Finite Group Databasebeta

← C31×#11163 #21467922

Subgroups — C31×#11163 #21467922

Order 7936.

958 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
1C2×C31×#418C211yesmaximal, characteristic
2C22×C31×#102C211yesmaximal, characteristic
3C22×C31×#100C211yesmaximal, characteristic
4C2×C31×#343C211yesmaximal, characteristic, complemented
5C2×C31×#341C211yesmaximal, characteristic, complemented
6C31×#1736C211yesmaximal, characteristic, complemented
7C31×#1729C211yesmaximal, characteristic, complemented
8C23×D4×C31C2211yescharacteristic
9C22×M16×C31C2211yescharacteristic
10C22×M16×C31C2211yescharacteristic
11C22×M16×C31C2211yescharacteristic
12C23×C8×C31C2211yescharacteristic
13C2×C31×#117C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C31×#418—22no—
16C31×#418—22no—
17C2×C31×#102—22no—
18C2×C31×#102—22no—
19C2×C31×#102—22no—
20C2×C31×#102—22no—
21C2×C31×#100—22no—
22C2×C31×#100—22no—
23C2×C31×#100C414yescomplemented
24C31×#343—22no—
25C31×#341—22no—
26C31×#340—22no—
27C31×#336—22no—
28C25×C31—21no—
29C22×D4×C31—21no—
30C22×D4×C31—21no—
31C22×D4×C31—21no—
32C22×D4×C31—21no—
33C22×D4×C31—21no—
34C22×D4×C31—21no—
35C22×D4×C31—21no—
36C22×D4×C31—21no—
37C22×D4×C31—21no—
38C22×D4×C31—21no—
39C22×D4×C31—21no—
40C22×D4×C31C2×C412yes—
41C22×D4×C31D412yes—
42C22×D4×C31D412yes—
43C23×C4×C31—21no—
44C23×C4×C31C2311yescharacteristic
45C2×M16×C31—21no—
46C2×M16×C31—21no—
47C2×M16×C31—21no—
48C2×M16×C31—21no—
49C2×M16×C31—21no—
50C2×M16×C31—21no—
51C2×M16×C31—21no—
52C2×M16×C31—21no—
53C2×M16×C31—21no—
54C2×M16×C31—21no—
55C2×M16×C31—21no—
56C2×M16×C31—21no—
57C2×M16×C31—21no—
58C2×M16×C31—21no—
59C2×M16×C31—21no—
60C2×M16×C31C2×C412yes—
61C2×M16×C31C2×C412yes—
62C2×M16×C31D412yes—
63C22×C8×C31—21no—
64C22×C8×C31—21no—
65C22×C8×C31—21no—
66C22×C8×C31—21no—
67C22×C8×C31—21no—
68C22×C8×C31—21no—
69C22×C8×C31—21no—
70C22×C8×C31—21no—
71C22×C8×C31—21no—
72C22×C8×C31D412yes—
73C31×#117—21no—
74C31×#117—21no—
75C31×#117—21no—
76C31×#117—21no—
77C2×C4⋊C4×C31—21no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31—21no—
80C2×C4⋊C4×C31—21no—
81C2×C4⋊C4×C31—21no—
82C2×C4⋊C4×C31D412yes—
83C2×C4⋊C4×C31D412yes—
84C2×C22⋊C4×C31—21no—
85C2×C42×C31—21no—
86C31×#102—28no—
87C31×#102—28no—
88C31×#100—28no—
89C24×C31—22no—
90C24×C31—22no—
91C24×C31—22no—
92C24×C31—41no—
93C24×C31—41no—
94C24×C31—41no—
95C24×C31—41no—
96C24×C31—82no—
97C24×C31—82no—
98C24×C31#4111yescharacteristic
99C2×D4×C31—22no—
100C2×D4×C31—22no—
101C2×D4×C31—22no—
102C2×D4×C31—22no—
103C2×D4×C31—22no—
104C2×D4×C31—22no—
105C2×D4×C31—22no—
106C2×D4×C31—22no—
107C2×D4×C31—22no—
108C2×D4×C31—22no—
109C2×D4×C31—22no—
110C2×D4×C31—22no—
111C2×D4×C31—22no—
112C2×D4×C31—22no—
113C2×D4×C31—22no—
114C2×D4×C31—41no—
115C2×D4×C31—41no—
116C2×D4×C31—41no—
117C2×D4×C31—41no—
118C2×D4×C31—41no—
119C2×D4×C31—41no—
120C2×D4×C31—41no—
121C2×D4×C31—41no—
122C2×D4×C31—41no—
123C2×D4×C31—41no—
124C2×D4×C31—41no—
125C2×D4×C31—41no—
126C2×D4×C31C22⋊C414yes—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—41no—
130C22×C4×C31—41no—
131C22×C4×C31—82no—
132C22×C4×C31C22×C411yescharacteristic
133C22×C4×C31C2×D411yescharacteristic
134C22×C4×C31C2×D411yescharacteristic
135C22×C4×C31C2×D411yescharacteristic
136C22×C4×C31C2×D411yescharacteristic
