Finite Group Databasebeta

← C31×#23879 #21480638

Subgroups — C31×#23879 #21480638

Order 7936.

1840 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C31×#3489C211yesmaximal, characteristic, complemented
3C2×C31×#454C212yesmaximal, complemented
4C31×#3003C211yesmaximal, characteristic, complemented
5C31×#2435C211yesmaximal, characteristic, complemented
6C31×#2006C212yesmaximal, complemented
7C31×#2003C212yesmaximal, complemented
8C31×#1901C211yesmaximal, characteristic, complemented
9C31×#1883C212yesmaximal, complemented
10C31×#1871C211yesmaximal, characteristic, complemented
11C31×#1789C211yesmaximal, characteristic, complemented
12C2×C31×2−1+4C2211yescharacteristic, complemented
13C22×#41×C31C2211yescharacteristic
14C23×D4×C31C2211yescharacteristic
15C2×C31×AGL(1,ℤ/8)—21no—
16C2×C31×AGL(1,ℤ/8)—21no—
17C2×C31×AGL(1,ℤ/8)—28no—
18C2×C31×AGL(1,ℤ/8)C2212yes—
19C2×C31×AGL(1,ℤ/8)C2212yes—
20C2×C31×AGL(1,ℤ/8)C2212yescomplemented
21C22×SD16×C31—21no—
22C22×D8×C31—21no—
23C22×M16×C31C2211yescharacteristic
24D4×Q8×C31—21no—
25C31×#548—21no—
26C31×#547—21no—
27C31×#547—22no—
28C31×#546—21no—
29C31×#546—22no—
30C31×#537—21no—
31C31×#537C2211yescharacteristic, complemented
32C31×#536—21no—
33C31×#536C2211yescharacteristic, complemented
34C2×C31×#124C2212yescomplemented
35C31×#525—21no—
36C31×#525C2211yescharacteristic
37C2×C31×C22⋊Q8—21no—
38C2×C31×C22⋊Q8C2211yescharacteristic
39C31×#520C2211yescharacteristic, complemented
40C31×#454—28no—
41C31×#450—21no—
42C31×#450—21no—
43C31×#447—21no—
44C31×#447—21no—
45C2×C31×#104C2212yescomplemented
46C2×C31×#104C2212yescomplemented
47C2×C31×#104C2212yescomplemented
48C31×#418C2212yescomplemented
49C2×C31×#101C2212yescomplemented
50C31×#407C2211yescharacteristic
51C31×#394—22no—
52C31×#390C2212yescomplemented
53C31×#379—22no—
54C4×C22⋊C4×C31C2211yescharacteristic
55C31×#343C2212yescomplemented
56C31×#339C2212yescomplemented
57C25×C31—21no—
58C31×2−1+4—24no—
59C31×2−1+4—42no—
60C2×#41×C31—21no—
61C2×#41×C31—21no—
62C2×#41×C31—21no—
63C2×#41×C31—22no—
64C2×#41×C31—21no—
65C2×#41×C31—24no—
66C2×#41×C31—42no—
67C2×#41×C31D411yescharacteristic
68C2×#41×C31D411yescharacteristic
69C2×#41×C31C2311yescharacteristic
70C2×#41×C31C2311yescharacteristic
71C2×#41×C31C2311yescharacteristic
72C22×Q8×C31—21no—
73C22×Q8×C31—21no—
74C22×Q8×C31D411yescharacteristic
75C22×Q8×C31C2311yescharacteristic
76C22×D4×C31—24no—
77C22×D4×C31—21no—
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31—21no—
83C22×D4×C31—42no—
84C22×D4×C31D411yescharacteristic
85C22×D4×C31C2312yes—
86C23×C4×C31—21no—
87C23×C4×C31C2311yescharacteristic
88C31×AGL(1,ℤ/8)—28no—
89C31×AGL(1,ℤ/8)—28no—
90C31×AGL(1,ℤ/8)—24no—
91C31×AGL(1,ℤ/8)—24no—
92C31×AGL(1,ℤ/8)—24no—
93C31×AGL(1,ℤ/8)—24no—
94C31×AGL(1,ℤ/8)—42no—
