Finite Group Databasebeta

← C137×#9402 #46858788

Subgroups — C137×#9402 #46858788

Order 35072.

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

normal subgroups only

This group has 486 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#2546×C137C211yesmaximal, characteristic
3#1801×C137C211yesmaximal, characteristic
4#1546×C137C212yesmaximal
5#1303×C137C212yesmaximal
6C2×C4⋊Q8×C137—21no—
7C2×C4⋊Q8×C137C2211yescharacteristic
8C2×C4×Q8×C137C2211yescharacteristic
9#446×C137—24no—
10#432×C137—22no—
11#431×C137C2212yes—
12#423×C137C2212yes—
13C2×#101×C137—21no—
14#398×C137C414yes—
15#391×C137—21no—
16#389×C137—22no—
17C4×C4⋊C4×C137C2211yescharacteristic
18#343×C137—21no—
19#332×C137—24no—
20C22×Q8×C137—21no—
21C22×Q8×C137D411yescharacteristic
22C2×M16×C137—22no—
23C4⋊Q8×C137—22no—
24C4⋊Q8×C137—22no—
25C4⋊Q8×C137—44no—
26C4×Q8×C137—22no—
27C4×Q8×C137—22no—
28C2×C4⋊C4×C137—21no—
29C2×C4⋊C4×C137—24no—
30C2×C4⋊C4×C137—21no—
31C2×C4⋊C4×C137C2×C412yes—
32C2×C4⋊C4×C137C2×C412yes—
33C2×C4⋊C4×C137D411yescharacteristic
34C2×C42×C137—21no—
35C2×C42×C137D412yes—
36C2×C42×C137C2311yescharacteristic
37C4⋊C8×C137—24no—
38C4⋊C8×C137—22no—
39C4⋊C8×C137—22no—
40C4⋊C8×C137D414yes—
41#101×C137—42no—
42C22⋊C8×C137—22no—
43#97×C137—24no—
44C4×C8×C137—22no—
45#95×C137—24no—
46#95×C137C2×C412yes—
47C2×Q8×C137—22no—
48C2×Q8×C137—21no—
49C2×Q8×C137—22no—
50C2×Q8×C137—21no—
51C2×Q8×C137—42no—
52C2×Q8×C137—42no—
53C2×Q8×C137—41no—
54C2×Q8×C137—41no—
55C22×C4×C137—22no—
56C22×C4×C137—22no—
57C22×C4×C137C22⋊C412yes—
58C22×C4×C137C22⋊C412yes—
59C22×C4×C137C22×C411yescharacteristic
60C22×C4×C137C2×D411yescharacteristic
61C22×C4×C137C2×D411yescharacteristic
62M16×C137—42no—
63M16×C137—42no—
64C2×C8×C137—24no—
65C2×C8×C137—42no—
66C4⋊C4×C137—24no—
67C4⋊C4×C137—24no—
68C4⋊C4×C137—22no—
69C4⋊C4×C137—24no—
70C4⋊C4×C137—48no—
71C4⋊C4×C137—41no—
72C4⋊C4×C137—41no—
73C42×C137—22no—
74C42×C137—22no—
75C42×C137—42no—
76C42×C137C2×D412yes—
77C42×C137#4112yes—
78C23×C137C2×C22⋊C411yescharacteristic
79Q8×C137—42no—
80Q8×C137—42no—
81Q8×C137—82no—
82Q8×C137—82no—
83C2×C4×C137—22no—
84C2×C4×C137—24no—
85C2×C4×C137—22no—
86C2×C4×C137—22no—
87C2×C4×C137—22no—
88C2×C4×C137—22no—
89C2×C4×C137—41no—
90C2×C4×C137—42no—
91C2×C4×C137—42no—
92C2×C4×C137—42no—
93C2×C4×C137—42no—
94C2×C4×C137—42no—
95C2×C4×C137—42no—
96C2×C4×C137C4×D412yes—
97C2×C4×C137#12011yescharacteristic
98C2×C4×C137#12112yes—
99C2×C4×C137#12311yescharacteristic
100C2×C4×C137AGL(1,ℤ/8)12yes—
101C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
102C2×C4×C137#13711yescharacteristic
103C8×C137—44no—
104C8×C137—82no—
105C22×C137—21no—
106C22×C137—21no—
107C22×C137#38611yescharacteristic
108C22×C137#41711yescharacteristic
109C22×C137#41811yescharacteristic
110C4×C137—21no—
111C4×C137—22no—
112C4×C137—44no—
113C4×C137—42no—
114C4×C137—42no—
115C4×C137—82no—
116C4×C137#45612yes—
117C4×C137#46812yes—
118C4×C137#46912yes—
119C2×C137—21no—
120C2×C137—21no—
