Finite Group Databasebeta

← C137×#10365 #46859751

Subgroups — C137×#10365 #46859751

Order 35072.

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

normal subgroups only

This group has 400 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#2859×C137C211yesmaximal, characteristic
2#1994×C137C211yesmaximal, characteristic
3#1518×C137C212yesmaximal
4#1286×C137C212yesmaximal
5#1276×C137C211yesmaximal, characteristic
6#533×C137C2211yescharacteristic
7C2×#125×C137—21no—
8#431×C137C2212yes—
9#423×C137C2211yescharacteristic
10#389×C137—24no—
11#384×C137—21no—
12#382×C137C2212yes—
13C43×C137C2211yescharacteristic
14#339×C137—21no—
15#339×C137—21no—
16#328×C137—24no—
17C2×M16×C137—21no—
18C4⋊Q8×C137Q812yes—
19#125×C137—21no—
20#125×C137—42no—
21#125×C137—42no—
22C22⋊Q8×C137—22no—
23C4×Q8×C137—22no—
24#117×C137—21no—
25C2×C4⋊C4×C137—24no—
26C2×C4⋊C4×C137—24no—
27C2×C4⋊C4×C137—22no—
28C2×C42×C137—22no—
29C2×C42×C137D411yescharacteristic
30C2×C42×C137D411yescharacteristic
31C2×C42×C137C2311yescharacteristic
32C4⋊C8×C137—22no—
33C4⋊C8×C137—22no—
34C22⋊C8×C137—22no—
35C4×C8×C137—22no—
36#95×C137—22no—
37#95×C137D414yes—
38C2×Q8×C137—22no—
39C22×C4×C137—21no—
40C22×C4×C137—21no—
41C22×C4×C137—24no—
42C22×C4×C137C2×D412yes—
43C22×C4×C137C2×D411yescharacteristic
44M16×C137—41no—
45M16×C137—41no—
46C2×C8×C137—42no—
47C2×C8×C137—41no—
48C4⋊C4×C137—22no—
49C4⋊C4×C137—22no—
50C4⋊C4×C137—48no—
51C4⋊C4×C137—48no—
52C4⋊C4×C137—42no—
53C4⋊C4×C137—42no—
54C4⋊C4×C137—42no—
55C22⋊C4×C137—41no—
56C42×C137—21no—
57C42×C137—21no—
58C42×C137—44no—
59C42×C137—41no—
60C42×C137SD1612yes—
61C42×C137Q1612yes—
62C42×C137C2×Q811yescharacteristic
63C42×C137#4111yescharacteristic
64C42×C137#4112yes—
65C23×C137#12011yescharacteristic
66Q8×C137—82no—
67C2×C4×C137—24no—
68C2×C4×C137—22no—
69C2×C4×C137—22no—
70C2×C4×C137—42no—
71C2×C4×C137—42no—
72C2×C4×C137—48no—
73C2×C4×C137—42no—
74C2×C4×C137—44no—
75C2×C4×C137C22⋊Q812yes—
76C2×C4×C137C22⋊Q811yescharacteristic
77C2×C4×C137#12412yes—
78C2×C4×C137#12411yescharacteristic
79C2×C4×C137C2×SD1611yescharacteristic
80C2×C4×C137C2×Q1611yescharacteristic
81C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
82C2×C4×C137#13711yescharacteristic
83C8×C137—82no—
84C8×C137—81no—
85C22×C137—22no—
86C22×C137#39311yescharacteristic
87C22×C137#45011yescharacteristic
88C22×C137#45111yescharacteristic
89C4×C137—24no—
90C4×C137—22no—
91C4×C137—22no—
92C4×C137—42no—
93C4×C137—84no—
94C4×C137—82no—
95C4×C137#47511yescharacteristic
96C4×C137#47711yescharacteristic
97C4×C137#48711yescharacteristic
98C4×C137#48911yescharacteristic
99C2×C137—21no—
100C2×C137—21no—
101C2×C137#202411yescharacteristic
102C2×C137#203112yes—
103#10365C13711yesmaximal, characteristic, direct product factor, Sylow
104C137#1036511yescharacteristic, direct product factor, Sylow
105#2859C2×C13711yescharacteristic
106#1994C2×C13711yescharacteristic
107#1518C2×C13712yes—
108#1286C2×C13712yes—
109#1276C2×C13711yescharacteristic
110#533C22×C13711yescharacteristic
111C2×#125—21no—
112#431C22×C13712yes—
113#423C22×C13711yescharacteristic
114#389—24no—
115#384—21no—
116#382C22×C13712yes—
117C43C22×C13711yescharacteristic
118#339—21no—
119#339—21no—
120#328—24no—
121C2×M16—21no—
122C4⋊Q8Q8×C13712yes—
123#125—21no—
124#125—42no—
125#125—42no—
126C22⋊Q8—22no—
127C4×Q8—22no—
128#117—21no—
129C2×C4⋊C4—24no—
130C2×C4⋊C4—24no—
131C2×C4⋊C4—22no—
132C2×C42—22no—
133C2×C42D4×C13711yescharacteristic
134C2×C42D4×C13711yescharacteristic
135C2×C42C23×C13711yescharacteristic
136C4⋊C8—22no—
137C4⋊C8—22no—
138C22⋊C8—22no—
139C4×C8—22no—
140#95—22no—
141#95D4×C13714yes—
142C2×Q8—22no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—24no—
146C22×C4C2×D4×C13712yes—
147C22×C4C2×D4×C13711yescharacteristic
148M16—41no—
149M16—41no—
150C2×C8—42no—
151C2×C8—41no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—48no—
155C4⋊C4—48no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C22⋊C4—41no—
160C42—21no—
161C42—21no—
162C42—44no—
163C42—41no—
164C42SD16×C13712yes—
165C42Q16×C13712yes—
166C42C2×Q8×C13711yescharacteristic
167C42#41×C13711yescharacteristic
168C42#41×C13712yes—
169C23#120×C13711yescharacteristic
170Q8—82no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—48no—
177C2×C4—42no—
178C2×C4—44no—
179C2×C4C22⋊Q8×C13712yes—
180C2×C4C22⋊Q8×C13711yescharacteristic
181C2×C4#124×C13712yes—
182C2×C4#124×C13711yescharacteristic
183C2×C4C2×SD16×C13711yescharacteristic
184C2×C4C2×Q16×C13711yescharacteristic
185C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
186C2×C4#137×C13711yescharacteristic
187C8—82no—
188C8—81no—
189C22—22no—
190C22#393×C13711yescharacteristic
191C22#450×C13711yescharacteristic
192C22#451×C13711yescharacteristic
193C4—24no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—84no—
198C4—82no—
199C4#475×C13711yescharacteristic
200C4#477×C13711yescharacteristic
201C4#487×C13711yescharacteristic
202C4#489×C13711yescharacteristic
203C2—21no—
204C2—21no—
205C2#2024×C13711yescharacteristic
206C2#2031×C13712yes—
subgroupG/H
center, socleC22×C137#393
commutator, Frattini, cosocleC2×C42C23×C137
prime radicalC23×C137#120
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
103. #10365C137direct (N × H)
104. C137#10365direct (N × H)

Maximal subgroups

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

subgroupindex
#2859×C1372
#1994×C1372
#1518×C1372
#1286×C1372
#1276×C1372
#10365137