Finite Group Databasebeta

← C2×C31×#2029 #21480224

Subgroups — C2×C31×#2029 #21480224

Order 7936.

2818 conjugacy classes of subgroups; only the 350 normal subgroups are shown.

normal subgroups only

This group has 2818 conjugacy classes of subgroups — too many to draw. Only its 350 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×#543C211yesmaximal, characteristic, complemented
2C2×C31×#379C213yesmaximal
3C31×#2029C218yesmaximal, direct product factor
4C2×C31×#342C213yesmaximal, complemented
5C26×C31C2211yescharacteristic
6C31×#543—26no—
7C31×#543C2214yescomplemented
8C2×C31×C22⋊Q8—26no—
9C22×C22⋊C4×C31—26no—
10C22×C22⋊C4×C31C2213yes—
11C22×C22⋊C4×C31C2213yes—
12C31×#379—26no—
13C31×#379C22112yes—
14C31×#342C22112yescomplemented
15C25×C31—23no—
16C25×C31—23no—
17C25×C31—26no—
18C25×C31—48no—
19C25×C31Q814yescomplemented
20C25×C31C2312yes—
21C25×C31C2311yescharacteristic
22C22×Q8×C31—22no—
23C23×C4×C31—23no—
24C23×C4×C31D416yes—
25C31×C22⋊Q8—224no—
26C31×C22⋊Q8—224no—
27C2×C4⋊C4×C31—26no—
28C2×C22⋊C4×C31—26no—
29C2×C22⋊C4×C31—26no—
30C2×C22⋊C4×C31—212no—
31C2×C22⋊C4×C31—23no—
32C2×C22⋊C4×C31—224no—
33C2×C22⋊C4×C31—424no—
34C2×C22⋊C4×C31D416yes—
35C2×C22⋊C4×C31C2316yes—
36C2×C22⋊C4×C31C2316yes—
37C24×C31—224no—
38C24×C31—212no—
39C24×C31—26no—
40C24×C31—212no—
41C24×C31—26no—
42C24×C31—416no—
43C24×C31—48no—
44C24×C31—44no—
45C24×C31—412no—
46C24×C31—424no—
47C24×C31—448no—
48C24×C31—43no—
49C24×C31—41no—
50C24×C31—46no—
51C24×C31—46no—
52C24×C31C2×D413yes—
53C24×C31C2×D413yes—
54C24×C31C2×Q812yes—
55C24×C31C2×Q814yescomplemented
56C24×C31#4116yes—
57C24×C31C2411yescharacteristic
58C2×Q8×C31—28no—
59C2×Q8×C31—84no—
60C22×C4×C31—26no—
61C22×C4×C31—26no—
62C22×C4×C31—26no—
63C22×C4×C31—412no—
64C22×C4×C31—412no—
65C22×C4×C31—46no—
66C22×C4×C31C2×D4112yes—
67C4⋊C4×C31—224no—
68C22⋊C4×C31—212no—
69C22⋊C4×C31—212no—
70C22⋊C4×C31—212no—
71C22⋊C4×C31—448no—
72C22⋊C4×C31—46no—
73C2×#2029C3111yesmaximal, characteristic, direct product factor, Sylow
74C23×C31—212no—
75C23×C31—224no—
76C23×C31—248no—
77C23×C31—212no—
78C23×C31—46no—
79C23×C31—44no—
80C23×C31—48no—
81C23×C31—412no—
82C23×C31—42no—
83C23×C31—412no—
84C23×C31—424no—
85C23×C31—448no—
86C23×C31—424no—
87C23×C31—448no—
88C23×C31—424no—
89C23×C31—448no—
90C23×C31—42no—
91C23×C31—46no—
92C23×C31—412no—
93C23×C31—44no—
94C23×C31—48no—
95C23×C31#12013yes—
96C23×C31#12011yescharacteristic
97C23×C31C22⋊Q816yes—
98C23×C31C22⋊Q816yes—
99C23×C31#12416yes—
100C23×C31#12416yes—
101C23×C31C22×D413yes—
102C23×C31C22×Q811yescharacteristic
103C23×C31C2×#4113yes—
104Q8×C31—88no—
105C2×C4×C31—212no—
106C2×C4×C31—412no—
107C2×C4×C31—412no—
108C2×C4×C31—412no—
109C2×C4×C31—46no—
110C2×C4×C31—86no—
111C2×C4×C31—812no—
112C2×#543C2×C3111yescharacteristic, complemented
113C2×#379C2×C3113yes—
114#2029C2×C3118yesdirect product factor
115C2×#342C2×C3113yescomplemented
116C22×C31—26no—
117C22×C31—26no—
118C22×C31—212no—
119C22×C31—212no—
120C22×C31—224no—
121C22×C31—46no—
122C22×C31—46no—
123C22×C31—41no—
124C22×C31—43no—
125C22×C31—424no—
126C22×C31—412no—
127C22×C31—448no—
128C22×C31—44no—
129C22×C31—48no—
130C22×C31—416no—
131C22×C31#39316yes—
132C22×C31#39312yes—
133C22×C31B(4,𝔽2)14yes—
134C22×C31C2×#12011yescharacteristic
135C22×C31C2×C22⋊Q813yes—
136C22×C31C2×#12413yes—
137C4×C31—412no—
138C4×C31—86no—
139C26C22×C3111yescharacteristic
140#543—26no—
