Finite Group Databasebeta

← C31×#23399 #21480158

Subgroups — C31×#23399 #21480158

Order 7936.

2062 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#575C211yesmaximal, characteristic, complemented
2C31×#3449C211yesmaximal, characteristic, complemented
3C2×C31×#532C211yesmaximal, characteristic, complemented
4C22×C31×#104C211yesmaximal, characteristic, complemented
5C31×#2896C211yesmaximal, characteristic, complemented
6C2×C31×#413C211yesmaximal, characteristic, complemented
7C31×#2005C212yesmaximal, complemented
8C31×#2004C212yesmaximal, complemented
9C31×#2003C212yesmaximal, complemented
10C31×#2002C212yesmaximal, complemented
11C2×C31×#339C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic
13C22×#41×C31C2211yescharacteristic
14C22×#41×C31C2211yescharacteristic
15C31×#575—24no—
16C31×#575—24no—
17C2×C31×#137—21no—
18C2×C31×#137C2212yes—
19C2×C31×AGL(1,ℤ/8)—21no—
20C2×C31×AGL(1,ℤ/8)C2212yes—
21C2×C31×#135—22no—
22C22×M16×C31C2211yescharacteristic
23C22×M16×C31C2211yescharacteristic
24C31×#537—22no—
25C31×#536—21no—
26C31×#536C2212yes—
27C31×#535—21no—
28C31×#535C2212yes—
29C31×#534—22no—
30C31×#532—24no—
31C31×#532—22no—
32C31×#532—24no—
33C2×C31×C4⋊Q8C2211yescharacteristic, complemented
34C2×C31×#127C2211yescharacteristic, complemented
35C2×C31×#124C2211yescharacteristic, complemented
36C2×C31×#124C2211yescharacteristic, complemented
37C31×#525—22no—
38C31×#525—22no—
39C2×C31×#121—22no—
40C2×C4×D4×C31—22no—
41C2×C31×#117C2211yescharacteristic
42C22×C42×C31C2211yescharacteristic
43C2×C31×#104—24no—
44C2×C31×#104C2212yes—
45C2×C31×#104C2212yes—
46C31×#419C2212yescomplemented
47C31×#418C2212yescomplemented
48C31×#417—22no—
49C31×#416—22no—
50C31×#413—24no—
51C2×C31×#101C2212yescomplemented
52C2×C31×#100C2212yescomplemented
53C31×#339C2212yescomplemented
54C31×#339C2212yescomplemented
55C2×#41×C31—22no—
56C2×#41×C31—21no—
57C2×#41×C31—21no—
58C2×#41×C31—22no—
59C2×#41×C31—22no—
60C2×#41×C31—22no—
61C2×#41×C31—21no—
62C2×#41×C31—21no—
63C2×#41×C31—21no—
64C2×#41×C31—21no—
65C2×#41×C31—22no—
66C2×#41×C31—21no—
67C2×#41×C31—21no—
68C2×#41×C31—22no—
69C2×#41×C31—21no—
70C2×#41×C31—21no—
71C2×#41×C31—22no—
72C2×#41×C31—22no—
73C2×#41×C31—22no—
74C2×#41×C31—22no—
75C2×#41×C31—22no—
76C2×#41×C31D412yescomplemented
77C2×#41×C31D414yescomplemented
78C2×#41×C31C2312yes—
79C22×Q8×C31D411yescharacteristic, complemented
80C22×Q8×C31C2311yescharacteristic
81C22×Q8×C31C2311yescharacteristic
82C22×D4×C31—22no—
83C22×D4×C31—21no—
84C22×D4×C31—21no—
85C22×D4×C31D412yes—
86C22×D4×C31D411yescharacteristic, complemented
87C22×D4×C31C2311yescharacteristic
88C22×D4×C31C2311yescharacteristic
89C23×C4×C31—21no—
90C23×C4×C31—21no—
91C23×C4×C31—21no—
92C23×C4×C31D412yes—
