C22⋊D29—44no—
72C22⋊D29—42no—
73C2×Dic29—21no—
74C2×Dic29C2×D411yescharacteristic
75D116—22no—
76D116—22no—
77D116—44no—
78C4×D29—24no—
79C4×D29C2×D412yes—
80C4×D29#4112yes—
81#6599—42no—
82#1887—291nomaximal, Sylow
83C22×C29—22no—
84C22×C29—42no—
85C22×C29—42no—
86C22×C29—41no—
87C22×C29C2×C22⋊C411yescharacteristic
88C2×D29—22no—
89C2×D29—22no—
90C2×D29—44no—
91C2×D29—42no—
92C2×D29—42no—
93C2×D29—41no—
94C2×D29—82no—
95C2×D29—82no—
96C2×D29—82no—
97C2×D29#12011yescharacteristic
98C2×D29#12311yescharacteristic
99#1181—44no—
100C4×C29—22no—
101C4×C29C4×D412yes—
102Dic29—22no—
103Dic29#12112yes—
104C2×#127—291no—
105#518—291no—
106#418—292no—
107C2×#100—291no—
108#339—292no—
109C2×C29—21no—
110C2×C29—42no—
111C2×C29—81no—
112C2×C29#38611yescharacteristic
113D29—21no—
114D29—42no—
115D29—81no—
116D29#45312yes—
117C22×D4—291no—
118C22×D4—291no—
119C22×D4—582no—
120C2×M16—292no—
121#127—291no—
122#127—291no—
123#127—291no—
124#127—582no—
125#127#118111yescharacteristic, complemented
126C4×D4—584no—
127#117—292no—
128C2×C22⋊C4—582no—
129C2×C42—291no—
130#102—584no—
131#100—582no—
132C29#188711yescharacteristic, complemented, Sylow
133C24—292no—
134C24—581no—
135C2×D4—22no—
136C2×D4—292no—
137C2×D4—291no—
138C2×D4—291no—
139C2×D4—582no—
140C2×D4—582no—
141C2×D4—582no—
142C2×D4—582no—
143C2×D4—582no—
144C2×D4—581no—
145C2×D4—582no—
146C2×D4—582no—
147C2×D4—1168no—
148C2×D4C2×#118111yescharacteristic
149C2×D4C2×#118111yescharacteristic, complemented
150C22×C4—291no—
151C22×C4—581no—
152C22×C4—584no—
153M16—582no—
154M16—582no—
155C2×C8—582no—
156C4⋊C4—294no—
157C22⋊C4—582no—
158C22⋊C4—584no—
159C42—291no—
160C42—581no—
161C42—582no—
162C42C2×#118111yescharacteristic, complemented
163C23—21no—
164C23—291no—
165C23—292no—
166C23—582no—
167C23—582no—
168C23—581no—
169C23—1161no—
170C23—1161no—
171C23—1164no—
172C23—1164no—
173C23C22⋊#118112yes—
174D4—22no—
175D4—22no—
176D4—44no—
177D4—584no—
178D4—582no—
179D4—582no—
180D4—1164no—
181D4—1162no—
182D4—1164no—
183D4—1164no—
184C2×C4—21no—
185C2×C4—291no—
186C2×C4—292no—
187C2×C4—292no—
188C2×C4—584no—
189C2×C4—581no—
190C2×C4—584no—
191C2×C4—2324no—
192C2×C4C22×#118111yescharacteristic
193C8—1162no—
194C22—22no—
195C22—42no—
196C22—42no—
197C22—41no—
198C22—291no—
199C22—291no—
200C22—582no—
201C22—582no—
202C22—1162no—
203C22—1162no—
204C22—1164no—
205C22—1161no—
206C22—2322no—
207C22—2322no—
208C22—2322no—
209C22C2×C22⋊#118111yescharacteristic
210C4—22no—
211C4—292no—
212C4—582no—
213C4—1164no—
214C4D4×#118112yes—
215C2—21no—
216C2—42no—
217C2—81no—
218C2—292no—
219C2—581no—
220C2—1162no—
221C2—2321no—
222C2#1427211111yescharacteristic
subgroupG/H
centerC2#14272111
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#127C4
socleC2×C29#386
prime radical#127×D29C2
cosocleC2×C4×D29C23
hypercenter#127#1181
hypocenterC29#1887
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #14272230C2semidirect
2. #14272155C2semidirect
3. D29⋊#100C2semidirect
4. #14272034C2semidirect
13. C29×#127C4semidirect
15. #11745302C4semidirect
16. #11745302C4semidirect
17. #11745236C4semidirect
26. C2×D4×C29C2×C4semidirect
38. C2×D116C2×C4semidirect
44. C4⋊#1181D4semidirect
48. C42×C29C2×C4semidirect
50. C4×Dic29C2×C4semidirect
125. #127#1181semidirect
132. C29#1887semidirect
149. C2×D4C2×#1181semidirect
162. C42C2×#1181semidirect

Maximal subgroups

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

subgroupindex
#142722302
#142721552
D29⋊#1002
#142720342
#127×D292
#188729