Finite Group Databasebeta

← C2×C31×#1897 #21477737

Subgroups — C2×C31×#1897 #21477737

Order 7936.

1954 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#525C211yesmaximal, characteristic
2C22×C31×#117C211yesmaximal, characteristic, complemented
3C22×C31×#104C212yesmaximal, complemented
4C2×C31×#407C211yesmaximal, characteristic, complemented
5C31×#1897C218yesmaximal, direct product factor
6C2×C31×#339C212yesmaximal, complemented
7C22×#41×C31C2211yescharacteristic
8C24×C4×C31C2211yescharacteristic
9C22×M16×C31C2212yes—
10C31×#525—22no—
11C31×#525—22no—
12C31×#525C414yescomplemented
13C31×#525C2214yes—
14C2×C31×#123—21no—
15C2×C31×C22⋊Q8C412yescomplemented
16C2×C31×#121C412yescomplemented
17C2×C31×#120—21no—
18C2×C4×D4×C31—22no—
19C2×C31×#117—22no—
20C2×C31×#117—28no—
21C2×C31×#117C2211yescharacteristic
22C2×C31×#117C2214yescomplemented
23C22×C4⋊C4×C31—21no—
24C22×C22⋊C4×C31—21no—
25C22×C42×C31C2212yes—
26C2×C31×#104—28no—
27C2×C31×#104C2218yescomplemented
28C31×#407—22no—
29C31×#407C2214yescomplemented
30C2×C31×C22⋊C8—22no—
31C31×#339C2218yescomplemented
32C25×C31D411yescharacteristic
33C2×#41×C31—21no—
34C2×#41×C31—21no—
35C2×#41×C31—24no—
36C2×#41×C31—24no—
37C2×#41×C31C2×C412yes—
38C2×#41×C31C2312yes—
39C22×Q8×C31C2×C411yescharacteristic
40C22×D4×C31—22no—
41C22×D4×C31—21no—
42C22×D4×C31C2×C411yescharacteristic
43C23×C4×C31—24no—
44C23×C4×C31—24no—
45C23×C4×C31—22no—
46C23×C4×C31—21no—
47C23×C4×C31C2×C412yes—
48C23×C4×C31C2×C412yes—
49C23×C4×C31D411yescharacteristic
50C23×C4×C31D412yes—
51C23×C4×C31D412yes—
52C23×C4×C31D412yes—
53C23×C4×C31C2312yes—
54C23×C4×C31C2311yescharacteristic
55C2×M16×C31—22no—
56C2×M16×C31—24no—
57C2×M16×C31—24no—
58C2×M16×C31C2314yes—
59C22×C8×C31—22no—
60C31×#123—24no—
61C31×#123—24no—
62C31×C22⋊Q8—24no—
63C31×C22⋊Q8C2×C418yescomplemented
64C31×#121—24no—
65C31×#121C2×C418yescomplemented
66C31×#120—24no—
67C31×#120—24no—
68C4×D4×C31—28no—
69C4×D4×C31—28no—
70C31×#117—216no—
71C31×#117—21no—
72C31×#117—21no—
73C31×#117—216no—
74C31×#117C2×C412yes—
75C31×#117C2312yes—
76C2×C4⋊C4×C31—28no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—24no—
79C2×C4⋊C4×C31C2×C412yes—
80C2×C22⋊C4×C31—28no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—24no—
83C2×C22⋊C4×C31—21no—
84C2×C22⋊C4×C31—22no—
85C2×C42×C31—22no—
86C2×C42×C31—24no—
87C2×C42×C31—21no—
88C2×C42×C31D418yescomplemented
89C2×C42×C31C2314yes—
90C31×#104—216no—
91C31×C22⋊C8—28no—
92C24×C31—22no—
93C24×C31—22no—
94C24×C31—21no—
95C24×C31—44no—
96C24×C31C22⋊C412yes—
97C24×C31C22⋊C412yes—
98C24×C31C2×D411yescharacteristic
99C24×C31C2×D412yes—