93C23×C4×C31C2311yescharacteristic
94C31×#137—28no—
95C31×#137—24no—
96C31×#137—24no—
97C31×AGL(1,ℤ/8)—28no—
98C31×AGL(1,ℤ/8)—24no—
99C31×AGL(1,ℤ/8)—24no—
100C31×#135—216no—
101C2×Q16×C31—22no—
102C2×SD16×C31—22no—
103C2×SD16×C31—22no—
104C2×D8×C31—22no—
105C2×M16×C31—21no—
106C2×M16×C31—22no—
107C2×M16×C31—21no—
108C2×M16×C31—22no—
109C2×M16×C31—22no—
110C2×M16×C31D414yescomplemented
111C2×M16×C31C2312yes—
112C2×M16×C31C2312yes—
113C22×C8×C31—21no—
114C22×C8×C31—21no—
115C31×C4⋊Q8—22no—
116C31×C4⋊Q8—22no—
117C31×C4⋊Q8—22no—
118C31×#127—22no—
119C31×#127—22no—
120C31×#127—22no—
121C31×#124—22no—
122C31×#124—22no—
123C31×#124—22no—
124C31×#124—22no—
125C31×#124—22no—
126C31×#124—22no—
127C31×#123—24no—
128C31×#123—24no—
129C31×C22⋊Q8—24no—
130C31×C22⋊Q8—24no—
131C31×#121—216no—
132C31×#121—24no—
133C31×#121—28no—
134C31×#121—24no—
135C31×#120—24no—
136C31×#120—24no—
137C4×D4×C31—216no—
138C4×D4×C31—28no—
139C31×#117—21no—
140C31×#117—21no—
141C31×#117D412yescomplemented
142C31×#117C2312yes—
143C2×C4⋊C4×C31—22no—
144C2×C4⋊C4×C31D412yescomplemented
145C2×C22⋊C4×C31—21no—
146C2×C22⋊C4×C31—22no—
147C2×C22⋊C4×C31—22no—
148C2×C42×C31—21no—
149C2×C42×C31—22no—
150C2×C42×C31—21no—
151C2×C42×C31D414yescomplemented
152C2×C42×C31C2311yescharacteristic
153C2×C42×C31C2311yescharacteristic
154C31×#104—24no—
155C31×#104—24no—
156C31×#103—24no—
157C31×#102—24no—
158C31×#101—24no—
159C31×#100—24no—
160C24×C31—21no—
161C24×C31—21no—
162C24×C31C2×D412yes—
163C24×C31C2×D411yescharacteristic
164#41×C31—24no—
165#41×C31—24no—
166#41×C31—24no—
167#41×C31—24no—
168#41×C31—24no—
169#41×C31—24no—
170#41×C31—22no—
171#41×C31—22no—
172#41×C31—22no—
173#41×C31—22no—
174#41×C31—42no—
175#41×C31—42no—
176#41×C31—42no—
177#41×C31—42no—
178#41×C31—42no—
179#41×C31—42no—
180#41×C31—42no—
181#41×C31—42no—
182#41×C31—42no—
183#41×C31—42no—
184#41×C31—42no—
185#41×C31—42no—
186#41×C31—42no—
187#41×C31—42no—
188#41×C31—42no—
189#41×C31—42no—
190C2×Q8×C31—21no—
191C2×Q8×C31—21no—
192C2×Q8×C31—21no—
193C2×Q8×C31—21no—
194C2×Q8×C31—21no—
195C2×Q8×C31—21no—
196C2×Q8×C31—21no—
197C2×Q8×C31—21no—
198C2×Q8×C31—22no—
199C2×Q8×C31—22no—
200C2×Q8×C31—21no—
201C2×Q8×C31—21no—
202C2×Q8×C31—21no—
203C2×Q8×C31—21no—
204C2×Q8×C31C2×D412yes—
205C2×Q8×C31C2×D412yes—
206C2×D4×C31—28no—
207C2×D4×C31—22no—
208C2×D4×C31—22no—
209C2×D4×C31—24no—
210C2×D4×C31—22no—
211C2×D4×C31—24no—
212C2×D4×C31—24no—
213C2×D4×C31—22no—
214C2×D4×C31—28no—
215C2×D4×C31—22no—
216C2×D4×C31—21no—
217C2×D4×C31—22no—
218C2×D4×C31—21no—
219C2×D4×C31—21no—
220C2×D4×C31—21no—
221C2×D4×C31—21no—
222C2×D4×C31—21no—
223C2×D4×C31—21no—
224C2×D4×C31—21no—
225C2×D4×C31—21no—
226C2×D4×C31—21no—
227C2×D4×C31—21no—
228C2×D4×C31—21no—
229C2×D4×C31—48no—
