Finite Group Databasebeta

← C31×#3241 #16843174

Subgroups — C31×#3241 #16843174

Order 3968.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#544C211yesmaximal, characteristic, complemented
2C31×#540C211yesmaximal, characteristic
3C31×#501C211yesmaximal, characteristic, complemented
4C31×#499C211yesmaximal, characteristic, complemented
5C31×#490C211yesmaximal, characteristic, complemented
6C31×#486C211yesmaximal, characteristic, complemented
7C31×#482C211yesmaximal, characteristic, complemented
8C31×#482C211yesmaximal, characteristic, complemented
9C31×#481C211yesmaximal, characteristic, complemented
10C31×#480C211yesmaximal, characteristic, complemented
11C31×#478C211yesmaximal, characteristic, complemented
12C31×#478C211yesmaximal, characteristic, complemented
13C31×#476C211yesmaximal, characteristic, complemented
14C31×#474C211yesmaximal, characteristic, complemented
15C31×#433C211yesmaximal, characteristic, complemented
16C31×C4⋊Q8—21no—
17C31×C4⋊Q8C2211yescharacteristic
18C31×C4⋊Q8C2211yescharacteristic
19C31×#127C2211yescharacteristic
20C31×#125—21no—
21C31×#125C2211yescharacteristic
22C31×#125C2211yescharacteristic
23C31×#125C2211yescharacteristic
24C31×#123—21no—
25C31×#123—21no—
26C31×C22⋊Q8—21no—
27C31×C22⋊Q8—21no—
28C31×#121—21no—
29C31×#121—21no—
30C31×#121C2211yescharacteristic
31C31×#121C2211yescharacteristic
32C4×D4×C31C2211yescharacteristic
33C4×D4×C31C2211yescharacteristic
34C31×#117C2211yescharacteristic
35C31×#117C2211yescharacteristic
36C2×C4⋊C4×C31C2211yescharacteristic
37C31×#107C2211yescharacteristic
38C31×#107C2211yescharacteristic
39C31×#107C2211yescharacteristic
40C31×#107C2211yescharacteristic
41C31×#106C2211yescharacteristic
42C31×#106C2211yescharacteristic
43C31×#106C2211yescharacteristic
44C31×#106C2211yescharacteristic
45C31×C4⋊C8C2211yescharacteristic
46C31×C4⋊C8C2211yescharacteristic
47C31×#102C2211yescharacteristic
48C31×#102C2211yescharacteristic
49C31×#102C2211yescharacteristic
50C31×#102C2211yescharacteristic
51C31×#102C2211yescharacteristic
52C31×#102C2211yescharacteristic
53C31×#102C2211yescharacteristic
54C31×#102C2211yescharacteristic
55C31×C22⋊C8C2211yescharacteristic
56C31×C22⋊C8C2211yescharacteristic
57C31×#97C2211yescharacteristic
58C4×C8×C31C2211yescharacteristic
59C2×Q8×C31—21no—
60C2×Q8×C31—21no—
61C2×D4×C31—21no—
62C2×D4×C31—21no—
63C2×D4×C31—21no—
64C2×D4×C31—21no—
65C2×D4×C31C2311yescharacteristic
66C2×D4×C31C2311yescharacteristic
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31C2311yescharacteristic
71C2×C8×C31C2311yescharacteristic
72C2×C8×C31C2311yescharacteristic
73C2×C8×C31C2311yescharacteristic
74C2×C8×C31C2311yescharacteristic
75C4⋊C4×C31—21no—
76C4⋊C4×C31—21no—
77C4⋊C4×C31—21no—
78C4⋊C4×C31—21no—
79C4⋊C4×C31—21no—
80C4⋊C4×C31—21no—
81C4⋊C4×C31—21no—
82C4⋊C4×C31—21no—
83C4⋊C4×C31—21no—
84C4⋊C4×C31D411yescharacteristic
85C4⋊C4×C31D411yescharacteristic
86C4⋊C4×C31C2311yescharacteristic
87C4⋊C4×C31C2311yescharacteristic
88C4⋊C4×C31C2311yescharacteristic
89C4⋊C4×C31C2311yescharacteristic
90C4⋊C4×C31C2311yescharacteristic
91C4⋊C4×C31C2311yescharacteristic
92C22⋊C4×C31—21no—
93C22⋊C4×C31—21no—
