Finite Group Databasebeta

← C31×#10574 #21467333

Subgroups — C31×#10574 #21467333

Order 7936.

494 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 162 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×#2551C211yesmaximal, characteristic
2C31×#1948C212yesmaximal
3C31×#1844C211yesmaximal, characteristic
4C31×#1296C211yesmaximal, characteristic
5C31×#1279C212yesmaximal
6C2×C31×C4⋊Q8—22no—
7C2×C31×#106—22no—
8C2×C31×#106—22no—
9C2×C31×C4⋊C8C2212yes—
10C2×C4×C8×C31C2211yescharacteristic
11C31×#395—22no—
12C31×#389—22no—
13C31×#384C2211yescharacteristic
14C31×#384C2211yescharacteristic
15C4×C4⋊C4×C31C2212yes—
16C31×#340—22no—
17C22×Q8×C31—22no—
18C22×C8×C31—21no—
19C22×C8×C31—22no—
20C31×C4⋊Q8—44no—
21C31×C4⋊Q8—44no—
22C2×C4⋊C4×C31—24no—
23C2×C4⋊C4×C31—22no—
24C2×C4⋊C4×C31—21no—
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×#106—44no—
32C31×#106—44no—
33C31×C4⋊C8—22no—
34C31×C4⋊C8Q814yescomplemented
35C4×C8×C31—21no—
36C4×C8×C31Q812yescomplemented
37C31×#95—22no—
38C31×#95—22no—
39C2×Q8×C31—48no—
40C2×Q8×C31—82no—
41C22×C4×C31—22no—
42C22×C4×C31—22no—
43C22×C4×C31—22no—
44C22×C4×C31—41no—
45C22×C4×C31C2×D411yescharacteristic
46C22×C4×C31C2×D412yes—
47C2×C8×C31—22no—
48C2×C8×C31—22no—
49C2×C8×C31—22no—
50C2×C8×C31—24no—
51C2×C8×C31—42no—
52C2×C8×C31—42no—
53C4⋊C4×C31—22no—
54C4⋊C4×C31—22no—
55C4⋊C4×C31—48no—
56C4⋊C4×C31—42no—
57C4⋊C4×C31—42no—
58C4⋊C4×C31—42no—
59C4⋊C4×C31—42no—
60C4⋊C4×C31—42no—
61C4⋊C4×C31—42no—
62C4⋊C4×C31SD1614yes—
63C4⋊C4×C31SD1614yes—
64C42×C31—42no—
65C42×C31—42no—
66C42×C31C2×Q811yescharacteristic
67C42×C31C2×Q812yes—
68C42×C31#4111yescharacteristic
69#10574C3111yesmaximal, characteristic, direct product factor, Sylow
70C23×C31#12011yescharacteristic
71Q8×C31—88no—
72C2×C4×C31—21no—
73C2×C4×C31—21no—
74C2×C4×C31—24no—
75C2×C4×C31—24no—
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—82no—
83C2×C4×C31—81no—
84C2×C4×C31C22⋊Q811yescharacteristic
85C2×C4×C31C22⋊Q812yes—
86C2×C4×C31C4⋊Q811yescharacteristic
87C2×C4×C31C4⋊Q812yes—
88C2×C4×C31C2×SD1612yes—
89C2×C4×C31C2×SD1612yes—
90C2×C4×C31AGL(1,ℤ/8)12yes—
91C2×C4×C31#13712yes—
92C8×C31—24no—
93C8×C31—44no—
94#2551C2×C3111yescharacteristic
95#1948C2×C3112yes—
96#1844C2×C3111yescharacteristic
97#1296C2×C3111yescharacteristic
98#1279C2×C3112yes—
99C22×C31#39511yescharacteristic
100C22×C31#44812yes—
101C22×C31#45012yes—
102C22×C31#45311yescharacteristic
103C22×C31#45611yescharacteristic
104C4×C31—21no—
105C4×C31—21no—
106C4×C31—44no—
107C4×C31—44no—
108C4×C31—82no—
109C4×C31—161no—
110C4×C31#47512yes—
111C4×C31#47612yes—
112C4×C31#49812yes—
113C4×C31#50112yes—