137C22×C4×C31C2×D411yescharacteristic
138C22×C4×C31C2×D411yescharacteristic
139C22×C4×C31#4111yescharacteristic
140C22×C4×C31#4111yescharacteristic
141C22×C4×C31#4111yescharacteristic
142C22×C4×C31#4111yescharacteristic
143C22×C4×C31#4111yescharacteristic
144C22×C4×C31#4111yescharacteristic
145C22×C4×C31#4111yescharacteristic
146M16×C31—22no—
147M16×C31—22no—
148M16×C31—22no—
149M16×C31—22no—
150M16×C31—22no—
151M16×C31—22no—
152M16×C31—41no—
153M16×C31—41no—
154M16×C31—41no—
155M16×C31—41no—
156M16×C31—41no—
157M16×C31—41no—
158C2×C8×C31—22no—
159C2×C8×C31—22no—
160C2×C8×C31—22no—
161C2×C8×C31—22no—
162C2×C8×C31—22no—
163C2×C8×C31—22no—
164C2×C8×C31—41no—
165C2×C8×C31—41no—
166C2×C8×C31—41no—
167C2×C8×C31—41no—
168C2×C8×C31—41no—
169C2×C8×C31—41no—
170C2×C8×C31—41no—
171C2×C8×C31—41no—
172C2×C8×C31—41no—
173C2×C8×C31—41no—
174C4⋊C4×C31—22no—
175C4⋊C4×C31—22no—
176C4⋊C4×C31—22no—
177C4⋊C4×C31—22no—
178C4⋊C4×C31—41no—
179C4⋊C4×C31—41no—
180C22⋊C4×C31—41no—
181C22⋊C4×C31—41no—
182C42×C31—41no—
183C42×C31—41no—
184#11163C3111yesmaximal, characteristic, direct product factor, Sylow
185C23×C31—22no—
186C23×C31—22no—
187C23×C31—24no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—42no—
191C23×C31—42no—
192C23×C31—42no—
193C23×C31—42no—
194C23×C31—84no—
195C23×C31—84no—
196C23×C31—82no—
197C23×C31—82no—
198C23×C31—84no—
199C23×C31—84no—
200C23×C31—82no—
201C23×C31—82no—
202C23×C31—82no—
203C23×C31—82no—
204C23×C31#11711yescharacteristic
205C23×C31#12111yescharacteristic
206C23×C31#12311yescharacteristic
207C23×C31#12311yescharacteristic
208C23×C31#12311yescharacteristic
209C23×C31#12411yescharacteristic
210C23×C31#12611yescharacteristic
211D4×C31—24no—
212D4×C31—24no—
213D4×C31—42no—
214D4×C31—42no—
215D4×C31—42no—
216D4×C31—42no—
217D4×C31—42no—
218D4×C31—42no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—82no—
224C2×C4×C31—82no—
225C2×C4×C31—82no—
226C2×C4×C31C2×C22⋊C411yescharacteristic
227C2×C4×C31#11711yescharacteristic
228C2×C4×C31C4×D411yescharacteristic
229C2×C4×C31C4×D411yescharacteristic
230C2×C4×C31C4×D411yescharacteristic
231C2×C4×C31C4×D411yescharacteristic
232C2×C4×C31#12011yescharacteristic
233C2×C4×C31#12011yescharacteristic
234C2×C4×C31#12111yescharacteristic
235C2×C4×C31#12111yescharacteristic
236C2×C4×C31#12111yescharacteristic
237C2×C4×C31#12111yescharacteristic
238C2×C4×C31#12111yescharacteristic
239C2×C4×C31#12111yescharacteristic
240C2×C4×C31#12111yescharacteristic
241C2×C4×C31#12311yescharacteristic
242C2×C4×C31#12311yescharacteristic
243C2×C4×C31#12311yescharacteristic
244C2×C4×C31#12311yescharacteristic
245C2×C4×C31#12311yescharacteristic
246C2×C4×C31#12311yescharacteristic
247C2×C4×C31#12311yescharacteristic
248C2×C4×C31#12411yescharacteristic
249C2×C4×C31#12411yescharacteristic
250C2×C4×C31#12411yescharacteristic
251C2×C4×C31#12611yescharacteristic
252C2×C4×C31#12611yescharacteristic
253C2×C4×C31#12611yescharacteristic
254C8×C31—42no—
255C8×C31—42no—
256C8×C31—42no—
257C8×C31—42no—
258C2×#418C2×C3111yescharacteristic
259C22×#102C2×C3111yescharacteristic
260C22×#100C2×C3111yescharacteristic
261C2×#343C2×C3111yescharacteristic, complemented
262C2×#341C2×C3111yescharacteristic, complemented
263#1736C2×C3111yescharacteristic, complemented
264#1729C2×C3111yescharacteristic, complemented
