Finite Group Databasebeta

← C137×#9153 #46858539

Subgroups — C137×#9153 #46858539

Order 35072.

586 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 150 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#2855×C137C211yesmaximal, characteristic
2C2×#383×C137C211yesmaximal, characteristic
3#1817×C137C211yesmaximal, characteristic
4C2×#328×C137C212yesmaximal
5#1294×C137C212yesmaximal
6C2×C22⋊Q8×C137C2211yescharacteristic
7C22×C42×C137C2211yescharacteristic
8C2×C22⋊C8×C137C2212yes—
9#391×C137C412yescomplemented
10#389×C137C412yescomplemented
11#387×C137—22no—
12#385×C137—21no—
13#383×C137—24no—
14#381×C137—21no—
15#380×C137C2211yescharacteristic
16C2×#95×C137—21no—
17C2×#95×C137—21no—
18C2×#95×C137C2212yes—
19#336×C137—22no—
20#328×C137—24no—
21C22×Q8×C137C2×C411yescharacteristic
22C23×C4×C137—22no—
23C23×C4×C137D411yescharacteristic
24C23×C4×C137D411yescharacteristic
25C23×C4×C137C2311yescharacteristic
26C22×C8×C137—22no—
27C22⋊Q8×C137—22no—
28C22⋊Q8×C137—22no—
29C2×C4⋊C4×C137—22no—
30C2×C4⋊C4×C137—21no—
31C2×C4⋊C4×C137C2×C411yescharacteristic
32C2×C4⋊C4×C137C2×C412yes—
33C2×C22⋊C4×C137—21no—
34C2×C22⋊C4×C137—21no—
35C2×C42×C137—22no—
36C2×C42×C137—22no—
37C2×C42×C137C2×C412yes—
38C2×C42×C137D412yes—
39C22⋊C8×C137—22no—
40C22⋊C8×C137—22no—
41#95×C137—24no—
42#95×C137—24no—
43#95×C137—22no—
44#95×C137—22no—
45#95×C137—22no—
46#95×C137—22no—
47#95×C137—21no—
48#95×C137D414yes—
49C24×C137C2×D411yescharacteristic
50C2×Q8×C137—22no—
51C2×Q8×C137—42no—
52C22×C4×C137—21no—
53C22×C4×C137—21no—
54C22×C4×C137—21no—
55C22×C4×C137—21no—
56C22×C4×C137—22no—
57C22×C4×C137—22no—
58C22×C4×C137—22no—
59C22×C4×C137—21no—
60C22×C4×C137—21no—
61C22×C4×C137—24no—
62C22×C4×C137—42no—
63C22×C4×C137—42no—
64C22×C4×C137—44no—
65C22×C4×C137—44no—
66C22×C4×C137—42no—
67C22×C4×C137—42no—
68C22×C4×C137C22⋊C412yes—
69C22×C4×C137C22⋊C412yes—
70C22×C4×C137C22×C411yescharacteristic
71C22×C4×C137C2×D411yescharacteristic
72C22×C4×C137C2×D412yes—
73C22×C4×C137#4112yes—
74C2×C8×C137—44no—
75C2×C8×C137—42no—
76C4⋊C4×C137—22no—
77C4⋊C4×C137—42no—
78C4⋊C4×C137—44no—
79C4⋊C4×C137—42no—
80C22⋊C4×C137—41no—
81C22⋊C4×C137—41no—
82C22⋊C4×C137—42no—
83C42×C137—24no—
84C42×C137—24no—
85C23×C137—22no—
86C23×C137—22no—
87C23×C137C2×C22⋊C411yescharacteristic
88C23×C137#12011yescharacteristic
89C23×C137#12311yescharacteristic
90C23×C137#13512yes—
91C23×C137#13712yes—
92Q8×C137—82no—
93C2×C4×C137—22no—
94C2×C4×C137—22no—
95C2×C4×C137—22no—
96C2×C4×C137—22no—
97C2×C4×C137—22no—
98C2×C4×C137—22no—
99C2×C4×C137—22no—
100C2×C4×C137—22no—
101C2×C4×C137—42no—
102C2×C4×C137—42no—
103C2×C4×C137—42no—
104C2×C4×C137—42no—
105C2×C4×C137—42no—
106C2×C4×C137—42no—
107C2×C4×C137—44no—
108C2×C4×C137—44no—
109C2×C4×C137—41no—
110C2×C4×C137—41no—
111C2×C4×C137—42no—
112C2×C4×C137—42no—
113C2×C4×C137—42no—
114C2×C4×C137—42no—
115C2×C4×C137—42no—
116C2×C4×C137—44no—
117C2×C4×C137—84no—
118C2×C4×C137—84no—
119C2×C4×C137C4×D412yes—
120C2×C4×C137#12112yes—
121C8×C137—82no—
122C22×C137—21no—
123C22×C137—21no—
124C22×C137—21no—
125C22×C137—21no—
126C22×C137—24no—
127C22×C137—24no—
128C22×C137#38611yescharacteristic
129C22×C137#41012yes—
130C22×C137#41611yescharacteristic
131C22×C137#41911yescharacteristic
132C22×C137#42112yes—
133C22×C137#45212yes—
134C22×C137#48512yes—
135C4×C137—22no—
136C4×C137—22no—
137C4×C137—42no—
138C4×C137—42no—
139C4×C137—84no—
140C4×C137—81no—
141C4×C137—81no—
142C4×C137—82no—
143C2×C137—22no—
144C2×C137—22no—
