Finite Group Databasebeta

← C31×#10368 #21467127

Subgroups — C31×#10368 #21467127

Order 7936.

402 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C31×#2864C211yesmaximal, characteristic, complemented
2C31×#1962C211yesmaximal, characteristic
3C31×#1517C212yesmaximal
4C31×#1286C212yesmaximal, complemented
5C31×#1276C211yesmaximal, characteristic, complemented
6C31×#532C2211yescharacteristic
7C31×#431C2212yes—
8C31×#423C2211yescharacteristic
9C2×C31×#104—22no—
10C31×#389—22no—
11C31×#387—24no—
12C31×#382C2212yes—
13C43×C31C2211yescharacteristic
14C31×#327—24no—
15C2×#41×C31—21no—
16C2×M16×C31—21no—
17C31×C4⋊Q8Q811yescharacteristic
18C31×#127Q811yescharacteristic
19C31×#124—21no—
20C31×#121—22no—
21C4×D4×C31—22no—
22C2×C4⋊C4×C31—24no—
23C2×C4⋊C4×C31—22no—
24C2×C42×C31—22no—
25C2×C42×C31D412yes—
26C2×C42×C31C2311yescharacteristic
27C31×C4⋊C8—22no—
28C31×C4⋊C8—22no—
29C31×#104—44no—
30C31×C22⋊C8—22no—
31C4×C8×C31—22no—
32C31×#95—24no—
33C31×#95—22no—
34C31×#95D414yes—
35#41×C31—42no—
36#41×C31—42no—
37C2×Q8×C31—21no—
38C2×D4×C31—21no—
39C2×D4×C31—22no—
40C2×D4×C31—41no—
41C22×C4×C31—22no—
42C22×C4×C31—24no—
43C22×C4×C31—41no—
44C22×C4×C31C2×D412yes—
45C22×C4×C31C2×D411yescharacteristic
46M16×C31—42no—
47C2×C8×C31—42no—
48C2×C8×C31—41no—
49C4⋊C4×C31—22no—
50C4⋊C4×C31—48no—
51C4⋊C4×C31—42no—
52C4⋊C4×C31—42no—
53C22⋊C4×C31—42no—
54C42×C31—22no—
55C42×C31—22no—
56C42×C31—44no—
57C42×C31C2×Q811yescharacteristic
58C42×C31#4111yescharacteristic
59C42×C31#4112yes—
60#10368C3111yesmaximal, characteristic, direct product factor, Sylow
61C23×C31—41no—
62C23×C31#12011yescharacteristic
63Q8×C31—42no—
64D4×C31—42no—
65D4×C31—82no—
66D4×C31—82no—
67C2×C4×C31—24no—
68C2×C4×C31—42no—
69C2×C4×C31—42no—
70C2×C4×C31—42no—
71C2×C4×C31—48no—
72C2×C4×C31—41no—
73C2×C4×C31—44no—
74C2×C4×C31—81no—
75C2×C4×C31—81no—
76C2×C4×C31C22⋊Q812yes—
77C2×C4×C31C22⋊Q811yescharacteristic
78C2×C4×C31#12412yes—
79C2×C4×C31#12411yescharacteristic
80C2×C4×C31#13512yes—
81C2×C4×C31AGL(1,ℤ/8)12yes—
82C8×C31—82no—
83C8×C31—81no—
84#2864C2×C3111yescharacteristic, complemented
85#1962C2×C3111yescharacteristic
86#1517C2×C3112yes—
87#1286C2×C3112yescomplemented
88#1276C2×C3111yescharacteristic, complemented
89C22×C31—22no—
90C22×C31—81no—
91C22×C31—82no—
92C22×C31#39311yescharacteristic
93C22×C31#44912yes—
94C4×C31—22no—
95C4×C31—22no—
96C4×C31—44no—
97C4×C31—84no—
98C4×C31—81no—
99C4×C31#47812yes—
100C4×C31#48811yescharacteristic
101C4×C31#49011yescharacteristic
102#532C22×C3111yescharacteristic
103#431C22×C3112yes—
104#423C22×C3111yescharacteristic
105C2×#104—22no—
106#389—22no—
107#387—24no—
108#382C22×C3112yes—
109C43C22×C3111yescharacteristic
110#327—24no—
111C2×C31—22no—
112C2×C31—161no—
113C2×C31#202511yescharacteristic
114C2×C31#203112yes—
115C2×#41—21no—
116C2×M16—21no—
117C4⋊Q8Q8×C3111yescharacteristic
118#127Q8×C3111yescharacteristic
119#124—21no—
120#121—22no—
121C4×D4—22no—
122C2×C4⋊C4—24no—
123C2×C4⋊C4—22no—
124C2×C42—22no—
125C2×C42D4×C3112yes—
126C2×C42C23×C3111yescharacteristic
127C4⋊C8—22no—
128C4⋊C8—22no—
129#104—44no—
130C22⋊C8—22no—
131C4×C8—22no—
132#95—24no—
133#95—22no—
134#95D4×C3114yes—
135C31#1036811yescharacteristic, direct product factor, Sylow
136#41—42no—
137#41—42no—
138C2×Q8—21no—
139C2×D4—21no—
140C2×D4—22no—
141C2×D4—41no—
142C22×C4—22no—
143C22×C4—24no—
144C22×C4—41no—
145C22×C4C2×D4×C3112yes—
146C22×C4C2×D4×C3111yescharacteristic
147M16—42no—
148C2×C8—42no—
149C2×C8—41no—
150C4⋊C4—22no—
151C4⋊C4—48no—
152C4⋊C4—42no—
153C4⋊C4—42no—
154C22⋊C4—42no—
155C42—22no—
156C42—22no—
157C42—44no—
158C42C2×Q8×C3111yescharacteristic
159C42#41×C3111yescharacteristic
160C42#41×C3112yes—
161C23—41no—
162C23C31×#12011yescharacteristic
163Q8—42no—
164D4—42no—
165D4—82no—
166D4—82no—
167C2×C4—24no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—48no—
172C2×C4—44no—
173C2×C4—41no—
174C2×C4—81no—
175C2×C4—81no—
176C2×C4C31×C22⋊Q812yes—
177C2×C4C31×C22⋊Q811yescharacteristic
178C2×C4C31×#12412yes—
179C2×C4C31×#12411yescharacteristic
180C2×C4C31×#13512yes—
181C2×C4C31×AGL(1,ℤ/8)12yes—
182C8—82no—
183C8—81no—
184C22—22no—
185C22—81no—
186C22—82no—
187C22C31×#39311yescharacteristic
188C22C31×#44912yes—
189C4—22no—
190C4—22no—
191C4—44no—
192C4—84no—
193C4—81no—
194C4C31×#47812yes—
195C4C31×#48811yescharacteristic
196C4C31×#49011yescharacteristic
197C2—22no—
198C2—161no—
199C2C31×#202511yescharacteristic
200C2C31×#203112yes—
subgroupG/H
center, socleC22×C31#393
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC31×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2864C2semidirect
4. C31×#1286C2semidirect
5. C31×#1276C2semidirect
60. #10368C31direct (N × H)
84. #2864C2×C31semidirect
87. #1286C2×C31semidirect
88. #1276C2×C31semidirect
135. C31#10368direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28642
C31×#19622
C31×#15172
C31×#12862
C31×#12762
#1036831