Finite Group Databasebeta

← C31×#13585 #21470344

Subgroups — C31×#13585 #21470344

Order 7936.

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

normal subgroups only

This group has 458 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×#3151C211yesmaximal, characteristic
2C31×#2126C212yesmaximal, complemented
3C31×#1408C214yesmaximal, complemented
4C2×C31×AGL(1,ℤ/8)—22no—
5C31×#532C2211yescharacteristic
6C2×C31×#127C411yescharacteristic, complemented
7C31×#496—22no—
8C31×#493C2212yes—
9C31×#492C412yescomplemented
10C31×#410—22no—
11C4×M16×C31C411yescharacteristic, complemented
12C31×#354—22no—
13C31×#353C2214yescomplemented
14C2×#41×C31D412yes—
15C22×D4×C31—21no—
16C22×D4×C31—41no—
17C31×AGL(1,ℤ/8)—44no—
18C31×AGL(1,ℤ/8)—44no—
19C2×SD16×C31—24no—
20C2×D8×C31—24no—
21C2×M16×C31—21no—
22C31×C4⋊Q8C2×C411yescharacteristic
23C31×#127—21no—
24C31×#127—41no—
25C31×#127C2×C412yes—
26C31×#127C2311yescharacteristic
27C31×#124D412yes—
28C31×#121—41no—
29C4×D4×C31—41no—
30C31×#117—42no—
31C2×C42×C31C2×C411yescharacteristic
32C31×#99—24no—
33C31×#99—42no—
34C31×#97—21no—
35C4×C8×C31C2×C412yes—
36C24×C31—41no—
37#41×C31—42no—
38#41×C31—42no—
39C2×Q8×C31C22⋊C412yes—
40C2×D4×C31—22no—
41C2×D4×C31—22no—
42C2×D4×C31—42no—
43C2×D4×C31—42no—
44C2×D4×C31—41no—
45C2×D4×C31—42no—
46C2×D4×C31—42no—
47C2×D4×C31—41no—
48C2×D4×C31—84no—
49C2×D4×C31C2×D412yes—
50C22×C4×C31—21no—
51C22×C4×C31—22no—
52C22×C4×C31C22⋊C411yescharacteristic
53SD16×C31—48no—
54D8×C31—48no—
55M16×C31—24no—
56C2×C8×C31—22no—
57C4⋊C4×C31—41no—
58C4⋊C4×C31—82no—
59C22⋊C4×C31—42no—
60C22⋊C4×C31—44no—
61C42×C31—21no—
62C42×C31—82no—
63C42×C31C22⋊C411yescharacteristic
64C42×C31C22×C411yescharacteristic
65#13585C3111yesmaximal, characteristic, direct product factor, Sylow
66C23×C31—22no—
67C23×C31—42no—
68C23×C31—81no—
69C23×C31—81no—
70C23×C31—84no—
71C23×C31#9911yescharacteristic
72Q8×C31—42no—
73D4×C31—42no—
74D4×C31—44no—
75D4×C31—82no—
76D4×C31—84no—
77D4×C31—82no—
78D4×C31—84no—
79D4×C31—82no—
80C2×C4×C31—21no—
81C2×C4×C31—22no—
82C2×C4×C31—21no—
83C2×C4×C31—22no—
84C2×C4×C31—42no—
85C2×C4×C31—42no—
86C2×C4×C31—42no—
87C2×C4×C31—84no—
88C2×C4×C31#9911yescharacteristic
89C2×C4×C31C2×C22⋊C411yescharacteristic
90C8×C31—24no—
91#3151C2×C3111yescharacteristic
92#2126C2×C3112yescomplemented
93#1408C2×C3114yescomplemented
94C22×C31—21no—
95C22×C31—41no—
96C22×C31—42no—
97C22×C31—82no—
98C22×C31—84no—
99C22×C31—82no—
100C22×C31—162no—
101C22×C31—162no—
102C22×C31C2×#9911yescharacteristic
103C4×C31—22no—
104C4×C31—21no—
105C4×C31—41no—
106C4×C31—42no—
107C4×C31—164no—
108C4×C31#35312yes—
109C2×AGL(1,ℤ/8)—22no—
110#532C22×C3111yescharacteristic
