Finite Group Databasebeta

← C31×#14357 #21471116

Subgroups — C31×#14357 #21471116

Order 7936.

3646 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#120C211yesmaximal, characteristic
2C2×C31×#390C211yesmaximal, characteristic, complemented
3C2×C31×#386C212yesmaximal, complemented
4C2×C31×#386C211yesmaximal, characteristic, complemented
5C2×C31×#379C212yesmaximal, complemented
6C31×#1440C212yesmaximal, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1438C212yesmaximal, complemented
9C31×#1437C212yesmaximal, complemented
10C26×C31C2211yescharacteristic
11C23×D4×C31C2212yes—
12C23×D4×C31C2211yescharacteristic
13C24×C4×C31C2211yescharacteristic, complemented
14C2×C31×#120—24no—
15C2×C31×#120—24no—
16C2×C31×#120C418yescomplemented
17C22×C4⋊C4×C31C2211yescharacteristic, complemented
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2212yescomplemented
27C22×C22⋊C4×C31C2211yescharacteristic, complemented
28C22×C42×C31C2211yescharacteristic, complemented
29C31×#390—24no—
30C31×#386—24no—
31C31×#386—28no—
32C31×#379—28no—
33C2×C31×#95C2212yescomplemented
34C2×C31×#95C2212yescomplemented
35C2×C31×#95C2212yescomplemented
36C2×C31×#95C2212yescomplemented
37C2×C31×#95C2212yescomplemented
38C25×C31—22no—
39C25×C31—22no—
40C25×C31—24no—
41C25×C31—24no—
42C25×C31—42no—
43C25×C31—42no—
44C25×C31—41no—
45C25×C31—41no—
46C25×C31—41no—
47C25×C31—41no—
48C25×C31C2×C414yescomplemented
49C25×C31C2311yescharacteristic
50C25×C31C2311yescharacteristic
51C25×C31C2312yes—
52C22×D4×C31—24no—
53C22×D4×C31—24no—
54C22×D4×C31—24no—
55C22×D4×C31—24no—
56C22×D4×C31—41no—
57C22×D4×C31—41no—
58C22×D4×C31—41no—
59C22×D4×C31—41no—
60C22×D4×C31—42no—
61C22×D4×C31—42no—
62C22×D4×C31C2×C418yes—
63C22×D4×C31C2×C414yes—
64C22×D4×C31D414yes—
65C22×D4×C31D414yes—
66C23×C4×C31—22no—
67C23×C4×C31—24no—
68C23×C4×C31—41no—
69C23×C4×C31—42no—
70C23×C4×C31—41no—
71C23×C4×C31C2312yes—
72C23×C4×C31C2312yes—
73C23×C4×C31C2312yes—
74C23×C4×C31C2312yes—
75C23×C4×C31C2312yes—
76C23×C4×C31C2311yescharacteristic
77C31×#120—232no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—41no—
80C2×C4⋊C4×C31—41no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—24no—
84C2×C22⋊C4×C31—24no—
85C2×C22⋊C4×C31—24no—
86C2×C22⋊C4×C31—24no—
87C2×C22⋊C4×C31—24no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—24no—
91C2×C22⋊C4×C31—24no—
92C2×C22⋊C4×C31—24no—
93C2×C22⋊C4×C31—24no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—24no—
96C2×C22⋊C4×C31—24no—
97C2×C22⋊C4×C31—42no—
98C2×C22⋊C4×C31—42no—
99C2×C22⋊C4×C31—42no—
100C2×C22⋊C4×C31—42no—
101C2×C22⋊C4×C31—42no—
102C2×C22⋊C4×C31—42no—
103C2×C22⋊C4×C31—42no—
104C2×C22⋊C4×C31—42no—
105C2×C22⋊C4×C31—42no—