95C31×AGL(1,ℤ/8)D418yescomplemented
96C2×SD16×C31—28no—
97C2×SD16×C31—22no—
98C2×SD16×C31—22no—
99C2×SD16×C31—22no—
100C2×D8×C31—28no—
101C2×D8×C31—22no—
102C2×D8×C31—22no—
103C2×D8×C31—22no—
104C2×M16×C31—21no—
105C2×M16×C31—24no—
106C2×M16×C31C2312yes—
107C2×M16×C31C2312yes—
108C22×C8×C31—21no—
109C31×C4⋊Q8—22no—
110C31×C4⋊Q8—21no—
111C31×#124—22no—
112C31×#124—21no—
113C31×#124—24no—
114C31×#124—42no—
115C31×#123—22no—
116C31×#123—22no—
117C31×#123—22no—
118C31×#123—21no—
119C31×#123—22no—
120C31×C22⋊Q8—22no—
121C31×C22⋊Q8—22no—
122C31×C22⋊Q8—22no—
123C31×C22⋊Q8—21no—
124C31×C22⋊Q8—21no—
125C31×C22⋊Q8—21no—
126C31×C22⋊Q8—21no—
127C31×C22⋊Q8—21no—
128C31×C22⋊Q8—21no—
129C31×C22⋊Q8—21no—
130C31×C22⋊Q8—21no—
131C31×C22⋊Q8D411yescharacteristic
132C31×C22⋊Q8D411yescharacteristic
133C31×#121—22no—
134C31×#121—22no—
135C31×#121—22no—
136C31×#121—21no—
137C31×#121—21no—
138C31×#121—22no—
139C31×#121D411yescharacteristic
140C31×#121D411yescharacteristic
141C31×#120—22no—
142C31×#120—21no—
143C4×Q8×C31—21no—
144C4×D4×C31—22no—
145C4×D4×C31—22no—
146C4×D4×C31—21no—
147C4×D4×C31—22no—
148C4×D4×C31—21no—
149C4×D4×C31—21no—
150C31×#117—21no—
151C31×#117C2311yescharacteristic
152C2×C4⋊C4×C31—22no—
153C2×C4⋊C4×C31—21no—
154C2×C4⋊C4×C31D412yes—
155C2×C4⋊C4×C31C2311yescharacteristic
156C2×C22⋊C4×C31—22no—
157C2×C22⋊C4×C31—21no—
158C2×C22⋊C4×C31—24no—
159C2×C22⋊C4×C31—24no—
160C2×C22⋊C4×C31D412yes—
161C2×C42×C31C2312yes—
162C31×#104—24no—
163C31×#104—24no—
164C31×#104—42no—
165C31×#102—22no—
166C31×#102—22no—
167C31×#101—24no—
168C31×C22⋊C8—21no—
169C31×C22⋊C8—21no—
170C31×#95—21no—
171C24×C31—22no—
172C24×C31—21no—
173C24×C31—44no—
174C24×C31—44no—
175C24×C31—41no—
176C24×C31—41no—
177C24×C31—82no—
178C24×C31C2×D411yescharacteristic
179#41×C31—22no—
180#41×C31—22no—
181#41×C31—22no—
182#41×C31—22no—
183#41×C31—22no—
184#41×C31—22no—
185#41×C31—22no—
186#41×C31—44no—
187#41×C31—41no—
188#41×C31—41no—
189#41×C31—44no—
190#41×C31—44no—
191#41×C31—48no—
192#41×C31—42no—
193#41×C31—42no—
194#41×C31C2×D414yes—
195C2×Q8×C31—22no—
196C2×Q8×C31—21no—
197C2×Q8×C31—22no—
198C2×Q8×C31—21no—
199C2×Q8×C31—21no—
200C2×Q8×C31—22no—
201C2×Q8×C31—22no—
202C2×Q8×C31—41no—
203C2×Q8×C31—44no—
204C2×Q8×C31—42no—
205C2×Q8×C31—42no—
206C2×Q8×C31C2×D411yescharacteristic
207C2×Q8×C31C2×D411yescharacteristic
208C2×Q8×C31C2×D411yescharacteristic
209C2×D4×C31—21no—
210C2×D4×C31—24no—
211C2×D4×C31—24no—
212C2×D4×C31—22no—
213C2×D4×C31—22no—
214C2×D4×C31—21no—
215C2×D4×C31—21no—
216C2×D4×C31—21no—
217C2×D4×C31—21no—
218C2×D4×C31—21no—
219C2×D4×C31—22no—
220C2×D4×C31—21no—
221C2×D4×C31—21no—
222C2×D4×C31—22no—
223C2×D4×C31—22no—
224C2×D4×C31—22no—
225C2×D4×C31—22no—
226C2×D4×C31—22no—
227C2×D4×C31—41no—
228C2×D4×C31—44no—
229C2×D4×C31—44no—
230C2×D4×C31—44no—