141#543C22×C3114yescomplemented
142C2×C22⋊Q8—26no—
143C22×C22⋊C4—26no—
144C22×C22⋊C4C22×C3113yes—
145C22×C22⋊C4C22×C3113yes—
146#379—26no—
147#379C22×C31112yes—
148#342C22×C31112yescomplemented
149C2×C31—23no—
150C2×C31—23no—
151C2×C31—26no—
152C2×C31—48no—
153C2×C31#202914yesdirect product factor
154C2×C31C2×#39311yescharacteristic
155C2×C31C2×B(4,𝔽2)12yes—
156C25—23no—
157C25—23no—
158C25—26no—
159C25—48no—
160C25Q8×C3114yescomplemented
161C25C23×C3112yes—
162C25C23×C3111yescharacteristic
163C22×Q8—22no—
164C23×C4—23no—
165C23×C4D4×C3116yes—
166C22⋊Q8—224no—
167C22⋊Q8—224no—
168C2×C4⋊C4—26no—
169C2×C22⋊C4—26no—
170C2×C22⋊C4—26no—
171C2×C22⋊C4—212no—
172C2×C22⋊C4—23no—
173C2×C22⋊C4—224no—
174C2×C22⋊C4—424no—
175C2×C22⋊C4D4×C3116yes—
176C2×C22⋊C4C23×C3116yes—
177C2×C22⋊C4C23×C3116yes—
178C31C2×#202911yescharacteristic, direct product factor, Sylow
179C24—224no—
180C24—212no—
181C24—26no—
182C24—212no—
183C24—26no—
184C24—416no—
185C24—44no—
186C24—48no—
187C24—412no—
188C24—424no—
189C24—448no—
190C24—43no—
191C24—41no—
192C24—46no—
193C24—46no—
194C24C2×D4×C3113yes—
195C24C2×D4×C3113yes—
196C24C2×Q8×C3112yes—
197C24C2×Q8×C3114yescomplemented
198C24#41×C3116yes—
199C24C24×C3111yescharacteristic
200C2×Q8—28no—
201C2×Q8—84no—
202C22×C4—26no—
203C22×C4—26no—
204C22×C4—26no—
205C22×C4—412no—
206C22×C4—412no—
207C22×C4—46no—
208C22×C4C2×D4×C31112yes—
209C4⋊C4—224no—
210C22⋊C4—212no—
211C22⋊C4—212no—
212C22⋊C4—212no—
213C22⋊C4—448no—
214C22⋊C4—46no—
215C23—212no—
216C23—224no—
217C23—248no—
218C23—212no—
219C23—46no—
220C23—44no—
221C23—48no—
222C23—412no—
223C23—42no—
224C23—412no—
225C23—424no—
226C23—448no—
227C23—424no—
228C23—448no—
229C23—424no—
230C23—448no—
231C23—48no—
232C23—42no—
233C23—46no—
234C23—412no—
235C23—44no—
236C23C31×#12013yes—
237C23C31×#12011yescharacteristic
238C23C31×C22⋊Q816yes—
239C23C31×C22⋊Q816yes—
240C23C31×#12416yes—
241C23C31×#12416yes—
242C23C22×D4×C3113yes—
243C23C22×Q8×C3111yescharacteristic
244C23C2×#41×C3113yes—
245Q8—88no—
246C2×C4—212no—
247C2×C4—412no—
248C2×C4—412no—
249C2×C4—412no—
250C2×C4—46no—
251C2×C4—86no—
252C2×C4—812no—
253C22—26no—
254C22—26no—
255C22—212no—
256C22—212no—
257C22—224no—
258C22—46no—
259C22—46no—
260C22—41no—
261C22—43no—
262C22—424no—
263C22—412no—
264C22—448no—
265C22—44no—
266C22—48no—
267C22—416no—
268C22C31×#39316yes—
269C22C31×#39312yes—
270C22C31×B(4,𝔽2)14yes—
271C22C2×C31×#12011yescharacteristic
272C22C2×C31×C22⋊Q813yes—
273C22C2×C31×#12413yes—
274C4—412no—
275C4—86no—
276C2—23no—
277C2—23no—
278C2—26no—
279C2—48no—
280C2C31×#202914yesdirect product factor
281C2C2×C31×#39311yescharacteristic
282C2C2×C31×B(4,𝔽2)12yes—
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC24C24×C31
prime radicalC26×C31C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#543C2semidirect
3. C31×#2029C2direct (N × H)
4. C2×C31×#342C2semidirect
7. C31×#543C22semidirect
14. C31×#342C22semidirect
19. C25×C31Q8semidirect
55. C24×C31C2×Q8semidirect
73. C2×#2029C31direct (N × H)
112. C2×#543C2×C31semidirect
114. #2029C2×C31direct (N × H)
115. C2×#342C2×C31semidirect
141. #543C22×C31semidirect
148. #342C22×C31semidirect
153. C2×C31#2029direct (N × H)
160. C25Q8×C31semidirect
178. C31C2×#2029direct (N × H)
197. C24C2×Q8×C31semidirect
280. C2C31×#2029direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5432
C2×C31×#3792
C31×#20292
C2×C31×#3422
C2×#202931