106C2×C22⋊C4×C31—41no—
107C2×C22⋊C4×C31—41no—
108C2×C22⋊C4×C31C2×C414yescomplemented
109C2×C22⋊C4×C31C2×C418yescomplemented
110C2×C22⋊C4×C31D418yescomplemented
111C2×C42×C31—22no—
112C2×C42×C31—41no—
113C2×C42×C31—41no—
114C31×#95—24no—
115C31×#95—24no—
116C31×#95—24no—
117C31×#95—42no—
118C31×#95—42no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31—22no—
122C24×C31—22no—
123C24×C31—22no—
124C24×C31—22no—
125C24×C31—22no—
126C24×C31—22no—
127C24×C31—21no—
128C24×C31—21no—
129C24×C31—22no—
130C24×C31—22no—
131C24×C31—22no—
132C24×C31—22no—
133C24×C31—22no—
134C24×C31—22no—
135C24×C31—22no—
136C24×C31—22no—
137C24×C31—22no—
138C24×C31—21no—
139C24×C31—21no—
140C24×C31—22no—
141C24×C31—21no—
142C24×C31—21no—
143C24×C31—21no—
144C24×C31—21no—
145C24×C31—22no—
146C24×C31—22no—
147C24×C31—28no—
148C24×C31—216no—
149C24×C31—44no—
150C24×C31—48no—
151C24×C31—44no—
152C24×C31—44no—
153C24×C31—48no—
154C24×C31—48no—
155C24×C31—48no—
156C24×C31—48no—
157C24×C31—48no—
158C24×C31—44no—
159C24×C31—48no—
160C24×C31—44no—
161C24×C31—44no—
162C24×C31—44no—
163C24×C31—44no—
164C24×C31—48no—
165C24×C31—48no—
166C24×C31—48no—
167C24×C31—48no—
168C24×C31—44no—
169C24×C31—44no—
170C24×C31C22×C412yes—
171C24×C31C22×C412yes—
172C24×C31C22×C414yes—
173C24×C31C2×D412yes—
174C24×C31C2×D412yes—
175C24×C31C2×D412yes—
176C24×C31C2×D412yes—
177C24×C31C2×D414yes—
178C24×C31#4114yes—
179C24×C31C2411yescharacteristic
180C2×D4×C31—216no—
181C2×D4×C31—216no—
182C2×D4×C31—44no—
183C2×D4×C31—44no—
184C2×D4×C31—48no—
185C2×D4×C31—44no—
186C2×D4×C31—44no—
187C2×D4×C31—44no—
188C2×D4×C31—44no—
189C2×D4×C31—48no—
190C2×D4×C31—48no—
191C2×D4×C31—48no—
192C2×D4×C31—48no—
193C2×D4×C31C22⋊C4116yescomplemented
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—22no—
202C22×C4×C31—22no—
203C22×C4×C31—22no—
204C22×C4×C31—22no—
205C22×C4×C31—22no—
206C22×C4×C31—22no—
207C22×C4×C31—22no—
208C22×C4×C31—22no—
209C22×C4×C31—22no—
210C22×C4×C31—22no—
211C22×C4×C31—22no—
212C22×C4×C31—22no—
213C22×C4×C31—22no—
214C22×C4×C31—22no—
215C22×C4×C31—22no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—22no—
220C22×C4×C31—22no—
221C22×C4×C31—22no—
222C22×C4×C31—22no—
223C22×C4×C31—22no—
224C22×C4×C31—22no—
225C22×C4×C31—22no—
226C22×C4×C31—22no—
227C22×C4×C31—22no—
228C22×C4×C31—22no—
229C22×C4×C31—22no—
230C22×C4×C31—44no—
231C22×C4×C31—48no—
232C22×C4×C31—48no—
233C22×C4×C31—44no—
234C22×C4×C31—44no—
235C22×C4×C31C22×C414yes—
236C22×C4×C31C22×C412yes—
237C22×C4×C31C2×D414yes—
238C22×C4×C31C2×D414yes—
239C22×C4×C31C2×D412yes—
240C22×C4×C31C2×D412yes—
241C4⋊C4×C31—44no—
242C22⋊C4×C31—28no—
243C22⋊C4×C31—216no—
244C22⋊C4×C31—48no—
245C22⋊C4×C31—48no—
