Finite Group Databasebeta

← C31×#23617 #21480376

Subgroups — C31×#23617 #21480376

Order 7936.

1178 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#428C211yesmaximal, characteristic, complemented
2C2×C31×#423C211yesmaximal, characteristic, complemented
3C2×C31×#417C211yesmaximal, characteristic
4C2×C31×#417C211yesmaximal, characteristic
5C31×#2297C211yesmaximal, characteristic
6C2×C31×#389C211yesmaximal, characteristic, complemented
7C31×#2068C212yesmaximal, complemented
8C31×#2067C212yesmaximal, complemented
9C31×#2066C212yesmaximal, complemented
10C31×#2065C212yesmaximal, complemented
11C31×#1736C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic
13C22×M16×C31C2211yescharacteristic
14C22×M16×C31C2211yescharacteristic
15C2×C31×#117C2211yescharacteristic
16C22×C4⋊C4×C31—21no—
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C42×C31C2211yescharacteristic
20C31×#428—24no—
21C2×C31×#107C2212yes—
22C2×C31×#106C2212yes—
23C31×#423—24no—
24C2×C31×C4⋊C8C2212yes—
25C2×C31×C4⋊C8C2212yes—
26C31×#417—24no—
27C31×#417—24no—
28C2×C31×#103C2212yes—
29C2×C31×#103C2212yes—
30C2×C31×#102C2212yes—
31C2×C31×#102C2212yes—
32C31×#391C2211yescharacteristic
33C31×#391C2211yescharacteristic
34C31×#390C2211yescharacteristic
35C31×#390C2211yescharacteristic
36C31×#389—21no—
37C31×#389—21no—
38C31×#389C2212yes—
39C31×#389C2212yes—
40C31×#386—21no—
41C31×#386—21no—
42C4×C22⋊C4×C31—21no—
43C4×C22⋊C4×C31—21no—
44C2×C31×#95—21no—
45C31×#340C2212yes—
46C31×#340C2212yes—
47C2×#41×C31—22no—
48C2×#41×C31—22no—
49C2×#41×C31—22no—
50C2×#41×C31—22no—
51C2×#41×C31—22no—
52C2×#41×C31Q814yes—
53C22×Q8×C31C2311yescharacteristic
54C22×D4×C31—21no—
55C22×D4×C31C2311yescharacteristic
56C23×C4×C31—21no—
57C23×C4×C31—21no—
58C23×C4×C31—21no—
59C23×C4×C31D411yescharacteristic
60C23×C4×C31D411yescharacteristic
61C23×C4×C31C2311yescharacteristic
62C2×M16×C31—22no—
63C2×M16×C31—22no—
64C2×M16×C31—22no—
65C2×M16×C31—22no—
66C2×M16×C31—22no—
67C2×M16×C31D414yes—
68C22×C8×C31C2312yes—
69C22×C8×C31C2312yes—
70C31×#117—22no—
71C31×#117—22no—
72C2×C4⋊C4×C31—21no—
73C2×C4⋊C4×C31—22no—
74C2×C4⋊C4×C31—22no—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31—44no—
80C2×C4⋊C4×C31D414yes—
81C2×C4⋊C4×C31C2312yes—
82C2×C4⋊C4×C31C2311yescharacteristic
83C2×C4⋊C4×C31C2311yescharacteristic
84C2×C4⋊C4×C31C2312yes—
85C2×C22⋊C4×C31—21no—
86C2×C22⋊C4×C31—21no—
87C2×C22⋊C4×C31—21no—
88C2×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31—21no—
90C2×C42×C31—22no—
91C2×C42×C31—22no—
92C2×C42×C31—21no—
93C2×C42×C31D411yescharacteristic
94C2×C42×C31D411yescharacteristic
95C2×C42×C31C2311yescharacteristic
96C2×C42×C31C2311yescharacteristic
97C31×#107—24no—
98C31×#106—24no—
99C31×C4⋊C8—24no—
100C31×C4⋊C8—24no—
101C31×#103—24no—
102C31×#103—24no—
103C31×#102—24no—
104C31×#102—24no—
105C31×#95—22no—
106C31×#95—22no—
107C31×#95—21no—
108C31×#95—21no—
109C31×#95—21no—
110C31×#95—21no—
111C24×C31—21no—
112C24×C31C2×D411yescharacteristic
113#41×C31—28no—
114#41×C31—28no—
115#41×C31—44no—
116#41×C31—44no—
117C2×Q8×C31—21no—
118C2×Q8×C31—21no—
119C2×Q8×C31—21no—
120C2×Q8×C31—21no—
121C2×Q8×C31—21no—
122C2×Q8×C31C2×Q812yes—
123C2×D4×C31—24no—
124C2×D4×C31—21no—
125C2×D4×C31—21no—
126C2×D4×C31—21no—
127C2×D4×C31—21no—
128C2×D4×C31—21no—
129C2×D4×C31—42no—
130C2×D4×C31—42no—
131C2×D4×C31C2×Q812yes—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—24no—
