Finite Group Databasebeta

← C137×#9401 #46858787

Subgroups — C137×#9401 #46858787

Order 35072.

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

normal subgroups only

This group has 534 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#2975×C137C211yesmaximal, characteristic
2#2547×C137C211yesmaximal, characteristic
3#1800×C137C211yesmaximal, characteristic
4#1546×C137C212yesmaximal, complemented
5#1303×C137C212yesmaximal, complemented
6C2×C4⋊Q8×C137C2211yescharacteristic
7C2×#124×C137—21no—
8C2×C4×D4×C137C2211yescharacteristic
9#436×C137—24no—
10#431×C137C2212yes—
11#423×C137C2212yes—
12C2×#100×C137—21no—
13#407×C137—22no—
14#397×C137C414yes—
15#391×C137—21no—
16#380×C137—22no—
17C4×C4⋊C4×C137C2211yescharacteristic
18#343×C137—21no—
19#332×C137—24no—
20C22×Q8×C137—21no—
21C22×D4×C137D411yescharacteristic
22C23×C4×C137D412yes—
23C2×M16×C137—24no—
24C2×M16×C137—22no—
25C4⋊Q8×C137—22no—
26C4⋊Q8×C137—22no—
27#124×C137—44no—
28C4×D4×C137—22no—
29C4×D4×C137—22no—
30C2×C4⋊C4×C137—21no—
31C2×C4⋊C4×C137—21no—
32C2×C4⋊C4×C137C2×C412yes—
33C2×C4⋊C4×C137D411yescharacteristic
34C2×C22⋊C4×C137—24no—
35C2×C22⋊C4×C137C2×C412yes—
36C2×C42×C137—21no—
37C2×C42×C137C2311yescharacteristic
38C4⋊C8×C137—22no—
39C4⋊C8×C137—22no—
40C4⋊C8×C137D414yes—
41#100×C137—42no—
42C22⋊C8×C137—24no—
43C22⋊C8×C137—22no—
44C4×C8×C137—22no—
45#95×C137—24no—
46#95×C137C2×C412yes—
47C24×C137C22⋊C412yes—
48C2×Q8×C137—42no—
49C2×Q8×C137—42no—
50C2×Q8×C137—41no—
51C2×Q8×C137—41no—
52C2×D4×C137—22no—
53C2×D4×C137—21no—
54C2×D4×C137—22no—
55C2×D4×C137—21no—
56C22×C4×C137—22no—
57C22×C4×C137—22no—
58C22×C4×C137—22no—
59C22×C4×C137—22no—
60C22×C4×C137—44no—
61C22×C4×C137C22⋊C412yes—
62C22×C4×C137C22×C411yescharacteristic
63C22×C4×C137C2×D411yescharacteristic
64C22×C4×C137C2×D411yescharacteristic
65M16×C137—42no—
66M16×C137—42no—
67M16×C137—84no—
68C2×C8×C137—24no—
69C2×C8×C137—42no—
70C4⋊C4×C137—22no—
71C4⋊C4×C137—24no—
72C4⋊C4×C137—42no—
73C4⋊C4×C137—41no—
74C4⋊C4×C137—41no—
75C22⋊C4×C137—24no—
76C22⋊C4×C137—48no—
77C42×C137—42no—
78C42×C137C2×D412yes—
79C42×C137#4112yes—
80C23×C137—22no—
81C23×C137—22no—
82C23×C137—22no—
83C23×C137—42no—
84C23×C137—42no—
85C23×C137C2×C22⋊C411yescharacteristic
86Q8×C137—82no—
87Q8×C137—82no—
88D4×C137—42no—
89D4×C137—42no—
90C2×C4×C137—22no—
91C2×C4×C137—22no—
92C2×C4×C137—41no—
93C2×C4×C137—44no—
94C2×C4×C137—42no—
95C2×C4×C137—42no—
96C2×C4×C137—42no—
97C2×C4×C137—42no—
98C2×C4×C137—42no—
99C2×C4×C137—42no—
100C2×C4×C137—42no—
101C2×C4×C137—82no—
102C2×C4×C137C4×D412yes—
103C2×C4×C137#12011yescharacteristic
104C2×C4×C137#12112yes—
105C2×C4×C137#12311yescharacteristic
106C2×C4×C137AGL(1,ℤ/8)12yes—
107C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
108C2×C4×C137#13711yescharacteristic
109C8×C137—44no—
110C8×C137—82no—
111C22×C137—21no—
112C22×C137—21no—
113C22×C137—44no—
114C22×C137—42no—
115C22×C137—42no—
116C22×C137—42no—
117C22×C137—82no—
118C22×C137#38611yescharacteristic
119C22×C137#41711yescharacteristic
120C22×C137#41811yescharacteristic
121C4×C137—21no—
122C4×C137—22no—
123C4×C137—42no—
124C4×C137—82no—
125C4×C137—82no—
126C4×C137#45512yes—
127C4×C137#46812yes—
128C4×C137#46912yes—
129C2×C137—21no—
130C2×C137—21no—
131C2×C137—82no—
132C2×C137#188511yescharacteristic
133C2×C137#189511yescharacteristic
134C2×C137#191511yescharacteristic
