Finite Group Databasebeta

← C137×#10585 #46859971

Subgroups — C137×#10585 #46859971

Order 35072.

382 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 114 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#2845×C137C211yesmaximal, characteristic
2#1847×C137C212yesmaximal
3#1836×C137C211yesmaximal, characteristic
4#1295×C137C211yesmaximal, characteristic
5#1295×C137C212yesmaximal
6C2×#107×C137—22no—
7C2×#106×C137—22no—
8C2×#97×C137C2211yescharacteristic
9C2×#97×C137C2212yes—
10#398×C137—22no—
11#398×C137—22no—
12#398×C137—22no—
13#384×C137C2211yescharacteristic
14#382×C137C2211yescharacteristic
15#382×C137C2212yes—
16#340×C137—22no—
17C22×C8×C137—22no—
18C22×C8×C137—21no—
19C2×C4⋊C4×C137—22no—
20C2×C4⋊C4×C137—21no—
21C2×C4⋊C4×C137—22no—
22C2×C4⋊C4×C137—22no—
23C2×C4⋊C4×C137—22no—
24C2×C4⋊C4×C137D412yes—
25C2×C4⋊C4×C137D412yes—
26C2×C4⋊C4×C137D412yes—
27C2×C42×C137C2311yescharacteristic
28#107×C137—44no—
29#106×C137—44no—
30#97×C137—22no—
31#97×C137—21no—
32#97×C137Q814yes—
33#97×C137Q812yes—
34#95×C137—22no—
35#95×C137—22no—
36#95×C137—22no—
37#95×C137—22no—
38C22×C4×C137—22no—
39C22×C4×C137—22no—
40C22×C4×C137—22no—
41C22×C4×C137—41no—
42C22×C4×C137C2×D412yes—
43C22×C4×C137C2×D411yescharacteristic
44C2×C8×C137—24no—
45C2×C8×C137—24no—
46C2×C8×C137—24no—
47C2×C8×C137—22no—
48C2×C8×C137—41no—
49C2×C8×C137—41no—
50C4⋊C4×C137—42no—
51C4⋊C4×C137—42no—
52C4⋊C4×C137—42no—
53C4⋊C4×C137—42no—
54C4⋊C4×C137—42no—
55C4⋊C4×C137—42no—
56C4⋊C4×C137—82no—
57C4⋊C4×C137—82no—
58C4⋊C4×C137—82no—
59C42×C137C2×Q812yes—
60C42×C137C2×Q811yescharacteristic
61C42×C137#4111yescharacteristic
62C23×C137#12011yescharacteristic
63C2×C4×C137—22no—
64C2×C4×C137—21no—
65C2×C4×C137—21no—
66C2×C4×C137—22no—
67C2×C4×C137—42no—
68C2×C4×C137—42no—
69C2×C4×C137—42no—
70C2×C4×C137—42no—
71C2×C4×C137—42no—
72C2×C4×C137—42no—
73C2×C4×C137—42no—
74C2×C4×C137—42no—
75C2×C4×C137—42no—
76C2×C4×C137—82no—
77C2×C4×C137—81no—
78C2×C4×C137C22⋊Q812yes—
79C2×C4×C137C22⋊Q811yescharacteristic
80C2×C4×C137C4⋊Q812yes—
81C2×C4×C137C4⋊Q811yescharacteristic
82C8×C137—28no—
83C8×C137—42no—
84C22×C137#39511yescharacteristic
85C22×C137#45312yes—
86C22×C137#45411yescharacteristic
87C22×C137#45511yescharacteristic
88C22×C137#45612yes—
89C4×C137—22no—
90C4×C137—22no—
91C4×C137—21no—
92C4×C137—21no—
93C4×C137—82no—
94C4×C137—82no—
95C4×C137—82no—
96C4×C137—161no—
97C2×C137#165611yescharacteristic
98C2×C137#166112yes—
99C2×C137#166311yescharacteristic
100C2×C137#206012yes—
101C2×C137#206111yescharacteristic
102#10585C13711yesmaximal, characteristic, direct product factor, Sylow
103C137#1058511yescharacteristic, direct product factor, Sylow
104#2845C2×C13711yescharacteristic
105#1847C2×C13712yes—
106#1836C2×C13711yescharacteristic
107#1295C2×C13711yescharacteristic
108#1295C2×C13712yes—
109C2×#107—22no—
110C2×#106—22no—
111C2×#97C22×C13711yescharacteristic
112C2×#97C22×C13712yes—
113#398—22no—
114#398—22no—
115#398—22no—
116#384C22×C13711yescharacteristic
117#382C22×C13711yescharacteristic
118#382C22×C13712yes—
119#340—22no—
120C22×C8—22no—
121C22×C8—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4D4×C13712yes—
128C2×C4⋊C4D4×C13712yes—
129C2×C4⋊C4D4×C13712yes—
130C2×C42C23×C13711yescharacteristic
131#107—44no—
132#106—44no—
133#97—22no—
134#97—21no—
135#97Q8×C13714yes—
136#97Q8×C13712yes—
137#95—22no—
138#95—22no—
139#95—22no—
140#95—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—41no—
145C22×C4C2×D4×C13712yes—
146C22×C4C2×D4×C13711yescharacteristic
147C2×C8—24no—
148C2×C8—24no—
149C2×C8—24no—
150C2×C8—22no—
151C2×C8—41no—
152C2×C8—41no—
153C4⋊C4—42no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C4⋊C4—82no—
160C4⋊C4—82no—
161C4⋊C4—82no—
162C42C2×Q8×C13712yes—
163C42C2×Q8×C13711yescharacteristic
164C42#41×C13711yescharacteristic
165C23#120×C13711yescharacteristic
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—82no—
180C2×C4—81no—
181C2×C4C22⋊Q8×C13712yes—
182C2×C4C22⋊Q8×C13711yescharacteristic
183C2×C4C4⋊Q8×C13712yes—
184C2×C4C4⋊Q8×C13711yescharacteristic
185C8—28no—
186C8—42no—
187C22#395×C13711yescharacteristic
188C22#453×C13712yes—
189C22#454×C13711yescharacteristic
190C22#455×C13711yescharacteristic
191C22#456×C13712yes—
192C4—22no—
193C4—22no—
194C4—21no—
195C4—21no—
196C4—82no—
197C4—82no—
198C4—82no—
199C4—161no—
200C2#1656×C13711yescharacteristic
201C2#1661×C13712yes—
202C2#1663×C13711yescharacteristic
203C2#2060×C13712yes—
204C2#2061×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
102. #10585C137direct (N × H)
103. C137#10585direct (N × H)

Maximal subgroups

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

subgroupindex
#2845×C1372
#1847×C1372
#1836×C1372
#1295×C1372
#10585137