Finite Group Databasebeta

← C31×#3102 #16843035

Subgroups — C31×#3102 #16843035

Order 3968.

396 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#529C211yesmaximal, characteristic, complemented
2C4×#41×C31C211yesmaximal, characteristic, complemented
3C31×#485C211yesmaximal, characteristic, complemented
4C31×#482C211yesmaximal, characteristic, complemented
5C31×#479C211yesmaximal, characteristic, complemented
6C31×#478C211yesmaximal, characteristic, complemented
7C31×#464C211yesmaximal, characteristic, complemented
8C31×#463C211yesmaximal, characteristic, complemented
9C31×#452C211yesmaximal, characteristic, complemented
10C31×#449C211yesmaximal, characteristic
11C4×Q16×C31C211yesmaximal, characteristic, complemented
12C4×SD16×C31C211yesmaximal, characteristic, complemented
13C4×SD16×C31C211yesmaximal, characteristic, complemented
14C4×D8×C31C211yesmaximal, characteristic, complemented
15C31×#431C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C2×Q16×C31C2211yescharacteristic
18C2×SD16×C31C2211yescharacteristic
19C2×SD16×C31C2211yescharacteristic
20C2×D8×C31C2211yescharacteristic
21C31×#126—21no—
22C31×#125C2211yescharacteristic
23C31×#124C2211yescharacteristic
24C31×#123—21no—
25C31×C22⋊Q8C2211yescharacteristic
26C31×#121C2211yescharacteristic
27C4×Q8×C31C2211yescharacteristic
28C4×Q8×C31C2211yescharacteristic
29C4×Q8×C31C2211yescharacteristic
30C4×D4×C31—21no—
31C4×D4×C31—21no—
32C4×D4×C31—21no—
33C4×D4×C31C2211yescharacteristic
34C4×D4×C31C2211yescharacteristic
35C4×D4×C31C2211yescharacteristic
36C31×#117—21no—
37C31×#117—21no—
38C31×#117C2211yescharacteristic
39C2×C42×C31—21no—
40C2×C42×C31C2211yescharacteristic
41C31×#107C2211yescharacteristic
42C31×#107C2211yescharacteristic
43C31×#106C2211yescharacteristic
44C31×#106C2211yescharacteristic
45C31×C4⋊C8C2211yescharacteristic
46C31×C4⋊C8C2211yescharacteristic
47C31×#103C2211yescharacteristic
48C31×#103C2211yescharacteristic
49C31×#103C2211yescharacteristic
50C31×#103C2211yescharacteristic
51C31×#102C2211yescharacteristic
52C31×#102C2211yescharacteristic
53C31×#102C2211yescharacteristic
54C31×#102C2211yescharacteristic
55C31×C22⋊C8C2211yescharacteristic
56C31×C22⋊C8C2211yescharacteristic
57C4×C8×C31C2211yescharacteristic
58C4×C8×C31C2211yescharacteristic
59#41×C31—22no—
60#41×C31—22no—
61C2×Q8×C31C2311yescharacteristic
62C2×Q8×C31C2311yescharacteristic
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×C31—21no—
71C22×C4×C31D411yescharacteristic
72C22×C4×C31D411yescharacteristic
73C22×C4×C31C2311yescharacteristic
74Q16×C31—22no—
75SD16×C31—22no—
76SD16×C31—22no—
77D8×C31—22no—
78C2×C8×C31C2311yescharacteristic
79C2×C8×C31C2311yescharacteristic
80C2×C8×C31C2311yescharacteristic
81C2×C8×C31C2311yescharacteristic
82C4⋊C4×C31—21no—
83C4⋊C4×C31—21no—
84C4⋊C4×C31—21no—
85C4⋊C4×C31—21no—
86C4⋊C4×C31—21no—
87C4⋊C4×C31—21no—
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×C31—21no—
98C22⋊C4×C31—21no—
99C22⋊C4×C31—21no—
100C42×C31—21no—
101C42×C31—21no—
102C42×C31—21no—
103C42×C31—21no—
104C42×C31D411yescharacteristic
105C42×C31D411yescharacteristic
106C42×C31C2311yescharacteristic
107C42×C31C2311yescharacteristic
