Finite Group Databasebeta

← C2×C31×#1660 #21475742

Subgroups — C2×C31×#1660 #21475742

Order 7936.

958 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#563C211yesmaximal, characteristic
2C2×C31×#501C212yesmaximal, complemented
3C2×C31×#497C211yesmaximal, characteristic
4C31×#1660C218yesmaximal, direct product factor
5C2×C31×#330C212yesmaximal, complemented
6C2×C31×#329C211yesmaximal, characteristic
7C22×Q16×C31—21no—
8C22×SD16×C31—21no—
9C31×#563—24no—
10C31×#563—22no—
11C31×#563C2214yes—
12C2×C31×C4⋊Q8—21no—
13C2×C31×C4⋊Q8C2211yescharacteristic
14C2×C31×#126—22no—
15C2×C31×#125C2212yes—
16C2×C31×#124C2211yescharacteristic
17C2×C31×#123—21no—
18C2×C31×C22⋊Q8—22no—
19C31×#501—24no—
20C31×#501C2218yescomplemented
21C31×#497—22no—
22C31×#497C2214yes—
23C2×C31×#107—22no—
24C2×C31×#106—22no—
25C2×C31×#97C2211yescharacteristic
26C2×C31×#97C2212yes—
27C31×#330C2218yescomplemented
28C31×#329C2214yes—
29C22×Q8×C31—21no—
30C22×Q8×C31—21no—
31C22×Q8×C31D411yescharacteristic
32C22×D4×C31D411yescharacteristic
33C23×C4×C31—21no—
34C2×Q16×C31—24no—
35C2×Q16×C31—44no—
36C2×SD16×C31—24no—
37C2×SD16×C31—44no—
38C22×C8×C31—22no—
39C22×C8×C31—21no—
40C31×C4⋊Q8—24no—
41C31×C4⋊Q8—24no—
42C31×C4⋊Q8—22no—
43C31×C4⋊Q8—21no—
44C31×C4⋊Q8C2312yes—
45C31×#126—28no—
46C31×#126—28no—
47C31×#125—22no—
48C31×#125—22no—
49C31×#125D414yes—
50C31×#125C2314yes—
51C31×#124—22no—
52C31×#124D412yes—
53C31×#124C2312yes—
54C31×#123—24no—
55C31×#123—24no—
56C31×C22⋊Q8—28no—
57C31×C22⋊Q8—28no—
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—22no—
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31D412yes—
63C2×C4⋊C4×C31D412yes—
64C2×C22⋊C4×C31—22no—
65C2×C22⋊C4×C31—21no—
66C2×C22⋊C4×C31—22no—
67C2×C42×C31—21no—
68C2×C42×C31C2311yescharacteristic
69C31×#107—28no—
70C31×#106—28no—
71C31×#97—21no—
72C31×#97—22no—
73C31×#97C2312yes—
74C31×#97C2314yes—
75C24×C31—21no—
76C2×Q8×C31—24no—
77C2×Q8×C31—21no—
78C2×Q8×C31—22no—
79C2×Q8×C31—42no—
80C2×Q8×C31—42no—
81C2×Q8×C31—42no—
82C2×Q8×C31—41no—
83C2×Q8×C31—82no—
84C2×Q8×C31C2×D412yes—
85C2×D4×C31—21no—
86C2×D4×C31—42no—
87C2×D4×C31C2×D412yes—
88C22×C4×C31—22no—
89C22×C4×C31—21no—
90C22×C4×C31—22no—
91C22×C4×C31—24no—
92C22×C4×C31—41no—
93C22×C4×C31—82no—
94C22×C4×C31C2×D412yes—
95C22×C4×C31C2×D411yescharacteristic
96Q16×C31—48no—
97SD16×C31—48no—
98C2×C8×C31—28no—
99C2×C8×C31—24no—
100C2×C8×C31—24no—
101C2×C8×C31—22no—
102C4⋊C4×C31—28no—
103C4⋊C4×C31—24no—
104C4⋊C4×C31—24no—
105C4⋊C4×C31—22no—
106C4⋊C4×C31—22no—
107C4⋊C4×C31—24no—
108C4⋊C4×C31—24no—