114C2×C4⋊Q8—22no—
115C2×#106—22no—
116C2×#106—22no—
117C2×C4⋊C8C22×C3112yes—
118C2×C4×C8C22×C3111yescharacteristic
119#395—22no—
120#389—22no—
121#384C22×C3111yescharacteristic
122#384C22×C3111yescharacteristic
123C4×C4⋊C4C22×C3112yes—
124#340—22no—
125C2×C31#162311yescharacteristic
126C2×C31#162911yescharacteristic
127C2×C31#165112yes—
128C2×C31#205812yes—
129C2×C31#206011yescharacteristic
130C22×Q8—22no—
131C22×C8—21no—
132C22×C8—22no—
133C4⋊Q8—44no—
134C4⋊Q8—44no—
135C2×C4⋊C4—24no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4D4×C3112yes—
140C2×C4⋊C4D4×C3112yes—
141C2×C4⋊C4D4×C3112yes—
142C2×C42—22no—
143C2×C42C23×C3111yescharacteristic
144#106—44no—
145#106—44no—
146C4⋊C8—22no—
147C4⋊C8Q8×C3114yescomplemented
148C4×C8—21no—
149C4×C8Q8×C3112yescomplemented
150#95—22no—
151#95—22no—
152C31#1057411yescharacteristic, direct product factor, Sylow
153C2×Q8—48no—
154C2×Q8—82no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—41no—
159C22×C4C2×D4×C3111yescharacteristic
160C22×C4C2×D4×C3112yes—
161C2×C8—22no—
162C2×C8—22no—
163C2×C8—22no—
164C2×C8—24no—
165C2×C8—42no—
166C2×C8—42no—
167C4⋊C4—22no—
168C4⋊C4—22no—
169C4⋊C4—42no—
170C4⋊C4—48no—
171C4⋊C4—42no—
172C4⋊C4—42no—
173C4⋊C4—42no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4SD16×C3114yes—
177C4⋊C4SD16×C3114yes—
178C42—42no—
179C42—42no—
180C42C2×Q8×C3111yescharacteristic
181C42C2×Q8×C3112yes—
182C42#41×C3111yescharacteristic
183C23C31×#12011yescharacteristic
184Q8—88no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—24no—
188C2×C4—24no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—42no—
195C2×C4—82no—
196C2×C4—81no—
197C2×C4C31×C22⋊Q811yescharacteristic
198C2×C4C31×C22⋊Q812yes—
199C2×C4C31×C4⋊Q811yescharacteristic
200C2×C4C31×C4⋊Q812yes—
201C2×C4C2×SD16×C3112yes—
202C2×C4C2×SD16×C3112yes—
203C2×C4C31×AGL(1,ℤ/8)12yes—
204C2×C4C31×#13712yes—
205C8—24no—
206C8—44no—
207C22C31×#39511yescharacteristic
208C22C31×#44812yes—
209C22C31×#45012yes—
210C22C31×#45311yescharacteristic
211C22C31×#45611yescharacteristic
212C4—21no—
213C4—21no—
214C4—44no—
215C4—44no—
216C4—82no—
217C4—161no—
218C4C31×#47512yes—
219C4C31×#47612yes—
220C4C31×#49812yes—
221C4C31×#50112yes—
222C2C31×#162311yescharacteristic
223C2C31×#162911yescharacteristic
224C2C31×#165112yes—
225C2C31×#205812yes—
226C2C31×#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
34. C31×C4⋊C8Q8semidirect
36. C4×C8×C31Q8semidirect
69. #10574C31direct (N × H)
147. C4⋊C8Q8×C31semidirect
149. C4×C8Q8×C31semidirect
152. C31#10574direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25512
C31×#19482
C31×#18442
C31×#12962
C31×#12792
#1057431