111C2×#127C4×C3111yescharacteristic, complemented
112#496—22no—
113#493C22×C3112yes—
114#492C4×C3112yescomplemented
115#410—22no—
116C4×M16C4×C3111yescharacteristic, complemented
117#354—22no—
118#353C22×C3114yescomplemented
119C2×C31—21no—
120C2×C31—41no—
121C2×C31—82no—
122C2×C31—162no—
123C2×C31C2×#35311yescharacteristic
124C2×#41D4×C3112yes—
125C22×D4—21no—
126C22×D4—41no—
127AGL(1,ℤ/8)—44no—
128AGL(1,ℤ/8)—44no—
129C2×SD16—24no—
130C2×D8—24no—
131C2×M16—21no—
132C4⋊Q8C2×C4×C3111yescharacteristic
133#127—21no—
134#127—41no—
135#127C2×C4×C3112yes—
136#127C23×C3111yescharacteristic
137#124D4×C3112yes—
138#121—41no—
139C4×D4—41no—
140#117—42no—
141C2×C42C2×C4×C3111yescharacteristic
142#99—24no—
143#99—42no—
144#97—21no—
145C4×C8C2×C4×C3112yes—
146C31#1358511yescharacteristic, direct product factor, Sylow
147C24—41no—
148#41—42no—
149#41—42no—
150C2×Q8C22⋊C4×C3112yes—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—42no—
154C2×D4—42no—
155C2×D4—41no—
156C2×D4—42no—
157C2×D4—42no—
158C2×D4—41no—
159C2×D4—84no—
160C2×D4C2×D4×C3112yes—
161C22×C4—21no—
162C22×C4—22no—
163C22×C4C22⋊C4×C3111yescharacteristic
164SD16—48no—
165D8—48no—
166M16—24no—
167C2×C8—22no—
168C4⋊C4—41no—
169C4⋊C4—82no—
170C22⋊C4—42no—
171C22⋊C4—44no—
172C42—21no—
173C42—82no—
174C42C22⋊C4×C3111yescharacteristic
175C42C22×C4×C3111yescharacteristic
176C23—22no—
177C23—42no—
178C23—81no—
179C23—81no—
180C23—84no—
181C23C31×#9911yescharacteristic
182Q8—42no—
183D4—42no—
184D4—44no—
185D4—82no—
186D4—84no—
187D4—82no—
188D4—84no—
189D4—82no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—84no—
198C2×C4C31×#9911yescharacteristic
199C2×C4C2×C22⋊C4×C3111yescharacteristic
200C8—24no—
201C22—21no—
202C22—41no—
203C22—42no—
204C22—82no—
205C22—84no—
206C22—82no—
207C22—162no—
208C22—162no—
209C22C2×C31×#9911yescharacteristic
210C4—22no—
211C4—21no—
212C4—41no—
213C4—42no—
214C4—164no—
215C4C31×#35312yes—
216C2—21no—
217C2—41no—
218C2—82no—
219C2—162no—
220C2C2×C31×#35311yescharacteristic
subgroupG/H
center, socleC2×C31C2×#353
commutatorC42C22×C4×C31
Frattini, cosocle#127C23×C31
prime radicalC31×#3151C2
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C31×#532 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C31×#2126C2semidirect
3. C31×#1408C2semidirect
6. C2×C31×#127C4semidirect
9. C31×#492C4semidirect
11. C4×M16×C31C4semidirect
13. C31×#353C22semidirect
65. #13585C31direct (N × H)
92. #2126C2×C31semidirect
93. #1408C2×C31semidirect
111. C2×#127C4×C31semidirect
114. #492C4×C31semidirect
116. C4×M16C4×C31semidirect
118. #353C22×C31semidirect
146. C31#13585direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31512
C31×#21262
C31×#14082
#1358531