Finite Group Databasebeta

← C137×#11506 #46860892

Subgroups — C137×#11506 #46860892

Order 35072.

598 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C2×#391×C137C211yesmaximal, characteristic
2#1463×C137C212yesmaximal
3#1319×C137C214yesmaximal, complemented
4C23×Q8×C137C411yescharacteristic
5C22×C4⋊C4×C137C2211yescharacteristic
6C22×C42×C137C411yescharacteristic
7#407×C137—22no—
8#391×C137—22no—
9#391×C137C412yes—
10#391×C137C2212yes—
11C2×#95×C137—22no—
12#324×C137—22no—
13#324×C137C2214yes—
14C22×Q8×C137—24no—
15C22×Q8×C137—21no—
16C22×Q8×C137—42no—
17C22×Q8×C137—41no—
18C22×Q8×C137—41no—
19C22×Q8×C137C2×C412yes—
20C23×C4×C137—21no—
21C23×C4×C137—21no—
22C23×C4×C137C2×C411yescharacteristic
23C23×C4×C137D412yes—
24C2×M16×C137—42no—
25C2×C4⋊C4×C137—41no—
26C2×C4⋊C4×C137—41no—
27C2×C4⋊C4×C137C2×C411yescharacteristic
28C2×C4⋊C4×C137D412yes—
29C2×C4⋊C4×C137C2311yescharacteristic
30C2×C42×C137—21no—
31C2×C42×C137—42no—
32C2×C42×C137C2×C412yes—
33C22⋊C8×C137—24no—
34C22⋊C8×C137—42no—
35#95×C137—24no—
36#95×C137—24no—
37C24×C137C22⋊C411yescharacteristic
38C2×Q8×C137—24no—
39C2×Q8×C137—22no—
40C2×Q8×C137—48no—
41C2×Q8×C137—48no—
42C2×Q8×C137—42no—
43C2×Q8×C137—42no—
44C2×Q8×C137—42no—
45C2×Q8×C137—42no—
46C2×Q8×C137M1614yescomplemented
47C22×C4×C137—21no—
48C22×C4×C137—21no—
49C22×C4×C137—22no—
50C22×C4×C137—22no—
51C22×C4×C137—24no—
52C22×C4×C137—24no—
53C22×C4×C137—22no—
54C22×C4×C137—22no—
55C22×C4×C137—22no—
56C22×C4×C137—22no—
57C22×C4×C137—42no—
58C22×C4×C137—42no—
59C22×C4×C137—42no—
60C22×C4×C137—41no—
61C22×C4×C137—41no—
62C22×C4×C137—44no—
63C22×C4×C137C22⋊C411yescharacteristic
64C22×C4×C137C22⋊C412yes—
65C22×C4×C137C22×C411yescharacteristic
66C22×C4×C137C2×D412yes—
67M16×C137—84no—
68C2×C8×C137—44no—
69C4⋊C4×C137—41no—
70C4⋊C4×C137—42no—
71C4⋊C4×C137—41no—
72C42×C137—42no—
73C42×C137—42no—
74C23×C137—22no—
75C23×C137—22no—
76C23×C137—21no—
77C23×C137—21no—
78C23×C137#9911yescharacteristic
79C23×C137#9911yescharacteristic
80C23×C137C2×C22⋊C411yescharacteristic
81Q8×C137—44no—
82Q8×C137—48no—
83Q8×C137—44no—
84C2×C4×C137—24no—
85C2×C4×C137—24no—
86C2×C4×C137—21no—
87C2×C4×C137—21no—
88C2×C4×C137—21no—
89C2×C4×C137—21no—
90C2×C4×C137—24no—
91C2×C4×C137—24no—
92C2×C4×C137—22no—
93C2×C4×C137—22no—
94C2×C4×C137—48no—
95C2×C4×C137—42no—
96C2×C4×C137—44no—
97C2×C4×C137—44no—
98C2×C4×C137—44no—
99C2×C4×C137—42no—
100C2×C4×C137—42no—
101C2×C4×C137—42no—
102C2×C4×C137—42no—
103C2×C4×C137—42no—
104C2×C4×C137—82no—
105C2×C4×C137#10012yes—
106C2×C4×C137C2×M1612yes—
107C8×C137—84no—
108C22×C137—24no—
109C22×C137—24no—
110C22×C137—21no—
111C22×C137—21no—
112C22×C137—21no—
113C22×C137—21no—
114C22×C137—21no—
115C22×C137—21no—
116C22×C137#35412yes—
117C22×C137#35612yes—
118C22×C137#40711yescharacteristic
119C22×C137C2×#9911yescharacteristic
120C22×C137C2×#10011yescharacteristic
121C4×C137—22no—
122C4×C137—22no—
123C4×C137—44no—
124C4×C137—42no—
125C4×C137—42no—
126C4×C137—44no—
127C2×C137—21no—
128C2×C137—22no—
129C2×C137—22no—
130C2×C137—21no—
131C2×C137#146211yescharacteristic
132C2×C137C2×#35411yescharacteristic
133C2×C137C2×#35611yescharacteristic