231C2×D4×C31—42no—
232C2×D4×C31—42no—
233C2×D4×C31—44no—
234C2×D4×C31—41no—
235C2×D4×C31—41no—
236C2×D4×C31C2×D411yescharacteristic
237C2×D4×C31C2×D411yescharacteristic
238C2×D4×C31C2×D414yes—
239C2×D4×C31C2×D411yescharacteristic
240C22×C4×C31—21no—
241C22×C4×C31—22no—
242C22×C4×C31—22no—
243C22×C4×C31—22no—
244C22×C4×C31—22no—
245C22×C4×C31—21no—
246C22×C4×C31—22no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—22no—
252C22×C4×C31—44no—
253C22×C4×C31C2×D412yes—
254C22×C4×C31C2×D411yescharacteristic
255C22×C4×C31C2×D411yescharacteristic
256C22×C4×C31C2×D411yescharacteristic
257C22×C4×C31C2×D411yescharacteristic
258C22×C4×C31C2×D411yescharacteristic
259C22×C4×C31C2×D412yes—
260C22×C4×C31C2411yescharacteristic
261SD16×C31—28no—
262SD16×C31—28no—
263SD16×C31—44no—
264D8×C31—28no—
265D8×C31—28no—
266D8×C31—44no—
267M16×C31—24no—
268M16×C31—22no—
269M16×C31—22no—
270M16×C31—22no—
271M16×C31C2×D414yes—
272C2×C8×C31—24no—
273C2×C8×C31—22no—
274C2×C8×C31—22no—
275C4⋊C4×C31—22no—
276C4⋊C4×C31—22no—
277C4⋊C4×C31—22no—
278C4⋊C4×C31—22no—
279C4⋊C4×C31—21no—
280C4⋊C4×C31—22no—
281C4⋊C4×C31—22no—
282C4⋊C4×C31—21no—
283C4⋊C4×C31—21no—
284C4⋊C4×C31—21no—
285C4⋊C4×C31C2×D411yescharacteristic
286C4⋊C4×C31C2×D411yescharacteristic
287C22⋊C4×C31—22no—
288C22⋊C4×C31—22no—
289C22⋊C4×C31—22no—
290C22⋊C4×C31—22no—
291C22⋊C4×C31—22no—
292C22⋊C4×C31—21no—
293C22⋊C4×C31—22no—
294C22⋊C4×C31—22no—
295C22⋊C4×C31—21no—
296C22⋊C4×C31—21no—
297C22⋊C4×C31—21no—
298C22⋊C4×C31—21no—
299C22⋊C4×C31—48no—
300C22⋊C4×C31—42no—
301C22⋊C4×C31—84no—
302C42×C31—22no—
303C42×C31—21no—
304C42×C31—22no—
305C42×C31—22no—
306#23879C3111yesmaximal, characteristic, direct product factor, Sylow
307C23×C31—21no—
308C23×C31—22no—
309C23×C31—22no—
310C23×C31—21no—
311C23×C31—21no—
312C23×C31—24no—
313C23×C31—41no—
314C23×C31—42no—
315C23×C31—44no—
316C23×C31—44no—
317C23×C31—44no—
318C23×C31—44no—
319C23×C31—42no—
320C23×C31—42no—
321C23×C31—42no—
322C23×C31—81no—
323C23×C31—82no—
324C23×C31—82no—
325C23×C31—82no—
326C23×C31—816no—
327C23×C31—82no—
328C23×C31#12011yescharacteristic
329C23×C31#12011yescharacteristic
330C23×C31C22×D411yescharacteristic
331Q8×C31—21no—
332Q8×C31—21no—
333Q8×C31—21no—
334Q8×C31—22no—
335Q8×C31—42no—
336Q8×C31—44no—
337Q8×C31—41no—
338Q8×C31—41no—
339Q8×C31—42no—
340Q8×C31#12012yes—
341D4×C31—24no—
342D4×C31—21no—
343D4×C31—24no—
344D4×C31—21no—
345D4×C31—21no—
346D4×C31—22no—
347D4×C31—24no—
348D4×C31—42no—
349D4×C31—42no—
350D4×C31—44no—
351D4×C31—44no—
352D4×C31—42no—
353D4×C31—44no—
354D4×C31—42no—
355D4×C31—42no—
356D4×C31—42no—
357D4×C31—42no—
358D4×C31—42no—
359D4×C31—81no—
360D4×C31—82no—
361D4×C31#12012yes—
362C2×C4×C31—21no—
363C2×C4×C31—22no—
364C2×C4×C31—21no—
365C2×C4×C31—21no—
366C2×C4×C31—21no—
367C2×C4×C31—21no—
