Finite Group Databasebeta

← C31×#23924 #21480683

Subgroups — C31×#23924 #21480683

Order 7936.

1952 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#537C211yesmaximal, characteristic, complemented
2C2×C31×#535C211yesmaximal, characteristic, complemented
3C2×C31×#449C212yesmaximal, complemented
4C2×C31×#450C211yesmaximal, characteristic, complemented
5C2×C31×#447C211yesmaximal, characteristic, complemented
6C31×#2000C212yesmaximal, complemented
7C31×#1999C212yesmaximal, complemented
8C31×#1875C211yesmaximal, characteristic, complemented
9C31×#1874C212yesmaximal, complemented
10C31×#1873C211yesmaximal, characteristic, complemented
11C31×#1780C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic
13C22×#41×C31C2211yescharacteristic, complemented
14C23×D4×C31C2211yescharacteristic
15C22×SD16×C31C2212yes—
16C22×D8×C31C2212yes—
17C31×#537—24no—
18C31×#537—24no—
19C31×#535—28no—
20C2×C31×#127—21no—
21C2×C31×#124—21no—
22C2×C31×C22⋊Q8—21no—
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C31×C22⋊Q8C2211yescharacteristic, complemented
25C2×C31×#121—21no—
26C2×C31×#121—21no—
27C2×C31×#121—21no—
28C2×C31×#121C2212yes—
29C2×C31×#121C2212yes—
30C2×C31×#121C2211yescharacteristic
31C2×C31×#121C2211yescharacteristic, complemented
32C2×C31×#120—21no—
33C2×C31×#120—21no—
34C2×C31×#117C2211yescharacteristic
35C22×C4⋊C4×C31C2211yescharacteristic, complemented
36C31×#450—24no—
37C31×#449—28no—
38C31×#447—24no—
39C2×C31×#103C2212yescomplemented
40C2×C31×#102C2212yes—
41C2×C31×#102C2212yes—
42C2×C31×#102C2212yescomplemented
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic
45C2×C31×C22⋊C8C2212yescomplemented
46C2×C31×C22⋊C8C2212yescomplemented
47C31×#340C2212yescomplemented
48C31×#340C2212yescomplemented
49C25×C31—21no—
50C2×#41×C31—22no—
51C2×#41×C31—22no—
52C2×#41×C31—24no—
53C2×#41×C31—22no—
54C2×#41×C31—22no—
55C2×#41×C31—24no—
56C2×#41×C31—42no—
57C2×#41×C31—42no—
58C22×Q8×C31D411yescharacteristic
59C22×Q8×C31C2311yescharacteristic
60C22×D4×C31—21no—
61C22×D4×C31—22no—
62C22×D4×C31—22no—
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31—24no—
66C22×D4×C31—21no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—42no—
70C22×D4×C31D411yescharacteristic
71C22×D4×C31D411yescharacteristic
72C22×D4×C31D411yescharacteristic
73C22×D4×C31C2312yes—
74C22×D4×C31C2311yescharacteristic
75C23×C4×C31—21no—
76C23×C4×C31—21no—
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C2×SD16×C31—24no—
81C2×SD16×C31—24no—
82C2×SD16×C31—42no—
83C2×D8×C31—24no—
84C2×D8×C31—24no—
85C2×D8×C31—42no—
86C22×C8×C31C2312yes—
87C22×C8×C31C2312yes—
88C31×#127—28no—
89C31×#124—28no—
90C31×C22⋊Q8—28no—
91C31×C22⋊Q8—22no—
92C31×C22⋊Q8—22no—
93C31×C22⋊Q8—22no—
94C31×C22⋊Q8D414yescomplemented
95C31×#121—28no—
96C31×#121—28no—
97C31×#121—28no—
98C31×#121—24no—
99C31×#121—22no—
100C31×#121—24no—
101C31×#121—22no—
102C31×#121—24no—
103C31×#121—22no—
104C31×#121D414yescomplemented
105C31×#121D418yescomplemented
106C31×#120—28no—
107C31×#120—28no—
108C31×#117—24no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—22no—
113C2×C4⋊C4×C31—22no—
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2312yes—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—22no—
