Finite Group Databasebeta

← C137×#13594 #46862980

Subgroups — C137×#13594 #46862980

Order 35072.

326 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 90 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#3135×C137C211yesmaximal, characteristic
2#2126×C137C212yesmaximal
3#1412×C137C214yesmaximal, complemented
4#533×C137C411yescharacteristic, complemented
5#532×C137C2211yescharacteristic
6#491×C137C412yescomplemented
7#490×C137C2212yes—
8#489×C137—22no—
9#416×C137—22no—
10#410×C137—22no—
11C2×#97×C137C411yescharacteristic, complemented
12#354×C137—22no—
13#353×C137C2214yes—
14C2×#41×C137D412yes—
15C22×C8×C137—21no—
16C4⋊Q8×C137—21no—
17C4⋊Q8×C137C2×C411yescharacteristic
18#127×C137C2311yescharacteristic
19#125×C137C2×C412yes—
20#124×C137D412yes—
21C22⋊Q8×C137—41no—
22#121×C137—41no—
23C4×Q8×C137—41no—
24C4×D4×C137—41no—
25#117×C137—21no—
26#117×C137—42no—
27C2×C42×C137C2×C411yescharacteristic
28#103×C137—24no—
29#102×C137—24no—
30#99×C137—24no—
31#99×C137—42no—
32#97×C137—21no—
33#97×C137C2×C412yes—
34#41×C137—42no—
35#41×C137—42no—
36C2×Q8×C137—41no—
37C2×Q8×C137C22⋊C412yes—
38C2×D4×C137—22no—
39C2×D4×C137—41no—
40C2×D4×C137C2×D412yes—
41C22×C4×C137—21no—
42C22×C4×C137—22no—
43C22×C4×C137C22⋊C411yescharacteristic
44C2×C8×C137—22no—
45C2×C8×C137—41no—
46C2×C8×C137—41no—
47C4⋊C4×C137—22no—
48C4⋊C4×C137—41no—
49C4⋊C4×C137—42no—
50C4⋊C4×C137—41no—
51C4⋊C4×C137—82no—
52C22⋊C4×C137—42no—
53C22⋊C4×C137—41no—
54C22⋊C4×C137—44no—
55C42×C137—21no—
56C42×C137—41no—
57C42×C137—82no—
58C42×C137C22⋊C411yescharacteristic
59C42×C137C22×C411yescharacteristic
60C23×C137—22no—
61C23×C137#9911yescharacteristic
62Q8×C137—42no—
63Q8×C137—82no—
64D4×C137—42no—
65D4×C137—82no—
66D4×C137—82no—
67C2×C4×C137—21no—
68C2×C4×C137—21no—
69C2×C4×C137—21no—
70C2×C4×C137—21no—
71C2×C4×C137—22no—
72C2×C4×C137—42no—
73C2×C4×C137—42no—
74C2×C4×C137—42no—
75C2×C4×C137—81no—
76C2×C4×C137—84no—
77C2×C4×C137#9911yescharacteristic
78C2×C4×C137C2×C22⋊C411yescharacteristic
79C8×C137—42no—
80C22×C137—21no—
81C22×C137—41no—
82C22×C137—42no—
83C22×C137—82no—
84C22×C137C2×#9911yescharacteristic
85C4×C137—21no—
86C4×C137—41no—
87C4×C137—41no—
88C4×C137—42no—
89C4×C137—82no—
90C4×C137—164no—
91C4×C137#35411yescharacteristic
92C4×C137#35411yescharacteristic
93C2×C137—21no—
94C2×C137—41no—
95C2×C137—82no—
96C2×C137C2×#35411yescharacteristic
97#13594C13711yesmaximal, characteristic, direct product factor, Sylow
98C137#1359411yescharacteristic, direct product factor, Sylow
99#3135C2×C13711yescharacteristic
100#2126C2×C13712yes—
101#1412C2×C13714yescomplemented
102#533C4×C13711yescharacteristic, complemented
103#532C22×C13711yescharacteristic
104#491C4×C13712yescomplemented
105#490C22×C13712yes—
106#489—22no—
107#416—22no—
108#410—22no—
109C2×#97C4×C13711yescharacteristic, complemented
110#354—22no—
111#353C22×C13714yes—
112C2×#41D4×C13712yes—
113C22×C8—21no—
114C4⋊Q8—21no—
115C4⋊Q8C2×C4×C13711yescharacteristic
116#127C23×C13711yescharacteristic
117#125C2×C4×C13712yes—
118#124D4×C13712yes—
119C22⋊Q8—41no—
120#121—41no—
121C4×Q8—41no—
122C4×D4—41no—
123#117—21no—
124#117—42no—
125C2×C42C2×C4×C13711yescharacteristic
126#103—24no—
127#102—24no—
128#99—24no—
129#99—42no—
130#97—21no—
131#97C2×C4×C13712yes—
132#41—42no—
133#41—42no—
134C2×Q8—41no—
135C2×Q8C22⋊C4×C13712yes—
136C2×D4—22no—
137C2×D4—41no—
138C2×D4C2×D4×C13712yes—
139C22×C4—21no—
140C22×C4—22no—
141C22×C4C22⋊C4×C13711yescharacteristic
142C2×C8—22no—
143C2×C8—41no—
144C2×C8—41no—
145C4⋊C4—22no—
146C4⋊C4—41no—
147C4⋊C4—42no—
148C4⋊C4—41no—
149C4⋊C4—82no—
150C22⋊C4—42no—
151C22⋊C4—41no—
152C22⋊C4—44no—
153C42—21no—
154C42—41no—
155C42—82no—
156C42C22⋊C4×C13711yescharacteristic
157C42C22×C4×C13711yescharacteristic
158C23—22no—
159C23#99×C13711yescharacteristic
160Q8—42no—
161Q8—82no—
162D4—42no—
163D4—82no—
164D4—82no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—81no—
174C2×C4—84no—
175C2×C4#99×C13711yescharacteristic
176C2×C4C2×C22⋊C4×C13711yescharacteristic
177C8—42no—
178C22—21no—
179C22—41no—
180C22—42no—
181C22—82no—
182C22C2×#99×C13711yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—42no—
187C4—82no—
188C4—164no—
189C4#354×C13711yescharacteristic
190C4#354×C13711yescharacteristic
191C2—21no—
192C2—41no—
193C2—82no—
194C2C2×#354×C13711yescharacteristic
subgroupG/H
centerC4×C137#354
commutatorC42C22×C4×C137
Frattini, cosocle#127C23×C137
socleC2×C137C2×#354
prime radical#532×C137C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C137 ◁ C2×C4×C137 ◁ C22×C4×C137 ◁ #532×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1412×C137C2semidirect
4. #533×C137C4semidirect
6. #491×C137C4semidirect
11. C2×#97×C137C4semidirect
97. #13594C137direct (N × H)
98. C137#13594direct (N × H)
101. #1412C2×C137semidirect
102. #533C4×C137semidirect
104. #491C4×C137semidirect
109. C2×#97C4×C137semidirect

Maximal subgroups

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

subgroupindex
#3135×C1372
#2126×C1372
#1412×C1372
#13594137