Finite Group Databasebeta

← C31×#10955 #21467714

Subgroups — C31×#10955 #21467714

Order 7936.

900 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#421C211yesmaximal, characteristic
2C2×C31×#421C211yesmaximal, characteristic
3C2×C31×#413C211yesmaximal, characteristic
4C31×#2873C211yesmaximal, characteristic, complemented
5C31×#1742C211yesmaximal, characteristic, complemented
6C31×#1738C211yesmaximal, characteristic, complemented
7C2×C31×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C22×M16×C31C2211yescharacteristic
10C22×M16×C31C2211yescharacteristic
11C22×M16×C31C2211yescharacteristic
12C22×M16×C31C2211yescharacteristic
13C2×C31×#117C2211yescharacteristic
14C2×C31×#117C2211yescharacteristic
15C31×#421—22no—
16C31×#421—22no—
17C31×#421—22no—
18C31×#421C414yescomplemented
19C2×C31×#104—22no—
20C2×C31×#104C414yescomplemented
21C31×#413—22no—
22C31×#413—22no—
23C2×C31×#101C412yescomplemented
24C2×C31×#100C412yescomplemented
25C31×#405—22no—
26C31×#405—22no—
27C4×M16×C31—22no—
28C31×#343—22no—
29C31×#341—22no—
30C31×H(3,ℤ/4)—22no—
31C2×#41×C31—21no—
32C2×#41×C31—21no—
33C2×#41×C31—21no—
34C2×#41×C31—21no—
35C2×#41×C31—21no—
36C2×#41×C31—21no—
37C2×#41×C31—21no—
38C2×#41×C31—21no—
39C2×#41×C31—21no—
40C2×#41×C31—21no—
41C2×#41×C31C2×C412yes—
42C2×#41×C31C2×C412yes—
43C22×Q8×C31C2×C411yescharacteristic
44C22×D4×C31—21no—
45C22×D4×C31C2×C411yescharacteristic
46C23×C4×C31—21no—
47C23×C4×C31C2311yescharacteristic
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×C31—21no—
61C2×M16×C31—21no—
62C2×M16×C31—21no—
63C2×M16×C31—21no—
64C2×M16×C31C2×C412yes—
65C2×M16×C31C2×C412yes—
66C2×M16×C31C2×C412yes—
67C2×M16×C31C2×C412yes—
68C2×M16×C31D412yes—
69C2×M16×C31D412yes—
70C2×M16×C31D412yes—
71C2×M16×C31D412yes—
72C22×C8×C31—21no—
73C22×C8×C31—21no—
74C22×C8×C31—21no—
75C22×C8×C31—21no—
76C31×#117—21no—
77C31×#117—21no—
78C31×#117—21no—
79C31×#117—21no—
80C31×#117—21no—
81C31×#117—21no—
82C31×#117C2×C412yes—
83C31×#117D412yes—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31—21no—
86C2×C22⋊C4×C31—21no—
87C2×C22⋊C4×C31—21no—
88C2×C42×C31C2×C412yes—
89C2×C42×C31D412yes—
90C31×#104—28no—
91C31×#104—28no—
92C31×#101—24no—
93C31×#100—24no—
94C31×#97—24no—
95C4×C8×C31—24no—
96C24×C31—21no—
97C24×C31#4111yescharacteristic
98#41×C31—22no—
99#41×C31—22no—
100#41×C31—22no—
101#41×C31—22no—
102#41×C31—22no—
103#41×C31—22no—
104#41×C31—22no—
105#41×C31—22no—
106#41×C31—41no—
107#41×C31—41no—
108#41×C31—41no—
109#41×C31—41no—
110#41×C31—41no—
111#41×C31—41no—
112#41×C31—41no—
113#41×C31—41no—
114C2×Q8×C31—21no—
115C2×Q8×C31—21no—
116C2×Q8×C31—21no—
117C2×Q8×C31—21no—
118C2×Q8×C31—21no—
119C2×Q8×C31C4212yes—
120C2×D4×C31—22no—
121C2×D4×C31—22no—
122C2×D4×C31—21no—
123C2×D4×C31—21no—
124C2×D4×C31—21no—
125C2×D4×C31—21no—
126C2×D4×C31—21no—
127C2×D4×C31—41no—
128C2×D4×C31—41no—
129C2×D4×C31—41no—
130C2×D4×C31—41no—
131C2×D4×C31C4212yes—
132C22×C4×C31—21no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—41no—
138C22×C4×C31—41no—
139C22×C4×C31—41no—
140C22×C4×C31—41no—
141C22×C4×C31C22×C411yescharacteristic
142C22×C4×C31C22×C411yescharacteristic
143C22×C4×C31C22×C411yescharacteristic
144C22×C4×C31C2×D411yescharacteristic
145C22×C4×C31C2×D411yescharacteristic
146C22×C4×C31C2×D411yescharacteristic
