Finite Group Databasebeta

← C31×#15181 #21471940

Subgroups — C31×#15181 #21471940

Order 7936.

2314 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C31C211yesmaximal, characteristic
2C2×C31×#389C211yesmaximal, characteristic, complemented
3C2×C31×#380C212yesmaximal, complemented
4C2×C31×#380C212yesmaximal, complemented
5C31×#1442C212yesmaximal, complemented
6C31×#1439C214yesmaximal, complemented
7C31×#1438C212yesmaximal
8C31×C4⋊#95C211yesmaximal, characteristic, complemented
9C23×D4×C31C2211yescharacteristic
10C24×C4×C31C2212yes—
11C2×C4×D4×C31—28no—
12C2×C4×D4×C31—24no—
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2214yes—
20C22×C22⋊C4×C31C2214yes—
21C22×C42×C31C2211yescharacteristic
22C31×#389—24no—
23C31×#380—28no—
24C31×#380—28no—
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2214yes—
28C2×C31×#95C2214yes—
29C2×C31×#95C2212yes—
30C25×C31C2312yes—
31C22×D4×C31—24no—
32C22×D4×C31—24no—
33C22×D4×C31—22no—
34C22×D4×C31—22no—
35C22×D4×C31Q814yes—
36C23×C4×C31—24no—
37C23×C4×C31—24no—
38C23×C4×C31—24no—
39C23×C4×C31—24no—
40C23×C4×C31—24no—
41C23×C4×C31—24no—
42C23×C4×C31D418yes—
43C23×C4×C31C2312yes—
44C23×C4×C31C2314yes—
45C23×C4×C31C2311yescharacteristic
46C23×C4×C31C2312yes—
47C23×C4×C31C2312yes—
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2311yescharacteristic
50C4×D4×C31—232no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31—22no—
53C2×C4⋊C4×C31—22no—
54C2×C4⋊C4×C31—22no—
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31—24no—
57C2×C4⋊C4×C31—24no—
58C2×C4⋊C4×C31—24no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—24no—
61C2×C4⋊C4×C31—44no—
62C2×C4⋊C4×C31D414yescomplemented
63C2×C22⋊C4×C31—24no—
64C2×C22⋊C4×C31—24no—
65C2×C22⋊C4×C31—24no—
66C2×C22⋊C4×C31—28no—
67C2×C22⋊C4×C31—28no—
68C2×C22⋊C4×C31—28no—
69C2×C22⋊C4×C31—44no—
70C2×C22⋊C4×C31—44no—
71C2×C22⋊C4×C31—44no—
72C2×C42×C31—24no—
73C2×C42×C31D414yes—
74C31×#95—28no—
75C31×#95—28no—
76C31×#95—24no—
77C31×#95—24no—
78C31×#95—42no—
79C24×C31—22no—
80C24×C31—22no—
81C24×C31—22no—
82C24×C31—22no—
83C24×C31—22no—
84C24×C31—22no—
85C24×C31—22no—
86C24×C31—22no—
87C24×C31—22no—
88C24×C31—22no—
89C24×C31—22no—
90C24×C31—22no—
91C24×C31C2×D414yes—
92C24×C31C2×Q814yes—
93C24×C31#4114yes—
94C24×C31C2411yescharacteristic
95C2×D4×C31—28no—
96C2×D4×C31—28no—
97C2×D4×C31—216no—
98C2×D4×C31—216no—
99C2×D4×C31—28no—
100C22×C4×C31—22no—
101C22×C4×C31—22no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—24no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—21no—
113C22×C4×C31—24no—
114C22×C4×C31—22no—
115C22×C4×C31—21no—
116C22×C4×C31—216no—
117C22×C4×C31—216no—
118C22×C4×C31—216no—
119C22×C4×C31—24no—
120C22×C4×C31—24no—
121C22×C4×C31—24no—
122C22×C4×C31—22no—
123C22×C4×C31—24no—
124C22×C4×C31—24no—
125C22×C4×C31—24no—
126C22×C4×C31—24no—
127C22×C4×C31—22no—
128C22×C4×C31—24no—
129C22×C4×C31—24no—
130C22×C4×C31—22no—
131C22×C4×C31—48no—
132C22×C4×C31—48no—
133C22×C4×C31—48no—
134C22×C4×C31—48no—
