Finite Group Databasebeta

← C31×#18220 #21474979

Subgroups — C31×#18220 #21474979

Order 7936.

958 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3502C211yesmaximal, characteristic, complemented
2C31×#3101C212yesmaximal
3C31×#2536C211yesmaximal, characteristic
4C31×#1611C214yesmaximal, complemented
5C31×#1599C214yesmaximal
6C31×#1518C212yesmaximal, complemented
7C31×#1461C211yesmaximal, characteristic, complemented
8Q82×C31—22no—
9C31×#557—22no—
10C31×#557—24no—
11C31×#544—21no—
12C31×#544C2214yes—
13C31×#533—22no—
14C31×#533C2212yes—
15C2×C31×C22⋊Q8—21no—
16C31×#519—21no—
17C2×C4×Q8×C31C2211yescharacteristic
18C2×C4×D4×C31C2211yescharacteristic
19C31×#483C2214yes—
20C31×#476—22no—
21C31×#461—22no—
22C31×#450C2214yes—
23C4×SD16×C31—24no—
24C31×#431C2212yes—
25C31×#398C2212yes—
26C31×#394C2212yes—
27C31×#388—22no—
28C31×#382C2211yescharacteristic
29C31×#380—21no—
30C31×#328C2218yes—
31C31×#324C2214yes—
32C22×Q8×C31D411yescharacteristic
33C22×D4×C31C2311yescharacteristic
34C23×C4×C31—21no—
35C2×SD16×C31—24no—
36C31×C4⋊Q8—22no—
37C31×C4⋊Q8—22no—
38C31×C4⋊Q8—24no—
39C31×C4⋊Q8—28no—
40C31×C4⋊Q8D412yes—
41C31×C4⋊Q8D412yes—
42C31×#125—24no—
43C31×#125—24no—
44C31×#125—28no—
45C31×#125—22no—
46C31×C22⋊Q8—22no—
47C31×C22⋊Q8—24no—
48C31×C22⋊Q8—44no—
49C31×C22⋊Q8C2314yes—
50C4×Q8×C31—24no—
51C4×Q8×C31—24no—
52C4×Q8×C31—24no—
53C4×Q8×C31—24no—
54C4×Q8×C31—22no—
55C4×Q8×C31—22no—
56C4×Q8×C31—22no—
57C4×Q8×C31D414yes—
58C4×D4×C31—22no—
59C4×D4×C31—22no—
60C31×#117—24no—
61C31×#117—22no—
62C2×C4⋊C4×C31—22no—
63C2×C4⋊C4×C31—21no—
64C2×C4⋊C4×C31D411yescharacteristic
65C2×C4⋊C4×C31C2311yescharacteristic
66C2×C4⋊C4×C31C2312yes—
67C2×C22⋊C4×C31—21no—
68C2×C22⋊C4×C31—22no—
69C2×C22⋊C4×C31—22no—
70C2×C42×C31D412yes—
71C2×C42×C31C2311yescharacteristic
72C31×#106—24no—
73C31×C4⋊C8—22no—
74C31×#103—24no—
75C31×#102—24no—
76C31×C22⋊C8C2314yes—
77C4×C8×C31—22no—
78C31×#95—22no—
79C31×#95—21no—
80C31×#95C2312yes—
81C24×C31—21no—
82C2×Q8×C31—24no—
83C2×Q8×C31—22no—
84C2×Q8×C31—22no—
85C2×Q8×C31—22no—
86C2×Q8×C31SD1614yescomplemented
87C2×Q8×C31C2×D414yes—
88C2×D4×C31—22no—
89C2×D4×C31—42no—
90C22×C4×C31—22no—
91C22×C4×C31—21no—
92C22×C4×C31—42no—
93C22×C4×C31—42no—
94C22×C4×C31—42no—
95C22×C4×C31C2×D412yes—
96C22×C4×C31C2×D412yes—
97C22×C4×C31C2×D411yescharacteristic
98C22×C4×C31C2×D411yescharacteristic
99C22×C4×C31C2411yescharacteristic
100SD16×C31—48no—
101C2×C8×C31—24no—
102C4⋊C4×C31—24no—
103C4⋊C4×C31—24no—
104C4⋊C4×C31—24no—
105C4⋊C4×C31—28no—
106C4⋊C4×C31—22no—
107C4⋊C4×C31—22no—
108C4⋊C4×C31—22no—
109C4⋊C4×C31—22no—
110C4⋊C4×C31—24no—
111C4⋊C4×C31—24no—
112C4⋊C4×C31—24no—
113C4⋊C4×C31—22no—
114C4⋊C4×C31—42no—
115C4⋊C4×C31—44no—
116C4⋊C4×C31C2×D414yes—
117C22⋊C4×C31—24no—
