Finite Group Databasebeta

← C31×#13996 #21470755

Subgroups — C31×#13996 #21470755

Order 7936.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#123C211yesmaximal, characteristic
2C2×C31×#386C211yesmaximal, characteristic
3C2×C31×#386C211yesmaximal, characteristic
4C2×C31×#385C211yesmaximal, characteristic, complemented
5C2×C31×#381C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C22×C31×#95C211yesmaximal, characteristic, complemented
8C31×#1445C212yesmaximal, complemented
9C31×#1439C212yesmaximal, complemented
10C31×#1437C212yesmaximal, complemented
11C31×C4⋊#95C212yesmaximal, complemented
12C23×D4×C31C2211yescharacteristic
13C24×C4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C24×C4×C31C2211yescharacteristic
16C2×C31×#123—24no—
17C2×C31×#123—24no—
18C2×C31×#123C418yescomplemented
19C22×C4⋊C4×C31C2212yes—
20C22×C4⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C42×C31C2212yes—
29C31×#386—24no—
30C31×#386—24no—
31C31×#385—24no—
32C31×#381—24no—
33C4×C22⋊C4×C31—24no—
34C2×C31×#95—24no—
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2212yes—
41C2×C31×#95C2212yes—
42C2×C31×#95C2212yes—
43C2×C31×#95C2211yescharacteristic
44C25×C31C2311yescharacteristic
45C25×C31C2311yescharacteristic
46C22×D4×C31—22no—
47C22×D4×C31—22no—
48C22×D4×C31—22no—
49C22×D4×C31—22no—
50C22×D4×C31—22no—
51C22×D4×C31—22no—
52C22×D4×C31C2×C414yes—
53C23×C4×C31—22no—
54C23×C4×C31—22no—
55C23×C4×C31—22no—
56C23×C4×C31—22no—
57C23×C4×C31—22no—
58C23×C4×C31—22no—
59C23×C4×C31—22no—
60C23×C4×C31—22no—
61C23×C4×C31—22no—
62C23×C4×C31—24no—
63C23×C4×C31—24no—
64C23×C4×C31—22no—
65C23×C4×C31—22no—
66C23×C4×C31—42no—
67C23×C4×C31—42no—
68C23×C4×C31C2×C414yes—
69C23×C4×C31D414yes—
70C23×C4×C31C2311yescharacteristic
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2312yes—
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2312yes—
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2312yes—
77C23×C4×C31C2312yes—
78C23×C4×C31C2311yescharacteristic
79C31×#123—232no—
80C2×C4⋊C4×C31—24no—
81C2×C4⋊C4×C31—24no—
82C2×C4⋊C4×C31—24no—
83C2×C4⋊C4×C31—24no—
84C2×C4⋊C4×C31—42no—
85C2×C4⋊C4×C31C2×C418yescomplemented
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—24no—
94C2×C22⋊C4×C31—22no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—24no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—42no—
99C2×C22⋊C4×C31—42no—
100C2×C22⋊C4×C31C2×C414yes—
101C2×C22⋊C4×C31C2×C418yescomplemented
102C2×C22⋊C4×C31D414yes—
103C2×C22⋊C4×C31D414yes—
104C2×C22⋊C4×C31D414yes—
105C2×C42×C31—24no—
106C2×C42×C31—24no—
107C2×C42×C31—42no—
108C31×#95—24no—
109C31×#95—24no—
110C31×#95—24no—
111C31×#95—24no—
112C31×#95—24no—
113C31×#95—24no—
114C31×#95—24no—
115C31×#95—22no—
116C31×#95—22no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31—21no—
122C24×C31—21no—
123C24×C31—21no—
124C24×C31—21no—
125C24×C31—22no—
126C24×C31—22no—
127C24×C31—21no—
128C24×C31—21no—
129C24×C31—22no—
130C24×C31—22no—
