Finite Group Databasebeta

← C4×C31×#327 #21464973

Subgroups — C4×C31×#327 #21464973

Order 7936.

816 conjugacy classes of subgroups.

The subgroup lattice has 464 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
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×C4×C8×C31—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×#327C418yesdirect product factor
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—24no—
47C2×C42×C31—21no—
48C2×C42×C31—42no—
49C2×C42×C31—42no—
50C2×C42×C31—42no—
51C2×C42×C31C2×C411yescharacteristic
52C2×C42×C31C2×C411yescharacteristic
53C2×C42×C31D411yescharacteristic
54C2×C42×C31D411yescharacteristic
55C31×C22⋊C8—22no—
56C31×C22⋊C8C2×C414yescomplemented
57C4×C8×C31—42no—
58C31×#95—24no—
59C31×#95—21no—
60C31×#95—21no—
61C31×#95—21no—
62C31×#95—22no—
63C31×#95C2×C414yescomplemented
64C24×C31—21no—
65C24×C31C2×D411yescharacteristic
66C2×D4×C31—24no—
67C2×D4×C31—21no—
68C2×D4×C31—41no—
69C2×D4×C31—41no—
70C2×D4×C31—41no—
71C2×D4×C31—41no—
72C2×D4×C31—42no—
73C2×D4×C31C4212yescomplemented
74C22×C4×C31—22no—
75C22×C4×C31—22no—
76C22×C4×C31—24no—
77C22×C4×C31—24no—
78C22×C4×C31—21no—
79C22×C4×C31—24no—
80C22×C4×C31—22no—
81C22×C4×C31—22no—
82C22×C4×C31—21no—
83C22×C4×C31—21no—
84C22×C4×C31—41no—
85C22×C4×C31—41no—
86C22×C4×C31—41no—
87C22×C4×C31—42no—
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×C31C22⋊C411yescharacteristic
95C22×C4×C31C22⋊C411yescharacteristic
96C22×C4×C31C22⋊C411yescharacteristic
97C22×C4×C31C22⋊C411yescharacteristic
98C22×C4×C31D812yes—
99C22×C4×C31SD1612yes—
100C22×C4×C31C22×C411yescharacteristic
101C22×C4×C31C22×C412yes—
102C22×C4×C31C2×D411yescharacteristic
103C22×C4×C31#4112yes—
104C2×C8×C31—24no—
105C2×C8×C31—42no—
106C2×C8×C31—42no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—41no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31—42no—
111C4⋊C4×C31C4212yescomplemented
112C22⋊C4×C31—24no—
113C22⋊C4×C31—42no—
114C22⋊C4×C31—41no—
115C22⋊C4×C31—41no—
116C22⋊C4×C31—42no—
117C22⋊C4×C31—42no—
118C42×C31—22no—
119C42×C31—22no—
120C42×C31—41no—
121C42×C31—41no—
122C42×C31—48no—
123C42×C31—42no—
124C4×#327C3111yesmaximal, characteristic, direct product factor, Sylow
125C23×C31—21no—
126C23×C31—21no—
127C23×C31—21no—
128C23×C31—21no—
129C23×C31—22no—
130C23×C31—41no—
131C23×C31—41no—
132C23×C31—41no—
133C23×C31—41no—
134C23×C31—41no—
135C23×C31—41no—
136C23×C31C2×C22⋊C411yescharacteristic
137C23×C31C4×D412yes—
138C23×C31C2×D811yescharacteristic
139C23×C31C2×SD1611yescharacteristic
140C23×C31#13512yes—
141D4×C31—42no—
142D4×C31—42no—
143D4×C31—44no—
144D4×C31—44no—
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—24no—
154C2×C4×C31—24no—
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#10212yes—
180C2×C4×C31#10212yes—
181C2×C4×C31#10412yes—
182C2×C4×C31#10412yes—
183C2×C4×C31C2×C4211yescharacteristic
184C2×C4×C31#11711yescharacteristic
185C2×C4×C31C4×D412yes—
186C8×C31—44no—
187C4×#121C2×C3111yescharacteristic
188C4×C22⋊C8C2×C3111yescharacteristic, complemented
189C2×#327C2×C3112yes—
190C4×#95C2×C3111yescharacteristic, complemented
191#1294C2×C3112yescomplemented
192C22×C31—21no—
193C22×C31—21no—
