Finite Group Databasebeta

← C137×#9399 #46858785

Subgroups — C137×#9399 #46858785

Order 35072.

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

normal subgroups only

This group has 514 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#2563×C137C211yesmaximal, characteristic
3#1800×C137C211yesmaximal, characteristic
4#1548×C137C212yesmaximal, complemented
5#1303×C137C212yesmaximal, complemented
6C2×C4⋊Q8×C137C2211yescharacteristic
7C2×C4×D4×C137C2211yescharacteristic
8#436×C137—24no—
9#431×C137C2212yes—
10#423×C137C2212yes—
11C2×#100×C137—21no—
12#407×C137—22no—
13#393×C137C414yes—
14#390×C137—21no—
15#382×C137—21no—
16#380×C137—22no—
17C4×C4⋊C4×C137C2211yescharacteristic
18#343×C137—21no—
19#333×C137—24no—
20C22×Q8×C137C2×C412yes—
21C22×D4×C137D411yescharacteristic
22C23×C4×C137D412yes—
23C2×M16×C137—24no—
24C2×M16×C137—22no—
25C4⋊Q8×C137—22no—
26C4⋊Q8×C137—22no—
27C4×D4×C137—22no—
28C4×D4×C137—22no—
29C2×C4⋊C4×C137—21no—
30C2×C4⋊C4×C137—21no—
31C2×C4⋊C4×C137—21no—
32C2×C4⋊C4×C137D411yescharacteristic
33C2×C22⋊C4×C137—24no—
34C2×C22⋊C4×C137C2×C412yes—
35C2×C42×C137—21no—
36C2×C42×C137C2311yescharacteristic
37C4⋊C8×C137—22no—
38C4⋊C8×C137—22no—
39C4⋊C8×C137D414yes—
40#100×C137—42no—
41C22⋊C8×C137—24no—
42C22⋊C8×C137—22no—
43C4×C8×C137—22no—
44#95×C137—24no—
45#95×C137C2×C412yes—
46C24×C137C22⋊C412yes—
47C2×Q8×C137—24no—
48C2×Q8×C137—82no—
49C2×D4×C137—22no—
50C2×D4×C137—21no—
51C2×D4×C137—22no—
52C2×D4×C137—21no—
53C22×C4×C137—22no—
54C22×C4×C137—22no—
55C22×C4×C137—22no—
56C22×C4×C137—22no—
57C22×C4×C137—44no—
58C22×C4×C137C22⋊C412yes—
59C22×C4×C137C22×C411yescharacteristic
60C22×C4×C137C2×D411yescharacteristic
61C22×C4×C137C2×D411yescharacteristic
62M16×C137—42no—
63M16×C137—42no—
64M16×C137—84no—
65C2×C8×C137—24no—
66C2×C8×C137—42no—
67C4⋊C4×C137—22no—
68C4⋊C4×C137—42no—
69C4⋊C4×C137—41no—
70C4⋊C4×C137—42no—
71C4⋊C4×C137—41no—
72C22⋊C4×C137—24no—
73C22⋊C4×C137—84no—
74C42×C137—41no—
75C42×C137—41no—
76C42×C137C2×D412yes—
77C42×C137#4112yes—
78C23×C137—22no—
79C23×C137—22no—
80C23×C137—22no—
81C23×C137—42no—
82C23×C137—42no—
83C23×C137C2×C22⋊C411yescharacteristic
84Q8×C137—84no—
85D4×C137—42no—
86D4×C137—42no—
87C2×C4×C137—22no—
88C2×C4×C137—22no—
89C2×C4×C137—41no—
90C2×C4×C137—44no—
91C2×C4×C137—42no—
92C2×C4×C137—42no—
93C2×C4×C137—44no—
94C2×C4×C137—42no—
95C2×C4×C137—42no—
96C2×C4×C137—42no—
97C2×C4×C137—82no—
98C2×C4×C137C4×D412yes—
99C2×C4×C137#12011yescharacteristic
100C2×C4×C137#12112yes—
101C2×C4×C137#12311yescharacteristic
102C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
103C2×C4×C137#13712yes—
104C2×C4×C137#13711yescharacteristic
105C8×C137—44no—
106C8×C137—82no—
107C22×C137—21no—
108C22×C137—21no—
109C22×C137—44no—
110C22×C137—42no—
111C22×C137—42no—
112C22×C137—42no—
113C22×C137—82no—
114C22×C137#38611yescharacteristic
115C22×C137#41711yescharacteristic
116C22×C137#41911yescharacteristic
117C4×C137—21no—
118C4×C137—22no—
119C4×C137—42no—
120C4×C137—82no—
121C4×C137—82no—
122C4×C137#45512yes—
123C4×C137#46812yes—
124C4×C137#47012yes—
125C2×C137—21no—
126C2×C137—21no—
127C2×C137—82no—
128C2×C137#188511yescharacteristic
