Finite Group Databasebeta

← C31×#16707 #21473466

Subgroups — C31×#16707 #21473466

Order 7936.

1306 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#1445C212yesmaximal, complemented
2C31×#1442C212yesmaximal, complemented
3C31×#1442C212yesmaximal, complemented
4C31×#1442C212yesmaximal, complemented
5C31×#1439C211yesmaximal, characteristic
6C31×#1439C212yesmaximal
7C31×#1439C211yesmaximal, characteristic
8C31×C22⋊#95C212yesmaximal
9C31×C22⋊#95C211yesmaximal, characteristic
10C24×C4×C31C2211yescharacteristic
11C22×C4⋊C4×C31C2212yes—
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C22⋊C4×C31C2212yes—
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2211yescharacteristic
17C22×C22⋊C4×C31C2211yescharacteristic
18C2×C31×#95C2212yes—
19C2×C31×#95C2212yes—
20C2×C31×#95C2212yes—
21C2×C31×#95C2212yes—
22C2×C31×#95C2212yes—
23C2×C31×#95C2212yes—
24C2×C31×#95C2212yes—
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2211yescharacteristic
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2211yescharacteristic
31C25×C31C2311yescharacteristic
32C23×C4×C31—22no—
33C23×C4×C31—24no—
34C23×C4×C31—41no—
35C23×C4×C31—42no—
36C23×C4×C31—41no—
37C23×C4×C31C2312yes—
38C23×C4×C31C2312yes—
39C23×C4×C31C2312yes—
40C23×C4×C31C2312yes—
41C23×C4×C31C2311yescharacteristic
42C23×C4×C31C2311yescharacteristic
43C23×C4×C31C2312yes—
44C23×C4×C31C2312yes—
45C2×C4⋊C4×C31—24no—
46C2×C4⋊C4×C31—42no—
47C2×C4⋊C4×C31—42no—
48C2×C4⋊C4×C31—42no—
49C2×C4⋊C4×C31—42no—
50C2×C4⋊C4×C31—41no—
51C2×C4⋊C4×C31—41no—
52C2×C22⋊C4×C31—24no—
53C2×C22⋊C4×C31—22no—
54C2×C22⋊C4×C31—24no—
55C2×C22⋊C4×C31—24no—
56C2×C22⋊C4×C31—41no—
57C2×C22⋊C4×C31—41no—
58C2×C22⋊C4×C31—42no—
59C2×C22⋊C4×C31—42no—
60C2×C22⋊C4×C31—41no—
61C2×C22⋊C4×C31—41no—
62C2×C22⋊C4×C31—42no—
63C2×C22⋊C4×C31Q814yes—
64C31×#95—24no—
65C31×#95—24no—
66C31×#95—24no—
67C31×#95—41no—
68C31×#95—42no—
69C31×#95—41no—
70C31×#95—42no—
71C31×#95—42no—
72C31×#95—42no—
73C31×#95—42no—
74C31×#95—42no—
75C31×#95—42no—
76C31×#95—42no—
77C24×C31—22no—
78C24×C31—22no—
79C24×C31—21no—
80C24×C31—22no—
81C24×C31—21no—
82C24×C31—22no—
83C24×C31—21no—
84C24×C31—21no—
85C24×C31C2×Q812yes—
86C24×C31#4112yes—
87C24×C31#4112yes—
88C24×C31C2411yescharacteristic
89C22×C4×C31—22no—
90C22×C4×C31—22no—
91C22×C4×C31—22no—
92C22×C4×C31—22no—
93C22×C4×C31—22no—
94C22×C4×C31—22no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—22no—
98C22×C4×C31—22no—
99C22×C4×C31—22no—
100C22×C4×C31—22no—
101C22×C4×C31—22no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—22no—
106C22×C4×C31—21no—
107C22×C4×C31—21no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
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—44no—
138C22×C4×C31—48no—
139C22×C4×C31—48no—
140C22×C4×C31—44no—
141C22×C4×C31—44no—
142C22×C4×C31C2×Q812yes—
143C22×C4×C31C2×Q812yes—
144C22×C4×C31#4114yes—
145C22×C4×C31#4114yes—
146C4⋊C4×C31—48no—
147C4⋊C4×C31—44no—
148C4⋊C4×C31—44no—
149C22⋊C4×C31—44no—
150C22⋊C4×C31—48no—
151C22⋊C4×C31—48no—
152C22⋊C4×C31—44no—
153#16707C3111yesmaximal, characteristic, direct product factor, Sylow
154C23×C31—24no—
155C23×C31—22no—
156C23×C31—24no—
157C23×C31—22no—
158C23×C31—22no—
159C23×C31—22no—
160C23×C31—22no—
161C23×C31—22no—
162C23×C31—24no—
163C23×C31—24no—
164C23×C31—24no—
165C23×C31—24no—
166C23×C31—42no—
167C23×C31—42no—
168C23×C31—42no—
169C23×C31—42no—
170C23×C31—41no—
171C23×C31—42no—
172C23×C31—41no—
173C23×C31—41no—
174C23×C31—41no—
175C23×C31—42no—
176C23×C31#12514yes—
