Finite Group Databasebeta

← C31×#11084 #21467843

Subgroups — C31×#11084 #21467843

Order 7936.

878 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#424C211yesmaximal, characteristic, complemented
2C2×C31×#421C211yesmaximal, characteristic
3C2×C31×#421C211yesmaximal, characteristic
4C2×C31×#408C211yesmaximal, characteristic
5C31×#1738C211yesmaximal, characteristic, complemented
6C2×C31×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
7C31×#1729C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C22×M16×C31C2211yescharacteristic
10C22×M16×C31C2211yescharacteristic
11C22×M16×C31C2211yescharacteristic
12C23×C8×C31C2211yescharacteristic
13C2×C31×#117C2211yescharacteristic
14C2×C31×#117C2211yescharacteristic
15C31×#424—22no—
16C31×#424—22no—
17C2×C31×C4⋊C8—22no—
18C31×#421—22no—
19C31×#421—22no—
20C31×#421—22no—
21C31×#421C414yescomplemented
22C2×C31×#104—22no—
23C2×C31×#104—22no—
24C31×#408—22no—
25C31×#408—22no—
26C2×C31×C22⋊C8—22no—
27C31×#341—22no—
28C31×H(3,ℤ/4)—22no—
29C31×#336—22no—
30C2×#41×C31—21no—
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×C31C2×C412yes—
41C2×#41×C31D412yes—
42C22×Q8×C31Q811yescharacteristic
43C22×D4×C31—21no—
44C22×D4×C31Q811yescharacteristic
45C23×C4×C31—21no—
46C23×C4×C31C2311yescharacteristic
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×C31—21no—
61C2×M16×C31—21no—
62C2×M16×C31—21no—
63C2×M16×C31C2×C412yes—
64C2×M16×C31D412yes—
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×C31—21no—
73C22×C8×C31D412yes—
74C22×C8×C31D412yes—
75C31×#117—21no—
76C31×#117—21no—
77C31×#117—21no—
78C31×#117—21no—
79C31×#117—21no—
80C31×#117—21no—
81C31×#117C2×C412yes—
82C31×#117D412yes—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31—21no—
85C2×C22⋊C4×C31—21no—
86C2×C22⋊C4×C31—21no—
87C2×C42×C31D412yes—
88C2×C42×C31D412yes—
89C31×C4⋊C8—28no—
90C31×#104—28no—
91C31×#104—28no—
92C31×C22⋊C8—28no—
93C24×C31—21no—
94C24×C31#4111yescharacteristic
95#41×C31—22no—
96#41×C31—22no—
97#41×C31—22no—
98#41×C31—22no—
99#41×C31—22no—
100#41×C31—22no—
101#41×C31—22no—
102#41×C31—22no—
103#41×C31—41no—
104#41×C31—41no—
105#41×C31—41no—
106#41×C31—41no—
107#41×C31—41no—
108#41×C31—41no—
109#41×C31—41no—
110#41×C31—41no—
111C2×Q8×C31—21no—
112C2×Q8×C31—21no—
113C2×Q8×C31—21no—
114C2×Q8×C31—21no—
115C2×Q8×C31—21no—
116C2×Q8×C31C4⋊C412yes—
117C2×D4×C31—22no—
118C2×D4×C31—22no—
119C2×D4×C31—21no—
120C2×D4×C31—21no—
121C2×D4×C31—21no—
122C2×D4×C31—21no—
123C2×D4×C31—21no—
124C2×D4×C31—41no—
125C2×D4×C31—41no—
126C2×D4×C31—41no—
127C2×D4×C31—41no—
128C2×D4×C31C4⋊C412yes—
129C22×C4×C31—21no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—41no—
135C22×C4×C31—41no—
136C22×C4×C31—41no—
137C22×C4×C31—41no—
138C22×C4×C31C22×C411yescharacteristic
139C22×C4×C31C2×D411yescharacteristic
140C22×C4×C31C2×D411yescharacteristic
141C22×C4×C31C2×D411yescharacteristic
142C22×C4×C31C2×D411yescharacteristic
143C22×C4×C31C2×D411yescharacteristic
144C22×C4×C31C2×D411yescharacteristic
145C22×C4×C31C2×D411yescharacteristic
146C22×C4×C31C2×Q811yescharacteristic
