Finite Group Databasebeta

← C137×#9435 #46858821

Subgroups — C137×#9435 #46858821

Order 35072.

504 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 126 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#3152×C137C211yesmaximal, characteristic
2#2979×C137C211yesmaximal, characteristic
3#1560×C137C211yesmaximal, characteristic
4#1549×C137C212yesmaximal, complemented
5#1299×C137C212yesmaximal, complemented
6C2×#137×C137—22no—
7#532×C137C2211yescharacteristic
8C2×C4⋊Q8×C137C2211yescharacteristic
9#497×C137C414yes—
10#494×C137—21no—
11#492×C137—21no—
12#436×C137—22no—
13C8×D4×C137—22no—
14#431×C137C2212yes—
15#423×C137C2212yes—
16#408×C137—22no—
17C4×M16×C137C2211yescharacteristic
18#333×C137—21no—
19#332×C137—22no—
20#332×C137—22no—
21#331×C137—21no—
22C2×#41×C137D412yes—
23C22×Q8×C137—21no—
24#137×C137—44no—
25#137×C137—44no—
26C2×Q16×C137—24no—
27C2×SD16×C137—24no—
28C2×M16×C137—21no—
29C2×M16×C137—22no—
30C2×M16×C137—22no—
31C22×C8×C137—22no—
32C4⋊Q8×C137—22no—
33C4⋊Q8×C137—21no—
34C4⋊Q8×C137C2×C412yes—
35C4⋊Q8×C137D411yescharacteristic
36#127×C137D411yescharacteristic
37#124×C137C2×C412yes—
38#121×C137—22no—
39C4×D4×C137—22no—
40C2×C4⋊C4×C137—22no—
41C2×C42×C137C2311yescharacteristic
42C4⋊C8×C137—22no—
43C4⋊C8×C137—22no—
44C4⋊C8×C137D412yes—
45C4⋊C8×C137D412yes—
46C22⋊C8×C137—24no—
47C22⋊C8×C137—22no—
48#97×C137C2×C412yes—
49C4×C8×C137—21no—
50C4×C8×C137—22no—
51#41×C137—42no—
52#41×C137—42no—
53C2×Q8×C137—22no—
54C2×Q8×C137—42no—
55C2×Q8×C137—42no—
56C2×Q8×C137—41no—
57C2×Q8×C137C22⋊C412yes—
58C2×D4×C137—22no—
59C2×D4×C137—22no—
60C2×D4×C137C22⋊C412yes—
61C22×C4×C137—22no—
62C22×C4×C137—41no—
63C22×C4×C137C2×D411yescharacteristic
64C22×C4×C137#4112yes—
65Q16×C137—48no—
66SD16×C137—48no—
67M16×C137—22no—
68M16×C137—22no—
69M16×C137—82no—
70M16×C137—82no—
71C2×C8×C137—22no—
72C2×C8×C137—22no—
73C2×C8×C137—22no—
74C2×C8×C137—42no—
75C2×C8×C137—82no—
76C4⋊C4×C137—22no—
77C4⋊C4×C137—24no—
78C4⋊C4×C137—42no—
79C22⋊C4×C137—24no—
80C42×C137C22×C411yescharacteristic
81C42×C137C2×D411yescharacteristic
82C42×C137C2×D412yes—
83C23×C137—22no—
84C23×C137#12311yescharacteristic
85Q8×C137—42no—
86Q8×C137—44no—
87Q8×C137—81no—
88Q8×C137—81no—
89D4×C137—42no—
90D4×C137—42no—
91D4×C137—42no—
92D4×C137—82no—
93C2×C4×C137—21no—
94C2×C4×C137—21no—
95C2×C4×C137—22no—
96C2×C4×C137—22no—
97C2×C4×C137—22no—
98C2×C4×C137—42no—
99C2×C4×C137—42no—
100C2×C4×C137—42no—
101C2×C4×C137—82no—
102C2×C4×C137C2×C22⋊C411yescharacteristic
103C2×C4×C137C4×D412yes—
104C2×C4×C137#12011yescharacteristic
105C2×C4×C137#12112yes—
106C8×C137—24no—
107C8×C137—42no—
108C8×C137—42no—
109C8×C137—82no—
110C22×C137—21no—
111C22×C137—22no—
112C22×C137—42no—
113C22×C137—44no—
114C22×C137#38611yescharacteristic
115C4×C137—21no—
116C4×C137—22no—
117C4×C137—42no—
118C4×C137—82no—
119C4×C137#45311yescharacteristic
120C4×C137#45311yescharacteristic
121C4×C137#47112yes—
122C4×C137#47312yes—
123C2×C137—41no—
124C2×C137—82no—
125C2×C137#188711yescharacteristic