230C2×D4×C31—41no—
231C2×D4×C31—41no—
232C2×D4×C31—42no—
233C2×D4×C31—42no—
234C2×D4×C31—42no—
235C2×D4×C31C2×D412yes—
236C2×D4×C31C2×D412yes—
237C22×C4×C31—21no—
238C22×C4×C31—24no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—22no—
243C22×C4×C31—24no—
244C22×C4×C31—24no—
245C22×C4×C31—22no—
246C22×C4×C31—22no—
247C22×C4×C31—22no—
248C22×C4×C31—24no—
249C22×C4×C31—22no—
250C22×C4×C31—44no—
251C22×C4×C31—41no—
252C22×C4×C31—41no—
253C22×C4×C31—42no—
254C22×C4×C31—42no—
255C22×C4×C31—42no—
256C22×C4×C31C2×D412yes—
257C22×C4×C31C2×D411yescharacteristic
258C22×C4×C31C2×D412yes—
259C22×C4×C31C2×D411yescharacteristic
260C22×C4×C31C2×D411yescharacteristic
261C22×C4×C31C2×D412yes—
262C22×C4×C31C2×D412yes—
263C22×C4×C31C2×D411yescharacteristic
264C22×C4×C31C2×D411yescharacteristic
265C22×C4×C31#4112yes—
266C22×C4×C31C2411yescharacteristic
267Q16×C31—28no—
268SD16×C31—28no—
269SD16×C31—28no—
270D8×C31—28no—
271M16×C31—24no—
272M16×C31—22no—
273M16×C31—22no—
274M16×C31—22no—
275M16×C31—42no—
276M16×C31C2×D414yes—
277C2×C8×C31—24no—
278C2×C8×C31—22no—
279C2×C8×C31—22no—
280C2×C8×C31—42no—
281C4⋊C4×C31—28no—
282C4⋊C4×C31—28no—
283C4⋊C4×C31—22no—
284C4⋊C4×C31C2×D414yes—
285C22⋊C4×C31—28no—
286C22⋊C4×C31—28no—
287C22⋊C4×C31—28no—
288C22⋊C4×C31—28no—
289C22⋊C4×C31—22no—
290C22⋊C4×C31—22no—
291C42×C31—24no—
292C42×C31—22no—
293C42×C31—21no—
294C42×C31—21no—
295C42×C31—22no—
296C42×C31C2×D412yes—
297C42×C31C2×D412yes—
298#23399C3111yesmaximal, characteristic, direct product factor, Sylow
299C23×C31—22no—
300C23×C31—22no—
301C23×C31—22no—
302C23×C31—22no—
303C23×C31—22no—
304C23×C31—42no—
305C23×C31—44no—
306C23×C31—44no—
307C23×C31—41no—
308C23×C31—41no—
309C23×C31—42no—
310C23×C31—82no—
311C23×C31#12011yescharacteristic
312C23×C31#12011yescharacteristic
313C23×C31#12012yes—
314C23×C31#12112yes—
315C23×C31C22×D411yescharacteristic
316Q8×C31—22no—
317Q8×C31—22no—
318Q8×C31—22no—
319Q8×C31—22no—
320Q8×C31—41no—
321Q8×C31—41no—
322Q8×C31—41no—
323Q8×C31—41no—
324Q8×C31—41no—
325Q8×C31—41no—
326Q8×C31—42no—
327D4×C31—22no—
328D4×C31—22no—
329D4×C31—22no—
330D4×C31—22no—
331D4×C31—416no—
332D4×C31—42no—
333D4×C31—42no—
334D4×C31—44no—
335D4×C31—44no—
336D4×C31—44no—
337D4×C31—44no—
338D4×C31—44no—
339D4×C31—41no—
340D4×C31—41no—
341D4×C31—41no—
342D4×C31—41no—
343D4×C31—41no—
344D4×C31—41no—
345D4×C31—42no—
346D4×C31—88no—
347C2×C4×C31—24no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—24no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—48no—
357C2×C4×C31—42no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—42no—
361C2×C4×C31—42no—
362C2×C4×C31—42no—
363C2×C4×C31—44no—
364C2×C4×C31—44no—
365C2×C4×C31—44no—
366C2×C4×C31—44no—
367C2×C4×C31—44no—
368C2×C4×C31—82no—
