Finite Group Databasebeta

← C31×#9979 #21466738

Subgroups — C31×#9979 #21466738

Order 7936.

492 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3189C211yesmaximal, characteristic
2C31×#3095C212yesmaximal
3C31×#1818C211yesmaximal, characteristic
4C31×#1472C212yesmaximal
5C31×#1293C211yesmaximal, characteristic
6C2×C31×C22⋊Q8C2212yes—
7C2×C31×#117C2211yescharacteristic
8C31×#485—24no—
9C31×#484—22no—
10C31×#484—22no—
11C31×#483—22no—
12C31×#467—22no—
13C31×#451—22no—
14C31×#428—22no—
15C31×#419—22no—
16C31×#407C2212yes—
17C2×C31×C22⋊C8C2211yescharacteristic
18C2×C31×C22⋊C8C2211yescharacteristic
19C31×#336—22no—
20C31×#324—24no—
21C22×Q8×C31D412yes—
22C23×C4×C31C2311yescharacteristic
23C2×Q16×C31—22no—
24C2×M16×C31—22no—
25C22×C8×C31—21no—
26C22×C8×C31D412yes—
27C31×C22⋊Q8—22no—
28C31×C22⋊Q8—22no—
29C31×C22⋊Q8—22no—
30C31×C22⋊Q8—22no—
31C31×#117—22no—
32C31×#117—22no—
33C2×C4⋊C4×C31—22no—
34C2×C4⋊C4×C31D412yes—
35C2×C4⋊C4×C31D411yescharacteristic
36C2×C4⋊C4×C31D411yescharacteristic
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—22no—
39C2×C42×C31—21no—
40C31×#107—24no—
41C31×#107—22no—
42C31×#106—24no—
43C31×#103—24no—
44C31×#103—24no—
45C31×#103—24no—
46C31×C22⋊C8—22no—
47C31×C22⋊C8—22no—
48C31×C22⋊C8—22no—
49C31×C22⋊C8D414yes—
50C24×C31#4111yescharacteristic
51C2×Q8×C31—22no—
52C2×Q8×C31—22no—
53C2×Q8×C31—44no—
54C22×C4×C31—21no—
55C22×C4×C31—21no—
56C22×C4×C31—22no—
57C22×C4×C31—22no—
58C22×C4×C31—42no—
59C22×C4×C31C2×D412yes—
60C22×C4×C31C2×D411yescharacteristic
61C22×C4×C31C2×D411yescharacteristic
62C22×C4×C31C2×D412yes—
63Q16×C31—82no—
64M16×C31—44no—
65C2×C8×C31—22no—
66C2×C8×C31—24no—
67C2×C8×C31—42no—
68C2×C8×C31—42no—
69C2×C8×C31—41no—
70C4⋊C4×C31—22no—
71C4⋊C4×C31—22no—
72C4⋊C4×C31—22no—
73C4⋊C4×C31—22no—
74C4⋊C4×C31—42no—
75C4⋊C4×C31—42no—
76C22⋊C4×C31—42no—
77C22⋊C4×C31—42no—
78C22⋊C4×C31—42no—
79C42×C31—41no—
80C42×C31—41no—
81#9979C3111yesmaximal, characteristic, direct product factor, Sylow
82C23×C31—22no—
83C23×C31—41no—
84C23×C31—41no—
85C23×C31#12112yes—
86C23×C31#12111yescharacteristic
87Q8×C31—44no—
88Q8×C31—44no—
89C2×C4×C31—22no—
90C2×C4×C31—24no—
91C2×C4×C31—41no—
92C2×C4×C31—42no—
93C2×C4×C31—42no—
94C2×C4×C31—44no—
95C2×C4×C31—41no—
96C2×C4×C31—41no—
97C2×C4×C31—42no—
98C2×C4×C31—42no—
99C2×C4×C31—42no—
100C2×C4×C31—82no—
101C2×C4×C31#12012yes—
102C2×C4×C31#12011yescharacteristic
103C2×C4×C31#12711yescharacteristic
104C8×C31—44no—
105C8×C31—42no—
106C8×C31—81no—
107#3189C2×C3111yescharacteristic
108#3095C2×C3112yes—
109#1818C2×C3111yescharacteristic
110#1472C2×C3112yes—
111#1293C2×C3111yescharacteristic
112C22×C31—21no—
113C22×C31—21no—
114C22×C31—22no—
115C22×C31—22no—
116C22×C31—22no—
117C22×C31—82no—