129C2×C137#189411yescharacteristic
130C2×C137#191411yescharacteristic
131#9399C13711yesmaximal, characteristic, direct product factor, Sylow
132C137#939911yescharacteristic, direct product factor, Sylow
133#2975C2×C13711yescharacteristic
134#2563C2×C13711yescharacteristic
135#1800C2×C13711yescharacteristic
136#1548C2×C13712yescomplemented
137#1303C2×C13712yescomplemented
138C2×C4⋊Q8C22×C13711yescharacteristic
139C2×C4×D4C22×C13711yescharacteristic
140#436—24no—
141#431C22×C13712yes—
142#423C22×C13712yes—
143C2×#100—21no—
144#407—22no—
145#393C4×C13714yes—
146#390—21no—
147#382—21no—
148#380—22no—
149C4×C4⋊C4C22×C13711yescharacteristic
150#343—21no—
151#333—24no—
152C22×Q8C2×C4×C13712yes—
153C22×D4D4×C13711yescharacteristic
154C23×C4D4×C13712yes—
155C2×M16—24no—
156C2×M16—22no—
157C4⋊Q8—22no—
158C4⋊Q8—22no—
159C4×D4—22no—
160C4×D4—22no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4D4×C13711yescharacteristic
165C2×C22⋊C4—24no—
166C2×C22⋊C4C2×C4×C13712yes—
167C2×C42—21no—
168C2×C42C23×C13711yescharacteristic
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8D4×C13714yes—
172#100—42no—
173C22⋊C8—24no—
174C22⋊C8—22no—
175C4×C8—22no—
176#95—24no—
177#95C2×C4×C13712yes—
178C24C22⋊C4×C13712yes—
179C2×Q8—24no—
180C2×Q8—82no—
181C2×D4—22no—
182C2×D4—21no—
183C2×D4—22no—
184C2×D4—21no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—44no—
190C22×C4C22⋊C4×C13712yes—
191C22×C4C22×C4×C13711yescharacteristic
192C22×C4C2×D4×C13711yescharacteristic
193C22×C4C2×D4×C13711yescharacteristic
194M16—42no—
195M16—42no—
196M16—84no—
197C2×C8—24no—
198C2×C8—42no—
199C4⋊C4—22no—
200C4⋊C4—42no—
201C4⋊C4—41no—
202C4⋊C4—42no—
203C4⋊C4—41no—
204C22⋊C4—24no—
205C22⋊C4—84no—
206C42—41no—
207C42—41no—
208C42C2×D4×C13712yes—
209C42#41×C13712yes—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23C2×C22⋊C4×C13711yescharacteristic
216Q8—84no—
217D4—42no—
218D4—42no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—44no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—44no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—82no—
230C2×C4C4×D4×C13712yes—
231C2×C4#120×C13711yescharacteristic
232C2×C4#121×C13712yes—
233C2×C4#123×C13711yescharacteristic
234C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
235C2×C4#137×C13712yes—
236C2×C4#137×C13711yescharacteristic
237C8—44no—
238C8—82no—
239C22—21no—
240C22—21no—
241C22—44no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—82no—
246C22#386×C13711yescharacteristic
247C22#417×C13711yescharacteristic
248C22#419×C13711yescharacteristic
249C4—21no—
250C4—22no—
251C4—42no—
252C4—82no—
253C4—82no—
254C4#455×C13712yes—
255C4#468×C13712yes—
256C4#470×C13712yes—
257C2—21no—
258C2—21no—
259C2—82no—
260C2#1885×C13711yescharacteristic
261C2#1894×C13711yescharacteristic
262C2#1914×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. #1548×C137C2semidirect
5. #1303×C137C2semidirect
131. #9399C137direct (N × H)
132. C137#9399direct (N × H)
136. #1548C2×C137semidirect
137. #1303C2×C137semidirect

Maximal subgroups

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

subgroupindex
#2975×C1372
#2563×C1372
#1800×C1372
#1548×C1372
#1303×C1372
#9399137