Finite Group Databasebeta

← C31×#14314 #21471073

Subgroups — C31×#14314 #21471073

Order 7936.

1310 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#398C211yesmaximal, characteristic
2C2×C31×#389C211yesmaximal, characteristic
3C2×C31×#387C212yesmaximal
4C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
5C31×#1445C211yesmaximal, characteristic
6C31×#1443C212yesmaximal
7C31×#1442C211yesmaximal, characteristic
8C31×#1441C212yesmaximal
9C31×#1441C211yesmaximal, characteristic
10C31×#1436C212yesmaximal
11C31×#1434C211yesmaximal, characteristic
12C22×C4⋊C4×C31C2212yes—
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2212yes—
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C42×C31C2211yescharacteristic
19C22×C42×C31C2211yescharacteristic
20C22×C42×C31C2211yescharacteristic
21C31×#398C418yescomplemented
22C31×#389—24no—
23C31×#387—28no—
24C4×C4⋊C4×C31—24no—
25C2×C31×#95C2212yes—
26C2×C31×#95C2211yescharacteristic
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2212yes—
39C23×C4×C31C2312yes—
40C23×C4×C31C2312yes—
41C23×C4×C31C2311yescharacteristic
42C23×C4×C31C2312yes—
43C23×C4×C31C2312yes—
44C23×C4×C31C2311yescharacteristic
45C23×C4×C31C2311yescharacteristic
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2311yescharacteristic
50C2×C4⋊C4×C31—22no—
51C2×C4⋊C4×C31—22no—
52C2×C4⋊C4×C31—24no—
53C2×C4⋊C4×C31—22no—
54C2×C4⋊C4×C31—22no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—24no—
59C2×C4⋊C4×C31—24no—
60C2×C4⋊C4×C31—22no—
61C2×C4⋊C4×C31—24no—
62C2×C4⋊C4×C31—24no—
63C2×C4⋊C4×C31—42no—
64C2×C4⋊C4×C31C2×C418yes—
65C2×C4⋊C4×C31C2×C414yes—
66C2×C4⋊C4×C31C2×C414yes—
67C2×C42×C31—22no—
68C2×C42×C31—22no—
69C2×C42×C31—22no—
70C2×C42×C31—42no—
71C2×C42×C31—42no—
72C2×C42×C31D414yes—
73C2×C42×C31D414yes—
74C31×#95—22no—
75C31×#95—22no—
76C31×#95—24no—
77C31×#95—24no—
78C31×#95—24no—
79C31×#95—24no—
80C31×#95—24no—
81C31×#95—24no—
82C31×#95—22no—
83C31×#95—42no—
84C31×#95—42no—
85C31×#95—42no—
86C31×#95C2×C418yes—
87C31×#95C2×C414yes—
88C24×C31C2411yescharacteristic
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—21no—
93C22×C4×C31—22no—
94C22×C4×C31—22no—
95C22×C4×C31—22no—
96C22×C4×C31—22no—
97C22×C4×C31—21no—
98C22×C4×C31—22no—
99C22×C4×C31—21no—
100C22×C4×C31—21no—
101C22×C4×C31—22no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—21no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—21no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—21no—
111C22×C4×C31—21no—
112C22×C4×C31—21no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31C22×C414yes—
140C22×C4×C31C22×C412yes—
141C22×C4×C31C22×C414yes—
142C22×C4×C31C22×C412yes—
143C22×C4×C31C22×C412yes—
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2×D412yes—
146C22×C4×C31C2×D412yes—
147C22×C4×C31C2×D412yes—
148C22×C4×C31C2×D412yes—
149C22×C4×C31C2×D412yes—
150C22×C4×C31#4112yes—
151C22×C4×C31#4112yes—
152C22×C4×C31#4112yes—
153C22×C4×C31#4112yes—
154C4⋊C4×C31—28no—
155C4⋊C4×C31—28no—
156C4⋊C4×C31—216no—
157C4⋊C4×C31—28no—
158C4⋊C4×C31—44no—
159C4⋊C4×C31—48no—
160C42×C31—28no—
161C42×C31—44no—
162C42×C31—44no—
163#14314C3111yesmaximal, characteristic, direct product factor, Sylow
164C23×C31C23×C411yescharacteristic
165C23×C31C22×D411yescharacteristic
166C23×C31C22×D411yescharacteristic
167C23×C31C2×#4111yescharacteristic
168C23×C31C2×#4111yescharacteristic
169C23×C31C2×#4111yescharacteristic
170C23×C31C2×#4111yescharacteristic
