Finite Group Databasebeta

← C31×#10472 #21467231

Subgroups — C31×#10472 #21467231

Order 7936.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#459C211yesmaximal, characteristic
2C31×#1957C211yesmaximal, characteristic, complemented
3C31×#1954C211yesmaximal, characteristic, complemented
4C31×#1802C211yesmaximal, characteristic, complemented
5C2×C31×#335C211yesmaximal, characteristic, complemented
6C2×C31×#331C211yesmaximal, characteristic, complemented
7C31×#1296C211yesmaximal, characteristic, complemented
8C22×D8×C31—21no—
9C2×C31×#127C2211yescharacteristic
10C2×C4×D4×C31C2211yescharacteristic
11C31×#459—22no—
12C31×#459—22no—
13C2×C31×C4⋊C8C2211yescharacteristic
14C2×C31×C4⋊C8C2211yescharacteristic
15C2×C31×C4⋊C8C2211yescharacteristic
16C2×C31×#102—21no—
17C2×C31×#102—21no—
18C2×C31×#102—21no—
19C2×C31×#102—21no—
20C2×C31×C22⋊C8—21no—
21C2×C31×C22⋊C8—21no—
22C2×C4×C8×C31C2211yescharacteristic
23C31×#384C2211yescharacteristic
24C31×#340—21no—
25C31×#335—22no—
26C31×#331—22no—
27C22×D4×C31—21no—
28C22×D4×C31—21no—
29C22×D4×C31—21no—
30C22×D4×C31D411yescharacteristic
31C23×C4×C31—21no—
32C2×D8×C31—24no—
33C2×D8×C31—42no—
34C2×D8×C31—42no—
35C22×C8×C31—21no—
36C22×C8×C31—21no—
37C22×C8×C31—21no—
38C22×C8×C31D411yescharacteristic
39C22×C8×C31D411yescharacteristic
40C31×#127—21no—
41C31×#127—21no—
42C31×#127—21no—
43C31×#127D412yes—
44C4×D4×C31—21no—
45C4×D4×C31—21no—
46C4×D4×C31—21no—
47C4×D4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31D411yescharacteristic
52C2×C22⋊C4×C31—21no—
53C2×C42×C31C2311yescharacteristic
54C31×C4⋊C8—21no—
55C31×C4⋊C8—21no—
56C31×C4⋊C8—21no—
57C31×C4⋊C8—21no—
58C31×C4⋊C8—21no—
59C31×C4⋊C8D412yes—
60C31×#102—24no—
61C31×#102—42no—
62C31×#102—42no—
63C31×#102—42no—
64C31×C22⋊C8—42no—
65C31×C22⋊C8—42no—
66C4×C8×C31—21no—
67C4×C8×C31—21no—
68C24×C31—21no—
69C24×C31—41no—
70C2×D4×C31—21no—
71C2×D4×C31—22no—
72C2×D4×C31—22no—
73C2×D4×C31—21no—
74C2×D4×C31—22no—
75C2×D4×C31—21no—
76C2×D4×C31—21no—
77C2×D4×C31—21no—
78C2×D4×C31—41no—
79C2×D4×C31—41no—
80C2×D4×C31—41no—
81C2×D4×C31—41no—
82C2×D4×C31—41no—
83C2×D4×C31—41no—
84C2×D4×C31—41no—
85C2×D4×C31—41no—
86C2×D4×C31—41no—
87C2×D4×C31—41no—
88C2×D4×C31—41no—
89C2×D4×C31—81no—
90C2×D4×C31—81no—
91C2×D4×C31D812yes—
92C22×C4×C31—21no—
93C22×C4×C31—41no—
94C22×C4×C31—41no—
95C22×C4×C31—41no—
96C22×C4×C31—41no—
97C22×C4×C31—41no—
98C22×C4×C31—41no—
99C22×C4×C31—41no—
100C22×C4×C31C2×D411yescharacteristic
101C22×C4×C31C2×D411yescharacteristic
102C22×C4×C31#4111yescharacteristic
103D8×C31—48no—
104C2×C8×C31—21no—
105C2×C8×C31—21no—
106C2×C8×C31—22no—
107C2×C8×C31—21no—
108C2×C8×C31—21no—
109C2×C8×C31—21no—
110C2×C8×C31—41no—
111C2×C8×C31—41no—
112C2×C8×C31—41no—
113C2×C8×C31—41no—
114C2×C8×C31—41no—
115C2×C8×C31—41no—
116C2×C8×C31—41no—
117C2×C8×C31—41no—
118C2×C8×C31D812yescomplemented
119C4⋊C4×C31—21no—
120C4⋊C4×C31—21no—
121C4⋊C4×C31—41no—
122C4⋊C4×C31—41no—
123C4⋊C4×C31—41no—
124C4⋊C4×C31—41no—
125C4⋊C4×C31—81no—
126C22⋊C4×C31—41no—
127C22⋊C4×C31—41no—
128C42×C31C2×D411yescharacteristic
129C42×C31C2×D411yescharacteristic
130C42×C31#4111yescharacteristic
131C42×C31#4111yescharacteristic
132#10472C3111yesmaximal, characteristic, direct product factor, Sylow
133C23×C31—22no—
134C23×C31—41no—
135C23×C31—41no—
136C23×C31—41no—
137C23×C31—41no—
138C23×C31—41no—
139C23×C31—41no—
140C23×C31—42no—
141C23×C31—81no—
142C23×C31—81no—
143C23×C31—81no—
144C23×C31—81no—
145C23×C31—81no—
146C23×C31—81no—
147C23×C31#12111yescharacteristic