135C22×C4×C31C2×D414yes—
136C22×C4×C31C2×D414yes—
137C22×C4×C31C2×D412yes—
138C22×C4×C31C2×D412yes—
139C22×C4×C31C2×D414yes—
140C22×C4×C31C2×D412yes—
141C22×C4×C31C2×D412yes—
142C22×C4×C31C2×Q812yes—
143C22×C4×C31#4112yes—
144C22×C4×C31#4112yes—
145C22×C4×C31#4114yes—
146C4⋊C4×C31—28no—
147C4⋊C4×C31—28no—
148C4⋊C4×C31—48no—
149C4⋊C4×C31—44no—
150C4⋊C4×C31—48no—
151C22⋊C4×C31—216no—
152C22⋊C4×C31—416no—
153C22⋊C4×C31—416no—
154C42×C31—28no—
155#15181C3111yesmaximal, characteristic, direct product factor, Sylow
156C23×C31—24no—
157C23×C31—24no—
158C23×C31—24no—
159C23×C31—24no—
160C23×C31—24no—
161C23×C31—24no—
162C23×C31—24no—
163C23×C31—24no—
164C23×C31—24no—
165C23×C31—24no—
166C23×C31—24no—
167C23×C31—24no—
168C23×C31—24no—
169C23×C31—24no—
170C23×C31—24no—
171C23×C31—24no—
172C23×C31—24no—
173C23×C31—24no—
174C23×C31—42no—
175C23×C31—42no—
176C23×C31—42no—
177C23×C31—42no—
178C23×C31—42no—
179C23×C31—42no—
180C23×C31—42no—
181C23×C31—42no—
182C23×C31—42no—
183C23×C31—42no—
184C23×C31—42no—
185C23×C31—42no—
186C23×C31—42no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31C22⋊Q818yes—
191C23×C31C22×D412yes—
192C23×C31C22×D411yescharacteristic
193C23×C31C22×D411yescharacteristic
194C23×C31C22×Q811yescharacteristic
195C23×C31C2×#4111yescharacteristic
196C23×C31C2×#4112yes—
197C23×C31C2×#4112yes—
198C23×C31C2×#4111yescharacteristic
199C23×C31H(5,𝔽2)12yes—
200C23×C31H(5,𝔽2)11yescharacteristic
201C23×C312−1+411yescharacteristic
202D4×C31—232no—
203C2×C4×C31—22no—
204C2×C4×C31—24no—
205C2×C4×C31—22no—
206C2×C4×C31—24no—
207C2×C4×C31—22no—
208C2×C4×C31—24no—
209C2×C4×C31—24no—
210C2×C4×C31—24no—
211C2×C4×C31—24no—
212C2×C4×C31—22no—
213C2×C4×C31—22no—
214C2×C4×C31—28no—
215C2×C4×C31—42no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—44no—
224C2×C4×C31—432no—
225C2×C4×C31—42no—
226C2×C4×C31—44no—
227C2×C4×C31—44no—
228C2×C4×C31—44no—
229C2×C4×C31—44no—
230C2×C4×C31—42no—
231C2×C4×C31—42no—
232C2×C4×C31—44no—
233C2×C4×C31—44no—
234C2×C4×C31—44no—
235C2×C4×C31—44no—
236C2×C4×C31—44no—
237C2×C4×C31#12014yes—
238C2×C4×C31#12114yes—
239C2×C4×C31#12118yes—
240C2×C4×C31C22⋊Q814yes—
241C2×C4×C31#12318yes—
242C2×C4×C31#12414yes—
243C22×C4×D4C2×C3111yescharacteristic
244C2×#389C2×C3111yescharacteristic, complemented
245C2×#380C2×C3112yescomplemented
246C2×#380C2×C3112yescomplemented
247#1442C2×C3112yescomplemented
248#1439C2×C3114yescomplemented
249#1438C2×C3112yes—
250C4⋊#95C2×C3111yescharacteristic, complemented
251C22×C31—28no—
252C22×C31—28no—
253C22×C31—28no—
254C22×C31—44no—
255C22×C31—44no—
256C22×C31—44no—
257C22×C31—44no—
258C22×C31—44no—
259C22×C31—44no—
260C22×C31—44no—
261C22×C31—44no—
262C22×C31—44no—
263C22×C31—44no—
264C22×C31—44no—
265C22×C31—44no—
266C22×C31C2×#12011yescharacteristic
267C22×C31C2×#12112yes—
268C22×C31C2×#12111yescharacteristic
269C22×C31C2×C22⋊Q811yescharacteristic
270C22×C31C2×C22⋊Q812yes—
271C22×C31C2×#12312yes—
272C22×C31#52511yescharacteristic