147C22×C4×C31C2×D411yescharacteristic
148C22×C4×C31C2×D411yescharacteristic
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31#4111yescharacteristic
151C22×C4×C31#4111yescharacteristic
152C22×C4×C31#4111yescharacteristic
153C22×C4×C31#4111yescharacteristic
154C22×C4×C31#4111yescharacteristic
155M16×C31—22no—
156M16×C31—22no—
157M16×C31—22no—
158M16×C31—22no—
159M16×C31—22no—
160M16×C31—22no—
161M16×C31—22no—
162M16×C31—22no—
163M16×C31—22no—
164M16×C31—22no—
165M16×C31—41no—
166M16×C31—41no—
167M16×C31—41no—
168M16×C31—41no—
169M16×C31C22⋊C414yes—
170M16×C31C22⋊C414yes—
171C2×C8×C31—22no—
172C2×C8×C31—22no—
173C2×C8×C31—22no—
174C2×C8×C31—22no—
175C2×C8×C31—22no—
176C2×C8×C31—22no—
177C2×C8×C31—22no—
178C2×C8×C31—22no—
179C2×C8×C31—41no—
180C2×C8×C31—41no—
181C2×C8×C31—41no—
182C2×C8×C31—41no—
183C4⋊C4×C31—22no—
184C4⋊C4×C31—22no—
185C4⋊C4×C31—41no—
186C4⋊C4×C31—41no—
187C22⋊C4×C31—22no—
188C22⋊C4×C31—22no—
189C22⋊C4×C31—41no—
190C22⋊C4×C31—41no—
191C42×C31—22no—
192C42×C31—22no—
193C42×C31—22no—
194C42×C31C22⋊C414yes—
195#10955C3111yesmaximal, characteristic, direct product factor, Sylow
196C23×C31—22no—
197C23×C31—41no—
198C23×C31—41no—
199C23×C31—81no—
200C23×C31—82no—
201C23×C31#11711yescharacteristic
202C23×C31C4×D411yescharacteristic
203C23×C31C4×D411yescharacteristic
204C23×C31#12111yescharacteristic
205C23×C31#12311yescharacteristic
206C23×C31#12411yescharacteristic
207C23×C31#12611yescharacteristic
208Q8×C31—22no—
209Q8×C31—22no—
210Q8×C31—41no—
211Q8×C31—41no—
212D4×C31—22no—
213D4×C31—22no—
214D4×C31—42no—
215D4×C31—42no—
216D4×C31—42no—
217D4×C31—42no—
218D4×C31—41no—
219D4×C31—41no—
220C2×C4×C31—22no—
221C2×C4×C31—24no—
222C2×C4×C31—41no—
223C2×C4×C31—41no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—42no—
228C2×C4×C31—42no—
229C2×C4×C31—82no—
230C2×C4×C31—82no—
231C2×C4×C31C2×C4211yescharacteristic
232C2×C4×C31C2×C22⋊C411yescharacteristic
233C2×C4×C31C2×C22⋊C411yescharacteristic
234C2×C4×C31C2×C22⋊C411yescharacteristic
235C2×C4×C31#11711yescharacteristic
236C2×C4×C31#11711yescharacteristic
237C2×C4×C31C4×D411yescharacteristic
238C2×C4×C31C4×D411yescharacteristic
239C2×C4×C31C4×D411yescharacteristic
240C2×C4×C31C4×D411yescharacteristic
241C2×C4×C31C4×D411yescharacteristic
242C2×C4×C31C4×D411yescharacteristic
243C2×C4×C31C4×D411yescharacteristic
244C2×C4×C31C4×D411yescharacteristic
245C2×C4×C31C4×D411yescharacteristic
246C2×C4×C31C4×D411yescharacteristic
247C2×C4×C31#12011yescharacteristic
248C2×C4×C31#12111yescharacteristic
249C2×C4×C31#12111yescharacteristic
250C2×C4×C31#12111yescharacteristic
251C2×C4×C31#12111yescharacteristic
252C2×C4×C31#12111yescharacteristic
253C2×C4×C31#12311yescharacteristic
254C2×C4×C31#12311yescharacteristic
255C2×C4×C31#12411yescharacteristic
256C2×C4×C31#12411yescharacteristic
257C2×C4×C31#12611yescharacteristic
258C2×C4×C31#12711yescharacteristic
259C8×C31—24no—
260C8×C31—24no—
261C8×C31—42no—
262C8×C31—42no—
263C2×#421C2×C3111yescharacteristic
264C2×#421C2×C3111yescharacteristic
265C2×#413C2×C3111yescharacteristic
266#2873C2×C3111yescharacteristic, complemented
267#1742C2×C3111yescharacteristic, complemented
268#1738C2×C3111yescharacteristic, complemented
269C2×H(3,ℤ/4)C2×C3111yescharacteristic, complemented
270C22×C31—41no—
271C22×C31—41no—
272C22×C31—41no—
