Finite Group Databasebeta

← C31×#8218 #21464977

Subgroups — C31×#8218 #21464977

Order 7936.

804 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C31×#121C211yesmaximal, characteristic
2C31×#1749C211yesmaximal, characteristic, complemented
3C2×C31×#327C212yesmaximal
4C4×C31×#95C211yesmaximal, characteristic, complemented
5C31×#1294C212yesmaximal, complemented
6C2×C31×#121C2211yescharacteristic
7C2×C4×D4×C31—21no—
8C2×C4×D4×C31C411yescharacteristic, complemented
9C22×C42×C31—21no—
10C22×C42×C31C2211yescharacteristic
11C2×C31×C22⋊C8C2212yes—
12C2×C31×#97—21no—
13C31×#390C411yescharacteristic, complemented
14C31×#389C411yescharacteristic, complemented
15C31×#388—21no—
16C31×#386—21no—
17C31×#380C2211yescharacteristic
18C4×C4⋊C4×C31C411yescharacteristic, complemented
19C4×C22⋊C4×C31—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—44no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C42×C31—24no—
46C2×C42×C31—21no—
47C2×C42×C31—42no—
48C2×C42×C31—42no—
49C2×C42×C31—42no—
50C2×C42×C31C2×C411yescharacteristic
51C2×C42×C31C2×C411yescharacteristic
52C2×C42×C31D411yescharacteristic
53C2×C42×C31D411yescharacteristic
54C31×C22⋊C8—22no—
55C31×C22⋊C8C2×C414yescomplemented
56C31×#97—42no—
57C31×#95—24no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95—21no—
61C31×#95—22no—
62C31×#95C2×C414yescomplemented
63C24×C31—21no—
64C24×C31C2×D411yescharacteristic
65C2×D4×C31—24no—
66C2×D4×C31—21no—
67C2×D4×C31—41no—
68C2×D4×C31—41no—
69C2×D4×C31—42no—
70C2×D4×C31—41no—
71C2×D4×C31—41no—
72C2×D4×C31C4212yescomplemented
73C22×C4×C31—21no—
74C22×C4×C31—21no—
75C22×C4×C31—22no—
76C22×C4×C31—22no—
77C22×C4×C31—24no—
78C22×C4×C31—24no—
79C22×C4×C31—21no—
80C22×C4×C31—24no—
81C22×C4×C31—22no—
82C22×C4×C31—22no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—41no—
86C22×C4×C31—41no—
87C22×C4×C31—41no—
88C22×C4×C31—42no—
89C22×C4×C31—42no—
90C22×C4×C31—42no—
91C22×C4×C31—42no—
92C22×C4×C31—42no—
93C22×C4×C31—42no—
94C22×C4×C31—42no—
95C22×C4×C31C22⋊C411yescharacteristic
96C22×C4×C31C22⋊C411yescharacteristic
97C22×C4×C31C22⋊C411yescharacteristic
98C22×C4×C31C22⋊C411yescharacteristic
99C22×C4×C31C22×C411yescharacteristic
100C22×C4×C31C22×C412yes—
101C22×C4×C31C2×D411yescharacteristic
102C22×C4×C31#4112yes—
103C2×C8×C31—24no—
104C2×C8×C31—42no—
105C2×C8×C31—42no—
106C4⋊C4×C31—21no—
107C4⋊C4×C31—42no—
108C4⋊C4×C31—41no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31C4212yescomplemented
111C22⋊C4×C31—24no—
112C22⋊C4×C31—42no—
113C22⋊C4×C31—42no—
114C22⋊C4×C31—42no—
115C22⋊C4×C31—42no—
116C42×C31—22no—
117C42×C31—22no—
118C42×C31—41no—
119C42×C31—41no—
120C42×C31—48no—
121C42×C31—42no—
122#8218C3111yesmaximal, characteristic, direct product factor, Sylow
123C23×C31—21no—
124C23×C31—21no—
125C23×C31—21no—
126C23×C31—21no—
127C23×C31—22no—
128C23×C31—41no—
129C23×C31—41no—
130C23×C31—41no—
131C23×C31—41no—
132C23×C31—41no—
133C23×C31—41no—
134C23×C31C2×C22⋊C411yescharacteristic
135C23×C31C4×D412yes—
136C23×C31AGL(1,ℤ/8)11yescharacteristic
137C23×C31AGL(1,ℤ/8)12yes—
138C23×C31#13711yescharacteristic
139D4×C31—42no—
140D4×C31—42no—
141D4×C31—44no—
142D4×C31—44no—
143C2×C4×C31—24no—
144C2×C4×C31—24no—
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—21no—
153C2×C4×C31—21no—
154C2×C4×C31—21no—
