Finite Group Databasebeta

← C2×C31×#1913 #21477772

Subgroups — C2×C31×#1913 #21477772

Order 7936.

2078 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#534C211yesmaximal, characteristic
2C2×C31×#518C211yesmaximal, characteristic, complemented
3C22×C31×#99C211yesmaximal, characteristic, complemented
4C22×C31×#99C212yesmaximal, complemented
5C31×#1913C218yesmaximal, direct product factor
6C2×C31×#342C212yesmaximal, complemented
7C23×D4×C31C2211yescharacteristic
8C23×D4×C31C2211yescharacteristic
9C31×#534—22no—
10C31×#534—22no—
11C31×#534C414yescomplemented
12C31×#534C2214yes—
13C2×C31×#123—21no—
14C2×C31×#123C412yescomplemented
15C2×C31×#121—22no—
16C2×C31×#120—21no—
17C2×C31×#120C412yescomplemented
18C31×#518—22no—
19C31×#518—24no—
20C31×#518C2214yescomplemented
21C2×C4×D4×C31—24no—
22C2×C31×#117—21no—
23C22×C22⋊C4×C31—21no—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2212yes—
27C2×C31×#99—22no—
28C2×C31×#99—22no—
29C2×C31×#99—24no—
30C2×C31×#99—24no—
31C2×C31×#99C2214yescomplemented
32C2×C31×#99C2218yescomplemented
33C31×#342C2218yescomplemented
34C25×C31C2×C411yescharacteristic, complemented
35C25×C31D411yescharacteristic
36C25×C31C2311yescharacteristic
37C22×D4×C31—22no—
38C22×D4×C31—22no—
39C22×D4×C31—22no—
40C22×D4×C31—22no—
41C22×D4×C31—22no—
42C22×D4×C31—22no—
43C22×D4×C31—21no—
44C22×D4×C31—21no—
45C22×D4×C31—21no—
46C22×D4×C31—21no—
47C22×D4×C31—22no—
48C22×D4×C31—22no—
49C22×D4×C31—22no—
50C22×D4×C31C2×C412yes—
51C22×D4×C31C2×C412yes—
52C22×D4×C31C2×C412yescomplemented
53C22×D4×C31D412yes—
54C22×D4×C31D412yes—
55C22×D4×C31D412yes—
56C22×D4×C31C2312yes—
57C22×D4×C31C2312yes—
58C23×C4×C31—22no—
59C23×C4×C31—22no—
60C23×C4×C31—21no—
61C23×C4×C31—22no—
62C23×C4×C31C2×C411yescharacteristic, complemented
63C23×C4×C31D411yescharacteristic
64C31×#123—24no—
65C31×#123—24no—
66C31×#123—24no—
67C31×#123C2×C418yescomplemented
68C31×#121—28no—
69C31×#121—28no—
70C31×#120—24no—
71C31×#120—24no—
72C31×#120—24no—
73C31×#120C2×C418yescomplemented
74C4×D4×C31—216no—
75C4×D4×C31—216no—
76C31×#117—24no—
77C31×#117—24no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—22no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31—24no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—22no—
84C2×C22⋊C4×C31—24no—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—21no—
88C2×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31—21no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—22no—
94C2×C22⋊C4×C31—22no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31C2×C412yescomplemented
97C2×C22⋊C4×C31C2×C412yescomplemented
98C2×C22⋊C4×C31D414yescomplemented
99C2×C22⋊C4×C31D414yescomplemented
100C2×C22⋊C4×C31C2314yes—
101C2×C22⋊C4×C31C2312yes—
102C2×C22⋊C4×C31C2314yes—
