Finite Group Databasebeta

← C31×#11468 #21468227

Subgroups — C31×#11468 #21468227

Order 7936.

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

normal subgroups only

This group has 398 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×#2929C211yesmaximal, characteristic
2C2×C31×C22⋊C16C212yesmaximal, complemented
3C31×#1323C212yesmaximal, complemented
4C31×#1315C212yesmaximal, complemented
5C2×C31×#131C411yescharacteristic
6C23×C8×C31C2211yescharacteristic
7C31×#525C411yescharacteristic
8C22×C16×C31—22no—
9C31×#435—22no—
10C8×D4×C31—22no—
11C31×#424C2211yescharacteristic
12C31×#408C2211yescharacteristic
13C31×#407C411yescharacteristic
14C31×#405C411yescharacteristic
15C31×C22⋊C16—22no—
16C31×C22⋊C16C2214yes—
17C2×#41×C31C2×C411yescharacteristic
18C23×C4×C31C2×C411yescharacteristic
19C31×#131—42no—
20C2×M16×C31—21no—
21C2×M16×C31C2×C411yescharacteristic
22C2×M16×C31C2×C411yescharacteristic
23C22×C8×C31—21no—
24C22×C8×C31—42no—
25C22×C8×C31C2×C411yescharacteristic
26C22×C8×C31D412yes—
27C22×C8×C31D412yes—
28C22×C8×C31C2311yescharacteristic
29C31×#123—21no—
30C31×C22⋊Q8C812yes—
31C31×#121C812yes—
32C31×#120—21no—
33C4×D4×C31—22no—
34C31×#117C2×C411yescharacteristic
35C2×C16×C31—24no—
36C2×C16×C31—44no—
37C31×C4⋊C8—22no—
38C31×C22⋊C8—22no—
39C31×C22⋊C8—22no—
40C31×#97—21no—
41C4×C8×C31—21no—
42C24×C31M1611yescharacteristic
43#41×C31—41no—
44#41×C31—41no—
45C2×Q8×C31C2×C811yescharacteristic
46C2×D4×C31—22no—
47C2×D4×C31—21no—
48C2×D4×C31C2×C811yescharacteristic
49C22×C4×C31—21no—
50C22×C4×C31—41no—
51C22×C4×C31—41no—
52C22×C4×C31C22⋊C412yes—
53C22×C4×C31C2×C812yes—
54C22×C4×C31M1611yescharacteristic
55C22×C4×C31C22×C411yescharacteristic
56M16×C31—42no—
57M16×C31—41no—
58M16×C31—41no—
59C2×C8×C31—24no—
60C2×C8×C31—22no—
61C2×C8×C31—21no—
62C2×C8×C31—21no—
63C2×C8×C31—42no—
64C2×C8×C31—41no—
65C2×C8×C31—42no—
66C2×C8×C31C22⋊C411yescharacteristic
67C2×C8×C31C22⋊C411yescharacteristic
68C2×C8×C31C2×D412yes—
69C4⋊C4×C31—22no—
70C4⋊C4×C31C2×C812yes—
71C22⋊C4×C31—22no—
72C22⋊C4×C31—21no—
73C22⋊C4×C31—22no—
74C42×C31—21no—
75C16×C31—44no—
76#11468C3111yesmaximal, characteristic, direct product factor, Sylow
77C23×C31—24no—
78C23×C31—21no—
79C23×C31—41no—
80C23×C31C22⋊C812yes—
81C23×C31C2×M1611yescharacteristic
82Q8×C31—41no—
83D4×C31—41no—
84D4×C31—42no—
85D4×C31—44no—
86C2×C4×C31—21no—
87C2×C4×C31—22no—
88C2×C4×C31—21no—
89C2×C4×C31—22no—
90C2×C4×C31—22no—
91C2×C4×C31—21no—
92C2×C4×C31—42no—
93C2×C4×C31—41no—
94C2×C4×C31—41no—
95C2×C4×C31—41no—
96C2×C4×C31C22⋊C812yes—
97C2×C4×C31C2×C22⋊C411yescharacteristic
98C2×C4×C31C22×C811yescharacteristic
99C8×C31—22no—
100C8×C31—21no—
101C8×C31—41no—
102C8×C31—41no—
103C8×C31#9912yes—
104#2929C2×C3111yescharacteristic
105C2×C22⋊C16C2×C3112yescomplemented
106#1323C2×C3112yescomplemented
107#1315C2×C3112yescomplemented
108C22×C31—22no—
109C22×C31—22no—
110C22×C31—22no—
111C22×C31—21no—
112C22×C31—44no—
113C22×C31—42no—
114C22×C31—41no—
115C22×C31#35014yes—
116C22×C31C2×C22⋊C811yescharacteristic
117C4×C31—22no—
118C4×C31—21no—
119C4×C31—42no—
120C4×C31—41no—
121C4×C31C2×#9911yescharacteristic
122C4×C31#41311yescharacteristic
