Finite Group Databasebeta

← C31×#13589 #21470348

Subgroups — C31×#13589 #21470348

Order 7936.

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

normal subgroups only

This group has 408 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×#3147C211yesmaximal, characteristic
2C31×#2132C212yesmaximal, complemented
3C31×#1411C212yesmaximal, complemented
4C31×#1410C212yesmaximal, complemented
5C2×C31×#135—22no—
6C31×#532C411yescharacteristic
7C31×#532C2211yescharacteristic
8C31×#495—22no—
9C31×#494C2211yescharacteristic
10C31×#493C411yescharacteristic
11C31×#492C411yescharacteristic
12C31×#492C2211yescharacteristic
13C31×#413—22no—
14C2×C4×C8×C31C411yescharacteristic
15C31×#356C2214yes—
16C31×#355—22no—
17C2×#41×C31—21no—
18C2×#41×C31D412yes—
19C31×#135—44no—
20C31×#135—44no—
21C2×Q16×C31—22no—
22C2×SD16×C31—22no—
23C2×SD16×C31—22no—
24C2×D8×C31—22no—
25C2×M16×C31—42no—
26C22×C8×C31—21no—
27C31×C4⋊Q8C2×C411yescharacteristic
28C31×C4⋊Q8C2311yescharacteristic
29C31×#127C2×C411yescharacteristic
30C31×#127C2×C411yescharacteristic
31C31×#124—21no—
32C31×#124D412yes—
33C31×#121—41no—
34C31×#121—41no—
35C4×D4×C31—41no—
36C4×D4×C31—41no—
37C2×C42×C31C2×C411yescharacteristic
38C31×#101—24no—
39C31×#100—42no—
40C4×C8×C31—21no—
41C4×C8×C31C2×C411yescharacteristic
42C4×C8×C31C2×C411yescharacteristic
43#41×C31—42no—
44#41×C31—42no—
45#41×C31—42no—
46#41×C31—42no—
47C2×Q8×C31—21no—
48C2×Q8×C31C2×D412yes—
49C2×D4×C31—22no—
50C2×D4×C31—21no—
51C2×D4×C31—41no—
52C2×D4×C31—41no—
53C2×D4×C31—41no—
54C2×D4×C31C22⋊C412yes—
55C22×C4×C31—21no—
56C22×C4×C31—22no—
57C22×C4×C31—41no—
58C22×C4×C31C22⋊C411yescharacteristic
59Q16×C31—44no—
60SD16×C31—44no—
61SD16×C31—44no—
62D8×C31—44no—
63M16×C31—44no—
64M16×C31—82no—
65C2×C8×C31—22no—
66C2×C8×C31—22no—
67C2×C8×C31—21no—
68C2×C8×C31—21no—
69C2×C8×C31—82no—
70C4⋊C4×C31—41no—
71C4⋊C4×C31—41no—
72C22⋊C4×C31—42no—
73C22⋊C4×C31—42no—
74C42×C31—21no—
75C42×C31C22⋊C411yescharacteristic
76C42×C31C22×C411yescharacteristic
77#13589C3111yesmaximal, characteristic, direct product factor, Sylow
78C23×C31—22no—
79C23×C31—41no—
80C23×C31#9911yescharacteristic
81Q8×C31—42no—
82Q8×C31—42no—
83D4×C31—42no—
84D4×C31—42no—
85D4×C31—82no—
86D4×C31—82no—
87D4×C31—82no—
88D4×C31—82no—
89C2×C4×C31—21no—
90C2×C4×C31—21no—
91C2×C4×C31—21no—
92C2×C4×C31—21no—
93C2×C4×C31—22no—
94C2×C4×C31—42no—
95C2×C4×C31—42no—
96C2×C4×C31—42no—
97C2×C4×C31—41no—
98C2×C4×C31—81no—
99C2×C4×C31—81no—
100C2×C4×C31#9911yescharacteristic
101C2×C4×C31C2×C22⋊C411yescharacteristic
102C8×C31—22no—
103C8×C31—22no—
104C8×C31—84no—
105#3147C2×C3111yescharacteristic
106#2132C2×C3112yescomplemented
107#1411C2×C3112yescomplemented
108#1410C2×C3112yescomplemented
109C22×C31—21no—
110C22×C31—41no—
111C22×C31—42no—
112C22×C31—82no—
113C22×C31—82no—
114C22×C31—81no—
115C22×C31C2×#9911yescharacteristic
116C4×C31—22no—
117C4×C31—21no—
118C4×C31—41no—
119C4×C31—42no—
120C4×C31—81no—
121C4×C31#35311yescharacteristic