368C2×C4×C31—22no—
369C2×C4×C31—22no—
370C2×C4×C31—24no—
371C2×C4×C31—21no—
372C2×C4×C31—22no—
373C2×C4×C31—21no—
374C2×C4×C31—21no—
375C2×C4×C31—22no—
376C2×C4×C31—21no—
377C2×C4×C31—24no—
378C2×C4×C31—42no—
379C2×C4×C31—42no—
380C2×C4×C31—42no—
381C2×C4×C31—44no—
382C2×C4×C31—44no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—42no—
386C2×C4×C31—42no—
387C2×C4×C31—42no—
388C2×C4×C31—42no—
389C2×C4×C31—42no—
390C2×C4×C31—82no—
391C2×C4×C31#12011yescharacteristic
392C2×C4×C31#12011yescharacteristic
393C2×C4×C31C22×D411yescharacteristic
394C2×C4×C31C22×D412yes—
395C2×C4×C31C22×D411yescharacteristic
396C2×C4×C31H(5,𝔽2)12yes—
397C8×C31—24no—
398C8×C31—42no—
399C22×AGL(1,ℤ/8)C2×C3111yescharacteristic, complemented
400#3489C2×C3111yescharacteristic, complemented
401C2×#454C2×C3112yescomplemented
402#3003C2×C3111yescharacteristic, complemented
403#2435C2×C3111yescharacteristic, complemented
404#2006C2×C3112yescomplemented
405#2003C2×C3112yescomplemented
406#1901C2×C3111yescharacteristic, complemented
407#1883C2×C3112yescomplemented
408#1871C2×C3111yescharacteristic, complemented
409#1789C2×C3111yescharacteristic, complemented
410C22×C31—21no—
411C22×C31—21no—
412C22×C31—21no—
413C22×C31—21no—
414C22×C31—21no—
415C22×C31—22no—
416C22×C31—21no—
417C22×C31—21no—
418C22×C31—44no—
419C22×C31—48no—
420C22×C31—41no—
421C22×C31—41no—
422C22×C31—41no—
423C22×C31—41no—
424C22×C31—44no—
425C22×C31—41no—
426C22×C31—41no—
427C22×C31—41no—
428C22×C31—41no—
429C22×C31—84no—
430C22×C31—84no—
431C22×C31—88no—
432C22×C31—88no—
433C22×C31—82no—
434C22×C31—82no—
435C22×C31#45412yescomplemented
436C22×C31C2×#12011yescharacteristic
437C22×C31D4212yes—
438C4×C31—21no—
439C4×C31—21no—
440C4×C31—22no—
441C4×C31—42no—
442C4×C31—41no—
443C4×C31—41no—
444C4×C31—41no—
445C4×C31—42no—
446C4×C31—41no—
447C4×C31—82no—
448C4×C31C2×#12011yescharacteristic
449C4×C31#53411yescharacteristic
450C4×C31D4212yes—
451C2×2−1+4C22×C3111yescharacteristic, complemented
452C22×#41C22×C3111yescharacteristic
453C23×D4C22×C3111yescharacteristic
454C2×AGL(1,ℤ/8)—21no—
455C2×AGL(1,ℤ/8)—21no—
456C2×AGL(1,ℤ/8)—28no—
457C2×AGL(1,ℤ/8)C22×C3112yes—
458C2×AGL(1,ℤ/8)C22×C3112yes—
459C2×AGL(1,ℤ/8)C22×C3112yescomplemented
460C22×SD16—21no—
461C22×D8—21no—
462C22×M16C22×C3111yescharacteristic
463D4×Q8—21no—
464#548—21no—
465#547—21no—
466#547—22no—
467#546—21no—
468#546—22no—
469#537—21no—
470#537C22×C3111yescharacteristic, complemented
471#536—21no—
472#536C22×C3111yescharacteristic, complemented
473C2×#124C22×C3112yescomplemented
474#525—21no—
475#525C22×C3111yescharacteristic
476C2×C22⋊Q8—21no—
477C2×C22⋊Q8C22×C3111yescharacteristic
478#520C22×C3111yescharacteristic, complemented
479#454—28no—
480#450—21no—
481#450—21no—
482#447—21no—
483#447—21no—