369C2×C4×C31#12012yes—
370C2×C4×C31#12012yes—
371C2×C4×C31#12012yes—
372C2×C4×C31#12011yescharacteristic
373C2×C4×C31#12011yescharacteristic
374C2×C4×C31#12112yes—
375C2×C4×C31#12112yes—
376C2×C4×C31#12112yes—
377C2×C4×C31#12112yes—
378C2×C4×C31#12112yes—
379C2×C4×C31#12712yes—
380C2×C4×C31#12712yes—
381C2×C4×C31C22×D411yescharacteristic
382C2×C4×C31C22×D411yescharacteristic
383C2×C4×C31C22×D411yescharacteristic
384C2×C4×C31C22×D411yescharacteristic
385C2×C4×C31C22×D411yescharacteristic
386C2×C4×C31C2×#4111yescharacteristic
387C8×C31—24no—
388C8×C31—42no—
389C2×#575C2×C3111yescharacteristic, complemented
390#3449C2×C3111yescharacteristic, complemented
391C2×#532C2×C3111yescharacteristic, complemented
392C22×#104C2×C3111yescharacteristic, complemented
393#2896C2×C3111yescharacteristic, complemented
394C2×#413C2×C3111yescharacteristic, complemented
395#2005C2×C3112yescomplemented
396#2004C2×C3112yescomplemented
397#2003C2×C3112yescomplemented
398#2002C2×C3112yescomplemented
399C2×#339C2×C3111yescharacteristic, complemented
400C22×C31—22no—
401C22×C31—22no—
402C22×C31—22no—
403C22×C31—42no—
404C22×C31—42no—
405C22×C31—44no—
406C22×C31—44no—
407C22×C31—42no—
408C22×C31—42no—
409C22×C31—42no—
410C22×C31—44no—
411C22×C31—44no—
412C22×C31—82no—
413C22×C31—82no—
414C22×C31—84no—
415C22×C31—82no—
416C22×C31#39212yes—
417C22×C31#39212yes—
418C22×C31C2×#12011yescharacteristic
419C22×C31C2×#12011yescharacteristic
420C22×C31C2×#12111yescharacteristic
421C4×C31—24no—
422C4×C31—42no—
423C4×C31—42no—
424C4×C31—42no—
425C4×C31—42no—
426C4×C31—44no—
427C4×C31#39212yes—
428C4×C31#39212yes—
429C4×C31C2×#12011yescharacteristic
430C4×C31C2×#12111yescharacteristic
431C4×C31C2×#12111yescharacteristic
432C4×C31C2×#12711yescharacteristic
433C22×#41C22×C3111yescharacteristic
434C22×#41C22×C3111yescharacteristic
435C22×#41C22×C3111yescharacteristic
436#575—24no—
437#575—24no—
438C2×#137—21no—
439C2×#137C22×C3112yes—
440C2×AGL(1,ℤ/8)—21no—
441C2×AGL(1,ℤ/8)C22×C3112yes—
442C2×#135—22no—
443C22×M16C22×C3111yescharacteristic
444C22×M16C22×C3111yescharacteristic
445#537—22no—
446#536—21no—
447#536C22×C3112yes—
448#535—21no—
449#535C22×C3112yes—
450#534—22no—
451#532—24no—
452#532—22no—
453#532—24no—
454C2×C4⋊Q8C22×C3111yescharacteristic, complemented
455C2×#127C22×C3111yescharacteristic, complemented
456C2×#124C22×C3111yescharacteristic, complemented
457C2×#124C22×C3111yescharacteristic, complemented
458#525—22no—
459#525—22no—
460C2×#121—22no—
461C2×C4×D4—22no—
462C2×#117C22×C3111yescharacteristic
463C22×C42C22×C3111yescharacteristic
464C2×#104—24no—
465C2×#104C22×C3112yes—
466C2×#104C22×C3112yes—
467#419C22×C3112yescomplemented
468#418C22×C3112yescomplemented
469#417—22no—
470#416—22no—
471#413—24no—
