Finite Group Databasebeta

← C31×#10281 #21467040

Subgroups — C31×#10281 #21467040

Order 7936.

690 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3206C211yesmaximal, characteristic, complemented
2C31×#3205C211yesmaximal, characteristic
3C31×#2858C211yesmaximal, characteristic, complemented
4C31×#1962C211yesmaximal, characteristic, complemented
5C31×#1548C211yesmaximal, characteristic, complemented
6C31×#1545C211yesmaximal, characteristic, complemented
7C31×#1276C211yesmaximal, characteristic, complemented
8C31×#532C2211yescharacteristic
9C2×C31×C4⋊Q8C2211yescharacteristic
10C2×C31×#127C2211yescharacteristic
11C2×C31×#124—22no—
12C31×#493—21no—
13C31×#492—21no—
14C31×#487—21no—
15C31×#486—21no—
16C31×#461—22no—
17C31×#459—22no—
18C31×#448—22no—
19C31×#447—22no—
20C31×#431C2211yescharacteristic
21C31×#431C2211yescharacteristic
22C31×#423C2211yescharacteristic
23C2×C31×#104—22no—
24C31×#390—22no—
25C31×#390—22no—
26C43×C31C2211yescharacteristic
27C31×#333—22no—
28C31×#331—22no—
29C2×#41×C31—21no—
30C22×Q8×C31D412yes—
31C22×D4×C31—21no—
32C22×D4×C31—21no—
33C22×D4×C31D412yes—
34C2×SD16×C31—24no—
35C2×D8×C31—24no—
36C2×M16×C31—21no—
37C31×C4⋊Q8—21no—
38C31×C4⋊Q8—21no—
39C31×C4⋊Q8—21no—
40C31×C4⋊Q8—21no—
41C31×C4⋊Q8D411yescharacteristic
42C31×#127—21no—
43C31×#127—21no—
44C31×#127—21no—
45C31×#127—21no—
46C31×#127D411yescharacteristic
47C31×#124—21no—
48C31×#124—48no—
49C31×#121—21no—
50C31×#121—21no—
51C4×D4×C31—21no—
52C4×D4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C22⋊C4×C31—28no—
56C2×C42×C31—21no—
57C2×C42×C31—21no—
58C2×C42×C31D412yes—
59C2×C42×C31C2311yescharacteristic
60C31×C4⋊C8—21no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8D412yes—
63C31×C4⋊C8D412yes—
64C31×#104—44no—
65C31×#103—24no—
66C31×#102—24no—
67C31×C22⋊C8—21no—
68C31×C22⋊C8—21no—
69C4×C8×C31—21no—
70C4×C8×C31—21no—
71C24×C31—22no—
72#41×C31—42no—
73#41×C31—42no—
74C2×Q8×C31—22no—
75C2×Q8×C31—21no—
76C2×Q8×C31—22no—
77C2×Q8×C31—44no—
78C2×D4×C31—22no—
79C2×D4×C31—21no—
80C2×D4×C31—21no—
81C2×D4×C31—21no—
82C2×D4×C31—22no—
83C2×D4×C31—44no—
84C2×D4×C31—44no—
85C2×D4×C31—41no—
86C2×D4×C31—41no—
87C2×D4×C31—41no—
88C2×D4×C31—41no—
89C2×D4×C31—41no—
90C2×D4×C31—42no—
91C2×D4×C31—42no—
92C22×C4×C31—22no—
93C22×C4×C31—22no—
94C22×C4×C31—41no—
95C22×C4×C31C2×D411yescharacteristic
96C22×C4×C31C2×D411yescharacteristic
97C22×C4×C31C2×D411yescharacteristic
98SD16×C31—84no—
99D8×C31—84no—
100M16×C31—42no—
101C2×C8×C31—22no—
102C2×C8×C31—22no—
103C2×C8×C31—41no—
104C4⋊C4×C31—21no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—41no—
107C4⋊C4×C31—41no—
108C4⋊C4×C31—41no—
109C4⋊C4×C31—41no—
110C22⋊C4×C31—416no—
111C22⋊C4×C31—41no—
112C22⋊C4×C31—41no—
113C42×C31—24no—
114C42×C31—22no—
115C42×C31—22no—
116C42×C31—42no—
117C42×C31C2×D411yescharacteristic
118C42×C31C2×D411yescharacteristic
119C42×C31C2×D411yescharacteristic
