Finite Group Databasebeta

← C31×#3343 #16843276

Subgroups — C31×#3343 #16843276

Order 3968.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#552C211yesmaximal, characteristic, complemented
2C31×#547C211yesmaximal, characteristic
3C31×#501C211yesmaximal, characteristic, complemented
4C31×#484C211yesmaximal, characteristic, complemented
5C31×#483C211yesmaximal, characteristic, complemented
6C31×#482C211yesmaximal, characteristic, complemented
7C31×#480C211yesmaximal, characteristic, complemented
8C31×#478C211yesmaximal, characteristic, complemented
9C31×#477C211yesmaximal, characteristic, complemented
10C31×#468C211yesmaximal, characteristic, complemented
11C31×#465C211yesmaximal, characteristic, complemented
12C31×#440C211yesmaximal, characteristic, complemented
13C31×#435C211yesmaximal, characteristic, complemented
14C31×#428C211yesmaximal, characteristic, complemented
15C2×C31×#107C211yesmaximal, characteristic, complemented
16C2×#41×C31—21no—
17C2×SD16×C31C2211yescharacteristic
18C2×M16×C31C2211yescharacteristic
19C22×C8×C31C2211yescharacteristic
20C31×C4⋊Q8C2211yescharacteristic
21C31×#126—21no—
22C31×#125—21no—
23C31×#125C2211yescharacteristic
24C31×#123—21no—
25C31×#123—21no—
26C31×#123—21no—
27C31×C22⋊Q8—21no—
28C31×C22⋊Q8C2211yescharacteristic
29C31×C22⋊Q8C2211yescharacteristic
30C31×#121C2211yescharacteristic
31C31×#121C2211yescharacteristic
32C4×Q8×C31C2211yescharacteristic
33C4×D4×C31C2211yescharacteristic
34C4×D4×C31C2211yescharacteristic
35C31×#117—21no—
36C31×#117C2211yescharacteristic
37C2×C4⋊C4×C31C2211yescharacteristic
38C2×C4⋊C4×C31C2211yescharacteristic
39C2×C4⋊C4×C31C2211yescharacteristic
40C31×#107C2211yescharacteristic
41C31×#107C2211yescharacteristic
42C31×#107C2211yescharacteristic
43C31×#107C2211yescharacteristic
44C31×#107C2211yescharacteristic
45C31×#107C2211yescharacteristic
46C31×#106C2211yescharacteristic
47C31×#106C2211yescharacteristic
48C31×#106C2211yescharacteristic
49C31×C4⋊C8C2211yescharacteristic
50C31×#103C2211yescharacteristic
51C31×#103C2211yescharacteristic
52C31×#103C2211yescharacteristic
53C31×#102C2211yescharacteristic
54C31×#102C2211yescharacteristic
55C31×#102C2211yescharacteristic
56C31×C22⋊C8C2211yescharacteristic
57C31×C22⋊C8C2211yescharacteristic
58C31×#97C2211yescharacteristic
59#41×C31—44no—
60C2×Q8×C31—21no—
61C2×Q8×C31C2311yescharacteristic
62C2×D4×C31—21no—
63C2×D4×C31—21no—
64C2×D4×C31D411yescharacteristic
65C2×D4×C31C2311yescharacteristic
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31C2311yescharacteristic
71C22×C4×C31C2311yescharacteristic
72SD16×C31—22no—
73M16×C31—22no—
74C2×C8×C31—22no—
75C2×C8×C31C2311yescharacteristic
76C2×C8×C31C2311yescharacteristic
77C2×C8×C31C2311yescharacteristic
78C2×C8×C31C2311yescharacteristic
79C4⋊C4×C31—21no—
80C4⋊C4×C31—21no—
81C4⋊C4×C31—21no—
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×C31D411yescharacteristic
89C4⋊C4×C31C2311yescharacteristic
90C4⋊C4×C31C2311yescharacteristic
91C4⋊C4×C31C2311yescharacteristic
92C4⋊C4×C31C2311yescharacteristic
93C4⋊C4×C31C2311yescharacteristic
94C4⋊C4×C31C2311yescharacteristic
95C22⋊C4×C31—21no—
96C22⋊C4×C31—21no—
97C22⋊C4×C31—21no—
98C22⋊C4×C31—21no—
99C22⋊C4×C31—21no—
100C22⋊C4×C31—21no—
