Finite Group Databasebeta

← C31×#8220 #21464979

Subgroups — C31×#8220 #21464979

Order 7936.

724 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C31×#121C211yesmaximal, characteristic
2C4×C31×C22⋊C8C211yesmaximal, characteristic, complemented
3C2×C31×#327C212yesmaximal
4C31×#1434C211yesmaximal, characteristic, complemented
5C31×#1294C212yesmaximal, complemented
6C2×C31×#121C2211yescharacteristic
7C2×C4×D4×C31—21no—
8C2×C4×D4×C31C411yescharacteristic, complemented
9C22×C42×C31C2211yescharacteristic
10C2×C31×C22⋊C8C2212yes—
11C2×C4×C8×C31—21no—
12C31×#390C411yescharacteristic, complemented
13C31×#389C411yescharacteristic, complemented
14C31×#388—21no—
15C31×#386—21no—
16C31×#380C2211yescharacteristic
17C4×C4⋊C4×C31C411yescharacteristic, complemented
18C4×C22⋊C4×C31—21no—
19C2×C31×#95—21no—
20C2×C31×#95—21no—
21C2×C31×#95C2212yes—
22C31×#336—21no—
23C31×#327C418yescomplemented
24C22×D4×C31—21no—
25C22×D4×C31C2×C411yescharacteristic
26C23×C4×C31—22no—
27C23×C4×C31—21no—
28C23×C4×C31D411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C23×C4×C31C2311yescharacteristic
31C22×C8×C31—22no—
32C31×#121—22no—
33C31×#121C2×C414yes—
34C4×D4×C31—42no—
35C4×D4×C31—42no—
36C4×D4×C31—42no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C4⋊C4×C31C2×C411yescharacteristic
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C42×C31—21no—
47C2×C42×C31—42no—
48C2×C42×C31C2×C411yescharacteristic
49C2×C42×C31C2×C411yescharacteristic
50C2×C42×C31D411yescharacteristic
51C2×C42×C31D411yescharacteristic
52C31×C22⋊C8—22no—
53C31×C22⋊C8C2×C414yescomplemented
54C4×C8×C31—42no—
55C31×#95—21no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95—22no—
59C31×#95—42no—
60C31×#95—42no—
61C31×#95C2×C414yescomplemented
62C24×C31—21no—
63C24×C31C2×D411yescharacteristic
64C2×D4×C31—24no—
65C2×D4×C31—21no—
66C2×D4×C31—41no—
67C2×D4×C31—41no—
68C2×D4×C31—41no—
69C2×D4×C31—41no—
70C2×D4×C31—42no—
71C2×D4×C31C4212yes—
72C22×C4×C31—21no—
73C22×C4×C31—22no—
74C22×C4×C31—22no—
75C22×C4×C31—21no—
76C22×C4×C31—21no—
77C22×C4×C31—24no—
78C22×C4×C31—41no—
79C22×C4×C31—41no—
80C22×C4×C31—41no—
81C22×C4×C31—41no—
82C22×C4×C31—41no—
83C22×C4×C31—42no—
84C22×C4×C31—42no—
85C22×C4×C31—42no—
86C22×C4×C31—42no—
87C22×C4×C31—42no—
88C22×C4×C31—42no—
89C22×C4×C31—42no—
90C22×C4×C31—42no—
91C22×C4×C31—42no—
92C22×C4×C31C22⋊C411yescharacteristic
93C22×C4×C31C22⋊C411yescharacteristic
94C22×C4×C31C22⋊C411yescharacteristic
95C22×C4×C31C22⋊C411yescharacteristic
96C22×C4×C31D812yes—
97C22×C4×C31SD1612yes—
98C22×C4×C31C22×C411yescharacteristic
99C22×C4×C31C22×C412yes—
100C22×C4×C31C2×D411yescharacteristic
101C22×C4×C31#4112yes—
102C2×C8×C31—24no—
103C2×C8×C31—42no—
104C2×C8×C31—42no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—41no—
107C4⋊C4×C31—41no—
108C4⋊C4×C31—42no—
109C4⋊C4×C31C4212yes—
110C22⋊C4×C31—24no—
111C22⋊C4×C31—42no—
112C22⋊C4×C31—41no—
113C22⋊C4×C31—41no—
114C22⋊C4×C31—42no—
115C22⋊C4×C31—42no—
116C42×C31—22no—
117C42×C31—22no—
118C42×C31—41no—
119C42×C31—41no—
120C42×C31—42no—
121#8220C3111yesmaximal, characteristic, direct product factor, Sylow
122C23×C31—21no—
123C23×C31—21no—
124C23×C31—21no—
125C23×C31—21no—
126C23×C31—22no—
127C23×C31—41no—
128C23×C31—41no—
129C23×C31—41no—
130C23×C31—41no—
131C23×C31—41no—
132C23×C31—41no—
133C23×C31C2×C22⋊C411yescharacteristic
134C23×C31C4×D412yes—
135C23×C31C2×D811yescharacteristic
136C23×C31C2×SD1611yescharacteristic
