Finite Group Databasebeta

← C31×#11771 #21468530

Subgroups — C31×#11771 #21468530

Order 7936.

292 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3177C211yesmaximal, characteristic
2C31×#2166C211yesmaximal, characteristic
3C31×#1747C211yesmaximal, characteristic
4C31×#1342C212yesmaximal
5C31×#1340C212yesmaximal
6C31×#541—21no—
7C31×#499C411yescharacteristic, complemented
8C31×#494C411yescharacteristic, complemented
9C31×#491—21no—
10C31×#470C2212yes—
11C31×#467—21no—
12C31×#441C412yescomplemented
13C4×Q16×C31—21no—
14C31×#405—21no—
15C31×#405C2211yescharacteristic
16C31×#364—21no—
17C31×#349C2212yes—
18C31×#347—21no—
19C31×#338C2211yescharacteristic
20C31×H(3,ℤ/4)—21no—
21C31×H(3,ℤ/4)C2211yescharacteristic
22C2×Q16×C31—21no—
23C2×Q16×C31C2×C412yes—
24C2×M16×C31—21no—
25C2×M16×C31C2311yescharacteristic
26C22×C8×C31D411yescharacteristic
27C31×C4⋊Q8—21no—
28C31×#126—42no—
29C31×#125—21no—
30C31×#125—42no—
31C31×C22⋊Q8—22no—
32C4×Q8×C31—22no—
33C31×#117—21no—
34C31×#117D411yescharacteristic
35C31×M32—22no—
36C31×#107—21no—
37C31×#106C2×C412yes—
38C31×#103—22no—
39C31×#103—22no—
40C31×#97—22no—
41C31×#97C2×C411yescharacteristic
42C31×#97D411yescharacteristic
43C4×C8×C31—22no—
44C4×C8×C31C2×C411yescharacteristic
45C4×C8×C31D411yescharacteristic
46C2×Q8×C31—22no—
47C22×C4×C31C2×D411yescharacteristic
48Q16×C31—42no—
49Q16×C31—41no—
50Q16×C31—41no—
51M16×C31—41no—
52M16×C31—41no—
53M16×C31—41no—
54C2×C8×C31—21no—
55C2×C8×C31—21no—
56C2×C8×C31—22no—
57C2×C8×C31C22⋊C411yescharacteristic
58C2×C8×C31C22⋊C411yescharacteristic
59C2×C8×C31C22×C411yescharacteristic
60C2×C8×C31C2×D411yescharacteristic
61C4⋊C4×C31—21no—
62C4⋊C4×C31—22no—
63C4⋊C4×C31—41no—
64C4⋊C4×C31—42no—
65C4⋊C4×C31—42no—
66C4⋊C4×C31—42no—
67C4⋊C4×C31—42no—
68C22⋊C4×C31—21no—
69C22⋊C4×C31—41no—
70C22⋊C4×C31—42no—
71C42×C31—22no—
72C42×C31—42no—
73C42×C31C22⋊C411yescharacteristic
74C42×C31C22⋊C411yescharacteristic
75C16×C31—42no—
76#11771C3111yesmaximal, characteristic, direct product factor, Sylow
77C23×C31AGL(1,ℤ/8)11yescharacteristic
78Q8×C31—42no—
79Q8×C31—42no—
80C2×C4×C31—21no—
81C2×C4×C31—21no—
82C2×C4×C31—21no—
83C2×C4×C31—21no—
84C2×C4×C31—42no—
85C2×C4×C31—42no—
86C2×C4×C31—42no—
87C2×C4×C31C2×C22⋊C411yescharacteristic
88C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
89C8×C31—21no—
90C8×C31—21no—
91C8×C31—21no—
92C8×C31—42no—
93C8×C31#10411yescharacteristic
94C8×C31#10411yescharacteristic
95#3177C2×C3111yescharacteristic
96#2166C2×C3111yescharacteristic
97#1747C2×C3111yescharacteristic
98#1342C2×C3112yes—
99#1340C2×C3112yes—
100C22×C31—21no—
101C22×C31—41no—
102C22×C31#41811yescharacteristic
103C4×C31—21no—
104C4×C31—41no—
105C4×C31—41no—
106C4×C31—82no—
107C4×C31—82no—
108C4×C31—82no—
109C4×C31#41011yescharacteristic