147C22×C4×C31#4111yescharacteristic
148C22×C4×C31#4111yescharacteristic
149C22×C4×C31#4111yescharacteristic
150C22×C4×C31#4111yescharacteristic
151C22×C4×C31#4111yescharacteristic
152M16×C31—22no—
153M16×C31—22no—
154M16×C31—22no—
155M16×C31—22no—
156M16×C31—41no—
157M16×C31—41no—
158M16×C31—41no—
159M16×C31—41no—
160M16×C31—41no—
161M16×C31—41no—
162M16×C31—41no—
163M16×C31—41no—
164C2×C8×C31—22no—
165C2×C8×C31—22no—
166C2×C8×C31—22no—
167C2×C8×C31—22no—
168C2×C8×C31—22no—
169C2×C8×C31—22no—
170C2×C8×C31—22no—
171C2×C8×C31—22no—
172C2×C8×C31—41no—
173C2×C8×C31—41no—
174C2×C8×C31—41no—
175C2×C8×C31—41no—
176C2×C8×C31—41no—
177C2×C8×C31—41no—
178C2×C8×C31—41no—
179C2×C8×C31—41no—
180C4⋊C4×C31—22no—
181C4⋊C4×C31—22no—
182C4⋊C4×C31—41no—
183C4⋊C4×C31—41no—
184C22⋊C4×C31—22no—
185C22⋊C4×C31—22no—
186C22⋊C4×C31—41no—
187C22⋊C4×C31—41no—
188C42×C31—22no—
189C42×C31—22no—
190C42×C31—22no—
191C42×C31C22⋊C414yes—
192#11084C3111yesmaximal, characteristic, direct product factor, Sylow
193C23×C31—22no—
194C23×C31—42no—
195C23×C31—44no—
196C23×C31—41no—
197C23×C31—41no—
198C23×C31C4×D411yescharacteristic
199C23×C31#12111yescharacteristic
200C23×C31C22⋊Q811yescharacteristic
201C23×C31#12311yescharacteristic
202C23×C31#12311yescharacteristic
203C23×C31#12311yescharacteristic
204C23×C31#12611yescharacteristic
205Q8×C31—22no—
206Q8×C31—22no—
207Q8×C31—41no—
208Q8×C31—41no—
209D4×C31—22no—
210D4×C31—22no—
211D4×C31—42no—
212D4×C31—42no—
213D4×C31—42no—
214D4×C31—42no—
215D4×C31—41no—
216D4×C31—41no—
217C2×C4×C31—22no—
218C2×C4×C31—24no—
219C2×C4×C31—44no—
220C2×C4×C31—41no—
221C2×C4×C31—41no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—44no—
227C2×C4×C31—42no—
228C2×C4×C31C2×C22⋊C411yescharacteristic
229C2×C4×C31C2×C4⋊C411yescharacteristic
230C2×C4×C31#11711yescharacteristic
231C2×C4×C31C4×D411yescharacteristic
232C2×C4×C31C4×D411yescharacteristic
233C2×C4×C31C4×D411yescharacteristic
234C2×C4×C31#12011yescharacteristic
235C2×C4×C31#12011yescharacteristic
236C2×C4×C31#12011yescharacteristic
237C2×C4×C31#12111yescharacteristic
238C2×C4×C31#12111yescharacteristic
239C2×C4×C31#12111yescharacteristic
240C2×C4×C31#12111yescharacteristic
241C2×C4×C31#12111yescharacteristic
242C2×C4×C31#12111yescharacteristic
243C2×C4×C31#12111yescharacteristic
244C2×C4×C31C22⋊Q811yescharacteristic
245C2×C4×C31C22⋊Q811yescharacteristic
246C2×C4×C31C22⋊Q811yescharacteristic
247C2×C4×C31C22⋊Q811yescharacteristic
248C2×C4×C31C22⋊Q811yescharacteristic
249C2×C4×C31#12311yescharacteristic
250C2×C4×C31#12311yescharacteristic
251C2×C4×C31#12411yescharacteristic
252C2×C4×C31#12411yescharacteristic
253C2×C4×C31#12411yescharacteristic
254C2×C4×C31#12611yescharacteristic
255C2×C4×C31#12711yescharacteristic
256C8×C31—42no—
257C8×C31—42no—
258C8×C31—42no—
259C8×C31—42no—
260C2×#424C2×C3111yescharacteristic, complemented
261C2×#421C2×C3111yescharacteristic
262C2×#421C2×C3111yescharacteristic
263C2×#408C2×C3111yescharacteristic
264#1738C2×C3111yescharacteristic, complemented
265C2×H(3,ℤ/4)C2×C3111yescharacteristic, complemented