137C23×C31#13512yes—
138D4×C31—42no—
139D4×C31—42no—
140D4×C31—44no—
141D4×C31—44no—
142C2×C4×C31—21no—
143C2×C4×C31—21no—
144C2×C4×C31—21no—
145C2×C4×C31—21no—
146C2×C4×C31—21no—
147C2×C4×C31—21no—
148C2×C4×C31—21no—
149C2×C4×C31—21no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—22no—
153C2×C4×C31—21no—
154C2×C4×C31—21no—
155C2×C4×C31—21no—
156C2×C4×C31—42no—
157C2×C4×C31—42no—
158C2×C4×C31—42no—
159C2×C4×C31—42no—
160C2×C4×C31—44no—
161C2×C4×C31—41no—
162C2×C4×C31—41no—
163C2×C4×C31—44no—
164C2×C4×C31—44no—
165C2×C4×C31—41no—
166C2×C4×C31—41no—
167C2×C4×C31—41no—
168C2×C4×C31—41no—
169C2×C4×C31—41no—
170C2×C4×C31—41no—
171C2×C4×C31—44no—
172C2×C4×C31—84no—
173C2×C4×C31—82no—
174C2×C4×C31—82no—
175C2×C4×C31—82no—
176C2×C4×C31—82no—
177C2×C4×C31#9912yes—
178C2×C4×C31#10212yes—
179C2×C4×C31#10212yes—
180C2×C4×C31C2×C4211yescharacteristic
181C2×C4×C31#11711yescharacteristic
182C2×C4×C31C4×D412yes—
183C8×C31—44no—
184C4×#121C2×C3111yescharacteristic
185C4×C22⋊C8C2×C3111yescharacteristic, complemented
186C2×#327C2×C3112yes—
187#1434C2×C3111yescharacteristic, complemented
188#1294C2×C3112yescomplemented
189C22×C31—22no—
190C22×C31—22no—
191C22×C31—22no—
192C22×C31—21no—
193C22×C31—21no—
194C22×C31—21no—
195C22×C31—21no—
196C22×C31—22no—
197C22×C31—42no—
198C22×C31—42no—
199C22×C31—42no—
200C22×C31—81no—
201C22×C31—81no—
202C22×C31—81no—
203C22×C31—81no—
204C22×C31C4×C22⋊C411yescharacteristic
205C22×C31C2×#9911yescharacteristic
206C22×C31#41011yescharacteristic
207C22×C31C2×#10211yescharacteristic
208C22×C31#41611yescharacteristic
209C22×C31#42111yescharacteristic
210C22×C31#42111yescharacteristic
211C22×C31C4×D812yes—
212C22×C31C4×SD1612yes—
213C4×C31—22no—
214C4×C31—21no—
215C4×C31—21no—
216C4×C31—22no—
217C4×C31—22no—
218C4×C31—22no—
219C4×C31—42no—
220C4×C31—41no—
221C4×C31—84no—
222C4×C31—81no—
223C4×C31—81no—
224C2×#121C22×C3111yescharacteristic
225C2×C4×D4—21no—
226C2×C4×D4C4×C3111yescharacteristic, complemented
227C22×C42C22×C3111yescharacteristic
228C2×C22⋊C8C22×C3112yes—
229C2×C4×C8—21no—
230#390C4×C3111yescharacteristic, complemented
231#389C4×C3111yescharacteristic, complemented
232#388—21no—
233#386—21no—
234#380C22×C3111yescharacteristic
235C4×C4⋊C4C4×C3111yescharacteristic, complemented
236C4×C22⋊C4—21no—
237C2×#95—21no—
238C2×#95—21no—
239C2×#95C22×C3112yes—
240#336—21no—
241#327C4×C3118yescomplemented
242C2×C31—22no—
243C2×C31—22no—
244C2×C31—82no—
245C2×C31#151611yescharacteristic
246C2×C31#151711yescharacteristic
247C2×C31#151911yescharacteristic
248C2×C31#152111yescharacteristic
249C2×C31C4×#9911yescharacteristic
250C2×C31#175911yescharacteristic
251C2×C31C4×#10211yescharacteristic
252C22×D4—21no—
253C22×D4C2×C4×C3111yescharacteristic
254C23×C4—22no—
255C23×C4—21no—
256C23×C4D4×C3111yescharacteristic
257C23×C4D4×C3111yescharacteristic
258C23×C4C23×C3111yescharacteristic
259C22×C8—22no—
260#121—22no—
261#121C2×C4×C3114yes—
262C4×D4—42no—
263C4×D4—42no—
264C4×D4—42no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4C2×C4×C3111yescharacteristic
267C2×C4⋊C4C2×C4×C3111yescharacteristic
268C2×C4⋊C4C2×C4×C3111yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C42—21no—
275C2×C42—42no—
276C2×C42C2×C4×C3111yescharacteristic
277C2×C42C2×C4×C3111yescharacteristic
278C2×C42D4×C3111yescharacteristic
279C2×C42D4×C3111yescharacteristic
280C22⋊C8—22no—
281C22⋊C8C2×C4×C3114yescomplemented
282C4×C8—42no—
