Finite Group Databasebeta

← C31×#32902 #21489661

Subgroups — C31×#32902 #21489661

Order 7936.

2008 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C31C211yesmaximal, characteristic, complemented
2C2×C31×#459C212yesmaximal, complemented
3C2×C31×#447C212yesmaximal, complemented
4C31×#2856C211yesmaximal, characteristic, complemented
5C31×#1879C214yesmaximal, complemented
6C31×#1874C212yesmaximal, complemented
7C31×#1802C212yesmaximal, complemented
8C31×#1797C211yesmaximal, characteristic, complemented
9C23×D4×C31C2211yescharacteristic
10C24×C4×C31—21no—
11C22×D8×C31C2214yes—
12C2×C31×#127C2211yescharacteristic, complemented
13C2×C31×#121—21no—
14C2×C31×#121—21no—
15C2×C31×#121C2212yes—
16C2×C4×D4×C31—28no—
17C2×C4×D4×C31—21no—
18C2×C4×D4×C31—21no—
19C2×C4×D4×C31C2212yes—
20C2×C4×D4×C31C2212yes—
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31—21no—
23C22×C42×C31C2211yescharacteristic
24C31×#459—28no—
25C31×#447—28no—
26C2×C31×C4⋊C8C2212yescomplemented
27C2×C31×#102C2214yes—
28C2×C31×#102C2214yescomplemented
29C2×C31×C22⋊C8C2212yes—
30C31×#390—21no—
31C31×#390—21no—
32C31×#390C2212yescomplemented
33C31×#384C2211yescharacteristic, complemented
34C31×#340C2214yescomplemented
35C31×#336C2212yescomplemented
36C25×C31—21no—
37C22×D4×C31—24no—
38C22×D4×C31—24no—
39C22×D4×C31—22no—
40C22×D4×C31—21no—
41C22×D4×C31—21no—
42C22×D4×C31—21no—
43C22×D4×C31—22no—
44C22×D4×C31D414yescomplemented
45C22×D4×C31C2312yes—
46C22×D4×C31C2312yes—
47C23×C4×C31—28no—
48C23×C4×C31—21no—
49C23×C4×C31—22no—
50C23×C4×C31—22no—
51C23×C4×C31—44no—
52C23×C4×C31—44no—
53C23×C4×C31D411yescharacteristic
54C23×C4×C31D411yescharacteristic
55C23×C4×C31C2311yescharacteristic
56C2×D8×C31—28no—
57C2×D8×C31—28no—
58C2×D8×C31—28no—
59C22×C8×C31C2314yes—
60C31×#127—24no—
61C31×#121—24no—
62C31×#121—24no—
63C31×#121—44no—
64C31×#121—44no—
65C4×D4×C31—28no—
66C4×D4×C31—28no—
67C4×D4×C31—24no—
68C4×D4×C31—24no—
69C4×D4×C31—24no—
70C4×D4×C31D418yescomplemented
71C2×C4⋊C4×C31—21no—
72C2×C4⋊C4×C31—24no—
73C2×C4⋊C4×C31—21no—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31C2312yes—
76C2×C4⋊C4×C31C2312yes—
77C2×C22⋊C4×C31—28no—
78C2×C22⋊C4×C31—22no—
79C2×C22⋊C4×C31—22no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—22no—
83C2×C42×C31—24no—
84C2×C42×C31D411yescharacteristic
85C2×C42×C31D411yescharacteristic
86C2×C42×C31C2311yescharacteristic
87C2×C42×C31C2311yescharacteristic
88C31×C4⋊C8—24no—
89C31×#102—28no—
90C31×#102—28no—
91C31×C22⋊C8—24no—
92C24×C31—24no—
93C24×C31—24no—
94C24×C31—24no—
95C24×C31—22no—
96C24×C31—22no—
97C24×C31—42no—
98C24×C31—42no—
99C24×C31—42no—
100C24×C31—42no—
101C24×C31C2×D411yescharacteristic
102C2×D4×C31—24no—
103C2×D4×C31—24no—
104C2×D4×C31—216no—
105C2×D4×C31—216no—
106C2×D4×C31—24no—
107C2×D4×C31—22no—
108C2×D4×C31—24no—
109C2×D4×C31—22no—
110C2×D4×C31—22no—
111C2×D4×C31—22no—
112C2×D4×C31—22no—
113C2×D4×C31—24no—
114C2×D4×C31—42no—
115C2×D4×C31—42no—
116C2×D4×C31—44no—
117C2×D4×C31—44no—
118C2×D4×C31—44no—
119C2×D4×C31—42no—
120C2×D4×C31—42no—
121C2×D4×C31—42no—
122C2×D4×C31—42no—
123C2×D4×C31C2×D414yes—
124C2×D4×C31C2×D414yes—
125C2×D4×C31#4114yes—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—24no—
131C22×C4×C31—28no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—28no—
136C22×C4×C31—22no—
137C22×C4×C31—41no—
138C22×C4×C31—44no—
139C22×C4×C31—432no—
140C22×C4×C31—42no—
141C22×C4×C31—42no—
142C22×C4×C31—44no—
143C22×C4×C31—44no—
