Finite Group Databasebeta

← C31×#8347 #21465106

Subgroups — C31×#8347 #21465106

Order 7936.

906 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3492C211yesmaximal, characteristic
2C31×#1896C212yesmaximal, complemented
3C31×#1504C212yesmaximal, complemented
4C31×#1463C211yesmaximal, characteristic, complemented
5C31×#1436C211yesmaximal, characteristic, complemented
6C31×#554—22no—
7C31×#553—22no—
8C31×#552—22no—
9C31×#547—22no—
10C31×#544C411yescharacteristic, complemented
11C31×#539—21no—
12C31×#539C412yescomplemented
13C31×#537C411yescharacteristic, complemented
14C31×#525—21no—
15C31×#525—21no—
16C31×#525C2212yes—
17C31×#520—21no—
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C42×C31C2211yescharacteristic
20C2×C31×#104—22no—
21C31×#407C2212yes—
22C2×C31×#95—21no—
23C2×C31×#95—21no—
24C2×C31×#95C2211yescharacteristic
25C31×#339—22no—
26C31×#328—22no—
27C31×#327—22no—
28C31×#324—21no—
29C31×#324—21no—
30C2×#41×C31—21no—
31C2×#41×C31—21no—
32C2×#41×C31D412yes—
33C23×C4×C31—21no—
34C23×C4×C31—21no—
35C23×C4×C31D411yescharacteristic
36C23×C4×C31D411yescharacteristic
37C23×C4×C31C2311yescharacteristic
38C2×M16×C31—22no—
39C31×C4⋊Q8—22no—
40C31×#126—22no—
41C31×#126—22no—
42C31×#125—22no—
43C31×#125—22no—
44C31×#125—22no—
45C31×#123—22no—
46C31×#123—22no—
47C31×#123—22no—
48C31×#123—22no—
49C31×#123—22no—
50C31×C22⋊Q8—21no—
51C31×C22⋊Q8—21no—
52C31×C22⋊Q8—21no—
53C31×C22⋊Q8—22no—
54C31×C22⋊Q8—22no—
55C31×C22⋊Q8—21no—
56C31×C22⋊Q8—22no—
57C31×C22⋊Q8C2×C412yes—
58C31×C22⋊Q8D412yes—
59C31×#121—21no—
60C31×#121—21no—
61C31×#121—21no—
62C31×#121—22no—
63C31×#121—21no—
64C31×#121C2×C412yes—
65C31×#121D412yes—
66C31×#120—22no—
67C4×Q8×C31—22no—
68C4×D4×C31—22no—
69C4×D4×C31—22no—
70C4×D4×C31—22no—
71C4×D4×C31—22no—
72C4×D4×C31—22no—
73C4×D4×C31—22no—
74C4×D4×C31—22no—
75C31×#117—22no—
76C31×#117—21no—
77C31×#117—21no—
78C31×#117D412yes—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31C2×C411yescharacteristic
83C2×C4⋊C4×C31C2×C411yescharacteristic
84C2×C4⋊C4×C31D411yescharacteristic
85C2×C4⋊C4×C31D411yescharacteristic
86C2×C42×C31—22no—
87C2×C42×C31—42no—
88C31×#104—44no—
89C31×C22⋊C8—22no—
90C31×C22⋊C8—22no—
91C31×#95—24no—
92C31×#95—22no—
93C31×#95—42no—
94C24×C31C2×D411yescharacteristic
95#41×C31—42no—
96#41×C31—42no—
97#41×C31—42no—
98#41×C31—42no—
99#41×C31—81no—
100#41×C31—81no—
101C2×Q8×C31—21no—
102C2×Q8×C31—21no—
103C2×Q8×C31C22⋊C412yes—
104C2×D4×C31—21no—
105C2×D4×C31—22no—
106C2×D4×C31—22no—
107C2×D4×C31—22no—
108C2×D4×C31—21no—
109C2×D4×C31C22⋊C412yes—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—21no—
115C22×C4×C31—21no—
116C22×C4×C31—21no—
117C22×C4×C31—22no—
118C22×C4×C31—21no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—41no—
123C22×C4×C31—41no—
124C22×C4×C31—41no—
125C22×C4×C31—41no—
126C22×C4×C31—41no—
127C22×C4×C31—41no—
128C22×C4×C31—41no—
129C22×C4×C31—41no—
130C22×C4×C31—41no—
131C22×C4×C31—41no—
132C22×C4×C31—41no—
133C22×C4×C31—41no—
134C22×C4×C31—41no—
135C22×C4×C31—41no—
136C22×C4×C31—41no—
137C22×C4×C31C22⋊C411yescharacteristic
138C22×C4×C31C22⋊C411yescharacteristic
139C22×C4×C31C22⋊C411yescharacteristic
140C22×C4×C31C22⋊C411yescharacteristic
141C22×C4×C31C22×C411yescharacteristic
142C22×C4×C31C2×D412yes—
143C22×C4×C31C2×D412yes—
144C22×C4×C31C2×D411yescharacteristic
145M16×C31—42no—
146M16×C31—42no—
147C2×C8×C31—42no—
148C4⋊C4×C31—21no—
149C4⋊C4×C31—22no—
150C4⋊C4×C31—21no—
151C4⋊C4×C31—21no—
152C4⋊C4×C31—21no—
153C4⋊C4×C31—22no—
154C4⋊C4×C31—22no—
155C4⋊C4×C31—22no—
156C4⋊C4×C31—22no—
157C4⋊C4×C31—22no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—22no—