121C2×C22⋊C4×C31—22no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C42×C31—21no—
125C31×#103—24no—
126C31×#102—24no—
127C31×#102—24no—
128C31×#102—24no—
129C31×C22⋊C8—22no—
130C31×C22⋊C8—22no—
131C31×C22⋊C8—24no—
132C31×C22⋊C8—42no—
133C24×C31—24no—
134C24×C31—21no—
135C24×C31—22no—
136C24×C31—42no—
137C24×C31—42no—
138C24×C31—82no—
139C24×C31—82no—
140C24×C31C2×D411yescharacteristic
141C24×C31C2×D411yescharacteristic
142C24×C31C2×D411yescharacteristic
143#41×C31—48no—
144#41×C31—48no—
145#41×C31—48no—
146#41×C31—48no—
147C2×Q8×C31—22no—
148C2×Q8×C31—22no—
149C2×Q8×C31—21no—
150C2×Q8×C31—22no—
151C2×Q8×C31—22no—
152C2×Q8×C31—41no—
153C2×Q8×C31C2×D412yes—
154C2×D4×C31—24no—
155C2×D4×C31—24no—
156C2×D4×C31—22no—
157C2×D4×C31—22no—
158C2×D4×C31—22no—
159C2×D4×C31—22no—
160C2×D4×C31—28no—
161C2×D4×C31—24no—
162C2×D4×C31—28no—
163C2×D4×C31—24no—
164C2×D4×C31—22no—
165C2×D4×C31—22no—
166C2×D4×C31—22no—
167C2×D4×C31—22no—
168C2×D4×C31—22no—
169C2×D4×C31—22no—
170C2×D4×C31—21no—
171C2×D4×C31—22no—
172C2×D4×C31—22no—
173C2×D4×C31—22no—
174C2×D4×C31—48no—
175C2×D4×C31—48no—
176C2×D4×C31—41no—
177C2×D4×C31—41no—
178C2×D4×C31—41no—
179C2×D4×C31—42no—
180C2×D4×C31—42no—
181C2×D4×C31—42no—
182C2×D4×C31—42no—
183C2×D4×C31—82no—
184C2×D4×C31—82no—
185C2×D4×C31—82no—
186C2×D4×C31—82no—
187C2×D4×C31—82no—
188C2×D4×C31—82no—
189C2×D4×C31C2×D412yes—
190C2×D4×C31C2×D414yes—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—24no—
197C22×C4×C31—22no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—24no—
202C22×C4×C31—22no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—22no—
206C22×C4×C31—42no—
207C22×C4×C31—42no—
208C22×C4×C31—82no—
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D414yes—
213C22×C4×C31C2×D412yes—
214C22×C4×C31C2×D412yes—
215C22×C4×C31C2411yescharacteristic
216SD16×C31—48no—
217D8×C31—48no—
218C2×C8×C31—22no—
219C2×C8×C31—22no—
220C2×C8×C31—22no—
221C2×C8×C31—22no—
222C2×C8×C31—22no—
223C2×C8×C31—22no—
224C4⋊C4×C31—24no—
225C4⋊C4×C31—24no—
226C4⋊C4×C31—24no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—22no—
230C4⋊C4×C31C2×D412yes—
231C4⋊C4×C31C2×D412yes—
232C4⋊C4×C31C2×D414yes—
233C22⋊C4×C31—24no—
234C22⋊C4×C31—28no—
235C22⋊C4×C31—24no—
236C22⋊C4×C31—24no—
237C22⋊C4×C31—24no—
238C22⋊C4×C31—28no—
239C22⋊C4×C31—24no—
240C42×C31—24no—
241#23924C3111yesmaximal, characteristic, direct product factor, Sylow
242C23×C31—21no—
243C23×C31—21no—
244C23×C31—21no—
245C23×C31—21no—
246C23×C31—22no—
247C23×C31—22no—
248C23×C31—22no—
249C23×C31—22no—
250C23×C31—21no—
251C23×C31—22no—
252C23×C31—24no—
253C23×C31—21no—
254C23×C31—21no—
255C23×C31—22no—
256C23×C31—22no—
257C23×C31—48no—
258C23×C31—41no—
259C23×C31—42no—
260C23×C31—41no—
261C23×C31—42no—
262C23×C31—42no—
263C23×C31—42no—
264C23×C31—42no—
265C23×C31—42no—
266C23×C31—42no—
267C23×C31—42no—
268C23×C31—84no—
269C23×C31—84no—
270C23×C31—88no—
271C23×C31—88no—
272C23×C31#12012yes—
273C23×C31#12012yes—
274C23×C31C22×D411yescharacteristic
275Q8×C31—24no—
276Q8×C31—44no—
277Q8×C31—42no—
278D4×C31—24no—
279D4×C31—24no—
280D4×C31—24no—
281D4×C31—44no—
282D4×C31—44no—
283D4×C31—48no—
284D4×C31—44no—
285D4×C31—48no—
286D4×C31—42no—
287D4×C31—42no—
