Finite Group Databasebeta

← C31×#15125 #21471884

Subgroups — C31×#15125 #21471884

Order 7936.

2038 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×C31×#393C212yesmaximal
3C2×C31×#380C212yesmaximal
4C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
5C31×#1446C212yesmaximal, complemented
6C31×#1442C212yesmaximal, complemented
7C31×#1439C212yesmaximal
8C31×C4⋊#95C212yesmaximal, complemented
9C31×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×Q8×C31C2212yes—
11C24×C4×C31C2211yescharacteristic
12C2×C31×C4⋊Q8—28no—
13C2×C31×C4⋊Q8—24no—
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2212yes—
16C22×C4⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2214yes—
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2211yescharacteristic
20C22×C42×C31C2211yescharacteristic
21C22×C42×C31C2211yescharacteristic
22C31×#393—28no—
23C31×#380—28no—
24C4×C22⋊C4×C31—24no—
25C2×C31×#95C2214yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2211yescharacteristic
29C2×C31×#95C2214yes—
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2214yes—
32C25×C31C2311yescharacteristic
33C22×Q8×C31—28no—
34C22×Q8×C31—24no—
35C22×Q8×C31—24no—
36C22×Q8×C31—24no—
37C22×Q8×C31—44no—
38C23×C4×C31—22no—
39C23×C4×C31—24no—
40C23×C4×C31—24no—
41C23×C4×C31—22no—
42C23×C4×C31Q814yescomplemented
43C23×C4×C31C2314yes—
44C23×C4×C31C2311yescharacteristic
45C23×C4×C31C2314yes—
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2311yescharacteristic
50C23×C4×C31C2311yescharacteristic
51C31×C4⋊Q8—232no—
52C2×C4⋊C4×C31—28no—
53C2×C4⋊C4×C31—24no—
54C2×C4⋊C4×C31—24no—
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31—24no—
57C2×C4⋊C4×C31—24no—
58C2×C4⋊C4×C31—24no—
59C2×C4⋊C4×C31D418yes—
60C2×C22⋊C4×C31—22no—
61C2×C22⋊C4×C31—22no—
62C2×C22⋊C4×C31—22no—
63C2×C22⋊C4×C31—22no—
64C2×C22⋊C4×C31—28no—
65C2×C22⋊C4×C31—28no—
66C2×C22⋊C4×C31—44no—
67C2×C22⋊C4×C31D414yes—
68C2×C22⋊C4×C31Q814yescomplemented
69C2×C42×C31—24no—
70C2×C42×C31—22no—
71C2×C42×C31—24no—
72C2×C42×C31D414yes—
73C31×#95—22no—
74C31×#95—22no—
75C31×#95—28no—
76C31×#95—28no—
77C31×#95—24no—
78C31×#95—24no—
79C31×#95—44no—
80C24×C31—21no—
81C24×C31—22no—
82C24×C31—21no—
83C24×C31—21no—
84C24×C31—21no—
85C24×C31—22no—
86C24×C31—22no—
87C24×C31—22no—
88C24×C31C2×D412yes—
89C24×C31C2×Q812yes—
90C24×C31C2×Q812yes—
91C24×C31C2411yescharacteristic
92C2×Q8×C31—216no—
93C2×Q8×C31—416no—
94C2×Q8×C31—416no—
95C2×Q8×C31—48no—
96C2×Q8×C31—48no—
97C22×C4×C31—22no—
98C22×C4×C31—22no—
99C22×C4×C31—22no—
100C22×C4×C31—22no—
101C22×C4×C31—21no—
102C22×C4×C31—22no—
103C22×C4×C31—21no—
104C22×C4×C31—21no—
105C22×C4×C31—24no—
106C22×C4×C31—24no—
107C22×C4×C31—24no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—21no—
111C22×C4×C31—21no—
112C22×C4×C31—21no—
113C22×C4×C31—22no—
114C22×C4×C31—24no—
115C22×C4×C31—22no—
116C22×C4×C31—24no—
117C22×C4×C31—24no—
118C22×C4×C31—22no—
119C22×C4×C31—28no—
120C22×C4×C31—216no—
121C22×C4×C31—24no—
122C22×C4×C31—24no—
123C22×C4×C31—24no—
124C22×C4×C31—24no—
125C22×C4×C31—24no—
126C22×C4×C31—24no—
127C22×C4×C31—24no—
128C22×C4×C31—44no—
129C22×C4×C31—44no—
130C22×C4×C31—48no—
131C22×C4×C31C2×D412yes—
132C22×C4×C31C2×D418yes—
133C22×C4×C31C2×D412yes—
