Finite Group Databasebeta

← C31×#13596 #21470355

Subgroups — C31×#13596 #21470355

Order 7936.

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
1C31×#3142C211yesmaximal, characteristic
2C31×#2126C212yesmaximal
3C31×#1412C214yesmaximal, complemented
4C31×#532C2211yescharacteristic
5C2×C31×#125C411yescharacteristic, complemented
6C31×#491C412yescomplemented
7C31×#490C2212yes—
8C31×#488—22no—
9C31×#417—22no—
10C31×#410—22no—
11C4×M16×C31C411yescharacteristic, complemented
12C31×#354—22no—
13C31×#353C2214yes—
14C2×#41×C31D412yes—
15C2×M16×C31—21no—
16C31×C4⋊Q8C2×C411yescharacteristic
17C31×#127C2311yescharacteristic
18C31×#125—21no—
19C31×#125—41no—
20C31×#125C2×C412yes—
21C31×#124D412yes—
22C31×#121—41no—
23C4×D4×C31—41no—
24C31×#117—42no—
25C2×C4⋊C4×C31—21no—
26C2×C4⋊C4×C31—41no—
27C2×C42×C31C2×C411yescharacteristic
28C31×#103—24no—
29C31×#102—24no—
30C31×#99—24no—
31C31×#99—42no—
32C31×#97C2×C412yes—
33C4×C8×C31—21no—
34#41×C31—42no—
35#41×C31—42no—
36C2×Q8×C31C22⋊C412yes—
37C2×D4×C31—22no—
38C2×D4×C31—41no—
39C2×D4×C31C2×D412yes—
40C22×C4×C31—21no—
41C22×C4×C31—22no—
42C22×C4×C31—41no—
43C22×C4×C31C22⋊C411yescharacteristic
44M16×C31—42no—
45C2×C8×C31—22no—
46C4⋊C4×C31—22no—
47C4⋊C4×C31—41no—
48C4⋊C4×C31—42no—
49C4⋊C4×C31—42no—
50C4⋊C4×C31—41no—
51C4⋊C4×C31—82no—
52C22⋊C4×C31—42no—
53C22⋊C4×C31—44no—
54C42×C31—21no—
55C42×C31—82no—
56C42×C31C22⋊C411yescharacteristic
57C42×C31C22×C411yescharacteristic
58#13596C3111yesmaximal, characteristic, direct product factor, Sylow
59C23×C31—22no—
60C23×C31#9911yescharacteristic
61Q8×C31—42no—
62D4×C31—42no—
63D4×C31—82no—
64D4×C31—82no—
65C2×C4×C31—22no—
66C2×C4×C31—21no—
67C2×C4×C31—21no—
68C2×C4×C31—22no—
69C2×C4×C31—42no—
70C2×C4×C31—42no—
71C2×C4×C31—42no—
72C2×C4×C31—81no—
73C2×C4×C31—82no—
74C2×C4×C31—84no—
75C2×C4×C31#9911yescharacteristic
76C2×C4×C31C2×C22⋊C411yescharacteristic
77C8×C31—42no—
78#3142C2×C3111yescharacteristic
79#2126C2×C3112yes—
80#1412C2×C3114yescomplemented
81C22×C31—21no—
82C22×C31—41no—
83C22×C31—42no—
84C22×C31—82no—
85C22×C31C2×#9911yescharacteristic
86C4×C31—21no—
87C4×C31—41no—
88C4×C31—41no—
89C4×C31—42no—
90C4×C31—82no—
91C4×C31—164no—
92C4×C31#35412yes—
93#532C22×C3111yescharacteristic
94C2×#125C4×C3111yescharacteristic, complemented
95#491C4×C3112yescomplemented
96#490C22×C3112yes—
97#488—22no—
98#417—22no—
99#410—22no—
100C4×M16C4×C3111yescharacteristic, complemented
101#354—22no—
102#353C22×C3114yes—
103C2×C31—21no—
104C2×C31—41no—
105C2×C31—82no—
106C2×C31C2×#35411yescharacteristic
107C2×#41D4×C3112yes—
108C2×M16—21no—
109C4⋊Q8C2×C4×C3111yescharacteristic
110#127C23×C3111yescharacteristic
111#125—21no—
112#125—41no—
113#125C2×C4×C3112yes—
114#124D4×C3112yes—
115#121—41no—
116C4×D4—41no—
117#117—42no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—41no—
120C2×C42C2×C4×C3111yescharacteristic
121#103—24no—
122#102—24no—
123#99—24no—
124#99—42no—
125#97C2×C4×C3112yes—
126C4×C8—21no—
127C31#1359611yescharacteristic, direct product factor, Sylow
128#41—42no—
129#41—42no—
130C2×Q8C22⋊C4×C3112yes—
131C2×D4—22no—
132C2×D4—41no—
133C2×D4C2×D4×C3112yes—
134C22×C4—21no—
135C22×C4—22no—
136C22×C4—41no—
137C22×C4C22⋊C4×C3111yescharacteristic
138M16—42no—
139C2×C8—22no—
140C4⋊C4—22no—
141C4⋊C4—41no—
142C4⋊C4—42no—
143C4⋊C4—42no—
144C4⋊C4—41no—
145C4⋊C4—82no—
146C22⋊C4—42no—
147C22⋊C4—44no—
148C42—21no—
149C42—82no—
150C42C22⋊C4×C3111yescharacteristic
151C42C22×C4×C3111yescharacteristic
152C23—22no—
153C23C31×#9911yescharacteristic
154Q8—42no—
155D4—42no—
156D4—82no—
157D4—82no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—81no—
166C2×C4—82no—
167C2×C4—84no—
168C2×C4C31×#9911yescharacteristic
169C2×C4C2×C22⋊C4×C3111yescharacteristic
170C8—42no—
171C22—21no—
172C22—41no—
173C22—42no—
174C22—82no—
175C22C2×C31×#9911yescharacteristic
176C4—21no—
177C4—41no—
178C4—41no—
179C4—42no—
180C4—82no—
181C4—164no—
182C4C31×#35412yes—
183C2—21no—
184C2—41no—
185C2—82no—
186C2C2×C31×#35411yescharacteristic
subgroupG/H
center, socleC2×C31C2×#354
commutatorC42C22×C4×C31
Frattini, cosocle#127C23×C31
prime radicalC31×#532C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C31×#532 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1412C2semidirect
5. C2×C31×#125C4semidirect
6. C31×#491C4semidirect
11. C4×M16×C31C4semidirect
58. #13596C31direct (N × H)
80. #1412C2×C31semidirect
94. C2×#125C4×C31semidirect
95. #491C4×C31semidirect
100. C4×M16C4×C31semidirect
127. C31#13596direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31422
C31×#21262
C31×#14122
#1359631