101C22⋊C4×C31D411yescharacteristic
102C22⋊C4×C31D411yescharacteristic
103C42×C31—21no—
104C42×C31—21no—
105C42×C31C2311yescharacteristic
106C23×C31—21no—
107C23×C31C2×D411yescharacteristic
108C23×C31C2×D411yescharacteristic
109Q8×C31—21no—
110Q8×C31—21no—
111Q8×C31—42no—
112D4×C31—22no—
113D4×C31—21no—
114D4×C31—21no—
115D4×C31—42no—
116D4×C31—42no—
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—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—42no—
129C2×C4×C31—42no—
130C2×C4×C31—42no—
131C2×C4×C31—42no—
132C2×C4×C31C2×D411yescharacteristic
133C2×C4×C31C2×D411yescharacteristic
134C2×C4×C31C2×D411yescharacteristic
135C2×C4×C31C2×D411yescharacteristic
136C2×C4×C31C2411yescharacteristic
137C8×C31—21no—
138C8×C31—21no—
139C8×C31—21no—
140C8×C31#4112yescomplemented
141#3343C3111yesmaximal, characteristic, direct product factor, Sylow
142C22×C31—21no—
143C22×C31—21no—
144C22×C31—21no—
145C22×C31—21no—
146C22×C31—21no—
147C22×C31—41no—
148C22×C31—41no—
149C22×C31—41no—
150C22×C31AGL(1,ℤ/8)12yes—
151C22×C31C22×D411yescharacteristic
152C4×C31—21no—
153C4×C31—21no—
154C4×C31—21no—
155C4×C31—21no—
156C4×C31—41no—
157C4×C31—41no—
158C4×C31—41no—
159C4×C31—41no—
160C4×C31—41no—
161C4×C31—41no—
162C4×C31—41no—
163C4×C31C2×#4111yescharacteristic
164C4×C312−1+411yescharacteristic
165#552C2×C3111yescharacteristic, complemented
166#547C2×C3111yescharacteristic
167#501C2×C3111yescharacteristic, complemented
168#484C2×C3111yescharacteristic, complemented
169#483C2×C3111yescharacteristic, complemented
170#482C2×C3111yescharacteristic, complemented
171#480C2×C3111yescharacteristic, complemented
172#478C2×C3111yescharacteristic, complemented
173#477C2×C3111yescharacteristic, complemented
174#468C2×C3111yescharacteristic, complemented
175#465C2×C3111yescharacteristic, complemented
176#440C2×C3111yescharacteristic, complemented
177#435C2×C3111yescharacteristic, complemented
178#428C2×C3111yescharacteristic, complemented
179C2×#107C2×C3111yescharacteristic, complemented
180C2×C31—22no—
181C2×C31—41no—
182C2×C31—81no—
183C2×C31#54711yescharacteristic
184C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C31#57811yescharacteristic
186C2×#41—21no—
187C2×SD16C22×C3111yescharacteristic
188C2×M16C22×C3111yescharacteristic
189C22×C8C22×C3111yescharacteristic
190C4⋊Q8C22×C3111yescharacteristic
191#126—21no—
192#125—21no—
193#125C22×C3111yescharacteristic
194#123—21no—
195#123—21no—
196#123—21no—
197C22⋊Q8—21no—
198C22⋊Q8C22×C3111yescharacteristic
199C22⋊Q8C22×C3111yescharacteristic
200#121C22×C3111yescharacteristic
201#121C22×C3111yescharacteristic
202C4×Q8C22×C3111yescharacteristic
203C4×D4C22×C3111yescharacteristic
204C4×D4C22×C3111yescharacteristic
205#117—21no—
206#117C22×C3111yescharacteristic
207C2×C4⋊C4C22×C3111yescharacteristic
208C2×C4⋊C4C22×C3111yescharacteristic
209C2×C4⋊C4C22×C3111yescharacteristic
210#107C22×C3111yescharacteristic
211#107C22×C3111yescharacteristic
212#107C22×C3111yescharacteristic
213#107C22×C3111yescharacteristic
214#107C22×C3111yescharacteristic
215#107C22×C3111yescharacteristic
216#106C22×C3111yescharacteristic
217#106C22×C3111yescharacteristic
218#106C22×C3111yescharacteristic
219C4⋊C8C22×C3111yescharacteristic
220#103C22×C3111yescharacteristic