144C22×C4×C31—44no—
145C22×C4×C31D814yescomplemented
146C22×C4×C31C2×D411yescharacteristic
147C22×C4×C31C2×D411yescharacteristic
148C22×C4×C31C2×D411yescharacteristic
149C22×C4×C31C2×D412yes—
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31#4112yes—
153C22×C4×C31C2411yescharacteristic
154D8×C31—416no—
155C2×C8×C31—24no—
156C2×C8×C31—24no—
157C2×C8×C31—24no—
158C4⋊C4×C31—24no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—22no—
161C4⋊C4×C31—22no—
162C4⋊C4×C31—42no—
163C4⋊C4×C31—42no—
164C4⋊C4×C31C2×D414yes—
165C22⋊C4×C31—28no—
166C22⋊C4×C31—28no—
167C22⋊C4×C31—44no—
168C22⋊C4×C31—44no—
169C22⋊C4×C31—44no—
170C42×C31—22no—
171C42×C31—22no—
172C42×C31—22no—
173C42×C31C2×D414yes—
174#32902C3111yesmaximal, characteristic, direct product factor, Sylow
175C23×C31—21no—
176C23×C31—21no—
177C23×C31—21no—
178C23×C31—21no—
179C23×C31—216no—
180C23×C31—24no—
181C23×C31—24no—
182C23×C31—24no—
183C23×C31—48no—
184C23×C31—48no—
185C23×C31—48no—
186C23×C31—48no—
187C23×C31—48no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—42no—
191C23×C31—42no—
192C23×C31—48no—
193C23×C31—42no—
194C23×C31—42no—
195C23×C31—42no—
196C23×C31—42no—
197C23×C31—42no—
198C23×C31—42no—
199C23×C31—42no—
200C23×C31#12112yes—
201C23×C31C2×D812yes—
202C23×C31AGL(1,ℤ/8)12yes—
203C23×C31C22×D411yescharacteristic
204D4×C31—216no—
205D4×C31—24no—
206D4×C31—24no—
207D4×C31—24no—
208D4×C31—44no—
209D4×C31—44no—
210D4×C31—84no—
211D4×C31—88no—
212D4×C31—84no—
213D4×C31#12118yescomplemented
214C2×C4×C31—21no—
215C2×C4×C31—21no—
216C2×C4×C31—21no—
217C2×C4×C31—21no—
218C2×C4×C31—21no—
219C2×C4×C31—21no—
220C2×C4×C31—24no—
221C2×C4×C31—24no—
222C2×C4×C31—28no—
223C2×C4×C31—21no—
224C2×C4×C31—24no—
225C2×C4×C31—21no—
226C2×C4×C31—21no—
227C2×C4×C31—44no—
228C2×C4×C31—416no—
229C2×C4×C31—48no—
230C2×C4×C31—42no—
231C2×C4×C31—42no—
232C2×C4×C31—416no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31—42no—
236C2×C4×C31#12012yes—
237C2×C4×C31#12012yes—
238C2×C4×C31#12112yes—
239C2×C4×C31C2×D812yes—
240C2×C4×C31C2×D812yes—
241C2×C4×C31AGL(1,ℤ/8)12yes—
242C2×C4×C31C22×D411yescharacteristic
243C2×C4×C31C22×D412yes—
244C2×C4×C31C2×#4112yes—
245C2×C4×C31C2×#4111yescharacteristic
246C8×C31—44no—
247C22×C4×D4C2×C3111yescharacteristic, complemented
248C2×#459C2×C3112yescomplemented
249C2×#447C2×C3112yescomplemented
250#2856C2×C3111yescharacteristic, complemented
251#1879C2×C3114yescomplemented
252#1874C2×C3112yescomplemented
253#1802C2×C3112yescomplemented
254#1797C2×C3111yescharacteristic, complemented
255C22×C31—22no—
256C22×C31—22no—
257C22×C31—22no—
258C22×C31—22no—
259C22×C31—22no—
260C22×C31—22no—
261C22×C31—28no—
262C22×C31—432no—
263C22×C31—44no—
264C22×C31—44no—
265C22×C31—44no—
266C22×C31—44no—
267C22×C31—44no—
268C22×C31—44no—
269C22×C31—82no—
270C22×C31—82no—
271C22×C31—82no—
272C22×C31—82no—
273C22×C31—82no—
274C22×C31—82no—
275C22×C31—82no—
276C22×C31#45914yescomplemented
277C22×C31C2×#12011yescharacteristic
278C22×C31C2×#12111yescharacteristic
279C22×C31#52511yescharacteristic
280C22×C31C22×D811yescharacteristic
281C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C31#57511yescharacteristic
284C4×C31—22no—
285C4×C31—22no—
286C4×C31—22no—
287C4×C31—44no—
288C4×C31—41no—
289C4×C31—82no—
290C4×C31#44714yescomplemented
291C4×C31C2×#12112yes—
292C4×C31#52512yes—
293C23×D4C22×C3111yescharacteristic
294C24×C4—21no—
295C22×D8C22×C3114yes—
296C2×#127C22×C3111yescharacteristic, complemented