103C2×C42×C31—22no—
104C31×#99—28no—
105C31×#99—216no—
106C24×C31—21no—
107C24×C31—21no—
108C24×C31—21no—
109C24×C31—21no—
110C24×C31—21no—
111C24×C31—21no—
112C24×C31—22no—
113C24×C31—22no—
114C24×C31—82no—
115C24×C31—82no—
116C24×C31—82no—
117C24×C31C22⋊C412yes—
118C24×C31C22⋊C412yes—
119C24×C31C22×C411yescharacteristic
120C24×C31C22×C411yescharacteristic
121C24×C31C22×C412yescomplemented
122C24×C31C2×D412yes—
123C24×C31C2×D411yescharacteristic
124C24×C31C2×D411yescharacteristic
125C24×C31C2×D412yes—
126C24×C31C2×D411yescharacteristic
127C24×C31C2×D411yescharacteristic
128C24×C31C2×D412yes—
129C24×C31#4112yes—
130C24×C31#4112yes—
131C24×C31C2411yescharacteristic
132C2×D4×C31—24no—
133C2×D4×C31—24no—
134C2×D4×C31—24no—
135C2×D4×C31—24no—
136C2×D4×C31—24no—
137C2×D4×C31—24no—
138C2×D4×C31—24no—
139C2×D4×C31—24no—
140C2×D4×C31—24no—
141C2×D4×C31—24no—
142C2×D4×C31—24no—
143C2×D4×C31—24no—
144C2×D4×C31—22no—
145C2×D4×C31—22no—
146C2×D4×C31—24no—
147C2×D4×C31—24no—
148C2×D4×C31—24no—
149C2×D4×C31—22no—
150C2×D4×C31—22no—
151C2×D4×C31—24no—
152C2×D4×C31—28no—
153C2×D4×C31—41no—
154C2×D4×C31—42no—
155C2×D4×C31—41no—
156C2×D4×C31—42no—
157C2×D4×C31—42no—
158C2×D4×C31—42no—
159C2×D4×C31—42no—
160C2×D4×C31—41no—
161C2×D4×C31—42no—
162C2×D4×C31—41no—
163C2×D4×C31—84no—
164C2×D4×C31C22⋊C414yes—
165C2×D4×C31C22⋊C414yes—
166C2×D4×C31C22×C414yes—
167C2×D4×C31C2×D414yes—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—22no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—24no—
178C22×C4×C31—28no—
179C22×C4×C31—22no—
180C22×C4×C31—24no—
181C22×C4×C31—24no—
182C22×C4×C31—22no—
183C22×C4×C31—24no—
184C22×C4×C31—42no—
185C22×C4×C31—42no—
186C22×C4×C31—84no—
187C22×C4×C31—84no—
188C22×C4×C31—82no—
189C22×C4×C31—84no—
190C22×C4×C31C22⋊C412yes—
191C22×C4×C31C22⋊C412yes—
192C22×C4×C31C22×C412yescomplemented
193C22×C4×C31C2×D412yes—
194C4⋊C4×C31—28no—
195C4⋊C4×C31—28no—
196C22⋊C4×C31—28no—
197C22⋊C4×C31—22no—
198C22⋊C4×C31—22no—
199C22⋊C4×C31—28no—
200C22⋊C4×C31—24no—
201C22⋊C4×C31—24no—
202C22⋊C4×C31—24no—
203C22⋊C4×C31—22no—
204C22⋊C4×C31—28no—
205C22⋊C4×C31—24no—
206C22⋊C4×C31—24no—
207C22⋊C4×C31—42no—
208C22⋊C4×C31—42no—
209C22⋊C4×C31C22×C414yescomplemented
210C22⋊C4×C31C2×D418yescomplemented
211C42×C31—28no—
212C2×#1913C3111yesmaximal, characteristic, direct product factor, Sylow
213C23×C31—22no—
214C23×C31—22no—
215C23×C31—22no—
216C23×C31—22no—
217C23×C31—22no—
218C23×C31—22no—
219C23×C31—22no—
220C23×C31—24no—
221C23×C31—44no—
222C23×C31—42no—
223C23×C31—44no—
224C23×C31—42no—
225C23×C31—42no—
226C23×C31—44no—
227C23×C31—44no—
228C23×C31—44no—
229C23×C31—41no—
230C23×C31—42no—
231C23×C31—41no—
232C23×C31—82no—
233C23×C31—84no—
234C23×C31—81no—
235C23×C31—81no—
236C23×C31—82no—
237C23×C31—81no—
