Finite Group Databasebeta

← C2×C31×#2062 #21480322

Subgroups — C2×C31×#2062 #21480322

Order 7936.

1614 conjugacy classes of subgroups; only the 382 normal subgroups are shown.

normal subgroups only

This group has 1614 conjugacy classes of subgroups — too many to draw. Only its 382 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
2C2×C31×#385C213yesmaximal
3C31×#2062C218yesmaximal, direct product factor
4C2×C31×#342C213yesmaximal
5C24×C4×C31C2211yescharacteristic
6C31×#543—26no—
7C31×#543C2214yes—
8C2×C31×C22⋊Q8—23no—
9C2×C31×C22⋊Q8—23no—
10C22×C4⋊C4×C31—23no—
11C22×C22⋊C4×C31C2213yes—
12C22×C22⋊C4×C31C2213yes—
13C31×#385—26no—
14C31×#385C22112yes—
15C2×C31×#95—23no—
16C31×#342C22112yes—
17C25×C31C2311yescharacteristic
18C22×Q8×C31—21no—
19C22×Q8×C31—21no—
20C23×C4×C31—23no—
21C23×C4×C31—23no—
22C23×C4×C31—23no—
23C23×C4×C31—44no—
24C23×C4×C31D413yes—
25C23×C4×C31D413yes—
26C23×C4×C31C2312yes—
27C31×C22⋊Q8—212no—
28C31×C22⋊Q8—212no—
29C31×C22⋊Q8—212no—
30C31×C22⋊Q8—212no—
31C2×C4⋊C4×C31—23no—
32C2×C4⋊C4×C31—23no—
33C2×C4⋊C4×C31—212no—
34C2×C4⋊C4×C31—412no—
35C2×C22⋊C4×C31—26no—
36C2×C22⋊C4×C31—26no—
37C2×C22⋊C4×C31—23no—
38C2×C22⋊C4×C31—26no—
39C2×C22⋊C4×C31D416yes—
40C2×C22⋊C4×C31Q8112yescomplemented
41C2×C22⋊C4×C31C2316yes—
42C2×C22⋊C4×C31C2316yes—
43C31×#95—212no—
44C24×C31—42no—
45C24×C31—42no—
46C24×C31C2×D413yes—
47C24×C31C2×D413yes—
48C24×C31C2×Q816yes—
49C24×C31#4112yes—
50C24×C31C2411yescharacteristic
51C2×Q8×C31—24no—
52C2×Q8×C31—24no—
53C2×Q8×C31—82no—
54C2×Q8×C31—82no—
55C22×C4×C31—212no—
56C22×C4×C31—23no—
57C22×C4×C31—23no—
58C22×C4×C31—212no—
59C22×C4×C31—26no—
60C22×C4×C31—26no—
61C22×C4×C31—23no—
62C22×C4×C31—23no—
63C22×C4×C31—44no—
64C22×C4×C31—412no—
65C22×C4×C31—46no—
66C22×C4×C31—46no—
67C22×C4×C31—46no—
68C22×C4×C31—43no—
69C22×C4×C31—41no—
70C22×C4×C31—46no—
71C22×C4×C31—46no—
72C22×C4×C31C2×D416yes—
73C22×C4×C31C2×D416yes—
74C4⋊C4×C31—212no—
75C4⋊C4×C31—212no—
76C4⋊C4×C31—424no—
77C22⋊C4×C31—212no—
78C22⋊C4×C31—212no—
79C22⋊C4×C31—212no—
80C22⋊C4×C31—26no—
81C22⋊C4×C31C2×Q8112yescomplemented
82C2×#2062C3111yesmaximal, characteristic, direct product factor, Sylow
83C23×C31—26no—
84C23×C31—26no—
85C23×C31—43no—
86C23×C31—41no—
87C23×C31—43no—
88C23×C31—412no—
89C23×C31—44no—
90C23×C31—41no—
91C23×C31#12013yes—
92C23×C31#12011yescharacteristic
93C23×C31C22⋊Q816yes—
94C23×C31C22⋊Q816yes—
95C23×C31C4⋊Q816yes—
96C23×C31C4⋊Q816yes—
97C23×C31C22×D413yes—
98C23×C31C22×Q813yes—
99C23×C31C2×#4111yescharacteristic
100Q8×C31—84no—
101Q8×C31—84no—
102C2×C4×C31—212no—
103C2×C4×C31—26no—
104C2×C4×C31—26no—
105C2×C4×C31—212no—
106C2×C4×C31—46no—
107C2×C4×C31—424no—
108C2×C4×C31—46no—
109C2×C4×C31—46no—
110C2×C4×C31—412no—
111C2×C4×C31—42no—
112C2×C4×C31—44no—
113C2×C4×C31—46no—
114C2×C4×C31—46no—
115C2×C4×C31—46no—
116C2×C4×C31—46no—
117C2×C4×C31—83no—
118C2×C4×C31—83no—
119C2×#543C2×C3111yescharacteristic
120C2×#385C2×C3113yes—
121#2062C2×C3118yesdirect product factor
122C2×#342C2×C3113yes—
123C22×C31—212no—
124C22×C31—212no—
125C22×C31—23no—
126C22×C31—23no—
127C22×C31—23no—
128C22×C31—23no—
129C22×C31—46no—
130C22×C31—46no—
131C22×C31—43no—
132C22×C31—41no—
133C22×C31#39516yes—
134C22×C31#39512yes—
135C22×C31B(4,𝔽2)12yes—
136C22×C31#45812yes—
137C22×C31C2×#12011yescharacteristic
138C22×C31C2×C22⋊Q813yes—
139C22×C31C2×C4⋊Q813yes—
140C4×C31—412no—
141C4×C31—44no—