273C22×C31#52512yes—
274C22×C31C2×#12411yescharacteristic
275C22×C31#53511yescharacteristic
276C22×C31#53512yes—
277C22×C31#53711yescharacteristic
278C22×C31#53712yes—
279C22×C31#54612yes—
280C22×C31D4×Q811yescharacteristic
281C22×C31#55011yescharacteristic
282C22×C31#55212yes—
283C22×C31#55312yes—
284C22×C31#55312yes—
285C22×C31#55412yes—
286C22×C31#55411yescharacteristic
287C22×C31#55512yes—
288C22×C31#55611yescharacteristic
289C4×C31—24no—
290C4×C31—42no—
291C4×C31—44no—
292C4×C31—44no—
293C4×C31—82no—
294C4×C31—84no—
295C4×C31#39418yes—
296C23×D4C22×C3111yescharacteristic
297C24×C4C22×C3112yes—
298C2×C4×D4—28no—
299C2×C4×D4—24no—
300C22×C4⋊C4C22×C3111yescharacteristic
301C22×C4⋊C4C22×C3112yes—
302C22×C4⋊C4C22×C3111yescharacteristic
303C22×C4⋊C4C22×C3111yescharacteristic
304C22×C4⋊C4C22×C3112yes—
305C22×C22⋊C4C22×C3112yes—
306C22×C22⋊C4C22×C3114yes—
307C22×C22⋊C4C22×C3114yes—
308C22×C42C22×C3111yescharacteristic
309#389—24no—
310#380—28no—
311#380—28no—
312C2×#95C22×C3112yes—
313C2×#95C22×C3112yes—
314C2×#95C22×C3114yes—
315C2×#95C22×C3114yes—
316C2×#95C22×C3112yes—
317C2×C31—48no—
318C2×C31C2×#39411yescharacteristic
319C2×C31#241412yes—
320C2×C31#241712yes—
321C2×C31#248512yes—
322C2×C31#248712yes—
323C2×C31#253511yescharacteristic
324C2×C31#253811yescharacteristic
325C2×C31#256211yescharacteristic
326C2×C31#256311yescharacteristic
327C2×C31#261511yescharacteristic
328C2×C31#284811yescharacteristic
329C25C23×C3112yes—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4Q8×C3114yes—
335C23×C4—24no—
336C23×C4—24no—
337C23×C4—24no—
338C23×C4—24no—
339C23×C4—24no—
340C23×C4—24no—
341C23×C4D4×C3118yes—
342C23×C4C23×C3112yes—
343C23×C4C23×C3114yes—
344C23×C4C23×C3112yes—
345C23×C4C23×C3111yescharacteristic
346C23×C4C23×C3112yes—
347C23×C4C23×C3111yescharacteristic
348C23×C4C23×C3111yescharacteristic
349C4×D4—232no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4D4×C3114yescomplemented
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C42—24no—
372C2×C42D4×C3114yes—
373#95—28no—
374#95—28no—
375#95—24no—
376#95—24no—
377#95—42no—
378C31#1518111yescharacteristic, direct product factor, Sylow
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24C2×D4×C3114yes—
392C24C2×Q8×C3114yes—
393C24#41×C3114yes—
394C24C24×C3111yescharacteristic
395C2×D4—28no—
396C2×D4—28no—
397C2×D4—216no—
398C2×D4—216no—
399C2×D4—28no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—216no—
417C22×C4—216no—
418C22×C4—216no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—48no—
432C22×C4—48no—
433C22×C4—48no—
434C22×C4—48no—
435C22×C4C2×D4×C3114yes—
436C22×C4C2×D4×C3114yes—
437C22×C4C2×D4×C3112yes—
438C22×C4C2×D4×C3112yes—
439C22×C4C2×D4×C3114yes—
440C22×C4C2×D4×C3112yes—
441C22×C4C2×D4×C3112yes—
442C22×C4C2×Q8×C3112yes—
443C22×C4#41×C3112yes—
444C22×C4#41×C3112yes—
445C22×C4#41×C3114yes—
446C4⋊C4—28no—
447C4⋊C4—28no—
448C4⋊C4—48no—
449C4⋊C4—44no—
450C4⋊C4—48no—
451C22⋊C4—216no—
452C22⋊C4—416no—
453C22⋊C4—416no—