120C42×C31#4111yescharacteristic
121#10281C3111yesmaximal, characteristic, direct product factor, Sylow
122C23×C31—44no—
123C23×C31—44no—
124C23×C31—41no—
125C23×C31—42no—
126C23×C31—44no—
127C23×C31#12011yescharacteristic
128Q8×C31—44no—
129Q8×C31—42no—
130Q8×C31—82no—
131D4×C31—42no—
132D4×C31—42no—
133D4×C31—44no—
134D4×C31—42no—
135D4×C31—82no—
136D4×C31—82no—
137D4×C31—82no—
138D4×C31—82no—
139D4×C31—82no—
140D4×C31—81no—
141D4×C31—81no—
142C2×C4×C31—22no—
143C2×C4×C31—22no—
144C2×C4×C31—24no—
145C2×C4×C31—42no—
146C2×C4×C31—42no—
147C2×C4×C31—44no—
148C2×C4×C31—41no—
149C2×C4×C31—42no—
150C2×C4×C31—81no—
151C2×C4×C31—81no—
152C2×C4×C31#12011yescharacteristic
153C2×C4×C31#12011yescharacteristic
154C2×C4×C31#12111yescharacteristic
155C2×C4×C31#12111yescharacteristic
156C2×C4×C31#12111yescharacteristic
157C2×C4×C31#12711yescharacteristic
158C2×C4×C31#13512yes—
159C2×C4×C31AGL(1,ℤ/8)12yes—
160C8×C31—42no—
161C8×C31—42no—
162C8×C31—81no—
163#3206C2×C3111yescharacteristic, complemented
164#3205C2×C3111yescharacteristic
165#2858C2×C3111yescharacteristic, complemented
166#1962C2×C3111yescharacteristic, complemented
167#1548C2×C3111yescharacteristic, complemented
168#1545C2×C3111yescharacteristic, complemented
169#1276C2×C3111yescharacteristic, complemented
170C22×C31—21no—
171C22×C31—21no—
172C22×C31—88no—
173C22×C31—81no—
174C22×C31—82no—
175C22×C31—82no—
176C22×C31—81no—
177C22×C31—81no—
178C22×C31—82no—
179C22×C31#39211yescharacteristic
180C22×C31#44912yes—
181C4×C31—21no—
182C4×C31—21no—
183C4×C31—44no—
184C4×C31—82no—
185C4×C31—81no—
186C4×C31#45312yes—
187C4×C31#45512yes—
188C4×C31#46312yes—
189C4×C31#49511yescharacteristic
190C4×C31#49611yescharacteristic
191#532C22×C3111yescharacteristic
192C2×C4⋊Q8C22×C3111yescharacteristic
193C2×#127C22×C3111yescharacteristic
194C2×#124—22no—
195#493—21no—
196#492—21no—
197#487—21no—
198#486—21no—
199#461—22no—
200#459—22no—
201#448—22no—
202#447—22no—
203#431C22×C3111yescharacteristic
204#431C22×C3111yescharacteristic
205#423C22×C3111yescharacteristic
206C2×#104—22no—
207#390—22no—
208#390—22no—
209C43C22×C3111yescharacteristic
210#333—22no—
211#331—22no—
212C2×C31—22no—
213C2×C31—161no—
214C2×C31—162no—
215C2×C31#200211yescharacteristic
216C2×C31#200411yescharacteristic
217C2×C31#201211yescharacteristic
218C2×#41—21no—
219C22×Q8D4×C3112yes—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4D4×C3112yes—
223C2×SD16—24no—
224C2×D8—24no—
225C2×M16—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8D4×C3111yescharacteristic
231#127—21no—
232#127—21no—
233#127—21no—
234#127—21no—
235#127D4×C3111yescharacteristic
236#124—21no—
237#124—48no—
238#121—21no—
239#121—21no—
240C4×D4—21no—
241C4×D4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C22⋊C4—28no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42D4×C3112yes—
248C2×C42C23×C3111yescharacteristic