121C2×C137#188611yescharacteristic
122C2×C137#189511yescharacteristic
123C2×C137#191511yescharacteristic
124#9402C13711yesmaximal, characteristic, direct product factor, Sylow
125C137#940211yescharacteristic, direct product factor, Sylow
126#2983C2×C13711yescharacteristic
127#2546C2×C13711yescharacteristic
128#1801C2×C13711yescharacteristic
129#1546C2×C13712yes—
130#1303C2×C13712yes—
131C2×C4⋊Q8—21no—
132C2×C4⋊Q8C22×C13711yescharacteristic
133C2×C4×Q8C22×C13711yescharacteristic
134#446—24no—
135#432—22no—
136#431C22×C13712yes—
137#423C22×C13712yes—
138C2×#101—21no—
139#398C4×C13714yes—
140#391—21no—
141#389—22no—
142C4×C4⋊C4C22×C13711yescharacteristic
143#343—21no—
144#332—24no—
145C22×Q8—21no—
146C22×Q8D4×C13711yescharacteristic
147C2×M16—22no—
148C4⋊Q8—22no—
149C4⋊Q8—22no—
150C4⋊Q8—44no—
151C4×Q8—22no—
152C4×Q8—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—24no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4C2×C4×C13712yes—
157C2×C4⋊C4C2×C4×C13712yes—
158C2×C4⋊C4D4×C13711yescharacteristic
159C2×C42—21no—
160C2×C42D4×C13712yes—
161C2×C42C23×C13711yescharacteristic
162C4⋊C8—24no—
163C4⋊C8—22no—
164C4⋊C8—22no—
165C4⋊C8D4×C13714yes—
166#101—42no—
167C22⋊C8—22no—
168#97—24no—
169C4×C8—22no—
170#95—24no—
171#95C2×C4×C13712yes—
172C2×Q8—22no—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—21no—
176C2×Q8—42no—
177C2×Q8—42no—
178C2×Q8—41no—
179C2×Q8—41no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4C22⋊C4×C13712yes—
183C22×C4C22⋊C4×C13712yes—
184C22×C4C22×C4×C13711yescharacteristic
185C22×C4C2×D4×C13711yescharacteristic
186C22×C4C2×D4×C13711yescharacteristic
187M16—42no—
188M16—42no—
189C2×C8—24no—
190C2×C8—42no—
191C4⋊C4—24no—
192C4⋊C4—24no—
193C4⋊C4—22no—
194C4⋊C4—24no—
195C4⋊C4—48no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C42—22no—
199C42—22no—
200C42—42no—
201C42C2×D4×C13712yes—
202C42#41×C13712yes—
203C23C2×C22⋊C4×C13711yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—82no—
207Q8—82no—
208C2×C4—22no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4C4×D4×C13712yes—
222C2×C4#120×C13711yescharacteristic
223C2×C4#121×C13712yes—
224C2×C4#123×C13711yescharacteristic
225C2×C4AGL(1,ℤ/8)×C13712yes—
226C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
227C2×C4#137×C13711yescharacteristic
228C8—44no—
229C8—82no—
230C22—21no—
231C22—21no—
232C22#386×C13711yescharacteristic
233C22#417×C13711yescharacteristic
234C22#418×C13711yescharacteristic
235C4—21no—
236C4—22no—
237C4—44no—
238C4—42no—
239C4—42no—
240C4—82no—
241C4#456×C13712yes—
242C4#468×C13712yes—
243C4#469×C13712yes—
244C2—21no—
245C2—21no—
246C2#1886×C13711yescharacteristic
247C2#1895×C13711yescharacteristic
248C2#1915×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
124. #9402C137direct (N × H)
125. C137#9402direct (N × H)

Maximal subgroups

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

subgroupindex
#2983×C1372
#2546×C1372
#1801×C1372
#1546×C1372
#1303×C1372
#9402137