221#103C22×C3111yescharacteristic
222#103C22×C3111yescharacteristic
223#102C22×C3111yescharacteristic
224#102C22×C3111yescharacteristic
225#102C22×C3111yescharacteristic
226C22⋊C8C22×C3111yescharacteristic
227C22⋊C8C22×C3111yescharacteristic
228#97C22×C3111yescharacteristic
229C31#334311yescharacteristic, direct product factor, Sylow
230#41—44no—
231C2×Q8—21no—
232C2×Q8C23×C3111yescharacteristic
233C2×D4—21no—
234C2×D4—21no—
235C2×D4D4×C3111yescharacteristic
236C2×D4C23×C3111yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4C23×C3111yescharacteristic
242C22×C4C23×C3111yescharacteristic
243SD16—22no—
244M16—22no—
245C2×C8—22no—
246C2×C8C23×C3111yescharacteristic
247C2×C8C23×C3111yescharacteristic
248C2×C8C23×C3111yescharacteristic
249C2×C8C23×C3111yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4D4×C3111yescharacteristic
260C4⋊C4C23×C3111yescharacteristic
261C4⋊C4C23×C3111yescharacteristic
262C4⋊C4C23×C3111yescharacteristic
263C4⋊C4C23×C3111yescharacteristic
264C4⋊C4C23×C3111yescharacteristic
265C4⋊C4C23×C3111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4D4×C3111yescharacteristic
273C22⋊C4D4×C3111yescharacteristic
274C42—21no—
275C42—21no—
276C42C23×C3111yescharacteristic
277C23—21no—
278C23C2×D4×C3111yescharacteristic
279C23C2×D4×C3111yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—42no—
283D4—22no—
284D4—21no—
285D4—21no—
286D4—42no—
287D4—42no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4C2×D4×C3111yescharacteristic
304C2×C4C2×D4×C3111yescharacteristic
305C2×C4C2×D4×C3111yescharacteristic
306C2×C4C2×D4×C3111yescharacteristic
307C2×C4C24×C3111yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8#41×C3112yescomplemented
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22C31×AGL(1,ℤ/8)12yes—
321C22C22×D4×C3111yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4C2×#41×C3111yescharacteristic
334C4C31×2−1+411yescharacteristic
335C2—22no—
336C2—41no—
337C2—81no—
338C2C31×#54711yescharacteristic
339C2C2×C31×AGL(1,ℤ/8)11yescharacteristic
340C2C31×#57811yescharacteristic
subgroupG/H
center, socleC22×C31C22×D4
commutator, Frattini, cosocleC2×C4C24×C31
prime radicalC31×#547C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#552C2semidirect
3. C31×#501C2semidirect
4. C31×#484C2semidirect
5. C31×#483C2semidirect
6. C31×#482C2semidirect
7. C31×#480C2semidirect
8. C31×#478C2semidirect
9. C31×#477C2semidirect
10. C31×#468C2semidirect
11. C31×#465C2semidirect
12. C31×#440C2semidirect
13. C31×#435C2semidirect
14. C31×#428C2semidirect
15. C2×C31×#107C2semidirect
140. C8×C31#41semidirect
141. #3343C31direct (N × H)
165. #552C2×C31semidirect
167. #501C2×C31semidirect
168. #484C2×C31semidirect
169. #483C2×C31semidirect
170. #482C2×C31semidirect
171. #480C2×C31semidirect
172. #478C2×C31semidirect
173. #477C2×C31semidirect
174. #468C2×C31semidirect
175. #465C2×C31semidirect
176. #440C2×C31semidirect
177. #435C2×C31semidirect
178. #428C2×C31semidirect
179. C2×#107C2×C31semidirect
229. C31#3343direct (N × H)
311. C8#41×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#5522
C31×#5472
C31×#5012
C31×#4842
C31×#4832
C31×#4822
C31×#4802
C31×#4782
C31×#4772
C31×#4682
C31×#4652
C31×#4402
C31×#4352
C31×#4282
C2×C31×#1072
#334331