100#41×C31—28no—
101#41×C31—24no—
102#41×C31—24no—
103#41×C31—42no—
104#41×C31—44no—
105#41×C31—42no—
106C2×Q8×C31—21no—
107C2×Q8×C31—24no—
108C2×Q8×C31C22×C412yes—
109C2×D4×C31—28no—
110C2×D4×C31—22no—
111C2×D4×C31—22no—
112C2×D4×C31—21no—
113C2×D4×C31—24no—
114C2×D4×C31—48no—
115C2×D4×C31—42no—
116C2×D4×C31—42no—
117C2×D4×C31C22×C412yes—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—28no—
121C22×C4×C31—28no—
122C22×C4×C31—24no—
123C22×C4×C31—28no—
124C22×C4×C31—28no—
125C22×C4×C31—24no—
126C22×C4×C31—24no—
127C22×C4×C31—24no—
128C22×C4×C31—22no—
129C22×C4×C31—21no—
130C22×C4×C31—28no—
131C22×C4×C31—24no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—48no—
135C22×C4×C31—44no—
136C22×C4×C31C22⋊C412yes—
137C22×C4×C31C22⋊C414yes—
138C22×C4×C31C22⋊C414yes—
139C22×C4×C31C22⋊C412yes—
140C22×C4×C31C22×C414yes—
141C22×C4×C31C22×C411yescharacteristic
142C22×C4×C31C22×C411yescharacteristic
143C22×C4×C31C2×D412yes—
144C22×C4×C31C2×D414yes—
145C22×C4×C31C2×D411yescharacteristic
146C22×C4×C31C2×D411yescharacteristic
147C22×C4×C31C2×D414yes—
148C22×C4×C31C2×D411yescharacteristic
149C22×C4×C31#4114yes—
150C22×C4×C31C2411yescharacteristic
151M16×C31—24no—
152M16×C31—24no—
153M16×C31—44no—
154C2×C8×C31—24no—
155C2×C8×C31—44no—
156C4⋊C4×C31—216no—
157C4⋊C4×C31—28no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31C22×C414yes—
160C22⋊C4×C31—216no—
161C22⋊C4×C31—22no—
162C22⋊C4×C31—28no—
163C22⋊C4×C31—22no—
164C22⋊C4×C31—28no—
165C42×C31—22no—
166C42×C31—28no—
167C42×C31—24no—
168C42×C31—22no—
169C42×C31C2×D418yescomplemented
170C2×#1897C3111yesmaximal, characteristic, direct product factor, Sylow
171C23×C31—24no—
172C23×C31—22no—
173C23×C31—22no—
174C23×C31—24no—
175C23×C31—24no—
176C23×C31—24no—
177C23×C31—24no—
178C23×C31—22no—
179C23×C31—44no—
180C23×C31—44no—
181C23×C31—48no—
182C23×C31—48no—
183C23×C31—42no—
184C23×C31—44no—
185C23×C31C2×C22⋊C414yes—
186C23×C31C2×C22⋊C411yescharacteristic
187C23×C31C2×C22⋊C411yescharacteristic
188C23×C31#12012yes—
189C23×C31#12312yes—
190C23×C31C22×D411yescharacteristic
191Q8×C31—24no—
192Q8×C31—42no—
193D4×C31—24no—
194D4×C31—416no—
195D4×C31—42no—
196D4×C31—42no—
197D4×C31—44no—
198D4×C31—42no—
199C2×C4×C31—22no—
200C2×C4×C31—22no—
201C2×C4×C31—24no—
202C2×C4×C31—24no—
203C2×C4×C31—28no—
204C2×C4×C31—28no—
205C2×C4×C31—28no—
206C2×C4×C31—28no—
207C2×C4×C31—24no—
208C2×C4×C31—22no—
209C2×C4×C31—28no—
210C2×C4×C31—48no—
211C2×C4×C31—416no—
212C2×C4×C31—42no—
213C2×C4×C31—44no—
214C2×C4×C31—44no—
215C2×C4×C31—44no—
216C2×C4×C31C2×C22⋊C414yes—
217C2×C4×C31C2×C22⋊C411yescharacteristic