161C4⋊C4×C31—22no—
162C4⋊C4×C31C22⋊C412yes—
163C4⋊C4×C31C22⋊C412yes—
164C22⋊C4×C31—22no—
165C22⋊C4×C31—22no—
166C22⋊C4×C31—22no—
167C22⋊C4×C31—22no—
168C22⋊C4×C31—22no—
169C22⋊C4×C31—22no—
170C22⋊C4×C31—22no—
171C22⋊C4×C31—22no—
172C22⋊C4×C31—22no—
173C42×C31—22no—
174C42×C31—22no—
175C42×C31—22no—
176C42×C31—24no—
177C42×C31—42no—
178#8347C3111yesmaximal, characteristic, direct product factor, Sylow
179C23×C31—21no—
180C23×C31—21no—
181C23×C31—21no—
182C23×C31—21no—
183C23×C31—21no—
184C23×C31—21no—
185C23×C31—22no—
186C23×C31C2×C22⋊C411yescharacteristic
187C23×C31#12011yescharacteristic
188C23×C31#12011yescharacteristic
189Q8×C31—42no—
190Q8×C31—42no—
191Q8×C31—81no—
192D4×C31—42no—
193D4×C31—42no—
194D4×C31—42no—
195D4×C31—42no—
196D4×C31—42no—
197D4×C31—42no—
198D4×C31—42no—
199D4×C31—42no—
200D4×C31—81no—
201C2×C4×C31—21no—
202C2×C4×C31—21no—
203C2×C4×C31—22no—
204C2×C4×C31—22no—
205C2×C4×C31—24no—
206C2×C4×C31—22no—
207C2×C4×C31—22no—
208C2×C4×C31—21no—
209C2×C4×C31—22no—
210C2×C4×C31—21no—
211C2×C4×C31—21no—
212C2×C4×C31—21no—
213C2×C4×C31—21no—
214C2×C4×C31—41no—
215C2×C4×C31—41no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—44no—
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—41no—
227C2×C4×C31—41no—
228C2×C4×C31—41no—
229C2×C4×C31—41no—
230C2×C4×C31—42no—
231C2×C4×C31—42no—
232C2×C4×C31—42no—
233C2×C4×C31—82no—
234C2×C4×C31—81no—
235C2×C4×C31—82no—
236C2×C4×C31—81no—
237C2×C4×C31—81no—
238C2×C4×C31—81no—
239C2×C4×C31—81no—
240C2×C4×C31#10412yescomplemented
241C2×C4×C31C2×C22⋊C412yes—
242C2×C4×C31#12012yes—
243C8×C31—82no—
244#3492C2×C3111yescharacteristic
245#1896C2×C3112yescomplemented
246#1504C2×C3112yescomplemented
247#1463C2×C3111yescharacteristic, complemented
248#1436C2×C3111yescharacteristic, complemented
249C22×C31—21no—
250C22×C31—21no—
251C22×C31—21no—
252C22×C31—21no—
253C22×C31—21no—
254C22×C31—21no—
255C22×C31—21no—
256C22×C31—21no—
257C22×C31—21no—
258C22×C31—21no—
259C22×C31—21no—
260C22×C31—21no—
261C22×C31—21no—
262C22×C31—21no—
263C22×C31—42no—
264C22×C31—42no—
265C22×C31—42no—
266C22×C31#37911yescharacteristic
267C22×C31C2×#10411yescharacteristic
268C22×C31#42111yescharacteristic
269C22×C31#45411yescharacteristic
270C22×C31#45611yescharacteristic
271C22×C31B(4,𝔽2)11yescharacteristic
272C22×C31#45811yescharacteristic
273C4×C31—22no—
274C4×C31—22no—
275C4×C31—22no—
276C4×C31—44no—
277C4×C31—42no—
278C4×C31—41no—
279C4×C31—42no—
280C4×C31—41no—
281C4×C31—41no—
282C4×C31—42no—
283C4×C31—82no—
284#554—22no—
285#553—22no—
286#552—22no—
287#547—22no—
288#544C4×C3111yescharacteristic, complemented
289#539—21no—
290#539C4×C3112yescomplemented
291#537C4×C3111yescharacteristic, complemented
292#525—21no—
293#525—21no—
294#525C22×C3112yes—
295#520—21no—
296C22×C4⋊C4C22×C3111yescharacteristic
297C22×C42C22×C3111yescharacteristic
298C2×#104—22no—
299#407C22×C3112yes—
300C2×#95—21no—
301C2×#95—21no—
302C2×#95C22×C3111yescharacteristic
303#339—22no—
304#328—22no—
305#327—22no—
306#324—21no—
307#324—21no—
308C2×C31—21no—
309C2×C31—21no—
310C2×C31—21no—
311C2×C31—21no—
312C2×C31—21no—
313C2×C31—21no—
314C2×C31—82no—
315C2×C31#178911yescharacteristic
316C2×C31#179011yescharacteristic
317C2×C31#179311yescharacteristic
318C2×#41—21no—
319C2×#41—21no—
320C2×#41D4×C3112yes—
321C23×C4—21no—
322C23×C4—21no—
323C23×C4D4×C3111yescharacteristic
324C23×C4D4×C3111yescharacteristic
325C23×C4C23×C3111yescharacteristic
326C2×M16—22no—
327C4⋊Q8—22no—
328#126—22no—
329#126—22no—
330#125—22no—
331#125—22no—
332#125—22no—
333#123—22no—
334#123—22no—
335#123—22no—
336#123—22no—