135C22×C4×C31—21no—
136C22×C4×C31—22no—
137C22×C4×C31—24no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—22no—
143C22×C4×C31—41no—
144C22×C4×C31—41no—
145C22×C4×C31—42no—
146C22×C4×C31—42no—
147C22×C4×C31—42no—
148C22×C4×C31—42no—
149C22×C4×C31—42no—
150C22×C4×C31—42no—
151C22×C4×C31—42no—
152C22×C4×C31C2×D411yescharacteristic
153C22×C4×C31C2×D411yescharacteristic
154C22×C4×C31C2×D411yescharacteristic
155C22×C4×C31C2×D411yescharacteristic
156C22×C4×C31C2×D411yescharacteristic
157C22×C4×C31C2×D412yes—
158C22×C4×C31C2×D412yes—
159C22×C4×C31C2×Q812yes—
160C22×C4×C31#4112yes—
161C22×C4×C31#4112yes—
162C22×C4×C31#4112yes—
163C22×C4×C31C2411yescharacteristic
164M16×C31—28no—
165M16×C31—44no—
166C2×C8×C31—22no—
167C2×C8×C31—22no—
168C2×C8×C31—22no—
169C2×C8×C31—22no—
170C2×C8×C31—22no—
171C2×C8×C31C2×D414yes—
172C4⋊C4×C31—24no—
173C4⋊C4×C31—22no—
174C4⋊C4×C31—22no—
175C4⋊C4×C31—21no—
176C4⋊C4×C31—21no—
177C4⋊C4×C31—22no—
178C4⋊C4×C31—21no—
179C4⋊C4×C31—21no—
180C4⋊C4×C31—44no—
181C4⋊C4×C31—42no—
182C4⋊C4×C31—44no—
183C4⋊C4×C31C2×D414yes—
184C22⋊C4×C31—42no—
185C22⋊C4×C31—42no—
186C22⋊C4×C31—42no—
187C22⋊C4×C31—42no—
188C22⋊C4×C31—42no—
189C42×C31—22no—
190C42×C31—22no—
191C42×C31—21no—
192C42×C31—21no—
193C42×C31—21no—
194C42×C31—21no—
195C42×C31—42no—
196#23617C3111yesmaximal, characteristic, direct product factor, Sylow
197C23×C31—21no—
198C23×C31—21no—
199C23×C31—21no—
200C23×C31—21no—
201C23×C31—22no—
202C23×C31—41no—
203C23×C31—41no—
204C23×C31—41no—
205C23×C31—41no—
206C23×C31—41no—
207C23×C31—41no—
208C23×C31#12112yes—
209C23×C31#12112yes—
210C23×C31C22⋊Q812yes—
211C23×C31C22×D411yescharacteristic
212Q8×C31—22no—
213Q8×C31—22no—
214Q8×C31—41no—
215Q8×C31—41no—
216D4×C31—22no—
217D4×C31—22no—
218D4×C31—48no—
219D4×C31—41no—
220D4×C31—41no—
221C2×C4×C31—21no—
222C2×C4×C31—21no—
223C2×C4×C31—21no—
224C2×C4×C31—21no—
225C2×C4×C31—21no—
226C2×C4×C31—21no—
227C2×C4×C31—24no—
228C2×C4×C31—22no—
229C2×C4×C31—21no—
230C2×C4×C31—21no—
231C2×C4×C31—21no—
232C2×C4×C31—21no—
233C2×C4×C31—44no—
234C2×C4×C31—44no—
235C2×C4×C31—48no—
236C2×C4×C31—41no—
237C2×C4×C31—41no—
238C2×C4×C31—42no—
239C2×C4×C31—42no—
240C2×C4×C31—48no—
241C2×C4×C31—41no—
242C2×C4×C31—41no—
243C2×C4×C31—42no—
244C2×C4×C31—41no—
245C2×C4×C31—42no—
246C2×C4×C31—41no—
247C2×C4×C31—41no—
248C2×C4×C31—41no—
249C2×C4×C31—42no—
250C2×C4×C31—84no—
251C2×C4×C31#12114yes—
252C2×C4×C31#12112yes—
253C2×C4×C31#12112yes—
254C2×C4×C31C22⋊Q814yes—
255C2×C4×C31C22⋊Q814yes—
256C2×C4×C31C22⋊Q812yes—
257C2×C4×C31#12614yes—
258C2×C4×C31AGL(1,ℤ/8)12yes—
259C2×C4×C31#13712yes—
260C2×C4×C31C22×D411yescharacteristic
261C2×C4×C31C22×D411yescharacteristic
262C2×C4×C31C22×Q811yescharacteristic
263C2×C4×C31C2×#4111yescharacteristic
264C2×C4×C31C2×#4111yescharacteristic
265C2×C4×C31C2×#4111yescharacteristic
266C8×C31—24no—
267C8×C31—42no—
268C2×#428C2×C3111yescharacteristic, complemented
269C2×#423C2×C3111yescharacteristic, complemented
270C2×#417C2×C3111yescharacteristic
271C2×#417C2×C3111yescharacteristic
272#2297C2×C3111yescharacteristic
273C2×#389C2×C3111yescharacteristic, complemented
274#2068C2×C3112yescomplemented
275#2067C2×C3112yescomplemented
276#2066C2×C3112yescomplemented
277#2065C2×C3112yescomplemented
278#1736C2×C3111yescharacteristic, complemented
279C22×C31—22no—
280C22×C31—22no—
