Finite Group Databasebeta

← C31×#10534 #21467293

Subgroups — C31×#10534 #21467293

Order 7936.

358 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3255C211yesmaximal, characteristic
2C31×#1848C211yesmaximal, characteristic
3C31×#1561C212yesmaximal
4C31×#1493C212yesmaximal
5C31×#1309C211yesmaximal, characteristic
6C31×#533C2212yes—
7C31×#475—22no—
8C31×#470—22no—
9C31×#462—22no—
10C2×C31×#108—22no—
11C31×#423C2211yescharacteristic
12C31×#423C2212yes—
13C31×#423C2211yescharacteristic
14C2×C4×C8×C31C2211yescharacteristic
15C31×#332—22no—
16C31×#332—22no—
17C31×Q8⋊C8—24no—
18C2×Q16×C31—22no—
19C2×M16×C31—21no—
20C2×M16×C31—22no—
21C2×M16×C31D412yes—
22C22×C8×C31—21no—
23C31×C4⋊Q8D412yes—
24C31×C4⋊Q8D412yes—
25C31×#125—22no—
26C31×C22⋊Q8—22no—
27C31×C22⋊Q8—22no—
28C4×Q8×C31—22no—
29C4×Q8×C31—22no—
30C31×#117—22no—
31C2×C42×C31C2311yescharacteristic
32C31×#108—44no—
33C31×#106—22no—
34C31×C4⋊C8—22no—
35C31×C4⋊C8—22no—
36C31×C4⋊C8—22no—
37C31×C4⋊C8—22no—
38C31×#103—24no—
39C4×C8×C31—21no—
40C4×C8×C31D412yes—
41C2×Q8×C31—22no—
42C2×Q8×C31—22no—
43C22×C4×C31C2×D411yescharacteristic
44C22×C4×C31#4112yes—
45Q16×C31—82no—
46M16×C31—42no—
47M16×C31—42no—
48M16×C31—82no—
49C2×C8×C31—22no—
50C2×C8×C31—22no—
51C2×C8×C31—22no—
52C2×C8×C31—22no—
53C2×C8×C31—41no—
54C2×C8×C31—42no—
55C4⋊C4×C31—22no—
56C4⋊C4×C31—22no—
57C4⋊C4×C31—22no—
58C4⋊C4×C31—22no—
59C4⋊C4×C31—42no—
60C4⋊C4×C31—42no—
61C22⋊C4×C31—42no—
62C42×C31—42no—
63C42×C31C2×D412yes—
64C42×C31C2×D411yescharacteristic
65C42×C31#4111yescharacteristic
66#10534C3111yesmaximal, characteristic, direct product factor, Sylow
67C23×C31#12411yescharacteristic
68Q8×C31—42no—
69Q8×C31—42no—
70Q8×C31—42no—
71Q8×C31—42no—
72C2×C4×C31—21no—
73C2×C4×C31—21no—
74C2×C4×C31—22no—
75C2×C4×C31—22no—
76C2×C4×C31—42no—
77C2×C4×C31—42no—
78C2×C4×C31#12011yescharacteristic
79C2×C4×C31#12111yescharacteristic
80C2×C4×C31#12112yes—
81C2×C4×C31#12312yes—
82C8×C31—24no—
83C8×C31—42no—
84C8×C31—81no—
85C8×C31—82no—
86#3255C2×C3111yescharacteristic
87#1848C2×C3111yescharacteristic
88#1561C2×C3112yes—
89#1493C2×C3112yes—
90#1309C2×C3111yescharacteristic
91C22×C31—22no—
92C22×C31—21no—
93C22×C31#39411yescharacteristic
94C4×C31—22no—
95C4×C31—21no—
96C4×C31—82no—
97C4×C31—82no—
98C4×C31#45311yescharacteristic
99C4×C31#45611yescharacteristic
100C4×C31#47112yes—
101C4×C31#47312yes—
102#533C22×C3112yes—
103#475—22no—
104#470—22no—
105#462—22no—
106C2×#108—22no—
107#423C22×C3111yescharacteristic
108#423C22×C3112yes—
109#423C22×C3111yescharacteristic
110C2×C4×C8C22×C3111yescharacteristic
111#332—22no—
112#332—22no—
113Q8⋊C8—24no—
114C2×C31—41no—
115C2×C31#203911yescharacteristic
116C2×C31#205212yes—
117C2×Q16—22no—
118C2×M16—21no—
119C2×M16—22no—
120C2×M16D4×C3112yes—
121C22×C8—21no—
122C4⋊Q8D4×C3112yes—
123C4⋊Q8D4×C3112yes—
124#125—22no—
125C22⋊Q8—22no—
126C22⋊Q8—22no—
127C4×Q8—22no—
128C4×Q8—22no—
129#117—22no—
130C2×C42C23×C3111yescharacteristic
131#108—44no—
132#106—22no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137#103—24no—
138C4×C8—21no—
139C4×C8D4×C3112yes—
140C31#1053411yescharacteristic, direct product factor, Sylow
141C2×Q8—22no—
142C2×Q8—22no—
143C22×C4C2×D4×C3111yescharacteristic
144C22×C4#41×C3112yes—
145Q16—82no—
146M16—42no—
147M16—42no—
148M16—82no—
149C2×C8—22no—
150C2×C8—22no—
151C2×C8—22no—
152C2×C8—22no—
153C2×C8—41no—
154C2×C8—42no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C22⋊C4—42no—
162C42—42no—
163C42C2×D4×C3112yes—
164C42C2×D4×C3111yescharacteristic
165C42#41×C3111yescharacteristic
166C23C31×#12411yescharacteristic
167Q8—42no—
168Q8—42no—
169Q8—42no—
170Q8—42no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4C31×#12011yescharacteristic
178C2×C4C31×#12111yescharacteristic
179C2×C4C31×#12112yes—
180C2×C4C31×#12312yes—
181C8—24no—
182C8—42no—
183C8—81no—
184C8—82no—
185C22—22no—
186C22—21no—
187C22C31×#39411yescharacteristic
188C4—22no—
189C4—21no—
190C4—82no—
191C4—82no—
192C4C31×#45311yescharacteristic
193C4C31×#45611yescharacteristic
194C4C31×#47112yes—
195C4C31×#47312yes—
196C2—41no—
197C2C31×#203911yescharacteristic
198C2C31×#205212yes—
subgroupG/H
center, socleC22×C31#394
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC23×C31#124
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
66. #10534C31direct (N × H)
140. C31#10534direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32552
C31×#18482
C31×#15612
C31×#14932
C31×#13092
#1053431