134C22×C4×C31C2×D412yes—
135C22×C4×C31C2×D412yes—
136C22×C4×C31C2×D412yes—
137C22×C4×C31C2×D414yes—
138C22×C4×C31C2×Q812yes—
139C22×C4×C31C2×Q812yes—
140C22×C4×C31C2×Q812yes—
141C22×C4×C31C2×Q812yes—
142C22×C4×C31#4112yes—
143C22×C4×C31#4112yes—
144C22×C4×C31#4114yes—
145C22×C4×C31#4112yes—
146C4⋊C4×C31—216no—
147C4⋊C4×C31—216no—
148C4⋊C4×C31—48no—
149C22⋊C4×C31—28no—
150C22⋊C4×C31—28no—
151C22⋊C4×C31—416no—
152C42×C31—28no—
153C42×C31—44no—
154#15125C3111yesmaximal, characteristic, direct product factor, Sylow
155C23×C31—22no—
156C23×C31—22no—
157C23×C31—22no—
158C23×C31—24no—
159C23×C31—22no—
160C23×C31—22no—
161C23×C31—22no—
162C23×C31—24no—
163C23×C31—24no—
164C23×C31—24no—
165C23×C31—24no—
166C23×C31—24no—
167C23×C31—41no—
168C23×C31—41no—
169C23×C31—42no—
170C23×C31—41no—
171C23×C31—41no—
172C23×C31—42no—
173C23×C31—42no—
174C23×C31—42no—
175C23×C31—42no—
176C23×C31—42no—
177C23×C31C4⋊Q814yescomplemented
178C23×C31C22×D411yescharacteristic
179C23×C31C22×D412yes—
180C23×C31C22×D411yescharacteristic
181C23×C31C22×Q811yescharacteristic
182C23×C31C22×Q811yescharacteristic
183C23×C31C2×#4111yescharacteristic
184C23×C31C2×#4111yescharacteristic
185C23×C31C2×#4112yes—
186C23×C31C2×#4111yescharacteristic
187C23×C31H(5,𝔽2)12yes—
188C23×C312−1+412yes—
189Q8×C31—432no—
190C2×C4×C31—22no—
191C2×C4×C31—22no—
192C2×C4×C31—22no—
193C2×C4×C31—22no—
194C2×C4×C31—24no—
195C2×C4×C31—24no—
196C2×C4×C31—24no—
197C2×C4×C31—24no—
198C2×C4×C31—28no—
199C2×C4×C31—22no—
200C2×C4×C31—22no—
201C2×C4×C31—22no—
202C2×C4×C31—24no—
203C2×C4×C31—28no—
204C2×C4×C31—28no—
205C2×C4×C31—24no—
206C2×C4×C31—24no—
207C2×C4×C31—41no—
208C2×C4×C31—44no—
209C2×C4×C31—41no—
210C2×C4×C31—41no—
211C2×C4×C31—41no—
212C2×C4×C31—42no—
213C2×C4×C31—41no—
214C2×C4×C31—44no—
215C2×C4×C31—41no—
216C2×C4×C31—44no—
217C2×C4×C31—44no—
218C2×C4×C31—42no—
219C2×C4×C31—42no—
220C2×C4×C31—416no—
221C2×C4×C31—44no—
222C2×C4×C31—44no—
223C2×C4×C31—44no—
224C2×C4×C31—44no—
225C2×C4×C31—44no—
226C2×C4×C31—44no—
227C2×C4×C31—44no—
228C2×C4×C31#12014yes—
229C2×C4×C31#12114yes—
230C2×C4×C31C22⋊Q814yes—
231C2×C4×C31C22⋊Q814yes—
232C2×C4×C31C22⋊Q818yes—
233C2×C4×C31#12414yes—
234C2×C4×C31#12418yes—
235C22×C4⋊Q8C2×C3111yescharacteristic, complemented
236C2×#393C2×C3112yes—
237C2×#380C2×C3112yes—
238C2×C4×C22⋊C4C2×C3111yescharacteristic
239#1446C2×C3112yescomplemented
240#1442C2×C3112yescomplemented
241#1439C2×C3112yes—
242C4⋊#95C2×C3111yescharacteristic, complemented
243C4⋊#95C2×C3112yescomplemented
244C22×C31—24no—
245C22×C31—28no—
246C22×C31—42no—
247C22×C31—42no—
248C22×C31—42no—
249C22×C31—42no—
250C22×C31—42no—
251C22×C31—44no—
252C22×C31—44no—
253C22×C31—44no—
254C22×C31—42no—
255C22×C31C2×#12011yescharacteristic
256C22×C31C2×#12111yescharacteristic
257C22×C31C2×C22⋊Q811yescharacteristic
258C22×C31C2×C22⋊Q811yescharacteristic
259C22×C31C2×C22⋊Q812yes—
260C22×C31C2×#12411yescharacteristic
261C22×C31C2×#12412yes—
262C22×C31C2×C4⋊Q811yescharacteristic
263C22×C31#53211yescharacteristic
264C22×C31#53311yescharacteristic
265C22×C31#53311yescharacteristic
266C22×C31#53511yescharacteristic
267C22×C31#53611yescharacteristic
268C22×C31#54212yes—
269C22×C31#54412yes—
270C22×C31D4212yes—