131C24×C31C22×C412yes—
132C24×C31C22×C412yes—
133C24×C31C2×D412yes—
134C24×C31C2×D412yes—
135C24×C31C2×D412yes—
136C24×C31C2×D412yes—
137C24×C31#4112yes—
138C24×C31#4112yes—
139C24×C31C2411yescharacteristic
140C2×D4×C31—28no—
141C2×D4×C31—28no—
142C2×D4×C31—28no—
143C2×D4×C31—44no—
144C2×D4×C31—44no—
145C2×D4×C31—44no—
146C2×D4×C31—44no—
147C22×C4×C31—21no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—21no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—28no—
155C22×C4×C31—28no—
156C22×C4×C31—28no—
157C22×C4×C31—28no—
158C22×C4×C31—28no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—21no—
162C22×C4×C31—22no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—21no—
178C22×C4×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—28no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—44no—
199C22×C4×C31—48no—
200C22×C4×C31—48no—
201C22×C4×C31—48no—
202C22×C4×C31—48no—
203C22×C4×C31—44no—
204C22×C4×C31—44no—
205C22×C4×C31—44no—
206C22×C4×C31—44no—
207C22×C4×C31—44no—
208C22×C4×C31—44no—
209C22×C4×C31C22×C414yes—
210C22×C4×C31C22×C412yes—
211C22×C4×C31C22×C414yes—
212C22×C4×C31C2×D414yes—
213C22×C4×C31C2×D412yes—
214C22×C4×C31C2×D414yes—
215C22×C4×C31C2×D414yes—
216C22×C4×C31C2×D412yes—
217C22×C4×C31#4114yes—
218C22×C4×C31#4114yes—
219C4⋊C4×C31—216no—
220C4⋊C4×C31—48no—
221C22⋊C4×C31—28no—
222C22⋊C4×C31—216no—
223C22⋊C4×C31—48no—
224C22⋊C4×C31—44no—
225C22⋊C4×C31—44no—
226C22⋊C4×C31—44no—
227C22⋊C4×C31C22⋊C4116yescomplemented
228C42×C31—48no—
229#13996C3111yesmaximal, characteristic, direct product factor, Sylow
230C23×C31—24no—
231C23×C31—24no—
232C23×C31—22no—
233C23×C31—22no—
234C23×C31—24no—
235C23×C31—22no—
236C23×C31—22no—
237C23×C31—24no—
238C23×C31—24no—
239C23×C31—24no—
240C23×C31—24no—
241C23×C31—24no—
242C23×C31—24no—
243C23×C31—24no—
244C23×C31—24no—
245C23×C31—24no—
246C23×C31—22no—
247C23×C31—22no—
248C23×C31—22no—
249C23×C31—24no—
250C23×C31—24no—
251C23×C31—41no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31—41no—
256C23×C31—42no—
257C23×C31—41no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—42no—
261C23×C31—42no—
262C23×C31—42no—
263C23×C31—42no—
264C23×C31—42no—
265C23×C31—42no—
266C23×C31—42no—
267C23×C31—42no—
268C23×C31—42no—
269C23×C31C2×C22⋊C414yes—
270C23×C31C4×D414yes—
271C23×C31C4×D414yes—
272C23×C31#12114yes—
273C23×C31#12114yes—
274C23×C31#12414yes—
275C23×C31#12714yes—
276C23×C31C23×C411yescharacteristic
277C23×C31C22×D411yescharacteristic
278C23×C31C22×D411yescharacteristic
279C23×C31C22×D411yescharacteristic
280C23×C31C22×D411yescharacteristic
281C23×C31C2×#4111yescharacteristic
282C23×C31C2×#4111yescharacteristic
283C23×C31C2×#4112yes—
284C23×C31C2×#4112yes—
285C23×C31H(5,𝔽2)12yes—
286C23×C312−1+412yes—
287D4×C31—416no—
288C2×C4×C31—24no—
289C2×C4×C31—24no—
290C2×C4×C31—22no—
291C2×C4×C31—22no—
292C2×C4×C31—24no—
293C2×C4×C31—24no—
294C2×C4×C31—24no—
295C2×C4×C31—24no—
296C2×C4×C31—24no—
297C2×C4×C31—24no—