142C4×C31—46no—
143C4×C31—46no—
144C24×C4C22×C3111yescharacteristic
145#543—26no—
146#543C22×C3114yes—
147C2×C22⋊Q8—23no—
148C2×C22⋊Q8—23no—
149C22×C4⋊C4—23no—
150C22×C22⋊C4C22×C3113yes—
151C22×C22⋊C4C22×C3113yes—
152#385—26no—
153#385C22×C31112yes—
154C2×#95—23no—
155#342C22×C31112yes—
156C2×C31—23no—
157C2×C31—23no—
158C2×C31—26no—
159C2×C31#206214yesdirect product factor
160C2×C31C2×#39511yescharacteristic
161C2×C31C2×B(4,𝔽2)11yescharacteristic
162C2×C31C2×#45811yescharacteristic
163C25C23×C3111yescharacteristic
164C22×Q8—21no—
165C22×Q8—21no—
166C23×C4—23no—
167C23×C4—23no—
168C23×C4—23no—
169C23×C4—44no—
170C23×C4D4×C3113yes—
171C23×C4D4×C3113yes—
172C23×C4C23×C3112yes—
173C22⋊Q8—212no—
174C22⋊Q8—212no—
175C22⋊Q8—212no—
176C22⋊Q8—212no—
177C2×C4⋊C4—23no—
178C2×C4⋊C4—23no—
179C2×C4⋊C4—212no—
180C2×C4⋊C4—412no—
181C2×C22⋊C4—26no—
182C2×C22⋊C4—26no—
183C2×C22⋊C4—23no—
184C2×C22⋊C4—26no—
185C2×C22⋊C4D4×C3116yes—
186C2×C22⋊C4Q8×C31112yescomplemented
187C2×C22⋊C4C23×C3116yes—
188C2×C22⋊C4C23×C3116yes—
189#95—212no—
190C31C2×#206211yescharacteristic, direct product factor, Sylow
191C24—42no—
192C24—42no—
193C24C2×D4×C3113yes—
194C24C2×D4×C3113yes—
195C24C2×Q8×C3116yes—
196C24#41×C3112yes—
197C24C24×C3111yescharacteristic
198C2×Q8—24no—
199C2×Q8—24no—
200C2×Q8—82no—
201C2×Q8—82no—
202C22×C4—212no—
203C22×C4—23no—
204C22×C4—23no—
205C22×C4—212no—
206C22×C4—26no—
207C22×C4—26no—
208C22×C4—23no—
209C22×C4—23no—
210C22×C4—44no—
211C22×C4—412no—
212C22×C4—46no—
213C22×C4—46no—
214C22×C4—46no—
215C22×C4—43no—
216C22×C4—41no—
217C22×C4—46no—
218C22×C4—46no—
219C22×C4C2×D4×C3116yes—
220C22×C4C2×D4×C3116yes—
221C4⋊C4—212no—
222C4⋊C4—212no—
223C4⋊C4—424no—
224C22⋊C4—212no—
225C22⋊C4—212no—
226C22⋊C4—212no—
227C22⋊C4—26no—
228C22⋊C4C2×Q8×C31112yescomplemented
229C23—26no—
230C23—26no—
231C23—43no—
232C23—41no—
233C23—43no—
234C23—412no—
235C23—44no—
236C23—41no—
237C23C31×#12013yes—
238C23C31×#12011yescharacteristic
239C23C31×C22⋊Q816yes—
240C23C31×C22⋊Q816yes—
241C23C31×C4⋊Q816yes—
242C23C31×C4⋊Q816yes—
243C23C22×D4×C3113yes—
244C23C22×Q8×C3113yes—
245C23C2×#41×C3111yescharacteristic
246Q8—84no—
247Q8—84no—
248C2×C4—212no—
249C2×C4—26no—
250C2×C4—26no—
251C2×C4—212no—
252C2×C4—46no—
253C2×C4—424no—
254C2×C4—46no—
255C2×C4—46no—
256C2×C4—412no—
257C2×C4—44no—
258C2×C4—46no—
259C2×C4—46no—
260C2×C4—42no—
261C2×C4—46no—
262C2×C4—46no—
263C2×C4—83no—
264C2×C4—83no—
265C22—212no—
266C22—212no—
267C22—23no—
268C22—23no—
269C22—23no—
270C22—23no—
271C22—46no—
272C22—46no—
273C22—43no—
274C22—41no—
275C22C31×#39516yes—
276C22C31×#39512yes—
277C22C31×B(4,𝔽2)12yes—
278C22C31×#45812yes—
279C22C2×C31×#12011yescharacteristic
280C22C2×C31×C22⋊Q813yes—
281C22C2×C31×C4⋊Q813yes—
282C4—412no—
283C4—44no—
284C4—46no—
285C4—46no—
286C2—23no—
287C2—26no—
288C2—23no—
289C2C31×#206214yesdirect product factor
290C2C2×C31×#39511yescharacteristic
291C2C2×C31×B(4,𝔽2)11yescharacteristic
292C2C2×C31×#45811yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#2062C2direct (N × H)
40. C2×C22⋊C4×C31Q8semidirect
81. C22⋊C4×C31C2×Q8semidirect
82. C2×#2062C31direct (N × H)
121. #2062C2×C31direct (N × H)
159. C2×C31#2062direct (N × H)
186. C2×C22⋊C4Q8×C31semidirect
190. C31C2×#2062direct (N × H)
228. C22⋊C4C2×Q8×C31semidirect
289. C2C31×#2062direct (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×#3852
C31×#20622
C2×C31×#3422
C2×#206231