Finite Group Databasebeta

← C31×#8858 #21465617

Subgroups — C31×#8858 #21465617

Order 7936.

692 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2312C211yesmaximal, characteristic
2C31×#1853C211yesmaximal, characteristic, complemented
3C31×#1852C211yesmaximal, characteristic, complemented
4C2×C31×#323C211yesmaximal, characteristic
5C31×#1439C211yesmaximal, characteristic
6C31×#1294C211yesmaximal, characteristic, complemented
7C31×#1294C211yesmaximal, characteristic, complemented
8C22×C4⋊C4×C31C2211yescharacteristic
9C22×C22⋊C4×C31—21no—
10C22×C22⋊C4×C31C2211yescharacteristic
11C2×C31×#107—21no—
12C2×C31×#106—21no—
13C2×C31×C22⋊C8C2211yescharacteristic
14C2×C31×C22⋊C8C2211yescharacteristic
15C31×#388—21no—
16C31×#388—21no—
17C31×#388—21no—
18C31×#388—21no—
19C31×#380C2211yescharacteristic
20C31×#380C2211yescharacteristic
21C31×#379—21no—
22C4×C22⋊C4×C31—21no—
23C2×C31×#95—21no—
24C2×C31×#95C2211yescharacteristic
25C31×#340—21no—
26C31×#340—21no—
27C31×#323C414yescomplemented
28C25×C31D411yescharacteristic
29C23×C4×C31—21no—
30C23×C4×C31—21no—
31C23×C4×C31D411yescharacteristic
32C23×C4×C31C2311yescharacteristic
33C22×C8×C31—21no—
34C22×C8×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31—42no—
38C2×C4⋊C4×C31D411yescharacteristic
39C2×C4⋊C4×C31D411yescharacteristic
40C2×C4⋊C4×C31D411yescharacteristic
41C2×C4⋊C4×C31D411yescharacteristic
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31—21no—
48C2×C22⋊C4×C31—21no—
49C2×C22⋊C4×C31—21no—
50C2×C22⋊C4×C31—21no—
51C2×C22⋊C4×C31—21no—
52C2×C22⋊C4×C31—42no—
53C2×C22⋊C4×C31—42no—
54C2×C22⋊C4×C31—42no—
55C2×C22⋊C4×C31C2×C412yes—
56C2×C22⋊C4×C31Q812yes—
57C2×C42×C31—21no—
58C2×C42×C31—21no—
59C31×#107—42no—
60C31×#106—42no—
61C31×C22⋊C8—21no—
62C31×C22⋊C8—21no—
63C31×C22⋊C8C2×C412yes—
64C31×C22⋊C8C2×C412yes—
65C31×#95—21no—
66C31×#95—21no—
67C31×#95—21no—
68C31×#95—21no—
69C31×#95—21no—
70C31×#95—21no—
71C31×#95—42no—
72C24×C31—21no—
73C24×C31—21no—
74C24×C31—21no—
75C24×C31—21no—
76C24×C31—21no—
77C24×C31—21no—
78C24×C31—41no—
79C24×C31—41no—
80C24×C31—41no—
81C24×C31—41no—
82C24×C31C4⋊C412yes—
83C24×C31C2×D411yescharacteristic
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—22no—
87C22×C4×C31—22no—
88C22×C4×C31—21no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—41no—
93C22×C4×C31—41no—
94C22×C4×C31—41no—
95C22×C4×C31—41no—
96C22×C4×C31—41no—
97C22×C4×C31—41no—
98C22×C4×C31—41no—
99C22×C4×C31—41no—
100C22×C4×C31—41no—
101C22×C4×C31—41no—
102C22×C4×C31—41no—
103C22×C4×C31—41no—
104C22×C4×C31—41no—
105C22×C4×C31—41no—
106C22×C4×C31—41no—
107C22×C4×C31—41no—
108C22×C4×C31C4⋊C412yes—
109C22×C4×C31C22×C411yescharacteristic
110C22×C4×C31C2×D411yescharacteristic
111C22×C4×C31C2×D411yescharacteristic
112C22×C4×C31C2×Q811yescharacteristic
113C22×C4×C31#4111yescharacteristic
114C22×C4×C31#4111yescharacteristic
115C2×C8×C31—22no—
116C2×C8×C31—22no—
117C2×C8×C31—41no—
118C2×C8×C31—41no—
119C2×C8×C31—41no—
120C2×C8×C31—41no—
121C4⋊C4×C31—22no—
122C4⋊C4×C31—22no—
123C4⋊C4×C31—41no—
124C4⋊C4×C31—41no—
125C4⋊C4×C31—41no—
126C4⋊C4×C31—41no—
127C4⋊C4×C31—41no—
128C4⋊C4×C31—41no—
129C22⋊C4×C31—22no—
130C22⋊C4×C31—22no—
131C22⋊C4×C31—22no—
132C22⋊C4×C31—22no—
133C22⋊C4×C31—48no—
134C22⋊C4×C31—41no—
135C22⋊C4×C31—41no—
136C22⋊C4×C31—41no—
137C22⋊C4×C31—41no—
138C22⋊C4×C31—81no—
139C22⋊C4×C31—81no—
140C22⋊C4×C31—81no—
141C22⋊C4×C31—81no—
142C42×C31—81no—
143C42×C31—81no—
144#8858C3111yesmaximal, characteristic, direct product factor, Sylow
145C23×C31—21no—
146C23×C31—21no—
147C23×C31—21no—
148C23×C31—21no—
149C23×C31—22no—
150C23×C31—22no—
151C23×C31—22no—
152C23×C31—42no—
