Finite Group Databasebeta

← C31×#10522 #21467281

Subgroups — C31×#10522 #21467281

Order 7936.

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

normal subgroups only

This group has 402 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×#3249C211yesmaximal, characteristic
2C31×#1994C212yesmaximal
3C31×#1842C211yesmaximal, characteristic
4C31×#1550C212yesmaximal
5C31×#1292C211yesmaximal, characteristic
6C31×#533C2212yes—
7C31×#477—22no—
8C31×#467—22no—
9C31×#462—22no—
10C31×#423C2212yes—
11C2×C31×C4⋊C8—22no—
12C2×C31×C4⋊C8C2211yescharacteristic
13C2×C31×C4⋊C8C2211yescharacteristic
14C43×C31C2211yescharacteristic
15C31×#339—22no—
16C31×#339—22no—
17C31×#333—22no—
18C31×#332—22no—
19C2×Q16×C31—22no—
20C2×M16×C31—22no—
21C22×C8×C31—21no—
22C22×C8×C31D412yes—
23C31×C4⋊Q8D412yes—
24C31×C4⋊Q8D412yes—
25C31×#125—22no—
26C31×C22⋊Q8—22no—
27C31×C22⋊Q8—22no—
28C4×Q8×C31—22no—
29C4×Q8×C31—22no—
30C31×#117—22no—
31C2×C42×C31—21no—
32C2×C42×C31—21no—
33C2×C42×C31D411yescharacteristic
34C2×C42×C31D411yescharacteristic
35C2×C42×C31C2311yescharacteristic
36C31×#107—22no—
37C31×C4⋊C8—22no—
38C31×C4⋊C8—22no—
39C31×C4⋊C8—22no—
40C31×C4⋊C8—22no—
41C31×C4⋊C8—44no—
42C31×#103—24no—
43C2×Q8×C31—22no—
44C2×Q8×C31—22no—
45C22×C4×C31—21no—
46C22×C4×C31—21no—
47C22×C4×C31C2×D411yescharacteristic
48C22×C4×C31C2×D411yescharacteristic
49C22×C4×C31#4111yescharacteristic
50Q16×C31—82no—
51M16×C31—42no—
52M16×C31—42no—
53C2×C8×C31—22no—
54C2×C8×C31—42no—
55C2×C8×C31—42no—
56C2×C8×C31—41no—
57C2×C8×C31—42no—
58C4⋊C4×C31—22no—
59C4⋊C4×C31—22no—
60C4⋊C4×C31—22no—
61C4⋊C4×C31—22no—
62C4⋊C4×C31—42no—
63C4⋊C4×C31—42no—
64C22⋊C4×C31—42no—
65C42×C31—22no—
66C42×C31—22no—
67C42×C31—21no—
68C42×C31—22no—
69C42×C31—42no—
70C42×C31—42no—
71C42×C31Q1612yescomplemented
72C42×C31C2×D412yes—
73C42×C31#4112yes—
74#10522C3111yesmaximal, characteristic, direct product factor, Sylow
75C23×C31#12111yescharacteristic
76Q8×C31—42no—
77Q8×C31—42no—
78Q8×C31—82no—
79C2×C4×C31—22no—
80C2×C4×C31—22no—
81C2×C4×C31—22no—
82C2×C4×C31—21no—
83C2×C4×C31—21no—
84C2×C4×C31—22no—
85C2×C4×C31—41no—
86C2×C4×C31—41no—
87C2×C4×C31—41no—
88C2×C4×C31—42no—
89C2×C4×C31—42no—
90C2×C4×C31#12011yescharacteristic
91C2×C4×C31#12112yes—
92C2×C4×C31#12312yes—
93C2×C4×C31#12411yescharacteristic
94C2×C4×C31C2×Q1611yescharacteristic
95C2×C4×C31#13511yescharacteristic
96C2×C4×C31#13712yes—
97C8×C31—42no—
98C8×C31—81no—
99C8×C31—82no—
100#3249C2×C3111yescharacteristic
101#1994C2×C3112yes—
102#1842C2×C3111yescharacteristic
103#1550C2×C3112yes—
104#1292C2×C3111yescharacteristic
105C22×C31—21no—
106C22×C31—21no—
107C22×C31#39411yescharacteristic
108C22×C31#46711yescharacteristic
109C22×C31#47011yescharacteristic
110C4×C31—24no—
111C4×C31—22no—
112C4×C31—21no—
113C4×C31—42no—
