Finite Group Databasebeta

← C31×#8466 #21465225

Subgroups — C31×#8466 #21465225

Order 7936.

798 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3494C211yesmaximal, characteristic
2C31×#1964C211yesmaximal, characteristic, complemented
3C31×#1826C211yesmaximal, characteristic, complemented
4C31×#1825C211yesmaximal, characteristic, complemented
5C31×#1513C211yesmaximal, characteristic, complemented
6C31×#1501C211yesmaximal, characteristic, complemented
7C31×#1471C211yesmaximal, characteristic, complemented
8C31×#555—21no—
9C31×#553—21no—
10C31×#553—21no—
11C31×#551—22no—
12C31×#547—21no—
13C31×#546—22no—
14C31×#544C411yescharacteristic, complemented
15C31×#542—21no—
16C31×#540—21no—
17C31×#535C411yescharacteristic, complemented
18C31×#532—21no—
19C31×#529—21no—
20C31×#525C2211yescharacteristic
21C2×C31×#121C2211yescharacteristic
22C31×#520C411yescharacteristic, complemented
23C31×#518C411yescharacteristic, complemented
24C2×C31×#117C2211yescharacteristic
25C2×C31×#99—22no—
26C31×#407C2211yescharacteristic
27C2×C31×C22⋊C8C2211yescharacteristic
28C31×#380C2211yescharacteristic
29C4×C22⋊C4×C31C2211yescharacteristic
30C31×#340—21no—
31C31×#340—21no—
32C31×#339—21no—
33C31×#339—21no—
34C31×#328—21no—
35C31×#328—21no—
36C31×#327—21no—
37C31×#327—21no—
38C31×#323—22no—
39C2×#41×C31—22no—
40C2×#41×C31C2×C411yescharacteristic
41C22×D4×C31C2×C411yescharacteristic
42C22×D4×C31D412yes—
43C23×C4×C31C2311yescharacteristic
44C2×M16×C31—21no—
45C22×C8×C31—21no—
46C31×C4⋊Q8—21no—
47C31×C4⋊Q8—21no—
48C31×#127—21no—
49C31×#126—22no—
50C31×#126—22no—
51C31×#125—21no—
52C31×#125—21no—
53C31×#124—22no—
54C31×#124—22no—
55C31×#124—21no—
56C31×#123—22no—
57C31×#123—22no—
58C31×#123—22no—
59C31×#123—22no—
60C31×#123—21no—
61C31×C22⋊Q8—22no—
62C31×C22⋊Q8—22no—
63C31×C22⋊Q8D411yescharacteristic
64C31×C22⋊Q8D411yescharacteristic
65C31×#121—22no—
66C31×#121—22no—
67C31×#121—22no—
68C31×#121—21no—
69C31×#121—21no—
70C31×#121—21no—
71C31×#121—21no—
72C31×#121—21no—
73C31×#121—21no—
74C31×#121D411yescharacteristic
75C31×#121D411yescharacteristic
76C31×#120—22no—
77C31×#120—21no—
78C4×Q8×C31—21no—
79C4×D4×C31—22no—
80C4×D4×C31—22no—
81C4×D4×C31—21no—
82C4×D4×C31—22no—
83C4×D4×C31—21no—
84C4×D4×C31—21no—
85C4×D4×C31—21no—
86C4×D4×C31—21no—
87C4×D4×C31—21no—
88C4×D4×C31—21no—
89C31×#117—22no—
90C31×#117—21no—
91C31×#117—21no—
92C31×#117—21no—
93C31×#117C2×C411yescharacteristic
94C31×#117C2×C411yescharacteristic
95C31×#117C2×C411yescharacteristic
96C31×#117D411yescharacteristic
97C31×#117D411yescharacteristic
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31C2×C411yescharacteristic
101C2×C4⋊C4×C31D411yescharacteristic
102C2×C4⋊C4×C31D411yescharacteristic
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31D412yes—
108C2×C42×C31—21no—
109C2×C42×C31—21no—
110C31×#99—44no—
111C31×C22⋊C8—21no—
112C31×C22⋊C8—21no—
113C31×C22⋊C8—21no—
114C31×C22⋊C8—21no—
115C31×#95—21no—
116C31×#95—21no—
117C24×C31C22⋊C412yes—
118C24×C31C2×D411yescharacteristic
119#41×C31—42no—
120#41×C31—82no—
121#41×C31—82no—
122C2×Q8×C31—22no—
123C2×Q8×C31C22⋊C411yescharacteristic
124C2×D4×C31—21no—
125C2×D4×C31—21no—
126C2×D4×C31—22no—