472C2×#101C22×C3112yescomplemented
473C2×#100C22×C3112yescomplemented
474#339C22×C3112yescomplemented
475#339C22×C3112yescomplemented
476C2×C31—21no—
477C2×C31—21no—
478C2×C31—22no—
479C2×C31—22no—
480C2×C31—82no—
481C2×C31—82no—
482C2×C31—82no—
483C2×C31C2×#39211yescharacteristic
484C2×C31#301812yes—
485C2×#41—21no—
486C2×#41—21no—
487C2×#41—22no—
488C2×#41—21no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—21no—
497C2×#41—21no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—21no—
502C2×#41—21no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41D4×C3112yescomplemented
507C2×#41D4×C3114yescomplemented
508C2×#41C23×C3112yes—
509C22×Q8D4×C3111yescharacteristic, complemented
510C22×Q8C23×C3111yescharacteristic
511C22×Q8C23×C3111yescharacteristic
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C3112yes—
516C22×D4D4×C3111yescharacteristic, complemented
517C22×D4C23×C3111yescharacteristic
518C22×D4C23×C3111yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4D4×C3112yes—
523C23×C4C23×C3111yescharacteristic
524#137—28no—
525#137—24no—
526#137—24no—
527AGL(1,ℤ/8)—28no—
528AGL(1,ℤ/8)—24no—
529AGL(1,ℤ/8)—24no—
530#135—216no—
531C2×Q16—22no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×D8—22no—
535C2×M16—21no—
536C2×M16—22no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16D4×C3114yescomplemented
541C2×M16C23×C3112yes—
542C2×M16C23×C3112yes—
543C22×C8—21no—
544C22×C8—21no—
545C4⋊Q8—22no—
546C4⋊Q8—22no—
547C4⋊Q8—22no—
548#127—22no—
549#127—22no—
550#127—22no—
551#124—22no—
552#124—22no—
553#124—22no—
554#124—22no—
555#124—22no—
556#124—22no—
557#123—24no—
558#123—24no—
559C22⋊Q8—24no—
560C22⋊Q8—24no—
561#121—216no—
562#121—24no—
563#121—28no—
564#121—24no—
565#120—24no—
566#120—24no—
567C4×D4—216no—
568C4×D4—28no—
569#117—21no—
570#117—21no—
571#117D4×C3112yescomplemented
572#117C23×C3112yes—
573C2×C4⋊C4—22no—
574C2×C4⋊C4D4×C3112yescomplemented
575C2×C22⋊C4—21no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C42—21no—
579C2×C42—21no—
580C2×C42—22no—
581C2×C42D4×C3114yescomplemented
582C2×C42C23×C3111yescharacteristic
583C2×C42C23×C3111yescharacteristic
584#104—24no—
585#104—24no—
586#103—24no—
587#102—24no—
588#101—24no—
589#100—24no—
590C31#2339911yescharacteristic, direct product factor, Sylow
591C24—21no—
592C24—21no—
593C24C2×D4×C3112yes—
594C24C2×D4×C3111yescharacteristic
595#41—24no—
596#41—24no—
597#41—24no—
598#41—24no—
599#41—24no—
600#41—24no—
601#41—22no—
602#41—22no—
603#41—22no—
604#41—22no—
605#41—42no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614#41—42no—
615#41—42no—
616#41—42no—
617#41—42no—
618#41—42no—
619#41—42no—
620#41—42no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8C2×D4×C3112yes—