298C2×C4×C31—24no—
299C2×C4×C31—22no—
300C2×C4×C31—24no—
301C2×C4×C31—24no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—24no—
305C2×C4×C31—22no—
306C2×C4×C31—22no—
307C2×C4×C31—24no—
308C2×C4×C31—22no—
309C2×C4×C31—24no—
310C2×C4×C31—24no—
311C2×C4×C31—24no—
312C2×C4×C31—24no—
313C2×C4×C31—416no—
314C2×C4×C31—416no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—42no—
320C2×C4×C31—41no—
321C2×C4×C31—42no—
322C2×C4×C31—42no—
323C2×C4×C31—42no—
324C2×C4×C31—41no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—42no—
331C2×C4×C31—42no—
332C2×C4×C31—42no—
333C2×C4×C31—416no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—42no—
341C2×C4×C31—42no—
342C2×C4×C31—42no—
343C2×C4×C31—42no—
344C2×C4×C31C2×C22⋊C418yes—
345C2×C4×C31#12314yescomplemented
346C22×#123C2×C3111yescharacteristic
347C2×#386C2×C3111yescharacteristic
348C2×#386C2×C3111yescharacteristic
349C2×#385C2×C3111yescharacteristic, complemented
350C2×#381C2×C3111yescharacteristic, complemented
351C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
352C22×#95C2×C3111yescharacteristic, complemented
353#1445C2×C3112yescomplemented
354#1439C2×C3112yescomplemented
355#1437C2×C3112yescomplemented
356C4⋊#95C2×C3112yescomplemented
357C22×C31—24no—
358C22×C31—28no—
359C22×C31—28no—
360C22×C31—24no—
361C22×C31—24no—
362C22×C31—28no—
363C22×C31—28no—
364C22×C31—24no—
365C22×C31—24no—
366C22×C31—24no—
367C22×C31—42no—
368C22×C31—44no—
369C22×C31—44no—
370C22×C31—42no—
371C22×C31—42no—
372C22×C31—81no—
373C22×C31—81no—
374C22×C31—82no—
375C22×C31—82no—
376C22×C31—81no—
377C22×C31—81no—
378C22×C31#39018yes—
379C22×C31C22×C22⋊C411yescharacteristic
380C22×C31C2×C4×D411yescharacteristic
381C22×C31C2×C4×D411yescharacteristic
382C22×C31C4×#4112yes—
383C22×C31#52012yes—
384C22×C31C2×#12111yescharacteristic
385C22×C31C2×#12111yescharacteristic
386C22×C31C2×#12311yescharacteristic
387C22×C31#52511yescharacteristic
388C22×C31C2×#12411yescharacteristic
389C22×C31#52912yes—
390C22×C31C2×#12711yescharacteristic
391C22×C31#53411yescharacteristic
392C22×C31#53611yescharacteristic
393C22×C31#53912yes—
394C22×C31#54612yes—
395C22×C31#54612yes—
396C22×C31#54612yes—
397C22×C31#54712yes—
398C22×C31#54712yes—
399C22×C31#54712yes—
400C22×C31#55112yes—
401C22×C31#55212yes—
402C4×C31—28no—
403C4×C31—24no—
404C4×C31—42no—
405C4×C31—44no—
406C4×C31—44no—
407C4×C31—44no—
408C4×C31—42no—
409C4×C31—81no—
410C4×C31—81no—
411C23×D4C22×C3111yescharacteristic
412C24×C4C22×C3111yescharacteristic
413C24×C4C22×C3111yescharacteristic
414C24×C4C22×C3111yescharacteristic
415C2×#123—24no—
416C2×#123—24no—
417C2×#123C4×C3118yescomplemented
418C22×C4⋊C4C22×C3112yes—
419C22×C4⋊C4C22×C3112yes—
420C22×C22⋊C4C22×C3111yescharacteristic
421C22×C22⋊C4C22×C3111yescharacteristic
422C22×C22⋊C4C22×C3112yes—
423C22×C22⋊C4C22×C3112yes—
424C22×C22⋊C4C22×C3111yescharacteristic
425C22×C22⋊C4C22×C3111yescharacteristic
426C22×C22⋊C4C22×C3111yescharacteristic
