Finite Group Databasebeta

← C31×#17091 #21473850

Subgroups — C31×#17091 #21473850

Order 7936.

2430 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#396C211yesmaximal, characteristic, complemented
2C2×C31×#394C213yesmaximal, complemented
3C2×C31×#392C213yesmaximal, complemented
4C2×C31×#392C211yesmaximal, characteristic, complemented
5C31×#1443C211yesmaximal, characteristic, complemented
6C31×#1439C213yesmaximal, complemented
7C31×#1438C213yesmaximal, complemented
8C23×D4×C31C2213yes—
9C23×D4×C31C2213yes—
10C22×C4⋊C4×C31C2213yes—
11C22×C22⋊C4×C31C2213yes—
12C22×C22⋊C4×C31C2213yes—
13C22×C22⋊C4×C31C2213yes—
14C22×C22⋊C4×C31C2213yes—
15C22×C22⋊C4×C31C2211yescharacteristic
16C22×C22⋊C4×C31C2213yes—
17C31×#396—24no—
18C31×#394—212no—
19C31×#392—212no—
20C31×#392—24no—
21C2×C31×#95C2213yes—
22C2×C31×#95C2213yes—
23C2×C31×#95C2213yes—
24C2×C31×#95C2211yescharacteristic
25C25×C31C2313yes—
26C25×C31C2311yescharacteristic
27C22×D4×C31—26no—
28C22×D4×C31—26no—
29C22×D4×C31—26no—
30C22×D4×C31—26no—
31C22×D4×C31—26no—
32C22×D4×C31—26no—
33C22×D4×C31—43no—
34C22×D4×C31—43no—
35C22×D4×C31—43no—
36C22×D4×C31—43no—
37C22×D4×C31—43no—
38C22×D4×C31—43no—
39C22×D4×C31—43no—
40C22×D4×C31—43no—
41C23×C4×C31C2311yescharacteristic
42C23×C4×C31C2311yescharacteristic
43C23×C4×C31C2313yes—
44C23×C4×C31C2313yes—
45C23×C4×C31C2313yes—
46C2×C4⋊C4×C31—26no—
47C2×C4⋊C4×C31—26no—
48C2×C4⋊C4×C31—43no—
49C2×C22⋊C4×C31—26no—
50C2×C22⋊C4×C31—26no—
51C2×C22⋊C4×C31—26no—
52C2×C22⋊C4×C31—26no—
53C2×C22⋊C4×C31—26no—
54C2×C22⋊C4×C31—26no—
55C2×C22⋊C4×C31—26no—
56C2×C22⋊C4×C31—43no—
57C2×C22⋊C4×C31—43no—
58C2×C22⋊C4×C31—43no—
59C2×C22⋊C4×C31—43no—
60C2×C22⋊C4×C31—43no—
61C2×C22⋊C4×C31—43no—
62C2×C22⋊C4×C31—43no—
63C2×C22⋊C4×C31—43no—
64C2×C22⋊C4×C31D4112yescomplemented
65C31×#95—26no—
66C31×#95—26no—
67C31×#95—43no—
68C31×#95D414yescomplemented
69C24×C31—21no—
70C24×C31—23no—
71C24×C31—23no—
72C24×C31—23no—
73C24×C31—23no—
74C24×C31—23no—
75C24×C31—23no—
76C24×C31—23no—
77C24×C31—23no—
78C24×C31—23no—
79C24×C31—23no—
80C24×C31—23no—
81C24×C31—23no—
82C24×C31—23no—
83C24×C31—23no—
84C24×C31—23no—
85C24×C31—23no—
86C24×C31—23no—
87C24×C31—23no—
88C24×C31—21no—
89C24×C31C2×D416yes—
90C24×C31#4112yes—
91C24×C31C2411yescharacteristic
92C2×D4×C31—412no—
93C2×D4×C31—412no—
94C2×D4×C31—412no—
95C2×D4×C31—412no—
96C2×D4×C31—412no—
97C2×D4×C31—412no—
98C2×D4×C31—412no—
99C2×D4×C31—412no—
100C2×D4×C31—412no—
101C2×D4×C31—412no—
102C2×D4×C31—412no—
103C2×D4×C31—412no—
104C2×D4×C31—412no—
105C2×D4×C31—412no—
106C22×C4×C31—23no—
107C22×C4×C31—23no—
108C22×C4×C31—23no—
109C22×C4×C31—23no—
110C22×C4×C31—23no—
111C22×C4×C31—23no—
112C22×C4×C31—23no—
113C22×C4×C31—23no—
114C22×C4×C31—23no—
115C22×C4×C31—23no—
116C22×C4×C31—23no—
117C22×C4×C31—23no—
118C22×C4×C31—23no—
119C22×C4×C31—23no—
120C22×C4×C31—23no—
121C22×C4×C31—23no—
122C22×C4×C31—23no—