297C2×#121—21no—
298C2×#121—21no—
299C2×#121C22×C3112yes—
300C2×C4×D4—28no—
301C2×C4×D4—21no—
302C2×C4×D4—21no—
303C2×C4×D4C22×C3112yes—
304C2×C4×D4C22×C3112yes—
305C22×C4⋊C4C22×C3111yescharacteristic
306C22×C22⋊C4—21no—
307C22×C42C22×C3111yescharacteristic
308#459—28no—
309#447—28no—
310C2×C4⋊C8C22×C3112yescomplemented
311C2×#102C22×C3114yes—
312C2×#102C22×C3114yescomplemented
313C2×C22⋊C8C22×C3112yes—
314#390—21no—
315#390—21no—
316#390C22×C3112yescomplemented
317#384C22×C3111yescharacteristic, complemented
318#340C22×C3114yescomplemented
319#336C22×C3112yescomplemented
320C2×C31—24no—
321C2×C31—48no—
322C2×C31—162no—
323C2×C31#284711yescharacteristic
324C2×C31C2×#44711yescharacteristic
325C2×C31#300611yescharacteristic
326C2×C31C2×#45911yescharacteristic
327C2×C31#303611yescharacteristic
328C2×C31#310011yescharacteristic
329C2×C31#310911yescharacteristic
330C25—21no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—22no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4—22no—
338C22×D4D4×C3114yescomplemented
339C22×D4C23×C3112yes—
340C22×D4C23×C3112yes—
341C23×C4—28no—
342C23×C4—21no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—44no—
346C23×C4—44no—
347C23×C4D4×C3111yescharacteristic
348C23×C4D4×C3111yescharacteristic
349C23×C4C23×C3111yescharacteristic
350C2×D8—28no—
351C2×D8—28no—
352C2×D8—28no—
353C22×C8C23×C3114yes—
354#127—24no—
355#121—24no—
356#121—24no—
357#121—44no—
358#121—44no—
359C4×D4—28no—
360C4×D4—28no—
361C4×D4—24no—
362C4×D4—24no—
363C4×D4—24no—
364C4×D4D4×C3118yescomplemented
365C2×C4⋊C4—21no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4C23×C3112yes—
370C2×C4⋊C4C23×C3112yes—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C42—24no—
378C2×C42D4×C3111yescharacteristic
379C2×C42D4×C3111yescharacteristic
380C2×C42C23×C3111yescharacteristic
381C2×C42C23×C3111yescharacteristic
382C4⋊C8—24no—
383#102—28no—
384#102—28no—
385C22⋊C8—24no—
386C31#3290211yescharacteristic, direct product factor, Sylow
387C24—24no—
388C24—24no—
389C24—24no—
390C24—22no—
391C24—22no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24—42no—
396C24C2×D4×C3111yescharacteristic
397C2×D4—24no—
398C2×D4—24no—
399C2×D4—216no—
400C2×D4—216no—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—24no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—24no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—44no—
412C2×D4—44no—
413C2×D4—44no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4C2×D4×C3114yes—
419C2×D4C2×D4×C3114yes—
420C2×D4#41×C3114yes—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—28no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—28no—
431C22×C4—22no—
432C22×C4—41no—
433C22×C4—44no—
434C22×C4—432no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—44no—
438C22×C4—44no—
439C22×C4—44no—
440C22×C4D8×C3114yescomplemented
441C22×C4C2×D4×C3111yescharacteristic
442C22×C4C2×D4×C3111yescharacteristic
443C22×C4C2×D4×C3111yescharacteristic
444C22×C4C2×D4×C3112yes—
445C22×C4C2×D4×C3111yescharacteristic
446C22×C4C2×D4×C3111yescharacteristic
447C22×C4#41×C3112yes—
448C22×C4C24×C3111yescharacteristic
449D8—416no—
450C2×C8—24no—
451C2×C8—24no—
452C2×C8—24no—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4C2×D4×C3114yes—
460C22⋊C4—28no—
461C22⋊C4—28no—
462C22⋊C4—44no—
463C22⋊C4—44no—
464C22⋊C4—44no—
465C42—22no—
466C42—22no—
467C42—22no—