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8D4×C3112yes—
252C4⋊C8D4×C3112yes—
253#104—44no—
254#103—24no—
255#102—24no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C4×C8—21no—
259C4×C8—21no—
260C31#1028111yescharacteristic, direct product factor, Sylow
261C24—22no—
262#41—42no—
263#41—42no—
264C2×Q8—22no—
265C2×Q8—21no—
266C2×Q8—22no—
267C2×Q8—44no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—22no—
273C2×D4—44no—
274C2×D4—44no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—42no—
281C2×D4—42no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4C2×D4×C3111yescharacteristic
286C22×C4C2×D4×C3111yescharacteristic
287C22×C4C2×D4×C3111yescharacteristic
288SD16—84no—
289D8—84no—
290M16—42no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—41no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C22⋊C4—416no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C42—24no—
304C42—22no—
305C42—22no—
306C42—42no—
307C42C2×D4×C3111yescharacteristic
308C42C2×D4×C3111yescharacteristic
309C42C2×D4×C3111yescharacteristic
310C42#41×C3111yescharacteristic
311C23—44no—
312C23—44no—
313C23—44no—
314C23—41no—
315C23—42no—
316C23C31×#12011yescharacteristic
317Q8—44no—
318Q8—42no—
319Q8—82no—
320D4—42no—
321D4—42no—
322D4—44no—
323D4—42no—
324D4—82no—
325D4—82no—
326D4—82no—
327D4—82no—
328D4—82no—
329D4—81no—
330D4—81no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—44no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4C31×#12011yescharacteristic
342C2×C4C31×#12011yescharacteristic
343C2×C4C31×#12111yescharacteristic
344C2×C4C31×#12111yescharacteristic
345C2×C4C31×#12111yescharacteristic
346C2×C4C31×#12711yescharacteristic
347C2×C4C31×#13512yes—
348C2×C4C31×AGL(1,ℤ/8)12yes—
349C8—42no—
350C8—42no—
351C8—81no—
352C22—21no—
353C22—21no—
354C22—88no—
355C22—81no—
356C22—82no—
357C22—82no—
358C22—81no—
359C22—81no—
360C22—82no—
361C22C31×#39211yescharacteristic
362C22C31×#44912yes—
363C4—21no—
364C4—21no—
365C4—44no—
366C4—82no—
367C4—81no—
368C4C31×#45312yes—
369C4C31×#45512yes—
370C4C31×#46312yes—
371C4C31×#49511yescharacteristic
372C4C31×#49611yescharacteristic
373C2—22no—
374C2—162no—
375C2—161no—
376C2C31×#200211yescharacteristic
377C2C31×#200411yescharacteristic
378C2C31×#201211yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3205C2
LCSG ▷ C2×C42 ▷ 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×#3206C2semidirect
3. C31×#2858C2semidirect
4. C31×#1962C2semidirect
5. C31×#1548C2semidirect
6. C31×#1545C2semidirect
7. C31×#1276C2semidirect
121. #10281C31direct (N × H)
163. #3206C2×C31semidirect
165. #2858C2×C31semidirect
166. #1962C2×C31semidirect
167. #1548C2×C31semidirect
168. #1545C2×C31semidirect
169. #1276C2×C31semidirect
260. C31#10281direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32062
C31×#32052
C31×#28582
C31×#19622
C31×#15482
C31×#15452
C31×#12762
#1028131