Finite Group Databasebeta

← C137×#8935 #46858321

Subgroups — C137×#8935 #46858321

Order 35072.

412 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 126 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#2979×C137C211yesmaximal, characteristic
2#1962×C137C211yesmaximal, characteristic
3#1574×C137C212yesmaximal, complemented
4#1543×C137C211yesmaximal, characteristic
5#1276×C137C212yesmaximal, complemented
6#532×C137C2211yescharacteristic
7#436×C137—22no—
8C8×D4×C137—22no—
9#431×C137C2212yes—
10#431×C137C2212yes—
11#423×C137C2211yescharacteristic
12C2×#104×C137—22no—
13#408×C137—22no—
14C43×C137C2211yescharacteristic
15#335×C137—22no—
16#334×C137—22no—
17#333×C137C411yescharacteristic, complemented
18#333×C137C411yescharacteristic, complemented
19#331×C137C412yescomplemented
20C2×#41×C137D412yes—
21C2×M16×C137—22no—
22C2×M16×C137—21no—
23C22×C8×C137—22no—
24C4⋊Q8×C137C2×C411yescharacteristic
25#127×C137C2×C411yescharacteristic
26#124×C137Q812yes—
27#121×C137—22no—
28C4×D4×C137—22no—
29C2×C42×C137—21no—
30C2×C42×C137—22no—
31C2×C42×C137C2311yescharacteristic
32C4⋊C8×C137—22no—
33C4⋊C8×C137C2×C412yes—
34C4⋊C8×C137C2×C412yes—
35C4⋊C8×C137D412yes—
36C4⋊C8×C137D412yes—
37#104×C137—44no—
38C22⋊C8×C137—24no—
39C22⋊C8×C137—22no—
40C22⋊C8×C137—22no—
41C4×C8×C137—22no—
42C4×C8×C137—22no—
43#41×C137—42no—
44#41×C137—42no—
45C2×Q8×C137C4⋊C412yes—
46C2×D4×C137—22no—
47C2×D4×C137—22no—
48C2×D4×C137C4⋊C412yes—
49C22×C4×C137—22no—
50C22×C4×C137—41no—
51C22×C4×C137C2×D411yescharacteristic
52C22×C4×C137#4112yes—
53M16×C137—42no—
54M16×C137—82no—
55C2×C8×C137—22no—
56C2×C8×C137—22no—
57C2×C8×C137—22no—
58C2×C8×C137—22no—
59C2×C8×C137—41no—
60C2×C8×C137—82no—
61C4⋊C4×C137—22no—
62C22⋊C4×C137—24no—
63C42×C137—22no—
64C42×C137—24no—
65C42×C137—42no—
66C42×C137—41no—
67C42×C137C22×C411yescharacteristic
68C42×C137C2×D412yes—
69C42×C137C2×Q811yescharacteristic
70C23×C137—22no—
71C23×C137#12311yescharacteristic
72Q8×C137—42no—
73D4×C137—42no—
74D4×C137—42no—
75D4×C137—42no—
76D4×C137—82no—
77C2×C4×C137—22no—
78C2×C4×C137—22no—
79C2×C4×C137—21no—
80C2×C4×C137—21no—
81C2×C4×C137—22no—
82C2×C4×C137—42no—
83C2×C4×C137—44no—
84C2×C4×C137—42no—
85C2×C4×C137—42no—
86C2×C4×C137C2×C4⋊C411yescharacteristic
87C2×C4×C137C4×D412yes—
88C2×C4×C137#12011yescharacteristic
89C2×C4×C137C22⋊Q812yes—
90C8×C137—42no—
91C8×C137—42no—
92C8×C137—42no—
93C8×C137—42no—
94C8×C137—81no—
95C22×C137—21no—
96C22×C137—22no—
97C22×C137—42no—
98C22×C137—44no—
99C22×C137#38511yescharacteristic
100C4×C137—21no—
101C4×C137—22no—
102C4×C137—44no—
103C4×C137—42no—
104C4×C137#44312yes—
105C4×C137#44412yes—
106C4×C137#45311yescharacteristic
107C4×C137#45511yescharacteristic
108C2×C137—41no—
109C2×C137—82no—
110C2×C137#185611yescharacteristic
111C2×C137#186612yes—
112#8935C13711yesmaximal, characteristic, direct product factor, Sylow
113C137#893511yescharacteristic, direct product factor, Sylow