110C4×C31C2×#10411yescharacteristic
111#541—21no—
112#499C4×C3111yescharacteristic, complemented
113#494C4×C3111yescharacteristic, complemented
114#491—21no—
115#470C22×C3112yes—
116#467—21no—
117#441C4×C3112yescomplemented
118C4×Q16—21no—
119#405—21no—
120#405C22×C3111yescharacteristic
121#364—21no—
122#349C22×C3112yes—
123#347—21no—
124#338C22×C3111yescharacteristic
125H(3,ℤ/4)—21no—
126H(3,ℤ/4)C22×C3111yescharacteristic
127C2×C31—21no—
128C2×C31—41no—
129C2×C31#150511yescharacteristic
130C2×Q16—21no—
131C2×Q16C2×C4×C3112yes—
132C2×M16—21no—
133C2×M16C23×C3111yescharacteristic
134C22×C8D4×C3111yescharacteristic
135C4⋊Q8—21no—
136#126—42no—
137#125—21no—
138#125—42no—
139C22⋊Q8—22no—
140C4×Q8—22no—
141#117—21no—
142#117D4×C3111yescharacteristic
143M32—22no—
144#107—21no—
145#106C2×C4×C3112yes—
146#103—22no—
147#103—22no—
148#97—22no—
149#97C2×C4×C3111yescharacteristic
150#97D4×C3111yescharacteristic
151C4×C8—22no—
152C4×C8C2×C4×C3111yescharacteristic
153C4×C8D4×C3111yescharacteristic
154C31#1177111yescharacteristic, direct product factor, Sylow
155C2×Q8—22no—
156C22×C4C2×D4×C3111yescharacteristic
157Q16—42no—
158Q16—41no—
159Q16—41no—
160M16—41no—
161M16—41no—
162M16—41no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—22no—
166C2×C8C22⋊C4×C3111yescharacteristic
167C2×C8C22⋊C4×C3111yescharacteristic
168C2×C8C22×C4×C3111yescharacteristic
169C2×C8C2×D4×C3111yescharacteristic
170C4⋊C4—21no—
171C4⋊C4—22no—
172C4⋊C4—41no—
173C4⋊C4—42no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C22⋊C4—21no—
178C22⋊C4—41no—
179C22⋊C4—42no—
180C42—22no—
181C42—42no—
182C42C22⋊C4×C3111yescharacteristic
183C42C22⋊C4×C3111yescharacteristic
184C16—42no—
185C23C31×AGL(1,ℤ/8)11yescharacteristic
186Q8—42no—
187Q8—42no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4C2×C22⋊C4×C3111yescharacteristic
196C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
197C8—21no—
198C8—21no—
199C8—21no—
200C8—42no—
201C8C31×#10411yescharacteristic
202C8C31×#10411yescharacteristic
203C22—21no—
204C22—41no—
205C22C31×#41811yescharacteristic
206C4—21no—
207C4—41no—
208C4—41no—
209C4—82no—
210C4—82no—
211C4—82no—
212C4C31×#41011yescharacteristic
213C4C2×C31×#10411yescharacteristic
214C2—21no—
215C2—41no—
216C2C31×#150511yescharacteristic
subgroupG/H
center, socleC2×C31#1505
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 ◁ C31×#405 ◁ G

Complements

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

NH ≅ G/Ntype
7. C31×#499C4semidirect
8. C31×#494C4semidirect
12. C31×#441C4semidirect
76. #11771C31direct (N × H)
112. #499C4×C31semidirect
113. #494C4×C31semidirect
117. #441C4×C31semidirect
154. C31#11771direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31772
C31×#21662
C31×#17472
C31×#13422
C31×#13402
#1177131