145C2×C137#151512yes—
146C2×C137#152112yes—
147C2×C137#187311yescharacteristic
148C2×C137#189711yescharacteristic
149C2×C137#189911yescharacteristic
150#9153C13711yesmaximal, characteristic, direct product factor, Sylow
151C137#915311yescharacteristic, direct product factor, Sylow
152#2855C2×C13711yescharacteristic
153C2×#383C2×C13711yescharacteristic
154#1817C2×C13711yescharacteristic
155C2×#328C2×C13712yes—
156#1294C2×C13712yes—
157C2×C22⋊Q8C22×C13711yescharacteristic
158C22×C42C22×C13711yescharacteristic
159C2×C22⋊C8C22×C13712yes—
160#391C4×C13712yescomplemented
161#389C4×C13712yescomplemented
162#387—22no—
163#385—21no—
164#383—24no—
165#381—21no—
166#380C22×C13711yescharacteristic
167C2×#95—21no—
168C2×#95—21no—
169C2×#95C22×C13712yes—
170#336—22no—
171#328—24no—
172C22×Q8C2×C4×C13711yescharacteristic
173C23×C4—22no—
174C23×C4D4×C13711yescharacteristic
175C23×C4D4×C13711yescharacteristic
176C23×C4C23×C13711yescharacteristic
177C22×C8—22no—
178C22⋊Q8—22no—
179C22⋊Q8—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4C2×C4×C13711yescharacteristic
183C2×C4⋊C4C2×C4×C13712yes—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—21no—
186C2×C42—22no—
187C2×C42—22no—
188C2×C42C2×C4×C13712yes—
189C2×C42D4×C13712yes—
190C22⋊C8—22no—
191C22⋊C8—22no—
192#95—24no—
193#95—24no—
194#95—22no—
195#95—22no—
196#95—22no—
197#95—22no—
198#95—21no—
199#95D4×C13714yes—
200C24C2×D4×C13711yescharacteristic
201C2×Q8—22no—
202C2×Q8—42no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—24no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—44no—
216C22×C4—44no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4C22⋊C4×C13712yes—
220C22×C4C22⋊C4×C13712yes—
221C22×C4C22×C4×C13711yescharacteristic
222C22×C4C2×D4×C13711yescharacteristic
223C22×C4C2×D4×C13712yes—
224C22×C4#41×C13712yes—
225C2×C8—44no—
226C2×C8—42no—
227C4⋊C4—22no—
228C4⋊C4—42no—
229C4⋊C4—44no—
230C4⋊C4—42no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—42no—
234C42—24no—
235C42—24no—
236C23—22no—
237C23—22no—
238C23C2×C22⋊C4×C13711yescharacteristic
239C23#120×C13711yescharacteristic
240C23#123×C13711yescharacteristic
241C23#135×C13712yes—
242C23#137×C13712yes—
243Q8—82no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—44no—
268C2×C4—84no—
269C2×C4—84no—
270C2×C4C4×D4×C13712yes—
271C2×C4#121×C13712yes—
272C8—82no—
273C22—24no—
274C22—24no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22#386×C13711yescharacteristic
280C22#410×C13712yes—
281C22#416×C13711yescharacteristic
282C22#419×C13711yescharacteristic
283C22#421×C13712yes—
284C22#452×C13712yes—
285C22#485×C13712yes—
286C4—22no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—84no—
291C4—82no—
292C4—81no—
293C4—81no—
294C2—22no—
295C2—22no—
296C2#1515×C13712yes—
297C2#1521×C13712yes—
298C2#1873×C13711yescharacteristic
299C2#1897×C13711yescharacteristic
300C2#1899×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C2×C22⋊C4
commutatorC22×C4C22×C4×C137
Frattini, cosocleC23×C4C23×C137
prime radicalC24×C137C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C137 ◁ C22×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
9. #391×C137C4semidirect
10. #389×C137C4semidirect
150. #9153C137direct (N × H)
151. C137#9153direct (N × H)
160. #391C4×C137semidirect
161. #389C4×C137semidirect

Maximal subgroups

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

subgroupindex
#2855×C1372
C2×#383×C1372
#1817×C1372
C2×#328×C1372
#1294×C1372
#9153137