Finite Group Databasebeta

← C137×#7831 #46857217

Subgroups — C137×#7831 #46857217

Order 35072.

350 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 98 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#2809×C137C211yesmaximal, characteristic
2#2100×C137C212yesmaximal
3#2095×C137C211yesmaximal, characteristic
4#1272×C137C211yesmaximal, characteristic
5#1271×C137C212yesmaximal
6C2×#107×C137—21no—
7C2×#103×C137—21no—
8#400×C137—21no—
9#398×C137—22no—
10#391×C137—21no—
11#391×C137C2211yescharacteristic
12#389×C137C2212yes—
13#387×C137—22no—
14#384×C137C2211yescharacteristic
15#340×C137—22no—
16#340×C137—22no—
17#336×C137C2211yescharacteristic
18#336×C137C2212yes—
19C22×Q8×C137D411yescharacteristic
20C22×C8×C137—21no—
21C22×C8×C137—22no—
22C2×C4⋊C4×C137—22no—
23C2×C4⋊C4×C137—21no—
24C2×C4⋊C4×C137—22no—
25C2×C4⋊C4×C137—21no—
26C2×C4⋊C4×C137—21no—
27C2×C4⋊C4×C137D412yes—
28C2×C4⋊C4×C137D412yes—
29C2×C4⋊C4×C137D411yescharacteristic
30C2×C42×C137—21no—
31C2×C42×C137C2311yescharacteristic
32#107×C137—42no—
33#103×C137—42no—
34#95×C137—21no—
35#95×C137—22no—
36#95×C137—22no—
37#95×C137—22no—
38#95×C137—22no—
39C2×Q8×C137—21no—
40C2×Q8×C137—41no—
41C2×Q8×C137—41no—
42C2×Q8×C137Q1612yes—
43C22×C4×C137—21no—
44C22×C4×C137—21no—
45C22×C4×C137—22no—
46C22×C4×C137—22no—
47C22×C4×C137—41no—
48C22×C4×C137C2×D411yescharacteristic
49C22×C4×C137C2×D412yes—
50C2×C8×C137—22no—
51C2×C8×C137—41no—
52C2×C8×C137—41no—
53C2×C8×C137—42no—
54C2×C8×C137—42no—
55C2×C8×C137—42no—
56C4⋊C4×C137—22no—
57C4⋊C4×C137—22no—
58C4⋊C4×C137—41no—
59C4⋊C4×C137—42no—
60C4⋊C4×C137—41no—
61C4⋊C4×C137—41no—
62C4⋊C4×C137—44no—
63C4⋊C4×C137—42no—
64C4⋊C4×C137—42no—
65C4⋊C4×C137—81no—
66C4⋊C4×C137—81no—
67C42×C137—41no—
68C42×C137—81no—
69C23×C137#12011yescharacteristic
70Q8×C137—42no—
71Q8×C137—81no—
72C2×C4×C137—21no—
73C2×C4×C137—22no—
74C2×C4×C137—22no—
75C2×C4×C137—21no—
76C2×C4×C137—22no—
77C2×C4×C137—41no—
78C2×C4×C137—41no—
79C2×C4×C137—42no—
80C2×C4×C137—42no—
81C2×C4×C137—42no—
82C2×C4×C137—41no—
83C2×C4×C137—42no—
84C2×C4×C137—42no—
85C2×C4×C137—42no—
86C2×C4×C137—42no—
87C2×C4×C137—81no—
88C2×C4×C137—82no—
89C2×C4×C137C2×Q1611yescharacteristic
90C2×C4×C137#13512yes—
91C2×C4×C137#13711yescharacteristic
92C2×C4×C137#13712yes—
93C8×C137—42no—
94C8×C137—82no—
95C22×C137#45111yescharacteristic
96C22×C137#45212yes—
97C22×C137#45311yescharacteristic
98C22×C137#45412yes—
99C22×C137#45811yescharacteristic
100C4×C137—21no—
101C4×C137—21no—
102C4×C137—22no—
103C4×C137—22no—
104C4×C137—42no—
105C4×C137—82no—
106C4×C137—82no—
107C4×C137—81no—
108C4×C137—161no—
109C2×C137#161411yescharacteristic
110C2×C137#161512yes—
111C2×C137#163411yescharacteristic
112C2×C137#163612yes—
113C2×C137#165711yescharacteristic
114#7831C13711yesmaximal, characteristic, direct product factor, Sylow
115C137#783111yescharacteristic, direct product factor, Sylow
116#2809C2×C13711yescharacteristic
117#2100C2×C13712yes—
118#2095C2×C13711yescharacteristic
119#1272C2×C13711yescharacteristic
120#1271C2×C13712yes—
121C2×#107—21no—
122C2×#103—21no—
123#400—21no—
124#398—22no—
125#391—21no—
126#391C22×C13711yescharacteristic
127#389C22×C13712yes—
128#387—22no—
129#384C22×C13711yescharacteristic
130#340—22no—
131#340—22no—
132#336C22×C13711yescharacteristic
133#336C22×C13712yes—
134C22×Q8D4×C13711yescharacteristic
135C22×C8—21no—
136C22×C8—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4D4×C13712yes—
143C2×C4⋊C4D4×C13712yes—
144C2×C4⋊C4D4×C13711yescharacteristic
145C2×C42—21no—
146C2×C42C23×C13711yescharacteristic
147#107—42no—
148#103—42no—
149#95—21no—
150#95—22no—
151#95—22no—
152#95—22no—
153#95—22no—
154C2×Q8—21no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8Q16×C13712yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—41no—
163C22×C4C2×D4×C13711yescharacteristic
164C22×C4C2×D4×C13712yes—
165C2×C8—22no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—42no—
169C2×C8—42no—
170C2×C8—42no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—44no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—81no—
181C4⋊C4—81no—
182C42—41no—
183C42—81no—
184C23#120×C13711yescharacteristic
185Q8—42no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—81no—
203C2×C4—82no—
204C2×C4C2×Q16×C13711yescharacteristic
205C2×C4#135×C13712yes—
206C2×C4#137×C13711yescharacteristic
207C2×C4#137×C13712yes—
208C8—42no—
209C8—82no—
210C22#451×C13711yescharacteristic
211C22#452×C13712yes—
212C22#453×C13711yescharacteristic
213C22#454×C13712yes—
214C22#458×C13711yescharacteristic
215C4—21no—
216C4—21no—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—82no—
221C4—82no—
222C4—81no—
223C4—161no—
224C2#1614×C13711yescharacteristic
225C2#1615×C13712yes—
226C2#1634×C13711yescharacteristic
227C2#1636×C13712yes—
228C2#1657×C13711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C137#120
commutator, Frattini, cosocleC2×C42C23×C137
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
114. #7831C137direct (N × H)
115. C137#7831direct (N × H)

Maximal subgroups

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

subgroupindex
#2809×C1372
#2100×C1372
#2095×C1372
#1272×C1372
#1271×C1372
#7831137