246C22⋊C4×C31—48no—
247C22⋊C4×C31—48no—
248C22⋊C4×C31—48no—
249C22⋊C4×C31—48no—
250C22⋊C4×C31—44no—
251C22⋊C4×C31—48no—
252C42×C31—44no—
253#14357C3111yesmaximal, characteristic, direct product factor, Sylow
254C23×C31—24no—
255C23×C31—24no—
256C23×C31—24no—
257C23×C31—24no—
258C23×C31—22no—
259C23×C31—22no—
260C23×C31—24no—
261C23×C31—22no—
262C23×C31—22no—
263C23×C31—24no—
264C23×C31—24no—
265C23×C31—24no—
266C23×C31—24no—
267C23×C31—24no—
268C23×C31—22no—
269C23×C31—24no—
270C23×C31—22no—
271C23×C31—22no—
272C23×C31—22no—
273C23×C31—22no—
274C23×C31—22no—
275C23×C31—22no—
276C23×C31—22no—
277C23×C31—24no—
278C23×C31—24no—
279C23×C31—24no—
280C23×C31—24no—
281C23×C31—24no—
282C23×C31—24no—
283C23×C31—24no—
284C23×C31—24no—
285C23×C31—24no—
286C23×C31—24no—
287C23×C31—24no—
288C23×C31—24no—
289C23×C31—24no—
290C23×C31—24no—
291C23×C31—24no—
292C23×C31—24no—
293C23×C31—24no—
294C23×C31—24no—
295C23×C31—24no—
296C23×C31—432no—
297C23×C31—416no—
298C23×C31—416no—
299C23×C31—432no—
300C23×C31—416no—
301C23×C31—432no—
302C23×C31—416no—
303C23×C31—432no—
304C23×C31—416no—
305C23×C31—416no—
306C23×C31—416no—
307C23×C31—42no—
308C23×C31—42no—
309C23×C31—42no—
310C23×C31—42no—
311C23×C31—42no—
312C23×C31—42no—
313C23×C31—42no—
314C23×C31—42no—
315C23×C31—42no—
316C23×C31—42no—
317C23×C31—42no—
318C23×C31—42no—
319C23×C31—42no—
320C23×C31—42no—
321C23×C31—42no—
322C23×C31—42no—
323C23×C31—41no—
324C23×C31—42no—
325C23×C31—42no—
326C23×C31—41no—
327C23×C31—42no—
328C23×C31—42no—
329C23×C31—42no—
330C23×C31—42no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—42no—
334C23×C31—41no—
335C23×C31—42no—
336C23×C31—42no—
337C23×C31—42no—
338C23×C31—41no—
339C23×C31—42no—
340C23×C31—41no—
341C23×C31—42no—
342C23×C31—41no—
343C23×C31C2×C22⋊C414yes—
344C23×C31C2×C22⋊C414yes—
345C23×C31C4×D418yes—
346C23×C31C23×C411yescharacteristic
347C23×C31C22×D411yescharacteristic
348C23×C31C22×D411yescharacteristic
349C23×C31C22×D412yes—
350C23×C31C2×#4112yes—
351C23×C31H(5,𝔽2)11yescharacteristic
352C23×C31H(5,𝔽2)11yescharacteristic
353C23×C31H(5,𝔽2)11yescharacteristic
354C23×C31H(5,𝔽2)11yescharacteristic
355C23×C31H(5,𝔽2)12yes—
356C23×C31H(5,𝔽2)12yes—
357D4×C31—416no—
358D4×C31—432no—
359C2×C4×C31—22no—
360C2×C4×C31—22no—
361C2×C4×C31—22no—
362C2×C4×C31—22no—
363C2×C4×C31—22no—
364C2×C4×C31—22no—
365C2×C4×C31—24no—
366C2×C4×C31—24no—
367C2×C4×C31—24no—
368C2×C4×C31—24no—
369C2×C4×C31—24no—
370C2×C4×C31—24no—
371C2×C4×C31—24no—
372C2×C4×C31—24no—
373C2×C4×C31—24no—
374C2×C4×C31—416no—
375C2×C4×C31—42no—
376C2×C4×C31—42no—
377C2×C4×C31—42no—
378C2×C4×C31—42no—
379C2×C4×C31—42no—
380C2×C4×C31—42no—
381C2×C4×C31—42no—
382C2×C4×C31—42no—
383C2×C4×C31—42no—