171C23×C31H(5,𝔽2)12yes—
172C23×C312−1+412yes—
173C23×C312−1+412yes—
174C23×C312−1+412yes—
175C2×C4×C31—22no—
176C2×C4×C31—22no—
177C2×C4×C31—24no—
178C2×C4×C31—22no—
179C2×C4×C31—22no—
180C2×C4×C31—22no—
181C2×C4×C31—22no—
182C2×C4×C31—22no—
183C2×C4×C31—22no—
184C2×C4×C31—22no—
185C2×C4×C31—22no—
186C2×C4×C31—24no—
187C2×C4×C31—24no—
188C2×C4×C31—24no—
189C2×C4×C31—22no—
190C2×C4×C31—24no—
191C2×C4×C31—24no—
192C2×C4×C31—24no—
193C2×C4×C31—24no—
194C2×C4×C31—24no—
195C2×C4×C31—24no—
196C2×C4×C31—24no—
197C2×C4×C31—22no—
198C2×C4×C31—22no—
199C2×C4×C31—22no—
200C2×C4×C31—22no—
201C2×C4×C31—24no—
202C2×C4×C31—22no—
203C2×C4×C31—24no—
204C2×C4×C31—42no—
205C2×C4×C31—42no—
206C2×C4×C31—42no—
207C2×C4×C31—42no—
208C2×C4×C31—41no—
209C2×C4×C31—41no—
210C2×C4×C31—41no—
211C2×C4×C31—42no—
212C2×C4×C31—41no—
213C2×C4×C31—41no—
214C2×C4×C31—41no—
215C2×C4×C31—42no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—42no—
228C2×C4×C31—42no—
229C2×C4×C31—42no—
230C2×C4×C31—42no—
231C2×C4×C31—42no—
232C2×C4×C31—42no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31—42no—
236C2×C4×C31—42no—
237C2×C4×C31C4×D414yes—
238C2×C4×C31C4×D414yes—
239C2×C4×C31#12114yes—
240C2×#398C2×C3111yescharacteristic
241C2×#389C2×C3111yescharacteristic
242C2×#387C2×C3112yes—
243C2×C4×C4⋊C4C2×C3111yescharacteristic
244#1445C2×C3111yescharacteristic
245#1443C2×C3112yes—
246#1442C2×C3111yescharacteristic
247#1441C2×C3112yes—
248#1441C2×C3111yescharacteristic
249#1436C2×C3112yes—
250#1434C2×C3111yescharacteristic
251C22×C31C2×C4×D411yescharacteristic
252C22×C31C2×C4×D411yescharacteristic
253C22×C31C4×#4111yescharacteristic
254C22×C31#51912yes—
255C22×C31#52012yes—
256C22×C31C2×#12111yescharacteristic
257C22×C31#52511yescharacteristic
258C22×C31#52911yescharacteristic
259C22×C31#53211yescharacteristic
260C22×C31#53411yescharacteristic
261C22×C31#53611yescharacteristic
262C22×C31#53612yes—
263C22×C31#53611yescharacteristic
264C22×C31#53611yescharacteristic
265C22×C31#53712yes—
266C22×C31#53912yes—
267C22×C31#53912yes—
268C22×C31#53912yes—
269C22×C31#54112yes—
270C22×C31#54112yes—
271C22×C31#54112yes—
272C22×C31#54112yes—
273C22×C31#54212yes—
274C4×C31—24no—
275C4×C31—24no—
276C4×C31—24no—
277C4×C31—42no—
278C4×C31—44no—
279C4×C31—42no—
280C4×C31—42no—
281C4×C31—42no—
282C4×C31—44no—
283C4×C31—82no—
284C4×C31—82no—
285C22×C4⋊C4C22×C3112yes—
286C22×C4⋊C4C22×C3111yescharacteristic
287C22×C4⋊C4C22×C3111yescharacteristic
288C22×C4⋊C4C22×C3112yes—
289C22×C4⋊C4C22×C3111yescharacteristic
290C22×C4⋊C4C22×C3111yescharacteristic
291C22×C42C22×C3111yescharacteristic
292C22×C42C22×C3111yescharacteristic
293C22×C42C22×C3111yescharacteristic
294#398C4×C3118yescomplemented
295#389—24no—
296#387—28no—
297C4×C4⋊C4—24no—
298C2×#95C22×C3112yes—
299C2×#95C22×C3111yescharacteristic
300C2×#95C22×C3112yes—
301C2×#95C22×C3112yes—
302C2×#95C22×C3112yes—
303C2×#95C22×C3112yes—
304C2×#95C22×C3111yescharacteristic
305C2×#95C22×C3111yescharacteristic
306C2×#95C22×C3112yes—
307C2×#95C22×C3112yes—
308C2×#95C22×C3112yes—
309C2×#95C22×C3112yes—
310C2×#95C22×C3111yescharacteristic
311C2×#95C22×C3112yes—
312C2×C31C4×#12111yescharacteristic
313C2×C31#232211yescharacteristic
314C2×C31#232312yes—
315C2×C31#232711yescharacteristic
316C2×C31#233612yes—
317C2×C31#261811yescharacteristic
318C2×C31#262111yescharacteristic
319C2×C31#263411yescharacteristic
320C2×C31#263811yescharacteristic