337#123—22no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8—21no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—21no—
344C22⋊Q8—22no—
345C22⋊Q8C2×C4×C3112yes—
346C22⋊Q8D4×C3112yes—
347#121—21no—
348#121—21no—
349#121—21no—
350#121—22no—
351#121—21no—
352#121C2×C4×C3112yes—
353#121D4×C3112yes—
354#120—22no—
355C4×Q8—22no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363#117—22no—
364#117—21no—
365#117—21no—
366#117D4×C3112yes—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4C2×C4×C3111yescharacteristic
371C2×C4⋊C4C2×C4×C3111yescharacteristic
372C2×C4⋊C4D4×C3111yescharacteristic
373C2×C4⋊C4D4×C3111yescharacteristic
374C2×C42—22no—
375C2×C42—42no—
376#104—44no—
377C22⋊C8—22no—
378C22⋊C8—22no—
379#95—24no—
380#95—22no—
381#95—42no—
382C31#834711yescharacteristic, direct product factor, Sylow
383C24C2×D4×C3111yescharacteristic
384#41—42no—
385#41—42no—
386#41—42no—
387#41—42no—
388#41—81no—
389#41—81no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8C22⋊C4×C3112yes—
393C2×D4—21no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—21no—
398C2×D4C22⋊C4×C3112yes—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4C22⋊C4×C3111yescharacteristic
427C22×C4C22⋊C4×C3111yescharacteristic
428C22×C4C22⋊C4×C3111yescharacteristic
429C22×C4C22⋊C4×C3111yescharacteristic
430C22×C4C22×C4×C3111yescharacteristic
431C22×C4C2×D4×C3112yes—
432C22×C4C2×D4×C3112yes—
433C22×C4C2×D4×C3111yescharacteristic
434M16—42no—
435M16—42no—
436C2×C8—42no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4C22⋊C4×C3112yes—
452C4⋊C4C22⋊C4×C3112yes—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C42—22no—
463C42—22no—
464C42—22no—
465C42—24no—
466C42—42no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—22no—
474C23C2×C22⋊C4×C3111yescharacteristic
475C23C31×#12011yescharacteristic
476C23C31×#12011yescharacteristic
477Q8—42no—
478Q8—42no—
479Q8—81no—
480D4—42no—
481D4—42no—
482D4—42no—
483D4—42no—
484D4—42no—
485D4—42no—
486D4—42no—
487D4—42no—
488D4—81no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—44no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—82no—
522C2×C4—81no—
523C2×C4—82no—
524C2×C4—81no—
525C2×C4—81no—
526C2×C4—81no—
527C2×C4—81no—
528C2×C4C31×#10412yescomplemented
529C2×C4C2×C22⋊C4×C3112yes—
530C2×C4C31×#12012yes—
531C8—82no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22C31×#37911yescharacteristic
550C22C2×C31×#10411yescharacteristic
551C22C31×#42111yescharacteristic
552C22C31×#45411yescharacteristic
553C22C31×#45611yescharacteristic
554C22C31×B(4,𝔽2)11yescharacteristic
555C22C31×#45811yescharacteristic
556C4—22no—
557C4—22no—
558C4—22no—
559C4—44no—
560C4—41no—
561C4—42no—
562C4—41no—
563C4—41no—
564C4—42no—
565C4—42no—
566C4—82no—
567C2—21no—
568C2—21no—
569C2—21no—
570C2—21no—
571C2—21no—
572C2—21no—
573C2—82no—
574C2C31×#178911yescharacteristic
575C2C31×#179011yescharacteristic
576C2C31×#179311yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC31×#3492C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1896C2semidirect
3. C31×#1504C2semidirect
4. C31×#1463C2semidirect
5. C31×#1436C2semidirect
10. C31×#544C4semidirect
12. C31×#539C4semidirect
13. C31×#537C4semidirect
178. #8347C31direct (N × H)
240. C2×C4×C31#104semidirect
245. #1896C2×C31semidirect
246. #1504C2×C31semidirect
247. #1463C2×C31semidirect
248. #1436C2×C31semidirect
288. #544C4×C31semidirect
290. #539C4×C31semidirect
291. #537C4×C31semidirect
382. C31#8347direct (N × H)
528. C2×C4C31×#104semidirect

Maximal subgroups

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

subgroupindex
C31×#34922
C31×#18962
C31×#15042
C31×#14632
C31×#14362
#834731