Finite Group Databasebeta

← C31×#19745 #21476504

Subgroups — C31×#19745 #21476504

Order 7936.

994 conjugacy classes of subgroups; only the 254 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 254 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×#3184C213yesmaximal, complemented
2C31×#3151C213yesmaximal, complemented
3C31×#1721C213yesmaximal, complemented
4C31×#1715C213yesmaximal, complemented
5C31×#1712C211yesmaximal, characteristic, complemented
6C31×#1705C211yesmaximal, characteristic, complemented
7C31×#1455C211yesmaximal, characteristic, complemented
8C2×C31×AGL(1,ℤ/8)—26no—
9C31×#532C2213yes—
10C2×C31×#127C2211yescharacteristic
11C31×#498C2213yescomplemented
12C31×#496—26no—
13C31×#493C2213yes—
14C31×#493C2213yes—
15C31×#493C2213yescomplemented
16C31×#492C2213yes—
17C31×#492C2213yes—
18C31×#486C2216yescomplemented
19C31×#469—26no—
20C31×#442—26no—
21C4×M16×C31C2213yes—
22C31×#322C2213yescomplemented
23C82×C31C2211yescharacteristic, complemented
24C2×#41×C31—23no—
25C22×D4×C31—23no—
26C31×AGL(1,ℤ/8)—424no—
27C2×SD16×C31—26no—
28C2×SD16×C31—26no—
29C2×D8×C31—26no—
30C2×D8×C31—26no—
31C2×D8×C31—26no—
32C2×M16×C31D416yes—
33C31×C4⋊Q8C2313yes—
34C31×#127—23no—
35C31×#127C2313yes—
36C31×#127C2311yescharacteristic
37C31×#127C2311yescharacteristic
38C31×#124—23no—
39C31×#121—26no—
40C4×D4×C31—26no—
41C2×C42×C31C2311yescharacteristic
42C31×#106—26no—
43C31×#102—212no—
44C31×#97D416yes—
45C4×C8×C31C2313yes—
46C4×C8×C31C2313yes—
47C24×C31—41no—
48#41×C31—412no—
49C2×Q8×C31—23no—
50C2×D4×C31—26no—
51C2×D4×C31—23no—
52C2×D4×C31—23no—
53C2×D4×C31—23no—
54C2×D4×C31—412no—
55C2×D4×C31—43no—
56C2×D4×C31—43no—
57C22×C4×C31—43no—
58C22×C4×C31C2×D413yes—
59SD16×C31—412no—
60SD16×C31—412no—
61D8×C31—412no—
62D8×C31—412no—
63D8×C31—412no—
64M16×C31—212no—
65C2×C8×C31C2×D416yes—
66C2×C8×C31C2×D416yes—
67C4⋊C4×C31—26no—
68C22⋊C4×C31—46no—
69C42×C31C2×D413yes—
70C42×C31C2411yescharacteristic
71#19745C3111yesmaximal, characteristic, direct product factor, Sylow
72C23×C31—43no—
73C23×C31—41no—
74C23×C31—41no—
75C23×C31—86no—
76C23×C31#12711yescharacteristic
77Q8×C31—46no—
78D4×C31—46no—
79D4×C31—46no—
80D4×C31—46no—
81D4×C31—412no—
82D4×C31—86no—
83D4×C31—86no—
84C2×C4×C31—26no—
85C2×C4×C31—43no—
86C2×C4×C31—86no—
87C2×C4×C31#12713yes—
88C2×C4×C31C22×D413yes—
89C8×C31—26no—
90C8×C31AGL(1,ℤ/8)112yescomplemented
91#3184C2×C3113yescomplemented
92#3151C2×C3113yescomplemented
93#1721C2×C3113yescomplemented
94#1715C2×C3113yescomplemented
95#1712C2×C3111yescharacteristic, complemented
96#1705C2×C3111yescharacteristic, complemented
97#1455C2×C3111yescharacteristic, complemented
98C22×C31—23no—
99C22×C31—83no—
100C22×C31—83no—
101C22×C31—83no—
102C22×C31—86no—
103C22×C31—164no—
104C22×C31C2×#12711yescharacteristic
105C4×C31—23no—
106C4×C31—83no—
107C4×C31C2×AGL(1,ℤ/8)16yes—
108C2×AGL(1,ℤ/8)—26no—
109#532C22×C3113yes—
110C2×#127C22×C3111yescharacteristic
