Finite Group Databasebeta

← C137×#10439 #46859825

Subgroups — C137×#10439 #46859825

Order 35072.

478 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 146 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#2582×C137C211yesmaximal, characteristic
2#1845×C137C211yesmaximal, characteristic
3#1803×C137C212yesmaximal
4C2×Q8⋊C8×C137C212yesmaximal
5#1296×C137C211yesmaximal, characteristic
6C2×C4×Q8×C137C2212yes—
7C2×#107×C137—22no—
8C2×C4⋊C8×C137C2212yes—
9C2×#103×C137—22no—
10C2×C4×C8×C137C2211yescharacteristic
11#398×C137—22no—
12#391×C137—22no—
13#389×C137—22no—
14#384×C137C2211yescharacteristic
15#384×C137C2211yescharacteristic
16#340×C137—22no—
17Q8⋊C8×C137—24no—
18C22×Q8×C137D412yes—
19C22×C8×C137—21no—
20C22×C8×C137—22no—
21C4×Q8×C137—22no—
22C4×Q8×C137—22no—
23C4×Q8×C137—22no—
24C4×Q8×C137—22no—
25C2×C4⋊C4×C137—22no—
26C2×C4⋊C4×C137—22no—
27C2×C4⋊C4×C137—22no—
28C2×C4⋊C4×C137—21no—
29C2×C4⋊C4×C137—22no—
30C2×C4⋊C4×C137D412yes—
31C2×C4⋊C4×C137D412yes—
32C2×C42×C137—22no—
33C2×C42×C137C2311yescharacteristic
34#107×C137—44no—
35C4⋊C8×C137—22no—
36C4⋊C8×C137—22no—
37#103×C137—44no—
38C4×C8×C137—21no—
39C4×C8×C137D412yes—
40#95×C137—24no—
41#95×C137—22no—
42C2×Q8×C137—22no—
43C2×Q8×C137—22no—
44C2×Q8×C137—22no—
45C2×Q8×C137—22no—
46C2×Q8×C137—22no—
47C2×Q8×C137Q1614yes—
48C22×C4×C137—22no—
49C22×C4×C137—22no—
50C22×C4×C137—22no—
51C22×C4×C137—41no—
52C22×C4×C137C2×D411yescharacteristic
53C22×C4×C137C2×D412yes—
54C2×C8×C137—22no—
55C2×C8×C137—22no—
56C2×C8×C137—22no—
57C2×C8×C137—42no—
58C2×C8×C137—42no—
59C2×C8×C137—42no—
60C4⋊C4×C137—22no—
61C4⋊C4×C137—22no—
62C4⋊C4×C137—42no—
63C4⋊C4×C137—42no—
64C4⋊C4×C137—42no—
65C4⋊C4×C137—42no—
66C4⋊C4×C137—42no—
67C4⋊C4×C137—42no—
68C4⋊C4×C137—42no—
69C4⋊C4×C137—42no—
70C4⋊C4×C137—82no—
71C42×C137—42no—
72C42×C137—42no—
73C42×C137C2×D411yescharacteristic
74C42×C137#4111yescharacteristic
75C42×C137#4112yes—
76C23×C137#12011yescharacteristic
77Q8×C137—24no—
78Q8×C137—24no—
79Q8×C137—42no—
80Q8×C137—42no—
81C2×C4×C137—21no—
82C2×C4×C137—21no—
83C2×C4×C137—24no—
84C2×C4×C137—42no—
85C2×C4×C137—42no—
86C2×C4×C137—42no—
87C2×C4×C137—44no—
88C2×C4×C137—42no—
89C2×C4×C137—42no—
90C2×C4×C137—42no—
91C2×C4×C137—82no—
92C2×C4×C137—81no—
93C2×C4×C137#12111yescharacteristic
94C2×C4×C137#12112yes—
95C2×C4×C137#12312yes—
96C2×C4×C137#12411yescharacteristic
97C2×C4×C137C2×Q1612yes—
98C2×C4×C137#13512yes—
99C2×C4×C137AGL(1,ℤ/8)12yes—
100C2×C4×C137#13712yes—
101C8×C137—24no—
102C8×C137—82no—
103C22×C137#39411yescharacteristic
104C22×C137#44912yes—
105C22×C137#45112yes—
106C22×C137#45311yescharacteristic
107C22×C137#45611yescharacteristic
108C4×C137—21no—
109C4×C137—21no—
110C4×C137—44no—
111C4×C137—82no—
112C4×C137—82no—
113C4×C137—161no—
114C4×C137#46712yes—
115C4×C137#46812yes—
116C4×C137#48412yes—
117C4×C137#48512yes—
118C2×C137#162011yescharacteristic