126C2×C137#190812yes—
127#9435C13711yesmaximal, characteristic, direct product factor, Sylow
128C137#943511yescharacteristic, direct product factor, Sylow
129#3152C2×C13711yescharacteristic
130#2979C2×C13711yescharacteristic
131#1560C2×C13711yescharacteristic
132#1549C2×C13712yescomplemented
133#1299C2×C13712yescomplemented
134C2×#137—22no—
135#532C22×C13711yescharacteristic
136C2×C4⋊Q8C22×C13711yescharacteristic
137#497C4×C13714yes—
138#494—21no—
139#492—21no—
140#436—22no—
141C8×D4—22no—
142#431C22×C13712yes—
143#423C22×C13712yes—
144#408—22no—
145C4×M16C22×C13711yescharacteristic
146#333—21no—
147#332—22no—
148#332—22no—
149#331—21no—
150C2×#41D4×C13712yes—
151C22×Q8—21no—
152#137—44no—
153#137—44no—
154C2×Q16—24no—
155C2×SD16—24no—
156C2×M16—21no—
157C2×M16—22no—
158C2×M16—22no—
159C22×C8—22no—
160C4⋊Q8—22no—
161C4⋊Q8—21no—
162C4⋊Q8C2×C4×C13712yes—
163C4⋊Q8D4×C13711yescharacteristic
164#127D4×C13711yescharacteristic
165#124C2×C4×C13712yes—
166#121—22no—
167C4×D4—22no—
168C2×C4⋊C4—22no—
169C2×C42C23×C13711yescharacteristic
170C4⋊C8—22no—
171C4⋊C8—22no—
172C4⋊C8D4×C13712yes—
173C4⋊C8D4×C13712yes—
174C22⋊C8—24no—
175C22⋊C8—22no—
176#97C2×C4×C13712yes—
177C4×C8—21no—
178C4×C8—22no—
179#41—42no—
180#41—42no—
181C2×Q8—22no—
182C2×Q8—42no—
183C2×Q8—42no—
184C2×Q8—41no—
185C2×Q8C22⋊C4×C13712yes—
186C2×D4—22no—
187C2×D4—22no—
188C2×D4C22⋊C4×C13712yes—
189C22×C4—22no—
190C22×C4—41no—
191C22×C4C2×D4×C13711yescharacteristic
192C22×C4#41×C13712yes—
193Q16—48no—
194SD16—48no—
195M16—22no—
196M16—22no—
197M16—82no—
198M16—82no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—22no—
202C2×C8—42no—
203C2×C8—82no—
204C4⋊C4—22no—
205C4⋊C4—24no—
206C4⋊C4—42no—
207C22⋊C4—24no—
208C42C22×C4×C13711yescharacteristic
209C42C2×D4×C13711yescharacteristic
210C42C2×D4×C13712yes—
211C23—22no—
212C23#123×C13711yescharacteristic
213Q8—42no—
214Q8—44no—
215Q8—81no—
216Q8—81no—
217D4—42no—
218D4—42no—
219D4—42no—
220D4—82no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—82no—
230C2×C4C2×C22⋊C4×C13711yescharacteristic
231C2×C4C4×D4×C13712yes—
232C2×C4#120×C13711yescharacteristic
233C2×C4#121×C13712yes—
234C8—24no—
235C8—42no—
236C8—42no—
237C8—82no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—44no—
242C22#386×C13711yescharacteristic
243C4—21no—
244C4—22no—
245C4—42no—
246C4—82no—
247C4#453×C13711yescharacteristic
248C4#453×C13711yescharacteristic
249C4#471×C13712yes—
250C4#473×C13712yes—
251C2—41no—
252C2—82no—
253C2#1887×C13711yescharacteristic
254C2#1908×C13712yes—
subgroupG/H
center, socleC22×C137#386
commutatorC42C22×C4×C137
Frattini, cosocleC2×C42C23×C137
prime radical#532×C137C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1549×C137C2semidirect
5. #1299×C137C2semidirect
127. #9435C137direct (N × H)
128. C137#9435direct (N × H)
132. #1549C2×C137semidirect
133. #1299C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3152×C1372
#2979×C1372
#1560×C1372
#1549×C1372
#1299×C1372
#9435137