153C23×C31—42no—
154C23×C31—42no—
155C23×C31—42no—
156C23×C31—42no—
157C23×C31—42no—
158C23×C31—41no—
159C23×C31—41no—
160C23×C31—41no—
161C23×C31—41no—
162C23×C31—41no—
163C23×C31—41no—
164C23×C31—41no—
165C23×C31—41no—
166C23×C31—81no—
167C23×C31—81no—
168C23×C31—81no—
169C23×C31—81no—
170C23×C31—81no—
171C23×C31—81no—
172C23×C31C2×C4⋊C411yescharacteristic
173C23×C31#12011yescharacteristic
174C23×C31#12311yescharacteristic
175C23×C31#13511yescharacteristic
176C23×C31#13511yescharacteristic
177C23×C31AGL(1,ℤ/8)11yescharacteristic
178C23×C31#13711yescharacteristic
179C2×C4×C31—21no—
180C2×C4×C31—21no—
181C2×C4×C31—21no—
182C2×C4×C31—21no—
183C2×C4×C31—22no—
184C2×C4×C31—41no—
185C2×C4×C31—41no—
186C2×C4×C31—41no—
187C2×C4×C31—41no—
188C2×C4×C31—41no—
189C2×C4×C31—41no—
190C2×C4×C31—42no—
191C2×C4×C31—42no—
192C2×C4×C31—42no—
193C2×C4×C31—42no—
194C2×C4×C31—42no—
195C2×C4×C31—42no—
196C2×C4×C31—41no—
197C2×C4×C31—41no—
198C2×C4×C31—41no—
199C2×C4×C31—41no—
200C2×C4×C31—41no—
201C2×C4×C31—41no—
202C2×C4×C31—41no—
203C2×C4×C31—41no—
204C2×C4×C31—41no—
205C2×C4×C31—41no—
206C2×C4×C31—42no—
207C2×C4×C31—41no—
208C2×C4×C31—41no—
209C2×C4×C31—81no—
210C2×C4×C31—81no—
211C2×C4×C31—81no—
212C2×C4×C31—81no—
213C2×C4×C31—81no—
214C2×C4×C31—81no—
215C2×C4×C31—81no—
216C2×C4×C31—81no—
217C2×C4×C31—81no—
218C2×C4×C31C4×D411yescharacteristic
219C2×C4×C31C4×D411yescharacteristic
220C2×C4×C31C22⋊Q811yescharacteristic
221C2×C4×C31C22⋊Q811yescharacteristic
222C8×C31—42no—
223C8×C31—42no—
224#2312C2×C3111yescharacteristic
225#1853C2×C3111yescharacteristic, complemented
226#1852C2×C3111yescharacteristic, complemented
227C2×#323C2×C3111yescharacteristic
228#1439C2×C3111yescharacteristic
229#1294C2×C3111yescharacteristic, complemented
230#1294C2×C3111yescharacteristic, complemented
231C22×C31—21no—
232C22×C31—21no—
233C22×C31—21no—
234C22×C31—21no—
235C22×C31—21no—
236C22×C31—21no—
237C22×C31—21no—
238C22×C31—21no—
239C22×C31—21no—
240C22×C31—21no—
241C22×C31—21no—
242C22×C31—21no—
243C22×C31—44no—
244C22×C31—42no—
245C22×C31—42no—
246C22×C31—42no—
247C22×C31—82no—
248C22×C31—82no—
249C22×C31—82no—
250C22×C31—81no—
251C22×C31—81no—
252C22×C31—81no—
253C22×C31—81no—
254C22×C31#38511yescharacteristic
255C22×C31#42711yescharacteristic
256C22×C31#42811yescharacteristic
257C22×C31#44911yescharacteristic
258C22×C31#45211yescharacteristic
259C22×C31#45311yescharacteristic
260C22×C31#45511yescharacteristic
261C22×C31B(4,𝔽2)11yescharacteristic
262C22×C31#45811yescharacteristic
263C22×C31#48211yescharacteristic
264C22×C31#48511yescharacteristic
265C4×C31—21no—
266C4×C31—21no—
267C4×C31—21no—
268C4×C31—21no—
269C4×C31—42no—
270C4×C31—82no—
271C4×C31—81no—
272C4×C31—82no—
273C4×C31—81no—
274C4×C31—81no—
275C4×C31—81no—
276C22×C4⋊C4C22×C3111yescharacteristic
277C22×C22⋊C4—21no—
278C22×C22⋊C4C22×C3111yescharacteristic
279C2×#107—21no—
280C2×#106—21no—
281C2×C22⋊C8C22×C3111yescharacteristic
282C2×C22⋊C8C22×C3111yescharacteristic
283#388—21no—
284#388—21no—
285#388—21no—
286#388—21no—
287#380C22×C3111yescharacteristic
288#380C22×C3111yescharacteristic
289#379—21no—
290C4×C22⋊C4—21no—
291C2×#95—21no—
292C2×#95C22×C3111yescharacteristic
293#340—21no—
294#340—21no—
295#323C4×C3114yescomplemented
296C2×C31—21no—
297C2×C31—21no—
298C2×C31—21no—
299C2×C31—21no—
300C2×C31—82no—
301C2×C31#160011yescharacteristic
302C2×C31#160611yescharacteristic
303C2×C31#161211yescharacteristic
304C2×C31#161811yescharacteristic
305C2×C31#185411yescharacteristic
306C2×C31#185611yescharacteristic
307C2×C31#186711yescharacteristic
308C25D4×C3111yescharacteristic
309C23×C4—21no—