135#9401C13711yesmaximal, characteristic, direct product factor, Sylow
136C137#940111yescharacteristic, direct product factor, Sylow
137#2975C2×C13711yescharacteristic
138#2547C2×C13711yescharacteristic
139#1800C2×C13711yescharacteristic
140#1546C2×C13712yescomplemented
141#1303C2×C13712yescomplemented
142C2×C4⋊Q8C22×C13711yescharacteristic
143C2×#124—21no—
144C2×C4×D4C22×C13711yescharacteristic
145#436—24no—
146#431C22×C13712yes—
147#423C22×C13712yes—
148C2×#100—21no—
149#407—22no—
150#397C4×C13714yes—
151#391—21no—
152#380—22no—
153C4×C4⋊C4C22×C13711yescharacteristic
154#343—21no—
155#332—24no—
156C22×Q8—21no—
157C22×D4D4×C13711yescharacteristic
158C23×C4D4×C13712yes—
159C2×M16—24no—
160C2×M16—22no—
161C4⋊Q8—22no—
162C4⋊Q8—22no—
163#124—44no—
164C4×D4—22no—
165C4×D4—22no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4C2×C4×C13712yes—
169C2×C4⋊C4D4×C13711yescharacteristic
170C2×C22⋊C4—24no—
171C2×C22⋊C4C2×C4×C13712yes—
172C2×C42—21no—
173C2×C42C23×C13711yescharacteristic
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8D4×C13714yes—
177#100—42no—
178C22⋊C8—24no—
179C22⋊C8—22no—
180C4×C8—22no—
181#95—24no—
182#95C2×C4×C13712yes—
183C24C22⋊C4×C13712yes—
184C2×Q8—42no—
185C2×Q8—42no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×D4—22no—
189C2×D4—21no—
190C2×D4—22no—
191C2×D4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—44no—
197C22×C4C22⋊C4×C13712yes—
198C22×C4C22×C4×C13711yescharacteristic
199C22×C4C2×D4×C13711yescharacteristic
200C22×C4C2×D4×C13711yescharacteristic
201M16—42no—
202M16—42no—
203M16—84no—
204C2×C8—24no—
205C2×C8—42no—
206C4⋊C4—22no—
207C4⋊C4—24no—
208C4⋊C4—42no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C22⋊C4—24no—
212C22⋊C4—48no—
213C42—42no—
214C42C2×D4×C13712yes—
215C42#41×C13712yes—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—42no—
220C23—42no—
221C23C2×C22⋊C4×C13711yescharacteristic
222Q8—82no—
223Q8—82no—
224D4—42no—
225D4—42no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—44no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—82no—
238C2×C4C4×D4×C13712yes—
239C2×C4#120×C13711yescharacteristic
240C2×C4#121×C13712yes—
241C2×C4#123×C13711yescharacteristic
242C2×C4AGL(1,ℤ/8)×C13712yes—
243C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
244C2×C4#137×C13711yescharacteristic
245C8—44no—
246C8—82no—
247C22—21no—
248C22—21no—
249C22—44no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—82no—
254C22#386×C13711yescharacteristic
255C22#417×C13711yescharacteristic
256C22#418×C13711yescharacteristic
257C4—21no—
258C4—22no—
259C4—42no—
260C4—82no—
261C4—82no—
262C4#455×C13712yes—
263C4#468×C13712yes—
264C4#469×C13712yes—
265C2—21no—
266C2—21no—
267C2—82no—
268C2#1885×C13711yescharacteristic
269C2#1895×C13711yescharacteristic
270C2#1915×C13711yescharacteristic
subgroupG/H
center, socleC22×C137#386
commutatorC22×C4C22×C4×C137
Frattini, cosocleC2×C42C23×C137
prime radicalC22×D4×C137D4
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
4. #1546×C137C2semidirect
5. #1303×C137C2semidirect
135. #9401C137direct (N × H)
136. C137#9401direct (N × H)
140. #1546C2×C137semidirect
141. #1303C2×C137semidirect

Maximal subgroups

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

subgroupindex
#2975×C1372
#2547×C1372
#1800×C1372
#1546×C1372
#1303×C1372
#9401137