111#498C22×C3113yescomplemented
112#496—26no—
113#493C22×C3113yes—
114#493C22×C3113yes—
115#493C22×C3113yescomplemented
116#492C22×C3113yes—
117#492C22×C3113yes—
118#486C22×C3116yescomplemented
119#469—26no—
120#442—26no—
121C4×M16C22×C3113yes—
122#322C22×C3113yescomplemented
123C82C22×C3111yescharacteristic, complemented
124C2×C31—41no—
125C2×C31—163no—
126C2×C31—161no—
127C2×C31—161no—
128C2×C31#315113yes—
129C2×#41—23no—
130C22×D4—23no—
131AGL(1,ℤ/8)—424no—
132C2×SD16—26no—
133C2×SD16—26no—
134C2×D8—26no—
135C2×D8—26no—
136C2×D8—26no—
137C2×M16D4×C3116yes—
138C4⋊Q8C23×C3113yes—
139#127—23no—
140#127C23×C3111yescharacteristic
141#127C23×C3111yescharacteristic
142#127C23×C3113yes—
143#124—23no—
144#121—26no—
145C4×D4—26no—
146C2×C42C23×C3111yescharacteristic
147#106—26no—
148#102—212no—
149#97D4×C3116yes—
150C4×C8C23×C3113yes—
151C4×C8C23×C3113yes—
152C31#1974511yescharacteristic, direct product factor, Sylow
153C24—41no—
154#41—412no—
155C2×Q8—23no—
156C2×D4—26no—
157C2×D4—23no—
158C2×D4—23no—
159C2×D4—23no—
160C2×D4—412no—
161C2×D4—43no—
162C2×D4—43no—
163C22×C4—43no—
164C22×C4C2×D4×C3113yes—
165SD16—412no—
166SD16—412no—
167D8—412no—
168D8—412no—
169D8—412no—
170M16—212no—
171C2×C8C2×D4×C3116yes—
172C2×C8C2×D4×C3116yes—
173C4⋊C4—26no—
174C22⋊C4—46no—
175C42C2×D4×C3113yes—
176C42C24×C3111yescharacteristic
177C23—43no—
178C23—41no—
179C23—41no—
180C23—86no—
181C23C31×#12711yescharacteristic
182Q8—46no—
183D4—46no—
184D4—46no—
185D4—46no—
186D4—412no—
187D4—86no—
188D4—86no—
189C2×C4—26no—
190C2×C4—43no—
191C2×C4—86no—
192C2×C4C31×#12713yes—
193C2×C4C22×D4×C3113yes—
194C8—26no—
195C8C31×AGL(1,ℤ/8)112yescomplemented
196C22—23no—
197C22—83no—
198C22—83no—
199C22—83no—
200C22—86no—
201C22—164no—
202C22C2×C31×#12711yescharacteristic
203C4—23no—
204C4—83no—
205C4C2×C31×AGL(1,ℤ/8)16yes—
206C2—41no—
207C2—161no—
208C2—161no—
209C2—163no—
210C2C31×#315113yes—
subgroupG/H
center, socleC22×C31C2×#127
commutator, Frattini, cosocleC42C24×C31
LCSG ▷ 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×#3184C2semidirect
2. C31×#3151C2semidirect
3. C31×#1721C2semidirect
4. C31×#1715C2semidirect
5. C31×#1712C2semidirect
6. C31×#1705C2semidirect
7. C31×#1455C2semidirect
11. C31×#498C22semidirect
15. C31×#493C22semidirect
18. C31×#486C22semidirect
22. C31×#322C22semidirect
23. C82×C31C22semidirect
71. #19745C31direct (N × H)
90. C8×C31AGL(1,ℤ/8)semidirect
91. #3184C2×C31semidirect
92. #3151C2×C31semidirect
93. #1721C2×C31semidirect
94. #1715C2×C31semidirect
95. #1712C2×C31semidirect
96. #1705C2×C31semidirect
97. #1455C2×C31semidirect
111. #498C22×C31semidirect
115. #493C22×C31semidirect
118. #486C22×C31semidirect
122. #322C22×C31semidirect
123. C82C22×C31semidirect
152. C31#19745direct (N × H)
195. C8C31×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C31×#31842
C31×#31512
C31×#17212
C31×#17152
C31×#17122
C31×#17052
C31×#14552
#1974531