Finite Group Databasebeta

← C31×#13367 #21470126

Subgroups — C31×#13367 #21470126

Order 7936.

406 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 114 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×#3162C211yesmaximal, characteristic, complemented
2C31×#2140C212yesmaximal
3C31×#1972C211yesmaximal, characteristic
4C31×#1386C212yesmaximal, complemented
5C31×#1377C211yesmaximal, characteristic, complemented
6C22×D8×C31C2211yescharacteristic
7C31×#533—21no—
8C2×C31×M32C2212yes—
9C31×#501—24no—
10C31×#427—21no—
11C31×#427C2212yes—
12C2×C31×#106C2211yescharacteristic
13C2×C31×#102—21no—
14C2×C31×#97C2211yescharacteristic
15C31×#390—21no—
16C31×#357—24no—
17C22×D4×C31—21no—
18C2×D8×C31—22no—
19C2×D8×C31—22no—
20C2×D8×C31—21no—
21C2×D8×C31Q812yescomplemented
22C22×C8×C31D411yescharacteristic
23C22×C8×C31C2311yescharacteristic
24C31×C4⋊Q8—22no—
25C31×#125—22no—
26C31×C22⋊Q8—42no—
27C4×Q8×C31—42no—
28C31×#117—22no—
29C2×C4⋊C4×C31—21no—
30C2×C22⋊C4×C31—42no—
31C2×C42×C31D411yescharacteristic
32C31×M32—22no—
33C31×M32—22no—
34C2×C16×C31—22no—
35C31×#107—22no—
36C31×#107D414yes—
37C31×#106—22no—
38C31×#106—22no—
39C31×#106—22no—
40C31×#102—42no—
41C31×#97—22no—
42C24×C31—41no—
43C2×Q8×C31—42no—
44C2×D4×C31—22no—
45C2×D4×C31—41no—
46C2×D4×C31—41no—
47C2×D4×C31—41no—
48C2×D4×C31—41no—
49C2×D4×C31—41no—
50C22×C4×C31—41no—
51C22×C4×C31D812yes—
52C22×C4×C31C2×D411yescharacteristic
53D8×C31—24no—
54D8×C31—42no—
55C2×C8×C31—21no—
56C2×C8×C31—21no—
57C2×C8×C31SD1612yes—
58C2×C8×C31C2×D412yes—
59C2×C8×C31C2×Q811yescharacteristic
60C2×C8×C31#4112yes—
61C2×C8×C31#4111yescharacteristic
62C4⋊C4×C31—24no—
63C4⋊C4×C31—44no—
64C4⋊C4×C31—42no—
65C4⋊C4×C31—41no—
66C4⋊C4×C31—41no—
67C22⋊C4×C31—42no—
68C22⋊C4×C31—84no—
69C42×C31—21no—
70C42×C31—21no—
71C42×C31—42no—
72C16×C31—42no—
73#13367C3111yesmaximal, characteristic, direct product factor, Sylow
74C23×C31—42no—
75C23×C31—82no—
76C23×C31—82no—
77C23×C31—81no—
78C23×C31—81no—
79C23×C31C2×D811yescharacteristic
80Q8×C31—84no—
81D4×C31—42no—
82D4×C31—42no—
83D4×C31—81no—
84D4×C31—81no—
85C2×C4×C31—22no—
86C2×C4×C31—42no—
87C2×C4×C31—44no—
88C2×C4×C31—82no—
89C2×C4×C31—81no—
90C2×C4×C31#12011yescharacteristic
91C2×C4×C31C22⋊Q811yescharacteristic
92C2×C4×C31#12411yescharacteristic
93C2×C4×C31C2×SD1611yescharacteristic
94C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
95C2×C4×C31#13711yescharacteristic
96C8×C31—22no—
97C8×C31C22⋊Q812yes—
98C8×C31#12412yes—
99#3162C2×C3111yescharacteristic, complemented
100#2140C2×C3112yes—
101#1972C2×C3111yescharacteristic
102#1386C2×C3112yescomplemented
103#1377C2×C3111yescharacteristic, complemented
104C22×C31—22no—
105C22×C31—84no—
106C22×C31—82no—
107C22×C31—161no—
108C22×C31—161no—
109C22×C31—162no—
110C22×C31#44711yescharacteristic
111C22×C31#47411yescharacteristic
112C22×C31#48611yescharacteristic
113C4×C31—42no—
114C4×C31—84no—
115C4×C31—161no—
116C4×C31#39311yescharacteristic
117C4×C31#44811yescharacteristic
118C4×C31#47611yescharacteristic
119C4×C31#48911yescharacteristic