114C4×C31—82no—
115C4×C31—82no—
116C4×C31#45311yescharacteristic
117C4×C31#45611yescharacteristic
118C4×C31#46212yes—
119C4×C31#46412yes—
120#533C22×C3112yes—
121#477—22no—
122#467—22no—
123#462—22no—
124#423C22×C3112yes—
125C2×C4⋊C8—22no—
126C2×C4⋊C8C22×C3111yescharacteristic
127C2×C4⋊C8C22×C3111yescharacteristic
128C43C22×C3111yescharacteristic
129#339—22no—
130#339—22no—
131#333—22no—
132#332—22no—
133C2×C31—21no—
134C2×C31—21no—
135C2×C31#203911yescharacteristic
136C2×C31#205011yescharacteristic
137C2×C31#205611yescharacteristic
138C2×Q16—22no—
139C2×M16—22no—
140C22×C8—21no—
141C22×C8D4×C3112yes—
142C4⋊Q8D4×C3112yes—
143C4⋊Q8D4×C3112yes—
144#125—22no—
145C22⋊Q8—22no—
146C22⋊Q8—22no—
147C4×Q8—22no—
148C4×Q8—22no—
149#117—22no—
150C2×C42—21no—
151C2×C42—21no—
152C2×C42D4×C3111yescharacteristic
153C2×C42D4×C3111yescharacteristic
154C2×C42C23×C3111yescharacteristic
155#107—22no—
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—22no—
159C4⋊C8—22no—
160C4⋊C8—44no—
161#103—24no—
162C31#1052211yescharacteristic, direct product factor, Sylow
163C2×Q8—22no—
164C2×Q8—22no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4C2×D4×C3111yescharacteristic
168C22×C4C2×D4×C3111yescharacteristic
169C22×C4#41×C3111yescharacteristic
170Q16—82no—
171M16—42no—
172M16—42no—
173C2×C8—22no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—41no—
177C2×C8—42no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C22⋊C4—42no—
185C42—22no—
186C42—22no—
187C42—21no—
188C42—22no—
189C42—42no—
190C42—42no—
191C42Q16×C3112yescomplemented
192C42C2×D4×C3112yes—
193C42#41×C3112yes—
194C23C31×#12111yescharacteristic
195Q8—42no—
196Q8—42no—
197Q8—82no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4C31×#12011yescharacteristic
210C2×C4C31×#12112yes—
211C2×C4C31×#12312yes—
212C2×C4C31×#12411yescharacteristic
213C2×C4C2×Q16×C3111yescharacteristic
214C2×C4C31×#13511yescharacteristic
215C2×C4C31×#13712yes—
216C8—42no—
217C8—81no—
218C8—82no—
219C22—21no—
220C22—21no—
221C22C31×#39411yescharacteristic
222C22C31×#46711yescharacteristic
223C22C31×#47011yescharacteristic
224C4—24no—
225C4—21no—
226C4—22no—
227C4—42no—
228C4—82no—
229C4—82no—
230C4C31×#45311yescharacteristic
231C4C31×#45611yescharacteristic
232C4C31×#46212yes—
233C4C31×#46412yes—
234C2—21no—
235C2—21no—
236C2C31×#203911yescharacteristic
237C2C31×#205011yescharacteristic
238C2C31×#205611yescharacteristic
subgroupG/H
center, socleC22×C31#394
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC23×C31#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
71. C42×C31Q16semidirect
74. #10522C31direct (N × H)
162. C31#10522direct (N × H)
191. C42Q16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#32492
C31×#19942
C31×#18422
C31×#15502
C31×#12922
#1052231