123C2×#131C4×C3111yescharacteristic
124C23×C8C22×C3111yescharacteristic
125#525C4×C3111yescharacteristic
126C22×C16—22no—
127#435—22no—
128C8×D4—22no—
129#424C22×C3111yescharacteristic
130#408C22×C3111yescharacteristic
131#407C4×C3111yescharacteristic
132#405C4×C3111yescharacteristic
133C22⋊C16—22no—
134C22⋊C16C22×C3114yes—
135C2×C31—24no—
136C2×C31—41no—
137C2×C31—81no—
138C2×C31#145911yescharacteristic
139C2×C31C2×#35012yes—
140C2×#41C2×C4×C3111yescharacteristic
141C23×C4C2×C4×C3111yescharacteristic
142#131—42no—
143C2×M16—21no—
144C2×M16C2×C4×C3111yescharacteristic
145C2×M16C2×C4×C3111yescharacteristic
146C22×C8—21no—
147C22×C8—42no—
148C22×C8C2×C4×C3111yescharacteristic
149C22×C8D4×C3112yes—
150C22×C8D4×C3112yes—
151C22×C8C23×C3111yescharacteristic
152#123—21no—
153C22⋊Q8C8×C3112yes—
154#121C8×C3112yes—
155#120—21no—
156C4×D4—22no—
157#117C2×C4×C3111yescharacteristic
158C2×C16—24no—
159C2×C16—44no—
160C4⋊C8—22no—
161C22⋊C8—22no—
162C22⋊C8—22no—
163#97—21no—
164C4×C8—21no—
165C31#1146811yescharacteristic, direct product factor, Sylow
166C24M16×C3111yescharacteristic
167#41—41no—
168#41—41no—
169C2×Q8C2×C8×C3111yescharacteristic
170C2×D4—22no—
171C2×D4—21no—
172C2×D4C2×C8×C3111yescharacteristic
173C22×C4—21no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4C22⋊C4×C3112yes—
177C22×C4C2×C8×C3112yes—
178C22×C4M16×C3111yescharacteristic
179C22×C4C22×C4×C3111yescharacteristic
180M16—42no—
181M16—41no—
182M16—41no—
183C2×C8—24no—
184C2×C8—22no—
185C2×C8—21no—
186C2×C8—21no—
187C2×C8—42no—
188C2×C8—41no—
189C2×C8—42no—
190C2×C8C22⋊C4×C3111yescharacteristic
191C2×C8C22⋊C4×C3111yescharacteristic
192C2×C8C2×D4×C3112yes—
193C4⋊C4—22no—
194C4⋊C4C2×C8×C3112yes—
195C22⋊C4—22no—
196C22⋊C4—21no—
197C22⋊C4—22no—
198C42—21no—
199C16—44no—
200C23—24no—
201C23—21no—
202C23—41no—
203C23C31×C22⋊C812yes—
204C23C2×M16×C3111yescharacteristic
205Q8—41no—
206D4—41no—
207D4—42no—
208D4—44no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—42no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4C31×C22⋊C812yes—
220C2×C4C2×C22⋊C4×C3111yescharacteristic
221C2×C4C22×C8×C3111yescharacteristic
222C8—22no—
223C8—21no—
224C8—41no—
225C8—41no—
226C8C31×#9912yes—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—44no—
232C22—42no—
233C22—41no—
234C22C31×#35014yes—
235C22C2×C31×C22⋊C811yescharacteristic
236C4—22no—
237C4—21no—
238C4—42no—
239C4—41no—
240C4C2×C31×#9911yescharacteristic
241C4C31×#41311yescharacteristic
242C2—24no—
243C2—41no—
244C2—81no—
245C2C31×#145911yescharacteristic
246C2C2×C31×#35012yes—
subgroupG/H
centerC2×C8×C31C22⋊C4
commutatorC2×C4C22×C8×C31
Frattini, cosocleC22×C8C23×C31
socleC22×C31C2×C22⋊C8
prime radicalC31×#525C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C8×C31 ◁ C23×C8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×C22⋊C16C2semidirect
3. C31×#1323C2semidirect
4. C31×#1315C2semidirect
76. #11468C31direct (N × H)
105. C2×C22⋊C16C2×C31semidirect
106. #1323C2×C31semidirect
107. #1315C2×C31semidirect
165. C31#11468direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29292
C2×C31×C22⋊C162
C31×#13232
C31×#13152
#1146831