454C42—28no—
455C23—24no—
456C23—24no—
457C23—24no—
458C23—24no—
459C23—24no—
460C23—24no—
461C23—24no—
462C23—24no—
463C23—24no—
464C23—24no—
465C23—24no—
466C23—24no—
467C23—24no—
468C23—24no—
469C23—24no—
470C23—24no—
471C23—24no—
472C23—24no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23C31×C22⋊Q818yes—
490C23C22×D4×C3112yes—
491C23C22×D4×C3111yescharacteristic
492C23C22×D4×C3111yescharacteristic
493C23C22×Q8×C3111yescharacteristic
494C23C2×#41×C3111yescharacteristic
495C23C2×#41×C3112yes—
496C23C2×#41×C3112yes—
497C23C2×#41×C3111yescharacteristic
498C23C31×H(5,𝔽2)12yes—
499C23C31×H(5,𝔽2)11yescharacteristic
500C23C31×2−1+411yescharacteristic
501D4—232no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—28no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—44no—
523C2×C4—432no—
524C2×C4—42no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—44no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4C31×#12014yes—
537C2×C4C31×#12114yes—
538C2×C4C31×#12118yes—
539C2×C4C31×C22⋊Q814yes—
540C2×C4C31×#12318yes—
541C2×C4C31×#12414yes—
542C22—28no—
543C22—28no—
544C22—28no—
545C22—44no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22—44no—
551C22—44no—
552C22—44no—
553C22—44no—
554C22—44no—
555C22—44no—
556C22—44no—
557C22C2×C31×#12011yescharacteristic
558C22C2×C31×#12112yes—
559C22C2×C31×#12111yescharacteristic
560C22C2×C31×C22⋊Q811yescharacteristic
561C22C2×C31×C22⋊Q812yes—
562C22C2×C31×#12312yes—
563C22C31×#52512yes—
564C22C31×#52511yescharacteristic
565C22C2×C31×#12411yescharacteristic
566C22C31×#53511yescharacteristic
567C22C31×#53512yes—
568C22C31×#53712yes—
569C22C31×#53711yescharacteristic
570C22C31×#54612yes—
571C22D4×Q8×C3111yescharacteristic
572C22C31×#55011yescharacteristic
573C22C31×#55212yes—
574C22C31×#55312yes—
575C22C31×#55312yes—
576C22C31×#55412yes—
577C22C31×#55411yescharacteristic
578C22C31×#55512yes—
579C22C31×#55611yescharacteristic
580C4—24no—
581C4—42no—
582C4—44no—
583C4—44no—
584C4—82no—
585C4—84no—
586C4C31×#39418yes—
587C2—48no—
588C2C2×C31×#39411yescharacteristic
589C2C31×#241412yes—
590C2C31×#241712yes—
591C2C31×#248512yes—
592C2C31×#248712yes—
593C2C31×#253511yescharacteristic
594C2C31×#253811yescharacteristic
595C2C31×#256211yescharacteristic
596C2C31×#256311yescharacteristic
597C2C31×#261511yescharacteristic
598C2C31×#284811yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#389C2semidirect
3. C2×C31×#380C2semidirect
4. C2×C31×#380C2semidirect
5. C31×#1442C2semidirect
6. C31×#1439C2semidirect
8. C31×C4⋊#95C2semidirect
62. C2×C4⋊C4×C31D4semidirect
155. #15181C31direct (N × H)
244. C2×#389C2×C31semidirect
245. C2×#380C2×C31semidirect
246. C2×#380C2×C31semidirect
247. #1442C2×C31semidirect
248. #1439C2×C31semidirect
250. C4⋊#95C2×C31semidirect
361. C2×C4⋊C4D4×C31semidirect
378. C31#15181direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D4×C312
C2×C31×#3892
C2×C31×#3802
C31×#14422
C31×#14392
C31×#14382
C31×C4⋊#952
#1518131