Finite Group Databasebeta

← C31×#10285 #21467044

Subgroups — C31×#10285 #21467044

Order 7936.

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

normal subgroups only

This group has 542 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×#3227C212yesmaximal
2C31×#2862C211yesmaximal, characteristic, complemented
3C31×#1962C211yesmaximal, characteristic
4C31×#1549C212yesmaximal, complemented
5C31×#1276C211yesmaximal, characteristic, complemented
6C31×#532C2211yescharacteristic
7C2×C31×C4⋊Q8C2212yes—
8C31×#498—22no—
9C31×#486—22no—
10C31×#481—24no—
11C31×#476—24no—
12C31×#431C2212yes—
13C31×#423C2211yescharacteristic
14C2×C31×#104—22no—
15C31×#391—24no—
16C31×#382—22no—
17C43×C31C2211yescharacteristic
18C31×#332—24no—
19C2×#41×C31—21no—
20C22×Q8×C31—22no—
21C2×M16×C31—21no—
22C31×C4⋊Q8—22no—
23C31×C4⋊Q8—22no—
24C31×C4⋊Q8—22no—
25C31×C4⋊Q8—22no—
26C31×C4⋊Q8D411yescharacteristic
27C31×#127D411yescharacteristic
28C31×#124—21no—
29C31×#121—22no—
30C4×D4×C31—22no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31D414yes—
33C2×C42×C31—22no—
34C2×C42×C31D412yes—
35C2×C42×C31C2311yescharacteristic
36C31×#106—28no—
37C31×C4⋊C8—22no—
38C31×C4⋊C8D414yes—
39C31×#104—44no—
40C31×#102—28no—
41C31×C22⋊C8—22no—
42C4×C8×C31—22no—
43C31×#95—28no—
44#41×C31—42no—
45#41×C31—42no—
46C2×Q8×C31—21no—
47C2×Q8×C31—48no—
48C2×Q8×C31—42no—
49C2×Q8×C31—42no—
50C2×D4×C31—22no—
51C2×D4×C31—21no—
52C2×D4×C31—41no—
53C22×C4×C31—22no—
54C22×C4×C31—24no—
55C22×C4×C31—41no—
56C22×C4×C31C2×D412yes—
57C22×C4×C31C2×D411yescharacteristic
58M16×C31—42no—
59C2×C8×C31—24no—
60C2×C8×C31—41no—
61C4⋊C4×C31—24no—
62C4⋊C4×C31—22no—
63C4⋊C4×C31—24no—
64C4⋊C4×C31—42no—
65C4⋊C4×C31—42no—
66C22⋊C4×C31—42no—
67C42×C31—22no—
68C42×C31—44no—
69C42×C31SD1614yes—
70C42×C31C2×D411yescharacteristic
71C42×C31C2×D412yes—
72C42×C31#4111yescharacteristic
73#10285C3111yesmaximal, characteristic, direct product factor, Sylow
74C23×C31—41no—
75C23×C31#12011yescharacteristic
76Q8×C31—42no—
77Q8×C31—84no—
78Q8×C31—84no—
79D4×C31—44no—
80D4×C31—42no—
81D4×C31—82no—
82C2×C4×C31—24no—
83C2×C4×C31—24no—
84C2×C4×C31—44no—
85C2×C4×C31—48no—
86C2×C4×C31—41no—
87C2×C4×C31—44no—
88C2×C4×C31—81no—
89C2×C4×C31—81no—
90C2×C4×C31#12012yes—
91C2×C4×C31#12112yes—
92C2×C4×C31#12111yescharacteristic
93C2×C4×C31#12711yescharacteristic
94C2×C4×C31C2×SD1612yes—
95C2×C4×C31#13712yes—
96C8×C31—44no—
97C8×C31—81no—
98#3227C2×C3112yes—
99#2862C2×C3111yescharacteristic, complemented
100#1962C2×C3111yescharacteristic
101#1549C2×C3112yescomplemented
102#1276C2×C3111yescharacteristic, complemented
103C22×C31—22no—
104C22×C31—82no—
105C22×C31—81no—
106C22×C31#39211yescharacteristic
107C22×C31#44812yes—
108C4×C31—22no—
109C4×C31—44no—
110C4×C31—84no—
111C4×C31—81no—
