Finite Group Databasebeta

← C2×C31×#2916 #21516871

Subgroups — C2×C31×#2916 #21516871

Order 7936.

2586 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#568C212yesmaximal
2C22×C31×#131C211yesmaximal, characteristic
3C31×#2916C2116yesmaximal, direct product factor
4C2×C31×#430C216yesmaximal, complemented
5C22×C31×#108C216yesmaximal, complemented
6C22×#41×C31C2211yescharacteristic
7C31×#568—28no—
8C31×#568C22116yes—
9C2×C31×#131—28no—
10C2×C31×#131C418yes—
11C2×C31×#131C418yes—
12C2×C31×#131C2218yes—
13C22×M16×C31C22112yes—
14C22×M16×C31C2213yes—
15C23×C8×C31C2213yes—
16C31×#430C22148yescomplemented
17C2×C31×#108C2214yes—
18C2×C31×#108C22112yes—
19C2×C31×#108C22148yescomplemented
20C2×#41×C31C2×C414yes—
21C2×#41×C31C2×C414yes—
22C2×#41×C31D414yes—
23C2×#41×C31D414yes—
24C2×#41×C31Q814yes—
25C2×#41×C31C2314yes—
26C22×Q8×C31Q811yescharacteristic
27C22×D4×C31Q813yes—
28C23×C4×C31C2313yes—
29C31×#131—264no—
30C31×#131C2×C4164yes—
31C2×M16×C31—212no—
32C2×M16×C31—224no—
33C2×M16×C31C2×C4112yes—
34C2×M16×C31C2×C4112yes—
35C2×M16×C31C2318yes—
36C2×M16×C31C23148yes—
37C2×M16×C31C23112yes—
38C22×C8×C31—212no—
39C22×C8×C31C2×C4112yes—
40C22×C8×C31C2×C4112yes—
41C22×C8×C31C2311yescharacteristic
42C22×C8×C31C2313yes—
43C22×C8×C31C23112yes—
44C31×#108C23116yes—
45C31×#108C23148yes—
46C24×C31C2×Q813yes—
47#41×C31C4⋊C4116yes—
48#41×C31C4⋊C4116yes—
49#41×C31C22×C4116yes—
50#41×C31C2×D4116yes—
51C2×Q8×C31C4⋊C414yes—
52C2×Q8×C31C4⋊C414yes—
53C2×Q8×C31C2×Q814yes—
54C2×D4×C31C4⋊C4112yes—
55C2×D4×C31C4⋊C4112yes—
56C2×D4×C31C2×Q8112yes—
57C22×C4×C31C22×C416yes—
58C22×C4×C31C22×C416yes—
59C22×C4×C31C2×D416yes—
60C22×C4×C31C2×D416yes—
61C22×C4×C31C2×Q813yes—
62C22×C4×C31C2×Q816yes—
63C22×C4×C31C2416yes—
64C22×C4×C31C2411yescharacteristic
65M16×C31—28no—
66M16×C31—248no—
67M16×C31C22×C4148yes—
68M16×C31C24116yes—
69C2×C8×C31—248no—
70C2×C8×C31—28no—
71C2×C8×C31C22×C412yes—
72C2×C8×C31C22×C412yes—
73C2×C8×C31C22×C416yes—
74C2×C8×C31C22×C416yes—
75C2×C8×C31C22×C4148yes—
76C2×C8×C31C2412yes—
77C2×C8×C31C2416yes—
78C2×#2916C3111yesmaximal, characteristic, direct product factor, Sylow
79C23×C31—46no—
80C23×C31C2×C4⋊C416yes—
81C23×C31C2×C4⋊C416yes—
82C23×C31C22×Q811yescharacteristic
83C23×C31C22×Q816yes—
84Q8×C31C2×C4⋊C4116yes—
85D4×C31C2×C4⋊C4148yes—
86C2×C4×C31C2×C4⋊C416yes—
87C2×C4×C31C2×C4⋊C416yes—
88C2×C4×C31C2×C4⋊C4112yes—
89C2×C4×C31C2×C4⋊C4112yes—
90C2×C4×C31C23×C411yescharacteristic
91C2×C4×C31C23×C411yescharacteristic
92C2×C4×C31C23×C4112yes—
93C2×C4×C31C22×D4112yes—
94C2×C4×C31C22×D411yescharacteristic
95C2×C4×C31C22×D411yescharacteristic
96C2×C4×C31C22×Q811yescharacteristic
97C2×C4×C31C22×Q816yes—
98C2×C4×C31C2511yescharacteristic
99C8×C31—216no—
100C8×C31C23×C414yes—
101C8×C31C23×C4112yes—
102C2×#568C2×C3112yes—
103C22×#131C2×C3111yescharacteristic
104#2916C2×C31116yesdirect product factor
105C2×#430C2×C3116yescomplemented
106C22×#108C2×C3116yescomplemented
107C22×C31—22no—
108C22×C31—212no—
109C22×C31—46no—
110C22×C31—46no—
111C22×C31C22×C4⋊C411yescharacteristic
112C22×C31C22×C4⋊C4112yes—
113C22×C31C22×C4⋊C411yescharacteristic
114C22×C31C23×Q811yescharacteristic
115C4×C31C22×C4⋊C411yescharacteristic
116C4×C31C22×C4⋊C411yescharacteristic
117C4×C31C22×C4⋊C4112yes—
118C4×C31C24×C411yescharacteristic
119C4×C31C23×D411yescharacteristic
120C22×#41C22×C3111yescharacteristic
121#568—28no—
122#568C22×C31116yes—
123C2×#131—28no—
124C2×#131C4×C3118yes—
125C2×#131C4×C3118yes—
126C2×#131C22×C3118yes—
127C22×M16C22×C31112yes—
128C22×M16C22×C3113yes—
129C23×C8C22×C3113yes—
130#430C22×C31148yescomplemented