283#95—21no—
284#95—21no—
285#95—21no—
286#95—22no—
287#95—42no—
288#95—42no—
289#95C2×C4×C3114yescomplemented
290C31#822011yescharacteristic, direct product factor, Sylow
291C24—21no—
292C24C2×D4×C3111yescharacteristic
293C2×D4—24no—
294C2×D4—21no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—42no—
300C2×D4C42×C3112yes—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—24no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4C22⋊C4×C3111yescharacteristic
322C22×C4C22⋊C4×C3111yescharacteristic
323C22×C4C22⋊C4×C3111yescharacteristic
324C22×C4C22⋊C4×C3111yescharacteristic
325C22×C4D8×C3112yes—
326C22×C4SD16×C3112yes—
327C22×C4C22×C4×C3111yescharacteristic
328C22×C4C22×C4×C3112yes—
329C22×C4C2×D4×C3111yescharacteristic
330C22×C4#41×C3112yes—
331C2×C8—24no—
332C2×C8—42no—
333C2×C8—42no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—42no—
338C4⋊C4C42×C3112yes—
339C22⋊C4—24no—
340C22⋊C4—42no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—42no—
344C22⋊C4—42no—
345C42—22no—
346C42—22no—
347C42—41no—
348C42—41no—
349C42—42no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—22no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23C2×C22⋊C4×C3111yescharacteristic
362C23C4×D4×C3112yes—
363C23C2×D8×C3111yescharacteristic
364C23C2×SD16×C3111yescharacteristic
365C23C31×#13512yes—
366D4—42no—
367D4—42no—
368D4—44no—
369D4—44no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—44no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—44no—
400C2×C4—84no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4C31×#9912yes—
406C2×C4C31×#10212yes—
407C2×C4C31×#10212yes—
408C2×C4C2×C42×C3111yescharacteristic
409C2×C4C31×#11711yescharacteristic
410C2×C4C4×D4×C3112yes—
411C8—44no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—22no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22C4×C22⋊C4×C3111yescharacteristic
428C22C2×C31×#9911yescharacteristic
429C22C31×#41011yescharacteristic
430C22C2×C31×#10211yescharacteristic
431C22C31×#41611yescharacteristic
432C22C31×#42111yescharacteristic
433C22C31×#42111yescharacteristic
434C22C4×D8×C3112yes—
435C22C4×SD16×C3112yes—
436C4—22no—
437C4—21no—
438C4—21no—
439C4—22no—
440C4—22no—
441C4—22no—
442C4—42no—
443C4—41no—
444C4—84no—
445C4—81no—
446C4—81no—
447C2—22no—
448C2—22no—
449C2—82no—
450C2C31×#151611yescharacteristic
451C2C31×#151711yescharacteristic
452C2C31×#151911yescharacteristic
453C2C31×#152111yescharacteristic
454C2C4×C31×#9911yescharacteristic
455C2C31×#175911yescharacteristic
456C2C4×C31×#10211yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC2×C4C2×C42×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#121C22
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C31×C22⋊C8C2semidirect
4. C31×#1434C2semidirect
5. C31×#1294C2semidirect
8. C2×C4×D4×C31C4semidirect
12. C31×#390C4semidirect
13. C31×#389C4semidirect
17. C4×C4⋊C4×C31C4semidirect
23. C31×#327C4semidirect
53. C31×C22⋊C8C2×C4semidirect
61. C31×#95C2×C4semidirect
121. #8220C31direct (N × H)
185. C4×C22⋊C8C2×C31semidirect
187. #1434C2×C31semidirect
188. #1294C2×C31semidirect
226. C2×C4×D4C4×C31semidirect
230. #390C4×C31semidirect
231. #389C4×C31semidirect
235. C4×C4⋊C4C4×C31semidirect
241. #327C4×C31semidirect
281. C22⋊C8C2×C4×C31semidirect
289. #95C2×C4×C31semidirect
290. C31#8220direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C31×#1212
C4×C31×C22⋊C82
C2×C31×#3272
C31×#14342
C31×#12942
#822031