271C22×C31#54612yes—
272C22×C31#54712yes—
273C22×C31#54812yes—
274C22×C31D4×Q812yes—
275C22×C31#55412yes—
276C22×C31#55512yes—
277C22×C31#55612yes—
278C4×C31—24no—
279C4×C31—24no—
280C4×C31—42no—
281C4×C31—42no—
282C4×C31—48no—
283C4×C31—42no—
284C4×C31—84no—
285C4×C31#39318yescomplemented
286C23×Q8C22×C3112yes—
287C24×C4C22×C3111yescharacteristic
288C2×C4⋊Q8—28no—
289C2×C4⋊Q8—24no—
290C22×C4⋊C4C22×C3112yes—
291C22×C4⋊C4C22×C3112yes—
292C22×C4⋊C4C22×C3112yes—
293C22×C22⋊C4C22×C3114yes—
294C22×C22⋊C4C22×C3111yescharacteristic
295C22×C22⋊C4C22×C3111yescharacteristic
296C22×C42C22×C3111yescharacteristic
297C22×C42C22×C3111yescharacteristic
298#393—28no—
299#380—28no—
300C4×C22⋊C4—24no—
301C2×#95C22×C3114yes—
302C2×#95C22×C3112yes—
303C2×#95C22×C3112yes—
304C2×#95C22×C3111yescharacteristic
305C2×#95C22×C3114yes—
306C2×#95C22×C3111yescharacteristic
307C2×#95C22×C3114yes—
308C2×C31—44no—
309C2×C31C2×#39311yescharacteristic
310C2×C31#240811yescharacteristic
311C2×C31#240911yescharacteristic
312C2×C31#243912yes—
313C2×C31#244012yes—
314C2×C31#249112yes—
315C2×C31#249212yes—
316C2×C31#254711yescharacteristic
317C2×C31#256311yescharacteristic
318C2×C31#262811yescharacteristic
319C2×C31#285711yescharacteristic
320C25C23×C3111yescharacteristic
321C22×Q8—28no—
322C22×Q8—24no—
323C22×Q8—24no—
324C22×Q8—24no—
325C22×Q8—44no—
326C23×C4—22no—
327C23×C4—24no—
328C23×C4—24no—
329C23×C4—22no—
330C23×C4Q8×C3114yescomplemented
331C23×C4C23×C3114yes—
332C23×C4C23×C3114yes—
333C23×C4C23×C3111yescharacteristic
334C23×C4C23×C3111yescharacteristic
335C23×C4C23×C3111yescharacteristic
336C23×C4C23×C3111yescharacteristic
337C23×C4C23×C3111yescharacteristic
338C23×C4C23×C3111yescharacteristic
339C4⋊Q8—232no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4D4×C3118yes—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4D4×C3114yes—
356C2×C22⋊C4Q8×C3114yescomplemented
357C2×C42—24no—
358C2×C42—22no—
359C2×C42—24no—
360C2×C42D4×C3114yes—
361#95—22no—
362#95—22no—
363#95—28no—
364#95—28no—
365#95—24no—
366#95—24no—
367#95—44no—
368C31#1512511yescharacteristic, direct product factor, Sylow
369C24—21no—
370C24—22no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—22no—
375C24—22no—
376C24—22no—
377C24C2×D4×C3112yes—
378C24C2×Q8×C3112yes—
379C24C2×Q8×C3112yes—
380C24C24×C3111yescharacteristic
381C2×Q8—216no—
382C2×Q8—416no—
383C2×Q8—416no—
384C2×Q8—48no—
385C2×Q8—48no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—28no—
409C22×C4—216no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—44no—
418C22×C4—44no—
419C22×C4—48no—
420C22×C4C2×D4×C3112yes—
421C22×C4C2×D4×C3118yes—
422C22×C4C2×D4×C3112yes—
423C22×C4C2×D4×C3112yes—
424C22×C4C2×D4×C3112yes—
425C22×C4C2×D4×C3112yes—
426C22×C4C2×D4×C3114yes—
427C22×C4C2×Q8×C3112yes—
428C22×C4C2×Q8×C3112yes—
429C22×C4C2×Q8×C3112yes—
430C22×C4C2×Q8×C3112yes—
431C22×C4#41×C3112yes—
432C22×C4#41×C3112yes—
433C22×C4#41×C3114yes—
434C22×C4#41×C3112yes—
435C4⋊C4—216no—
436C4⋊C4—216no—
437C4⋊C4—48no—
438C22⋊C4—28no—
439C22⋊C4—28no—
440C22⋊C4—416no—
441C42—28no—
442C42—44no—
443C23—22no—
444C23—22no—
445C23—22no—
446C23—24no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—24no—
451C23—24no—
452C23—24no—
