Finite Group Databasebeta

← C31×#11838 #21468597

Subgroups — C31×#11838 #21468597

Order 7936.

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

normal subgroups only

This group has 280 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×#3185C211yesmaximal, characteristic
2C31×#2165C211yesmaximal, characteristic
3C31×#1841C211yesmaximal, characteristic
4C31×#1342C212yesmaximal
5C31×#1340C212yesmaximal
6C31×#533—21no—
7C31×#498C411yescharacteristic, complemented
8C31×#494C411yescharacteristic, complemented
9C31×#487—21no—
10C31×#470—21no—
11C31×#470C2212yes—
12C31×#441—21no—
13C31×#441C412yescomplemented
14C4×M16×C31C2211yescharacteristic
15C31×#364—21no—
16C31×#349C2212yes—
17C31×#347—21no—
18C31×#344—21no—
19C31×#339—21no—
20C31×#338C2211yescharacteristic
21C31×H(3,ℤ/4)C2211yescharacteristic
22C2×Q16×C31—21no—
23C2×Q16×C31C2×C412yes—
24C2×M16×C31—21no—
25C2×M16×C31D411yescharacteristic
26C2×M16×C31C2311yescharacteristic
27C31×C4⋊Q8—21no—
28C31×C4⋊Q8—21no—
29C31×#125—41no—
30C31×C22⋊Q8—22no—
31C31×C22⋊Q8—41no—
32C4×Q8×C31—22no—
33C4×Q8×C31—41no—
34C31×#117—21no—
35C31×#117—41no—
36C2×C42×C31D411yescharacteristic
37C31×M32—22no—
38C31×#106—21no—
39C31×#106C2×C412yes—
40C31×#103—22no—
41C31×#103—22no—
42C31×#97C2×C411yescharacteristic
43C31×#97D411yescharacteristic
44C4×C8×C31C2×C411yescharacteristic
45C4×C8×C31D411yescharacteristic
46C2×Q8×C31—22no—
47C2×Q8×C31—41no—
48C22×C4×C31—21no—
49C22×C4×C31C2×D411yescharacteristic
50Q16×C31—42no—
51Q16×C31—42no—
52M16×C31—41no—
53M16×C31—41no—
54M16×C31—41no—
55M16×C31—41no—
56C2×C8×C31—41no—
57C2×C8×C31C22⋊C411yescharacteristic
58C2×C8×C31C22⋊C411yescharacteristic
59C2×C8×C31C22×C411yescharacteristic
60C2×C8×C31C2×D411yescharacteristic
61C4⋊C4×C31—22no—
62C4⋊C4×C31—41no—
63C4⋊C4×C31—41no—
64C4⋊C4×C31—42no—
65C4⋊C4×C31—41no—
66C4⋊C4×C31—41no—
67C4⋊C4×C31—42no—
68C22⋊C4×C31—42no—
69C22⋊C4×C31—41no—
70C42×C31—21no—
71C42×C31—42no—
72C42×C31—41no—
73C42×C31C22⋊C411yescharacteristic
74C42×C31C22⋊C411yescharacteristic
75C16×C31—42no—
76#11838C3111yesmaximal, characteristic, direct product factor, Sylow
77C23×C31AGL(1,ℤ/8)11yescharacteristic
78Q8×C31—42no—
79Q8×C31—42no—
80Q8×C31—82no—
81C2×C4×C31—21no—
82C2×C4×C31—21no—
83C2×C4×C31—21no—
84C2×C4×C31—21no—
85C2×C4×C31—42no—
86C2×C4×C31—42no—
87C2×C4×C31—42no—
88C2×C4×C31—81no—
89C2×C4×C31C2×C22⋊C411yescharacteristic
90C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
91C8×C31—21no—
92C8×C31—21no—
93C8×C31—21no—
94C8×C31—21no—
95C8×C31—81no—
96#3185C2×C3111yescharacteristic
97#2165C2×C3111yescharacteristic
98#1841C2×C3111yescharacteristic
99#1342C2×C3112yes—
100#1340C2×C3112yes—
101C22×C31—21no—
102C22×C31—41no—
103C22×C31#41811yescharacteristic
104C4×C31—22no—
105C4×C31—21no—
106C4×C31—41no—
107C4×C31—82no—
108C4×C31—82no—
