Finite Group Databasebeta

← C137×#10290 #46859676

Subgroups — C137×#10290 #46859676

Order 35072.

912 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 912 conjugacy classes of subgroups — too many to draw. Only its 130 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#3208×C137C212yesmaximal, complemented
2#2867×C137C211yesmaximal, characteristic
3#1994×C137C211yesmaximal, characteristic, complemented
4#1545×C137C212yesmaximal, complemented
5#1276×C137C211yesmaximal, characteristic, complemented
6#533×C137C2211yescharacteristic
7C2×#127×C137—24no—
8C2×#127×C137—22no—
9C2×#127×C137C2212yes—
10#492×C137—22no—
11#486×C137—22no—
12#460×C137—24no—
13#450×C137—24no—
14#431×C137C2212yes—
15#423×C137C2211yescharacteristic
16C43×C137C2211yescharacteristic
17#339×C137—22no—
18#331×C137—24no—
19C22×D4×C137—28no—
20C22×D4×C137—22no—
21C22×D4×C137—22no—
22C22×D4×C137D414yes—
23C2×SD16×C137—28no—
24C2×M16×C137—21no—
25C4⋊Q8×C137D412yescomplemented
26#127×C137—22no—
27#127×C137—22no—
28#127×C137—22no—
29#127×C137—22no—
30#127×C137—416no—
31#127×C137—44no—
32#127×C137—44no—
33#125×C137—21no—
34C22⋊Q8×C137—22no—
35C4×Q8×C137—22no—
36#117×C137—21no—
37C2×C42×C137—22no—
38C2×C42×C137D412yes—
39C2×C42×C137C2311yescharacteristic
40C4⋊C8×C137—22no—
41C4⋊C8×C137D414yescomplemented
42#102×C137—28no—
43C22⋊C8×C137—22no—
44C4×C8×C137—22no—
45C24×C137—24no—
46C2×Q8×C137—22no—
47C2×D4×C137—24no—
48C2×D4×C137—24no—
49C2×D4×C137—48no—
50C2×D4×C137—432no—
51C2×D4×C137—416no—
52C2×D4×C137—48no—
53C2×D4×C137—42no—
54C2×D4×C137—42no—
55C2×D4×C137—42no—
56C2×D4×C137—42no—
57C2×D4×C137—44no—
58C2×D4×C137—44no—
59C22×C4×C137—22no—
60C22×C4×C137C2×D412yes—
61C22×C4×C137C2×D411yescharacteristic
62SD16×C137—88no—
63M16×C137—42no—
64C2×C8×C137—24no—
65C2×C8×C137—41no—
66C4⋊C4×C137—22no—
67C4⋊C4×C137—22no—
68C4⋊C4×C137—42no—
69C22⋊C4×C137—41no—
70C42×C137—28no—
71C42×C137—22no—
72C42×C137—41no—
73C42×C137SD1614yescomplemented
74C42×C137C2×D411yescharacteristic
75C42×C137C2×D412yes—
76C42×C137#4111yescharacteristic
77C23×C137—48no—
78C23×C137—48no—
79C23×C137—44no—
80C23×C137—48no—
81C23×C137#12011yescharacteristic
82Q8×C137—44no—
83D4×C137—48no—
84D4×C137—84no—
85D4×C137—832no—
86D4×C137—84no—
87D4×C137—84no—
88D4×C137—84no—
89D4×C137—82no—
90D4×C137—82no—
91C2×C4×C137—28no—
92C2×C4×C137—24no—
93C2×C4×C137—24no—
94C2×C4×C137—42no—
95C2×C4×C137#12012yes—
96C2×C4×C137#12112yes—
97C2×C4×C137#12111yescharacteristic
98C2×C4×C137#12711yescharacteristic
99C2×C4×C137C2×SD1612yes—
100C2×C4×C137AGL(1,ℤ/8)12yes—
101C8×C137—44no—
102C8×C137—81no—
103C22×C137—22no—
104C22×C137—816no—
105C22×C137—84no—
106C22×C137—84no—
107C22×C137—84no—
108C22×C137#39211yescharacteristic
109C22×C137#45012yes—
110C4×C137—28no—
111C4×C137—22no—
112C4×C137—82no—
113C4×C137#45314yes—
114C4×C137#46012yes—
115C4×C137#49211yescharacteristic
116C4×C137#49611yescharacteristic
117C2×C137—22no—
118C2×C137—164no—
119C2×C137#200212yes—
120C2×C137#201411yescharacteristic
121#10290C13711yesmaximal, characteristic, direct product factor, Sylow
122C137#1029011yescharacteristic, direct product factor, Sylow