265C22×C31—22no—
266C22×C31—22no—
267C22×C31—22no—
268C22×C31—22no—
269C22×C31—21no—
270C22×C31—21no—
271C22×C31—21no—
272C22×C31—21no—
273C22×C31—44no—
274C22×C31—84no—
275C22×C31—84no—
276C22×C31—84no—
277C22×C31—84no—
278C22×C31—84no—
279C22×C31—84no—
280C22×C31—82no—
281C22×C31—82no—
282C22×C31#38111yescharacteristic
283C22×C31#38811yescharacteristic
284C22×C31#38811yescharacteristic
285C22×C31#39411yescharacteristic
286C22×C31#39411yescharacteristic
287C22×C31#39711yescharacteristic
288C22×C31#39711yescharacteristic
289C22×C31#47112yes—
290C22×C31#47212yes—
291C4×C31—82no—
292C4×C31—82no—
293C4×C31#38611yescharacteristic
294C4×C31#38611yescharacteristic
295C4×C31#38811yescharacteristic
296C4×C31#38811yescharacteristic
297C4×C31#39411yescharacteristic
298C4×C31#39411yescharacteristic
299C4×C31#39711yescharacteristic
300C4×C31#39711yescharacteristic
301C23×D4C22×C3111yescharacteristic
302C22×M16C22×C3111yescharacteristic
303C22×M16C22×C3111yescharacteristic
304C22×M16C22×C3111yescharacteristic
305C23×C8C22×C3111yescharacteristic
306C2×#117C22×C3111yescharacteristic
307C22×C4⋊C4C22×C3111yescharacteristic
308#418—22no—
309#418—22no—
310C2×#102—22no—
311C2×#102—22no—
312C2×#102—22no—
313C2×#102—22no—
314C2×#100—22no—
315C2×#100—22no—
316C2×#100C4×C3114yescomplemented
317#343—22no—
318#341—22no—
319#340—22no—
320#336—22no—
321C2×C31—21no—
322C2×C31—21no—
323C2×C31—21no—
324C2×C31—21no—
325C2×C31—84no—
326C2×C31#144011yescharacteristic
327C2×C31#193112yes—
328C2×C31#204511yescharacteristic
329C2×C31#204611yescharacteristic
330C2×C31#205112yes—
331C25—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4—21no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—21no—
343C22×D4C2×C4×C3112yes—
344C22×D4D4×C3112yes—
345C22×D4D4×C3112yes—
346C23×C4—21no—
347C23×C4C23×C3111yescharacteristic
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16C2×C4×C3112yes—
364C2×M16C2×C4×C3112yes—
365C2×M16D4×C3112yes—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8D4×C3112yes—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4D4×C3112yes—
386C2×C4⋊C4D4×C3112yes—
387C2×C22⋊C4—21no—
388C2×C42—21no—
389#102—28no—
390#102—28no—
391#100—28no—
392C31#1116311yescharacteristic, direct product factor, Sylow
393C24—22no—
394C24—22no—
395C24—22no—
396C24—41no—
397C24—41no—
398C24—41no—
399C24—41no—
400C24—82no—
401C24—82no—
402C24#41×C3111yescharacteristic
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4C22⋊C4×C3114yes—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—82no—
436C22×C4C22×C4×C3111yescharacteristic
437C22×C4C2×D4×C3111yescharacteristic
438C22×C4C2×D4×C3111yescharacteristic
439C22×C4C2×D4×C3111yescharacteristic
440C22×C4C2×D4×C3111yescharacteristic
441C22×C4C2×D4×C3111yescharacteristic
442C22×C4C2×D4×C3111yescharacteristic
443C22×C4#41×C3111yescharacteristic
444C22×C4#41×C3111yescharacteristic
445C22×C4#41×C3111yescharacteristic
446C22×C4#41×C3111yescharacteristic
447C22×C4#41×C3111yescharacteristic
448C22×C4#41×C3111yescharacteristic
449C22×C4#41×C3111yescharacteristic
450M16—22no—
451M16—22no—
452M16—22no—
453M16—22no—
454M16—22no—
455M16—22no—
456M16—41no—
457M16—41no—
458M16—41no—
459M16—41no—
460M16—41no—
461M16—41no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—41no—