148D4×C31—22no—
149D4×C31—22no—
150D4×C31—42no—
151D4×C31—41no—
152D4×C31—42no—
153D4×C31—42no—
154D4×C31—42no—
155D4×C31—41no—
156D4×C31—82no—
157D4×C31—82no—
158D4×C31—81no—
159D4×C31—81no—
160D4×C31—81no—
161D4×C31—81no—
162C2×C4×C31—21no—
163C2×C4×C31—21no—
164C2×C4×C31—41no—
165C2×C4×C31—41no—
166C2×C4×C31—41no—
167C2×C4×C31—81no—
168C2×C4×C31—81no—
169C2×C4×C31—81no—
170C2×C4×C31—81no—
171C2×C4×C31—81no—
172C2×C4×C31—81no—
173C2×C4×C31—81no—
174C2×C4×C31#12011yescharacteristic
175C2×C4×C31#12111yescharacteristic
176C2×C4×C31#12111yescharacteristic
177C2×C4×C31#12311yescharacteristic
178C2×C4×C31#12311yescharacteristic
179C2×C4×C31#12411yescharacteristic
180C2×C4×C31C2×D811yescharacteristic
181C2×C4×C31C2×D811yescharacteristic
182C2×C4×C31#13511yescharacteristic
183C2×C4×C31#13511yescharacteristic
184C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C31#13711yescharacteristic
188C8×C31—22no—
189C8×C31—42no—
190C8×C31—41no—
191C8×C31—81no—
192C8×C31—81no—
193C2×#459C2×C3111yescharacteristic
194#1957C2×C3111yescharacteristic, complemented
195#1954C2×C3111yescharacteristic, complemented
196#1802C2×C3111yescharacteristic, complemented
197C2×#335C2×C3111yescharacteristic, complemented
198C2×#331C2×C3111yescharacteristic, complemented
199#1296C2×C3111yescharacteristic, complemented
200C22×C31—42no—
201C22×C31—42no—
202C22×C31—42no—
203C22×C31—81no—
204C22×C31—81no—
205C22×C31—81no—
206C22×C31—81no—
207C22×C31—82no—
208C22×C31—82no—
209C22×C31—82no—
210C22×C31—161no—
211C22×C31—161no—
212C22×C31—161no—
213C22×C31—161no—
214C22×C31#39411yescharacteristic
215C22×C31#45911yescharacteristic
216C22×C31#46311yescharacteristic
217C22×C31#46611yescharacteristic
218C22×C31#46811yescharacteristic
219C22×C31#47111yescharacteristic
220C22×C31#47211yescharacteristic
221C4×C31—21no—
222C4×C31—21no—
223C4×C31—81no—
224C4×C31—161no—
225C4×C31#44711yescharacteristic
226C4×C31#45211yescharacteristic
227C4×C31#45911yescharacteristic
228C4×C31#46311yescharacteristic
229C4×C31#46611yescharacteristic
230C4×C31#46911yescharacteristic
231C4×C31#48011yescharacteristic
232C4×C31#48211yescharacteristic
233C22×D8—21no—
234C2×#127C22×C3111yescharacteristic
235C2×C4×D4C22×C3111yescharacteristic
236#459—22no—
237#459—22no—
238C2×C4⋊C8C22×C3111yescharacteristic
239C2×C4⋊C8C22×C3111yescharacteristic
240C2×C4⋊C8C22×C3111yescharacteristic
241C2×#102—21no—
242C2×#102—21no—
243C2×#102—21no—
244C2×#102—21no—
245C2×C22⋊C8—21no—
246C2×C22⋊C8—21no—
247C2×C4×C8C22×C3111yescharacteristic
248#384C22×C3111yescharacteristic
249#340—21no—
250#335—22no—
251#331—22no—
252C2×C31—82no—
253C2×C31—162no—
254C2×C31#166711yescharacteristic
255C2×C31#168111yescharacteristic
256C2×C31#168511yescharacteristic
257C2×C31#169711yescharacteristic
258C2×C31#203311yescharacteristic
259C2×C31#205111yescharacteristic
260C2×C31#205411yescharacteristic
261C22×D4—21no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4D4×C3111yescharacteristic
265C23×C4—21no—
266C2×D8—24no—
267C2×D8—42no—
268C2×D8—42no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8D4×C3111yescharacteristic
273C22×C8D4×C3111yescharacteristic
274#127—21no—
275#127—21no—
276#127—21no—
277#127D4×C3112yes—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4D4×C3111yescharacteristic
286C2×C22⋊C4—21no—
287C2×C42C23×C3111yescharacteristic
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8D4×C3112yes—
294#102—24no—
295#102—42no—
296#102—42no—
297#102—42no—
298C22⋊C8—42no—
299C22⋊C8—42no—
300C4×C8—21no—