427C22×C42C22×C3112yes—
428#386—24no—
429#386—24no—
430#385—24no—
431#381—24no—
432C4×C22⋊C4—24no—
433C2×#95—24no—
434C2×#95C22×C3111yescharacteristic
435C2×#95C22×C3112yes—
436C2×#95C22×C3112yes—
437C2×#95C22×C3112yes—
438C2×#95C22×C3112yes—
439C2×#95C22×C3112yes—
440C2×#95C22×C3112yes—
441C2×#95C22×C3112yes—
442C2×#95C22×C3111yescharacteristic
443C2×C31—28no—
444C2×C31—82no—
445C2×C31C2×#39011yescharacteristic
446C2×C31C4×#12311yescharacteristic
447C2×C31#232211yescharacteristic
448C2×C31#233912yes—
449C2×C31#235912yes—
450C2×C31#241211yescharacteristic
451C2×C31#241311yescharacteristic
452C2×C31#242512yes—
453C2×C31#248812yes—
454C2×C31#250111yescharacteristic
455C2×C31#253911yescharacteristic
456C25C23×C3111yescharacteristic
457C25C23×C3111yescharacteristic
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4C2×C4×C3114yes—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—24no—
475C23×C4—24no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—42no—
479C23×C4—42no—
480C23×C4C2×C4×C3114yes—
481C23×C4D4×C3114yes—
482C23×C4C23×C3111yescharacteristic
483C23×C4C23×C3111yescharacteristic
484C23×C4C23×C3112yes—
485C23×C4C23×C3111yescharacteristic
486C23×C4C23×C3112yes—
487C23×C4C23×C3111yescharacteristic
488C23×C4C23×C3112yes—
489C23×C4C23×C3112yes—
490C23×C4C23×C3111yescharacteristic
491#123—232no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—42no—
497C2×C4⋊C4C2×C4×C3118yescomplemented
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4C2×C4×C3114yes—
513C2×C22⋊C4C2×C4×C3118yescomplemented
514C2×C22⋊C4D4×C3114yes—
515C2×C22⋊C4D4×C3114yes—
516C2×C22⋊C4D4×C3114yes—
517C2×C42—24no—
518C2×C42—24no—
519C2×C42—42no—
520#95—24no—
521#95—24no—
522#95—24no—
523#95—24no—
524#95—24no—
525#95—24no—
526#95—24no—
527#95—22no—
528#95—22no—
529C31#1399611yescharacteristic, direct product factor, Sylow
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24C22×C4×C3112yes—
545C24C22×C4×C3112yes—
546C24C2×D4×C3112yes—
547C24C2×D4×C3112yes—
548C24C2×D4×C3112yes—
549C24C2×D4×C3112yes—
550C24#41×C3112yes—
551C24#41×C3112yes—
552C24C24×C3111yescharacteristic
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—28no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4C22×C4×C3114yes—
623C22×C4C22×C4×C3112yes—
624C22×C4C22×C4×C3114yes—
625C22×C4C2×D4×C3114yes—
626C22×C4C2×D4×C3112yes—
627C22×C4C2×D4×C3114yes—
628C22×C4C2×D4×C3114yes—
629C22×C4C2×D4×C3112yes—
630C22×C4#41×C3114yes—
631C22×C4#41×C3114yes—
632C4⋊C4—216no—
633C4⋊C4—48no—
634C22⋊C4—28no—
635C22⋊C4—216no—
636C22⋊C4—48no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4C22⋊C4×C31116yescomplemented
641C42—48no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23C2×C22⋊C4×C3114yes—
682C23C4×D4×C3114yes—
683C23C4×D4×C3114yes—
684C23C31×#12114yes—
685C23C31×#12114yes—
686C23C31×#12414yes—
687C23C31×#12714yes—
688C23C23×C4×C3111yescharacteristic
689C23C22×D4×C3111yescharacteristic
690C23C22×D4×C3111yescharacteristic
