Finite Group Databasebeta

← C31×#10524 #21467283

Subgroups — C31×#10524 #21467283

Order 7936.

386 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3253C211yesmaximal, characteristic
2C31×#1849C211yesmaximal, characteristic, complemented
3C31×#1557C212yesmaximal, complemented
4C31×#1530C212yesmaximal, complemented
5C31×#1307C211yesmaximal, characteristic, complemented
6C31×#532C2212yes—
7C31×#476—22no—
8C31×#469—22no—
9C31×#459—22no—
10C31×#432C2212yes—
11C2×C31×#108—22no—
12C31×#423C2211yescharacteristic
13C31×#423C2211yescharacteristic
14C2×C31×#97C2211yescharacteristic
15C31×#332—22no—
16C31×#331—22no—
17C31×#329—24no—
18C2×#41×C31—22no—
19C2×D8×C31—22no—
20C2×M16×C31—21no—
21C2×M16×C31D412yes—
22C22×C8×C31—21no—
23C31×C4⋊Q8D412yes—
24C31×#127D412yes—
25C31×#124—22no—
26C31×#121—22no—
27C31×#121—22no—
28C4×D4×C31—22no—
29C4×D4×C31—22no—
30C2×C42×C31C2311yescharacteristic
31C31×#108—44no—
32C31×#106—22no—
33C31×C4⋊C8—22no—
34C31×C4⋊C8—22no—
35C31×C4⋊C8—22no—
36C31×#102—24no—
37C31×C22⋊C8—22no—
38C31×#97—22no—
39C31×#97—21no—
40C31×#97D412yes—
41#41×C31—84no—
42C2×Q8×C31—22no—
43C2×D4×C31—22no—
44C2×D4×C31—22no—
45C2×D4×C31—22no—
46C2×D4×C31—42no—
47C22×C4×C31—42no—
48C22×C4×C31C2×D411yescharacteristic
49C22×C4×C31#4112yes—
50D8×C31—82no—
51M16×C31—42no—
52M16×C31—42no—
53C2×C8×C31—22no—
54C2×C8×C31—22no—
55C2×C8×C31—22no—
56C2×C8×C31—22no—
57C2×C8×C31—41no—
58C2×C8×C31—42no—
59C4⋊C4×C31—22no—
60C4⋊C4×C31—22no—
61C22⋊C4×C31—42no—
62C22⋊C4×C31—42no—
63C42×C31C2×D412yes—
64C42×C31C2×D411yescharacteristic
65C42×C31#4111yescharacteristic
66#10524C3111yesmaximal, characteristic, direct product factor, Sylow
67C23×C31—42no—
68C23×C31#12411yescharacteristic
69Q8×C31—82no—
70D4×C31—42no—
71D4×C31—42no—
72D4×C31—82no—
73D4×C31—82no—
74D4×C31—84no—
75C2×C4×C31—21no—
76C2×C4×C31—21no—
77C2×C4×C31—42no—
78C2×C4×C31—42no—
79C2×C4×C31—84no—
80C2×C4×C31#12011yescharacteristic
81C2×C4×C31#12112yes—
82C2×C4×C31#12111yescharacteristic
83C2×C4×C31#12312yes—
84C8×C31—24no—
85C8×C31—42no—
86C8×C31—82no—
87C8×C31—81no—
88#3253C2×C3111yescharacteristic
89#1849C2×C3111yescharacteristic, complemented
90#1557C2×C3112yescomplemented
91#1530C2×C3112yescomplemented
92#1307C2×C3111yescharacteristic, complemented
93C22×C31—22no—
94C22×C31—21no—
95C22×C31—82no—
96C22×C31—82no—
97C22×C31—82no—
98C22×C31#39411yescharacteristic
99C4×C31—22no—
100C4×C31—22no—
101C4×C31—21no—
102C4×C31—82no—
103C4×C31#45311yescharacteristic
104C4×C31#45611yescharacteristic
105#532C22×C3112yes—
106#476—22no—
107#469—22no—
108#459—22no—
109#432C22×C3112yes—
110C2×#108—22no—
111#423C22×C3111yescharacteristic
112#423C22×C3111yescharacteristic
113C2×#97C22×C3111yescharacteristic
114#332—22no—
115#331—22no—
116#329—24no—
117C2×C31—41no—
118C2×C31—162no—
119C2×C31#203911yescharacteristic
120C2×C31#204812yes—
121C2×#41—22no—
122C2×D8—22no—
123C2×M16—21no—
124C2×M16D4×C3112yes—
125C22×C8—21no—
126C4⋊Q8D4×C3112yes—
127#127D4×C3112yes—
128#124—22no—
129#121—22no—
130#121—22no—
131C4×D4—22no—
132C4×D4—22no—
133C2×C42C23×C3111yescharacteristic
134#108—44no—
135#106—22no—
136C4⋊C8—22no—
137C4⋊C8—22no—
138C4⋊C8—22no—
139#102—24no—
140C22⋊C8—22no—
141#97—22no—
142#97—21no—
143#97D4×C3112yes—
144C31#1052411yescharacteristic, direct product factor, Sylow
145#41—84no—
146C2×Q8—22no—
147C2×D4—22no—
148C2×D4—22no—
149C2×D4—22no—
150C2×D4—42no—
151C22×C4—42no—
152C22×C4C2×D4×C3111yescharacteristic
153C22×C4#41×C3112yes—
154D8—82no—
155M16—42no—
156M16—42no—
157C2×C8—22no—
158C2×C8—22no—
159C2×C8—22no—
160C2×C8—22no—
161C2×C8—41no—
162C2×C8—42no—
163C4⋊C4—22no—
164C4⋊C4—22no—
165C22⋊C4—42no—
166C22⋊C4—42no—
167C42C2×D4×C3112yes—
168C42C2×D4×C3111yescharacteristic
169C42#41×C3111yescharacteristic
170C23—42no—
171C23C31×#12411yescharacteristic
172Q8—82no—
173D4—42no—
174D4—42no—
175D4—82no—
176D4—82no—
177D4—84no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—84no—
183C2×C4C31×#12011yescharacteristic
184C2×C4C31×#12112yes—
185C2×C4C31×#12111yescharacteristic
186C2×C4C31×#12312yes—
187C8—24no—
188C8—42no—
189C8—82no—
190C8—81no—
191C22—21no—
192C22—22no—
193C22—82no—
194C22—82no—
195C22—82no—
196C22C31×#39411yescharacteristic
197C4—21no—
198C4—22no—
199C4—22no—
200C4—82no—
201C4C31×#45311yescharacteristic
202C4C31×#45611yescharacteristic
203C2—41no—
204C2—162no—
205C2C31×#203911yescharacteristic
206C2C31×#204812yes—
subgroupG/H
center, socleC22×C31#394
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3253C2
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
2. C31×#1849C2semidirect
3. C31×#1557C2semidirect
4. C31×#1530C2semidirect
5. C31×#1307C2semidirect
66. #10524C31direct (N × H)
89. #1849C2×C31semidirect
90. #1557C2×C31semidirect
91. #1530C2×C31semidirect
92. #1307C2×C31semidirect
144. C31#10524direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32532
C31×#18492
C31×#15572
C31×#15302
C31×#13072
#1052431