Finite Group Databasebeta

← C31×#2127 #16842060

Subgroups — C31×#2127 #16842060

Order 3968.

286 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 84 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×#535C211yesmaximal, characteristic
2C2×C31×#99C212yesmaximal, complemented
3C31×#354C212yesmaximal, complemented
4C31×#353C212yesmaximal, complemented
5C2×#41×C31C411yescharacteristic, complemented
6C22×D4×C31C2211yescharacteristic
7C31×#127C411yescharacteristic, complemented
8C31×#127C2211yescharacteristic
9C31×#124C411yescharacteristic, complemented
10C31×#124C2211yescharacteristic
11C31×#121—22no—
12C31×#120—22no—
13C31×#117C411yescharacteristic, complemented
14C2×C22⋊C4×C31—22no—
15C31×#99—22no—
16C31×#99C2214yes—
17C24×C31D412yes—
18#41×C31—42no—
19C2×Q8×C31C2×C411yescharacteristic, complemented
20C2×D4×C31—21no—
21C2×D4×C31—22no—
22C2×D4×C31—22no—
23C2×D4×C31—42no—
24C2×D4×C31C2×C411yescharacteristic
25C2×D4×C31C2×C411yescharacteristic, complemented
26C2×D4×C31D412yes—
27C2×D4×C31C2311yescharacteristic
28C22×C4×C31—21no—
29C22×C4×C31—42no—
30C22×C4×C31C2×C411yescharacteristic
31C4⋊C4×C31—21no—
32C22⋊C4×C31—22no—
33C22⋊C4×C31—21no—
34C22⋊C4×C31—22no—
35C22⋊C4×C31—24no—
36C22⋊C4×C31—42no—
37C42×C31C2×C411yescharacteristic, complemented
38C42×C31C2×C411yescharacteristic, complemented
39C23×C31—22no—
40C23×C31—22no—
41C23×C31—21no—
42C23×C31—82no—
43C23×C31C22⋊C412yes—
44C23×C31C22⋊C411yescharacteristic
45C23×C31C2×D412yes—
46Q8×C31—41no—
47D4×C31—41no—
48D4×C31—42no—
49D4×C31—41no—
50D4×C31—41no—
51D4×C31—42no—
52D4×C31—82no—
53D4×C31—82no—
54C2×C4×C31—22no—
55C2×C4×C31—21no—
56C2×C4×C31—21no—
57C2×C4×C31—21no—
58C2×C4×C31—42no—
59C2×C4×C31—44no—
60C2×C4×C31—84no—
61C2×C4×C31C22⋊C411yescharacteristic
62C2×C4×C31C22×C411yescharacteristic
63#2127C3111yesmaximal, characteristic, direct product factor, Sylow
64C22×C31—22no—
65C22×C31—22no—
66C22×C31—41no—
67C22×C31—42no—
68C22×C31—42no—
69C22×C31—44no—
70C22×C31—42no—
71C22×C31—41no—
72C22×C31—82no—
73C22×C31#9912yes—
74C22×C31C2×C22⋊C411yescharacteristic
75C4×C31—21no—
76C4×C31—21no—
77C4×C31—41no—
78C4×C31—41no—
79C4×C31—41no—
80C4×C31—84no—
81#535C2×C3111yescharacteristic
82C2×#99C2×C3112yescomplemented
83#354C2×C3112yescomplemented
84#353C2×C3112yescomplemented
85C2×C31—21no—
86C2×C31—22no—
87C2×C31—42no—
88C2×C31—42no—
89C2×C31—81no—
90C2×C31C2×#9911yescharacteristic
91C2×#41C4×C3111yescharacteristic, complemented
92C22×D4C22×C3111yescharacteristic
93#127C4×C3111yescharacteristic, complemented
94#127C22×C3111yescharacteristic
95#124C4×C3111yescharacteristic, complemented
96#124C22×C3111yescharacteristic
97#121—22no—
98#120—22no—
99#117C4×C3111yescharacteristic, complemented
100C2×C22⋊C4—22no—
101#99—22no—
102#99C22×C3114yes—
103C31#212711yescharacteristic, direct product factor, Sylow
104C24D4×C3112yes—
105#41—42no—
106C2×Q8C2×C4×C3111yescharacteristic, complemented
107C2×D4—21no—
108C2×D4—22no—
109C2×D4—22no—
110C2×D4—42no—
111C2×D4C2×C4×C3111yescharacteristic
112C2×D4C2×C4×C3111yescharacteristic, complemented
113C2×D4D4×C3112yes—
114C2×D4C23×C3111yescharacteristic
115C22×C4—21no—
116C22×C4—42no—
117C22×C4C2×C4×C3111yescharacteristic
118C4⋊C4—21no—
119C22⋊C4—21no—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C22⋊C4—24no—
123C22⋊C4—42no—
124C42C2×C4×C3111yescharacteristic, complemented
125C42C2×C4×C3111yescharacteristic, complemented
126C23—22no—
127C23—22no—
128C23—21no—
129C23—82no—
130C23C22⋊C4×C3112yes—
131C23C22⋊C4×C3111yescharacteristic
132C23C2×D4×C3112yes—
133Q8—41no—
134D4—41no—
135D4—42no—
136D4—41no—
137D4—41no—
138D4—42no—
139D4—82no—
140D4—82no—
141C2×C4—22no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—42no—
146C2×C4—44no—
147C2×C4—84no—
148C2×C4C22⋊C4×C3111yescharacteristic
149C2×C4C22×C4×C3111yescharacteristic
150C22—22no—
151C22—22no—
152C22—41no—
153C22—42no—
154C22—42no—
155C22—44no—
156C22—42no—
157C22—41no—
158C22—82no—
159C22C31×#9912yes—
160C22C2×C22⋊C4×C3111yescharacteristic
161C4—21no—
162C4—21no—
163C4—41no—
164C4—41no—
165C4—41no—
166C4—84no—
167C2—21no—
168C2—22no—
169C2—42no—
170C2—42no—
171C2—81no—
172C2C2×C31×#9911yescharacteristic
subgroupG/H
center, socleC2×C31C2×#99
commutatorC2×C4C22×C4×C31
Frattini, cosocleC2×D4C23×C31
prime radicalC31×#535C2
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C23×C31 ◁ C22×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#99C2semidirect
3. C31×#354C2semidirect
4. C31×#353C2semidirect
5. C2×#41×C31C4semidirect
7. C31×#127C4semidirect
9. C31×#124C4semidirect
13. C31×#117C4semidirect
19. C2×Q8×C31C2×C4semidirect
25. C2×D4×C31C2×C4semidirect
37. C42×C31C2×C4semidirect
38. C42×C31C2×C4semidirect
63. #2127C31direct (N × H)
82. C2×#99C2×C31semidirect
83. #354C2×C31semidirect
84. #353C2×C31semidirect
91. C2×#41C4×C31semidirect
93. #127C4×C31semidirect
95. #124C4×C31semidirect
99. #117C4×C31semidirect
103. C31#2127direct (N × H)
106. C2×Q8C2×C4×C31semidirect
112. C2×D4C2×C4×C31semidirect
124. C42C2×C4×C31semidirect
125. C42C2×C4×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#5352
C2×C31×#992
C31×#3542
C31×#3532
#212731