Finite Group Databasebeta

← C31×#9436 #21466195

Subgroups — C31×#9436 #21466195

Order 7936.

400 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 126 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×#3139C211yesmaximal, characteristic
2C31×#2986C211yesmaximal, characteristic
3C31×#1561C211yesmaximal, characteristic
4C31×#1549C212yesmaximal
5C31×#1299C212yesmaximal
6C31×#533C2211yescharacteristic
7C2×C31×C4⋊Q8C2211yescharacteristic
8C31×#491C414yes—
9C31×#487—22no—
10C31×#446—22no—
11C8×Q8×C31—22no—
12C31×#433—22no—
13C31×#431C2212yes—
14C31×#423C2212yes—
15C31×#419—22no—
16C4×M16×C31C2211yescharacteristic
17C31×#332—22no—
18C31×#332—22no—
19C31×#332—22no—
20C22×Q8×C31—21no—
21C2×M16×C31—21no—
22C2×M16×C31—22no—
23C31×C4⋊Q8—22no—
24C31×C4⋊Q8—21no—
25C31×C4⋊Q8C2×C412yes—
26C31×C4⋊Q8D412yes—
27C31×#125C2×C412yes—
28C31×C22⋊Q8—22no—
29C4×Q8×C31—22no—
30C31×#117D412yes—
31C2×C4⋊C4×C31—22no—
32C2×C42×C31C2311yescharacteristic
33C31×C4⋊C8—24no—
34C31×C4⋊C8—22no—
35C31×C4⋊C8—22no—
36C31×C4⋊C8D412yes—
37C31×C4⋊C8D412yes—
38C31×#103—28no—
39C31×C22⋊C8—22no—
40C31×#97—22no—
41C31×#97C2×C412yes—
42C4×C8×C31—22no—
43C4×C8×C31—21no—
44C4×C8×C31—22no—
45C2×Q8×C31—22no—
46C2×Q8×C31—22no—
47C2×Q8×C31—44no—
48C2×Q8×C31—41no—
49C22×C4×C31—41no—
50C22×C4×C31C2×D411yescharacteristic
51C22×C4×C31#4112yes—
52M16×C31—42no—
53M16×C31—82no—
54C2×C8×C31—22no—
55C2×C8×C31—22no—
56C2×C8×C31—22no—
57C2×C8×C31—42no—
58C4⋊C4×C31—24no—
59C4⋊C4×C31—22no—
60C4⋊C4×C31—24no—
61C4⋊C4×C31—42no—
62C4⋊C4×C31C22⋊C414yes—
63C22⋊C4×C31—22no—
64C42×C31—22no—
65C42×C31C22×C411yescharacteristic
66C42×C31C2×D411yescharacteristic
67C42×C31C2×D412yes—
68#9436C3111yesmaximal, characteristic, direct product factor, Sylow
69C23×C31#12311yescharacteristic
70Q8×C31—44no—
71Q8×C31—42no—
72Q8×C31—42no—
73Q8×C31—82no—
74C2×C4×C31—22no—
75C2×C4×C31—22no—
76C2×C4×C31—22no—
77C2×C4×C31—24no—
78C2×C4×C31—42no—
79C2×C4×C31—82no—
80C2×C4×C31C2×C22⋊C411yescharacteristic
81C2×C4×C31C4×D412yes—
82C2×C4×C31#12011yescharacteristic
83C2×C4×C31#12112yes—
84C8×C31—42no—
85C8×C31—42no—
86C8×C31—42no—
87C8×C31—82no—
88#3139C2×C3111yescharacteristic
89#2986C2×C3111yescharacteristic
90#1561C2×C3111yescharacteristic
91#1549C2×C3112yes—
92#1299C2×C3112yes—
93C22×C31—21no—
94C22×C31—22no—
95C22×C31#38611yescharacteristic
96C4×C31—21no—
97C4×C31—22no—
98C4×C31—44no—
99C4×C31—82no—
100C4×C31#45412yes—
101C4×C31#47112yes—
102C4×C31#47312yes—
103#533C22×C3111yescharacteristic
104C2×C4⋊Q8C22×C3111yescharacteristic
105#491C4×C3114yes—
106#487—22no—
107#446—22no—
108C8×Q8—22no—
109#433—22no—
110#431C22×C3112yes—
111#423C22×C3112yes—
112#419—22no—
113C4×M16C22×C3111yescharacteristic
114#332—22no—
115#332—22no—
116#332—22no—
117C2×C31—41no—
118C2×C31#188811yescharacteristic
119C2×C31#190812yes—
120C22×Q8—21no—
121C2×M16—21no—
122C2×M16—22no—
123C4⋊Q8—22no—
124C4⋊Q8—21no—
125C4⋊Q8C2×C4×C3112yes—
126C4⋊Q8D4×C3112yes—
127#125C2×C4×C3112yes—
128C22⋊Q8—22no—
129C4×Q8—22no—
130#117D4×C3112yes—
131C2×C4⋊C4—22no—
132C2×C42C23×C3111yescharacteristic
133C4⋊C8—24no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8D4×C3112yes—
137C4⋊C8D4×C3112yes—
138#103—28no—
139C22⋊C8—22no—
140#97—22no—
141#97C2×C4×C3112yes—
142C4×C8—22no—
143C4×C8—21no—
144C4×C8—22no—
145C31#943611yescharacteristic, direct product factor, Sylow
146C2×Q8—22no—
147C2×Q8—22no—
148C2×Q8—44no—
149C2×Q8—41no—
150C22×C4—41no—
151C22×C4C2×D4×C3111yescharacteristic
152C22×C4#41×C3112yes—
153M16—42no—
154M16—82no—
155C2×C8—22no—
156C2×C8—22no—
157C2×C8—22no—
158C2×C8—42no—
159C4⋊C4—24no—
160C4⋊C4—22no—
161C4⋊C4—24no—
162C4⋊C4—42no—
163C4⋊C4C22⋊C4×C3114yes—
164C22⋊C4—22no—
165C42—22no—
166C42C22×C4×C3111yescharacteristic
167C42C2×D4×C3111yescharacteristic
168C42C2×D4×C3112yes—
169C23C31×#12311yescharacteristic
170Q8—44no—
171Q8—42no—
172Q8—42no—
173Q8—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—42no—
179C2×C4—82no—
180C2×C4C2×C22⋊C4×C3111yescharacteristic
181C2×C4C4×D4×C3112yes—
182C2×C4C31×#12011yescharacteristic
183C2×C4C31×#12112yes—
184C8—42no—
185C8—42no—
186C8—42no—
187C8—82no—
188C22—21no—
189C22—22no—
190C22C31×#38611yescharacteristic
191C4—21no—
192C4—22no—
193C4—44no—
194C4—82no—
195C4C31×#45412yes—
196C4C31×#47112yes—
197C4C31×#47312yes—
198C2—41no—
199C2C31×#188811yescharacteristic
200C2C31×#190812yes—
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC23×C31#123
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
68. #9436C31direct (N × H)
145. C31#9436direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31392
C31×#29862
C31×#15612
C31×#15492
C31×#12992
#943631