Finite Group Databasebeta

← C31×#12140 #21468899

Subgroups — C31×#12140 #21468899

Order 7936.

478 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2680C211yesmaximal, characteristic, complemented
2C31×#2039C211yesmaximal, characteristic, complemented
3C31×#1604C211yesmaximal, characteristic, complemented
4C31×#1598C211yesmaximal, characteristic
5C31×#1354C211yesmaximal, characteristic, complemented
6C31×#1345C211yesmaximal, characteristic, complemented
7C31×#1325C211yesmaximal, characteristic, complemented
8C31×#537C2211yescharacteristic
9C2×C31×#123—21no—
10C2×C31×C22⋊Q8—21no—
11C31×#448—21no—
12C31×#447—21no—
13C2×C31×#104—21no—
14C31×#417—21no—
15C31×#398—21no—
16C31×#397—21no—
17C31×#395C2211yescharacteristic
18C31×#394C2211yescharacteristic
19C31×#388—21no—
20C31×#385—21no—
21C31×#384C2211yescharacteristic
22C31×#343C2211yescharacteristic
23C31×#327—21no—
24C31×#327—21no—
25C31×#324C2211yescharacteristic
26C31×#324C2211yescharacteristic
27C2×#41×C31—21no—
28C22×Q8×C31D411yescharacteristic
29C22×D4×C31D411yescharacteristic
30C23×C4×C31—21no—
31C2×SD16×C31—41no—
32C2×D8×C31—41no—
33C2×M16×C31—21no—
34C31×#123—44no—
35C31×C22⋊Q8—44no—
36C31×C22⋊Q8—41no—
37C31×#121—21no—
38C31×#121—21no—
39C31×#121—41no—
40C2×C4⋊C4×C31—21no—
41C2×C4⋊C4×C31—21no—
42C2×C4⋊C4×C31—21no—
43C2×C4⋊C4×C31—21no—
44C2×C4⋊C4×C31—21no—
45C2×C4⋊C4×C31D411yescharacteristic
46C2×C4⋊C4×C31C2311yescharacteristic
47C2×C22⋊C4×C31—21no—
48C2×C22⋊C4×C31—21no—
49C2×C22⋊C4×C31—21no—
50C2×C22⋊C4×C31—21no—
51C2×C22⋊C4×C31—21no—
52C2×C42×C31D411yescharacteristic
53C31×#104—42no—
54C31×#103—41no—
55C31×#103—41no—
56C31×#102—41no—
57C31×#102—41no—
58C31×C22⋊C8—21no—
59C31×C22⋊C8—21no—
60C31×#95—21no—
61C31×#95—21no—
62C31×#95—21no—
63C31×#95D411yescharacteristic
64C31×#95D411yescharacteristic
65C24×C31—21no—
66#41×C31—41no—
67#41×C31—41no—
68#41×C31—41no—
69#41×C31—41no—
70C2×Q8×C31—21no—
71C2×Q8×C31—42no—
72C2×Q8×C31—41no—
73C2×D4×C31—21no—
74C2×D4×C31—21no—
75C2×D4×C31—21no—
76C2×D4×C31—41no—
77C2×D4×C31—42no—
78C2×D4×C31—41no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—21no—
83C22×C4×C31—21no—
84C22×C4×C31—41no—
85C22×C4×C31—42no—
86C22×C4×C31—42no—
87C22×C4×C31—81no—
88C22×C4×C31C2×D411yescharacteristic
89C22×C4×C31C2×D411yescharacteristic
90C22×C4×C31C2×D411yescharacteristic
91SD16×C31—82no—
92D8×C31—82no—
93M16×C31—41no—
94M16×C31—41no—
95C2×C8×C31—41no—
96C2×C8×C31—41no—
97C2×C8×C31—41no—
98C4⋊C4×C31—21no—
99C4⋊C4×C31—21no—
100C4⋊C4×C31—41no—
101C4⋊C4×C31—42no—
102C4⋊C4×C31—42no—
103C4⋊C4×C31—42no—
104C4⋊C4×C31—42no—
105C4⋊C4×C31—42no—
106C4⋊C4×C31—41no—
107C22⋊C4×C31—24no—
108C22⋊C4×C31—42no—
109C22⋊C4×C31—41no—
110C22⋊C4×C31—41no—
111C22⋊C4×C31—42no—
112C22⋊C4×C31—42no—
113C22⋊C4×C31—41no—
114C22⋊C4×C31—41no—
115C42×C31—21no—
116C42×C31—21no—
117#12140C3111yesmaximal, characteristic, direct product factor, Sylow
118C23×C31—22no—
119C23×C31—41no—
120C23×C31—41no—
121C23×C31—41no—
122C23×C31—41no—
123C23×C31—41no—
124C23×C31—41no—
125C23×C31—41no—
126C23×C31#12011yescharacteristic
127Q8×C31—41no—
128Q8×C31—41no—
129Q8×C31—42no—
130Q8×C31—81no—
131D4×C31—41no—
132D4×C31—41no—
133D4×C31—42no—
134D4×C31—81no—
135D4×C31—81no—
136D4×C31—81no—
137D4×C31—81no—
138D4×C31—81no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—22no—
142C2×C4×C31—22no—
143C2×C4×C31—21no—
144C2×C4×C31—21no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
160C2×C4×C31—41no—
161C2×C4×C31—81no—
162C2×C4×C31—81no—
163C2×C4×C31—84no—
164C2×C4×C31#13511yescharacteristic
165C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
166C8×C31—81no—
167C8×C31—81no—
168C8×C31—81no—
169#2680C2×C3111yescharacteristic, complemented
170#2039C2×C3111yescharacteristic, complemented
171#1604C2×C3111yescharacteristic, complemented
172#1598C2×C3111yescharacteristic
173#1354C2×C3111yescharacteristic, complemented
174#1345C2×C3111yescharacteristic, complemented
175#1325C2×C3111yescharacteristic, complemented
176C22×C31—21no—