94C22⋊C4×C31—21no—
95C22⋊C4×C31—21no—
96C22⋊C4×C31—21no—
97C22⋊C4×C31D411yescharacteristic
98C22⋊C4×C31D411yescharacteristic
99C42×C31—21no—
100C42×C31C2311yescharacteristic
101C42×C31C2311yescharacteristic
102C23×C31—21no—
103C23×C31—21no—
104C23×C31C2×D411yescharacteristic
105Q8×C31—81no—
106Q8×C31—81no—
107D4×C31—21no—
108D4×C31—21no—
109D4×C31—21no—
110D4×C31—21no—
111D4×C31—81no—
112D4×C31—81no—
113D4×C31—81no—
114D4×C31—81no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—81no—
124C2×C4×C31—81no—
125C2×C4×C31—81no—
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2×D411yescharacteristic
128C2×C4×C31C2×D411yescharacteristic
129C2×C4×C31C2×D411yescharacteristic
130C2×C4×C31C2×D411yescharacteristic
131C2×C4×C31C2411yescharacteristic
132C8×C31—21no—
133C8×C31—21no—
134C8×C31—21no—
135C8×C31—21no—
136#3241C3111yesmaximal, characteristic, direct product factor, Sylow
137C22×C31—21no—
138C22×C31—21no—
139C22×C31—21no—
140C22×C31—41no—
141C22×C31—41no—
142C22×C31—41no—
143C22×C31—41no—
144C22×C31—41no—
145C22×C31—41no—
146C22×C31C22×D411yescharacteristic
147C4×C31—21no—
148C4×C31—21no—
149C4×C31—21no—
150C4×C31—21no—
151C4×C31—21no—
152C4×C31—41no—
153C4×C31—41no—
154C4×C31—41no—
155C4×C31—41no—
156C4×C31—41no—
157C4×C31—41no—
158C4×C312−1+411yescharacteristic
159C4×C312−1+411yescharacteristic
160#544C2×C3111yescharacteristic, complemented
161#540C2×C3111yescharacteristic
162#501C2×C3111yescharacteristic, complemented
163#499C2×C3111yescharacteristic, complemented
164#490C2×C3111yescharacteristic, complemented
165#486C2×C3111yescharacteristic, complemented
166#482C2×C3111yescharacteristic, complemented
167#482C2×C3111yescharacteristic, complemented
168#481C2×C3111yescharacteristic, complemented
169#480C2×C3111yescharacteristic, complemented
170#478C2×C3111yescharacteristic, complemented
171#478C2×C3111yescharacteristic, complemented
172#476C2×C3111yescharacteristic, complemented
173#474C2×C3111yescharacteristic, complemented
174#433C2×C3111yescharacteristic, complemented
175C2×C31—41no—
176C2×C31—81no—
177C2×C31—81no—
178C2×C31#53611yescharacteristic
179C2×C31#57611yescharacteristic
180C2×C31#57711yescharacteristic
181C4⋊Q8—21no—
182C4⋊Q8C22×C3111yescharacteristic
183C4⋊Q8C22×C3111yescharacteristic
184#127C22×C3111yescharacteristic
185#125—21no—
186#125C22×C3111yescharacteristic
187#125C22×C3111yescharacteristic
188#125C22×C3111yescharacteristic
189#123—21no—
190#123—21no—
191C22⋊Q8—21no—
192C22⋊Q8—21no—
193#121—21no—
194#121—21no—
195#121C22×C3111yescharacteristic
196#121C22×C3111yescharacteristic
197C4×D4C22×C3111yescharacteristic
198C4×D4C22×C3111yescharacteristic
199#117C22×C3111yescharacteristic
200#117C22×C3111yescharacteristic
201C2×C4⋊C4C22×C3111yescharacteristic
202#107C22×C3111yescharacteristic
203#107C22×C3111yescharacteristic
204#107C22×C3111yescharacteristic
205#107C22×C3111yescharacteristic
206#106C22×C3111yescharacteristic
207#106C22×C3111yescharacteristic
208#106C22×C3111yescharacteristic
209#106C22×C3111yescharacteristic
210C4⋊C8C22×C3111yescharacteristic
211C4⋊C8C22×C3111yescharacteristic
212#102C22×C3111yescharacteristic