218C2×C4×C31C2×C22⋊C411yescharacteristic
219C2×C4×C31C4×D414yes—
220C2×C4×C31C4×D414yes—
221C2×C4×C31#12012yes—
222C2×C4×C31#12114yes—
223C2×C4×C31#12114yes—
224C2×C4×C31#12312yes—
225C2×C4×C31C23×C411yescharacteristic
226C2×C4×C31C22×D412yes—
227C2×C4×C31C22×D411yescharacteristic
228C2×C4×C31C2×#4112yes—
229C8×C31—44no—
230C2×#525C2×C3111yescharacteristic
231C22×#117C2×C3111yescharacteristic, complemented
232C22×#104C2×C3112yescomplemented
233C2×#407C2×C3111yescharacteristic, complemented
234#1897C2×C3118yesdirect product factor
235C2×#339C2×C3112yescomplemented
236C22×C31—22no—
237C22×C31—22no—
238C22×C31—24no—
239C22×C31—24no—
240C22×C31—24no—
241C22×C31—24no—
242C22×C31—24no—
243C22×C31—44no—
244C22×C31—44no—
245C22×C31—48no—
246C22×C31—48no—
247C22×C31—44no—
248C22×C31—42no—
249C22×C31—84no—
250C22×C31#38612yes—
251C22×C31#38612yes—
252C22×C31#42114yes—
253C22×C31C22×C22⋊C411yescharacteristic
254C22×C31C2×#12011yescharacteristic
255C22×C31C2×#12311yescharacteristic
256C4×C31—24no—
257C4×C31—48no—
258C4×C31—44no—
259C4×C31—42no—
260C4×C31#38612yes—
261C4×C31#38612yes—
262C4×C31C2×C4×D412yes—
263C4×C31C2×#12112yes—
264C22×#41C22×C3111yescharacteristic
265C24×C4C22×C3111yescharacteristic
266C22×M16C22×C3112yes—
267#525—22no—
268#525—22no—
269#525C4×C3114yescomplemented
270#525C22×C3114yes—
271C2×#123—21no—
272C2×C22⋊Q8C4×C3112yescomplemented
273C2×#121C4×C3112yescomplemented
274C2×#120—21no—
275C2×C4×D4—22no—
276C2×#117—22no—
277C2×#117—28no—
278C2×#117C22×C3111yescharacteristic
279C2×#117C22×C3114yescomplemented
280C22×C4⋊C4—21no—
281C22×C22⋊C4—21no—
282C22×C42C22×C3112yes—
283C2×#104—28no—
284C2×#104C22×C3118yescomplemented
285#407—22no—
286#407C22×C3114yescomplemented
287C2×C22⋊C8—22no—
288#339C22×C3118yescomplemented
289C2×C31—21no—
290C2×C31—21no—
291C2×C31—22no—
292C2×C31—44no—
293C2×C31—82no—
294C2×C31#189714yesdirect product factor
295C2×C31C2×#38611yescharacteristic
296C2×C31C2×#42112yes—
297C25D4×C3111yescharacteristic
298C2×#41—21no—
299C2×#41—21no—
300C2×#41—24no—
301C2×#41—24no—
302C2×#41C2×C4×C3112yes—
303C2×#41C23×C3112yes—
304C22×Q8C2×C4×C3111yescharacteristic
305C22×D4—22no—
306C22×D4—21no—
307C22×D4C2×C4×C3111yescharacteristic
308C23×C4—24no—
309C23×C4—24no—
310C23×C4—22no—
311C23×C4—21no—
312C23×C4C2×C4×C3112yes—
313C23×C4C2×C4×C3112yes—
314C23×C4D4×C3111yescharacteristic
315C23×C4D4×C3112yes—
316C23×C4D4×C3112yes—
317C23×C4D4×C3112yes—
318C23×C4C23×C3112yes—
319C23×C4C23×C3111yescharacteristic
320C2×M16—22no—
321C2×M16—24no—
322C2×M16—24no—
323C2×M16C23×C3114yes—
324C22×C8—22no—
325#123—24no—
326#123—24no—
