Finite Group Databasebeta

← C137×#11516 #46860902

Subgroups — C137×#11516 #46860902

Order 35072.

418 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 110 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#2317×C137C211yesmaximal, characteristic
2#1464×C137C212yesmaximal
3#1325×C137C214yesmaximal, complemented
4C2×#117×C137C411yescharacteristic
5C2×#117×C137C2211yescharacteristic
6C22×C4⋊C4×C137C411yescharacteristic
7#432×C137—22no—
8#389×C137—22no—
9#385×C137—22no—
10#384×C137C2212yes—
11#382×C137C412yes—
12#324×C137C2214yes—
13#323×C137—22no—
14C23×C4×C137—21no—
15C23×C4×C137C2×C411yescharacteristic
16#117×C137—24no—
17#117×C137—42no—
18C2×C4⋊C4×C137—21no—
19C2×C4⋊C4×C137—21no—
20C2×C4⋊C4×C137—24no—
21C2×C4⋊C4×C137—42no—
22C2×C4⋊C4×C137C2×C412yes—
23C2×C4⋊C4×C137C2×C411yescharacteristic
24C2×C4⋊C4×C137C2311yescharacteristic
25C2×C22⋊C4×C137—21no—
26C2×C22⋊C4×C137D412yes—
27C2×C42×C137C2×C412yes—
28C2×C42×C137D412yes—
29C4⋊C8×C137—42no—
30C22⋊C8×C137—24no—
31#97×C137—42no—
32#95×C137—24no—
33C24×C137C22⋊C411yescharacteristic
34C22×C4×C137—22no—
35C22×C4×C137—22no—
36C22×C4×C137—22no—
37C22×C4×C137—22no—
38C22×C4×C137—22no—
39C22×C4×C137—42no—
40C22×C4×C137—82no—
41C22×C4×C137C22⋊C412yes—
42C22×C4×C137C22⋊C411yescharacteristic
43C22×C4×C137C22×C411yescharacteristic
44C22×C4×C137C2×D412yes—
45C2×C8×C137—44no—
46C4⋊C4×C137—24no—
47C4⋊C4×C137—41no—
48C4⋊C4×C137—41no—
49C4⋊C4×C137—42no—
50C4⋊C4×C137—42no—
51C4⋊C4×C137—84no—
52C22⋊C4×C137—24no—
53C22⋊C4×C137—42no—
54C42×C137—22no—
55C42×C137—22no—
56C42×C137—22no—
57C42×C137M1614yes—
58C23×C137—21no—
59C23×C137—21no—
60C23×C137—41no—
61C23×C137—41no—
62C23×C137#10112yes—
63C23×C137C2×C22⋊C411yescharacteristic
64C2×C4×C137—28no—
65C2×C4×C137—21no—
66C2×C4×C137—21no—
67C2×C4×C137—21no—
68C2×C4×C137—21no—
69C2×C4×C137—24no—
70C2×C4×C137—22no—
71C2×C4×C137—22no—
72C2×C4×C137—42no—
73C2×C4×C137—42no—
74C2×C4×C137—42no—
75C2×C4×C137—42no—
76C2×C4×C137—44no—
77C2×C4×C137—42no—
78C2×C4×C137—84no—
79C2×C4×C137#9912yes—
80C2×C4×C137C2×M1612yes—
81C8×C137—84no—
82C22×C137—21no—
83C22×C137—21no—
84C22×C137—22no—
85C22×C137—42no—
86C22×C137—42no—
87C22×C137—41no—
88C22×C137—41no—
89C22×C137#40711yescharacteristic
90C22×C137C2×#9911yescharacteristic
91C22×C137C2×#10111yescharacteristic
92C4×C137—22no—
93C4×C137—22no—
94C4×C137—44no—
95C4×C137—42no—
96C4×C137—42no—
97C4×C137—82no—
98C2×C137—21no—
99C2×C137—21no—
100C2×C137—42no—
101C2×C137#146311yescharacteristic
102C2×C137#212811yescharacteristic
103C2×C137#213511yescharacteristic
104#11516C13711yesmaximal, characteristic, direct product factor, Sylow
105C137#1151611yescharacteristic, direct product factor, Sylow
106#2317C2×C13711yescharacteristic
107#1464C2×C13712yes—
108#1325C2×C13714yescomplemented
109C2×#117C4×C13711yescharacteristic
110C2×#117C22×C13711yescharacteristic
111C22×C4⋊C4C4×C13711yescharacteristic
112#432—22no—
113#389—22no—
114#385—22no—
115#384C22×C13712yes—
116#382C4×C13712yes—
117#324C22×C13714yes—
118#323—22no—
119C23×C4—21no—
120C23×C4C2×C4×C13711yescharacteristic
121#117—24no—
122#117—42no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—24no—
126C2×C4⋊C4—42no—
127C2×C4⋊C4C2×C4×C13712yes—
128C2×C4⋊C4C2×C4×C13711yescharacteristic
129C2×C4⋊C4C23×C13711yescharacteristic
130C2×C22⋊C4—21no—
131C2×C22⋊C4D4×C13712yes—
132C2×C42C2×C4×C13712yes—
133C2×C42D4×C13712yes—
134C4⋊C8—42no—
135C22⋊C8—24no—
136#97—42no—
137#95—24no—
138C24C22⋊C4×C13711yescharacteristic
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—42no—
145C22×C4—82no—
146C22×C4C22⋊C4×C13711yescharacteristic
147C22×C4C22⋊C4×C13712yes—
148C22×C4C22×C4×C13711yescharacteristic
149C22×C4C2×D4×C13712yes—
150C2×C8—44no—
151C4⋊C4—24no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—84no—
157C22⋊C4—24no—
158C22⋊C4—42no—
159C42—22no—
160C42—22no—
161C42—22no—
162C42M16×C13714yes—
163C23—21no—
164C23—21no—
165C23—41no—
166C23—41no—
167C23#101×C13712yes—
168C23C2×C22⋊C4×C13711yescharacteristic
169C2×C4—28no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—44no—
182C2×C4—42no—
183C2×C4—84no—
184C2×C4#99×C13712yes—
185C2×C4C2×M16×C13712yes—
186C8—84no—
187C22—21no—
188C22—21no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22#407×C13711yescharacteristic
195C22C2×#99×C13711yescharacteristic
196C22C2×#101×C13711yescharacteristic
197C4—22no—
198C4—22no—
199C4—44no—
200C4—42no—
201C4—42no—
202C4—82no—
203C2—21no—
204C2—21no—
205C2—42no—
206C2#1463×C13711yescharacteristic
207C2#2128×C13711yescharacteristic
208C2#2135×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#99
commutatorC22×C4C22×C4×C137
Frattini, cosocleC2×C4⋊C4C23×C137
prime radicalC24×C137C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C22×C4×C137 ◁ C2×#117×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1325×C137C2semidirect
104. #11516C137direct (N × H)
105. C137#11516direct (N × H)
108. #1325C2×C137semidirect

Maximal subgroups

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

subgroupindex
#2317×C1372
#1464×C1372
#1325×C1372
#11516137