109C4⋊C4×C31—24no—
110C4⋊C4×C31—42no—
111C4⋊C4×C31C2×D414yes—
112C4⋊C4×C31C2×D414yes—
113C22⋊C4×C31—28no—
114C22⋊C4×C31—24no—
115C22⋊C4×C31—24no—
116C22⋊C4×C31—24no—
117C42×C31—24no—
118C42×C31C2×D412yes—
119C42×C31C2×D411yescharacteristic
120C42×C31C2411yescharacteristic
121C2×#1660C3111yesmaximal, characteristic, direct product factor, Sylow
122C23×C31—22no—
123C23×C31—42no—
124C23×C31—44no—
125C23×C31#12011yescharacteristic
126Q8×C31—42no—
127Q8×C31—42no—
128Q8×C31—42no—
129Q8×C31—81no—
130Q8×C31—82no—
131Q8×C31—84no—
132D4×C31—42no—
133D4×C31—81no—
134C2×C4×C31—22no—
135C2×C4×C31—24no—
136C2×C4×C31—24no—
137C2×C4×C31—22no—
138C2×C4×C31—24no—
139C2×C4×C31—44no—
140C2×C4×C31—42no—
141C2×C4×C31—44no—
142C2×C4×C31—42no—
143C2×C4×C31—84no—
144C2×C4×C31—82no—
145C2×C4×C31#12012yes—
146C2×C4×C31#12011yescharacteristic
147C2×C4×C31C22×D412yes—
148C2×C4×C31C22×D411yescharacteristic
149C8×C31—28no—
150C8×C31—24no—
151C2×#563C2×C3111yescharacteristic
152C2×#501C2×C3112yescomplemented
153C2×#497C2×C3111yescharacteristic
154#1660C2×C3118yesdirect product factor
155C2×#330C2×C3112yescomplemented
156C2×#329C2×C3111yescharacteristic
157C22×C31—42no—
158C22×C31—44no—
159C22×C31—84no—
160C22×C31#45312yes—
161C22×C31#45614yes—
162C22×C31C2×#12011yescharacteristic
163C4×C31—21no—
164C4×C31—21no—
165C4×C31—22no—
166C4×C31—22no—
167C4×C31—44no—
168C4×C31—42no—
169C4×C31—44no—
170C4×C31—82no—
171C22×Q16—21no—
172C22×SD16—21no—
173#563—24no—
174#563—22no—
175#563C22×C3114yes—
176C2×C4⋊Q8—21no—
177C2×C4⋊Q8C22×C3111yescharacteristic
178C2×#126—22no—
179C2×#125C22×C3112yes—
180C2×#124C22×C3111yescharacteristic
181C2×#123—21no—
182C2×C22⋊Q8—22no—
183#501—24no—
184#501C22×C3118yescomplemented
185#497—22no—
186#497C22×C3114yes—
187C2×#107—22no—
188C2×#106—22no—
189C2×#97C22×C3111yescharacteristic
190C2×#97C22×C3112yes—
191#330C22×C3118yescomplemented
192#329C22×C3114yes—
193C2×C31—82no—
194C2×C31#166014yesdirect product factor
195C2×C31C2×#45311yescharacteristic
196C2×C31C2×#45612yes—
197C22×Q8—21no—
198C22×Q8—21no—
199C22×Q8D4×C3111yescharacteristic
200C22×D4D4×C3111yescharacteristic
201C23×C4—21no—
202C2×Q16—24no—
203C2×Q16—44no—
204C2×SD16—24no—
205C2×SD16—44no—
206C22×C8—21no—
207C22×C8—22no—
208C4⋊Q8—24no—
209C4⋊Q8—24no—
210C4⋊Q8—22no—
211C4⋊Q8—21no—
212C4⋊Q8C23×C3112yes—
213#126—28no—
214#126—28no—
215#125—22no—
216#125—22no—
217#125D4×C3114yes—
218#125C23×C3114yes—
219#124—22no—
220#124D4×C3112yes—
221#124C23×C3112yes—
222#123—24no—
223#123—24no—
224C22⋊Q8—28no—