127C2×D4×C31—22no—
128C2×D4×C31—22no—
129C2×D4×C31—21no—
130C2×D4×C31—22no—
131C2×D4×C31—21no—
132C2×D4×C31—21no—
133C2×D4×C31—42no—
134C2×D4×C31—42no—
135C2×D4×C31—42no—
136C2×D4×C31C22⋊C411yescharacteristic
137C22×C4×C31—21no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
143C22×C4×C31—42no—
144C22×C4×C31—41no—
145C22×C4×C31—41no—
146C22×C4×C31C22⋊C412yes—
147C22×C4×C31C22×C411yescharacteristic
148C22×C4×C31C2×D411yescharacteristic
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31C2×D411yescharacteristic
153M16×C31—42no—
154C2×C8×C31—42no—
155C2×C8×C31—41no—
156C2×C8×C31—41no—
157C4⋊C4×C31—22no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—22no—
161C4⋊C4×C31—21no—
162C4⋊C4×C31—21no—
163C4⋊C4×C31—21no—
164C4⋊C4×C31—21no—
165C4⋊C4×C31—21no—
166C4⋊C4×C31—21no—
167C4⋊C4×C31—42no—
168C4⋊C4×C31C22⋊C411yescharacteristic
169C4⋊C4×C31C22⋊C411yescharacteristic
170C4⋊C4×C31C22⋊C411yescharacteristic
171C4⋊C4×C31C22⋊C411yescharacteristic
172C4⋊C4×C31C22⋊C411yescharacteristic
173C4⋊C4×C31C22⋊C411yescharacteristic
174C22⋊C4×C31—22no—
175C22⋊C4×C31—22no—
176C22⋊C4×C31—22no—
177C22⋊C4×C31—22no—
178C22⋊C4×C31—22no—
179C22⋊C4×C31—21no—
180C22⋊C4×C31—21no—
181C22⋊C4×C31—21no—
182C22⋊C4×C31—21no—
183C22⋊C4×C31—21no—
184C22⋊C4×C31—21no—
185C22⋊C4×C31—21no—
186C22⋊C4×C31—22no—
187C22⋊C4×C31—22no—
188C22⋊C4×C31—21no—
189C22⋊C4×C31—21no—
190C22⋊C4×C31—22no—
191C22⋊C4×C31—41no—
192C22⋊C4×C31—42no—
193C42×C31—22no—
194C42×C31—21no—
195C42×C31—21no—
196C42×C31—21no—
197C42×C31—21no—
198C42×C31—21no—
199C42×C31—42no—
200#8466C3111yesmaximal, characteristic, direct product factor, Sylow
201C23×C31—21no—
202C23×C31—21no—
203C23×C31—22no—
204C23×C31—21no—
205C23×C31—41no—
206C23×C31—41no—
207C23×C31—42no—
208C23×C31—42no—
209C23×C31—42no—
210C23×C31C2×C22⋊C411yescharacteristic
211C23×C31#12011yescharacteristic
212C23×C31#12011yescharacteristic
213Q8×C31—41no—
214Q8×C31—82no—
215D4×C31—41no—
216D4×C31—42no—
217D4×C31—42no—
218D4×C31—42no—
219D4×C31—41no—
220D4×C31—42no—
221D4×C31—41no—
222D4×C31—42no—
223D4×C31—81no—
224D4×C31—82no—
225D4×C31—82no—
226D4×C31—82no—
227C2×C4×C31—22no—
228C2×C4×C31—22no—
229C2×C4×C31—22no—
230C2×C4×C31—21no—
231C2×C4×C31—21no—
232C2×C4×C31—21no—
233C2×C4×C31—21no—
234C2×C4×C31—21no—
235C2×C4×C31—21no—
236C2×C4×C31—21no—
237C2×C4×C31—22no—
238C2×C4×C31—41no—
239C2×C4×C31—41no—
240C2×C4×C31—41no—
241C2×C4×C31—41no—
242C2×C4×C31—41no—
243C2×C4×C31—42no—
244C2×C4×C31—42no—
245C2×C4×C31—42no—
246C2×C4×C31—81no—
247C2×C4×C31—82no—
248C2×C4×C31—82no—
249C2×C4×C31—82no—
250C2×C4×C31—81no—
251C2×C4×C31—81no—
252C2×C4×C31—81no—
253C2×C4×C31—81no—
254C2×C4×C31—81no—
255C2×C4×C31C2×C22⋊C411yescharacteristic
256C2×C4×C31C2×C22⋊C411yescharacteristic
257C2×C4×C31#12011yescharacteristic
258C2×C4×C31#12011yescharacteristic
259C8×C31—81no—
260C8×C31—81no—
261#3494C2×C3111yescharacteristic
262#1964C2×C3111yescharacteristic, complemented
263#1826C2×C3111yescharacteristic, complemented
264#1825C2×C3111yescharacteristic, complemented
265#1513C2×C3111yescharacteristic, complemented
266#1501C2×C3111yescharacteristic, complemented
267#1471C2×C3111yescharacteristic, complemented
268C22×C31—21no—
