Finite Group Databasebeta

← C31×#2065 #16841998

Subgroups — C31×#2065 #16841998

Order 3968.

284 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C2×C31×#106C211yesmaximal, characteristic, complemented
2C2×C31×C4⋊C8C211yesmaximal, characteristic, complemented
3C2×C31×#102C211yesmaximal, characteristic
4C2×C31×#102C211yesmaximal, characteristic
5C31×#390C211yesmaximal, characteristic
6C31×#389C211yesmaximal, characteristic, complemented
7C31×#340C211yesmaximal, characteristic, complemented
8C22×D4×C31C2211yescharacteristic
9C22×C8×C31C2211yescharacteristic
10C22×C8×C31C2211yescharacteristic
11C2×C4⋊C4×C31—21no—
12C2×C4⋊C4×C31C2211yescharacteristic
13C2×C4⋊C4×C31C2211yescharacteristic
14C2×C4⋊C4×C31C2211yescharacteristic
15C2×C22⋊C4×C31—21no—
16C2×C22⋊C4×C31—21no—
17C2×C42×C31C2211yescharacteristic
18C31×#106—22no—
19C31×C4⋊C8—22no—
20C31×#102—22no—
21C31×#102—22no—
22C31×#95—21no—
23C24×C31—21no—
24C2×D4×C31—21no—
25C2×D4×C31—21no—
26C2×D4×C31—21no—
27C2×D4×C31—21no—
28C2×D4×C31—21no—
29C2×D4×C31Q812yes—
30C22×C4×C31—21no—
31C22×C4×C31—21no—
32C22×C4×C31—21no—
33C22×C4×C31D411yescharacteristic
34C22×C4×C31D411yescharacteristic
35C22×C4×C31C2311yescharacteristic
36C2×C8×C31—21no—
37C2×C8×C31—21no—
38C2×C8×C31—21no—
39C2×C8×C31—21no—
40C2×C8×C31—21no—
41C2×C8×C31D412yes—
42C4⋊C4×C31—21no—
43C4⋊C4×C31—21no—
44C4⋊C4×C31—21no—
45C4⋊C4×C31—21no—
46C4⋊C4×C31—21no—
47C4⋊C4×C31—42no—
48C4⋊C4×C31D412yes—
49C22⋊C4×C31—42no—
50C22⋊C4×C31—42no—
51C42×C31—21no—
52C42×C31—21no—
53C23×C31—22no—
54C23×C31—41no—
55C23×C31—41no—
56C23×C31—41no—
57C23×C31—41no—
58C23×C31—41no—
59C23×C31—41no—
60C23×C31C2×D411yescharacteristic
61D4×C31—22no—
62D4×C31—22no—
63D4×C31—41no—
64D4×C31—41no—
65C2×C4×C31—21no—
66C2×C4×C31—21no—
67C2×C4×C31—21no—
68C2×C4×C31—22no—
69C2×C4×C31—21no—
70C2×C4×C31—21no—
71C2×C4×C31—41no—
72C2×C4×C31—41no—
73C2×C4×C31—41no—
74C2×C4×C31—41no—
75C2×C4×C31—41no—
76C2×C4×C31—41no—
77C2×C4×C31—41no—
78C2×C4×C31—41no—
79C2×C4×C31SD1612yes—
80C2×C4×C31C2×D411yescharacteristic
81C2×C4×C31C2×D411yescharacteristic
82C2×C4×C31C2×Q811yescharacteristic
83C2×C4×C31#4111yescharacteristic
84C2×C4×C31#4111yescharacteristic
85C2×C4×C31#4111yescharacteristic
86C8×C31—22no—
87C8×C31—41no—
88#2065C3111yesmaximal, characteristic, direct product factor, Sylow
89C22×C31—42no—
90C22×C31—42no—
91C22×C31—42no—
92C22×C31—81no—
93C22×C31—81no—
94C22×C31—81no—
95C22×C31—81no—
96C22×C31#12111yescharacteristic
97C22×C31#12111yescharacteristic
98C22×C31C22⋊Q811yescharacteristic
99C22×C31C2×SD1611yescharacteristic
100C22×C31#13511yescharacteristic
101C22×C31AGL(1,ℤ/8)11yescharacteristic
102C22×C31AGL(1,ℤ/8)11yescharacteristic
103C4×C31—22no—
104C4×C31—42no—
105C4×C31—41no—
106C4×C31—81no—
107C4×C31—81no—
108C4×C31#12111yescharacteristic
109C4×C31C22⋊Q811yescharacteristic
110C4×C31C22⋊Q811yescharacteristic
111C4×C31#12611yescharacteristic
112C2×#106C2×C3111yescharacteristic, complemented
113C2×C4⋊C8C2×C3111yescharacteristic, complemented
114C2×#102C2×C3111yescharacteristic
115C2×#102C2×C3111yescharacteristic