327C22⋊Q8—24no—
328C22⋊Q8C2×C4×C3118yescomplemented
329#121—24no—
330#121C2×C4×C3118yescomplemented
331#120—24no—
332#120—24no—
333C4×D4—28no—
334C4×D4—28no—
335#117—216no—
336#117—21no—
337#117—21no—
338#117—216no—
339#117C2×C4×C3112yes—
340#117C23×C3112yes—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4C2×C4×C3112yes—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—22no—
350C2×C42—22no—
351C2×C42—24no—
352C2×C42—21no—
353C2×C42D4×C3118yescomplemented
354C2×C42C23×C3114yes—
355#104—216no—
356C22⋊C8—28no—
357C31C2×#189711yescharacteristic, direct product factor, Sylow
358C24—22no—
359C24—22no—
360C24—21no—
361C24—44no—
362C24C22⋊C4×C3112yes—
363C24C22⋊C4×C3112yes—
364C24C2×D4×C3111yescharacteristic
365C24C2×D4×C3112yes—
366#41—28no—
367#41—24no—
368#41—24no—
369#41—42no—
370#41—44no—
371#41—42no—
372C2×Q8—21no—
373C2×Q8—24no—
374C2×Q8C22×C4×C3112yes—
375C2×D4—28no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—21no—
379C2×D4—24no—
380C2×D4—48no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4C22×C4×C3112yes—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—28no—
387C22×C4—28no—
388C22×C4—24no—
389C22×C4—28no—
390C22×C4—28no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—28no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—48no—
401C22×C4—44no—
402C22×C4C22⋊C4×C3112yes—
403C22×C4C22⋊C4×C3114yes—
404C22×C4C22⋊C4×C3114yes—
405C22×C4C22⋊C4×C3112yes—
406C22×C4C22×C4×C3114yes—
407C22×C4C22×C4×C3111yescharacteristic
408C22×C4C22×C4×C3111yescharacteristic
409C22×C4C2×D4×C3112yes—
410C22×C4C2×D4×C3114yes—
411C22×C4C2×D4×C3111yescharacteristic
412C22×C4C2×D4×C3111yescharacteristic
413C22×C4C2×D4×C3111yescharacteristic
414C22×C4C2×D4×C3114yes—
415C22×C4#41×C3114yes—
416C22×C4C24×C3111yescharacteristic
417M16—24no—
418M16—24no—
419M16—44no—
420C2×C8—24no—
421C2×C8—44no—
422C4⋊C4—216no—
423C4⋊C4—28no—
424C4⋊C4—22no—
425C4⋊C4C22×C4×C3114yes—
426C22⋊C4—216no—
427C22⋊C4—22no—
428C22⋊C4—28no—
429C22⋊C4—22no—
430C22⋊C4—28no—
431C42—22no—
432C42—28no—
433C42—24no—
434C42—22no—
435C42C2×D4×C3118yescomplemented
436C23—24no—
437C23—24no—
438C23—24no—
439C23—22no—
440C23—22no—
441C23—24no—
442C23—24no—
443C23—22no—
444C23—44no—
445C23—44no—
446C23—48no—
447C23—48no—
448C23—44no—
449C23—42no—
450C23C2×C22⋊C4×C3114yes—
451C23C2×C22⋊C4×C3111yescharacteristic
452C23C2×C22⋊C4×C3111yescharacteristic
453C23C31×#12012yes—
454C23C31×#12312yes—
455C23C22×D4×C3111yescharacteristic
456Q8—24no—
457Q8—42no—
458D4—24no—
459D4—416no—
460D4—42no—
461D4—42no—
462D4—44no—
463D4—42no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—28no—