177C22×C31—21no—
178C22×C31—42no—
179C22×C31—42no—
180C22×C31—42no—
181C22×C31—81no—
182C22×C31—81no—
183C22×C31—81no—
184C22×C31—81no—
185C22×C31—81no—
186C22×C31—81no—
187C22×C31—81no—
188C22×C31#44911yescharacteristic
189C22×C31#45411yescharacteristic
190C22×C31B(4,𝔽2)11yescharacteristic
191C4×C31—21no—
192C4×C31—21no—
193C4×C31—42no—
194C4×C31—41no—
195C4×C31—41no—
196C4×C31—42no—
197C4×C31—81no—
198C4×C31—81no—
199C4×C31—81no—
200C4×C31—81no—
201#537C22×C3111yescharacteristic
202C2×#123—21no—
203C2×C22⋊Q8—21no—
204#448—21no—
205#447—21no—
206C2×#104—21no—
207#417—21no—
208#398—21no—
209#397—21no—
210#395C22×C3111yescharacteristic
211#394C22×C3111yescharacteristic
212#388—21no—
213#385—21no—
214#384C22×C3111yescharacteristic
215#343C22×C3111yescharacteristic
216#327—21no—
217#327—21no—
218#324C22×C3111yescharacteristic
219#324C22×C3111yescharacteristic
220C2×C31—21no—
221C2×C31—21no—
222C2×C31—82no—
223C2×C31—161no—
224C2×C31#159711yescharacteristic
225C2×C31#219611yescharacteristic
226C2×C31#220311yescharacteristic
227C2×#41—21no—
228C22×Q8D4×C3111yescharacteristic
229C22×D4D4×C3111yescharacteristic
230C23×C4—21no—
231C2×SD16—41no—
232C2×D8—41no—
233C2×M16—21no—
234#123—44no—
235C22⋊Q8—44no—
236C22⋊Q8—41no—
237#121—21no—
238#121—21no—
239#121—41no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4D4×C3111yescharacteristic
246C2×C4⋊C4C23×C3111yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C42D4×C3111yescharacteristic
253#104—42no—
254#103—41no—
255#103—41no—
256#102—41no—
257#102—41no—
258C22⋊C8—21no—
259C22⋊C8—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95D4×C3111yescharacteristic
264#95D4×C3111yescharacteristic
265C31#1214011yescharacteristic, direct product factor, Sylow
266C24—21no—
267#41—41no—
268#41—41no—
269#41—41no—
270#41—41no—
271C2×Q8—21no—
272C2×Q8—42no—
273C2×Q8—41no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—42no—
279C2×D4—41no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—81no—
289C22×C4C2×D4×C3111yescharacteristic
290C22×C4C2×D4×C3111yescharacteristic
291C22×C4C2×D4×C3111yescharacteristic
292SD16—82no—
293D8—82no—
294M16—41no—
295M16—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C22⋊C4—24no—
309C22⋊C4—42no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—42no—
313C22⋊C4—42no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C42—21no—
317C42—21no—
318C23—22no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23C31×#12011yescharacteristic
327Q8—41no—
328Q8—41no—
329Q8—42no—
330Q8—81no—
331D4—41no—
332D4—41no—
333D4—42no—
334D4—81no—
335D4—81no—
336D4—81no—
337D4—81no—
338D4—81no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—84no—
364C2×C4C31×#13511yescharacteristic
365C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
366C8—81no—
367C8—81no—
368C8—81no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22C31×#44911yescharacteristic
382C22C31×#45411yescharacteristic
383C22C31×B(4,𝔽2)11yescharacteristic
384C4—21no—
385C4—21no—
386C4—42no—
387C4—41no—
388C4—41no—
389C4—42no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—81no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2—161no—
398C2C31×#159711yescharacteristic
399C2C31×#219611yescharacteristic
400C2C31×#220311yescharacteristic
subgroupG/H
center, socleC22×C31B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC31×#1598C2
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C2×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2680C2semidirect
2. C31×#2039C2semidirect
3. C31×#1604C2semidirect
5. C31×#1354C2semidirect
6. C31×#1345C2semidirect
7. C31×#1325C2semidirect
117. #12140C31direct (N × H)
169. #2680C2×C31semidirect
170. #2039C2×C31semidirect
171. #1604C2×C31semidirect
173. #1354C2×C31semidirect
174. #1345C2×C31semidirect
175. #1325C2×C31semidirect
265. C31#12140direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26802
C31×#20392
C31×#16042
C31×#15982
C31×#13542
C31×#13452
C31×#13252
#1214031