301C4×C8—21no—
302C31#1047211yescharacteristic, direct product factor, Sylow
303C24—21no—
304C24—41no—
305C2×D4—21no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—22no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—81no—
325C2×D4—81no—
326C2×D4D8×C3112yes—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4C2×D4×C3111yescharacteristic
336C22×C4C2×D4×C3111yescharacteristic
337C22×C4#41×C3111yescharacteristic
338D8—48no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—22no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8D8×C3112yescomplemented
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—81no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C42C2×D4×C3111yescharacteristic
364C42C2×D4×C3111yescharacteristic
365C42#41×C3111yescharacteristic
366C42#41×C3111yescharacteristic
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—42no—
375C23—81no—
376C23—81no—
377C23—81no—
378C23—81no—
379C23—81no—
380C23—81no—
381C23C31×#12111yescharacteristic
382D4—22no—
383D4—22no—
384D4—42no—
385D4—41no—
386D4—42no—
387D4—42no—
388D4—42no—
389D4—41no—
390D4—82no—
391D4—82no—
392D4—81no—
393D4—81no—
394D4—81no—
395D4—81no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4C31×#12011yescharacteristic
409C2×C4C31×#12111yescharacteristic
410C2×C4C31×#12111yescharacteristic
411C2×C4C31×#12311yescharacteristic
412C2×C4C31×#12311yescharacteristic
413C2×C4C31×#12411yescharacteristic
414C2×C4C2×D8×C3111yescharacteristic
415C2×C4C2×D8×C3111yescharacteristic
416C2×C4C31×#13511yescharacteristic
417C2×C4C31×#13511yescharacteristic
418C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
419C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
420C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
421C2×C4C31×#13711yescharacteristic
422C8—22no—
423C8—42no—
424C8—41no—
425C8—81no—
426C8—81no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—82no—
435C22—82no—
436C22—82no—
437C22—161no—
438C22—161no—
439C22—161no—
440C22—161no—
441C22C31×#39411yescharacteristic
442C22C31×#45911yescharacteristic
443C22C31×#46311yescharacteristic
444C22C31×#46611yescharacteristic
445C22C31×#46811yescharacteristic
446C22C31×#47111yescharacteristic
447C22C31×#47211yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—161no—
452C4C31×#44711yescharacteristic
453C4C31×#45211yescharacteristic
454C4C31×#45911yescharacteristic
455C4C31×#46311yescharacteristic
456C4C31×#46611yescharacteristic
457C4C31×#46911yescharacteristic
458C4C31×#48011yescharacteristic
459C4C31×#48211yescharacteristic
460C2—82no—
461C2—162no—
462C2C31×#166711yescharacteristic
463C2C31×#168111yescharacteristic
464C2C31×#168511yescharacteristic
465C2C31×#169711yescharacteristic
466C2C31×#203311yescharacteristic
467C2C31×#205111yescharacteristic
468C2C31×#205411yescharacteristic
subgroupG/H
center, socleC23×C31#121
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#459C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1957C2semidirect
3. C31×#1954C2semidirect
4. C31×#1802C2semidirect
5. C2×C31×#335C2semidirect
6. C2×C31×#331C2semidirect
7. C31×#1296C2semidirect
118. C2×C8×C31D8semidirect
132. #10472C31direct (N × H)
194. #1957C2×C31semidirect
195. #1954C2×C31semidirect
196. #1802C2×C31semidirect
197. C2×#335C2×C31semidirect
198. C2×#331C2×C31semidirect
199. #1296C2×C31semidirect
302. C31#10472direct (N × H)
353. C2×C8D8×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4592
C31×#19572
C31×#19542
C31×#18022
C2×C31×#3352
C2×C31×#3312
C31×#12962
#1047231