194C22×C31—22no—
195C22×C31—22no—
196C22×C31—22no—
197C22×C31—21no—
198C22×C31—21no—
199C22×C31—22no—
200C22×C31—42no—
201C22×C31—42no—
202C22×C31—42no—
203C22×C31—81no—
204C22×C31—81no—
205C22×C31—81no—
206C22×C31—81no—
207C22×C31C4×C22⋊C411yescharacteristic
208C22×C31C2×#9911yescharacteristic
209C22×C31#41011yescharacteristic
210C22×C31C2×#10211yescharacteristic
211C22×C31#41611yescharacteristic
212C22×C31C2×#10411yescharacteristic
213C22×C31C2×#10411yescharacteristic
214C22×C31C4×D812yes—
215C22×C31C4×SD1612yes—
216C4×C31—22no—
217C4×C31—22no—
218C4×C31—21no—
219C4×C31—21no—
220C4×C31—22no—
221C4×C31—48no—
222C4×C31—41no—
223C4×C31—42no—
224C4×C31—81no—
225C4×C31—81no—
226C4×C31#32714yesdirect product factor
227C2×#121C22×C3111yescharacteristic
228C2×C4×D4—21no—
229C2×C4×D4C4×C3111yescharacteristic, complemented
230C22×C42—21no—
231C22×C42C22×C3111yescharacteristic
232C2×C22⋊C8C22×C3112yes—
233C2×C4×C8—21no—
234#390C4×C3111yescharacteristic, complemented
235#389C4×C3111yescharacteristic, complemented
236#388—21no—
237#386—21no—
238#380C22×C3111yescharacteristic
239C4×C4⋊C4C4×C3111yescharacteristic, complemented
240C4×C22⋊C4—21no—
241C2×#95—21no—
242C2×#95C22×C3112yes—
243#336—21no—
244#327C4×C3118yesdirect product factor
245C2×C31—22no—
246C2×C31—22no—
247C2×C31—82no—
248C2×C31C2×#32711yescharacteristic
249C2×C31#150011yescharacteristic
250C2×C31#150111yescharacteristic
251C2×C31#150211yescharacteristic
252C2×C31C4×#9911yescharacteristic
253C2×C31C4×#10411yescharacteristic
254C2×C31C4×#10211yescharacteristic
255C22×D4—21no—
256C22×D4C2×C4×C3111yescharacteristic
257C23×C4—22no—
258C23×C4—21no—
259C23×C4D4×C3111yescharacteristic
260C23×C4D4×C3111yescharacteristic
261C23×C4C23×C3111yescharacteristic
262C22×C8—22no—
263#121—22no—
264#121C2×C4×C3114yes—
265C4×D4—42no—
266C4×D4—42no—
267C4×D4—42no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4C2×C4×C3111yescharacteristic
270C2×C4⋊C4C2×C4×C3111yescharacteristic
271C2×C4⋊C4C2×C4×C3111yescharacteristic
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C42—24no—
278C2×C42—21no—
279C2×C42—42no—
280C2×C42—42no—
281C2×C42—42no—
282C2×C42C2×C4×C3111yescharacteristic
283C2×C42C2×C4×C3111yescharacteristic
284C2×C42D4×C3111yescharacteristic
285C2×C42D4×C3111yescharacteristic
286C22⋊C8—22no—
287C22⋊C8C2×C4×C3114yescomplemented
288C4×C8—42no—
289#95—24no—
290#95—21no—
291#95—21no—
292#95—21no—
293#95—22no—
294#95C2×C4×C3114yescomplemented
295C31C4×#32711yescharacteristic, direct product factor, Sylow
296C24—21no—
297C24C2×D4×C3111yescharacteristic
298C2×D4—24no—
299C2×D4—21no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—42no—
305C2×D4C42×C3112yescomplemented
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—24no—
309C22×C4—24no—
310C22×C4—21no—
311C22×C4—24no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4C22⋊C4×C3111yescharacteristic
327C22×C4C22⋊C4×C3111yescharacteristic
328C22×C4C22⋊C4×C3111yescharacteristic
329C22×C4C22⋊C4×C3111yescharacteristic
330C22×C4D8×C3112yes—
331C22×C4SD16×C3112yes—
332C22×C4C22×C4×C3111yescharacteristic
333C22×C4C22×C4×C3112yes—
334C22×C4C2×D4×C3111yescharacteristic