238C23×C31—82no—
239C23×C31—81no—
240C23×C31—82no—
241C23×C31—82no—
242C23×C31—82no—
243C23×C31—82no—
244C23×C31—82no—
245C23×C31—82no—
246C23×C31—84no—
247C23×C31C2×C22⋊C411yescharacteristic
248C23×C31C2×C22⋊C414yes—
249C23×C31C2×C22⋊C411yescharacteristic
250C23×C31C2×C22⋊C411yescharacteristic
251C23×C31C2×C22⋊C411yescharacteristic
252C23×C31C4×D412yes—
253C23×C31C4×D412yes—
254C23×C31C4×D412yes—
255C23×C31C4×D412yes—
256C23×C31#12011yescharacteristic
257C23×C31#12011yescharacteristic
258C23×C31#12012yes—
259C23×C31#12112yes—
260C23×C31#12112yes—
261C23×C31#12112yes—
262C23×C31#12112yes—
263C23×C31#12311yescharacteristic
264C23×C31#12311yescharacteristic
265C23×C31#12312yes—
266C23×C31C23×C411yescharacteristic
267C23×C31C22×D411yescharacteristic
268C23×C31C22×D411yescharacteristic
269C23×C31C22×D412yes—
270C23×C31C2×#4112yes—
271D4×C31—28no—
272D4×C31—28no—
273D4×C31—28no—
274D4×C31—28no—
275D4×C31—42no—
276D4×C31—44no—
277D4×C31—42no—
278D4×C31—42no—
279D4×C31—42no—
280D4×C31—44no—
281D4×C31—88no—
282C2×C4×C31—22no—
283C2×C4×C31—22no—
284C2×C4×C31—22no—
285C2×C4×C31—22no—
286C2×C4×C31—22no—
287C2×C4×C31—22no—
288C2×C4×C31—24no—
289C2×C4×C31—22no—
290C2×C4×C31—24no—
291C2×C4×C31—28no—
292C2×C4×C31—48no—
293C2×C4×C31—44no—
294C2×C4×C31—41no—
295C2×C4×C31—42no—
296C2×C4×C31—41no—
297C2×C4×C31—44no—
298C2×C4×C31—84no—
299C2×C4×C31—84no—
300C2×C4×C31—88no—
301C2×C4×C31—82no—
302C2×C4×C31—82no—
303C2×C4×C31—84no—
304C2×C4×C31—84no—
305C2×C4×C31—84no—
306C2×C4×C31C2×C22⋊C414yes—
307C2×#534C2×C3111yescharacteristic
308C2×#518C2×C3111yescharacteristic, complemented
309C22×#99C2×C3111yescharacteristic, complemented
310C22×#99C2×C3112yescomplemented
311#1913C2×C3118yesdirect product factor
312C2×#342C2×C3112yescomplemented
313C22×C31—22no—
314C22×C31—22no—
315C22×C31—24no—
316C22×C31—24no—
317C22×C31—22no—
318C22×C31—24no—
319C22×C31—41no—
320C22×C31—42no—
321C22×C31—42no—
322C22×C31—42no—
323C22×C31—41no—
324C22×C31—42no—
325C22×C31—41no—
326C22×C31—41no—
327C22×C31—42no—
328C22×C31—41no—
329C22×C31—41no—
330C22×C31—41no—
331C22×C31—41no—
332C22×C31—42no—
333C22×C31—42no—
334C22×C31—42no—
335C22×C31—42no—
336C22×C31—42no—
337C22×C31—44no—
338C22×C31—44no—
339C22×C31—44no—
340C22×C31—44no—
341C22×C31—44no—
342C22×C31—42no—
343C22×C31—82no—
344C22×C31—82no—
345C22×C31—82no—
346C22×C31—84no—
347C22×C31—82no—
348C22×C31—84no—
349C22×C31—82no—
350C22×C31#38611yescharacteristic
351C22×C31#38611yescharacteristic
352C22×C31#38611yescharacteristic
353C22×C31#38612yes—
354C22×C31#38612yes—
355C22×C31#38611yescharacteristic
356C22×C31C22×C22⋊C411yescharacteristic
357C22×C31C2×C4×D412yes—
358C22×C31C2×#12011yescharacteristic
359C22×C31C2×#12112yes—
360C22×C31C2×#12311yescharacteristic
361C4×C31—24no—