119C2×C137#163311yescharacteristic
120C2×C137#164812yes—
121C2×C137#203612yes—
122C2×C137#203911yescharacteristic
123#10439C13711yesmaximal, characteristic, direct product factor, Sylow
124C137#1043911yescharacteristic, direct product factor, Sylow
125#2582C2×C13711yescharacteristic
126#1845C2×C13711yescharacteristic
127#1803C2×C13712yes—
128C2×Q8⋊C8C2×C13712yes—
129#1296C2×C13711yescharacteristic
130C2×C4×Q8C22×C13712yes—
131C2×#107—22no—
132C2×C4⋊C8C22×C13712yes—
133C2×#103—22no—
134C2×C4×C8C22×C13711yescharacteristic
135#398—22no—
136#391—22no—
137#389—22no—
138#384C22×C13711yescharacteristic
139#384C22×C13711yescharacteristic
140#340—22no—
141Q8⋊C8—24no—
142C22×Q8D4×C13712yes—
143C22×C8—21no—
144C22×C8—22no—
145C4×Q8—22no—
146C4×Q8—22no—
147C4×Q8—22no—
148C4×Q8—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4D4×C13712yes—
155C2×C4⋊C4D4×C13712yes—
156C2×C42—22no—
157C2×C42C23×C13711yescharacteristic
158#107—44no—
159C4⋊C8—22no—
160C4⋊C8—22no—
161#103—44no—
162C4×C8—21no—
163C4×C8D4×C13712yes—
164#95—24no—
165#95—22no—
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—22no—
170C2×Q8—22no—
171C2×Q8Q16×C13714yes—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—41no—
176C22×C4C2×D4×C13711yescharacteristic
177C22×C4C2×D4×C13712yes—
178C2×C8—22no—
179C2×C8—22no—
180C2×C8—22no—
181C2×C8—42no—
182C2×C8—42no—
183C2×C8—42no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—82no—
195C42—42no—
196C42—42no—
197C42C2×D4×C13711yescharacteristic
198C42#41×C13711yescharacteristic
199C42#41×C13712yes—
200C23#120×C13711yescharacteristic
201Q8—24no—
202Q8—24no—
203Q8—42no—
204Q8—42no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—24no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—44no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—82no—
216C2×C4—81no—
217C2×C4#121×C13711yescharacteristic
218C2×C4#121×C13712yes—
219C2×C4#123×C13712yes—
220C2×C4#124×C13711yescharacteristic
221C2×C4C2×Q16×C13712yes—
222C2×C4#135×C13712yes—
223C2×C4AGL(1,ℤ/8)×C13712yes—
224C2×C4#137×C13712yes—
225C8—24no—
226C8—82no—
227C22#394×C13711yescharacteristic
228C22#449×C13712yes—
229C22#451×C13712yes—
230C22#453×C13711yescharacteristic
231C22#456×C13711yescharacteristic
232C4—21no—
233C4—21no—
234C4—44no—
235C4—82no—
236C4—82no—
237C4—161no—
238C4#467×C13712yes—
239C4#468×C13712yes—
240C4#484×C13712yes—
241C4#485×C13712yes—
242C2#1620×C13711yescharacteristic
243C2#1633×C13711yescharacteristic
244C2#1648×C13712yes—
245C2#2036×C13712yes—
246C2#2039×C13711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C137#120
commutator, Frattini, cosocleC2×C42C23×C137
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
123. #10439C137direct (N × H)
124. C137#10439direct (N × H)

Maximal subgroups

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

subgroupindex
#2582×C1372
#1845×C1372
#1803×C1372
C2×Q8⋊C8×C1372
#1296×C1372
#10439137