269C22×C31—21no—
270C22×C31—21no—
271C22×C31—21no—
272C22×C31—21no—
273C22×C31—21no—
274C22×C31—21no—
275C22×C31—21no—
276C22×C31—41no—
277C22×C31—42no—
278C22×C31—42no—
279C22×C31—41no—
280C22×C31—41no—
281C22×C31—42no—
282C22×C31—81no—
283C22×C31—81no—
284C22×C31—162no—
285C22×C31#37911yescharacteristic
286C22×C31#45311yescharacteristic
287C22×C31#45511yescharacteristic
288C4×C31—21no—
289C4×C31—21no—
290C4×C31—21no—
291C4×C31—41no—
292C4×C31—41no—
293C4×C31—42no—
294C4×C31—41no—
295C4×C31—41no—
296C4×C31—41no—
297C4×C31—41no—
298C4×C31—41no—
299C4×C31—82no—
300C4×C31—161no—
301C4×C31#41012yes—
302#555—21no—
303#553—21no—
304#553—21no—
305#551—22no—
306#547—21no—
307#546—22no—
308#544C4×C3111yescharacteristic, complemented
309#542—21no—
310#540—21no—
311#535C4×C3111yescharacteristic, complemented
312#532—21no—
313#529—21no—
314#525C22×C3111yescharacteristic
315C2×#121C22×C3111yescharacteristic
316#520C4×C3111yescharacteristic, complemented
317#518C4×C3111yescharacteristic, complemented
318C2×#117C22×C3111yescharacteristic
319C2×#99—22no—
320#407C22×C3111yescharacteristic
321C2×C22⋊C8C22×C3111yescharacteristic
322#380C22×C3111yescharacteristic
323C4×C22⋊C4C22×C3111yescharacteristic
324#340—21no—
325#340—21no—
326#339—21no—
327#339—21no—
328#328—21no—
329#328—21no—
330#327—21no—
331#327—21no—
332#323—22no—
333C2×C31—21no—
334C2×C31—21no—
335C2×C31—41no—
336C2×C31—41no—
337C2×C31—81no—
338C2×C31—82no—
339C2×C31#178211yescharacteristic
340C2×C31#179211yescharacteristic
341C2×C31#179411yescharacteristic
342C2×#41—22no—
343C2×#41C2×C4×C3111yescharacteristic
344C22×D4C2×C4×C3111yescharacteristic
345C22×D4D4×C3112yes—
346C23×C4C23×C3111yescharacteristic
347C2×M16—21no—
348C22×C8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351#127—21no—
352#126—22no—
353#126—22no—
354#125—21no—
355#125—21no—
356#124—22no—
357#124—22no—
358#124—21no—
359#123—22no—
360#123—22no—
361#123—22no—
362#123—22no—
363#123—21no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8D4×C3111yescharacteristic
367C22⋊Q8D4×C3111yescharacteristic
368#121—22no—
369#121—22no—
370#121—22no—
371#121—21no—
372#121—21no—
373#121—21no—
374#121—21no—
375#121—21no—
376#121—21no—
377#121D4×C3111yescharacteristic
378#121D4×C3111yescharacteristic
379#120—22no—
380#120—21no—
381C4×Q8—21no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—21no—
385C4×D4—22no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392#117—22no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117C2×C4×C3111yescharacteristic
397#117C2×C4×C3111yescharacteristic
398#117C2×C4×C3111yescharacteristic
399#117D4×C3111yescharacteristic
400#117D4×C3111yescharacteristic
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4C2×C4×C3111yescharacteristic
404C2×C4⋊C4D4×C3111yescharacteristic
405C2×C4⋊C4D4×C3111yescharacteristic
406C2×C22⋊C4—22no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4D4×C3112yes—
411C2×C42—21no—
412C2×C42—21no—
413#99—44no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418#95—21no—
419#95—21no—
420C31#846611yescharacteristic, direct product factor, Sylow
421C24C22⋊C4×C3112yes—
422C24C2×D4×C3111yescharacteristic
423#41—42no—
424#41—82no—