273C22×C31—41no—
274C22×C31—41no—
275C22×C31—41no—
276C22×C31—41no—
277C22×C31—42no—
278C22×C31—82no—
279C22×C31—82no—
280C22×C31—82no—
281C22×C31C4×C22⋊C411yescharacteristic
282C22×C31#38611yescharacteristic
283C22×C31#38811yescharacteristic
284C22×C31#38811yescharacteristic
285C22×C31#38811yescharacteristic
286C22×C31#38811yescharacteristic
287C22×C31#39011yescharacteristic
288C4×C31—44no—
289C4×C31—42no—
290C4×C31—82no—
291C4×C31C4×C22⋊C411yescharacteristic
292C4×C31C4×C22⋊C411yescharacteristic
293C4×C31#38611yescharacteristic
294C4×C31#38611yescharacteristic
295C4×C31#38811yescharacteristic
296C4×C31#38811yescharacteristic
297C4×C31#39011yescharacteristic
298C4×C31#39011yescharacteristic
299C22×#41C22×C3111yescharacteristic
300C22×M16C22×C3111yescharacteristic
301C22×M16C22×C3111yescharacteristic
302C22×M16C22×C3111yescharacteristic
303C22×M16C22×C3111yescharacteristic
304C2×#117C22×C3111yescharacteristic
305C2×#117C22×C3111yescharacteristic
306#421—22no—
307#421—22no—
308#421—22no—
309#421C4×C3114yescomplemented
310C2×#104—22no—
311C2×#104C4×C3114yescomplemented
312#413—22no—
313#413—22no—
314C2×#101C4×C3112yescomplemented
315C2×#100C4×C3112yescomplemented
316#405—22no—
317#405—22no—
318C4×M16—22no—
319#343—22no—
320#341—22no—
321H(3,ℤ/4)—22no—
322C2×C31—21no—
323C2×C31—21no—
324C2×C31—21no—
325C2×C31—21no—
326C2×C31—21no—
327C2×C31—21no—
328C2×C31—21no—
329C2×C31—82no—
330C2×C31#143711yescharacteristic
331C2×#41—21no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41C2×C4×C3112yes—
342C2×#41C2×C4×C3112yes—
343C22×Q8C2×C4×C3111yescharacteristic
344C22×D4—21no—
345C22×D4C2×C4×C3111yescharacteristic
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×M16—21no—
364C2×M16C2×C4×C3112yes—
365C2×M16C2×C4×C3112yes—
366C2×M16C2×C4×C3112yes—
367C2×M16C2×C4×C3112yes—
368C2×M16D4×C3112yes—
369C2×M16D4×C3112yes—
370C2×M16D4×C3112yes—
371C2×M16D4×C3112yes—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117C2×C4×C3112yes—
383#117D4×C3112yes—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C42C2×C4×C3112yes—
389C2×C42D4×C3112yes—
390#104—28no—
391#104—28no—
392#101—24no—
393#100—24no—
394#97—24no—
395C4×C8—24no—
396C31#1095511yescharacteristic, direct product factor, Sylow
397C24—21no—
398C24#41×C3111yescharacteristic
399#41—22no—
400#41—22no—
401#41—22no—
402#41—22no—
403#41—22no—
404#41—22no—
405#41—22no—
406#41—22no—
407#41—41no—
408#41—41no—
409#41—41no—
410#41—41no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8C42×C3112yes—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4C42×C3112yes—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4C22×C4×C3111yescharacteristic
443C22×C4C22×C4×C3111yescharacteristic
444C22×C4C22×C4×C3111yescharacteristic
445C22×C4C2×D4×C3111yescharacteristic
446C22×C4C2×D4×C3111yescharacteristic
447C22×C4C2×D4×C3111yescharacteristic
448C22×C4C2×D4×C3111yescharacteristic
449C22×C4C2×D4×C3111yescharacteristic
450C22×C4C2×D4×C3111yescharacteristic
451C22×C4#41×C3111yescharacteristic
452C22×C4#41×C3111yescharacteristic
453C22×C4#41×C3111yescharacteristic
454C22×C4#41×C3111yescharacteristic
455C22×C4#41×C3111yescharacteristic
456M16—22no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—22no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16C22⋊C4×C3114yes—