288D4×C31—42no—
289D4×C31—84no—
290D4×C31—88no—
291D4×C31—84no—
292D4×C31—88no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—24no—
298C2×C4×C31—24no—
299C2×C4×C31—24no—
300C2×C4×C31—24no—
301C2×C4×C31—24no—
302C2×C4×C31—21no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—22no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—48no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—42no—
312C2×C4×C31—42no—
313C2×C4×C31—42no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—84no—
318C2×C4×C31#12012yes—
319C2×C4×C31#12012yes—
320C2×C4×C31C22×D411yescharacteristic
321C2×C4×C31C22×D411yescharacteristic
322C2×C4×C31C22×D412yes—
323C2×C4×C31H(5,𝔽2)12yes—
324C8×C31—42no—
325C8×C31—42no—
326C2×#537C2×C3111yescharacteristic, complemented
327C2×#535C2×C3111yescharacteristic, complemented
328C2×#449C2×C3112yescomplemented
329C2×#450C2×C3111yescharacteristic, complemented
330C2×#447C2×C3111yescharacteristic, complemented
331#2000C2×C3112yescomplemented
332#1999C2×C3112yescomplemented
333#1875C2×C3111yescharacteristic, complemented
334#1874C2×C3112yescomplemented
335#1873C2×C3111yescharacteristic, complemented
336#1780C2×C3111yescharacteristic, complemented
337C22×C31—22no—
338C22×C31—22no—
339C22×C31—22no—
340C22×C31—22no—
341C22×C31—24no—
342C22×C31—42no—
343C22×C31—42no—
344C22×C31—41no—
345C22×C31—41no—
346C22×C31—42no—
347C22×C31—42no—
348C22×C31—41no—
349C22×C31—44no—
350C22×C31—42no—
351C22×C31—41no—
352C22×C31—42no—
353C22×C31—41no—
354C22×C31—42no—
355C22×C31—42no—
356C22×C31—44no—
357C22×C31—44no—
358C22×C31—816no—
359C22×C31—82no—
360C22×C31—82no—
361C22×C31—82no—
362C22×C31—82no—
363C22×C31—82no—
364C22×C31—82no—
365C22×C31C2×#12011yescharacteristic
366C22×C31C2×#12011yescharacteristic
367C22×C31#53411yescharacteristic
368C22×C31#57612yes—
369C22×C31#57712yes—
370C4×C31—22no—
371C4×C31—22no—
372C4×C31—41no—
373C4×C31—42no—
374C4×C31—42no—
375C4×C31—42no—
376C4×C31—44no—
377C4×C31D4212yes—
378C4×C31D4212yes—
379C22×#41C22×C3111yescharacteristic
380C22×#41C22×C3111yescharacteristic, complemented
381C23×D4C22×C3111yescharacteristic
382C22×SD16C22×C3112yes—
383C22×D8C22×C3112yes—
384#537—24no—
385#537—24no—
386#535—28no—
387C2×#127—21no—
388C2×#124—21no—
389C2×C22⋊Q8—21no—
390C2×C22⋊Q8C22×C3111yescharacteristic
391C2×C22⋊Q8C22×C3111yescharacteristic, complemented
392C2×#121—21no—
393C2×#121—21no—
394C2×#121—21no—
395C2×#121C22×C3112yes—
396C2×#121C22×C3112yes—
397C2×#121C22×C3111yescharacteristic
398C2×#121C22×C3111yescharacteristic, complemented
399C2×#120—21no—
400C2×#120—21no—
401C2×#117C22×C3111yescharacteristic
402C22×C4⋊C4C22×C3111yescharacteristic, complemented
403#450—24no—
404#449—28no—
405#447—24no—
406C2×#103C22×C3112yescomplemented
407C2×#102C22×C3112yes—
408C2×#102C22×C3112yes—
409C2×#102C22×C3112yescomplemented
410C2×C22⋊C8C22×C3111yescharacteristic
411C2×C22⋊C8C22×C3111yescharacteristic
412C2×C22⋊C8C22×C3112yescomplemented
413C2×C22⋊C8C22×C3112yescomplemented
414#340C22×C3112yescomplemented
415#340C22×C3112yescomplemented
416C2×C31—42no—
417C2×C31—42no—
418C2×C31—81no—
419C2×C31—82no—
420C2×C31—84no—
421C2×C31#240311yescharacteristic
422C2×C31#300811yescharacteristic
423C2×C31#301011yescharacteristic