266#1729C2×C3111yescharacteristic, complemented
267C22×C31—22no—
268C22×C31—22no—
269C22×C31—22no—
270C22×C31—41no—
271C22×C31—41no—
272C22×C31—41no—
273C22×C31—41no—
274C22×C31—44no—
275C22×C31—42no—
276C22×C31—82no—
277C22×C31—82no—
278C22×C31#38511yescharacteristic
279C22×C31#38611yescharacteristic
280C22×C31#38811yescharacteristic
281C22×C31#39411yescharacteristic
282C22×C31#39611yescharacteristic
283C22×C31#39711yescharacteristic
284C22×C31#39911yescharacteristic
285C4×C31—44no—
286C4×C31—42no—
287C4×C31—82no—
288C4×C31#38011yescharacteristic
289C4×C31#38511yescharacteristic
290C4×C31#38811yescharacteristic
291C4×C31#39011yescharacteristic
292C4×C31#39211yescharacteristic
293C4×C31#39311yescharacteristic
294C4×C31#39411yescharacteristic
295C4×C31#39611yescharacteristic
296C22×#41C22×C3111yescharacteristic
297C22×M16C22×C3111yescharacteristic
298C22×M16C22×C3111yescharacteristic
299C22×M16C22×C3111yescharacteristic
300C23×C8C22×C3111yescharacteristic
301C2×#117C22×C3111yescharacteristic
302C2×#117C22×C3111yescharacteristic
303#424—22no—
304#424—22no—
305C2×C4⋊C8—22no—
306#421—22no—
307#421—22no—
308#421—22no—
309#421C4×C3114yescomplemented
310C2×#104—22no—
311C2×#104—22no—
312#408—22no—
313#408—22no—
314C2×C22⋊C8—22no—
315#341—22no—
316H(3,ℤ/4)—22no—
317#336—22no—
318C2×C31—21no—
319C2×C31—21no—
320C2×C31—21no—
321C2×C31—21no—
322C2×C31—21no—
323C2×C31—21no—
324C2×C31—82no—
325C2×C31#143911yescharacteristic
326C2×C31#209812yes—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41C2×C4×C3112yes—
338C2×#41D4×C3112yes—
339C22×Q8Q8×C3111yescharacteristic
340C22×D4—21no—
341C22×D4Q8×C3111yescharacteristic
342C23×C4—21no—
343C23×C4C23×C3111yescharacteristic
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
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×M16C2×C4×C3112yes—
361C2×M16D4×C3112yes—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8D4×C3112yes—
371C22×C8D4×C3112yes—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117C2×C4×C3112yes—
379#117D4×C3112yes—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C42D4×C3112yes—
385C2×C42D4×C3112yes—
386C4⋊C8—28no—
387#104—28no—
388#104—28no—
389C22⋊C8—28no—
390C31#1108411yescharacteristic, direct product factor, Sylow
391C24—21no—
392C24#41×C3111yescharacteristic
393#41—22no—
394#41—22no—
395#41—22no—
396#41—22no—
397#41—22no—
398#41—22no—
399#41—22no—
400#41—22no—
401#41—41no—
402#41—41no—
403#41—41no—
404#41—41no—
405#41—41no—
406#41—41no—
407#41—41no—
408#41—41no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8C4⋊C4×C3112yes—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4C4⋊C4×C3112yes—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
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×C4C2×D4×C3111yescharacteristic
444C22×C4C2×Q8×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—41no—
455M16—41no—
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—22no—
469C2×C8—22no—
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—41no—
481C4⋊C4—41no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C42—22no—
487C42—22no—
