Finite Group Databasebeta

← C31×#10523 #21467282

Subgroups — C31×#10523 #21467282

Order 7936.

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

normal subgroups only

This group has 382 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×#1831C211yesmaximal, characteristic
4C31×#1550C212yesmaximal
5C31×#1292C211yesmaximal, characteristic
6C31×#533C2212yes—
7C31×#477—22no—
8C31×#467—22no—
9C31×#462—22no—
10C31×#423C2212yes—
11C2×C31×C4⋊C8C2211yescharacteristic
12C2×C31×C4⋊C8C2211yescharacteristic
13C43×C31C2211yescharacteristic
14C31×#339—22no—
15C31×#339—22no—
16C31×#336—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×#103—24no—
42C2×Q8×C31—22no—
43C2×Q8×C31—22no—
44C22×C4×C31—21no—
45C22×C4×C31—21no—
46C22×C4×C31C2×D411yescharacteristic
47C22×C4×C31C2×D411yescharacteristic
48C22×C4×C31#4111yescharacteristic
49Q16×C31—82no—
50M16×C31—42no—
51M16×C31—42no—
52C2×C8×C31—22no—
53C2×C8×C31—42no—
54C2×C8×C31—42no—
55C2×C8×C31—41no—
56C2×C8×C31—42no—
57C4⋊C4×C31—22no—
58C4⋊C4×C31—22no—
59C4⋊C4×C31—22no—
60C4⋊C4×C31—22no—
61C4⋊C4×C31—42no—
62C4⋊C4×C31—42no—
63C22⋊C4×C31—42no—
64C42×C31—21no—
65C42×C31—22no—
66C42×C31—41no—
67C42×C31—41no—
68C42×C31—42no—
69C42×C31—42no—
70C42×C31Q1612yescomplemented
71C42×C31C2×D412yes—
72C42×C31#4112yes—
73#10523C3111yesmaximal, characteristic, direct product factor, Sylow
74C23×C31#12111yescharacteristic
75Q8×C31—42no—
76Q8×C31—42no—
77Q8×C31—82no—
78C2×C4×C31—21no—
79C2×C4×C31—21no—
80C2×C4×C31—22no—
81C2×C4×C31—22no—
82C2×C4×C31—41no—
83C2×C4×C31—41no—
84C2×C4×C31—41no—
85C2×C4×C31—41no—
86C2×C4×C31—41no—
87C2×C4×C31—42no—
88C2×C4×C31—42no—
89C2×C4×C31#12011yescharacteristic
90C2×C4×C31#12112yes—
91C2×C4×C31#12312yes—
92C2×C4×C31#12411yescharacteristic
93C2×C4×C31C2×Q1611yescharacteristic
94C2×C4×C31#13511yescharacteristic
95C2×C4×C31#13712yes—
96C8×C31—42no—
97C8×C31—81no—
98C8×C31—82no—
99#3249C2×C3111yescharacteristic
100#1994C2×C3112yes—
101#1831C2×C3111yescharacteristic
102#1550C2×C3112yes—
103#1292C2×C3111yescharacteristic
104C22×C31—21no—
105C22×C31—21no—
106C22×C31#39411yescharacteristic
107C22×C31#46711yescharacteristic
108C22×C31#47011yescharacteristic
109C4×C31—22no—
110C4×C31—21no—
111C4×C31—42no—
112C4×C31—42no—
113C4×C31—82no—
114C4×C31—82no—
115C4×C31#45411yescharacteristic
116C4×C31#45511yescharacteristic
117C4×C31#46212yes—
118C4×C31#46412yes—
119#533C22×C3112yes—
120#477—22no—
121#467—22no—
122#462—22no—
123#423C22×C3112yes—
124C2×C4⋊C8C22×C3111yescharacteristic
125C2×C4⋊C8C22×C3111yescharacteristic
126C43C22×C3111yescharacteristic
127#339—22no—
128#339—22no—
129#336—22no—
130#333—22no—
131#332—22no—
132C2×C31—21no—
133C2×C31—21no—
134C2×C31#204011yescharacteristic
135C2×C31#205011yescharacteristic
136C2×C31#205611yescharacteristic
137C2×Q16—22no—
138C2×M16—22no—
139C22×C8—21no—
140C22×C8D4×C3112yes—
141C4⋊Q8D4×C3112yes—
142C4⋊Q8D4×C3112yes—
143#125—22no—
144C22⋊Q8—22no—
145C22⋊Q8—22no—
146C4×Q8—22no—
147C4×Q8—22no—
148#117—22no—
149C2×C42—21no—
150C2×C42—21no—
151C2×C42D4×C3111yescharacteristic
152C2×C42D4×C3111yescharacteristic
153C2×C42C23×C3111yescharacteristic
154#107—22no—
155C4⋊C8—22no—
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—22no—
159#103—24no—
160C31#1052311yescharacteristic, direct product factor, Sylow
161C2×Q8—22no—
162C2×Q8—22no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4C2×D4×C3111yescharacteristic
166C22×C4C2×D4×C3111yescharacteristic
167C22×C4#41×C3111yescharacteristic
168Q16—82no—
169M16—42no—
170M16—42no—
171C2×C8—22no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—41no—
175C2×C8—42no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C22⋊C4—42no—
183C42—21no—
184C42—22no—
185C42—41no—
186C42—41no—
187C42—42no—
188C42—42no—
189C42Q16×C3112yescomplemented
190C42C2×D4×C3112yes—
191C42#41×C3112yes—
192C23C31×#12111yescharacteristic
193Q8—42no—
194Q8—42no—
195Q8—82no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4C31×#12011yescharacteristic
208C2×C4C31×#12112yes—
209C2×C4C31×#12312yes—
210C2×C4C31×#12411yescharacteristic
211C2×C4C2×Q16×C3111yescharacteristic
212C2×C4C31×#13511yescharacteristic
213C2×C4C31×#13712yes—
214C8—42no—
215C8—81no—
216C8—82no—
217C22—21no—
218C22—21no—
219C22C31×#39411yescharacteristic
220C22C31×#46711yescharacteristic
221C22C31×#47011yescharacteristic
222C4—21no—
223C4—22no—
224C4—42no—
225C4—42no—
226C4—82no—
227C4—82no—
228C4C31×#45411yescharacteristic
229C4C31×#45511yescharacteristic
230C4C31×#46212yes—
231C4C31×#46412yes—
232C2—21no—
233C2—21no—
234C2C31×#204011yescharacteristic
235C2C31×#205011yescharacteristic
236C2C31×#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
70. C42×C31Q16semidirect
73. #10523C31direct (N × H)
160. C31#10523direct (N × H)
189. 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×#18312
C31×#15502
C31×#12922
#1052331