213#102C22×C3111yescharacteristic
214#102C22×C3111yescharacteristic
215#102C22×C3111yescharacteristic
216#102C22×C3111yescharacteristic
217#102C22×C3111yescharacteristic
218#102C22×C3111yescharacteristic
219#102C22×C3111yescharacteristic
220C22⋊C8C22×C3111yescharacteristic
221C22⋊C8C22×C3111yescharacteristic
222#97C22×C3111yescharacteristic
223C4×C8C22×C3111yescharacteristic
224C31#324111yescharacteristic, direct product factor, Sylow
225C2×Q8—21no—
226C2×Q8—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4C23×C3111yescharacteristic
232C2×D4C23×C3111yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4C23×C3111yescharacteristic
237C2×C8C23×C3111yescharacteristic
238C2×C8C23×C3111yescharacteristic
239C2×C8C23×C3111yescharacteristic
240C2×C8C23×C3111yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4D4×C3111yescharacteristic
251C4⋊C4D4×C3111yescharacteristic
252C4⋊C4C23×C3111yescharacteristic
253C4⋊C4C23×C3111yescharacteristic
254C4⋊C4C23×C3111yescharacteristic
255C4⋊C4C23×C3111yescharacteristic
256C4⋊C4C23×C3111yescharacteristic
257C4⋊C4C23×C3111yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4D4×C3111yescharacteristic
264C22⋊C4D4×C3111yescharacteristic
265C42—21no—
266C42C23×C3111yescharacteristic
267C42C23×C3111yescharacteristic
268C23—21no—
269C23—21no—
270C23C2×D4×C3111yescharacteristic
271Q8—81no—
272Q8—81no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—81no—
280D4—81no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4C2×D4×C3111yescharacteristic
293C2×C4C2×D4×C3111yescharacteristic
294C2×C4C2×D4×C3111yescharacteristic
295C2×C4C2×D4×C3111yescharacteristic
296C2×C4C2×D4×C3111yescharacteristic
297C2×C4C24×C3111yescharacteristic
298C8—21no—
299C8—21no—
300C8—21no—
301C8—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22C22×D4×C3111yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4C31×2−1+411yescharacteristic
324C4C31×2−1+411yescharacteristic
325C2—41no—
326C2—81no—
327C2—81no—
328C2C31×#53611yescharacteristic
329C2C31×#57611yescharacteristic
330C2C31×#57711yescharacteristic
subgroupG/H
center, socleC22×C31C22×D4
commutator, Frattini, cosocleC2×C4C24×C31
prime radicalC31×#540C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#544C2semidirect
3. C31×#501C2semidirect
4. C31×#499C2semidirect
5. C31×#490C2semidirect
6. C31×#486C2semidirect
7. C31×#482C2semidirect
8. C31×#482C2semidirect
9. C31×#481C2semidirect
10. C31×#480C2semidirect
11. C31×#478C2semidirect
12. C31×#478C2semidirect
13. C31×#476C2semidirect
14. C31×#474C2semidirect
15. C31×#433C2semidirect
136. #3241C31direct (N × H)
160. #544C2×C31semidirect
162. #501C2×C31semidirect
163. #499C2×C31semidirect
164. #490C2×C31semidirect
165. #486C2×C31semidirect
166. #482C2×C31semidirect
167. #482C2×C31semidirect
168. #481C2×C31semidirect
169. #480C2×C31semidirect
170. #478C2×C31semidirect
171. #478C2×C31semidirect
172. #476C2×C31semidirect
173. #474C2×C31semidirect
174. #433C2×C31semidirect
224. C31#3241direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#5442
C31×#5402
C31×#5012
C31×#4992
C31×#4902
C31×#4862
C31×#4822
C31×#4812
C31×#4802
C31×#4782
C31×#4762
C31×#4742
C31×#4332
#324131