424C2×C31#301212yes—
425C2×C31#319812yes—
426C25—21no—
427C2×#41—22no—
428C2×#41—22no—
429C2×#41—24no—
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—24no—
433C2×#41—42no—
434C2×#41—42no—
435C22×Q8D4×C3111yescharacteristic
436C22×Q8C23×C3111yescharacteristic
437C22×D4—21no—
438C22×D4—22no—
439C22×D4—22no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—24no—
443C22×D4—21no—
444C22×D4—22no—
445C22×D4—22no—
446C22×D4—42no—
447C22×D4D4×C3111yescharacteristic
448C22×D4D4×C3111yescharacteristic
449C22×D4D4×C3111yescharacteristic
450C22×D4C23×C3112yes—
451C22×D4C23×C3111yescharacteristic
452C23×C4—21no—
453C23×C4—21no—
454C23×C4C23×C3111yescharacteristic
455C23×C4C23×C3111yescharacteristic
456C23×C4C23×C3111yescharacteristic
457C2×SD16—24no—
458C2×SD16—24no—
459C2×SD16—42no—
460C2×D8—24no—
461C2×D8—24no—
462C2×D8—42no—
463C22×C8C23×C3112yes—
464C22×C8C23×C3112yes—
465#127—28no—
466#124—28no—
467C22⋊Q8—28no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8D4×C3114yescomplemented
472#121—28no—
473#121—28no—
474#121—28no—
475#121—24no—
476#121—22no—
477#121—24no—
478#121—22no—
479#121—24no—
480#121—22no—
481#121D4×C3118yescomplemented
482#121D4×C3114yescomplemented
483#120—28no—
484#120—28no—
485#117—24no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4C23×C3111yescharacteristic
492C2×C4⋊C4C23×C3111yescharacteristic
493C2×C4⋊C4C23×C3112yes—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C42—21no—
502#103—24no—
503#102—24no—
504#102—24no—
505#102—24no—
506C22⋊C8—22no—
507C22⋊C8—22no—
508C22⋊C8—24no—
509C22⋊C8—42no—
510C31#2392411yescharacteristic, direct product factor, Sylow
511C24—24no—
512C24—21no—
513C24—22no—
514C24—42no—
515C24—42no—
516C24—82no—
517C24—82no—
518C24C2×D4×C3111yescharacteristic
519C24C2×D4×C3111yescharacteristic
520C24C2×D4×C3111yescharacteristic
521#41—48no—
522#41—48no—
523#41—48no—
524#41—48no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—21no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—41no—
531C2×Q8C2×D4×C3112yes—
532C2×D4—24no—
533C2×D4—24no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—28no—
539C2×D4—24no—
540C2×D4—28no—
541C2×D4—24no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—48no—
553C2×D4—48no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—82no—
562C2×D4—82no—
563C2×D4—82no—
564C2×D4—82no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4C2×D4×C3112yes—
568C2×D4C2×D4×C3114yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—82no—
587C22×C4C2×D4×C3111yescharacteristic
588C22×C4C2×D4×C3111yescharacteristic
589C22×C4C2×D4×C3111yescharacteristic
590C22×C4C2×D4×C3114yes—
591C22×C4C2×D4×C3112yes—
592C22×C4C2×D4×C3112yes—
593C22×C4C24×C3111yescharacteristic
594SD16—48no—
595D8—48no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—22no—
608C4⋊C4C2×D4×C3112yes—
609C4⋊C4C2×D4×C3112yes—
610C4⋊C4C2×D4×C3114yes—
611C22⋊C4—24no—
612C22⋊C4—28no—
613C22⋊C4—24no—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—28no—
617C22⋊C4—24no—
618C42—24no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—21no—
628C23—22no—
629C23—24no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—22no—
634C23—48no—
635C23—41no—
636C23—42no—