112C4×C31#45414yes—
113C4×C31#46112yes—
114C4×C31#49211yescharacteristic
115C4×C31#49711yescharacteristic
116#532C22×C3111yescharacteristic
117C2×C4⋊Q8C22×C3112yes—
118#498—22no—
119#486—22no—
120#481—24no—
121#476—24no—
122#431C22×C3112yes—
123#423C22×C3111yescharacteristic
124C2×#104—22no—
125#391—24no—
126#382—22no—
127C43C22×C3111yescharacteristic
128#332—24no—
129C2×C31—22no—
130C2×C31—161no—
131C2×C31#200312yes—
132C2×C31#201311yescharacteristic
133C2×#41—21no—
134C22×Q8—22no—
135C2×M16—21no—
136C4⋊Q8—22no—
137C4⋊Q8—22no—
138C4⋊Q8—22no—
139C4⋊Q8—22no—
140C4⋊Q8D4×C3111yescharacteristic
141#127D4×C3111yescharacteristic
142#124—21no—
143#121—22no—
144C4×D4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4D4×C3114yes—
147C2×C42—22no—
148C2×C42D4×C3112yes—
149C2×C42C23×C3111yescharacteristic
150#106—28no—
151C4⋊C8—22no—
152C4⋊C8D4×C3114yes—
153#104—44no—
154#102—28no—
155C22⋊C8—22no—
156C4×C8—22no—
157#95—28no—
158C31#1028511yescharacteristic, direct product factor, Sylow
159#41—42no—
160#41—42no—
161C2×Q8—21no—
162C2×Q8—48no—
163C2×Q8—42no—
164C2×Q8—42no—
165C2×D4—22no—
166C2×D4—21no—
167C2×D4—41no—
168C22×C4—22no—
169C22×C4—24no—
170C22×C4—41no—
171C22×C4C2×D4×C3112yes—
172C22×C4C2×D4×C3111yescharacteristic
173M16—42no—
174C2×C8—24no—
175C2×C8—41no—
176C4⋊C4—24no—
177C4⋊C4—22no—
178C4⋊C4—24no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C22⋊C4—42no—
182C42—22no—
183C42—44no—
184C42SD16×C3114yes—
185C42C2×D4×C3111yescharacteristic
186C42C2×D4×C3112yes—
187C42#41×C3111yescharacteristic
188C23—41no—
189C23C31×#12011yescharacteristic
190Q8—42no—
191Q8—84no—
192Q8—84no—
193D4—44no—
194D4—42no—
195D4—82no—
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—44no—
199C2×C4—48no—
200C2×C4—41no—
201C2×C4—44no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4C31×#12012yes—
205C2×C4C31×#12112yes—
206C2×C4C31×#12111yescharacteristic
207C2×C4C31×#12711yescharacteristic
208C2×C4C2×SD16×C3112yes—
209C2×C4C31×#13712yes—
210C8—44no—
211C8—81no—
212C22—22no—
213C22—82no—
214C22—81no—
215C22C31×#39211yescharacteristic
216C22C31×#44812yes—
217C4—22no—
218C4—44no—
219C4—84no—
220C4—81no—
221C4C31×#45414yes—
222C4C31×#46112yes—
223C4C31×#49211yescharacteristic
224C4C31×#49711yescharacteristic
225C2—22no—
226C2—161no—
227C2C31×#200312yes—
228C2C31×#201311yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC31×#532C22
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×#2862C2semidirect
4. C31×#1549C2semidirect
5. C31×#1276C2semidirect
73. #10285C31direct (N × H)
99. #2862C2×C31semidirect
101. #1549C2×C31semidirect
102. #1276C2×C31semidirect
158. C31#10285direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32272
C31×#28622
C31×#19622
C31×#15492
C31×#12762
#1028531