Finite Group Databasebeta

← C31×#10352 #21467111

Subgroups — C31×#10352 #21467111

Order 7936.

416 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 138 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×#2571C211yesmaximal, characteristic
2C31×#1987C212yesmaximal
3C31×#1956C211yesmaximal, characteristic
4C31×#1296C211yesmaximal, characteristic
5C31×#1279C212yesmaximal
6C2×C31×C4⋊Q8C2211yescharacteristic
7C2×C31×C4⋊C8C2212yes—
8C2×C31×#103—22no—
9C2×C4×C8×C31C2211yescharacteristic
10C31×#400—22no—
11C31×#389—22no—
12C31×#384C2211yescharacteristic
13C31×#382—22no—
14C4×C4⋊C4×C31C2212yes—
15C31×#340—22no—
16C31×#340—22no—
17C22×Q8×C31—21no—
18C22×C8×C31—21no—
19C22×C8×C31—22no—
20C31×C4⋊Q8—22no—
21C31×C4⋊Q8—21no—
22C31×C4⋊Q8Q812yes—
23C2×C4⋊C4×C31—22no—
24C2×C4⋊C4×C31—22no—
25C2×C4⋊C4×C31—22no—
26C2×C4⋊C4×C31D412yes—
27C2×C4⋊C4×C31D412yes—
28C2×C4⋊C4×C31D412yes—
29C2×C42×C31—22no—
30C2×C42×C31C2311yescharacteristic
31C31×C4⋊C8—22no—
32C31×C4⋊C8—22no—
33C31×#103—44no—
34C4×C8×C31—22no—
35C31×#95—22no—
36C31×#95—24no—
37C31×#95—22no—
38C2×Q8×C31—22no—
39C2×Q8×C31—42no—
40C2×Q8×C31—42no—
41C2×Q8×C31—41no—
42C22×C4×C31—22no—
43C22×C4×C31—22no—
44C22×C4×C31—22no—
45C22×C4×C31—41no—
46C22×C4×C31C2×D411yescharacteristic
47C22×C4×C31C2×D412yes—
48C2×C8×C31—22no—
49C2×C8×C31—41no—
50C2×C8×C31—41no—
51C2×C8×C31—42no—
52C2×C8×C31—42no—
53C2×C8×C31—42no—
54C4⋊C4×C31—24no—
55C4⋊C4×C31—22no—
56C4⋊C4×C31—22no—
57C4⋊C4×C31—22no—
58C4⋊C4×C31—22no—
59C4⋊C4×C31—42no—
60C4⋊C4×C31—42no—
61C4⋊C4×C31—42no—
62C4⋊C4×C31—42no—
63C4⋊C4×C31—82no—
64C42×C31—42no—
65C42×C31—42no—
66C42×C31C2×Q811yescharacteristic
67C42×C31#4112yes—
68C42×C31#4111yescharacteristic
69#10352C3111yesmaximal, characteristic, direct product factor, Sylow
70C23×C31#12011yescharacteristic
71Q8×C31—44no—
72Q8×C31—82no—
73C2×C4×C31—21no—
74C2×C4×C31—21no—
75C2×C4×C31—42no—
76C2×C4×C31—42no—
77C2×C4×C31—42no—
78C2×C4×C31—42no—
79C2×C4×C31—42no—
80C2×C4×C31—44no—
81C2×C4×C31—42no—
82C2×C4×C31—42no—
83C2×C4×C31—42no—
84C2×C4×C31—81no—
85C2×C4×C31—81no—
86C2×C4×C31C22⋊Q811yescharacteristic
87C2×C4×C31C22⋊Q812yes—
88C2×C4×C31#12411yescharacteristic
89C2×C4×C31#12412yes—
90C2×C4×C31#13512yes—
91C2×C4×C31#13512yes—
92C2×C4×C31#13712yes—
93C2×C4×C31#13712yes—
94C8×C31—42no—
95C8×C31—82no—
96#2571C2×C3111yescharacteristic
97#1987C2×C3112yes—
98#1956C2×C3111yescharacteristic
99#1296C2×C3111yescharacteristic
100#1279C2×C3112yes—
101C22×C31#39311yescharacteristic
102C22×C31#45212yes—
103C22×C31#45212yes—
104C22×C31#45311yescharacteristic
105C22×C31#45411yescharacteristic
