Finite Group Databasebeta

← C31×#10087 #21466846

Subgroups — C31×#10087 #21466846

Order 7936.

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

normal subgroups only

This group has 500 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
1C2×C31×#501C212yesmaximal
2C31×#2822C211yesmaximal, characteristic
3C31×#1960C211yesmaximal, characteristic
4C2×C31×#330C212yesmaximal
5C31×#1295C211yesmaximal, characteristic
6C2×C31×C4⋊Q8C2211yescharacteristic
7C2×C31×#125C2212yes—
8C31×#501—24no—
9C31×#501—24no—
10C2×C31×#107—22no—
11C2×C31×#106—22no—
12C2×C31×#103—22no—
13C2×C31×#97C2211yescharacteristic
14C2×C31×#97C2212yes—
15C31×#400—22no—
16C31×#398—22no—
17C31×#398—22no—
18C31×#382C2211yescharacteristic
19C31×#330—24no—
20C22×Q8×C31—21no—
21C22×C8×C31—22no—
22C22×C8×C31—21no—
23C31×C4⋊Q8—22no—
24C31×C4⋊Q8—21no—
25C31×C4⋊Q8D412yes—
26C31×#125—22no—
27C31×#125—22no—
28C31×#125—22no—
29C31×#125—22no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31—22no—
33C2×C4⋊C4×C31—22no—
34C2×C4⋊C4×C31D412yes—
35C2×C4⋊C4×C31D412yes—
36C2×C4⋊C4×C31D412yes—
37C2×C42×C31C2311yescharacteristic
38C31×#107—28no—
39C31×#106—28no—
40C31×#103—44no—
41C31×#97—22no—
42C31×#97—22no—
43C31×#97D414yes—
44C31×#95—24no—
45C31×#95—22no—
46C31×#95—22no—
47C2×Q8×C31—22no—
48C2×Q8×C31—42no—
49C2×Q8×C31—42no—
50C2×Q8×C31—41no—
51C22×C4×C31—22no—
52C22×C4×C31—22no—
53C22×C4×C31—22no—
54C22×C4×C31—41no—
55C22×C4×C31C2×D412yes—
56C22×C4×C31C2×D411yescharacteristic
57C2×C8×C31—28no—
58C2×C8×C31—24no—
59C2×C8×C31—22no—
60C2×C8×C31—41no—
61C2×C8×C31—41no—
62C4⋊C4×C31—22no—
63C4⋊C4×C31—24no—
64C4⋊C4×C31—22no—
65C4⋊C4×C31—22no—
66C4⋊C4×C31—22no—
67C4⋊C4×C31—42no—
68C4⋊C4×C31—42no—
69C4⋊C4×C31—42no—
70C4⋊C4×C31—42no—
71C4⋊C4×C31—42no—
72C4⋊C4×C31—42no—
73C4⋊C4×C31—82no—
74C42×C31C2×D411yescharacteristic
75C42×C31C2×D412yes—
76C42×C31#4111yescharacteristic
77#10087C3111yesmaximal, characteristic, direct product factor, Sylow
78C23×C31#12011yescharacteristic
79Q8×C31—44no—
80Q8×C31—82no—
81C2×C4×C31—21no—
82C2×C4×C31—21no—
83C2×C4×C31—24no—
84C2×C4×C31—42no—
85C2×C4×C31—42no—
86C2×C4×C31—42no—
87C2×C4×C31—42no—
88C2×C4×C31—42no—
89C2×C4×C31—42no—
90C2×C4×C31—44no—
91C2×C4×C31—44no—
92C2×C4×C31—81no—
93C2×C4×C31—81no—
94C2×C4×C31#12012yes—
95C2×C4×C31#12112yes—
96C2×C4×C31#12111yescharacteristic
97C2×C4×C31#12711yescharacteristic
98C8×C31—28no—
99C8×C31—42no—
100C2×#501C2×C3112yes—
101#2822C2×C3111yescharacteristic
102#1960C2×C3111yescharacteristic
103C2×#330C2×C3112yes—
104#1295C2×C3111yescharacteristic
105C22×C31#39211yescharacteristic
106C22×C31#45311yescharacteristic
107C22×C31#45411yescharacteristic
108C22×C31#45614yes—
109C4×C31—22no—
110C4×C31—22no—
111C4×C31—21no—
112C4×C31—21no—
113C4×C31—82no—
114C4×C31—82no—
115C4×C31—82no—
116C4×C31—82no—
117C2×C4⋊Q8C22×C3111yescharacteristic
118C2×#125C22×C3112yes—
119#501—24no—
120#501—24no—
121C2×#107—22no—
122C2×#106—22no—
123C2×#103—22no—
124C2×#97C22×C3111yescharacteristic
125C2×#97C22×C3112yes—
126#400—22no—
127#398—22no—
128#398—22no—
129#382C22×C3111yescharacteristic
130#330—24no—
131C2×C31#166012yes—
132C2×C31#166312yes—
133C2×C31#200512yes—
134C2×C31#200611yescharacteristic
135C22×Q8—21no—
136C22×C8—22no—
137C22×C8—21no—
138C4⋊Q8—22no—
139C4⋊Q8—21no—
140C4⋊Q8D4×C3112yes—
141#125—22no—
142#125—22no—
143#125—22no—
144#125—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4D4×C3112yes—
150C2×C4⋊C4D4×C3112yes—
151C2×C4⋊C4D4×C3112yes—
152C2×C42C23×C3111yescharacteristic
153#107—28no—
154#106—28no—
155#103—44no—
156#97—22no—
157#97—22no—
158#97D4×C3114yes—
159#95—24no—
160#95—22no—
161#95—22no—
162C31#1008711yescharacteristic, direct product factor, Sylow
163C2×Q8—22no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—41no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—41no—
171C22×C4C2×D4×C3112yes—
172C22×C4C2×D4×C3111yescharacteristic
173C2×C8—28no—
174C2×C8—24no—
175C2×C8—22no—
176C2×C8—41no—
177C2×C8—41no—
178C4⋊C4—22no—
179C4⋊C4—24no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—82no—
190C42C2×D4×C3111yescharacteristic
191C42C2×D4×C3112yes—
192C42#41×C3111yescharacteristic
193C23C31×#12011yescharacteristic
194Q8—44no—
195Q8—82no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—44no—
203C2×C4—44no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—81no—
208C2×C4—81no—
209C2×C4C31×#12012yes—
210C2×C4C31×#12112yes—
211C2×C4C31×#12111yescharacteristic
212C2×C4C31×#12711yescharacteristic
213C8—28no—
214C8—42no—
215C22C31×#39211yescharacteristic
216C22C31×#45311yescharacteristic
217C22C31×#45411yescharacteristic
218C22C31×#45614yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—82no—
225C4—82no—
226C4—82no—
227C2C31×#166012yes—
228C2C31×#166312yes—
229C2C31×#200512yes—
230C2C31×#200611yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
77. #10087C31direct (N × H)
162. C31#10087direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5012
C31×#28222
C31×#19602
C2×C31×#3302
C31×#12952
#1008731