Finite Group Databasebeta

← C31×#10576 #21467335

Subgroups — C31×#10576 #21467335

Order 7936.

406 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 146 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×#1948C212yesmaximal
3C31×#1845C211yesmaximal, characteristic
4C31×#1296C211yesmaximal, characteristic
5C31×#1279C212yesmaximal
6C2×C31×#107—22no—
7C2×C31×#106—22no—
8C2×C31×C4⋊C8C2212yes—
9C2×C4×C8×C31C2211yescharacteristic
10C31×#400—22no—
11C31×#389—22no—
12C31×#384C2211yescharacteristic
13C31×#384C2211yescharacteristic
14C31×#382—22no—
15C4×C4⋊C4×C31C2212yes—
16C31×#340—22no—
17C22×C8×C31—21no—
18C22×C8×C31—22no—
19C2×C4⋊C4×C31—22no—
20C2×C4⋊C4×C31—22no—
21C2×C4⋊C4×C31—21no—
22C2×C4⋊C4×C31—22no—
23C2×C4⋊C4×C31D412yes—
24C2×C4⋊C4×C31D412yes—
25C2×C4⋊C4×C31D412yes—
26C2×C42×C31—22no—
27C2×C42×C31C2311yescharacteristic
28C31×#107—44no—
29C31×#106—44no—
30C31×C4⋊C8—22no—
31C31×C4⋊C8Q814yes—
32C4×C8×C31—21no—
33C4×C8×C31Q812yes—
34C31×#95—22no—
35C31×#95—24no—
36C31×#95—22no—
37C22×C4×C31—22no—
38C22×C4×C31—22no—
39C22×C4×C31—22no—
40C22×C4×C31—41no—
41C22×C4×C31C2×D411yescharacteristic
42C22×C4×C31C2×D412yes—
43C2×C8×C31—22no—
44C2×C8×C31—22no—
45C2×C8×C31—22no—
46C2×C8×C31—24no—
47C2×C8×C31—42no—
48C2×C8×C31—42no—
49C4⋊C4×C31—22no—
50C4⋊C4×C31—22no—
51C4⋊C4×C31—22no—
52C4⋊C4×C31—22no—
53C4⋊C4×C31—42no—
54C4⋊C4×C31—42no—
55C4⋊C4×C31—42no—
56C4⋊C4×C31—42no—
57C4⋊C4×C31—42no—
58C4⋊C4×C31—42no—
59C4⋊C4×C31—82no—
60C42×C31—42no—
61C42×C31—42no—
62C42×C31C2×Q811yescharacteristic
63C42×C31C2×Q812yes—
64C42×C31#4111yescharacteristic
65#10576C3111yesmaximal, characteristic, direct product factor, Sylow
66C23×C31#12011yescharacteristic
67C2×C4×C31—21no—
68C2×C4×C31—21no—
69C2×C4×C31—42no—
70C2×C4×C31—44no—
71C2×C4×C31—42no—
72C2×C4×C31—42no—
73C2×C4×C31—42no—
74C2×C4×C31—42no—
75C2×C4×C31—42no—
76C2×C4×C31—42no—
77C2×C4×C31—82no—
78C2×C4×C31—81no—
79C2×C4×C31C22⋊Q811yescharacteristic
80C2×C4×C31C22⋊Q812yes—
81C2×C4×C31C4⋊Q811yescharacteristic
82C2×C4×C31C4⋊Q812yes—
83C2×C4×C31#13512yes—
84C2×C4×C31#13512yes—
85C2×C4×C31AGL(1,ℤ/8)12yes—
86C2×C4×C31#13712yes—
87C8×C31—24no—
88C8×C31—44no—
89#2571C2×C3111yescharacteristic
90#1948C2×C3112yes—
91#1845C2×C3111yescharacteristic
92#1296C2×C3111yescharacteristic
93#1279C2×C3112yes—
94C22×C31#39511yescharacteristic
95C22×C31#44912yes—
96C22×C31#45212yes—
97C22×C31#45311yescharacteristic
98C22×C31#45611yescharacteristic
99C4×C31—21no—
100C4×C31—21no—
101C4×C31—82no—
102C4×C31—82no—
103C4×C31—82no—
104C4×C31—161no—
105C4×C31#47812yes—
106C4×C31#47912yes—
107C4×C31#49912yes—
108C4×C31#50112yes—
109C2×#107—22no—
110C2×#106—22no—
111C2×C4⋊C8C22×C3112yes—
112C2×C4×C8C22×C3111yescharacteristic
113#400—22no—
114#389—22no—
115#384C22×C3111yescharacteristic
116#384C22×C3111yescharacteristic
117#382—22no—
118C4×C4⋊C4C22×C3112yes—
119#340—22no—
120C2×C31#162011yescharacteristic
121C2×C31#163411yescharacteristic
122C2×C31#165012yes—
123C2×C31#205912yes—
124C2×C31#206011yescharacteristic
125C22×C8—21no—
126C22×C8—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4D4×C3112yes—
132C2×C4⋊C4D4×C3112yes—
133C2×C4⋊C4D4×C3112yes—
134C2×C42—22no—
135C2×C42C23×C3111yescharacteristic
136#107—44no—
137#106—44no—
138C4⋊C8—22no—
139C4⋊C8Q8×C3114yes—
140C4×C8—21no—
141C4×C8Q8×C3112yes—
142#95—22no—
143#95—24no—
144#95—22no—
145C31#1057611yescharacteristic, direct product factor, Sylow
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—41no—
150C22×C4C2×D4×C3111yescharacteristic
151C22×C4C2×D4×C3112yes—
152C2×C8—22no—
153C2×C8—22no—
154C2×C8—22no—
155C2×C8—24no—
156C2×C8—42no—
157C2×C8—42no—
158C4⋊C4—22no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—42no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—82no—
169C42—42no—
170C42—42no—
171C42C2×Q8×C3111yescharacteristic
172C42C2×Q8×C3112yes—
173C42#41×C3111yescharacteristic
174C23C31×#12011yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—44no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—81no—
187C2×C4C31×C22⋊Q811yescharacteristic
188C2×C4C31×C22⋊Q812yes—
189C2×C4C31×C4⋊Q811yescharacteristic
190C2×C4C31×C4⋊Q812yes—
191C2×C4C31×#13512yes—
192C2×C4C31×#13512yes—
193C2×C4C31×AGL(1,ℤ/8)12yes—
194C2×C4C31×#13712yes—
195C8—24no—
196C8—44no—
197C22C31×#39511yescharacteristic
198C22C31×#44912yes—
199C22C31×#45212yes—
200C22C31×#45311yescharacteristic
201C22C31×#45611yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—82no—
206C4—82no—
207C4—161no—
208C4C31×#47812yes—
209C4C31×#47912yes—
210C4C31×#49912yes—
211C4C31×#50112yes—
212C2C31×#162011yescharacteristic
213C2C31×#163411yescharacteristic
214C2C31×#165012yes—
215C2C31×#205912yes—
216C2C31×#206011yescharacteristic
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
65. #10576C31direct (N × H)
145. C31#10576direct (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×#19482
C31×#18452
C31×#12962
C31×#12792
#1057631