Finite Group Databasebeta

← C31×#7401 #21464160

Subgroups — C31×#7401 #21464160

Order 7936.

234 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 42 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×#2020C211yesmaximal, characteristic
2C31×#1392C211yesmaximal, characteristic
3C31×#1321C211yesmaximal, characteristic
4C2×C31×#137—21no—
5C22×Q16×C31C411yescharacteristic
6C31×#413—21no—
7C2×C31×#101—21no—
8C31×#408C2211yescharacteristic
9C31×#349—21no—
10C31×#341C411yescharacteristic
11C2×#41×C31D411yescharacteristic
12C22×Q8×C31—21no—
13C31×#137—42no—
14C31×#137—42no—
15C2×Q16×C31—41no—
16C2×Q16×C31—41no—
17C2×Q16×C31—42no—
18C2×SD16×C31—41no—
19C2×M16×C31—21no—
20C2×M16×C31—41no—
21C2×M16×C31D411yescharacteristic
22C22×C8×C31C2×C411yescharacteristic
23C31×M32—41no—
24C31×#101—42no—
25C31×#101—41no—
26C31×#100—22no—
27C31×C22⋊C8—41no—
28#41×C31—41no—
29#41×C31—41no—
30C2×Q8×C31—22no—
31C2×Q8×C31—41no—
32C2×Q8×C31—41no—
33C2×Q8×C31—41no—
34C2×Q8×C31—41no—
35C2×Q8×C31—41no—
36C2×Q8×C31D811yescharacteristic
37C2×D4×C31—21no—
38C2×D4×C31SD1611yescharacteristic
39C22×C4×C31—21no—
40C22×C4×C31—41no—
41C22×C4×C31C22⋊C411yescharacteristic
42Q16×C31—42no—
43Q16×C31—44no—
44Q16×C31—42no—
45SD16×C31—44no—
46M16×C31—22no—
47M16×C31—41no—
48M16×C31—41no—
49M16×C31—42no—
50M16×C31—81no—
51C2×C8×C31—21no—
52C2×C8×C31—21no—
53C2×C8×C31—41no—
54C2×C8×C31—41no—
55C2×C8×C31—81no—
56C16×C31—81no—
57#7401C3111yesmaximal, characteristic, direct product factor, Sylow
58C23×C31—21no—
59C23×C31#10411yescharacteristic
60Q8×C31—41no—
61Q8×C31—42no—
62Q8×C31—42no—
63Q8×C31—81no—
64Q8×C31—81no—
65D4×C31—41no—
66D4×C31—81no—
67C2×C4×C31—21no—
68C2×C4×C31—21no—
69C2×C4×C31—21no—
70C2×C4×C31—41no—
71C2×C4×C31—41no—
72C2×C4×C31—42no—
73C2×C4×C31—81no—
74C2×C4×C31—81no—
75C2×C4×C31#9911yescharacteristic
76C2×C4×C31#10211yescharacteristic
77C8×C31—42no—
78C8×C31—41no—
79C8×C31—41no—
80C8×C31—82no—
81#2020C2×C3111yescharacteristic
82#1392C2×C3111yescharacteristic
83#1321C2×C3111yescharacteristic
84C22×C31—21no—
85C22×C31—41no—
86C22×C31—41no—
87C22×C31—81no—
88C22×C31#32711yescharacteristic
89C4×C31—21no—
90C4×C31—41no—
91C4×C31—82no—
92C4×C31AΣL(1,𝔽16)11yescharacteristic
93C4×C31#35311yescharacteristic
94C2×#137—21no—
95C22×Q16C4×C3111yescharacteristic
96#413—21no—
97C2×#101—21no—
98#408C22×C3111yescharacteristic
99#349—21no—
100#341C4×C3111yescharacteristic
101C2×C31—21no—
102C2×C31—41no—
103C2×C31—81no—
104C2×C31#134311yescharacteristic
105C2×#41D4×C3111yescharacteristic
106C22×Q8—21no—
107#137—42no—
108#137—42no—
109C2×Q16—41no—
110C2×Q16—41no—
111C2×Q16—42no—
112C2×SD16—41no—
113C2×M16—21no—
114C2×M16—41no—
115C2×M16D4×C3111yescharacteristic
116C22×C8C2×C4×C3111yescharacteristic
117M32—41no—
118#101—42no—
119#101—41no—
120#100—22no—
121C22⋊C8—41no—
122C31#740111yescharacteristic, direct product factor, Sylow
123#41—41no—
124#41—41no—
125C2×Q8—22no—
126C2×Q8—41no—
127C2×Q8—41no—
128C2×Q8—41no—
129C2×Q8—41no—
130C2×Q8—41no—
131C2×Q8D8×C3111yescharacteristic
132C2×D4—21no—
133C2×D4SD16×C3111yescharacteristic
134C22×C4—21no—
135C22×C4—41no—
136C22×C4C22⋊C4×C3111yescharacteristic
137Q16—42no—
138Q16—42no—
139Q16—44no—
140SD16—44no—
141M16—22no—
142M16—41no—
143M16—41no—
144M16—42no—
145M16—81no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—41no—
149C2×C8—41no—
150C2×C8—81no—
151C16—81no—
152C23—21no—
153C23C31×#10411yescharacteristic
154Q8—41no—
155Q8—42no—
156Q8—42no—
157Q8—81no—
158Q8—81no—
159D4—41no—
160D4—81no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—42no—
167C2×C4—81no—
168C2×C4—81no—
169C2×C4C31×#9911yescharacteristic
170C2×C4C31×#10211yescharacteristic
171C8—42no—
172C8—41no—
173C8—41no—
174C8—82no—
175C22—21no—
176C22—41no—
177C22—41no—
178C22—81no—
179C22C31×#32711yescharacteristic
180C4—21no—
181C4—41no—
182C4—82no—
183C4C31×AΣL(1,𝔽16)11yescharacteristic
184C4C31×#35311yescharacteristic
185C2—21no—
186C2—41no—
187C2—81no—
188C2C31×#134311yescharacteristic
subgroupG/H
center, socleC2×C31#1343
commutatorC22×C8C2×C4×C31
Frattini, cosocle#408C22×C31
prime radicalC2×#41×C31D4
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C31×#408 ◁ G

Complements

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

NH ≅ G/Ntype
57. #7401C31direct (N × H)
122. C31#7401direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#20202
C31×#13922
C31×#13212
#740131