362C4×C31—48no—
363C4×C31—44no—
364C4×C31—42no—
365C4×C31—84no—
366C23×D4C22×C3111yescharacteristic
367C23×D4C22×C3111yescharacteristic
368#534—22no—
369#534—22no—
370#534C4×C3114yescomplemented
371#534C22×C3114yes—
372C2×#123—21no—
373C2×#123C4×C3112yescomplemented
374C2×#121—22no—
375C2×#120—21no—
376C2×#120C4×C3112yescomplemented
377#518—22no—
378#518—24no—
379#518C22×C3114yescomplemented
380C2×C4×D4—24no—
381C2×#117—21no—
382C22×C22⋊C4—21no—
383C22×C22⋊C4C22×C3112yes—
384C22×C22⋊C4C22×C3111yescharacteristic
385C22×C22⋊C4C22×C3112yes—
386C2×#99—22no—
387C2×#99—22no—
388C2×#99—24no—
389C2×#99—24no—
390C2×#99C22×C3114yescomplemented
391C2×#99C22×C3118yescomplemented
392#342C22×C3118yescomplemented
393C2×C31—21no—
394C2×C31—21no—
395C2×C31—22no—
396C2×C31—21no—
397C2×C31—21no—
398C2×C31—22no—
399C2×C31—21no—
400C2×C31—22no—
401C2×C31—21no—
402C2×C31—22no—
403C2×C31—44no—
404C2×C31—82no—
405C2×C31#191312yesdirect product factor
406C2×C31C2×#38611yescharacteristic
407C25C2×C4×C3111yescharacteristic, complemented
408C25D4×C3111yescharacteristic
409C25C23×C3111yescharacteristic
410C22×D4—22no—
411C22×D4—22no—
412C22×D4—22no—
413C22×D4—22no—
414C22×D4—21no—
415C22×D4—21no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4—22no—
419C22×D4—22no—
420C22×D4—22no—
421C22×D4—22no—
422C22×D4—22no—
423C22×D4C2×C4×C3112yes—
424C22×D4C2×C4×C3112yes—
425C22×D4C2×C4×C3112yescomplemented
426C22×D4D4×C3112yes—
427C22×D4D4×C3112yes—
428C22×D4D4×C3112yes—
429C22×D4C23×C3112yes—
430C22×D4C23×C3112yes—
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—21no—
434C23×C4—22no—
435C23×C4C2×C4×C3111yescharacteristic, complemented
436C23×C4D4×C3111yescharacteristic
437#123—24no—
438#123—24no—
439#123—24no—
440#123C2×C4×C3118yescomplemented
441#121—28no—
442#121—28no—
443#120—24no—
444#120—24no—
445#120—24no—
446#120C2×C4×C3118yescomplemented
447C4×D4—216no—
448C4×D4—216no—
449#117—24no—
450#117—24no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4C2×C4×C3112yescomplemented
470C2×C22⋊C4C2×C4×C3112yescomplemented
471C2×C22⋊C4D4×C3114yescomplemented
472C2×C22⋊C4D4×C3114yescomplemented
473C2×C22⋊C4C23×C3114yes—
474C2×C22⋊C4C23×C3112yes—
475C2×C22⋊C4C23×C3114yes—
476C2×C42—22no—
477#99—28no—
478#99—216no—
479C31C2×#191311yescharacteristic, direct product factor, Sylow
480C24—21no—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—21no—
485C24—21no—
486C24—22no—
487C24—22no—
488C24—82no—
489C24—82no—
490C24—82no—
491C24C22⋊C4×C3112yes—
492C24C22⋊C4×C3112yes—
493C24C22×C4×C3111yescharacteristic
494C24C22×C4×C3111yescharacteristic
495C24C22×C4×C3112yescomplemented
496C24C2×D4×C3112yes—
497C24C2×D4×C3111yescharacteristic
498C24C2×D4×C3111yescharacteristic
499C24C2×D4×C3112yes—
500C24C2×D4×C3111yescharacteristic