384C2×C4×C31—42no—
385C2×C4×C31—42no—
386C2×C4×C31—42no—
387C2×C4×C31—42no—
388C2×C4×C31—42no—
389C2×C4×C31—42no—
390C2×C4×C31—42no—
391C2×C4×C31—42no—
392C2×C4×C31—42no—
393C2×C4×C31—42no—
394C2×C4×C31—42no—
395C2×C4×C31—42no—
396C2×C4×C31—42no—
397C2×C4×C31—42no—
398C2×C4×C31—42no—
399C2×C4×C31—42no—
400C2×C4×C31—42no—
401C2×C4×C31C2×C22⋊C414yes—
402C22×#120C2×C3111yescharacteristic
403C2×#390C2×C3111yescharacteristic, complemented
404C2×#386C2×C3112yescomplemented
405C2×#386C2×C3111yescharacteristic, complemented
406C2×#379C2×C3112yescomplemented
407#1440C2×C3112yescomplemented
408#1439C2×C3112yescomplemented
409#1438C2×C3112yescomplemented
410#1437C2×C3112yescomplemented
411C22×C31—24no—
412C22×C31—24no—
413C22×C31—28no—
414C22×C31—28no—
415C22×C31—28no—
416C22×C31—28no—
417C22×C31—28no—
418C22×C31—464no—
419C22×C31—44no—
420C22×C31—44no—
421C22×C31—44no—
422C22×C31—44no—
423C22×C31—44no—
424C22×C31—42no—
425C22×C31—42no—
426C22×C31—42no—
427C22×C31—42no—
428C22×C31—44no—
429C22×C31—44no—
430C22×C31—44no—
431C22×C31—44no—
432C22×C31—44no—
433C22×C31—42no—
434C22×C31—42no—
435C22×C31—44no—
436C22×C31—44no—
437C22×C31—44no—
438C22×C31—44no—
439C22×C31—44no—
440C22×C31—42no—
441C22×C31—44no—
442C22×C31—42no—
443C22×C31—42no—
444C22×C31—42no—
445C22×C31—44no—
446C22×C31—42no—
447C22×C31—42no—
448C22×C31—44no—
449C22×C31C22×C22⋊C411yescharacteristic
450C22×C31C2×C4×D412yes—
451C22×C31#51811yescharacteristic
452C22×C31#51811yescharacteristic
453C22×C31#51812yes—
454C22×C31#53411yescharacteristic
455C22×C31#53411yescharacteristic
456C22×C31#53411yescharacteristic
457C22×C31#53411yescharacteristic
458C22×C31#53412yes—
459C22×C31#53512yes—
460C22×C31#53812yes—
461C22×C31#53812yes—
462C22×C31D4212yes—
463C22×C31D4212yes—
464C22×C31D4211yescharacteristic
465C22×C31#54612yes—
466C22×C31#54612yes—
467C22×C31#54612yes—
468C22×C31#55111yescharacteristic
469C22×C31#56012yes—
470C22×C31#56011yescharacteristic
471C22×C31H(3,𝔽4)11yescharacteristic
472C4×C31—24no—
473C4×C31—44no—
474C4×C31—44no—
475C4×C31—44no—
476C4×C31—82no—
477C4×C31—82no—
478C26C22×C3111yescharacteristic
479C23×D4C22×C3112yes—
480C23×D4C22×C3111yescharacteristic
481C24×C4C22×C3111yescharacteristic, complemented
482C2×#120—24no—
483C2×#120—24no—
484C2×#120C4×C3118yescomplemented
485C22×C4⋊C4C22×C3111yescharacteristic, complemented
486C22×C22⋊C4C22×C3112yes—
487C22×C22⋊C4C22×C3112yes—
488C22×C22⋊C4C22×C3112yes—
489C22×C22⋊C4C22×C3112yes—
490C22×C22⋊C4C22×C3112yes—
491C22×C22⋊C4C22×C3111yescharacteristic
492C22×C22⋊C4C22×C3112yes—
493C22×C22⋊C4C22×C3112yes—
494C22×C22⋊C4C22×C3112yescomplemented
495C22×C22⋊C4C22×C3111yescharacteristic, complemented