636C2×Q8C2×D4×C3112yes—
637C2×D4—28no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—24no—
641C2×D4—22no—
642C2×D4—24no—
643C2×D4—24no—
644C2×D4—22no—
645C2×D4—28no—
646C2×D4—22no—
647C2×D4—21no—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—48no—
661C2×D4—41no—
662C2×D4—41no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4C2×D4×C3112yes—
667C2×D4C2×D4×C3112yes—
668C22×C4—21no—
669C22×C4—24no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—24no—
675C22×C4—22no—
676C22×C4—24no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—24no—
680C22×C4—22no—
681C22×C4—44no—
682C22×C4—41no—
683C22×C4—41no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4C2×D4×C3112yes—
688C22×C4C2×D4×C3111yescharacteristic
689C22×C4C2×D4×C3111yescharacteristic
690C22×C4C2×D4×C3112yes—
691C22×C4C2×D4×C3111yescharacteristic
692C22×C4C2×D4×C3112yes—
693C22×C4C2×D4×C3112yes—
694C22×C4C2×D4×C3111yescharacteristic
695C22×C4C2×D4×C3111yescharacteristic
696C22×C4#41×C3112yes—
697C22×C4C24×C3111yescharacteristic
698Q16—28no—
699SD16—28no—
700SD16—28no—
701D8—28no—
702M16—24no—
703M16—22no—
704M16—22no—
705M16—22no—
706M16—42no—
707M16C2×D4×C3114yes—
708C2×C8—24no—
709C2×C8—22no—
710C2×C8—22no—
711C2×C8—42no—
712C4⋊C4—28no—
713C4⋊C4—28no—
714C4⋊C4—22no—
715C4⋊C4C2×D4×C3114yes—
716C22⋊C4—28no—
717C22⋊C4—28no—
718C22⋊C4—28no—
719C22⋊C4—28no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C42—24no—
723C42—22no—
724C42—21no—
725C42—21no—
726C42—22no—
727C42C2×D4×C3112yes—
728C42C2×D4×C3112yes—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—42no—
735C23—44no—
736C23—44no—
737C23—41no—
738C23—41no—
739C23—42no—
740C23—82no—
741C23C31×#12011yescharacteristic
742C23C31×#12011yescharacteristic
743C23C31×#12012yes—
744C23C31×#12112yes—
745C23C22×D4×C3111yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754Q8—41no—
755Q8—41no—
756Q8—42no—
757D4—22no—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—416no—
762D4—42no—
763D4—42no—
764D4—44no—
765D4—44no—
766D4—44no—
767D4—44no—
768D4—44no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—41no—
775D4—42no—
776D4—88no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—48no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—82no—
799C2×C4C31×#12012yes—
800C2×C4C31×#12012yes—
801C2×C4C31×#12012yes—
802C2×C4C31×#12011yescharacteristic
803C2×C4C31×#12011yescharacteristic
804C2×C4C31×#12112yes—
805C2×C4C31×#12112yes—
806C2×C4C31×#12112yes—
807C2×C4C31×#12112yes—
808C2×C4C31×#12112yes—
809C2×C4C31×#12712yes—
810C2×C4C31×#12712yes—
811C2×C4C22×D4×C3111yescharacteristic
812C2×C4C22×D4×C3111yescharacteristic
813C2×C4C22×D4×C3111yescharacteristic
814C2×C4C22×D4×C3111yescharacteristic
815C2×C4C22×D4×C3111yescharacteristic