120C22×D8C22×C3111yescharacteristic
121#533—21no—
122C2×M32C22×C3112yes—
123#501—24no—
124#427—21no—
125#427C22×C3112yes—
126C2×#106C22×C3111yescharacteristic
127C2×#102—21no—
128C2×#97C22×C3111yescharacteristic
129#390—21no—
130#357—24no—
131C2×C31—21no—
132C2×C31—21no—
133C2×C31—162no—
134C2×C31#202311yescharacteristic
135C2×C31#219012yes—
136C22×D4—21no—
137C2×D8—22no—
138C2×D8—22no—
139C2×D8—21no—
140C2×D8Q8×C3112yescomplemented
141C22×C8D4×C3111yescharacteristic
142C22×C8C23×C3111yescharacteristic
143C4⋊Q8—22no—
144#125—22no—
145C22⋊Q8—42no—
146C4×Q8—42no—
147#117—22no—
148C2×C4⋊C4—21no—
149C2×C22⋊C4—42no—
150C2×C42D4×C3111yescharacteristic
151M32—22no—
152M32—22no—
153C2×C16—22no—
154#107—22no—
155#107D4×C3114yes—
156#106—22no—
157#106—22no—
158#106—22no—
159#102—42no—
160#97—22no—
161C31#1336711yescharacteristic, direct product factor, Sylow
162C24—41no—
163C2×Q8—42no—
164C2×D4—22no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4—41no—
168C2×D4—41no—
169C2×D4—41no—
170C22×C4—41no—
171C22×C4D8×C3112yes—
172C22×C4C2×D4×C3111yescharacteristic
173D8—24no—
174D8—42no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8SD16×C3112yes—
178C2×C8C2×D4×C3112yes—
179C2×C8C2×Q8×C3111yescharacteristic
180C2×C8#41×C3112yes—
181C2×C8#41×C3111yescharacteristic
182C4⋊C4—24no—
183C4⋊C4—44no—
184C4⋊C4—42no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C22⋊C4—42no—
188C22⋊C4—84no—
189C42—21no—
190C42—21no—
191C42—42no—
192C16—42no—
193C23—42no—
194C23—82no—
195C23—82no—
196C23—81no—
197C23—81no—
198C23C2×D8×C3111yescharacteristic
199Q8—84no—
200D4—42no—
201D4—42no—
202D4—81no—
203D4—81no—
204C2×C4—22no—
205C2×C4—42no—
206C2×C4—44no—
207C2×C4—82no—
208C2×C4—81no—
209C2×C4C31×#12011yescharacteristic
210C2×C4C31×C22⋊Q811yescharacteristic
211C2×C4C31×#12411yescharacteristic
212C2×C4C2×SD16×C3111yescharacteristic
213C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
214C2×C4C31×#13711yescharacteristic
215C8—22no—
216C8C31×C22⋊Q812yes—
217C8C31×#12412yes—
218C22—22no—
219C22—84no—
220C22—82no—
221C22—161no—
222C22—161no—
223C22—162no—
224C22C31×#44711yescharacteristic
225C22C31×#47411yescharacteristic
226C22C31×#48611yescharacteristic
227C4—42no—
228C4—84no—
229C4—161no—
230C4C31×#39311yescharacteristic
231C4C31×#44811yescharacteristic
232C4C31×#47611yescharacteristic
233C4C31×#48911yescharacteristic
234C2—21no—
235C2—21no—
236C2—162no—
237C2C31×#202311yescharacteristic
238C2C31×#219012yes—
subgroupG/H
center, socleC22×C31#447
commutator, Frattini, cosocleC22×C8C23×C31
prime radicalC22×D8×C31C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C31×#97 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3162C2semidirect
4. C31×#1386C2semidirect
5. C31×#1377C2semidirect
21. C2×D8×C31Q8semidirect
73. #13367C31direct (N × H)
99. #3162C2×C31semidirect
102. #1386C2×C31semidirect
103. #1377C2×C31semidirect
140. C2×D8Q8×C31semidirect
161. C31#13367direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31622
C31×#21402
C31×#19722
C31×#13862
C31×#13772
#1336731