469C2×C4—28no—
470C2×C4—28no—
471C2×C4—28no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—28no—
475C2×C4—48no—
476C2×C4—416no—
477C2×C4—44no—
478C2×C4—42no—
479C2×C4—44no—
480C2×C4—44no—
481C2×C4C2×C22⋊C4×C3114yes—
482C2×C4C2×C22⋊C4×C3111yescharacteristic
483C2×C4C2×C22⋊C4×C3111yescharacteristic
484C2×C4C4×D4×C3114yes—
485C2×C4C4×D4×C3114yes—
486C2×C4C31×#12012yes—
487C2×C4C31×#12114yes—
488C2×C4C31×#12114yes—
489C2×C4C31×#12312yes—
490C2×C4C23×C4×C3111yescharacteristic
491C2×C4C22×D4×C3112yes—
492C2×C4C22×D4×C3111yescharacteristic
493C2×C4C2×#41×C3112yes—
494C8—44no—
495C22—22no—
496C22—22no—
497C22—24no—
498C22—24no—
499C22—24no—
500C22—24no—
501C22—24no—
502C22—44no—
503C22—44no—
504C22—48no—
505C22—48no—
506C22—44no—
507C22—42no—
508C22—84no—
509C22C31×#38612yes—
510C22C31×#38612yes—
511C22C31×#42114yes—
512C22C22×C22⋊C4×C3111yescharacteristic
513C22C2×C31×#12011yescharacteristic
514C22C2×C31×#12311yescharacteristic
515C4—24no—
516C4—48no—
517C4—44no—
518C4—42no—
519C4C31×#38612yes—
520C4C31×#38612yes—
521C4C2×C4×D4×C3112yes—
522C4C2×C31×#12112yes—
523C2—21no—
524C2—21no—
525C2—22no—
526C2—44no—
527C2—82no—
528C2C31×#189714yesdirect product factor
529C2C2×C31×#38611yescharacteristic
530C2C2×C31×#42112yes—
subgroupG/H
centerC22×C4×C31C2×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
socleC23×C31C2×C22⋊C4
prime radicalC2×C31×#525C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C31×#117C2semidirect
3. C22×C31×#104C2semidirect
4. C2×C31×#407C2semidirect
5. C31×#1897C2direct (N × H)
6. C2×C31×#339C2semidirect
12. C31×#525C4semidirect
15. C2×C31×C22⋊Q8C4semidirect
16. C2×C31×#121C4semidirect
22. C2×C31×#117C22semidirect
27. C2×C31×#104C22semidirect
29. C31×#407C22semidirect
31. C31×#339C22semidirect
63. C31×C22⋊Q8C2×C4semidirect
65. C31×#121C2×C4semidirect
88. C2×C42×C31D4semidirect
169. C42×C31C2×D4semidirect
170. C2×#1897C31direct (N × H)
231. C22×#117C2×C31semidirect
232. C22×#104C2×C31semidirect
233. C2×#407C2×C31semidirect
234. #1897C2×C31direct (N × H)
235. C2×#339C2×C31semidirect
269. #525C4×C31semidirect
272. C2×C22⋊Q8C4×C31semidirect
273. C2×#121C4×C31semidirect
279. C2×#117C22×C31semidirect
284. C2×#104C22×C31semidirect
286. #407C22×C31semidirect
288. #339C22×C31semidirect
294. C2×C31#1897direct (N × H)
328. C22⋊Q8C2×C4×C31semidirect
330. #121C2×C4×C31semidirect
353. C2×C42D4×C31semidirect
357. C31C2×#1897direct (N × H)
435. C42C2×D4×C31semidirect
528. C2C31×#1897direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5252
C22×C31×#1172
C22×C31×#1042
C2×C31×#4072
C31×#18972
C2×C31×#3392
C2×#189731