109C4×C31—161no—
110C4×C31#41011yescharacteristic
111C4×C31#42111yescharacteristic
112#533—21no—
113#498C4×C3111yescharacteristic, complemented
114#494C4×C3111yescharacteristic, complemented
115#487—21no—
116#470—21no—
117#470C22×C3112yes—
118#441—21no—
119#441C4×C3112yescomplemented
120C4×M16C22×C3111yescharacteristic
121#364—21no—
122#349C22×C3112yes—
123#347—21no—
124#344—21no—
125#339—21no—
126#338C22×C3111yescharacteristic
127H(3,ℤ/4)C22×C3111yescharacteristic
128C2×C31—21no—
129C2×C31—41no—
130C2×C31#151411yescharacteristic
131C2×Q16—21no—
132C2×Q16C2×C4×C3112yes—
133C2×M16—21no—
134C2×M16D4×C3111yescharacteristic
135C2×M16C23×C3111yescharacteristic
136C4⋊Q8—21no—
137C4⋊Q8—21no—
138#125—41no—
139C22⋊Q8—22no—
140C22⋊Q8—41no—
141C4×Q8—22no—
142C4×Q8—41no—
143#117—21no—
144#117—41no—
145C2×C42D4×C3111yescharacteristic
146M32—22no—
147#106—21no—
148#106C2×C4×C3112yes—
149#103—22no—
150#103—22no—
151#97C2×C4×C3111yescharacteristic
152#97D4×C3111yescharacteristic
153C4×C8C2×C4×C3111yescharacteristic
154C4×C8D4×C3111yescharacteristic
155C31#1183811yescharacteristic, direct product factor, Sylow
156C2×Q8—22no—
157C2×Q8—41no—
158C22×C4—21no—
159C22×C4C2×D4×C3111yescharacteristic
160Q16—42no—
161Q16—42no—
162M16—41no—
163M16—41no—
164M16—41no—
165M16—41no—
166C2×C8—41no—
167C2×C8C22⋊C4×C3111yescharacteristic
168C2×C8C22⋊C4×C3111yescharacteristic
169C2×C8C22×C4×C3111yescharacteristic
170C2×C8C2×D4×C3111yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—42no—
178C22⋊C4—42no—
179C22⋊C4—41no—
180C42—21no—
181C42—42no—
182C42—41no—
183C42C22⋊C4×C3111yescharacteristic
184C42C22⋊C4×C3111yescharacteristic
185C16—42no—
186C23C31×AGL(1,ℤ/8)11yescharacteristic
187Q8—42no—
188Q8—42no—
189Q8—82no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—81no—
198C2×C4C2×C22⋊C4×C3111yescharacteristic
199C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
200C8—21no—
201C8—21no—
202C8—21no—
203C8—21no—
204C8—81no—
205C22—21no—
206C22—41no—
207C22C31×#41811yescharacteristic
208C4—22no—
209C4—21no—
210C4—41no—
211C4—82no—
212C4—82no—
213C4—161no—
214C4C31×#41011yescharacteristic
215C4C31×#42111yescharacteristic
216C2—21no—
217C2—41no—
218C2C31×#151411yescharacteristic
subgroupG/H
center, socleC2×C31#1514
commutatorC2×C8C22×C4×C31
Frattini, cosocleC2×M16C23×C31
prime radicalC23×C31AGL(1,ℤ/8)
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C4×M16×C31 ◁ G

Complements

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

NH ≅ G/Ntype
7. C31×#498C4semidirect
8. C31×#494C4semidirect
13. C31×#441C4semidirect
76. #11838C31direct (N × H)
113. #498C4×C31semidirect
114. #494C4×C31semidirect
119. #441C4×C31semidirect
155. C31#11838direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31852
C31×#21652
C31×#18412
C31×#13422
C31×#13402
#1183831