118C22×C31#39211yescharacteristic
119C22×C31#47312yes—
120C4×C31—22no—
121C4×C31—21no—
122C4×C31—81no—
123C4×C31—82no—
124C4×C31—81no—
125C4×C31—82no—
126C4×C31#45812yes—
127C2×C22⋊Q8C22×C3112yes—
128C2×#117C22×C3111yescharacteristic
129#485—24no—
130#484—22no—
131#484—22no—
132#483—22no—
133#467—22no—
134#451—22no—
135#428—22no—
136#419—22no—
137#407C22×C3112yes—
138C2×C22⋊C8C22×C3111yescharacteristic
139C2×C22⋊C8C22×C3111yescharacteristic
140#336—22no—
141#324—24no—
142C2×C31—22no—
143C2×C31—42no—
144C2×C31#201711yescharacteristic
145C2×C31#202011yescharacteristic
146C2×C31#202211yescharacteristic
147C22×Q8D4×C3112yes—
148C23×C4C23×C3111yescharacteristic
149C2×Q16—22no—
150C2×M16—22no—
151C22×C8—21no—
152C22×C8D4×C3112yes—
153C22⋊Q8—22no—
154C22⋊Q8—22no—
155C22⋊Q8—22no—
156C22⋊Q8—22no—
157#117—22no—
158#117—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4D4×C3111yescharacteristic
161C2×C4⋊C4D4×C3111yescharacteristic
162C2×C4⋊C4D4×C3112yes—
163C2×C22⋊C4—21no—
164C2×C22⋊C4—22no—
165C2×C42—21no—
166#107—24no—
167#107—22no—
168#106—24no—
169#103—24no—
170#103—24no—
171#103—24no—
172C22⋊C8—22no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175C22⋊C8D4×C3114yes—
176C31#997911yescharacteristic, direct product factor, Sylow
177C24#41×C3111yescharacteristic
178C2×Q8—22no—
179C2×Q8—22no—
180C2×Q8—44no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—42no—
186C22×C4C2×D4×C3112yes—
187C22×C4C2×D4×C3111yescharacteristic
188C22×C4C2×D4×C3111yescharacteristic
189C22×C4C2×D4×C3112yes—
190Q16—82no—
191M16—44no—
192C2×C8—22no—
193C2×C8—24no—
194C2×C8—42no—
195C2×C8—42no—
196C2×C8—41no—
197C4⋊C4—22no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C22⋊C4—42no—
204C22⋊C4—42no—
205C22⋊C4—42no—
206C42—41no—
207C42—41no—
208C23—22no—
209C23—41no—
210C23—41no—
211C23C31×#12112yes—
212C23C31×#12111yescharacteristic
213Q8—44no—
214Q8—44no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—44no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—82no—
227C2×C4C31×#12012yes—
228C2×C4C31×#12011yescharacteristic
229C2×C4C31×#12711yescharacteristic
230C8—44no—
231C8—42no—
232C8—81no—
233C22—21no—
234C22—21no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—82no—
239C22C31×#39211yescharacteristic
240C22C31×#47312yes—
241C4—22no—
242C4—21no—
243C4—81no—
244C4—82no—
245C4—81no—
246C4—82no—
247C4C31×#45812yes—
248C2—22no—
249C2—42no—
250C2C31×#201711yescharacteristic
251C2C31×#202011yescharacteristic
252C2C31×#202211yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31#41
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
81. #9979C31direct (N × H)
176. C31#9979direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31892
C31×#30952
C31×#18182
C31×#14722
C31×#12932
#997931