123C22×C4×C31—23no—
124C22×C4×C31—23no—
125C22×C4×C31—21no—
126C22×C4×C31—23no—
127C22×C4×C31—23no—
128C22×C4×C31—23no—
129C22×C4×C31—21no—
130C22×C4×C31C2×D416yes—
131C22×C4×C31C2×D416yes—
132C22×C4×C31C2×D416yes—
133C4⋊C4×C31—412no—
134C22⋊C4×C31—412no—
135C22⋊C4×C31—412no—
136C22⋊C4×C31—412no—
137C22⋊C4×C31—412no—
138C22⋊C4×C31—412no—
139C22⋊C4×C31—44no—
140#17091C3111yesmaximal, characteristic, direct product factor, Sylow
141C23×C31—26no—
142C23×C31—26no—
143C23×C31—26no—
144C23×C31—26no—
145C23×C31—26no—
146C23×C31—26no—
147C23×C31—26no—
148C23×C31—26no—
149C23×C31—26no—
150C23×C31—22no—
151C23×C31—43no—
152C23×C31—43no—
153C23×C31—43no—
154C23×C31—43no—
155C23×C31—43no—
156C23×C31—43no—
157C23×C31—43no—
158C23×C31—43no—
159C23×C31—43no—
160C23×C31—43no—
161C23×C31—43no—
162C23×C31—43no—
163C23×C31—43no—
164C23×C31—43no—
165C23×C31—43no—
166C23×C31—43no—
167C23×C31—43no—
168C23×C31—43no—
169C23×C31—43no—
170C23×C31—43no—
171C23×C31—43no—
172C23×C31—43no—
173C23×C31—43no—
174C23×C31—43no—
175C23×C31—41no—
176C23×C31—43no—
177C23×C31—43no—
178C23×C31—43no—
179C23×C31—43no—
180C23×C31—43no—
181C23×C31—43no—
182C23×C31—43no—
183C23×C31—43no—
184C23×C31—43no—
185C23×C31—43no—
186C23×C31—43no—
187C23×C31—43no—
188C23×C31—43no—
189C23×C31C22×D413yes—
190C23×C31C22×D411yescharacteristic
191C23×C31C2×#4111yescharacteristic
192C23×C31H(5,𝔽2)13yes—
193C23×C31H(5,𝔽2)13yes—
194C23×C31H(5,𝔽2)13yes—
195C23×C312−1+411yescharacteristic
196D4×C31—448no—
197D4×C31—448no—
198C2×C4×C31—26no—
199C2×C4×C31—26no—
200C2×C4×C31—26no—
201C2×C4×C31—26no—
202C2×C4×C31—26no—
203C2×C4×C31—26no—
204C2×C4×C31—26no—
205C2×C4×C31—26no—
206C2×C4×C31—26no—
207C2×C4×C31—43no—
208C2×C4×C31—43no—
209C2×C4×C31—43no—
210C2×C4×C31—43no—
211C2×C4×C31—43no—
212C2×C4×C31—43no—
213C2×C4×C31—43no—
214C2×C4×C31—43no—
215C2×C4×C31—43no—
216C2×C4×C31—43no—
217C2×C4×C31—43no—
218C2×C4×C31—43no—
219C2×C4×C31—43no—
220C2×C4×C31—43no—
221C2×C4×C31—43no—
222C2×C4×C31—41no—
223C2×C4×C31—41no—
224C2×C4×C31—43no—
225C2×#396C2×C3111yescharacteristic, complemented
226C2×#394C2×C3113yescomplemented
227C2×#392C2×C3113yescomplemented
228C2×#392C2×C3111yescharacteristic, complemented
229#1443C2×C3111yescharacteristic, complemented
230#1439C2×C3113yescomplemented
231#1438C2×C3113yescomplemented
232C22×C31—42no—
233C22×C31—46no—
234C22×C31—46no—
235C22×C31—46no—
236C22×C31—46no—
237C22×C31—46no—
238C22×C31—46no—
239C22×C31—46no—
240C22×C31—46no—
241C22×C31—46no—
242C22×C31—83no—
243C22×C31—81no—
244C22×C31—83no—
245C22×C31—83no—
246C22×C31—83no—
247C22×C31—81no—
248C22×C31—83no—
249C22×C31—83no—
250C22×C31—83no—
251C22×C31—83no—
252C22×C31—83no—
253C22×C31—83no—
254C22×C31#53413yes—
255C22×C31#53513yes—
256C22×C31#53513yes—
257C22×C31#53713yes—
258C22×C31#53813yes—
259C22×C31D4213yes—
260C22×C31D4213yes—
261C22×C31#54613yes—
262C22×C31#54811yescharacteristic