155C2×C4×C31—28no—
156C2×C4×C31—22no—
157C2×C4×C31—21no—
158C2×C4×C31—21no—
159C2×C4×C31—21no—
160C2×C4×C31—42no—
161C2×C4×C31—42no—
162C2×C4×C31—44no—
163C2×C4×C31—44no—
164C2×C4×C31—44no—
165C2×C4×C31—44no—
166C2×C4×C31—44no—
167C2×C4×C31—44no—
168C2×C4×C31—41no—
169C2×C4×C31—41no—
170C2×C4×C31—44no—
171C2×C4×C31—41no—
172C2×C4×C31—41no—
173C2×C4×C31—41no—
174C2×C4×C31—41no—
175C2×C4×C31—41no—
176C2×C4×C31—41no—
177C2×C4×C31—84no—
178C2×C4×C31#9912yes—
179C2×C4×C31#10412yes—
180C2×C4×C31#10412yes—
181C2×C4×C31C2×C4211yescharacteristic
182C2×C4×C31#11711yescharacteristic
183C2×C4×C31C4×D412yes—
184C8×C31—44no—
185C4×#121C2×C3111yescharacteristic
186#1749C2×C3111yescharacteristic, complemented
187C2×#327C2×C3112yes—
188C4×#95C2×C3111yescharacteristic, complemented
189#1294C2×C3112yescomplemented
190C22×C31—22no—
191C22×C31—22no—
192C22×C31—21no—
193C22×C31—21no—
194C22×C31—22no—
195C22×C31—22no—
196C22×C31—21no—
197C22×C31—21no—
198C22×C31—42no—
199C22×C31—42no—
200C22×C31—42no—
201C22×C31—81no—
202C22×C31—81no—
203C22×C31—81no—
204C22×C31—81no—
205C22×C31C4×C22⋊C411yescharacteristic
206C22×C31C2×#9911yescharacteristic
207C22×C31#41011yescharacteristic
208C22×C31#41711yescharacteristic
209C22×C31#41811yescharacteristic
210C22×C31C2×#10411yescharacteristic
211C22×C31C2×#10411yescharacteristic
212C22×C31#44012yes—
213C22×C31#44212yes—
214C4×C31—22no—
215C4×C31—21no—
216C4×C31—21no—
217C4×C31—22no—
218C4×C31—22no—
219C4×C31—22no—
220C4×C31—48no—
221C4×C31—42no—
222C4×C31—41no—
223C4×C31—81no—
224C4×C31—81no—
225C2×#121C22×C3111yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4C4×C3111yescharacteristic, complemented
228C22×C42—21no—
229C22×C42C22×C3111yescharacteristic
230C2×C22⋊C8C22×C3112yes—
231C2×#97—21no—
232#390C4×C3111yescharacteristic, complemented
233#389C4×C3111yescharacteristic, complemented
234#388—21no—
235#386—21no—
236#380C22×C3111yescharacteristic
237C4×C4⋊C4C4×C3111yescharacteristic, complemented
238C4×C22⋊C4—21no—
239C2×#95—21no—
240C2×#95C22×C3112yes—
241#336—21no—
242#327C4×C3118yescomplemented
243C2×C31—22no—
244C2×C31—22no—
245C2×C31—82no—
246C2×C31#150411yescharacteristic
247C2×C31#150511yescharacteristic
248C2×C31#150711yescharacteristic
249C2×C31#150911yescharacteristic
250C2×C31C4×#9911yescharacteristic
251C2×C31C4×#10411yescharacteristic
252C2×C31#176211yescharacteristic
253C22×D4—21no—
254C22×D4C2×C4×C3111yescharacteristic
255C23×C4—22no—
256C23×C4—21no—
257C23×C4D4×C3111yescharacteristic
258C23×C4D4×C3111yescharacteristic
259C23×C4C23×C3111yescharacteristic
260C22×C8—22no—
261#121—22no—
262#121C2×C4×C3114yes—
263C4×D4—42no—
264C4×D4—44no—
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—24no—
275C2×C42—21no—
276C2×C42—42no—
277C2×C42—42no—
278C2×C42—42no—
279C2×C42C2×C4×C3111yescharacteristic
280C2×C42C2×C4×C3111yescharacteristic
281C2×C42D4×C3111yescharacteristic
282C2×C42D4×C3111yescharacteristic
283C22⋊C8—22no—
284C22⋊C8C2×C4×C3114yescomplemented
285#97—42no—
286#95—24no—
287#95—21no—
288#95—21no—
289#95—21no—
290#95—22no—
291#95C2×C4×C3114yescomplemented
292C31#821811yescharacteristic, direct product factor, Sylow
293C24—21no—
294C24C2×D4×C3111yescharacteristic
295C2×D4—24no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4C42×C3112yescomplemented
