Finite Group Databasebeta

← C31×#2023 #16841956

Subgroups — C31×#2023 #16841956

Order 3968.

326 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 108 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
1C2×C31×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×C31×#102C212yesmaximal
3C31×#390C211yesmaximal, characteristic
4C31×#340C212yesmaximal, complemented
5C31×#336C211yesmaximal, characteristic, complemented
6C22×Q8×C31—21no—
7C22×D4×C31C2211yescharacteristic
8C22×C8×C31C2212yes—
9C31×C4⋊Q8—24no—
10C2×C4⋊C4×C31—21no—
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×C4⋊C4×C31C2212yes—
13C2×C22⋊C4×C31—21no—
14C2×C22⋊C4×C31—21no—
15C2×C42×C31C2211yescharacteristic
16C31×#102—24no—
17C24×C31—21no—
18C2×Q8×C31—24no—
19C2×Q8×C31—42no—
20C2×Q8×C31—42no—
21C2×D4×C31—22no—
22C2×D4×C31—22no—
23C2×D4×C31—21no—
24C2×D4×C31Q812yescomplemented
25C22×C4×C31—22no—
26C22×C4×C31—21no—
27C22×C4×C31D411yescharacteristic
28C22×C4×C31D411yescharacteristic
29C22×C4×C31C2311yescharacteristic
30C2×C8×C31—22no—
31C2×C8×C31—22no—
32C2×C8×C31—22no—
33C4⋊C4×C31—24no—
34C4⋊C4×C31—22no—
35C4⋊C4×C31—22no—
36C4⋊C4×C31D414yes—
37C22⋊C4×C31—42no—
38C22⋊C4×C31—42no—
39C42×C31—22no—
40C23×C31—22no—
41C23×C31—41no—
42C23×C31—41no—
43C23×C31—41no—
44C23×C31—41no—
45C23×C31—41no—
46C23×C31—41no—
47C23×C31C2×D411yescharacteristic
48Q8×C31—48no—
49D4×C31—24no—
50D4×C31—42no—
51C2×C4×C31—21no—
52C2×C4×C31—21no—
53C2×C4×C31—21no—
54C2×C4×C31—21no—
55C2×C4×C31—24no—
56C2×C4×C31—42no—
57C2×C4×C31—42no—
58C2×C4×C31—41no—
59C2×C4×C31—41no—
60C2×C4×C31—41no—
61C2×C4×C31D812yes—
62C2×C4×C31SD1612yes—
63C2×C4×C31C2×D412yes—
64C2×C4×C31C2×Q811yescharacteristic
65C2×C4×C31#4112yes—
66C2×C4×C31#4111yescharacteristic
67C8×C31—42no—
68#2023C3111yesmaximal, characteristic, direct product factor, Sylow
69C22×C31—42no—
70C22×C31—42no—
71C22×C31—42no—
72C22×C31—81no—
73C22×C31—81no—
74C22×C31—81no—
75C22×C31—81no—
76C22×C31#12011yescharacteristic
77C22×C31C22⋊Q811yescharacteristic
78C22×C31#12411yescharacteristic
79C22×C31C2×D811yescharacteristic
80C22×C31C2×SD1611yescharacteristic
81C22×C31AGL(1,ℤ/8)11yescharacteristic
82C22×C31#13711yescharacteristic
83C4×C31—22no—
84C4×C31—22no—
85C4×C31—44no—
86C4×C31—81no—
87C4×C31C22⋊Q812yes—
88C4×C31#12412yes—
89C2×C4⋊Q8C2×C3111yescharacteristic, complemented
90C2×#102C2×C3112yes—
91#390C2×C3111yescharacteristic
92#340C2×C3112yescomplemented
93#336C2×C3111yescharacteristic, complemented
94C2×C31—82no—
95C2×C31#39311yescharacteristic
96C2×C31#44711yescharacteristic
97C2×C31#44811yescharacteristic
98C2×C31#47411yescharacteristic
99C2×C31#47611yescharacteristic
100C2×C31#48611yescharacteristic
101C2×C31#48911yescharacteristic
102C22×Q8—21no—
103C22×D4C22×C3111yescharacteristic
104C22×C8C22×C3112yes—
105C4⋊Q8—24no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4C22×C3111yescharacteristic
108C2×C4⋊C4C22×C3112yes—
109C2×C22⋊C4—21no—
110C2×C22⋊C4—21no—
111C2×C42C22×C3111yescharacteristic
112#102—24no—
113C31#202311yescharacteristic, direct product factor, Sylow
114C24—21no—
115C2×Q8—24no—
116C2×Q8—42no—
117C2×Q8—42no—
118C2×D4—22no—
119C2×D4—22no—
120C2×D4—21no—
121C2×D4Q8×C3112yescomplemented
122C22×C4—22no—
123C22×C4—21no—
124C22×C4D4×C3111yescharacteristic
125C22×C4D4×C3111yescharacteristic
126C22×C4C23×C3111yescharacteristic
127C2×C8—22no—
128C2×C8—22no—
129C2×C8—22no—
130C4⋊C4—24no—
131C4⋊C4—22no—
132C4⋊C4—22no—
133C4⋊C4D4×C3114yes—
134C22⋊C4—42no—
135C22⋊C4—42no—
136C42—22no—
137C23—22no—
138C23—41no—
139C23—41no—
140C23—41no—
141C23—41no—
142C23—41no—
143C23—41no—
144C23C2×D4×C3111yescharacteristic
145Q8—48no—
146D4—24no—
147D4—42no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—24no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4D8×C3112yes—
159C2×C4SD16×C3112yes—
160C2×C4C2×D4×C3112yes—
161C2×C4C2×Q8×C3111yescharacteristic
162C2×C4#41×C3112yes—
163C2×C4#41×C3111yescharacteristic
164C8—42no—
165C22—42no—
166C22—42no—
167C22—42no—
168C22—81no—
169C22—81no—
170C22—81no—
171C22—81no—
172C22C31×#12011yescharacteristic
173C22C31×C22⋊Q811yescharacteristic
174C22C31×#12411yescharacteristic
175C22C2×D8×C3111yescharacteristic
176C22C2×SD16×C3111yescharacteristic
177C22C31×AGL(1,ℤ/8)11yescharacteristic
178C22C31×#13711yescharacteristic
179C4—22no—
180C4—22no—
181C4—44no—
182C4—81no—
183C4C31×C22⋊Q812yes—
184C4C31×#12412yes—
185C2—82no—
186C2C31×#39311yescharacteristic
187C2C31×#44711yescharacteristic
188C2C31×#44811yescharacteristic
189C2C31×#47411yescharacteristic
190C2C31×#47611yescharacteristic
191C2C31×#48611yescharacteristic
192C2C31×#48911yescharacteristic
subgroupG/H
center, socleC23×C31C2×D4
commutator, Frattini, cosocleC22×C4C23×C31
prime radicalC22×D4×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×C4⋊Q8C2semidirect
4. C31×#340C2semidirect
5. C31×#336C2semidirect
24. C2×D4×C31Q8semidirect
68. #2023C31direct (N × H)
89. C2×C4⋊Q8C2×C31semidirect
92. #340C2×C31semidirect
93. #336C2×C31semidirect
113. C31#2023direct (N × H)
121. C2×D4Q8×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×C4⋊Q82
C2×C31×#1022
C31×#3902
C31×#3402
C31×#3362
#202331