425#41—82no—
426C2×Q8—22no—
427C2×Q8C22⋊C4×C3111yescharacteristic
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4C22⋊C4×C3111yescharacteristic
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—42no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4C22⋊C4×C3112yes—
451C22×C4C22×C4×C3111yescharacteristic
452C22×C4C2×D4×C3111yescharacteristic
453C22×C4C2×D4×C3111yescharacteristic
454C22×C4C2×D4×C3111yescharacteristic
455C22×C4C2×D4×C3111yescharacteristic
456C22×C4C2×D4×C3111yescharacteristic
457M16—42no—
458C2×C8—42no—
459C2×C8—41no—
460C2×C8—41no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—42no—
472C4⋊C4C22⋊C4×C3111yescharacteristic
473C4⋊C4C22⋊C4×C3111yescharacteristic
474C4⋊C4C22⋊C4×C3111yescharacteristic
475C4⋊C4C22⋊C4×C3111yescharacteristic
476C4⋊C4C22⋊C4×C3111yescharacteristic
477C4⋊C4C22⋊C4×C3111yescharacteristic
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—22no—
495C22⋊C4—41no—
496C22⋊C4—42no—
497C42—22no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—42no—
504C23—21no—
505C23—21no—
506C23—22no—
507C23—21no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23C2×C22⋊C4×C3111yescharacteristic
514C23C31×#12011yescharacteristic
515C23C31×#12011yescharacteristic
516Q8—41no—
517Q8—82no—
518D4—41no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—41no—
523D4—42no—
524D4—41no—
525D4—42no—
526D4—81no—
527D4—82no—
528D4—82no—
529D4—82no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—81no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4—82no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4C2×C22⋊C4×C3111yescharacteristic
559C2×C4C2×C22⋊C4×C3111yescharacteristic
560C2×C4C31×#12011yescharacteristic
561C2×C4C31×#12011yescharacteristic
562C8—81no—
563C8—81no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—41no—
573C22—42no—
574C22—41no—
575C22—42no—
576C22—42no—
577C22—41no—
578C22—81no—
579C22—81no—
580C22—162no—
581C22C31×#37911yescharacteristic
582C22C31×#45311yescharacteristic
583C22C31×#45511yescharacteristic
584C4—21no—
585C4—21no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—42no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—82no—
596C4—161no—
597C4C31×#41012yes—
598C2—21no—
599C2—21no—
600C2—41no—
601C2—41no—
602C2—82no—
603C2—81no—
604C2C31×#178211yescharacteristic
605C2C31×#179211yescharacteristic
606C2C31×#179411yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC31×#3494C2
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×#1964C2semidirect
3. C31×#1826C2semidirect
4. C31×#1825C2semidirect
5. C31×#1513C2semidirect
6. C31×#1501C2semidirect
7. C31×#1471C2semidirect
14. C31×#544C4semidirect
17. C31×#535C4semidirect
22. C31×#520C4semidirect
23. C31×#518C4semidirect
200. #8466C31direct (N × H)
262. #1964C2×C31semidirect
263. #1826C2×C31semidirect
264. #1825C2×C31semidirect
265. #1513C2×C31semidirect
266. #1501C2×C31semidirect
267. #1471C2×C31semidirect
308. #544C4×C31semidirect
311. #535C4×C31semidirect
316. #520C4×C31semidirect
317. #518C4×C31semidirect
420. C31#8466direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34942
C31×#19642
C31×#18262
C31×#18252
C31×#15132
C31×#15012
C31×#14712
#846631