816C2×C4C2×#41×C3111yescharacteristic
817C8—24no—
818C8—42no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—44no—
830C22—44no—
831C22—82no—
832C22—82no—
833C22—84no—
834C22—82no—
835C22C31×#39212yes—
836C22C31×#39212yes—
837C22C2×C31×#12011yescharacteristic
838C22C2×C31×#12011yescharacteristic
839C22C2×C31×#12111yescharacteristic
840C4—24no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—44no—
846C4C31×#39212yes—
847C4C31×#39212yes—
848C4C2×C31×#12011yescharacteristic
849C4C2×C31×#12111yescharacteristic
850C4C2×C31×#12111yescharacteristic
851C4C2×C31×#12711yescharacteristic
852C2—21no—
853C2—21no—
854C2—22no—
855C2—22no—
856C2—82no—
857C2—82no—
858C2—82no—
859C2C2×C31×#39211yescharacteristic
860C2C31×#301812yes—
subgroupG/H
centerC2×C4×C31#120
commutator, Frattini, cosocleC22×C4C24×C31
socleC22×C31C2×#120
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×#575C2semidirect
2. C31×#3449C2semidirect
3. C2×C31×#532C2semidirect
4. C22×C31×#104C2semidirect
5. C31×#2896C2semidirect
6. C2×C31×#413C2semidirect
7. C31×#2005C2semidirect
8. C31×#2004C2semidirect
9. C31×#2003C2semidirect
10. C31×#2002C2semidirect
11. C2×C31×#339C2semidirect
33. C2×C31×C4⋊Q8C22semidirect
34. C2×C31×#127C22semidirect
35. C2×C31×#124C22semidirect
36. C2×C31×#124C22semidirect
46. C31×#419C22semidirect
47. C31×#418C22semidirect
51. C2×C31×#101C22semidirect
52. C2×C31×#100C22semidirect
53. C31×#339C22semidirect
54. C31×#339C22semidirect
76. C2×#41×C31D4semidirect
77. C2×#41×C31D4semidirect
79. C22×Q8×C31D4semidirect
86. C22×D4×C31D4semidirect
110. C2×M16×C31D4semidirect
141. C31×#117D4semidirect
144. C2×C4⋊C4×C31D4semidirect
151. C2×C42×C31D4semidirect
298. #23399C31direct (N × H)
389. C2×#575C2×C31semidirect
390. #3449C2×C31semidirect
391. C2×#532C2×C31semidirect
392. C22×#104C2×C31semidirect
393. #2896C2×C31semidirect
394. C2×#413C2×C31semidirect
395. #2005C2×C31semidirect
396. #2004C2×C31semidirect
397. #2003C2×C31semidirect
398. #2002C2×C31semidirect
399. C2×#339C2×C31semidirect
454. C2×C4⋊Q8C22×C31semidirect
455. C2×#127C22×C31semidirect
456. C2×#124C22×C31semidirect
457. C2×#124C22×C31semidirect
467. #419C22×C31semidirect
468. #418C22×C31semidirect
472. C2×#101C22×C31semidirect
473. C2×#100C22×C31semidirect
474. #339C22×C31semidirect
475. #339C22×C31semidirect
506. C2×#41D4×C31semidirect
507. C2×#41D4×C31semidirect
509. C22×Q8D4×C31semidirect
516. C22×D4D4×C31semidirect
540. C2×M16D4×C31semidirect
571. #117D4×C31semidirect
574. C2×C4⋊C4D4×C31semidirect
581. C2×C42D4×C31semidirect
590. C31#23399direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5752
C31×#34492
C2×C31×#5322
C22×C31×#1042
C31×#28962
C2×C31×#4132
C31×#20052
C31×#20042
C31×#20032
C31×#20022
C2×C31×#3392
#2339931