484C2×#104C22×C3112yescomplemented
485C2×#104C22×C3112yescomplemented
486C2×#104C22×C3112yescomplemented
487#418C22×C3112yescomplemented
488C2×#101C22×C3112yescomplemented
489#407C22×C3111yescharacteristic
490#394—22no—
491#390C22×C3112yescomplemented
492#379—22no—
493C4×C22⋊C4C22×C3111yescharacteristic
494#343C22×C3112yescomplemented
495#339C22×C3112yescomplemented
496C2×C31—22no—
497C2×C31—22no—
498C2×C31—41no—
499C2×C31—42no—
500C2×C31—81no—
501C2×C31—81no—
502C2×C31—84no—
503C2×C31#240311yescharacteristic
504C2×C31C2×#45411yescharacteristic
505C2×C31#302111yescharacteristic
506C25—21no—
5072−1+4—24no—
5082−1+4—42no—
509C2×#41—21no—
510C2×#41—21no—
511C2×#41—21no—
512C2×#41—22no—
513C2×#41—21no—
514C2×#41—24no—
515C2×#41—42no—
516C2×#41D4×C3111yescharacteristic
517C2×#41D4×C3111yescharacteristic
518C2×#41C23×C3111yescharacteristic
519C2×#41C23×C3111yescharacteristic
520C2×#41C23×C3111yescharacteristic
521C22×Q8—21no—
522C22×Q8—21no—
523C22×Q8D4×C3111yescharacteristic
524C22×Q8C23×C3111yescharacteristic
525C22×D4—24no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—42no—
533C22×D4D4×C3111yescharacteristic
534C22×D4C23×C3112yes—
535C23×C4—21no—
536C23×C4C23×C3111yescharacteristic
537AGL(1,ℤ/8)—28no—
538AGL(1,ℤ/8)—28no—
539AGL(1,ℤ/8)—24no—
540AGL(1,ℤ/8)—24no—
541AGL(1,ℤ/8)—24no—
542AGL(1,ℤ/8)—24no—
543AGL(1,ℤ/8)—42no—
544AGL(1,ℤ/8)D4×C3118yescomplemented
545C2×SD16—28no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×D8—28no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—22no—
553C2×M16—21no—
554C2×M16—24no—
555C2×M16C23×C3112yes—
556C2×M16C23×C3112yes—
557C22×C8—21no—
558C4⋊Q8—22no—
559C4⋊Q8—21no—
560#124—22no—
561#124—21no—
562#124—24no—
563#124—42no—
564#123—22no—
565#123—22no—
566#123—22no—
567#123—21no—
568#123—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8D4×C3111yescharacteristic
581C22⋊Q8D4×C3111yescharacteristic
582#121—22no—
583#121—22no—
584#121—22no—
585#121—21no—
586#121—21no—
587#121—22no—
588#121D4×C3111yescharacteristic
589#121D4×C3111yescharacteristic
590#120—22no—
591#120—21no—
592C4×Q8—21no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—21no—
596C4×D4—22no—
597C4×D4—21no—
598C4×D4—21no—
599#117—21no—
600#117C23×C3111yescharacteristic
601C2×C4⋊C4—22no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4D4×C3112yes—
604C2×C4⋊C4C23×C3111yescharacteristic
605C2×C22⋊C4—22no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—24no—
609C2×C22⋊C4D4×C3112yes—
610C2×C42C23×C3112yes—
611#104—24no—
612#104—24no—
613#104—42no—
614#102—22no—
615#102—22no—
616#101—24no—
617C22⋊C8—21no—
618C22⋊C8—21no—
619#95—21no—
620C31#2387911yescharacteristic, direct product factor, Sylow
621C24—22no—
622C24—21no—
623C24—44no—
624C24—44no—
625C24—41no—
626C24—41no—
627C24—82no—