310C23×C4—21no—
311C23×C4D4×C3111yescharacteristic
312C23×C4C23×C3111yescharacteristic
313C22×C8—21no—
314C22×C8—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4D4×C3111yescharacteristic
319C2×C4⋊C4D4×C3111yescharacteristic
320C2×C4⋊C4D4×C3111yescharacteristic
321C2×C4⋊C4D4×C3111yescharacteristic
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4C2×C4×C3112yes—
336C2×C22⋊C4Q8×C3112yes—
337C2×C42—21no—
338C2×C42—21no—
339#107—42no—
340#106—42no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8C2×C4×C3112yes—
344C22⋊C8C2×C4×C3112yes—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—21no—
351#95—42no—
352C31#885811yescharacteristic, direct product factor, Sylow
353C24—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—21no—
359C24—41no—
360C24—41no—
361C24—41no—
362C24—41no—
363C24C4⋊C4×C3112yes—
364C24C2×D4×C3111yescharacteristic
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4C4⋊C4×C3112yes—
390C22×C4C22×C4×C3111yescharacteristic
391C22×C4C2×D4×C3111yescharacteristic
392C22×C4C2×D4×C3111yescharacteristic
393C22×C4C2×Q8×C3111yescharacteristic
394C22×C4#41×C3111yescharacteristic
395C22×C4#41×C3111yescharacteristic
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—41no—
399C2×C8—41no—
400C2×C8—41no—
401C2×C8—41no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—48no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—81no—
420C22⋊C4—81no—
421C22⋊C4—81no—
422C22⋊C4—81no—
423C42—81no—
424C42—81no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—22no—
430C23—22no—
431C23—22no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23—41no—
446C23—81no—
447C23—81no—
448C23—81no—
449C23—81no—
450C23—81no—
451C23—81no—
452C23C2×C4⋊C4×C3111yescharacteristic
453C23C31×#12011yescharacteristic
454C23C31×#12311yescharacteristic
455C23C31×#13511yescharacteristic
456C23C31×#13511yescharacteristic
457C23C31×AGL(1,ℤ/8)11yescharacteristic
458C23C31×#13711yescharacteristic
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4—81no—
498C2×C4C4×D4×C3111yescharacteristic
499C2×C4C4×D4×C3111yescharacteristic
500C2×C4C31×C22⋊Q811yescharacteristic
501C2×C4C31×C22⋊Q811yescharacteristic
502C8—42no—
503C8—42no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—44no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—82no—
521C22—82no—
522C22—82no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22C31×#38511yescharacteristic
528C22C31×#42711yescharacteristic
529C22C31×#42811yescharacteristic
530C22C31×#44911yescharacteristic
531C22C31×#45211yescharacteristic
532C22C31×#45311yescharacteristic
533C22C31×#45511yescharacteristic
534C22C31×B(4,𝔽2)11yescharacteristic
535C22C31×#45811yescharacteristic
536C22C31×#48211yescharacteristic
537C22C31×#48511yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—42no—
543C4—82no—
544C4—82no—
545C4—81no—
546C4—81no—
547C4—81no—
548C4—81no—
549C2—21no—
550C2—21no—
551C2—21no—
552C2—21no—
553C2—82no—
554C2C31×#160011yescharacteristic
555C2C31×#160611yescharacteristic
556C2C31×#161211yescharacteristic
557C2C31×#161811yescharacteristic
558C2C31×#185411yescharacteristic
559C2C31×#185611yescharacteristic
560C2C31×#186711yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1853C2semidirect
3. C31×#1852C2semidirect
6. C31×#1294C2semidirect
7. C31×#1294C2semidirect
27. C31×#323C4semidirect
144. #8858C31direct (N × H)
225. #1853C2×C31semidirect
226. #1852C2×C31semidirect
229. #1294C2×C31semidirect
230. #1294C2×C31semidirect
295. #323C4×C31semidirect
352. C31#8858direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23122
C31×#18532
C31×#18522
C2×C31×#3232
C31×#14392
C31×#12942
#885831