108C23×C31—21no—
109C23×C31—21no—
110C23×C31C2×D411yescharacteristic
111Q8×C31—21no—
112Q8×C31—21no—
113Q8×C31—21no—
114Q8×C31#4112yes—
115D4×C31—24no—
116D4×C31—21no—
117D4×C31—21no—
118D4×C31—21no—
119D4×C31—42no—
120D4×C31#4112yes—
121C2×C4×C31—24no—
122C2×C4×C31—21no—
123C2×C4×C31—22no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—41no—
132C2×C4×C31—42no—
133C2×C4×C31—42no—
134C2×C4×C31—42no—
135C2×C4×C31C2×D411yescharacteristic
136C2×C4×C31C2×D411yescharacteristic
137C2×C4×C31C2×D411yescharacteristic
138C2×C4×C31C2×D411yescharacteristic
139C2×C4×C31C2×D411yescharacteristic
140C2×C4×C31C2411yescharacteristic
141C8×C31—21no—
142C8×C31—21no—
143C8×C31—21no—
144C8×C31—21no—
145#3102C3111yesmaximal, characteristic, direct product factor, Sylow
146C22×C31—21no—
147C22×C31—22no—
148C22×C31—21no—
149C22×C31—21no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31C22×D411yescharacteristic
156C4×C31—21no—
157C4×C31—22no—
158C4×C31—21no—
159C4×C31—21no—
160C4×C31—21no—
161C4×C31—41no—
162C4×C31—41no—
163C4×C31—41no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31#13512yes—
167C4×C31C2×#4111yescharacteristic
168C4×C31C2×#4111yescharacteristic
169#529C2×C3111yescharacteristic, complemented
170C4×#41C2×C3111yescharacteristic, complemented
171#485C2×C3111yescharacteristic, complemented
172#482C2×C3111yescharacteristic, complemented
173#479C2×C3111yescharacteristic, complemented
174#478C2×C3111yescharacteristic, complemented
175#464C2×C3111yescharacteristic, complemented
176#463C2×C3111yescharacteristic, complemented
177#452C2×C3111yescharacteristic, complemented
178#449C2×C3111yescharacteristic
179C4×Q16C2×C3111yescharacteristic, complemented
180C4×SD16C2×C3111yescharacteristic, complemented
181C4×SD16C2×C3111yescharacteristic, complemented
182C4×D8C2×C3111yescharacteristic, complemented
183#431C2×C3111yescharacteristic, complemented
184C2×C31—41no—
185C2×C31—42no—
186C2×C31—81no—
187C2×C31#52511yescharacteristic
188C2×C31C2×#13511yescharacteristic
189C2×C31#57511yescharacteristic
190C2×#41C22×C3111yescharacteristic
191C2×Q16C22×C3111yescharacteristic
192C2×SD16C22×C3111yescharacteristic
193C2×SD16C22×C3111yescharacteristic
194C2×D8C22×C3111yescharacteristic
195#126—21no—
196#125C22×C3111yescharacteristic
197#124C22×C3111yescharacteristic
198#123—21no—
199C22⋊Q8C22×C3111yescharacteristic
200#121C22×C3111yescharacteristic
201C4×Q8C22×C3111yescharacteristic
202C4×Q8C22×C3111yescharacteristic
203C4×Q8C22×C3111yescharacteristic
204C4×D4—21no—
205C4×D4—21no—
206C4×D4—21no—
207C4×D4C22×C3111yescharacteristic
208C4×D4C22×C3111yescharacteristic
209C4×D4C22×C3111yescharacteristic
210#117—21no—
211#117—21no—
212#117C22×C3111yescharacteristic
213C2×C42—21no—
214C2×C42C22×C3111yescharacteristic
215#107C22×C3111yescharacteristic
216#107C22×C3111yescharacteristic
217#106C22×C3111yescharacteristic
218#106C22×C3111yescharacteristic
219C4⋊C8C22×C3111yescharacteristic
220C4⋊C8C22×C3111yescharacteristic
221#103C22×C3111yescharacteristic
222#103C22×C3111yescharacteristic
223#103C22×C3111yescharacteristic
224#103C22×C3111yescharacteristic
225#102C22×C3111yescharacteristic