263C22×C31#56011yescharacteristic
264C22×C31#56013yes—
265C22×C31#56013yes—
266C22×C31#56213yes—
267C4×C31—46no—
268C4×C31—46no—
269C4×C31—46no—
270C4×C31—81no—
271C4×C31—81no—
272C23×D4C22×C3113yes—
273C23×D4C22×C3113yes—
274C22×C4⋊C4C22×C3113yes—
275C22×C22⋊C4C22×C3113yes—
276C22×C22⋊C4C22×C3113yes—
277C22×C22⋊C4C22×C3113yes—
278C22×C22⋊C4C22×C3113yes—
279C22×C22⋊C4C22×C3111yescharacteristic
280C22×C22⋊C4C22×C3113yes—
281#396—24no—
282#394—212no—
283#392—212no—
284#392—24no—
285C2×#95C22×C3113yes—
286C2×#95C22×C3113yes—
287C2×#95C22×C3113yes—
288C2×#95C22×C3111yescharacteristic
289C2×C31—82no—
290C2×C31—86no—
291C2×C31#266913yes—
292C2×C31#267511yescharacteristic
293C2×C31#267613yes—
294C2×C31#267813yes—
295C2×C31#281313yes—
296C2×C31#281811yescharacteristic
297C2×C31#282511yescharacteristic
298C25C23×C3113yes—
299C25C23×C3111yescharacteristic
300C22×D4—26no—
301C22×D4—26no—
302C22×D4—26no—
303C22×D4—26no—
304C22×D4—26no—
305C22×D4—26no—
306C22×D4—43no—
307C22×D4—43no—
308C22×D4—43no—
309C22×D4—43no—
310C22×D4—43no—
311C22×D4—43no—
312C22×D4—43no—
313C22×D4—43no—
314C23×C4C23×C3111yescharacteristic
315C23×C4C23×C3111yescharacteristic
316C23×C4C23×C3113yes—
317C23×C4C23×C3113yes—
318C23×C4C23×C3113yes—
319C2×C4⋊C4—26no—
320C2×C4⋊C4—26no—
321C2×C4⋊C4—43no—
322C2×C22⋊C4—26no—
323C2×C22⋊C4—26no—
324C2×C22⋊C4—26no—
325C2×C22⋊C4—26no—
326C2×C22⋊C4—26no—
327C2×C22⋊C4—26no—
328C2×C22⋊C4—26no—
329C2×C22⋊C4—43no—
330C2×C22⋊C4—43no—
331C2×C22⋊C4—43no—
332C2×C22⋊C4—43no—
333C2×C22⋊C4—43no—
334C2×C22⋊C4—43no—
335C2×C22⋊C4—43no—
336C2×C22⋊C4—43no—
337C2×C22⋊C4D4×C31112yescomplemented
338#95—26no—
339#95—26no—
340#95—43no—
341#95D4×C3114yescomplemented
342C31#1709111yescharacteristic, direct product factor, Sylow
343C24—21no—
344C24—23no—
345C24—23no—
346C24—23no—
347C24—23no—
348C24—23no—
349C24—23no—
350C24—23no—
351C24—23no—
352C24—23no—
353C24—23no—
354C24—23no—
355C24—23no—
356C24—23no—
357C24—23no—
358C24—23no—
359C24—23no—
360C24—23no—
361C24—23no—
362C24—21no—
363C24C2×D4×C3116yes—
364C24#41×C3112yes—
365C24C24×C3111yescharacteristic
366C2×D4—412no—
367C2×D4—412no—
368C2×D4—412no—
369C2×D4—412no—
370C2×D4—412no—
371C2×D4—412no—
372C2×D4—412no—
373C2×D4—412no—
374C2×D4—412no—
375C2×D4—412no—
376C2×D4—412no—
377C2×D4—412no—
378C2×D4—412no—
379C2×D4—412no—
380C22×C4—23no—
381C22×C4—23no—
382C22×C4—23no—
383C22×C4—23no—
384C22×C4—23no—
385C22×C4—23no—
386C22×C4—23no—
387C22×C4—23no—
388C22×C4—23no—
389C22×C4—23no—
390C22×C4—23no—
391C22×C4—23no—
392C22×C4—23no—
393C22×C4—23no—
394C22×C4—23no—
395C22×C4—23no—
396C22×C4—23no—
397C22×C4—23no—
398C22×C4—23no—
399C22×C4—21no—
400C22×C4—23no—
401C22×C4—23no—
402C22×C4—23no—
403C22×C4—21no—
404C22×C4C2×D4×C3116yes—
405C22×C4C2×D4×C3116yes—
406C22×C4C2×D4×C3116yes—
407C4⋊C4—412no—
408C22⋊C4—412no—
409C22⋊C4—412no—
410C22⋊C4—412no—
411C22⋊C4—412no—