118C22⋊C4×C31—44no—
119C22⋊C4×C31—41no—
120C22⋊C4×C31—41no—
121C22⋊C4×C31—44no—
122C42×C31—28no—
123C42×C31—22no—
124C42×C31—22no—
125C42×C31—24no—
126C42×C31C2×D412yes—
127C42×C31C2×D412yes—
128#18220C3111yesmaximal, characteristic, direct product factor, Sylow
129C23×C31—22no—
130C23×C31—41no—
131C23×C31—41no—
132C23×C31—41no—
133C23×C31—41no—
134C23×C31—41no—
135C23×C31—41no—
136C23×C31C22×D411yescharacteristic
137Q8×C31—28no—
138Q8×C31—44no—
139Q8×C31—44no—
140Q8×C31—84no—
141D4×C31—24no—
142D4×C31—42no—
143C2×C4×C31—22no—
144C2×C4×C31—22no—
145C2×C4×C31—24no—
146C2×C4×C31—24no—
147C2×C4×C31—22no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—42no—
151C2×C4×C31—42no—
152C2×C4×C31—42no—
153C2×C4×C31—41no—
154C2×C4×C31—42no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—84no—
158C2×C4×C31#12011yescharacteristic
159C2×C4×C31#12011yescharacteristic
160C2×C4×C31#12012yes—
161C2×C4×C31C2×SD1614yes—
162C2×C4×C31C2×SD1612yes—
163C2×C4×C31#13712yes—
164C2×C4×C31C22×D412yes—
165C8×C31—44no—
166#3502C2×C3111yescharacteristic, complemented
167#3101C2×C3112yes—
168#2536C2×C3111yescharacteristic
169#1611C2×C3114yescomplemented
170#1599C2×C3114yes—
171#1518C2×C3112yescomplemented
172#1461C2×C3111yescharacteristic, complemented
173C22×C31—21no—
174C22×C31—21no—
175C22×C31—42no—
176C22×C31—42no—
177C22×C31—42no—
178C22×C31—81no—
179C22×C31—81no—
180C22×C31—81no—
181C22×C31—81no—
182C22×C31C2×#12011yescharacteristic
183C22×C31C22×SD1611yescharacteristic
184C22×C31C2×#13711yescharacteristic
185C4×C31—24no—
186C4×C31—21no—
187C4×C31—21no—
188C4×C31—22no—
189C4×C31—44no—
190C4×C31—42no—
191C4×C31—44no—
192C4×C31—82no—
193C4×C31—81no—
194C4×C31#44814yes—
195Q82—22no—
196#557—22no—
197#557—24no—
198#544—21no—
199#544C22×C3114yes—
200#533—22no—
201#533C22×C3112yes—
202C2×C22⋊Q8—21no—
203#519—21no—
204C2×C4×Q8C22×C3111yescharacteristic
205C2×C4×D4C22×C3111yescharacteristic
206#483C22×C3114yes—
207#476—22no—
208#461—22no—
209#450C22×C3114yes—
210C4×SD16—24no—
211#431C22×C3112yes—
212#398C22×C3112yes—
213#394C22×C3112yes—
214#388—22no—
215#382C22×C3111yescharacteristic
216#380—21no—
217#328C22×C3118yes—
218#324C22×C3114yes—
219C2×C31—21no—
220C2×C31—21no—
221C2×C31—82no—
222C2×C31C2×#44811yescharacteristic
223C2×C31#302011yescharacteristic
224C2×C31#302511yescharacteristic
225C22×Q8D4×C3111yescharacteristic
226C22×D4C23×C3111yescharacteristic
227C23×C4—21no—
228C2×SD16—24no—
229C4⋊Q8—22no—
230C4⋊Q8—22no—
231C4⋊Q8—24no—
232C4⋊Q8—28no—
233C4⋊Q8D4×C3112yes—
234C4⋊Q8D4×C3112yes—
235#125—24no—
236#125—24no—
237#125—28no—
238#125—22no—
239C22⋊Q8—22no—
240C22⋊Q8—24no—
241C22⋊Q8—44no—
242C22⋊Q8C23×C3114yes—
243C4×Q8—24no—
244C4×Q8—24no—
245C4×Q8—24no—
246C4×Q8—24no—