281C22×C31—22no—
282C22×C31—22no—
283C22×C31—22no—
284C22×C31—22no—
285C22×C31—42no—
286C22×C31—42no—
287C22×C31—42no—
288C22×C31—81no—
289C22×C31—81no—
290C22×C31—81no—
291C22×C31—81no—
292C22×C31#39614yes—
293C22×C31C2×#12111yescharacteristic
294C22×C31C2×#12111yescharacteristic
295C22×C31C2×C22⋊Q811yescharacteristic
296C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C31C2×#13711yescharacteristic
298C22×C31#57511yescharacteristic
299C22×C31#57511yescharacteristic
300C4×C31—22no—
301C4×C31—22no—
302C4×C31—42no—
303C4×C31—44no—
304C4×C31—41no—
305C4×C31—41no—
306C4×C31—81no—
307C4×C31—81no—
308C4×C31—82no—
309C4×C31#39614yes—
310C4×C31C2×#12111yescharacteristic
311C4×C31C2×C22⋊Q811yescharacteristic
312C4×C31C2×C22⋊Q811yescharacteristic
313C4×C31C2×#12611yescharacteristic
314C22×#41C22×C3111yescharacteristic
315C22×M16C22×C3111yescharacteristic
316C22×M16C22×C3111yescharacteristic
317C2×#117C22×C3111yescharacteristic
318C22×C4⋊C4—21no—
319C22×C4⋊C4C22×C3111yescharacteristic
320C22×C4⋊C4C22×C3111yescharacteristic
321C22×C42C22×C3111yescharacteristic
322#428—24no—
323C2×#107C22×C3112yes—
324C2×#106C22×C3112yes—
325#423—24no—
326C2×C4⋊C8C22×C3112yes—
327C2×C4⋊C8C22×C3112yes—
328#417—24no—
329#417—24no—
330C2×#103C22×C3112yes—
331C2×#103C22×C3112yes—
332C2×#102C22×C3112yes—
333C2×#102C22×C3112yes—
334#391C22×C3111yescharacteristic
335#391C22×C3111yescharacteristic
336#390C22×C3111yescharacteristic
337#390C22×C3111yescharacteristic
338#389—21no—
339#389—21no—
340#389C22×C3112yes—
341#389C22×C3112yes—
342#386—21no—
343#386—21no—
344C4×C22⋊C4—21no—
345C4×C22⋊C4—21no—
346C2×#95—21no—
347#340C22×C3112yes—
348#340C22×C3112yes—
349C2×C31—24no—
350C2×C31—82no—
351C2×C31C2×#39611yescharacteristic
352C2×C31#303611yescharacteristic
353C2×C31#303711yescharacteristic
354C2×C31#305511yescharacteristic
355C2×C31#305611yescharacteristic
356C2×C31#307911yescharacteristic
357C2×C31#308011yescharacteristic
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41—22no—
362C2×#41—22no—
363C2×#41Q8×C3114yes—
364C22×Q8C23×C3111yescharacteristic
365C22×D4—21no—
366C22×D4C23×C3111yescharacteristic
367C23×C4—21no—
368C23×C4—21no—
369C23×C4—21no—
370C23×C4D4×C3111yescharacteristic
371C23×C4D4×C3111yescharacteristic
372C23×C4C23×C3111yescharacteristic
373C2×M16—22no—
374C2×M16—22no—
375C2×M16—22no—
376C2×M16—22no—
377C2×M16—22no—
378C2×M16D4×C3114yes—
379C22×C8C23×C3112yes—
380C22×C8C23×C3112yes—
381#117—22no—
382#117—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4D4×C3114yes—
392C2×C4⋊C4C23×C3112yes—
393C2×C4⋊C4C23×C3111yescharacteristic
394C2×C4⋊C4C23×C3111yescharacteristic
395C2×C4⋊C4C23×C3112yes—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—21no—
404C2×C42D4×C3111yescharacteristic
405C2×C42D4×C3111yescharacteristic
406C2×C42C23×C3111yescharacteristic
407C2×C42C23×C3111yescharacteristic
408#107—24no—
409#106—24no—
410C4⋊C8—24no—
411C4⋊C8—24no—
412#103—24no—
413#103—24no—
414#102—24no—
415#102—24no—
416#95—22no—
417#95—22no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422C31#2361711yescharacteristic, direct product factor, Sylow
423C24—21no—
424C24C2×D4×C3111yescharacteristic
425#41—28no—
426#41—28no—
427#41—44no—
428#41—44no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8C2×Q8×C3112yes—
435C2×D4—24no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4C2×Q8×C3112yes—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4C2×D4×C3111yescharacteristic
