Finite Group Databasebeta

← C137×#9400 #46858786

Subgroups — C137×#9400 #46858786

Order 35072.

466 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 138 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#2983×C137C211yesmaximal, characteristic
2#2567×C137C211yesmaximal, characteristic
3#1801×C137C211yesmaximal, characteristic
4#1548×C137C212yesmaximal
5#1303×C137C212yesmaximal
6C2×C4⋊Q8×C137C2211yescharacteristic
7C2×C4×Q8×C137C2211yescharacteristic
8#446×C137—24no—
9#432×C137—22no—
10#431×C137C2212yes—
11#423×C137C2212yes—
12C2×#101×C137—21no—
13#395×C137C414yes—
14#391×C137—21no—
15#389×C137—22no—
16#384×C137—21no—
17C4×C4⋊C4×C137C2211yescharacteristic
18#343×C137—21no—
19#333×C137—24no—
20C22×Q8×C137C2×C412yes—
21C22×Q8×C137D411yescharacteristic
22C2×M16×C137—22no—
23C4⋊Q8×C137—22no—
24C4⋊Q8×C137—22no—
25C4×Q8×C137—22no—
26C4×Q8×C137—22no—
27C2×C4⋊C4×C137—21no—
28C2×C4⋊C4×C137—21no—
29C2×C4⋊C4×C137—21no—
30C2×C4⋊C4×C137—24no—
31C2×C4⋊C4×C137C2×C412yes—
32C2×C4⋊C4×C137D411yescharacteristic
33C2×C42×C137—21no—
34C2×C42×C137D412yes—
35C2×C42×C137C2311yescharacteristic
36C4⋊C8×C137—24no—
37C4⋊C8×C137—22no—
38C4⋊C8×C137—22no—
39C4⋊C8×C137D414yes—
40#101×C137—42no—
41C22⋊C8×C137—22no—
42#97×C137—24no—
43C4×C8×C137—22no—
44#95×C137—24no—
45#95×C137C2×C412yes—
46C2×Q8×C137—22no—
47C2×Q8×C137—21no—
48C2×Q8×C137—21no—
49C2×Q8×C137—22no—
50C2×Q8×C137—24no—
51C2×Q8×C137—82no—
52C22×C4×C137—22no—
53C22×C4×C137—22no—
54C22×C4×C137C22⋊C412yes—
55C22×C4×C137C22⋊C412yes—
56C22×C4×C137C22×C411yescharacteristic
57C22×C4×C137C2×D411yescharacteristic
58C22×C4×C137C2×D411yescharacteristic
59M16×C137—42no—
60M16×C137—42no—
61C2×C8×C137—24no—
62C2×C8×C137—42no—
63C4⋊C4×C137—24no—
64C4⋊C4×C137—24no—
65C4⋊C4×C137—22no—
66C4⋊C4×C137—41no—
67C4⋊C4×C137—42no—
68C4⋊C4×C137—41no—
69C4⋊C4×C137—84no—
70C42×C137—22no—
71C42×C137—22no—
72C42×C137—41no—
73C42×C137—41no—
74C42×C137C2×D412yes—
75C42×C137#4112yes—
76C23×C137C2×C22⋊C411yescharacteristic
77Q8×C137—42no—
78Q8×C137—42no—
79Q8×C137—84no—
80C2×C4×C137—22no—
81C2×C4×C137—24no—
82C2×C4×C137—22no—
83C2×C4×C137—22no—
84C2×C4×C137—22no—
85C2×C4×C137—22no—
86C2×C4×C137—41no—
87C2×C4×C137—42no—
88C2×C4×C137—42no—
89C2×C4×C137—42no—
90C2×C4×C137—44no—
91C2×C4×C137—42no—
92C2×C4×C137C4×D412yes—
93C2×C4×C137#12011yescharacteristic
94C2×C4×C137#12112yes—
95C2×C4×C137#12311yescharacteristic
96C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
97C2×C4×C137#13712yes—
98C2×C4×C137#13711yescharacteristic
99C8×C137—44no—
100C8×C137—82no—
101C22×C137—21no—
102C22×C137—21no—
103C22×C137#38611yescharacteristic
104C22×C137#41711yescharacteristic
105C22×C137#41911yescharacteristic
106C4×C137—21no—
107C4×C137—22no—
108C4×C137—44no—
109C4×C137—42no—
110C4×C137—42no—
111C4×C137—82no—
112C4×C137#45612yes—
113C4×C137#46812yes—
114C4×C137#47012yes—
115C2×C137—21no—
116C2×C137—21no—
117C2×C137#188611yescharacteristic
118C2×C137#189411yescharacteristic