122C4×C31#35311yescharacteristic
123C2×#135—22no—
124#532C4×C3111yescharacteristic
125#532C22×C3111yescharacteristic
126#495—22no—
127#494C22×C3111yescharacteristic
128#493C4×C3111yescharacteristic
129#492C4×C3111yescharacteristic
130#492C22×C3111yescharacteristic
131#413—22no—
132C2×C4×C8C4×C3111yescharacteristic
133#356C22×C3114yes—
134#355—22no—
135C2×C31—21no—
136C2×C31—41no—
137C2×C31—82no—
138C2×C31—161no—
139C2×C31C2×#35311yescharacteristic
140C2×#41—21no—
141C2×#41D4×C3112yes—
142#135—44no—
143#135—44no—
144C2×Q16—22no—
145C2×SD16—22no—
146C2×SD16—22no—
147C2×D8—22no—
148C2×M16—42no—
149C22×C8—21no—
150C4⋊Q8C2×C4×C3111yescharacteristic
151C4⋊Q8C23×C3111yescharacteristic
152#127C2×C4×C3111yescharacteristic
153#127C2×C4×C3111yescharacteristic
154#124—21no—
155#124D4×C3112yes—
156#121—41no—
157#121—41no—
158C4×D4—41no—
159C4×D4—41no—
160C2×C42C2×C4×C3111yescharacteristic
161#101—24no—
162#100—42no—
163C4×C8—21no—
164C4×C8C2×C4×C3111yescharacteristic
165C4×C8C2×C4×C3111yescharacteristic
166C31#1358911yescharacteristic, direct product factor, Sylow
167#41—42no—
168#41—42no—
169#41—42no—
170#41—42no—
171C2×Q8—21no—
172C2×Q8C2×D4×C3112yes—
173C2×D4—22no—
174C2×D4—21no—
175C2×D4—41no—
176C2×D4—41no—
177C2×D4—41no—
178C2×D4C22⋊C4×C3112yes—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—41no—
182C22×C4C22⋊C4×C3111yescharacteristic
183Q16—44no—
184SD16—44no—
185SD16—44no—
186D8—44no—
187M16—44no—
188M16—82no—
189C2×C8—22no—
190C2×C8—22no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—82no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C22⋊C4—42no—
197C22⋊C4—42no—
198C42—21no—
199C42C22⋊C4×C3111yescharacteristic
200C42C22×C4×C3111yescharacteristic
201C23—22no—
202C23—41no—
203C23C31×#9911yescharacteristic
204Q8—42no—
205Q8—42no—
206D4—42no—
207D4—42no—
208D4—82no—
209D4—82no—
210D4—82no—
211D4—82no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—41no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4C31×#9911yescharacteristic
224C2×C4C2×C22⋊C4×C3111yescharacteristic
225C8—22no—
226C8—22no—
227C8—84no—
228C22—21no—
229C22—41no—
230C22—42no—
231C22—82no—
232C22—82no—
233C22—81no—
234C22C2×C31×#9911yescharacteristic
235C4—22no—
236C4—21no—
237C4—41no—
238C4—42no—
239C4—81no—
240C4C31×#35311yescharacteristic
241C4C31×#35311yescharacteristic
242C2—21no—
243C2—41no—
244C2—82no—
245C2—161no—
246C2C2×C31×#35311yescharacteristic
subgroupG/H
centerC4×C31#353
commutatorC42C22×C4×C31
Frattini, cosocleC4⋊Q8C23×C31
socleC2×C31C2×#353
prime radicalC31×#3147C2
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×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×#2132C2semidirect
3. C31×#1411C2semidirect
4. C31×#1410C2semidirect
77. #13589C31direct (N × H)
106. #2132C2×C31semidirect
107. #1411C2×C31semidirect
108. #1410C2×C31semidirect
166. C31#13589direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31472
C31×#21322
C31×#14112
C31×#14102
#1358931