116#390C2×C3111yescharacteristic
117#389C2×C3111yescharacteristic, complemented
118#340C2×C3111yescharacteristic, complemented
119C2×C31—82no—
120C2×C31#39611yescharacteristic
121C2×C31#46011yescharacteristic
122C2×C31#46311yescharacteristic
123C2×C31#46511yescharacteristic
124C2×C31#46911yescharacteristic
125C2×C31#47611yescharacteristic
126C2×C31#47811yescharacteristic
127C22×D4C22×C3111yescharacteristic
128C22×C8C22×C3111yescharacteristic
129C22×C8C22×C3111yescharacteristic
130C2×C4⋊C4—21no—
131C2×C4⋊C4C22×C3111yescharacteristic
132C2×C4⋊C4C22×C3111yescharacteristic
133C2×C4⋊C4C22×C3111yescharacteristic
134C2×C22⋊C4—21no—
135C2×C22⋊C4—21no—
136C2×C42C22×C3111yescharacteristic
137#106—22no—
138C4⋊C8—22no—
139#102—22no—
140#102—22no—
141#95—21no—
142C31#206511yescharacteristic, direct product factor, Sylow
143C24—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4Q8×C3112yes—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4D4×C3111yescharacteristic
154C22×C4D4×C3111yescharacteristic
155C22×C4C23×C3111yescharacteristic
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8D4×C3112yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—42no—
168C4⋊C4D4×C3112yes—
169C22⋊C4—42no—
170C22⋊C4—42no—
171C42—21no—
172C42—21no—
173C23—22no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23—41no—
179C23—41no—
180C23C2×D4×C3111yescharacteristic
181D4—22no—
182D4—22no—
183D4—41no—
184D4—41no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4SD16×C3112yes—
200C2×C4C2×D4×C3111yescharacteristic
201C2×C4C2×D4×C3111yescharacteristic
202C2×C4C2×Q8×C3111yescharacteristic
203C2×C4#41×C3111yescharacteristic
204C2×C4#41×C3111yescharacteristic
205C2×C4#41×C3111yescharacteristic
206C8—22no—
207C8—41no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—81no—
212C22—81no—
213C22—81no—
214C22—81no—
215C22C31×#12111yescharacteristic
216C22C31×#12111yescharacteristic
217C22C31×C22⋊Q811yescharacteristic
218C22C2×SD16×C3111yescharacteristic
219C22C31×#13511yescharacteristic
220C22C31×AGL(1,ℤ/8)11yescharacteristic
221C22C31×AGL(1,ℤ/8)11yescharacteristic
222C4—22no—
223C4—42no—
224C4—41no—
225C4—81no—
226C4—81no—
227C4C31×#12111yescharacteristic
228C4C31×C22⋊Q811yescharacteristic
229C4C31×C22⋊Q811yescharacteristic
230C4C31×#12611yescharacteristic
231C2—82no—
232C2C31×#39611yescharacteristic
233C2C31×#46011yescharacteristic
234C2C31×#46311yescharacteristic
235C2C31×#46511yescharacteristic
236C2C31×#46911yescharacteristic
237C2C31×#47611yescharacteristic
238C2C31×#47811yescharacteristic
subgroupG/H
center, socleC23×C31C2×D4
commutator, Frattini, cosocleC22×C4C23×C31
prime radicalC22×D4×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#106C2semidirect
2. C2×C31×C4⋊C8C2semidirect
6. C31×#389C2semidirect
7. C31×#340C2semidirect
88. #2065C31direct (N × H)
112. C2×#106C2×C31semidirect
113. C2×C4⋊C8C2×C31semidirect
117. #389C2×C31semidirect
118. #340C2×C31semidirect
142. C31#2065direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#1062
C2×C31×C4⋊C82
C2×C31×#1022
C31×#3902
C31×#3892
C31×#3402
#206531