131C2×#108C22×C3114yes—
132C2×#108C22×C31112yes—
133C2×#108C22×C31148yescomplemented
134C2×C31—21no—
135C2×C31—21no—
136C2×C31—212no—
137C2×C31#291612yesdirect product factor
138C2×C31C23×C4⋊C411yescharacteristic
139C2×#41C2×C4×C3114yes—
140C2×#41C2×C4×C3114yes—
141C2×#41D4×C3114yes—
142C2×#41D4×C3114yes—
143C2×#41Q8×C3114yes—
144C2×#41C23×C3114yes—
145C22×Q8Q8×C3111yescharacteristic
146C22×D4Q8×C3113yes—
147C23×C4C23×C3113yes—
148#131—264no—
149#131C2×C4×C31164yes—
150C2×M16—212no—
151C2×M16—224no—
152C2×M16C2×C4×C31112yes—
153C2×M16C2×C4×C31112yes—
154C2×M16C23×C3118yes—
155C2×M16C23×C31148yes—
156C2×M16C23×C31112yes—
157C22×C8—212no—
158C22×C8C2×C4×C31112yes—
159C22×C8C2×C4×C31112yes—
160C22×C8C23×C3111yescharacteristic
161C22×C8C23×C3113yes—
162C22×C8C23×C31112yes—
163#108C23×C31116yes—
164#108C23×C31148yes—
165C31C2×#291611yescharacteristic, direct product factor, Sylow
166C24C2×Q8×C3113yes—
167#41C4⋊C4×C31116yes—
168#41C4⋊C4×C31116yes—
169#41C22×C4×C31116yes—
170#41C2×D4×C31116yes—
171C2×Q8C4⋊C4×C3114yes—
172C2×Q8C4⋊C4×C3114yes—
173C2×Q8C2×Q8×C3114yes—
174C2×D4C4⋊C4×C31112yes—
175C2×D4C4⋊C4×C31112yes—
176C2×D4C2×Q8×C31112yes—
177C22×C4C22×C4×C3116yes—
178C22×C4C22×C4×C3116yes—
179C22×C4C2×D4×C3116yes—
180C22×C4C2×D4×C3116yes—
181C22×C4C2×Q8×C3113yes—
182C22×C4C2×Q8×C3116yes—
183C22×C4C24×C3111yescharacteristic
184C22×C4C24×C3116yes—
185M16—28no—
186M16—248no—
187M16C22×C4×C31148yes—
188M16C24×C31116yes—
189C2×C8—28no—
190C2×C8—248no—
191C2×C8C22×C4×C3112yes—
192C2×C8C22×C4×C3112yes—
193C2×C8C22×C4×C3116yes—
194C2×C8C22×C4×C3116yes—
195C2×C8C22×C4×C31148yes—
196C2×C8C24×C3112yes—
197C2×C8C24×C3116yes—
198C23—46no—
199C23C2×C4⋊C4×C3116yes—
200C23C2×C4⋊C4×C3116yes—
201C23C22×Q8×C3111yescharacteristic
202C23C22×Q8×C3116yes—
203Q8C2×C4⋊C4×C31116yes—
204D4C2×C4⋊C4×C31148yes—
205C2×C4C2×C4⋊C4×C3116yes—
206C2×C4C2×C4⋊C4×C3116yes—
207C2×C4C2×C4⋊C4×C31112yes—
208C2×C4C2×C4⋊C4×C31112yes—
209C2×C4C23×C4×C3111yescharacteristic
210C2×C4C23×C4×C3111yescharacteristic
211C2×C4C23×C4×C31112yes—
212C2×C4C22×D4×C31112yes—
213C2×C4C22×D4×C3111yescharacteristic
214C2×C4C22×D4×C3111yescharacteristic
215C2×C4C22×Q8×C3111yescharacteristic
216C2×C4C22×Q8×C3116yes—
217C2×C4C25×C3111yescharacteristic
218C8—216no—
219C8C23×C4×C3114yes—
220C8C23×C4×C31112yes—
221C22—22no—
222C22—212no—
223C22—46no—
224C22—46no—
225C22C22×C4⋊C4×C3111yescharacteristic
226C22C22×C4⋊C4×C31112yes—
227C22C22×C4⋊C4×C3111yescharacteristic
228C22C23×Q8×C3111yescharacteristic
229C4C22×C4⋊C4×C3111yescharacteristic
230C4C22×C4⋊C4×C3111yescharacteristic
231C4C22×C4⋊C4×C31112yes—
232C4C24×C4×C3111yescharacteristic
233C4C23×D4×C3111yescharacteristic
234C2—21no—
235C2—21no—
236C2—212no—
237C2C31×#291612yesdirect product factor
238C2C23×C4⋊C4×C3111yescharacteristic
subgroupG/H
centerC2×C4×C31C22×D4
commutatorC4C24×C4×C31
Frattini, cosocleC2×C4C25×C31
socleC22×C31C22×C4⋊C4
prime radicalC22×#41×C31C22
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C22×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#2916C2direct (N × H)
4. C2×C31×#430C2semidirect
5. C22×C31×#108C2semidirect
16. C31×#430C22semidirect
19. C2×C31×#108C22semidirect
78. C2×#2916C31direct (N × H)
104. #2916C2×C31direct (N × H)
105. C2×#430C2×C31semidirect
106. C22×#108C2×C31semidirect
130. #430C22×C31semidirect
133. C2×#108C22×C31semidirect
137. C2×C31#2916direct (N × H)
165. C31C2×#2916direct (N × H)
237. C2C31×#2916direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5682
C22×C31×#1312
C31×#29162
C2×C31×#4302
C22×C31×#1082
C2×#291631