465C22×C4C2×D4×C3111yescharacteristic
466C22×C4C2×D4×C3111yescharacteristic
467C22×C4C2×D4×C3111yescharacteristic
468C22×C4C2×D4×C3111yescharacteristic
469C22×C4C2×D4×C3112yes—
470C22×C4C2×D4×C3112yes—
471C22×C4C2×Q8×C3112yes—
472C22×C4#41×C3112yes—
473C22×C4#41×C3112yes—
474C22×C4#41×C3112yes—
475C22×C4C24×C3111yescharacteristic
476M16—28no—
477M16—44no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8C2×D4×C3114yes—
484C4⋊C4—24no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—44no—
493C4⋊C4—42no—
494C4⋊C4—44no—
495C4⋊C4C2×D4×C3114yes—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—42no—
500C22⋊C4—42no—
501C42—22no—
502C42—22no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—42no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—22no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23C31×#12112yes—
520C23C31×#12112yes—
521C23C31×C22⋊Q812yes—
522C23C22×D4×C3111yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527D4—22no—
528D4—22no—
529D4—48no—
530D4—41no—
531D4—41no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—44no—
545C2×C4—44no—
546C2×C4—48no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—48no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—84no—
562C2×C4C31×#12112yes—
563C2×C4C31×#12112yes—
564C2×C4C31×#12114yes—
565C2×C4C31×C22⋊Q812yes—
566C2×C4C31×C22⋊Q814yes—
567C2×C4C31×C22⋊Q814yes—
568C2×C4C31×#12614yes—
569C2×C4C31×AGL(1,ℤ/8)12yes—
570C2×C4C31×#13712yes—
571C2×C4C22×D4×C3111yescharacteristic
572C2×C4C22×D4×C3111yescharacteristic
573C2×C4C22×Q8×C3111yescharacteristic
574C2×C4C2×#41×C3111yescharacteristic
575C2×C4C2×#41×C3111yescharacteristic
576C2×C4C2×#41×C3111yescharacteristic
577C8—24no—
578C8—42no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22C31×#39614yes—
593C22C2×C31×#12111yescharacteristic
594C22C2×C31×#12111yescharacteristic
595C22C2×C31×C22⋊Q811yescharacteristic
596C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
597C22C2×C31×#13711yescharacteristic
598C22C31×#57511yescharacteristic
599C22C31×#57511yescharacteristic
600C4—22no—
601C4—22no—
602C4—42no—
603C4—44no—
604C4—41no—
605C4—41no—
606C4—81no—
607C4—81no—
608C4—82no—
609C4C31×#39614yes—
610C4C2×C31×#12111yescharacteristic
611C4C2×C31×C22⋊Q811yescharacteristic
612C4C2×C31×C22⋊Q811yescharacteristic
613C4C2×C31×#12611yescharacteristic
614C2—24no—
615C2—82no—
616C2C2×C31×#39611yescharacteristic
617C2C31×#303611yescharacteristic
618C2C31×#303711yescharacteristic
619C2C31×#305511yescharacteristic
620C2C31×#305611yescharacteristic
621C2C31×#307911yescharacteristic
622C2C31×#308011yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#428C2semidirect
2. C2×C31×#423C2semidirect
6. C2×C31×#389C2semidirect
7. C31×#2068C2semidirect
8. C31×#2067C2semidirect
9. C31×#2066C2semidirect
10. C31×#2065C2semidirect
11. C31×#1736C2semidirect
196. #23617C31direct (N × H)
268. C2×#428C2×C31semidirect
269. C2×#423C2×C31semidirect
273. C2×#389C2×C31semidirect
274. #2068C2×C31semidirect
275. #2067C2×C31semidirect
276. #2066C2×C31semidirect
277. #2065C2×C31semidirect
278. #1736C2×C31semidirect
422. C31#23617direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4282
C2×C31×#4232
C2×C31×#4172
C31×#22972
C2×C31×#3892
C31×#20682
C31×#20672
C31×#20662
C31×#20652
C31×#17362
#2361731