321C2×C31#265512yes—
322C2×C31#266412yes—
323C23×C4C23×C3112yes—
324C23×C4C23×C3112yes—
325C23×C4C23×C3112yes—
326C23×C4C23×C3112yes—
327C23×C4C23×C3111yescharacteristic
328C23×C4C23×C3111yescharacteristic
329C23×C4C23×C3111yescharacteristic
330C23×C4C23×C3111yescharacteristic
331C23×C4C23×C3111yescharacteristic
332C23×C4C23×C3111yescharacteristic
333C23×C4C23×C3111yescharacteristic
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4C2×C4×C3118yes—
349C2×C4⋊C4C2×C4×C3114yes—
350C2×C4⋊C4C2×C4×C3114yes—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—42no—
355C2×C42—42no—
356C2×C42D4×C3114yes—
357C2×C42D4×C3114yes—
358#95—22no—
359#95—22no—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—22no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95C2×C4×C3118yes—
371#95C2×C4×C3114yes—
372C31#1431411yescharacteristic, direct product factor, Sylow
373C24C24×C3111yescharacteristic
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4C22×C4×C3114yes—
425C22×C4C22×C4×C3112yes—
426C22×C4C22×C4×C3114yes—
427C22×C4C22×C4×C3112yes—
428C22×C4C22×C4×C3112yes—
429C22×C4C2×D4×C3112yes—
430C22×C4C2×D4×C3112yes—
431C22×C4C2×D4×C3112yes—
432C22×C4C2×D4×C3112yes—
433C22×C4C2×D4×C3112yes—
434C22×C4C2×D4×C3112yes—
435C22×C4#41×C3112yes—
436C22×C4#41×C3112yes—
437C22×C4#41×C3112yes—
438C22×C4#41×C3112yes—
439C4⋊C4—28no—
440C4⋊C4—28no—
441C4⋊C4—216no—
442C4⋊C4—28no—
443C4⋊C4—44no—
444C4⋊C4—48no—
445C42—28no—
446C42—44no—
447C42—44no—
448C23C23×C4×C3111yescharacteristic
449C23C22×D4×C3111yescharacteristic
450C23C22×D4×C3111yescharacteristic
451C23C2×#41×C3111yescharacteristic
452C23C2×#41×C3111yescharacteristic
453C23C2×#41×C3111yescharacteristic
454C23C2×#41×C3111yescharacteristic
455C23C31×H(5,𝔽2)12yes—
456C23C31×2−1+412yes—
457C23C31×2−1+412yes—
458C23C31×2−1+412yes—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4C4×D4×C3114yes—
522C2×C4C4×D4×C3114yes—
523C2×C4C31×#12114yes—
524C22C2×C4×D4×C3111yescharacteristic
525C22C2×C4×D4×C3111yescharacteristic
526C22C4×#41×C3111yescharacteristic
527C22C31×#51912yes—
528C22C31×#52012yes—
529C22C2×C31×#12111yescharacteristic
530C22C31×#52511yescharacteristic
531C22C31×#52911yescharacteristic
532C22C31×#53211yescharacteristic
533C22C31×#53411yescharacteristic
534C22C31×#53611yescharacteristic
535C22C31×#53612yes—
536C22C31×#53611yescharacteristic
537C22C31×#53611yescharacteristic
538C22C31×#53712yes—
539C22C31×#53912yes—
540C22C31×#53912yes—
541C22C31×#53912yes—
542C22C31×#54112yes—
543C22C31×#54112yes—
544C22C31×#54112yes—
545C22C31×#54112yes—
546C22C31×#54212yes—
547C4—24no—
548C4—24no—
549C4—24no—
550C4—42no—
551C4—44no—
552C4—42no—
553C4—42no—
554C4—42no—
555C4—44no—
556C4—82no—
557C4—82no—
558C2C4×C31×#12111yescharacteristic
559C2C31×#232211yescharacteristic
560C2C31×#232312yes—
561C2C31×#232711yescharacteristic
562C2C31×#233612yes—
563C2C31×#261811yescharacteristic
564C2C31×#262111yescharacteristic
565C2C31×#263411yescharacteristic
566C2C31×#263811yescharacteristic
567C2C31×#265512yes—
568C2C31×#266412yes—
subgroupG/H
center, socle, prime radicalC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
21. C31×#398C4semidirect
163. #14314C31direct (N × H)
294. #398C4×C31semidirect
372. C31#14314direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3982
C2×C31×#3892
C2×C31×#3872
C2×C4×C4⋊C4×C312
C31×#14452
C31×#14432
C31×#14422
C31×#14412
C31×#14362
C31×#14342
#1431431