Finite Group Databasebeta

← C2×C31×#2060 #21480317

Subgroups — C2×C31×#2060 #21480317

Order 7936.

1218 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#544C211yesmaximal, characteristic
2C2×C31×#428C212yesmaximal
3C2×C31×#384C211yesmaximal, characteristic
4C31×#2060C218yesmaximal, direct product factor
5C2×C31×#343C211yesmaximal, characteristic
6C2×C31×#339C212yesmaximal
7C22×M16×C31C2212yes—
8C31×#544—24no—
9C31×#544—22no—
10C31×#544C2214yes—
11C2×C31×C4⋊Q8—22no—
12C2×C31×#125—22no—
13C2×C31×C22⋊Q8—22no—
14C2×C31×#117C2212yes—
15C22×C4⋊C4×C31—22no—
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C42×C31C2211yescharacteristic
19C31×#428—24no—
20C31×#428C2218yes—
21C2×C31×#107—22no—
22C2×C31×#106—22no—
23C31×#384—22no—
24C31×#384C2214yes—
25C31×#343C2214yes—
26C31×#339C2218yes—
27C22×Q8×C31—22no—
28C23×C4×C31—21no—
29C23×C4×C31—21no—
30C23×C4×C31D412yes—
31C23×C4×C31C2311yescharacteristic
32C2×M16×C31—22no—
33C2×M16×C31—24no—
34C2×M16×C31Q818yescomplemented
35C2×M16×C31C2314yes—
36C22×C8×C31—22no—
37C31×C4⋊Q8—28no—
38C31×C4⋊Q8—28no—
39C31×#125—28no—
40C31×#125—28no—
41C31×C22⋊Q8—28no—
42C31×C22⋊Q8—28no—
43C31×#117—22no—
44C31×#117—22no—
45C31×#117D414yes—
46C31×#117C2314yes—
47C2×C4⋊C4×C31—22no—
48C2×C4⋊C4×C31—24no—
49C2×C4⋊C4×C31—22no—
50C2×C4⋊C4×C31—22no—
51C2×C4⋊C4×C31—22no—
52C2×C4⋊C4×C31—22no—
53C2×C4⋊C4×C31—28no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—48no—
56C2×C4⋊C4×C31D412yes—
57C2×C4⋊C4×C31D412yes—
58C2×C4⋊C4×C31D412yes—
59C2×C4⋊C4×C31C2312yes—
60C2×C4⋊C4×C31C2312yes—
61C2×C22⋊C4×C31—22no—
62C2×C42×C31—21no—
63C2×C42×C31—22no—
64C2×C42×C31—22no—
65C2×C42×C31Q814yescomplemented
66C2×C42×C31C2312yes—
67C31×#107—28no—
68C31×#106—28no—
69C24×C31C2×D411yescharacteristic
70C2×Q8×C31—28no—
71C2×Q8×C31—84no—
72C22×C4×C31—24no—
73C22×C4×C31—24no—
74C22×C4×C31—24no—
75C22×C4×C31—22no—
76C22×C4×C31—22no—
77C22×C4×C31—22no—
78C22×C4×C31—22no—
79C22×C4×C31—22no—
80C22×C4×C31—22no—
81C22×C4×C31—44no—
82C22×C4×C31—44no—
83C22×C4×C31—41no—
84C22×C4×C31—41no—
85C22×C4×C31C2×D414yes—
86C22×C4×C31C2×D411yescharacteristic
87C22×C4×C31C2×D412yes—
88C22×C4×C31C2×D412yes—
89C22×C4×C31C2×Q814yes—
90C22×C4×C31C2×Q812yes—
91C22×C4×C31#4112yes—
92C22×C4×C31C2411yescharacteristic
93M16×C31—28no—
94M16×C31—24no—
95M16×C31C2×Q818yescomplemented
96C2×C8×C31—28no—
97C2×C8×C31—24no—
98C4⋊C4×C31—28no—
99C4⋊C4×C31—216no—
100C4⋊C4×C31—24no—
101C4⋊C4×C31—22no—
102C4⋊C4×C31—22no—
103C4⋊C4×C31—24no—
104C4⋊C4×C31—24no—
105C4⋊C4×C31—416no—
106C4⋊C4×C31—42no—
107C4⋊C4×C31C2×D414yes—
108C4⋊C4×C31C2×D414yes—
109C22⋊C4×C31—24no—
110C22⋊C4×C31—24no—
111C42×C31—24no—
112C42×C31—24no—
113C42×C31—24no—
114C42×C31—22no—
115C42×C31C2×Q814yescomplemented
116C2×#2060C3111yesmaximal, characteristic, direct product factor, Sylow