453C23—24no—
454C23—24no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23—41no—
459C23—41no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23C31×C4⋊Q814yescomplemented
466C23C22×D4×C3111yescharacteristic
467C23C22×D4×C3112yes—
468C23C22×D4×C3111yescharacteristic
469C23C22×Q8×C3111yescharacteristic
470C23C22×Q8×C3111yescharacteristic
471C23C2×#41×C3111yescharacteristic
472C23C2×#41×C3111yescharacteristic
473C23C2×#41×C3112yes—
474C23C2×#41×C3111yescharacteristic
475C23C31×H(5,𝔽2)12yes—
476C23C31×2−1+412yes—
477Q8—432no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—28no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—28no—
492C2×C4—28no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—41no—
496C2×C4—44no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—44no—
503C2×C4—41no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—416no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—44no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—44no—
515C2×C4—44no—
516C2×C4C31×#12014yes—
517C2×C4C31×#12114yes—
518C2×C4C31×C22⋊Q814yes—
519C2×C4C31×C22⋊Q814yes—
520C2×C4C31×C22⋊Q818yes—
521C2×C4C31×#12414yes—
522C2×C4C31×#12418yes—
523C22—24no—
524C22—28no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—44no—
531C22—44no—
532C22—44no—
533C22—42no—
534C22C2×C31×#12011yescharacteristic
535C22C2×C31×#12111yescharacteristic
536C22C2×C31×C22⋊Q811yescharacteristic
537C22C2×C31×C22⋊Q811yescharacteristic
538C22C2×C31×C22⋊Q812yes—
539C22C2×C31×#12411yescharacteristic
540C22C2×C31×#12412yes—
541C22C2×C31×C4⋊Q811yescharacteristic
542C22C31×#53211yescharacteristic
543C22C31×#53311yescharacteristic
544C22C31×#53311yescharacteristic
545C22C31×#53511yescharacteristic
546C22C31×#53611yescharacteristic
547C22C31×#54212yes—
548C22C31×#54412yes—
549C22D42×C3112yes—
550C22C31×#54612yes—
551C22C31×#54712yes—
552C22C31×#54812yes—
553C22D4×Q8×C3112yes—
554C22C31×#55412yes—
555C22C31×#55512yes—
556C22C31×#55612yes—
557C4—24no—
558C4—24no—
559C4—42no—
560C4—42no—
561C4—48no—
562C4—42no—
563C4—84no—
564C4C31×#39318yescomplemented
565C2—44no—
566C2C2×C31×#39311yescharacteristic
567C2C31×#240811yescharacteristic
568C2C31×#240911yescharacteristic
569C2C31×#243912yes—
570C2C31×#244012yes—
571C2C31×#249112yes—
572C2C31×#249212yes—
573C2C31×#254711yescharacteristic
574C2C31×#256311yescharacteristic
575C2C31×#262811yescharacteristic
576C2C31×#285711yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×C4⋊Q8C2semidirect
5. C31×#1446C2semidirect
6. C31×#1442C2semidirect
8. C31×C4⋊#95C2semidirect
9. C31×C4⋊#95C2semidirect
42. C23×C4×C31Q8semidirect
68. C2×C22⋊C4×C31Q8semidirect
154. #15125C31direct (N × H)
177. C23×C31C4⋊Q8semidirect
235. C22×C4⋊Q8C2×C31semidirect
239. #1446C2×C31semidirect
240. #1442C2×C31semidirect
242. C4⋊#95C2×C31semidirect
243. C4⋊#95C2×C31semidirect
285. C4×C31#393semidirect
330. C23×C4Q8×C31semidirect
356. C2×C22⋊C4Q8×C31semidirect
368. C31#15125direct (N × H)
465. C23C31×C4⋊Q8semidirect
564. C4C31×#393semidirect

Maximal subgroups

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

subgroupindex
C22×C31×C4⋊Q82
C2×C31×#3932
C2×C31×#3802
C2×C4×C22⋊C4×C312
C31×#14462
C31×#14422
C31×#14392
C31×C4⋊#952
#1512531