488C42—22no—
489C42C22⋊C4×C3114yes—
490C23—22no—
491C23—42no—
492C23—44no—
493C23—41no—
494C23—41no—
495C23C4×D4×C3111yescharacteristic
496C23C31×#12111yescharacteristic
497C23C31×C22⋊Q811yescharacteristic
498C23C31×#12311yescharacteristic
499C23C31×#12311yescharacteristic
500C23C31×#12311yescharacteristic
501C23C31×#12611yescharacteristic
502Q8—22no—
503Q8—22no—
504Q8—41no—
505Q8—41no—
506D4—22no—
507D4—22no—
508D4—42no—
509D4—42no—
510D4—42no—
511D4—42no—
512D4—41no—
513D4—41no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—44no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4C2×C22⋊C4×C3111yescharacteristic
526C2×C4C2×C4⋊C4×C3111yescharacteristic
527C2×C4C31×#11711yescharacteristic
528C2×C4C4×D4×C3111yescharacteristic
529C2×C4C4×D4×C3111yescharacteristic
530C2×C4C4×D4×C3111yescharacteristic
531C2×C4C31×#12011yescharacteristic
532C2×C4C31×#12011yescharacteristic
533C2×C4C31×#12011yescharacteristic
534C2×C4C31×#12111yescharacteristic
535C2×C4C31×#12111yescharacteristic
536C2×C4C31×#12111yescharacteristic
537C2×C4C31×#12111yescharacteristic
538C2×C4C31×#12111yescharacteristic
539C2×C4C31×#12111yescharacteristic
540C2×C4C31×#12111yescharacteristic
541C2×C4C31×C22⋊Q811yescharacteristic
542C2×C4C31×C22⋊Q811yescharacteristic
543C2×C4C31×C22⋊Q811yescharacteristic
544C2×C4C31×C22⋊Q811yescharacteristic
545C2×C4C31×C22⋊Q811yescharacteristic
546C2×C4C31×#12311yescharacteristic
547C2×C4C31×#12311yescharacteristic
548C2×C4C31×#12411yescharacteristic
549C2×C4C31×#12411yescharacteristic
550C2×C4C31×#12411yescharacteristic
551C2×C4C31×#12611yescharacteristic
552C2×C4C31×#12711yescharacteristic
553C8—42no—
554C8—42no—
555C8—42no—
556C8—42no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—44no—
565C22—42no—
566C22—82no—
567C22—82no—
568C22C31×#38511yescharacteristic
569C22C31×#38611yescharacteristic
570C22C31×#38811yescharacteristic
571C22C31×#39411yescharacteristic
572C22C31×#39611yescharacteristic
573C22C31×#39711yescharacteristic
574C22C31×#39911yescharacteristic
575C4—44no—
576C4—42no—
577C4—82no—
578C4C31×#38011yescharacteristic
579C4C31×#38511yescharacteristic
580C4C31×#38811yescharacteristic
581C4C31×#39011yescharacteristic
582C4C31×#39211yescharacteristic
583C4C31×#39311yescharacteristic
584C4C31×#39411yescharacteristic
585C4C31×#39611yescharacteristic
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—82no—
593C2C31×#143911yescharacteristic
594C2C31×#209812yes—
subgroupG/H
centerC2×C4×C31#127
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
socleC22×C31#399
prime radicalC22×#41×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#424C2semidirect
5. C31×#1738C2semidirect
6. C2×C31×H(3,ℤ/4)C2semidirect
7. C31×#1729C2semidirect
21. C31×#421C4semidirect
192. #11084C31direct (N × H)
260. C2×#424C2×C31semidirect
264. #1738C2×C31semidirect
265. C2×H(3,ℤ/4)C2×C31semidirect
266. #1729C2×C31semidirect
309. #421C4×C31semidirect
390. C31#11084direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4242
C2×C31×#4212
C2×C31×#4082
C31×#17382
C2×C31×H(3,ℤ/4)2
C31×#17292
#1108431