117C23×C31—22no—
118C23×C31—22no—
119C23×C31#12011yescharacteristic
120C23×C31#12011yescharacteristic
121C23×C31C22⋊Q812yes—
122C23×C31C4⋊Q812yes—
123C23×C31C22×D411yescharacteristic
124Q8×C31—88no—
125C2×C4×C31—24no—
126C2×C4×C31—216no—
127C2×C4×C31—24no—
128C2×C4×C31—24no—
129C2×C4×C31—24no—
130C2×C4×C31—24no—
131C2×C4×C31—24no—
132C2×C4×C31—44no—
133C2×C4×C31—44no—
134C2×C4×C31—44no—
135C2×C4×C31—44no—
136C2×C4×C31—44no—
137C2×C4×C31—42no—
138C2×C4×C31—82no—
139C2×C4×C31—82no—
140C2×C4×C31—82no—
141C2×C4×C31#12012yes—
142C2×C4×C31C22⋊Q814yes—
143C2×C4×C31C22⋊Q814yes—
144C2×C4×C31C22⋊Q812yes—
145C2×C4×C31C4⋊Q814yes—
146C2×C4×C31C4⋊Q814yes—
147C2×C4×C31C4⋊Q812yes—
148C2×C4×C31C22×D412yes—
149C2×C4×C31C22×Q812yes—
150C2×C4×C31C22×Q811yescharacteristic
151C2×C4×C31C2×#4111yescharacteristic
152C8×C31—28no—
153C2×#544C2×C3111yescharacteristic
154C2×#428C2×C3112yes—
155C2×#384C2×C3111yescharacteristic
156#2060C2×C3118yesdirect product factor
157C2×#343C2×C3111yescharacteristic
158C2×#339C2×C3112yes—
159C22×C31—24no—
160C22×C31—24no—
161C22×C31—21no—
162C22×C31—21no—
163C22×C31—21no—
164C22×C31—21no—
165C22×C31#39512yes—
166C22×C31#39512yes—
167C22×C31#45312yes—
168C22×C31#45612yes—
169C22×C31C2×#12011yescharacteristic
170C22×C31C2×C22⋊Q811yescharacteristic
171C22×C31C2×C4⋊Q811yescharacteristic
172C4×C31—28no—
173C4×C31—44no—
174C4×C31—44no—
175C4×C31—44no—
176C4×C31—82no—
177C4×C31#39514yes—
178C4×C31C2×C22⋊Q812yes—
179C4×C31C2×C4⋊Q812yes—
180C22×M16C22×C3112yes—
181#544—24no—
182#544—22no—
183#544C22×C3114yes—
184C2×C4⋊Q8—22no—
185C2×#125—22no—
186C2×C22⋊Q8—22no—
187C2×#117C22×C3112yes—
188C22×C4⋊C4—22no—
189C22×C4⋊C4C22×C3111yescharacteristic
190C22×C4⋊C4C22×C3111yescharacteristic
191C22×C42C22×C3111yescharacteristic
192#428—24no—
193#428C22×C3118yes—
194C2×#107—22no—
195C2×#106—22no—
196#384—22no—
197#384C22×C3114yes—
198#343C22×C3114yes—
199#339C22×C3118yes—
200C2×C31—21no—
201C2×C31—21no—
202C2×C31—22no—
203C2×C31#206014yesdirect product factor
204C2×C31C2×#39511yescharacteristic
205C2×C31C2×#45311yescharacteristic
206C2×C31C2×#45611yescharacteristic
207C22×Q8—22no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4D4×C3112yes—
211C23×C4C23×C3111yescharacteristic
212C2×M16—22no—
213C2×M16—24no—
214C2×M16Q8×C3118yescomplemented
215C2×M16C23×C3114yes—
216C22×C8—22no—
217C4⋊Q8—28no—
218C4⋊Q8—28no—
219#125—28no—
220#125—28no—
221C22⋊Q8—28no—
222C22⋊Q8—28no—
223#117—22no—
224#117—22no—
225#117D4×C3114yes—
226#117C23×C3114yes—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—28no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—48no—
236C2×C4⋊C4D4×C3112yes—
237C2×C4⋊C4D4×C3112yes—
238C2×C4⋊C4D4×C3112yes—
239C2×C4⋊C4C23×C3112yes—
240C2×C4⋊C4C23×C3112yes—
241C2×C22⋊C4—22no—
242C2×C42—22no—