637C23—41no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—84no—
646C23—84no—
647C23—88no—
648C23—88no—
649C23C31×#12012yes—
650C23C31×#12012yes—
651C23C22×D4×C3111yescharacteristic
652Q8—24no—
653Q8—44no—
654Q8—42no—
655D4—24no—
656D4—24no—
657D4—24no—
658D4—44no—
659D4—44no—
660D4—48no—
661D4—44no—
662D4—48no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—84no—
667D4—88no—
668D4—84no—
669D4—88no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—48no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—84no—
695C2×C4C31×#12012yes—
696C2×C4C31×#12012yes—
697C2×C4C22×D4×C3111yescharacteristic
698C2×C4C22×D4×C3111yescharacteristic
699C2×C4C22×D4×C3112yes—
700C2×C4C31×H(5,𝔽2)12yes—
701C8—42no—
702C8—42no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—24no—
708C22—42no—
709C22—42no—
710C22—41no—
711C22—41no—
712C22—42no—
713C22—42no—
714C22—41no—
715C22—44no—
716C22—42no—
717C22—41no—
718C22—42no—
719C22—41no—
720C22—42no—
721C22—42no—
722C22—44no—
723C22—44no—
724C22—816no—
725C22—82no—
726C22—82no—
727C22—82no—
728C22—82no—
729C22—82no—
730C22—82no—
731C22C2×C31×#12011yescharacteristic
732C22C2×C31×#12011yescharacteristic
733C22C31×#53411yescharacteristic
734C22C31×#57612yes—
735C22C31×#57712yes—
736C4—22no—
737C4—22no—
738C4—41no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—44no—
743C4D42×C3112yes—
744C4D42×C3112yes—
745C2—42no—
746C2—42no—
747C2—81no—
748C2—84no—
749C2—82no—
750C2C31×#240311yescharacteristic
751C2C31×#300811yescharacteristic
752C2C31×#301011yescharacteristic
753C2C31×#301212yes—
754C2C31×#319812yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#537C2semidirect
2. C2×C31×#535C2semidirect
3. C2×C31×#449C2semidirect
4. C2×C31×#450C2semidirect
5. C2×C31×#447C2semidirect
6. C31×#2000C2semidirect
7. C31×#1999C2semidirect
8. C31×#1875C2semidirect
9. C31×#1874C2semidirect
10. C31×#1873C2semidirect
11. C31×#1780C2semidirect
13. C22×#41×C31C22semidirect
24. C2×C31×C22⋊Q8C22semidirect
31. C2×C31×#121C22semidirect
35. C22×C4⋊C4×C31C22semidirect
39. C2×C31×#103C22semidirect
42. C2×C31×#102C22semidirect
45. C2×C31×C22⋊C8C22semidirect
46. C2×C31×C22⋊C8C22semidirect
47. C31×#340C22semidirect
48. C31×#340C22semidirect
94. C31×C22⋊Q8D4semidirect
104. C31×#121D4semidirect
105. C31×#121D4semidirect
241. #23924C31direct (N × H)
326. C2×#537C2×C31semidirect
327. C2×#535C2×C31semidirect
328. C2×#449C2×C31semidirect
329. C2×#450C2×C31semidirect
330. C2×#447C2×C31semidirect
331. #2000C2×C31semidirect
332. #1999C2×C31semidirect
333. #1875C2×C31semidirect
334. #1874C2×C31semidirect
335. #1873C2×C31semidirect
336. #1780C2×C31semidirect
380. C22×#41C22×C31semidirect
391. C2×C22⋊Q8C22×C31semidirect
398. C2×#121C22×C31semidirect
402. C22×C4⋊C4C22×C31semidirect
406. C2×#103C22×C31semidirect
409. C2×#102C22×C31semidirect
412. C2×C22⋊C8C22×C31semidirect
413. C2×C22⋊C8C22×C31semidirect
414. #340C22×C31semidirect
415. #340C22×C31semidirect
471. C22⋊Q8D4×C31semidirect
481. #121D4×C31semidirect
482. #121D4×C31semidirect
510. C31#23924direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5372
C2×C31×#5352
C2×C31×#4492
C2×C31×#4502
C2×C31×#4472
C31×#20002
C31×#19992
C31×#18752
C31×#18742
C31×#18732
C31×#17802
#2392431