134#11506C13711yesmaximal, characteristic, direct product factor, Sylow
135C137#1150611yescharacteristic, direct product factor, Sylow
136C2×#391C2×C13711yescharacteristic
137#1463C2×C13712yes—
138#1319C2×C13714yescomplemented
139C23×Q8C4×C13711yescharacteristic
140C22×C4⋊C4C22×C13711yescharacteristic
141C22×C42C4×C13711yescharacteristic
142#407—22no—
143#391—22no—
144#391C4×C13712yes—
145#391C22×C13712yes—
146C2×#95—22no—
147#324—22no—
148#324C22×C13714yes—
149C22×Q8—24no—
150C22×Q8—21no—
151C22×Q8—42no—
152C22×Q8—41no—
153C22×Q8—41no—
154C22×Q8C2×C4×C13712yes—
155C23×C4—21no—
156C23×C4—21no—
157C23×C4C2×C4×C13711yescharacteristic
158C23×C4D4×C13712yes—
159C2×M16—42no—
160C2×C4⋊C4—41no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4C2×C4×C13711yescharacteristic
163C2×C4⋊C4D4×C13712yes—
164C2×C4⋊C4C23×C13711yescharacteristic
165C2×C42—21no—
166C2×C42—42no—
167C2×C42C2×C4×C13712yes—
168C22⋊C8—24no—
169C22⋊C8—42no—
170#95—24no—
171#95—24no—
172C24C22⋊C4×C13711yescharacteristic
173C2×Q8—24no—
174C2×Q8—22no—
175C2×Q8—48no—
176C2×Q8—48no—
177C2×Q8—42no—
178C2×Q8—42no—
179C2×Q8—42no—
180C2×Q8—42no—
181C2×Q8M16×C13714yescomplemented
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—24no—
187C22×C4—24no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—42no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—44no—
198C22×C4C22⋊C4×C13711yescharacteristic
199C22×C4C22⋊C4×C13712yes—
200C22×C4C22×C4×C13711yescharacteristic
201C22×C4C2×D4×C13712yes—
202M16—84no—
203C2×C8—44no—
204C4⋊C4—41no—
205C4⋊C4—42no—
206C4⋊C4—41no—
207C42—42no—
208C42—42no—
209C23—21no—
210C23—21no—
211C23—22no—
212C23—22no—
213C23#99×C13711yescharacteristic
214C23#99×C13711yescharacteristic
215C23C2×C22⋊C4×C13711yescharacteristic
216Q8—44no—
217Q8—48no—
218Q8—44no—
219C2×C4—24no—
220C2×C4—24no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—24no—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—44no—
230C2×C4—44no—
231C2×C4—48no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—44no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—82no—
240C2×C4#100×C13712yes—
241C2×C4C2×M16×C13712yes—
242C8—84no—
243C22—24no—
244C22—24no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22#354×C13712yes—
252C22#356×C13712yes—
253C22#407×C13711yescharacteristic
254C22C2×#99×C13711yescharacteristic
255C22C2×#100×C13711yescharacteristic
256C4—22no—
257C4—22no—
258C4—44no—
259C4—42no—
260C4—42no—
261C4—44no—
262C2—21no—
263C2—21no—
264C2—22no—
265C2—22no—
266C2#1462×C13711yescharacteristic
267C2C2×#354×C13711yescharacteristic
268C2C2×#356×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#99
commutatorC22×C4C22×C4×C137
Frattini, cosocleC2×C4⋊C4C23×C137
prime radicalC24×C137C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C24×C137 ◁ C22×C4⋊C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1319×C137C2semidirect
46. C2×Q8×C137M16semidirect
134. #11506C137direct (N × H)
135. C137#11506direct (N × H)
138. #1319C2×C137semidirect
181. C2×Q8M16×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#391×C1372
#1463×C1372
#1319×C1372
#11506137