225C22⋊Q8—28no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4D4×C3112yes—
231C2×C4⋊C4D4×C3112yes—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—22no—
235C2×C42—21no—
236C2×C42C23×C3111yescharacteristic
237#107—28no—
238#106—28no—
239#97—21no—
240#97—22no—
241#97C23×C3114yes—
242#97C23×C3112yes—
243C31C2×#166011yescharacteristic, direct product factor, Sylow
244C24—21no—
245C2×Q8—24no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—42no—
251C2×Q8—41no—
252C2×Q8—82no—
253C2×Q8C2×D4×C3112yes—
254C2×D4—21no—
255C2×D4—42no—
256C2×D4C2×D4×C3112yes—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—24no—
261C22×C4—41no—
262C22×C4—82no—
263C22×C4C2×D4×C3112yes—
264C22×C4C2×D4×C3111yescharacteristic
265Q16—48no—
266SD16—48no—
267C2×C8—28no—
268C2×C8—24no—
269C2×C8—24no—
270C2×C8—22no—
271C4⋊C4—28no—
272C4⋊C4—24no—
273C4⋊C4—24no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—24no—
277C4⋊C4—24no—
278C4⋊C4—24no—
279C4⋊C4—42no—
280C4⋊C4C2×D4×C3114yes—
281C4⋊C4C2×D4×C3114yes—
282C22⋊C4—28no—
283C22⋊C4—24no—
284C22⋊C4—24no—
285C22⋊C4—24no—
286C42—24no—
287C42C2×D4×C3112yes—
288C42C2×D4×C3111yescharacteristic
289C42C24×C3111yescharacteristic
290C23—22no—
291C23—42no—
292C23—44no—
293C23C31×#12011yescharacteristic
294Q8—42no—
295Q8—42no—
296Q8—42no—
297Q8—81no—
298Q8—82no—
299Q8—84no—
300D4—42no—
301D4—81no—
302C2×C4—22no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—44no—
310C2×C4—42no—
311C2×C4—84no—
312C2×C4—82no—
313C2×C4C31×#12012yes—
314C2×C4C31×#12011yescharacteristic
315C2×C4C22×D4×C3112yes—
316C2×C4C22×D4×C3111yescharacteristic
317C8—28no—
318C8—24no—
319C22—42no—
320C22—44no—
321C22—84no—
322C22C31×#45312yes—
323C22C31×#45614yes—
324C22C2×C31×#12011yescharacteristic
325C4—21no—
326C4—21no—
327C4—22no—
328C4—22no—
329C4—44no—
330C4—42no—
331C4—44no—
332C4—82no—
333C2—82no—
334C2C31×#166014yesdirect product factor
335C2C2×C31×#45311yescharacteristic
336C2C2×C31×#45612yes—
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC22×D4×C31D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#501C2semidirect
4. C31×#1660C2direct (N × H)
5. C2×C31×#330C2semidirect
20. C31×#501C22semidirect
27. C31×#330C22semidirect
121. C2×#1660C31direct (N × H)
152. C2×#501C2×C31semidirect
154. #1660C2×C31direct (N × H)
155. C2×#330C2×C31semidirect
184. #501C22×C31semidirect
191. #330C22×C31semidirect
194. C2×C31#1660direct (N × H)
243. C31C2×#1660direct (N × H)
334. C2C31×#1660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5632
C2×C31×#5012
C2×C31×#4972
C31×#16602
C2×C31×#3302
C2×C31×#3292
C2×#166031