501C24C2×D4×C3111yescharacteristic
502C24C2×D4×C3112yes—
503C24#41×C3112yes—
504C24#41×C3112yes—
505C24C24×C3111yescharacteristic
506C2×D4—24no—
507C2×D4—24no—
508C2×D4—24no—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—24no—
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—24no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—24no—
526C2×D4—28no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—42no—
537C2×D4—84no—
538C2×D4C22⋊C4×C3114yes—
539C2×D4C22⋊C4×C3114yes—
540C2×D4C22×C4×C3114yes—
541C2×D4C2×D4×C3114yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—28no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—84no—
561C22×C4—84no—
562C22×C4—82no—
563C22×C4—84no—
564C22×C4C22⋊C4×C3112yes—
565C22×C4C22⋊C4×C3112yes—
566C22×C4C22×C4×C3112yescomplemented
567C22×C4C2×D4×C3112yes—
568C4⋊C4—28no—
569C4⋊C4—28no—
570C22⋊C4—28no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—28no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—22no—
578C22⋊C4—28no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4C22×C4×C3114yescomplemented
584C22⋊C4C2×D4×C3118yescomplemented
585C42—28no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—24no—
594C23—44no—
595C23—42no—
596C23—44no—
597C23—42no—
598C23—42no—
599C23—44no—
600C23—44no—
601C23—44no—
602C23—41no—
603C23—42no—
604C23—41no—
605C23—82no—
606C23—84no—
607C23—81no—
608C23—81no—
609C23—82no—
610C23—81no—
611C23—82no—
612C23—81no—
613C23—82no—
614C23—82no—
615C23—82no—
616C23—82no—
617C23—82no—
618C23—82no—
619C23—84no—
620C23C2×C22⋊C4×C3111yescharacteristic
621C23C2×C22⋊C4×C3114yes—
622C23C2×C22⋊C4×C3111yescharacteristic
623C23C2×C22⋊C4×C3111yescharacteristic
624C23C2×C22⋊C4×C3111yescharacteristic
625C23C4×D4×C3112yes—
626C23C4×D4×C3112yes—
627C23C4×D4×C3112yes—
628C23C4×D4×C3112yes—
629C23C31×#12011yescharacteristic
630C23C31×#12011yescharacteristic
631C23C31×#12012yes—
632C23C31×#12112yes—
633C23C31×#12112yes—
634C23C31×#12112yes—
635C23C31×#12112yes—
636C23C31×#12311yescharacteristic
637C23C31×#12311yescharacteristic
638C23C31×#12312yes—
639C23C23×C4×C3111yescharacteristic
640C23C22×D4×C3111yescharacteristic
641C23C22×D4×C3111yescharacteristic
642C23C22×D4×C3112yes—
643C23C2×#41×C3112yes—
644D4—28no—
645D4—28no—
646D4—28no—
647D4—28no—
648D4—42no—
649D4—44no—
650D4—42no—
651D4—42no—
652D4—42no—
653D4—44no—
654D4—88no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—28no—
665C2×C4—48no—
666C2×C4—44no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—44no—
671C2×C4—84no—
672C2×C4—84no—
673C2×C4—88no—
674C2×C4—82no—
675C2×C4—82no—
676C2×C4—84no—
677C2×C4—84no—
678C2×C4—84no—
679C2×C4C2×C22⋊C4×C3114yes—
680C22—22no—
681C22—22no—
682C22—24no—
683C22—24no—
684C22—22no—
685C22—24no—