247C4×Q8—22no—
248C4×Q8—22no—
249C4×Q8—22no—
250C4×Q8D4×C3114yes—
251C4×D4—22no—
252C4×D4—22no—
253#117—24no—
254#117—22no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4D4×C3111yescharacteristic
258C2×C4⋊C4C23×C3111yescharacteristic
259C2×C4⋊C4C23×C3112yes—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C42D4×C3112yes—
264C2×C42C23×C3111yescharacteristic
265#106—24no—
266C4⋊C8—22no—
267#103—24no—
268#102—24no—
269C22⋊C8C23×C3114yes—
270C4×C8—22no—
271#95—22no—
272#95—21no—
273#95C23×C3112yes—
274C31#1822011yescharacteristic, direct product factor, Sylow
275C24—21no—
276C2×Q8—24no—
277C2×Q8—22no—
278C2×Q8—22no—
279C2×Q8—22no—
280C2×Q8SD16×C3114yescomplemented
281C2×Q8C2×D4×C3114yes—
282C2×D4—22no—
283C2×D4—42no—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4C2×D4×C3112yes—
290C22×C4C2×D4×C3112yes—
291C22×C4C2×D4×C3111yescharacteristic
292C22×C4C2×D4×C3111yescharacteristic
293C22×C4C24×C3111yescharacteristic
294SD16—48no—
295C2×C8—24no—
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—28no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—24no—
307C4⋊C4—22no—
308C4⋊C4—42no—
309C4⋊C4—44no—
310C4⋊C4C2×D4×C3114yes—
311C22⋊C4—24no—
312C22⋊C4—44no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—44no—
316C42—28no—
317C42—22no—
318C42—22no—
319C42—24no—
320C42C2×D4×C3112yes—
321C42C2×D4×C3112yes—
322C23—22no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23C22×D4×C3111yescharacteristic
330Q8—28no—
331Q8—44no—
332Q8—44no—
333Q8—84no—
334D4—24no—
335D4—42no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—84no—
351C2×C4C31×#12011yescharacteristic
352C2×C4C31×#12011yescharacteristic
353C2×C4C31×#12012yes—
354C2×C4C2×SD16×C3114yes—
355C2×C4C2×SD16×C3112yes—
356C2×C4C31×#13712yes—
357C2×C4C22×D4×C3112yes—
358C8—44no—
359C22—21no—
360C22—21no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22C2×C31×#12011yescharacteristic
369C22C22×SD16×C3111yescharacteristic
370C22C2×C31×#13711yescharacteristic
371C4—24no—
372C4—21no—
373C4—21no—
374C4—22no—
375C4—44no—
376C4—42no—
377C4—44no—
378C4—82no—
379C4—81no—
380C4C31×#44814yes—
381C2—21no—
382C2—21no—
383C2—82no—
384C2C2×C31×#44811yescharacteristic
385C2C31×#302011yescharacteristic
386C2C31×#302511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3502C2semidirect
4. C31×#1611C2semidirect
6. C31×#1518C2semidirect
7. C31×#1461C2semidirect
86. C2×Q8×C31SD16semidirect
128. #18220C31direct (N × H)
166. #3502C2×C31semidirect
169. #1611C2×C31semidirect
171. #1518C2×C31semidirect
172. #1461C2×C31semidirect
274. C31#18220direct (N × H)
280. C2×Q8SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#35022
C31×#31012
C31×#25362
C31×#16112
C31×#15992
C31×#15182
C31×#14612
#1822031