468C42C2×D4×C3114yes—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—216no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—48no—
478C23—48no—
479C23—48no—
480C23—48no—
481C23—48no—
482C23—48no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23C31×#12112yes—
495C23C2×D8×C3112yes—
496C23C31×AGL(1,ℤ/8)12yes—
497C23C22×D4×C3111yescharacteristic
498D4—216no—
499D4—24no—
500D4—24no—
501D4—24no—
502D4—44no—
503D4—44no—
504D4—84no—
505D4—88no—
506D4—84no—
507D4C31×#12118yescomplemented
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—28no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—21no—
518C2×C4—24no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—44no—
522C2×C4—416no—
523C2×C4—48no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—416no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4C31×#12012yes—
531C2×C4C31×#12012yes—
532C2×C4C31×#12112yes—
533C2×C4C2×D8×C3112yes—
534C2×C4C2×D8×C3112yes—
535C2×C4C31×AGL(1,ℤ/8)12yes—
536C2×C4C22×D4×C3111yescharacteristic
537C2×C4C22×D4×C3112yes—
538C2×C4C2×#41×C3112yes—
539C2×C4C2×#41×C3111yescharacteristic
540C8—44no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—28no—
548C22—432no—
549C22—44no—
550C22—44no—
551C22—44no—
552C22—44no—
553C22—44no—
554C22—44no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—82no—
560C22—82no—
561C22—82no—
562C22C31×#45914yescomplemented
563C22C2×C31×#12011yescharacteristic
564C22C2×C31×#12111yescharacteristic
565C22C31×#52511yescharacteristic
566C22C22×D8×C3111yescharacteristic
567C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
568C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
569C22C31×#57511yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—44no—
574C4—41no—
575C4—82no—
576C4C31×#44714yescomplemented
577C4C2×C31×#12112yes—
578C4C31×#52512yes—
579C2—24no—
580C2—48no—
581C2—162no—
582C2C31×#284711yescharacteristic
583C2C2×C31×#44711yescharacteristic
584C2C31×#300611yescharacteristic
585C2C2×C31×#45911yescharacteristic
586C2C31×#303611yescharacteristic
587C2C31×#310011yescharacteristic
588C2C31×#310911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×D4×C31C2semidirect
2. C2×C31×#459C2semidirect
3. C2×C31×#447C2semidirect
4. C31×#2856C2semidirect
5. C31×#1879C2semidirect
6. C31×#1874C2semidirect
7. C31×#1802C2semidirect
8. C31×#1797C2semidirect
12. C2×C31×#127C22semidirect
26. C2×C31×C4⋊C8C22semidirect
28. C2×C31×#102C22semidirect
32. C31×#390C22semidirect
33. C31×#384C22semidirect
34. C31×#340C22semidirect
35. C31×#336C22semidirect
44. C22×D4×C31D4semidirect
70. C4×D4×C31D4semidirect
145. C22×C4×C31D8semidirect
174. #32902C31direct (N × H)
213. D4×C31#121semidirect
247. C22×C4×D4C2×C31semidirect
248. C2×#459C2×C31semidirect
249. C2×#447C2×C31semidirect
250. #2856C2×C31semidirect
251. #1879C2×C31semidirect
252. #1874C2×C31semidirect
253. #1802C2×C31semidirect
254. #1797C2×C31semidirect
276. C22×C31#459semidirect
290. C4×C31#447semidirect
296. C2×#127C22×C31semidirect
310. C2×C4⋊C8C22×C31semidirect
312. C2×#102C22×C31semidirect
316. #390C22×C31semidirect
317. #384C22×C31semidirect
318. #340C22×C31semidirect
319. #336C22×C31semidirect
338. C22×D4D4×C31semidirect
364. C4×D4D4×C31semidirect
386. C31#32902direct (N × H)
440. C22×C4D8×C31semidirect
507. D4C31×#121semidirect
562. C22C31×#459semidirect
576. C4C31×#447semidirect

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×#4592
C2×C31×#4472
C31×#28562
C31×#18792
C31×#18742
C31×#18022
C31×#17972
#3290231