496C22×C42C22×C3111yescharacteristic, complemented
497#390—24no—
498#386—24no—
499#386—28no—
500#379—28no—
501C2×#95C22×C3112yescomplemented
502C2×#95C22×C3112yescomplemented
503C2×#95C22×C3112yescomplemented
504C2×#95C22×C3112yescomplemented
505C2×#95C22×C3112yescomplemented
506C2×C31—44no—
507C2×C31—44no—
508C2×C31—48no—
509C2×C31#230811yescharacteristic
510C2×C31#232112yes—
511C2×C31D4×C22⋊C412yes—
512C2×C31#235811yescharacteristic
513C2×C31#237511yescharacteristic
514C2×C31#266812yes—
515C2×C31#266911yescharacteristic
516C2×C31#267812yes—
517C2×C31#267911yescharacteristic
518C2×C31#268411yescharacteristic
519C2×C31#269711yescharacteristic
520C25—22no—
521C25—22no—
522C25—24no—
523C25—24no—
524C25—42no—
525C25—42no—
526C25—41no—
527C25—41no—
528C25—41no—
529C25—41no—
530C25C2×C4×C3114yescomplemented
531C25C23×C3111yescharacteristic
532C25C23×C3111yescharacteristic
533C25C23×C3112yes—
534C22×D4—24no—
535C22×D4—24no—
536C22×D4—24no—
537C22×D4—24no—
538C22×D4—41no—
539C22×D4—41no—
540C22×D4—41no—
541C22×D4—41no—
542C22×D4—42no—
543C22×D4—42no—
544C22×D4C2×C4×C3118yes—
545C22×D4C2×C4×C3114yes—
546C22×D4D4×C3114yes—
547C22×D4D4×C3114yes—
548C23×C4—22no—
549C23×C4—24no—
550C23×C4—41no—
551C23×C4—42no—
552C23×C4—41no—
553C23×C4C23×C3112yes—
554C23×C4C23×C3112yes—
555C23×C4C23×C3112yes—
556C23×C4C23×C3112yes—
557C23×C4C23×C3112yes—
558C23×C4C23×C3111yescharacteristic
559#120—232no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4—41no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4—42no—
587C2×C22⋊C4—42no—
588C2×C22⋊C4—41no—
589C2×C22⋊C4—41no—
590C2×C22⋊C4C2×C4×C3114yescomplemented
591C2×C22⋊C4C2×C4×C3118yescomplemented
592C2×C22⋊C4D4×C3118yescomplemented
593C2×C42—22no—
594C2×C42—41no—
595C2×C42—41no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—42no—
600#95—42no—
601C31#1435711yescharacteristic, direct product factor, Sylow
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—21no—
611C24—21no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—21no—
622C24—21no—
623C24—22no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—28no—
631C24—216no—
632C24—44no—
633C24—48no—
634C24—44no—
635C24—44no—
636C24—48no—
637C24—48no—
638C24—48no—
639C24—48no—
640C24—48no—
641C24—44no—
642C24—48no—
643C24—44no—
644C24—44no—
645C24—44no—
646C24—44no—
647C24—48no—
648C24—48no—
649C24—48no—
650C24—48no—
651C24—44no—
652C24—44no—
653C24C22×C4×C3112yes—
654C24C22×C4×C3112yes—
655C24C22×C4×C3114yes—
656C24C2×D4×C3112yes—
657C24C2×D4×C3112yes—
658C24C2×D4×C3112yes—
659C24C2×D4×C3112yes—
660C24C2×D4×C3114yes—
661C24#41×C3114yes—
662C24C24×C3111yescharacteristic
663C2×D4—216no—
664C2×D4—216no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—48no—