243C2×C42—21no—
244C2×C42—22no—
245C2×C42Q8×C3114yescomplemented
246C2×C42C23×C3112yes—
247#107—28no—
248#106—28no—
249C31C2×#206011yescharacteristic, direct product factor, Sylow
250C24C2×D4×C3111yescharacteristic
251C2×Q8—28no—
252C2×Q8—84no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—44no—
263C22×C4—44no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4C2×D4×C3114yes—
267C22×C4C2×D4×C3111yescharacteristic
268C22×C4C2×D4×C3112yes—
269C22×C4C2×D4×C3112yes—
270C22×C4C2×Q8×C3114yes—
271C22×C4C2×Q8×C3112yes—
272C22×C4#41×C3112yes—
273C22×C4C24×C3111yescharacteristic
274M16—28no—
275M16—24no—
276M16C2×Q8×C3118yescomplemented
277C2×C8—28no—
278C2×C8—24no—
279C4⋊C4—28no—
280C4⋊C4—216no—
281C4⋊C4—24no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—24no—
285C4⋊C4—24no—
286C4⋊C4—416no—
287C4⋊C4—42no—
288C4⋊C4C2×D4×C3114yes—
289C4⋊C4C2×D4×C3114yes—
290C22⋊C4—24no—
291C22⋊C4—24no—
292C42—24no—
293C42—24no—
294C42—24no—
295C42—22no—
296C42C2×Q8×C3114yescomplemented
297C23—22no—
298C23—22no—
299C23C31×#12011yescharacteristic
300C23C31×#12011yescharacteristic
301C23C31×C22⋊Q812yes—
302C23C31×C4⋊Q812yes—
303C23C22×D4×C3111yescharacteristic
304Q8—88no—
305C2×C4—24no—
306C2×C4—216no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—42no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4C31×#12012yes—
322C2×C4C31×C22⋊Q812yes—
323C2×C4C31×C22⋊Q814yes—
324C2×C4C31×C22⋊Q814yes—
325C2×C4C31×C4⋊Q812yes—
326C2×C4C31×C4⋊Q814yes—
327C2×C4C31×C4⋊Q814yes—
328C2×C4C22×D4×C3112yes—
329C2×C4C22×Q8×C3112yes—
330C2×C4C22×Q8×C3111yescharacteristic
331C2×C4C2×#41×C3111yescharacteristic
332C8—28no—
333C22—24no—
334C22—24no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22C31×#39512yes—
340C22C31×#39512yes—
341C22C31×#45312yes—
342C22C31×#45612yes—
343C22C2×C31×#12011yescharacteristic
344C22C2×C31×C22⋊Q811yescharacteristic
345C22C2×C31×C4⋊Q811yescharacteristic
346C4—28no—
347C4—44no—
348C4—44no—
349C4—44no—
350C4—82no—
351C4C31×#39514yes—
352C4C2×C31×C22⋊Q812yes—
353C4C2×C31×C4⋊Q812yes—
354C2—21no—
355C2—22no—
356C2—21no—
357C2C31×#206014yesdirect product factor
358C2C2×C31×#39511yescharacteristic
359C2C2×C31×#45311yescharacteristic
360C2C2×C31×#45611yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#2060C2direct (N × H)
34. C2×M16×C31Q8semidirect
65. C2×C42×C31Q8semidirect
95. M16×C31C2×Q8semidirect
115. C42×C31C2×Q8semidirect
116. C2×#2060C31direct (N × H)
156. #2060C2×C31direct (N × H)
203. C2×C31#2060direct (N × H)
214. C2×M16Q8×C31semidirect
245. C2×C42Q8×C31semidirect
249. C31C2×#2060direct (N × H)
276. M16C2×Q8×C31semidirect
296. C42C2×Q8×C31semidirect
357. C2C31×#2060direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5442
C2×C31×#4282
C2×C31×#3842
C31×#20602
C2×C31×#3432
C2×C31×#3392
C2×#206031