628C24C2×D4×C3111yescharacteristic
629#41—22no—
630#41—22no—
631#41—22no—
632#41—22no—
633#41—22no—
634#41—22no—
635#41—22no—
636#41—44no—
637#41—41no—
638#41—41no—
639#41—44no—
640#41—44no—
641#41—48no—
642#41—42no—
643#41—42no—
644#41C2×D4×C3114yes—
645C2×Q8—22no—
646C2×Q8—21no—
647C2×Q8—22no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—22no—
651C2×Q8—22no—
652C2×Q8—41no—
653C2×Q8—44no—
654C2×Q8—42no—
655C2×Q8—42no—
656C2×Q8C2×D4×C3111yescharacteristic
657C2×Q8C2×D4×C3111yescharacteristic
658C2×Q8C2×D4×C3111yescharacteristic
659C2×D4—21no—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—22no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—44no—
684C2×D4—41no—
685C2×D4—41no—
686C2×D4C2×D4×C3111yescharacteristic
687C2×D4C2×D4×C3111yescharacteristic
688C2×D4C2×D4×C3114yes—
689C2×D4C2×D4×C3111yescharacteristic
690C22×C4—21no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—22no—
702C22×C4—44no—
703C22×C4C2×D4×C3112yes—
704C22×C4C2×D4×C3111yescharacteristic
705C22×C4C2×D4×C3111yescharacteristic
706C22×C4C2×D4×C3111yescharacteristic
707C22×C4C2×D4×C3111yescharacteristic
708C22×C4C2×D4×C3111yescharacteristic
709C22×C4C2×D4×C3112yes—
710C22×C4C24×C3111yescharacteristic
711SD16—28no—
712SD16—28no—
713SD16—44no—
714D8—28no—
715D8—28no—
716D8—44no—
717M16—24no—
718M16—22no—
719M16—22no—
720M16—22no—
721M16C2×D4×C3114yes—
722C2×C8—24no—
723C2×C8—22no—
724C2×C8—22no—
725C4⋊C4—22no—
726C4⋊C4—22no—
727C4⋊C4—22no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—22no—
731C4⋊C4—22no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4C2×D4×C3111yescharacteristic
736C4⋊C4C2×D4×C3111yescharacteristic
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—48no—
750C22⋊C4—42no—
751C22⋊C4—84no—
752C42—22no—
753C42—21no—
754C42—22no—
755C42—22no—
756C23—22no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—24no—
762C23—41no—
763C23—42no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—81no—
772C23—82no—
773C23—82no—
774C23—82no—
775C23—816no—
776C23—82no—
777C23C31×#12011yescharacteristic
778C23C31×#12011yescharacteristic
779C23C22×D4×C3111yescharacteristic
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—22no—
784Q8—42no—
785Q8—44no—
786Q8—41no—
787Q8—41no—
788Q8—42no—
789Q8C31×#12012yes—
790D4—24no—
791D4—21no—
792D4—24no—
793D4—21no—
794D4—21no—
795D4—22no—
796D4—24no—
797D4—42no—
798D4—42no—
799D4—44no—
800D4—44no—
801D4—42no—
802D4—44no—
803D4—42no—
804D4—42no—
805D4—42no—
806D4—42no—
807D4—42no—
808D4—81no—
809D4—82no—
810D4C31×#12012yes—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—21no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—24no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—82no—
840C2×C4C31×#12011yescharacteristic
841C2×C4C31×#12011yescharacteristic