686C22—41no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—41no—
691C22—42no—
692C22—41no—
693C22—41no—
694C22—42no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—44no—
705C22—44no—
706C22—44no—
707C22—44no—
708C22—44no—
709C22—42no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—84no—
714C22—82no—
715C22—84no—
716C22—82no—
717C22C31×#38611yescharacteristic
718C22C31×#38611yescharacteristic
719C22C31×#38611yescharacteristic
720C22C31×#38612yes—
721C22C31×#38612yes—
722C22C31×#38611yescharacteristic
723C22C22×C22⋊C4×C3111yescharacteristic
724C22C2×C4×D4×C3112yes—
725C22C2×C31×#12011yescharacteristic
726C22C2×C31×#12112yes—
727C22C2×C31×#12311yescharacteristic
728C4—24no—
729C4—48no—
730C4—44no—
731C4—42no—
732C4—84no—
733C2—21no—
734C2—21no—
735C2—22no—
736C2—21no—
737C2—21no—
738C2—22no—
739C2—21no—
740C2—22no—
741C2—21no—
742C2—22no—
743C2—44no—
744C2—82no—
745C2C31×#191312yesdirect product factor
746C2C2×C31×#38611yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC2×C31×#534C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#518C2semidirect
3. C22×C31×#99C2semidirect
4. C22×C31×#99C2semidirect
5. C31×#1913C2direct (N × H)
6. C2×C31×#342C2semidirect
11. C31×#534C4semidirect
14. C2×C31×#123C4semidirect
17. C2×C31×#120C4semidirect
20. C31×#518C22semidirect
31. C2×C31×#99C22semidirect
32. C2×C31×#99C22semidirect
33. C31×#342C22semidirect
34. C25×C31C2×C4semidirect
52. C22×D4×C31C2×C4semidirect
62. C23×C4×C31C2×C4semidirect
67. C31×#123C2×C4semidirect
73. C31×#120C2×C4semidirect
96. C2×C22⋊C4×C31C2×C4semidirect
97. C2×C22⋊C4×C31C2×C4semidirect
98. C2×C22⋊C4×C31D4semidirect
99. C2×C22⋊C4×C31D4semidirect
121. C24×C31C22×C4semidirect
192. C22×C4×C31C22×C4semidirect
209. C22⋊C4×C31C22×C4semidirect
210. C22⋊C4×C31C2×D4semidirect
212. C2×#1913C31direct (N × H)
308. C2×#518C2×C31semidirect
309. C22×#99C2×C31semidirect
310. C22×#99C2×C31semidirect
311. #1913C2×C31direct (N × H)
312. C2×#342C2×C31semidirect
370. #534C4×C31semidirect
373. C2×#123C4×C31semidirect
376. C2×#120C4×C31semidirect
379. #518C22×C31semidirect
390. C2×#99C22×C31semidirect
391. C2×#99C22×C31semidirect
392. #342C22×C31semidirect
405. C2×C31#1913direct (N × H)
407. C25C2×C4×C31semidirect
425. C22×D4C2×C4×C31semidirect
435. C23×C4C2×C4×C31semidirect
440. #123C2×C4×C31semidirect
446. #120C2×C4×C31semidirect
469. C2×C22⋊C4C2×C4×C31semidirect
470. C2×C22⋊C4C2×C4×C31semidirect
471. C2×C22⋊C4D4×C31semidirect
472. C2×C22⋊C4D4×C31semidirect
479. C31C2×#1913direct (N × H)
495. C24C22×C4×C31semidirect
566. C22×C4C22×C4×C31semidirect
583. C22⋊C4C22×C4×C31semidirect
584. C22⋊C4C2×D4×C31semidirect
745. C2C31×#1913direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5342
C2×C31×#5182
C22×C31×#992
C31×#19132
C2×C31×#3422
C2×#191331