106C4×C31—21no—
107C4×C31—21no—
108C4×C31—82no—
109C4×C31—82no—
110C4×C31—82no—
111C4×C31—82no—
112C4×C31#47912yes—
113C4×C31#47912yes—
114C4×C31#48812yes—
115C4×C31#49112yes—
116C2×C4⋊Q8C22×C3111yescharacteristic
117C2×C4⋊C8C22×C3112yes—
118C2×#103—22no—
119C2×C4×C8C22×C3111yescharacteristic
120#400—22no—
121#389—22no—
122#384C22×C3111yescharacteristic
123#382—22no—
124C4×C4⋊C4C22×C3112yes—
125#340—22no—
126#340—22no—
127C2×C31#163011yescharacteristic
128C2×C31#163411yescharacteristic
129C2×C31#163812yes—
130C2×C31#202612yes—
131C2×C31#202711yescharacteristic
132C22×Q8—21no—
133C22×C8—21no—
134C22×C8—22no—
135C4⋊Q8—22no—
136C4⋊Q8—21no—
137C4⋊Q8Q8×C3112yes—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4D4×C3112yes—
142C2×C4⋊C4D4×C3112yes—
143C2×C4⋊C4D4×C3112yes—
144C2×C42—22no—
145C2×C42C23×C3111yescharacteristic
146C4⋊C8—22no—
147C4⋊C8—22no—
148#103—44no—
149C4×C8—22no—
150#95—22no—
151#95—24no—
152#95—22no—
153C31#1035211yescharacteristic, direct product factor, Sylow
154C2×Q8—22no—
155C2×Q8—42no—
156C2×Q8—42no—
157C2×Q8—41no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—41no—
162C22×C4C2×D4×C3111yescharacteristic
163C22×C4C2×D4×C3112yes—
164C2×C8—22no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—42no—
168C2×C8—42no—
169C2×C8—42no—
170C4⋊C4—24no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4—82no—
180C42—42no—
181C42—42no—
182C42C2×Q8×C3111yescharacteristic
183C42#41×C3112yes—
184C42#41×C3111yescharacteristic
185C23C31×#12011yescharacteristic
186Q8—44no—
187Q8—82no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—44no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—81no—
200C2×C4—81no—
201C2×C4C31×C22⋊Q811yescharacteristic
202C2×C4C31×C22⋊Q812yes—
203C2×C4C31×#12411yescharacteristic
204C2×C4C31×#12412yes—
205C2×C4C31×#13512yes—
206C2×C4C31×#13512yes—
207C2×C4C31×#13712yes—
208C2×C4C31×#13712yes—
209C8—42no—
210C8—82no—
211C22C31×#39311yescharacteristic
212C22C31×#45212yes—
213C22C31×#45212yes—
214C22C31×#45311yescharacteristic
215C22C31×#45411yescharacteristic
216C4—21no—
217C4—21no—
218C4—82no—
219C4—82no—
220C4—82no—
221C4—82no—
222C4C31×#47912yes—
223C4C31×#47912yes—
224C4C31×#48812yes—
225C4C31×#49112yes—
226C2C31×#163011yescharacteristic
227C2C31×#163411yescharacteristic
228C2C31×#163812yes—
229C2C31×#202612yes—
230C2C31×#202711yescharacteristic
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
69. #10352C31direct (N × H)
153. C31#10352direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25712
C31×#19872
C31×#19562
C31×#12962
C31×#12792
#1035231