691C23C22×D4×C3111yescharacteristic
692C23C22×D4×C3111yescharacteristic
693C23C2×#41×C3111yescharacteristic
694C23C2×#41×C3111yescharacteristic
695C23C2×#41×C3112yes—
696C23C2×#41×C3112yes—
697C23C31×H(5,𝔽2)12yes—
698C23C31×2−1+412yes—
699D4—416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—416no—
726C2×C4—416no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—416no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4C2×C22⋊C4×C3118yes—
757C2×C4C31×#12314yescomplemented
758C22—24no—
759C22—28no—
760C22—28no—
761C22—24no—
762C22—24no—
763C22—28no—
764C22—28no—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—42no—
769C22—44no—
770C22—44no—
771C22—42no—
772C22—42no—
773C22—81no—
774C22—81no—
775C22—82no—
776C22—82no—
777C22—81no—
778C22—81no—
779C22C31×#39018yes—
780C22C22×C22⋊C4×C3111yescharacteristic
781C22C2×C4×D4×C3111yescharacteristic
782C22C2×C4×D4×C3111yescharacteristic
783C22C4×#41×C3112yes—
784C22C31×#52012yes—
785C22C2×C31×#12111yescharacteristic
786C22C2×C31×#12111yescharacteristic
787C22C2×C31×#12311yescharacteristic
788C22C31×#52511yescharacteristic
789C22C2×C31×#12411yescharacteristic
790C22C31×#52912yes—
791C22C2×C31×#12711yescharacteristic
792C22C31×#53411yescharacteristic
793C22C31×#53611yescharacteristic
794C22C31×#53912yes—
795C22C31×#54612yes—
796C22C31×#54612yes—
797C22C31×#54612yes—
798C22C31×#54712yes—
799C22C31×#54712yes—
800C22C31×#54712yes—
801C22C31×#55112yes—
802C22C31×#55212yes—
803C4—28no—
804C4—24no—
805C4—42no—
806C4—44no—
807C4—44no—
808C4—44no—
809C4—42no—
810C4—81no—
811C4—81no—
812C2—28no—
813C2—82no—
814C2C2×C31×#39011yescharacteristic
815C2C4×C31×#12311yescharacteristic
816C2C31×#232211yescharacteristic
817C2C31×#233912yes—
818C2C31×#235912yes—
819C2C31×#241211yescharacteristic
820C2C31×#241311yescharacteristic
821C2C31×#242512yes—
822C2C31×#248812yes—
823C2C31×#250111yescharacteristic
824C2C31×#253911yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C31×#385C2semidirect
5. C2×C31×#381C2semidirect
6. C2×C4×C22⋊C4×C31C2semidirect
7. C22×C31×#95C2semidirect
8. C31×#1445C2semidirect
9. C31×#1439C2semidirect
10. C31×#1437C2semidirect
11. C31×C4⋊#95C2semidirect
18. C2×C31×#123C4semidirect
85. C2×C4⋊C4×C31C2×C4semidirect
101. C2×C22⋊C4×C31C2×C4semidirect
227. C22⋊C4×C31C22⋊C4semidirect
229. #13996C31direct (N × H)
345. C2×C4×C31#123semidirect
349. C2×#385C2×C31semidirect
350. C2×#381C2×C31semidirect
351. C2×C4×C22⋊C4C2×C31semidirect
352. C22×#95C2×C31semidirect
353. #1445C2×C31semidirect
354. #1439C2×C31semidirect
355. #1437C2×C31semidirect
356. C4⋊#95C2×C31semidirect
417. C2×#123C4×C31semidirect
497. C2×C4⋊C4C2×C4×C31semidirect
513. C2×C22⋊C4C2×C4×C31semidirect
529. C31#13996direct (N × H)
640. C22⋊C4C22⋊C4×C31semidirect
757. C2×C4C31×#123semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1232
C2×C31×#3862
C2×C31×#3852
C2×C31×#3812
C2×C4×C22⋊C4×C312
C22×C31×#952
C31×#14452
C31×#14392
C31×#14372
C31×C4⋊#952
#1399631