177C23×C31C22×Q811yescharacteristic
178C23×C31C2×#4111yescharacteristic
179C23×C31C2×#4111yescharacteristic
180C23×C31C2×#4112yes—
181C23×C31C2×#4112yes—
182C23×C31H(5,𝔽2)11yescharacteristic
183C23×C31H(5,𝔽2)11yescharacteristic
184C23×C31H(5,𝔽2)12yes—
185C23×C31H(5,𝔽2)11yescharacteristic
186C23×C31H(5,𝔽2)12yes—
187C23×C312−1+411yescharacteristic
188C2×C4×C31—24no—
189C2×C4×C31—24no—
190C2×C4×C31—22no—
191C2×C4×C31—22no—
192C2×C4×C31—24no—
193C2×C4×C31—24no—
194C2×C4×C31—24no—
195C2×C4×C31—24no—
196C2×C4×C31—24no—
197C2×C4×C31—24no—
198C2×C4×C31—416no—
199C2×C4×C31—42no—
200C2×C4×C31—42no—
201C2×C4×C31—42no—
202C2×C4×C31—42no—
203C2×C4×C31—42no—
204C2×C4×C31—42no—
205C2×C4×C31—42no—
206C2×C4×C31—41no—
207C2×C4×C31—42no—
208C2×C4×C31—41no—
209C2×C4×C31—41no—
210C2×C4×C31—41no—
211C2×C4×C31—42no—
212C2×C4×C31—42no—
213C2×C4×C31—42no—
214C2×C4×C31—42no—
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×C31—42no—
238C2×C4×C31—42no—
239C2×C4×C31—42no—
240C2×C4×C31—42no—
241#1445C2×C3112yescomplemented
242#1442C2×C3112yescomplemented
243#1442C2×C3112yescomplemented
244#1442C2×C3112yescomplemented
245#1439C2×C3111yescharacteristic
246#1439C2×C3112yes—
247#1439C2×C3111yescharacteristic
248C22⋊#95C2×C3112yes—
249C22⋊#95C2×C3111yescharacteristic
250C22×C31—24no—
251C22×C31—28no—
252C22×C31—42no—
253C22×C31—44no—
254C22×C31—42no—
255C22×C31—44no—
256C22×C31—42no—
257C22×C31—42no—
258C22×C31—44no—
259C22×C31—42no—
260C22×C31—42no—
261C22×C31C2×#12511yescharacteristic
262C22×C31#52912yes—
263C22×C31#53812yes—
264C22×C31#53811yescharacteristic
265C22×C31#53811yescharacteristic
266C22×C31#53812yes—
267C22×C31#53812yes—
268C22×C31#53911yescharacteristic
269C22×C31#53911yescharacteristic
270C22×C31#54012yes—
271C22×C31#54012yes—
272C22×C31#54311yescharacteristic
273C22×C31#54411yescharacteristic
274C22×C31#55112yes—
275C22×C31#55111yescharacteristic
276C22×C31#55112yes—
277C22×C31#55212yes—
278C22×C31#55412yes—
279C22×C31#55412yes—
280C22×C31#55911yescharacteristic
281C22×C31#56011yescharacteristic
282C22×C31H(3,𝔽4)11yescharacteristic
283C22×C31#56212yes—
284C4×C31—44no—
285C4×C31—44no—
286C4×C31—42no—
287C4×C31—42no—
288C4×C31—82no—
289C4×C31—82no—
290C4×C31—82no—
291C4×C31—82no—
292C24×C4C22×C3111yescharacteristic
293C22×C4⋊C4C22×C3112yes—
294C22×C4⋊C4C22×C3111yescharacteristic
295C22×C4⋊C4C22×C3111yescharacteristic
296C22×C22⋊C4C22×C3112yes—
297C22×C22⋊C4C22×C3112yes—
298C22×C22⋊C4C22×C3111yescharacteristic
299C22×C22⋊C4C22×C3111yescharacteristic
300C2×#95C22×C3112yes—
301C2×#95C22×C3112yes—
302C2×#95C22×C3112yes—
303C2×#95C22×C3112yes—
304C2×#95C22×C3112yes—
305C2×#95C22×C3112yes—
306C2×#95C22×C3112yes—
307C2×#95C22×C3112yes—
308C2×#95C22×C3112yes—
309C2×#95C22×C3111yescharacteristic
310C2×#95C22×C3112yes—
311C2×#95C22×C3112yes—
312C2×#95C22×C3111yescharacteristic
313C2×C31—44no—
314C2×C31#250512yes—
315C2×C31#251711yescharacteristic
316C2×C31#264611yescharacteristic
317C2×C31#264812yes—
318C2×C31#273611yescharacteristic
319C2×C31#274312yes—
320C2×C31#274811yescharacteristic
321C2×C31#275211yescharacteristic
322C2×C31#276812yes—
323C2×C31#280411yescharacteristic
324C2×C31#282411yescharacteristic
325C25C23×C3111yescharacteristic
326C23×C4—22no—
327C23×C4—24no—
328C23×C4—41no—
329C23×C4—42no—
330C23×C4—41no—
331C23×C4C23×C3112yes—
332C23×C4C23×C3112yes—
333C23×C4C23×C3112yes—
334C23×C4C23×C3112yes—
335C23×C4C23×C3111yescharacteristic
336C23×C4C23×C3111yescharacteristic
337C23×C4C23×C3112yes—