226#102C22×C3111yescharacteristic
227#102C22×C3111yescharacteristic
228#102C22×C3111yescharacteristic
229C22⋊C8C22×C3111yescharacteristic
230C22⋊C8C22×C3111yescharacteristic
231C4×C8C22×C3111yescharacteristic
232C4×C8C22×C3111yescharacteristic
233C31#310211yescharacteristic, direct product factor, Sylow
234#41—22no—
235#41—22no—
236C2×Q8C23×C3111yescharacteristic
237C2×Q8C23×C3111yescharacteristic
238C2×D4—21no—
239C2×D4—21no—
240C2×D4C23×C3111yescharacteristic
241C2×D4C23×C3111yescharacteristic
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4D4×C3111yescharacteristic
247C22×C4D4×C3111yescharacteristic
248C22×C4C23×C3111yescharacteristic
249Q16—22no—
250SD16—22no—
251SD16—22no—
252D8—22no—
253C2×C8C23×C3111yescharacteristic
254C2×C8C23×C3111yescharacteristic
255C2×C8C23×C3111yescharacteristic
256C2×C8C23×C3111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4C23×C3111yescharacteristic
264C4⋊C4C23×C3111yescharacteristic
265C4⋊C4C23×C3111yescharacteristic
266C4⋊C4C23×C3111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42D4×C3111yescharacteristic
280C42D4×C3111yescharacteristic
281C42C23×C3111yescharacteristic
282C42C23×C3111yescharacteristic
283C23—21no—
284C23—21no—
285C23C2×D4×C3111yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8#41×C3112yes—
290D4—24no—
291D4—21no—
292D4—21no—
293D4—21no—
294D4—42no—
295D4#41×C3112yes—
296C2×C4—24no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4C2×D4×C3111yescharacteristic
311C2×C4C2×D4×C3111yescharacteristic
312C2×C4C2×D4×C3111yescharacteristic
313C2×C4C2×D4×C3111yescharacteristic
314C2×C4C2×D4×C3111yescharacteristic
315C2×C4C24×C3111yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C22×D4×C3111yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4C31×#13512yes—
341C4C2×#41×C3111yescharacteristic
342C4C2×#41×C3111yescharacteristic
343C2—41no—
344C2—42no—
345C2—81no—
346C2C31×#52511yescharacteristic
347C2C2×C31×#13511yescharacteristic
348C2C31×#57511yescharacteristic
subgroupG/H
centerC2×C4×C31C2×D4
commutator, Frattini, cosocleC2×C4C24×C31
socleC22×C31C22×D4
prime radicalC31×#449C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#529C2semidirect
2. C4×#41×C31C2semidirect
3. C31×#485C2semidirect
4. C31×#482C2semidirect
5. C31×#479C2semidirect
6. C31×#478C2semidirect
7. C31×#464C2semidirect
8. C31×#463C2semidirect
9. C31×#452C2semidirect
11. C4×Q16×C31C2semidirect
12. C4×SD16×C31C2semidirect
13. C4×SD16×C31C2semidirect
14. C4×D8×C31C2semidirect
15. C31×#431C2semidirect
145. #3102C31direct (N × H)
169. #529C2×C31semidirect
170. C4×#41C2×C31semidirect
171. #485C2×C31semidirect
172. #482C2×C31semidirect
173. #479C2×C31semidirect
174. #478C2×C31semidirect
175. #464C2×C31semidirect
176. #463C2×C31semidirect
177. #452C2×C31semidirect
179. C4×Q16C2×C31semidirect
180. C4×SD16C2×C31semidirect
181. C4×SD16C2×C31semidirect
182. C4×D8C2×C31semidirect
183. #431C2×C31semidirect
233. C31#3102direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#5292
C4×#41×C312
C31×#4852
C31×#4822
C31×#4792
C31×#4782
C31×#4642
C31×#4632
C31×#4522
C31×#4492
C4×Q16×C312
C4×SD16×C312
C4×D8×C312
C31×#4312
#310231