Finite Group Databasebeta

← C31×#10297 #21467056

Subgroups — C31×#10297 #21467056

Order 7936.

528 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 130 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×#3209C212yesmaximal
2C31×#2862C211yesmaximal, characteristic
3C31×#1994C211yesmaximal, characteristic
4C31×#1548C212yesmaximal
5C31×#1276C211yesmaximal, characteristic
6C31×#533C2211yescharacteristic
7C2×C31×C4⋊Q8C2212yes—
8C31×#494—22no—
9C31×#487—22no—
10C31×#462—24no—
11C31×#451—24no—
12C31×#431C2212yes—
13C31×#423C2211yescharacteristic
14C31×#391—24no—
15C31×#382—22no—
16C43×C31C2211yescharacteristic
17C31×#339—22no—
18C31×#333—24no—
19C22×Q8×C31D414yes—
20C2×Q16×C31—28no—
21C2×M16×C31—21no—
22C31×C4⋊Q8—22no—
23C31×C4⋊Q8—22no—
24C31×C4⋊Q8—22no—
25C31×C4⋊Q8—22no—
26C31×C4⋊Q8D412yes—
27C31×#125—21no—
28C31×C22⋊Q8—22no—
29C4×Q8×C31—22no—
30C31×#117—21no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31—22no—
33C2×C42×C31—22no—
34C2×C42×C31D412yes—
35C2×C42×C31C2311yescharacteristic
36C31×C4⋊C8—22no—
37C31×C4⋊C8D414yes—
38C31×#103—28no—
39C31×C22⋊C8—22no—
40C4×C8×C31—22no—
41C31×#95—28no—
42C2×Q8×C31—24no—
43C2×Q8×C31—22no—
44C2×Q8×C31—24no—
45C2×Q8×C31—48no—
46C22×C4×C31—22no—
47C22×C4×C31—24no—
48C22×C4×C31C2×D412yes—
49C22×C4×C31C2×D411yescharacteristic
50Q16×C31—88no—
51M16×C31—42no—
52C2×C8×C31—24no—
53C2×C8×C31—41no—
54C4⋊C4×C31—22no—
55C4⋊C4×C31—22no—
56C4⋊C4×C31—42no—
57C4⋊C4×C31—42no—
58C4⋊C4×C31—42no—
59C4⋊C4×C31—42no—
60C4⋊C4×C31—42no—
61C22⋊C4×C31—41no—
62C42×C31—22no—
63C42×C31—44no—
64C42×C31—41no—
65C42×C31Q1614yescomplemented
66C42×C31C2×D411yescharacteristic
67C42×C31C2×D412yes—
68C42×C31#4111yescharacteristic
69#10297C3111yesmaximal, characteristic, direct product factor, Sylow
70C23×C31#12011yescharacteristic
71Q8×C31—44no—
72Q8×C31—48no—
73Q8×C31—84no—
74C2×C4×C31—24no—
75C2×C4×C31—24no—
76C2×C4×C31—44no—
77C2×C4×C31—48no—
78C2×C4×C31—42no—
79C2×C4×C31—44no—
80C2×C4×C31#12012yes—
81C2×C4×C31#12112yes—
82C2×C4×C31#12111yescharacteristic
83C2×C4×C31#12711yescharacteristic
84C2×C4×C31C2×Q1612yes—
85C2×C4×C31#13712yes—
86C8×C31—44no—
87C8×C31—81no—
88#3209C2×C3112yes—
89#2862C2×C3111yescharacteristic
90#1994C2×C3111yescharacteristic
91#1548C2×C3112yes—
92#1276C2×C3111yescharacteristic
93C22×C31—22no—
94C22×C31#39211yescharacteristic
95C22×C31#45112yes—
96C4×C31—22no—
97C4×C31—44no—
98C4×C31—84no—
99C4×C31—82no—
100C4×C31#45514yes—
101C4×C31#46212yes—
102C4×C31#49411yescharacteristic
103C4×C31#49711yescharacteristic
104#533C22×C3111yescharacteristic
105C2×C4⋊Q8C22×C3112yes—
106#494—22no—
107#487—22no—
108#462—24no—
109#451—24no—
110#431C22×C3112yes—
111#423C22×C3111yescharacteristic
112#391—24no—
113#382—22no—
114C43C22×C3111yescharacteristic
115#339—22no—
116#333—24no—
117C2×C31—22no—
118C2×C31#200412yes—
119C2×C31#201611yescharacteristic
120C22×Q8D4×C3114yes—
121C2×Q16—28no—
122C2×M16—21no—
123C4⋊Q8—22no—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4⋊Q8—22no—
127C4⋊Q8D4×C3112yes—
128#125—21no—
129C22⋊Q8—22no—
130C4×Q8—22no—
131#117—21no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C42—22no—
135C2×C42D4×C3112yes—
136C2×C42C23×C3111yescharacteristic
137C4⋊C8—22no—
138C4⋊C8D4×C3114yes—
139#103—28no—
140C22⋊C8—22no—
141C4×C8—22no—
142#95—28no—
143C31#1029711yescharacteristic, direct product factor, Sylow
144C2×Q8—24no—
145C2×Q8—22no—
146C2×Q8—24no—
147C2×Q8—48no—
148C22×C4—22no—
149C22×C4—24no—
150C22×C4C2×D4×C3112yes—
151C22×C4C2×D4×C3111yescharacteristic
152Q16—88no—
153M16—42no—
154C2×C8—24no—
155C2×C8—41no—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C4⋊C4—42no—
163C22⋊C4—41no—
164C42—22no—
165C42—44no—
166C42—41no—
167C42Q16×C3114yescomplemented
168C42C2×D4×C3111yescharacteristic
169C42C2×D4×C3112yes—
170C42#41×C3111yescharacteristic
171C23C31×#12011yescharacteristic
172Q8—44no—
173Q8—48no—
174Q8—84no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—44no—
178C2×C4—48no—
179C2×C4—42no—
180C2×C4—44no—
181C2×C4C31×#12012yes—
182C2×C4C31×#12112yes—
183C2×C4C31×#12111yescharacteristic
184C2×C4C31×#12711yescharacteristic
185C2×C4C2×Q16×C3112yes—
186C2×C4C31×#13712yes—
187C8—44no—
188C8—81no—
189C22—22no—
190C22C31×#39211yescharacteristic
191C22C31×#45112yes—
192C4—22no—
193C4—44no—
194C4—84no—
195C4—82no—
196C4C31×#45514yes—
197C4C31×#46212yes—
198C4C31×#49411yescharacteristic
199C4C31×#49711yescharacteristic
200C2—22no—
201C2C31×#200412yes—
202C2C31×#201611yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC23×C31#120
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
65. C42×C31Q16semidirect
69. #10297C31direct (N × H)
143. C31#10297direct (N × H)
167. C42Q16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#32092
C31×#28622
C31×#19942
C31×#15482
C31×#12762
#1029731