338C23×C4C23×C3112yes—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—41no—
345C2×C4⋊C4—41no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4Q8×C3114yes—
358#95—24no—
359#95—24no—
360#95—24no—
361#95—41no—
362#95—42no—
363#95—41no—
364#95—42no—
365#95—42no—
366#95—42no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—42no—
371C31#1670711yescharacteristic, direct product factor, Sylow
372C24—22no—
373C24—22no—
374C24—21no—
375C24—22no—
376C24—21no—
377C24—22no—
378C24—21no—
379C24—21no—
380C24C2×Q8×C3112yes—
381C24#41×C3112yes—
382C24#41×C3112yes—
383C24C24×C3111yescharacteristic
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
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×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—44no—
433C22×C4—48no—
434C22×C4—48no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4C2×Q8×C3112yes—
438C22×C4C2×Q8×C3112yes—
439C22×C4#41×C3114yes—
440C22×C4#41×C3114yes—
441C4⋊C4—48no—
442C4⋊C4—44no—
443C4⋊C4—44no—
444C22⋊C4—44no—
445C22⋊C4—48no—
446C22⋊C4—48no—
447C22⋊C4—44no—
448C23—24no—
449C23—22no—
450C23—24no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—24no—
457C23—24no—
458C23—24no—
459C23—24no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—41no—
465C23—42no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—42no—
470C23C31×#12514yes—
471C23C22×Q8×C3111yescharacteristic
472C23C2×#41×C3111yescharacteristic
473C23C2×#41×C3111yescharacteristic
474C23C2×#41×C3112yes—
475C23C2×#41×C3112yes—
476C23C31×H(5,𝔽2)11yescharacteristic
477C23C31×H(5,𝔽2)11yescharacteristic
478C23C31×H(5,𝔽2)12yes—
479C23C31×H(5,𝔽2)11yescharacteristic
480C23C31×H(5,𝔽2)12yes—
481C23C31×2−1+411yescharacteristic
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—416no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
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×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C22—24no—
536C22—28no—
537C22—42no—
538C22—44no—
539C22—42no—
540C22—44no—
541C22—42no—
542C22—42no—
543C22—44no—
544C22—42no—
545C22—42no—
546C22C2×C31×#12511yescharacteristic
547C22C31×#52912yes—
548C22C31×#53812yes—
549C22C31×#53811yescharacteristic
550C22C31×#53811yescharacteristic
551C22C31×#53812yes—
552C22C31×#53812yes—
553C22C31×#53911yescharacteristic
554C22C31×#53911yescharacteristic
555C22C31×#54012yes—
556C22C31×#54012yes—
557C22C31×#54311yescharacteristic
558C22C31×#54411yescharacteristic
559C22C31×#55112yes—
560C22C31×#55111yescharacteristic
561C22C31×#55112yes—
562C22C31×#55212yes—
563C22C31×#55412yes—
564C22C31×#55412yes—
565C22C31×#55911yescharacteristic
566C22C31×#56011yescharacteristic
567C22C31×H(3,𝔽4)11yescharacteristic
568C22C31×#56212yes—
569C4—44no—
570C4—44no—
571C4—42no—
572C4—42no—
573C4—82no—
574C4—82no—
575C4—82no—
576C4—82no—
577C2—44no—
578C2C31×#250512yes—
579C2C31×#251711yescharacteristic
580C2C31×#264611yescharacteristic
581C2C31×#264812yes—
582C2C31×#273611yescharacteristic
583C2C31×#274312yes—
584C2C31×#274811yescharacteristic
585C2C31×#275211yescharacteristic
586C2C31×#276812yes—
587C2C31×#280411yescharacteristic
588C2C31×#282411yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#1445C2semidirect
2. C31×#1442C2semidirect
3. C31×#1442C2semidirect
4. C31×#1442C2semidirect
153. #16707C31direct (N × H)
241. #1445C2×C31semidirect
242. #1442C2×C31semidirect
243. #1442C2×C31semidirect
244. #1442C2×C31semidirect
371. C31#16707direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#14452
C31×#14422
C31×#14392
C31×C22⋊#952
#1670731