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—24no—
308C22×C4—24no—
309C22×C4—21no—
310C22×C4—24no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4C22⋊C4×C3111yescharacteristic
326C22×C4C22⋊C4×C3111yescharacteristic
327C22×C4C22⋊C4×C3111yescharacteristic
328C22×C4C22⋊C4×C3111yescharacteristic
329C22×C4C22×C4×C3111yescharacteristic
330C22×C4C22×C4×C3112yes—
331C22×C4C2×D4×C3111yescharacteristic
332C22×C4#41×C3112yes—
333C2×C8—24no—
334C2×C8—42no—
335C2×C8—42no—
336C4⋊C4—21no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—42no—
340C4⋊C4C42×C3112yescomplemented
341C22⋊C4—24no—
342C22⋊C4—42no—
343C22⋊C4—42no—
344C22⋊C4—42no—
345C22⋊C4—42no—
346C42—22no—
347C42—22no—
348C42—41no—
349C42—41no—
350C42—48no—
351C42—42no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—22no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23C2×C22⋊C4×C3111yescharacteristic
364C23C4×D4×C3112yes—
365C23C31×AGL(1,ℤ/8)11yescharacteristic
366C23C31×AGL(1,ℤ/8)12yes—
367C23C31×#13711yescharacteristic
368D4—42no—
369D4—42no—
370D4—44no—
371D4—44no—
372C2×C4—24no—
373C2×C4—24no—
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—21no—
384C2×C4—28no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—44no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—84no—
407C2×C4C31×#9912yes—
408C2×C4C31×#10412yes—
409C2×C4C31×#10412yes—
410C2×C4C2×C42×C3111yescharacteristic
411C2×C4C31×#11711yescharacteristic
412C2×C4C4×D4×C3112yes—
413C8—44no—
414C22—22no—
415C22—22no—
416C22—21no—
417C22—21no—
418C22—22no—
419C22—22no—
420C22—21no—
421C22—21no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22C4×C22⋊C4×C3111yescharacteristic
430C22C2×C31×#9911yescharacteristic
431C22C31×#41011yescharacteristic
432C22C31×#41711yescharacteristic
433C22C31×#41811yescharacteristic
434C22C2×C31×#10411yescharacteristic
435C22C2×C31×#10411yescharacteristic
436C22C31×#44012yes—
437C22C31×#44212yes—
438C4—22no—
439C4—21no—
440C4—21no—
441C4—22no—
442C4—22no—
443C4—22no—
444C4—48no—
445C4—42no—
446C4—41no—
447C4—81no—
448C4—81no—
449C2—22no—
450C2—22no—
451C2—82no—
452C2C31×#150411yescharacteristic
453C2C31×#150511yescharacteristic
454C2C31×#150711yescharacteristic
455C2C31×#150911yescharacteristic
456C2C4×C31×#9911yescharacteristic
457C2C4×C31×#10411yescharacteristic
458C2C31×#176211yescharacteristic
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. C31×#1749C2semidirect
4. C4×C31×#95C2semidirect
5. C31×#1294C2semidirect
8. C2×C4×D4×C31C4semidirect
13. C31×#390C4semidirect
14. C31×#389C4semidirect
18. C4×C4⋊C4×C31C4semidirect
23. C31×#327C4semidirect
55. C31×C22⋊C8C2×C4semidirect
62. C31×#95C2×C4semidirect
72. C2×D4×C31C42semidirect
110. C4⋊C4×C31C42semidirect
122. #8218C31direct (N × H)
186. #1749C2×C31semidirect
188. C4×#95C2×C31semidirect
189. #1294C2×C31semidirect
227. C2×C4×D4C4×C31semidirect
232. #390C4×C31semidirect
233. #389C4×C31semidirect
237. C4×C4⋊C4C4×C31semidirect
242. #327C4×C31semidirect
284. C22⋊C8C2×C4×C31semidirect
291. #95C2×C4×C31semidirect
292. C31#8218direct (N × H)
302. C2×D4C42×C31semidirect
340. C4⋊C4C42×C31semidirect

Maximal subgroups

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

subgroupindex
C4×C31×#1212
C31×#17492
C2×C31×#3272
C4×C31×#952
C31×#12942
#821831