Finite Group Databasebeta

← C31×#13600 #21470359

Subgroups — C31×#13600 #21470359

Order 7936.

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

normal subgroups only

This group has 318 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×#2132C212yesmaximal
3C31×#1413C214yesmaximal, complemented
4C31×#532C2211yescharacteristic
5C2×C31×#125C411yescharacteristic
6C31×#491C2212yes—
7C31×#490C412yes—
8C31×#488—22no—
9C31×#417—22no—
10C31×#413—22no—
11C4×M16×C31C411yescharacteristic
12C31×#356C2214yes—
13C31×#355—22no—
14C2×#41×C31D412yes—
15C2×M16×C31—21no—
16C2×M16×C31—42no—
17C31×C4⋊Q8C2311yescharacteristic
18C31×#127C2×C411yescharacteristic
19C31×#125—21no—
20C31×#125—41no—
21C31×#125C2×C412yes—
22C31×#124D412yes—
23C31×#121—41no—
24C4×D4×C31—41no—
25C2×C4⋊C4×C31—21no—
26C2×C4⋊C4×C31—41no—
27C2×C42×C31C2×C411yescharacteristic
28C31×#103—24no—
29C31×#102—24no—
30C31×#101—24no—
31C31×#100—42no—
32C31×#97C2×C412yes—
33C4×C8×C31—21no—
34#41×C31—42no—
35#41×C31—42no—
36C2×Q8×C31C2×D412yes—
37C2×D4×C31—22no—
38C2×D4×C31—41no—
39C2×D4×C31C22⋊C412yes—
40C22×C4×C31—21no—
41C22×C4×C31—22no—
42C22×C4×C31—41no—
43C22×C4×C31C22⋊C411yescharacteristic
44M16×C31—42no—
45M16×C31—44no—
46M16×C31—82no—
47C2×C8×C31—22no—
48C2×C8×C31—82no—
49C4⋊C4×C31—22no—
50C4⋊C4×C31—41no—
51C4⋊C4×C31—42no—
52C4⋊C4×C31—42no—
53C4⋊C4×C31—41no—
54C22⋊C4×C31—42no—
55C42×C31—21no—
56C42×C31C22⋊C411yescharacteristic
57C42×C31C22×C411yescharacteristic
58#13600C3111yesmaximal, 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#9911yescharacteristic
75C2×C4×C31C2×C22⋊C411yescharacteristic
76C8×C31—42no—
77C8×C31—84no—
78#3142C2×C3111yescharacteristic
79#2132C2×C3112yes—
80#1413C2×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#35412yes—
92#532C22×C3111yescharacteristic
93C2×#125C4×C3111yescharacteristic
94#491C22×C3112yes—
95#490C4×C3112yes—
96#488—22no—
97#417—22no—
98#413—22no—
99C4×M16C4×C3111yescharacteristic
100#356C22×C3114yes—
101#355—22no—
102C2×C31—21no—
103C2×C31—41no—
104C2×C31—82no—
105C2×C31C2×#35411yescharacteristic
106C2×#41D4×C3112yes—
107C2×M16—21no—
108C2×M16—42no—
109C4⋊Q8C23×C3111yescharacteristic
110#127C2×C4×C3111yescharacteristic
111#125—21no—
112#125—41no—
113#125C2×C4×C3112yes—
114#124D4×C3112yes—
115#121—41no—
116C4×D4—41no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—41no—
119C2×C42C2×C4×C3111yescharacteristic
120#103—24no—
121#102—24no—
122#101—24no—
123#100—42no—
124#97C2×C4×C3112yes—
125C4×C8—21no—
126C31#1360011yescharacteristic, direct product factor, Sylow
127#41—42no—
128#41—42no—
129C2×Q8C2×D4×C3112yes—
130C2×D4—22no—
131C2×D4—41no—
132C2×D4C22⋊C4×C3112yes—
133C22×C4—21no—
134C22×C4—22no—
135C22×C4—41no—
136C22×C4C22⋊C4×C3111yescharacteristic
137M16—42no—
138M16—44no—
139M16—82no—
140C2×C8—22no—
141C2×C8—82no—
142C4⋊C4—22no—
143C4⋊C4—41no—
144C4⋊C4—42no—
145C4⋊C4—42no—
146C4⋊C4—41no—
147C22⋊C4—42no—
148C42—21no—
149C42C22⋊C4×C3111yescharacteristic
150C42C22×C4×C3111yescharacteristic
151C23—22no—
152C23C31×#9911yescharacteristic
153Q8—42no—
154D4—42no—
155D4—82no—
156D4—82no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—81no—
165C2×C4—82no—
166C2×C4C31×#9911yescharacteristic
167C2×C4C2×C22⋊C4×C3111yescharacteristic
168C8—42no—
169C8—84no—
170C22—21no—
171C22—41no—
172C22—42no—
173C22—82no—
174C22C2×C31×#9911yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—42no—
179C4—82no—
180C4C31×#35412yes—
181C2—21no—
182C2—41no—
183C2—82no—
184C2C2×C31×#35411yescharacteristic
subgroupG/H
center, socleC2×C31C2×#354
commutatorC42C22×C4×C31
Frattini, cosocleC4⋊Q8C23×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×#1413C2semidirect
58. #13600C31direct (N × H)
80. #1413C2×C31semidirect
126. C31#13600direct (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×#21322
C31×#14132
#1360031