335C22×C4#41×C3112yes—
336C2×C8—24no—
337C2×C8—42no—
338C2×C8—42no—
339C4⋊C4—21no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—42no—
343C4⋊C4C42×C3112yescomplemented
344C22⋊C4—24no—
345C22⋊C4—42no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—42no—
349C22⋊C4—42no—
350C42—22no—
351C42—22no—
352C42—41no—
353C42—41no—
354C42—48no—
355C42—42no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—22no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23C2×C22⋊C4×C3111yescharacteristic
368C23C4×D4×C3112yes—
369C23C2×D8×C3111yescharacteristic
370C23C2×SD16×C3111yescharacteristic
371C23C31×#13512yes—
372D4—42no—
373D4—42no—
374D4—44no—
375D4—44no—
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—24no—
385C2×C4—24no—
386C2×C4—28no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—44no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—44no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—84no—
409C2×C4C31×#9912yes—
410C2×C4C31×#10212yes—
411C2×C4C31×#10212yes—
412C2×C4C31×#10412yes—
413C2×C4C31×#10412yes—
414C2×C4C2×C42×C3111yescharacteristic
415C2×C4C31×#11711yescharacteristic
416C2×C4C4×D4×C3112yes—
417C8—44no—
418C22—21no—
419C22—21no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—42no—
427C22—42no—
428C22—42no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22C4×C22⋊C4×C3111yescharacteristic
434C22C2×C31×#9911yescharacteristic
435C22C31×#41011yescharacteristic
436C22C2×C31×#10211yescharacteristic
437C22C31×#41611yescharacteristic
438C22C2×C31×#10411yescharacteristic
439C22C2×C31×#10411yescharacteristic
440C22C4×D8×C3112yes—
441C22C4×SD16×C3112yes—
442C4—22no—
443C4—22no—
444C4—21no—
445C4—21no—
446C4—22no—
447C4—48no—
448C4—41no—
449C4—42no—
450C4—81no—
451C4—81no—
452C4C31×#32714yesdirect product factor
453C2—22no—
454C2—22no—
455C2—82no—
456C2C2×C31×#32711yescharacteristic
457C2C31×#150011yescharacteristic
458C2C31×#150111yescharacteristic
459C2C31×#150211yescharacteristic
460C2C4×C31×#9911yescharacteristic
461C2C4×C31×#10411yescharacteristic
462C2C4×C31×#10211yescharacteristic
subgroupG/H
centerC22×C4×C31C22⋊C4
commutatorC2×C4C2×C42×C31
Frattini, cosocleC23×C4C23×C31
socleC23×C31C2×C22⋊C4
prime radicalC2×C31×#121C22
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×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. C4×C31×#95C2semidirect
5. C31×#1294C2semidirect
8. C2×C4×D4×C31C4semidirect
13. C31×#390C4semidirect
14. C31×#389C4semidirect
18. C4×C4⋊C4×C31C4semidirect
23. C31×#327C4direct (N × H)
56. C31×C22⋊C8C2×C4semidirect
63. C31×#95C2×C4semidirect
73. C2×D4×C31C42semidirect
111. C4⋊C4×C31C42semidirect
124. C4×#327C31direct (N × H)
188. C4×C22⋊C8C2×C31semidirect
190. C4×#95C2×C31semidirect
191. #1294C2×C31semidirect
226. C4×C31#327direct (N × H)
229. C2×C4×D4C4×C31semidirect
234. #390C4×C31semidirect
235. #389C4×C31semidirect
239. C4×C4⋊C4C4×C31semidirect
244. #327C4×C31direct (N × H)
287. C22⋊C8C2×C4×C31semidirect
294. #95C2×C4×C31semidirect
295. C31C4×#327direct (N × H)
305. C2×D4C42×C31semidirect
343. C4⋊C4C42×C31semidirect
452. C4C31×#327direct (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
C4×C31×#952
C31×#12942
C4×#32731