668C2×D4—44no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4C22⋊C4×C31116yescomplemented
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—44no—
714C22×C4—48no—
715C22×C4—48no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4C22×C4×C3114yes—
719C22×C4C22×C4×C3112yes—
720C22×C4C2×D4×C3114yes—
721C22×C4C2×D4×C3114yes—
722C22×C4C2×D4×C3112yes—
723C22×C4C2×D4×C3112yes—
724C4⋊C4—44no—
725C22⋊C4—28no—
726C22⋊C4—216no—
727C22⋊C4—48no—
728C22⋊C4—48no—
729C22⋊C4—48no—
730C22⋊C4—48no—
731C22⋊C4—48no—
732C22⋊C4—48no—
733C22⋊C4—44no—
734C22⋊C4—48no—
735C42—44no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—22no—
741C23—22no—
742C23—24no—
743C23—22no—
744C23—22no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—22no—
751C23—24no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—24no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—24no—
764C23—24no—
765C23—24no—
766C23—24no—
767C23—24no—
768C23—24no—
769C23—24no—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—432no—
779C23—416no—
780C23—416no—
781C23—432no—
782C23—416no—
783C23—432no—
784C23—416no—
785C23—432no—
786C23—416no—
787C23—416no—
788C23—416no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—41no—
806C23—42no—
807C23—42no—
808C23—41no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—41no—
814C23—41no—
815C23—42no—
816C23—41no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—41no—
821C23—42no—
822C23—41no—
823C23—42no—
824C23—41no—
825C23C2×C22⋊C4×C3114yes—
826C23C2×C22⋊C4×C3114yes—
827C23C4×D4×C3118yes—
828C23C23×C4×C3111yescharacteristic
829C23C22×D4×C3111yescharacteristic
830C23C22×D4×C3111yescharacteristic
831C23C22×D4×C3112yes—
832C23C2×#41×C3112yes—
833C23C31×H(5,𝔽2)11yescharacteristic
834C23C31×H(5,𝔽2)11yescharacteristic
835C23C31×H(5,𝔽2)11yescharacteristic
836C23C31×H(5,𝔽2)11yescharacteristic
837C23C31×H(5,𝔽2)12yes—
838C23C31×H(5,𝔽2)12yes—
839D4—416no—
840D4—432no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—416no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4C2×C22⋊C4×C3114yes—
884C22—24no—
885C22—24no—
886C22—28no—
887C22—28no—
888C22—28no—
889C22—28no—
890C22—28no—
891C22—464no—
892C22—44no—
893C22—44no—
894C22—44no—
895C22—44no—
896C22—44no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—44no—
901C22—42no—
902C22—44no—
903C22—44no—
904C22—44no—
905C22—44no—
906C22—42no—
907C22—44no—
908C22—42no—
909C22—44no—
910C22—44no—
911C22—44no—
912C22—44no—
913C22—42no—
914C22—44no—
915C22—42no—
916C22—42no—
917C22—44no—
918C22—42no—
919C22—42no—
920C22—44no—
921C22—42no—
922C22C22×C22⋊C4×C3111yescharacteristic
923C22C2×C4×D4×C3112yes—
924C22C31×#51811yescharacteristic
