Finite Group Databasebeta

← C31×#10525 #21467284

Subgroups — C31×#10525 #21467284

Order 7936.

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

normal subgroups only

This group has 370 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×#1838C211yesmaximal, 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—
11C31×#423C2211yescharacteristic
12C31×#423C2211yescharacteristic
13C2×C31×#97C2211yescharacteristic
14C31×#341—22no—
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×#106—22no—
32C31×C4⋊C8—22no—
33C31×C4⋊C8—22no—
34C31×C4⋊C8—22no—
35C31×#102—24no—
36C31×C22⋊C8—22no—
37C31×#97—22no—
38C31×#97—21no—
39C31×#97D412yes—
40#41×C31—84no—
41C2×Q8×C31—22no—
42C2×D4×C31—22no—
43C2×D4×C31—22no—
44C2×D4×C31—22no—
45C2×D4×C31—42no—
46C22×C4×C31—42no—
47C22×C4×C31C2×D411yescharacteristic
48C22×C4×C31#4112yes—
49D8×C31—82no—
50M16×C31—42no—
51M16×C31—42no—
52C2×C8×C31—22no—
53C2×C8×C31—22no—
54C2×C8×C31—41no—
55C2×C8×C31—41no—
56C2×C8×C31—41no—
57C2×C8×C31—42no—
58C4⋊C4×C31—22no—
59C4⋊C4×C31—22no—
60C22⋊C4×C31—42no—
61C22⋊C4×C31—42no—
62C42×C31C2×D412yes—
63C42×C31C2×D411yescharacteristic
64C42×C31#4111yescharacteristic
65#10525C3111yesmaximal, characteristic, direct product factor, Sylow
66C23×C31—42no—
67C23×C31#12411yescharacteristic
68Q8×C31—82no—
69D4×C31—42no—
70D4×C31—42no—
71D4×C31—82no—
72D4×C31—82no—
73D4×C31—84no—
74C2×C4×C31—21no—
75C2×C4×C31—21no—
76C2×C4×C31—42no—
77C2×C4×C31—42no—
78C2×C4×C31—84no—
79C2×C4×C31#12011yescharacteristic
80C2×C4×C31#12112yes—
81C2×C4×C31#12111yescharacteristic
82C2×C4×C31#12312yes—
83C8×C31—42no—
84C8×C31—42no—
85C8×C31—82no—
86C8×C31—81no—
87#3253C2×C3111yescharacteristic
88#1838C2×C3111yescharacteristic, complemented
89#1557C2×C3112yescomplemented
90#1530C2×C3112yescomplemented
91#1307C2×C3111yescharacteristic, complemented
92C22×C31—22no—
93C22×C31—21no—
94C22×C31—82no—
95C22×C31—82no—
96C22×C31—82no—
97C22×C31#39411yescharacteristic
98C4×C31—22no—
99C4×C31—22no—
100C4×C31—21no—
101C4×C31—82no—
102C4×C31#45411yescharacteristic
103C4×C31#45511yescharacteristic
104#532C22×C3112yes—
105#476—22no—
106#469—22no—
107#459—22no—
108#432C22×C3112yes—
109#423C22×C3111yescharacteristic
110#423C22×C3111yescharacteristic
111C2×#97C22×C3111yescharacteristic
112#341—22no—
113#332—22no—
114#331—22no—
115#329—24no—
116C2×C31—41no—
117C2×C31—162no—
118C2×C31#204011yescharacteristic
119C2×C31#204812yes—
120C2×#41—22no—
121C2×D8—22no—
122C2×M16—21no—
123C2×M16D4×C3112yes—
124C22×C8—21no—
125C4⋊Q8D4×C3112yes—
126#127D4×C3112yes—
127#124—22no—
128#121—22no—
129#121—22no—
130C4×D4—22no—
131C4×D4—22no—
132C2×C42C23×C3111yescharacteristic
133#106—22no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137#102—24no—
138C22⋊C8—22no—
139#97—22no—
140#97—21no—
141#97D4×C3112yes—
142C31#1052511yescharacteristic, direct product factor, Sylow
143#41—84no—
144C2×Q8—22no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—22no—
148C2×D4—42no—
149C22×C4—42no—
150C22×C4C2×D4×C3111yescharacteristic
151C22×C4#41×C3112yes—
152D8—82no—
153M16—42no—
154M16—42no—
155C2×C8—22no—
156C2×C8—22no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—42no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C22⋊C4—42no—
164C22⋊C4—42no—
165C42C2×D4×C3112yes—
166C42C2×D4×C3111yescharacteristic
167C42#41×C3111yescharacteristic
168C23—42no—
169C23C31×#12411yescharacteristic
170Q8—82no—
171D4—42no—
172D4—42no—
173D4—82no—
174D4—82no—
175D4—84no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—84no—
181C2×C4C31×#12011yescharacteristic
182C2×C4C31×#12112yes—
183C2×C4C31×#12111yescharacteristic
184C2×C4C31×#12312yes—
185C8—42no—
186C8—42no—
187C8—82no—
188C8—81no—
189C22—21no—
190C22—22no—
191C22—82no—
192C22—82no—
193C22—82no—
194C22C31×#39411yescharacteristic
195C4—21no—
196C4—22no—
197C4—22no—
198C4—82no—
199C4C31×#45411yescharacteristic
200C4C31×#45511yescharacteristic
201C2—41no—
202C2—162no—
203C2C31×#204011yescharacteristic
204C2C31×#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×#1838C2semidirect
3. C31×#1557C2semidirect
4. C31×#1530C2semidirect
5. C31×#1307C2semidirect
65. #10525C31direct (N × H)
88. #1838C2×C31semidirect
89. #1557C2×C31semidirect
90. #1530C2×C31semidirect
91. #1307C2×C31semidirect
142. C31#10525direct (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×#18382
C31×#15572
C31×#15302
C31×#13072
#1052531