123#3208C2×C13712yescomplemented
124#2867C2×C13711yescharacteristic
125#1994C2×C13711yescharacteristic, complemented
126#1545C2×C13712yescomplemented
127#1276C2×C13711yescharacteristic, complemented
128#533C22×C13711yescharacteristic
129C2×#127—24no—
130C2×#127—22no—
131C2×#127C22×C13712yes—
132#492—22no—
133#486—22no—
134#460—24no—
135#450—24no—
136#431C22×C13712yes—
137#423C22×C13711yescharacteristic
138C43C22×C13711yescharacteristic
139#339—22no—
140#331—24no—
141C22×D4—28no—
142C22×D4—22no—
143C22×D4—22no—
144C22×D4D4×C13714yes—
145C2×SD16—28no—
146C2×M16—21no—
147C4⋊Q8D4×C13712yescomplemented
148#127—22no—
149#127—22no—
150#127—22no—
151#127—22no—
152#127—416no—
153#127—44no—
154#127—44no—
155#125—21no—
156C22⋊Q8—22no—
157C4×Q8—22no—
158#117—21no—
159C2×C42—22no—
160C2×C42D4×C13712yes—
161C2×C42C23×C13711yescharacteristic
162C4⋊C8—22no—
163C4⋊C8D4×C13714yescomplemented
164#102—28no—
165C22⋊C8—22no—
166C4×C8—22no—
167C24—24no—
168C2×Q8—22no—
169C2×D4—24no—
170C2×D4—24no—
171C2×D4—48no—
172C2×D4—432no—
173C2×D4—416no—
174C2×D4—48no—
175C2×D4—42no—
176C2×D4—42no—
177C2×D4—42no—
178C2×D4—42no—
179C2×D4—44no—
180C2×D4—44no—
181C22×C4—22no—
182C22×C4C2×D4×C13712yes—
183C22×C4C2×D4×C13711yescharacteristic
184SD16—88no—
185M16—42no—
186C2×C8—24no—
187C2×C8—41no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—42no—
191C22⋊C4—41no—
192C42—28no—
193C42—22no—
194C42—41no—
195C42SD16×C13714yescomplemented
196C42C2×D4×C13711yescharacteristic
197C42C2×D4×C13712yes—
198C42#41×C13711yescharacteristic
199C23—48no—
200C23—48no—
201C23—44no—
202C23—48no—
203C23#120×C13711yescharacteristic
204Q8—44no—
205D4—48no—
206D4—84no—
207D4—832no—
208D4—84no—
209D4—84no—
210D4—84no—
211D4—82no—
212D4—82no—
213C2×C4—28no—
214C2×C4—24no—
215C2×C4—24no—
216C2×C4—42no—
217C2×C4#120×C13712yes—
218C2×C4#121×C13712yes—
219C2×C4#121×C13711yescharacteristic
220C2×C4#127×C13711yescharacteristic
221C2×C4C2×SD16×C13712yes—
222C2×C4AGL(1,ℤ/8)×C13712yes—
223C8—44no—
224C8—81no—
225C22—22no—
226C22—816no—
227C22—84no—
228C22—84no—
229C22—84no—
230C22#392×C13711yescharacteristic
231C22#450×C13712yes—
232C4—28no—
233C4—22no—
234C4—82no—
235C4#453×C13714yes—
236C4#460×C13712yes—
237C4#492×C13711yescharacteristic
238C4#496×C13711yescharacteristic
239C2—22no—
240C2—164no—
241C2#2002×C13712yes—
242C2#2014×C13711yescharacteristic
subgroupG/H
center, socleC22×C137#392
commutator, Frattini, cosocleC2×C42C23×C137
prime radical#2867×C137C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3208×C137C2semidirect
3. #1994×C137C2semidirect
4. #1545×C137C2semidirect
5. #1276×C137C2semidirect
25. C4⋊Q8×C137D4semidirect
41. C4⋊C8×C137D4semidirect
73. C42×C137SD16semidirect
121. #10290C137direct (N × H)
122. C137#10290direct (N × H)
123. #3208C2×C137semidirect
125. #1994C2×C137semidirect
126. #1545C2×C137semidirect
127. #1276C2×C137semidirect
147. C4⋊Q8D4×C137semidirect
163. C4⋊C8D4×C137semidirect
195. C42SD16×C137semidirect

Maximal subgroups

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

subgroupindex
#3208×C1372
#2867×C1372
#1994×C1372
#1545×C1372
#1276×C1372
#10290137