119C2×C137#191411yescharacteristic
120#9400C13711yesmaximal, characteristic, direct product factor, Sylow
121C137#940011yescharacteristic, direct product factor, Sylow
122#2983C2×C13711yescharacteristic
123#2567C2×C13711yescharacteristic
124#1801C2×C13711yescharacteristic
125#1548C2×C13712yes—
126#1303C2×C13712yes—
127C2×C4⋊Q8C22×C13711yescharacteristic
128C2×C4×Q8C22×C13711yescharacteristic
129#446—24no—
130#432—22no—
131#431C22×C13712yes—
132#423C22×C13712yes—
133C2×#101—21no—
134#395C4×C13714yes—
135#391—21no—
136#389—22no—
137#384—21no—
138C4×C4⋊C4C22×C13711yescharacteristic
139#343—21no—
140#333—24no—
141C22×Q8C2×C4×C13712yes—
142C22×Q8D4×C13711yescharacteristic
143C2×M16—22no—
144C4⋊Q8—22no—
145C4⋊Q8—22no—
146C4×Q8—22no—
147C4×Q8—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—24no—
152C2×C4⋊C4C2×C4×C13712yes—
153C2×C4⋊C4D4×C13711yescharacteristic
154C2×C42—21no—
155C2×C42D4×C13712yes—
156C2×C42C23×C13711yescharacteristic
157C4⋊C8—24no—
158C4⋊C8—22no—
159C4⋊C8—22no—
160C4⋊C8D4×C13714yes—
161#101—42no—
162C22⋊C8—22no—
163#97—24no—
164C4×C8—22no—
165#95—24no—
166#95C2×C4×C13712yes—
167C2×Q8—22no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—22no—
171C2×Q8—24no—
172C2×Q8—82no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4C22⋊C4×C13712yes—
176C22×C4C22⋊C4×C13712yes—
177C22×C4C22×C4×C13711yescharacteristic
178C22×C4C2×D4×C13711yescharacteristic
179C22×C4C2×D4×C13711yescharacteristic
180M16—42no—
181M16—42no—
182C2×C8—24no—
183C2×C8—42no—
184C4⋊C4—24no—
185C4⋊C4—24no—
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—42no—
189C4⋊C4—41no—
190C4⋊C4—84no—
191C42—22no—
192C42—22no—
193C42—41no—
194C42—41no—
195C42C2×D4×C13712yes—
196C42#41×C13712yes—
197C23C2×C22⋊C4×C13711yescharacteristic
198Q8—42no—
199Q8—42no—
200Q8—84no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—44no—
212C2×C4—42no—
213C2×C4C4×D4×C13712yes—
214C2×C4#120×C13711yescharacteristic
215C2×C4#121×C13712yes—
216C2×C4#123×C13711yescharacteristic
217C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
218C2×C4#137×C13712yes—
219C2×C4#137×C13711yescharacteristic
220C8—44no—
221C8—82no—
222C22—21no—
223C22—21no—
224C22#386×C13711yescharacteristic
225C22#417×C13711yescharacteristic
226C22#419×C13711yescharacteristic
227C4—21no—
228C4—22no—
229C4—44no—
230C4—42no—
231C4—42no—
232C4—82no—
233C4#456×C13712yes—
234C4#468×C13712yes—
235C4#470×C13712yes—
236C2—21no—
237C2—21no—
238C2#1886×C13711yescharacteristic
239C2#1894×C13711yescharacteristic
240C2#1914×C13711yescharacteristic
subgroupG/H
center, socleC22×C137#386
commutatorC22×C4C22×C4×C137
Frattini, cosocleC2×C42C23×C137
prime radicalC23×C137C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
120. #9400C137direct (N × H)
121. C137#9400direct (N × H)

Maximal subgroups

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

subgroupindex
#2983×C1372
#2567×C1372
#1801×C1372
#1548×C1372
#1303×C1372
#9400137