114#2979C2×C13711yescharacteristic
115#1962C2×C13711yescharacteristic
116#1574C2×C13712yescomplemented
117#1543C2×C13711yescharacteristic
118#1276C2×C13712yescomplemented
119#532C22×C13711yescharacteristic
120#436—22no—
121C8×D4—22no—
122#431C22×C13712yes—
123#431C22×C13712yes—
124#423C22×C13711yescharacteristic
125C2×#104—22no—
126#408—22no—
127C43C22×C13711yescharacteristic
128#335—22no—
129#334—22no—
130#333C4×C13711yescharacteristic, complemented
131#333C4×C13711yescharacteristic, complemented
132#331C4×C13712yescomplemented
133C2×#41D4×C13712yes—
134C2×M16—22no—
135C2×M16—21no—
136C22×C8—22no—
137C4⋊Q8C2×C4×C13711yescharacteristic
138#127C2×C4×C13711yescharacteristic
139#124Q8×C13712yes—
140#121—22no—
141C4×D4—22no—
142C2×C42—21no—
143C2×C42—22no—
144C2×C42C23×C13711yescharacteristic
145C4⋊C8—22no—
146C4⋊C8C2×C4×C13712yes—
147C4⋊C8C2×C4×C13712yes—
148C4⋊C8D4×C13712yes—
149C4⋊C8D4×C13712yes—
150#104—44no—
151C22⋊C8—24no—
152C22⋊C8—22no—
153C22⋊C8—22no—
154C4×C8—22no—
155C4×C8—22no—
156#41—42no—
157#41—42no—
158C2×Q8C4⋊C4×C13712yes—
159C2×D4—22no—
160C2×D4—22no—
161C2×D4C4⋊C4×C13712yes—
162C22×C4—22no—
163C22×C4—41no—
164C22×C4C2×D4×C13711yescharacteristic
165C22×C4#41×C13712yes—
166M16—42no—
167M16—82no—
168C2×C8—22no—
169C2×C8—22no—
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—41no—
173C2×C8—82no—
174C4⋊C4—22no—
175C22⋊C4—24no—
176C42—22no—
177C42—24no—
178C42—42no—
179C42—41no—
180C42C22×C4×C13711yescharacteristic
181C42C2×D4×C13712yes—
182C42C2×Q8×C13711yescharacteristic
183C23—22no—
184C23#123×C13711yescharacteristic
185Q8—42no—
186D4—42no—
187D4—42no—
188D4—42no—
189D4—82no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—42no—
196C2×C4—44no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4C2×C4⋊C4×C13711yescharacteristic
200C2×C4C4×D4×C13712yes—
201C2×C4#120×C13711yescharacteristic
202C2×C4C22⋊Q8×C13712yes—
203C8—42no—
204C8—42no—
205C8—42no—
206C8—42no—
207C8—81no—
208C22—21no—
209C22—22no—
210C22—42no—
211C22—44no—
212C22#385×C13711yescharacteristic
213C4—21no—
214C4—22no—
215C4—44no—
216C4—42no—
217C4#443×C13712yes—
218C4#444×C13712yes—
219C4#453×C13711yescharacteristic
220C4#455×C13711yescharacteristic
221C2—41no—
222C2—82no—
223C2#1856×C13711yescharacteristic
224C2#1866×C13712yes—
subgroupG/H
centerC2×C4×C137#120
commutatorC42C22×C4×C137
Frattini, cosocleC2×C42C23×C137
socleC22×C137#385
prime radical#532×C137C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1574×C137C2semidirect
5. #1276×C137C2semidirect
17. #333×C137C4semidirect
18. #333×C137C4semidirect
19. #331×C137C4semidirect
112. #8935C137direct (N × H)
113. C137#8935direct (N × H)
116. #1574C2×C137semidirect
118. #1276C2×C137semidirect
130. #333C4×C137semidirect
131. #333C4×C137semidirect
132. #331C4×C137semidirect

Maximal subgroups

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

subgroupindex
#2979×C1372
#1962×C1372
#1574×C1372
#1543×C1372
#1276×C1372
#8935137