842C2×C4C22×D4×C3111yescharacteristic
843C2×C4C22×D4×C3112yes—
844C2×C4C22×D4×C3111yescharacteristic
845C2×C4C31×H(5,𝔽2)12yes—
846C8—24no—
847C8—42no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—22no—
854C22—21no—
855C22—21no—
856C22—44no—
857C22—48no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—44no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—84no—
868C22—84no—
869C22—88no—
870C22—88no—
871C22—82no—
872C22—82no—
873C22C31×#45412yescomplemented
874C22C2×C31×#12011yescharacteristic
875C22D42×C3112yes—
876C4—21no—
877C4—21no—
878C4—22no—
879C4—42no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—42no—
884C4—41no—
885C4—82no—
886C4C2×C31×#12011yescharacteristic
887C4C31×#53411yescharacteristic
888C4D42×C3112yes—
889C2—22no—
890C2—22no—
891C2—41no—
892C2—42no—
893C2—84no—
894C2—81no—
895C2—81no—
896C2C31×#240311yescharacteristic
897C2C2×C31×#45411yescharacteristic
898C2C31×#302111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×AGL(1,ℤ/8)C2semidirect
2. C31×#3489C2semidirect
3. C2×C31×#454C2semidirect
4. C31×#3003C2semidirect
5. C31×#2435C2semidirect
6. C31×#2006C2semidirect
7. C31×#2003C2semidirect
8. C31×#1901C2semidirect
9. C31×#1883C2semidirect
10. C31×#1871C2semidirect
11. C31×#1789C2semidirect
12. C2×C31×2−1+4C22semidirect
20. C2×C31×AGL(1,ℤ/8)C22semidirect
31. C31×#537C22semidirect
33. C31×#536C22semidirect
34. C2×C31×#124C22semidirect
39. C31×#520C22semidirect
45. C2×C31×#104C22semidirect
46. C2×C31×#104C22semidirect
47. C2×C31×#104C22semidirect
48. C31×#418C22semidirect
49. C2×C31×#101C22semidirect
52. C31×#390C22semidirect
55. C31×#343C22semidirect
56. C31×#339C22semidirect
95. C31×AGL(1,ℤ/8)D4semidirect
306. #23879C31direct (N × H)
399. C22×AGL(1,ℤ/8)C2×C31semidirect
400. #3489C2×C31semidirect
401. C2×#454C2×C31semidirect
402. #3003C2×C31semidirect
403. #2435C2×C31semidirect
404. #2006C2×C31semidirect
405. #2003C2×C31semidirect
406. #1901C2×C31semidirect
407. #1883C2×C31semidirect
408. #1871C2×C31semidirect
409. #1789C2×C31semidirect
435. C22×C31#454semidirect
451. C2×2−1+4C22×C31semidirect
459. C2×AGL(1,ℤ/8)C22×C31semidirect
470. #537C22×C31semidirect
472. #536C22×C31semidirect
473. C2×#124C22×C31semidirect
478. #520C22×C31semidirect
484. C2×#104C22×C31semidirect
485. C2×#104C22×C31semidirect
486. C2×#104C22×C31semidirect
487. #418C22×C31semidirect
488. C2×#101C22×C31semidirect
491. #390C22×C31semidirect
494. #343C22×C31semidirect
495. #339C22×C31semidirect
544. AGL(1,ℤ/8)D4×C31semidirect
620. C31#23879direct (N × H)
873. C22C31×#454semidirect

Maximal subgroups

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

subgroupindex
C22×C31×AGL(1,ℤ/8)2
C31×#34892
C2×C31×#4542
C31×#30032
C31×#24352
C31×#20062
C31×#20032
C31×#19012
C31×#18832
C31×#18712
C31×#17892
#2387931