412C22⋊C4—412no—
413C22⋊C4—44no—
414C23—26no—
415C23—26no—
416C23—26no—
417C23—26no—
418C23—26no—
419C23—26no—
420C23—26no—
421C23—26no—
422C23—26no—
423C23—22no—
424C23—43no—
425C23—43no—
426C23—43no—
427C23—43no—
428C23—43no—
429C23—43no—
430C23—43no—
431C23—43no—
432C23—43no—
433C23—43no—
434C23—43no—
435C23—43no—
436C23—43no—
437C23—43no—
438C23—43no—
439C23—43no—
440C23—43no—
441C23—43no—
442C23—43no—
443C23—43no—
444C23—43no—
445C23—43no—
446C23—43no—
447C23—43no—
448C23—41no—
449C23—43no—
450C23—43no—
451C23—43no—
452C23—43no—
453C23—43no—
454C23—43no—
455C23—43no—
456C23—43no—
457C23—43no—
458C23—43no—
459C23—43no—
460C23—43no—
461C23—43no—
462C23C22×D4×C3113yes—
463C23C22×D4×C3111yescharacteristic
464C23C2×#41×C3111yescharacteristic
465C23C31×H(5,𝔽2)13yes—
466C23C31×H(5,𝔽2)13yes—
467C23C31×H(5,𝔽2)13yes—
468C23C31×2−1+411yescharacteristic
469D4—448no—
470D4—448no—
471C2×C4—26no—
472C2×C4—26no—
473C2×C4—26no—
474C2×C4—26no—
475C2×C4—26no—
476C2×C4—26no—
477C2×C4—26no—
478C2×C4—26no—
479C2×C4—26no—
480C2×C4—43no—
481C2×C4—43no—
482C2×C4—43no—
483C2×C4—43no—
484C2×C4—43no—
485C2×C4—43no—
486C2×C4—43no—
487C2×C4—43no—
488C2×C4—43no—
489C2×C4—43no—
490C2×C4—43no—
491C2×C4—43no—
492C2×C4—43no—
493C2×C4—43no—
494C2×C4—43no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—43no—
498C22—42no—
499C22—46no—
500C22—46no—
501C22—46no—
502C22—46no—
503C22—46no—
504C22—46no—
505C22—46no—
506C22—46no—
507C22—46no—
508C22—83no—
509C22—83no—
510C22—83no—
511C22—81no—
512C22—83no—
513C22—83no—
514C22—83no—
515C22—83no—
516C22—83no—
517C22—83no—
518C22—83no—
519C22—81no—
520C22C31×#53413yes—
521C22C31×#53513yes—
522C22C31×#53513yes—
523C22C31×#53713yes—
524C22C31×#53813yes—
525C22D42×C3113yes—
526C22D42×C3113yes—
527C22C31×#54613yes—
528C22C31×#54811yescharacteristic
529C22C31×#56013yes—
530C22C31×#56011yescharacteristic
531C22C31×#56013yes—
532C22C31×#56213yes—
533C4—46no—
534C4—46no—
535C4—46no—
536C4—81no—
537C4—81no—
538C2—82no—
539C2—86no—
540C2C31×#266913yes—
541C2C31×#267511yescharacteristic
542C2C31×#267613yes—
543C2C31×#267813yes—
544C2C31×#281313yes—
545C2C31×#281811yescharacteristic
546C2C31×#282511yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#396C2semidirect
2. C2×C31×#394C2semidirect
3. C2×C31×#392C2semidirect
4. C2×C31×#392C2semidirect
5. C31×#1443C2semidirect
6. C31×#1439C2semidirect
7. C31×#1438C2semidirect
64. C2×C22⋊C4×C31D4semidirect
68. C31×#95D4semidirect
140. #17091C31direct (N × H)
225. C2×#396C2×C31semidirect
226. C2×#394C2×C31semidirect
227. C2×#392C2×C31semidirect
228. C2×#392C2×C31semidirect
229. #1443C2×C31semidirect
230. #1439C2×C31semidirect
231. #1438C2×C31semidirect
337. C2×C22⋊C4D4×C31semidirect
341. #95D4×C31semidirect
342. C31#17091direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3962
C2×C31×#3942
C2×C31×#3922
C31×#14432
C31×#14392
C31×#14382
#1709131