925C22C31×#51811yescharacteristic
926C22C31×#51812yes—
927C22C31×#53411yescharacteristic
928C22C31×#53411yescharacteristic
929C22C31×#53411yescharacteristic
930C22C31×#53411yescharacteristic
931C22C31×#53412yes—
932C22C31×#53512yes—
933C22C31×#53812yes—
934C22C31×#53812yes—
935C22D42×C3112yes—
936C22D42×C3112yes—
937C22D42×C3111yescharacteristic
938C22C31×#54612yes—
939C22C31×#54612yes—
940C22C31×#54612yes—
941C22C31×#55111yescharacteristic
942C22C31×#56012yes—
943C22C31×#56011yescharacteristic
944C22C31×H(3,𝔽4)11yescharacteristic
945C4—24no—
946C4—44no—
947C4—44no—
948C4—44no—
949C4—82no—
950C4—82no—
951C2—44no—
952C2—48no—
953C2—44no—
954C2C31×#230811yescharacteristic
955C2C31×#232112yes—
956C2D4×C22⋊C4×C3112yes—
957C2C31×#235811yescharacteristic
958C2C31×#237511yescharacteristic
959C2C31×#266812yes—
960C2C31×#266911yescharacteristic
961C2C31×#267812yes—
962C2C31×#267911yescharacteristic
963C2C31×#268411yescharacteristic
964C2C31×#269711yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC22×C31×#120C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#390C2semidirect
3. C2×C31×#386C2semidirect
4. C2×C31×#386C2semidirect
5. C2×C31×#379C2semidirect
6. C31×#1440C2semidirect
7. C31×#1439C2semidirect
8. C31×#1438C2semidirect
9. C31×#1437C2semidirect
13. C24×C4×C31C22semidirect
16. C2×C31×#120C4semidirect
17. C22×C4⋊C4×C31C22semidirect
26. C22×C22⋊C4×C31C22semidirect
27. C22×C22⋊C4×C31C22semidirect
28. C22×C42×C31C22semidirect
33. C2×C31×#95C22semidirect
34. C2×C31×#95C22semidirect
35. C2×C31×#95C22semidirect
36. C2×C31×#95C22semidirect
37. C2×C31×#95C22semidirect
48. C25×C31C2×C4semidirect
108. C2×C22⋊C4×C31C2×C4semidirect
109. C2×C22⋊C4×C31C2×C4semidirect
110. C2×C22⋊C4×C31D4semidirect
193. C2×D4×C31C22⋊C4semidirect
253. #14357C31direct (N × H)
403. C2×#390C2×C31semidirect
404. C2×#386C2×C31semidirect
405. C2×#386C2×C31semidirect
406. C2×#379C2×C31semidirect
407. #1440C2×C31semidirect
408. #1439C2×C31semidirect
409. #1438C2×C31semidirect
410. #1437C2×C31semidirect
481. C24×C4C22×C31semidirect
484. C2×#120C4×C31semidirect
485. C22×C4⋊C4C22×C31semidirect
494. C22×C22⋊C4C22×C31semidirect
495. C22×C22⋊C4C22×C31semidirect
496. C22×C42C22×C31semidirect
501. C2×#95C22×C31semidirect
502. C2×#95C22×C31semidirect
503. C2×#95C22×C31semidirect
504. C2×#95C22×C31semidirect
505. C2×#95C22×C31semidirect
530. C25C2×C4×C31semidirect
590. C2×C22⋊C4C2×C4×C31semidirect
591. C2×C22⋊C4C2×C4×C31semidirect
592. C2×C22⋊C4D4×C31semidirect
601. C31#14357direct (N × H)
676. C2×D4C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1202
C2×C31×#3902
C2×C31×#3862
C2×C31×#3792
C31×#14402
C31×#14392
C31×#14382
C31×#14372
#1435731