469C2×C8—41no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C42—41no—
487C42—41no—
488C23—22no—
489C23—22no—
490C23—24no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—84no—
498C23—84no—
499C23—82no—
500C23—82no—
501C23—84no—
502C23—84no—
503C23—82no—
504C23—82no—
505C23—82no—
506C23—82no—
507C23C31×#11711yescharacteristic
508C23C31×#12111yescharacteristic
509C23C31×#12311yescharacteristic
510C23C31×#12311yescharacteristic
511C23C31×#12311yescharacteristic
512C23C31×#12411yescharacteristic
513C23C31×#12611yescharacteristic
514D4—24no—
515D4—24no—
516D4—42no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4C2×C22⋊C4×C3111yescharacteristic
530C2×C4C31×#11711yescharacteristic
531C2×C4C4×D4×C3111yescharacteristic
532C2×C4C4×D4×C3111yescharacteristic
533C2×C4C4×D4×C3111yescharacteristic
534C2×C4C4×D4×C3111yescharacteristic
535C2×C4C31×#12011yescharacteristic
536C2×C4C31×#12011yescharacteristic
537C2×C4C31×#12111yescharacteristic
538C2×C4C31×#12111yescharacteristic
539C2×C4C31×#12111yescharacteristic
540C2×C4C31×#12111yescharacteristic
541C2×C4C31×#12111yescharacteristic
542C2×C4C31×#12111yescharacteristic
543C2×C4C31×#12111yescharacteristic
544C2×C4C31×#12311yescharacteristic
545C2×C4C31×#12311yescharacteristic
546C2×C4C31×#12311yescharacteristic
547C2×C4C31×#12311yescharacteristic
548C2×C4C31×#12311yescharacteristic
549C2×C4C31×#12311yescharacteristic
550C2×C4C31×#12311yescharacteristic
551C2×C4C31×#12411yescharacteristic
552C2×C4C31×#12411yescharacteristic
553C2×C4C31×#12411yescharacteristic
554C2×C4C31×#12611yescharacteristic
555C2×C4C31×#12611yescharacteristic
556C2×C4C31×#12611yescharacteristic
557C8—42no—
558C8—42no—
559C8—42no—
560C8—42no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—44no—
570C22—84no—
571C22—84no—
572C22—84no—
573C22—84no—
574C22—84no—
575C22—84no—
576C22—82no—
577C22—82no—
578C22C31×#38111yescharacteristic
579C22C31×#38811yescharacteristic
580C22C31×#38811yescharacteristic
581C22C31×#39411yescharacteristic
582C22C31×#39411yescharacteristic
583C22C31×#39711yescharacteristic
584C22C31×#39711yescharacteristic
585C22C31×#47112yes—
586C22C31×#47212yes—
587C4—82no—
588C4—82no—
589C4C31×#38611yescharacteristic
590C4C31×#38611yescharacteristic
591C4C31×#38811yescharacteristic
592C4C31×#38811yescharacteristic
593C4C31×#39411yescharacteristic
594C4C31×#39411yescharacteristic
595C4C31×#39711yescharacteristic
596C4C31×#39711yescharacteristic
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—84no—
602C2C31×#144011yescharacteristic
603C2C31×#193112yes—
604C2C31×#204511yescharacteristic
605C2C31×#204611yescharacteristic
606C2C31×#205112yes—
subgroupG/H
center, socleC23×C31#121
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC23×D4×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C31×#343C2semidirect
5. C2×C31×#341C2semidirect
6. C31×#1736C2semidirect
7. C31×#1729C2semidirect
23. C2×C31×#100C4semidirect
184. #11163C31direct (N × H)
261. C2×#343C2×C31semidirect
262. C2×#341C2×C31semidirect
263. #1736C2×C31semidirect
264. #1729C2×C31semidirect
316. C2×#100C4×C31semidirect
392. C31#11163direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4182
C22×C31×#1022
C22×C31×#1002
C2×C31×#3432
C2×C31×#3412
C31×#17362
C31×#17292
#1116331