471M16C22⋊C4×C3114yes—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C42—22no—
493C42—22no—
494C42—22no—
495C42C22⋊C4×C3114yes—
496C23—22no—
497C23—41no—
498C23—41no—
499C23—81no—
500C23—82no—
501C23C31×#11711yescharacteristic
502C23C4×D4×C3111yescharacteristic
503C23C4×D4×C3111yescharacteristic
504C23C31×#12111yescharacteristic
505C23C31×#12311yescharacteristic
506C23C31×#12411yescharacteristic
507C23C31×#12611yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512D4—22no—
513D4—22no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—42no—
518D4—41no—
519D4—41no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—82no—
530C2×C4—82no—
531C2×C4C2×C42×C3111yescharacteristic
532C2×C4C2×C22⋊C4×C3111yescharacteristic
533C2×C4C2×C22⋊C4×C3111yescharacteristic
534C2×C4C2×C22⋊C4×C3111yescharacteristic
535C2×C4C31×#11711yescharacteristic
536C2×C4C31×#11711yescharacteristic
537C2×C4C4×D4×C3111yescharacteristic
538C2×C4C4×D4×C3111yescharacteristic
539C2×C4C4×D4×C3111yescharacteristic
540C2×C4C4×D4×C3111yescharacteristic
541C2×C4C4×D4×C3111yescharacteristic
542C2×C4C4×D4×C3111yescharacteristic
543C2×C4C4×D4×C3111yescharacteristic
544C2×C4C4×D4×C3111yescharacteristic
545C2×C4C4×D4×C3111yescharacteristic
546C2×C4C4×D4×C3111yescharacteristic
547C2×C4C31×#12011yescharacteristic
548C2×C4C31×#12111yescharacteristic
549C2×C4C31×#12111yescharacteristic
550C2×C4C31×#12111yescharacteristic
551C2×C4C31×#12111yescharacteristic
552C2×C4C31×#12111yescharacteristic
553C2×C4C31×#12311yescharacteristic
554C2×C4C31×#12311yescharacteristic
555C2×C4C31×#12411yescharacteristic
556C2×C4C31×#12411yescharacteristic
557C2×C4C31×#12611yescharacteristic
558C2×C4C31×#12711yescharacteristic
559C8—24no—
560C8—24no—
561C8—42no—
562C8—42no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—42no—
571C22—82no—
572C22—82no—
573C22—82no—
574C22C4×C22⋊C4×C3111yescharacteristic
575C22C31×#38611yescharacteristic
576C22C31×#38811yescharacteristic
577C22C31×#38811yescharacteristic
578C22C31×#38811yescharacteristic
579C22C31×#38811yescharacteristic
580C22C31×#39011yescharacteristic
581C4—44no—
582C4—42no—
583C4—82no—
584C4C4×C22⋊C4×C3111yescharacteristic
585C4C4×C22⋊C4×C3111yescharacteristic
586C4C31×#38611yescharacteristic
587C4C31×#38611yescharacteristic
588C4C31×#38811yescharacteristic
589C4C31×#38811yescharacteristic
590C4C31×#39011yescharacteristic
591C4C31×#39011yescharacteristic
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—82no—
600C2C31×#143711yescharacteristic
subgroupG/H
centerC4×C31#386
commutatorC2×C4C2×C42×C31
Frattini, cosocleC23×C4C23×C31
socleC2×C31#1437
prime radicalC22×#41×C31C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#2873C2semidirect
5. C31×#1742C2semidirect
6. C31×#1738C2semidirect
7. C2×C31×H(3,ℤ/4)C2semidirect
18. C31×#421C4semidirect
20. C2×C31×#104C4semidirect
23. C2×C31×#101C4semidirect
24. C2×C31×#100C4semidirect
195. #10955C31direct (N × H)
266. #2873C2×C31semidirect
267. #1742C2×C31semidirect
268. #1738C2×C31semidirect
269. C2×H(3,ℤ/4)C2×C31semidirect
309. #421C4×C31semidirect
311. C2×#104C4×C31semidirect
314. C2×#101C4×C31semidirect
315. C2×#100C4×C31semidirect
396. C31#10955direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4212
C2×C31×#4132
C31×#28732
C31×#17422
C31×#17382
C2×C31×H(3,ℤ/4)2
#1095531