Finite Group Databasebeta

← C31×#14358 #21471117

Subgroups — C31×#14358 #21471117

Order 7936.

3538 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#120C211yesmaximal, characteristic
2C2×C31×#390C212yesmaximal, complemented
3C2×C31×#388C212yesmaximal, complemented
4C2×C31×#379C212yesmaximal, complemented
5C31×#1439C212yesmaximal, complemented
6C31×#1438C212yesmaximal, complemented
7C31×#1438C211yesmaximal, characteristic, complemented
8C31×#1438C211yesmaximal, characteristic, complemented
9C31×#1437C212yesmaximal, complemented
10C26×C31C2211yescharacteristic
11C23×D4×C31C2212yes—
12C23×D4×C31C2211yescharacteristic
13C2×C31×#120—28no—
14C2×C31×#120C418yescomplemented
15C22×C4⋊C4×C31C2212yescomplemented
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2212yes—
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×C31C2211yescharacteristic, complemented
25C22×C22⋊C4×C31C2212yescomplemented
26C22×C22⋊C4×C31C2211yescharacteristic, complemented
27C22×C42×C31C2212yescomplemented
28C31×#390—28no—
29C31×#388—28no—
30C31×#379—28no—
31C2×C31×#95C2212yescomplemented
32C2×C31×#95C2212yescomplemented
33C2×C31×#95C2211yescharacteristic, complemented
34C2×C31×#95C2212yescomplemented
35C2×C31×#95C2211yescharacteristic, complemented
36C25×C31—24no—
37C25×C31—24no—
38C25×C31—24no—
39C25×C31—42no—
40C25×C31—42no—
41C25×C31—41no—
42C25×C31—41no—
43C25×C31—42no—
44C25×C31C2×C414yes—
45C25×C31C2311yescharacteristic
46C25×C31C2311yescharacteristic
47C25×C31C2312yes—
48C22×D4×C31—24no—
49C22×D4×C31—24no—
50C22×D4×C31—24no—
51C22×D4×C31—24no—
52C22×D4×C31—24no—
53C22×D4×C31—42no—
54C22×D4×C31—42no—
55C22×D4×C31—42no—
56C22×D4×C31—41no—
57C22×D4×C31—41no—
58C22×D4×C31C2×C418yes—
59C22×D4×C31C2×C414yes—
60C23×C4×C31C2312yes—
61C23×C4×C31C2312yes—
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2312yes—
64C23×C4×C31C2312yes—
65C23×C4×C31C2312yes—
66C31×#120—232no—
67C2×C4⋊C4×C31—24no—
68C2×C4⋊C4×C31—24no—
69C2×C4⋊C4×C31—42no—
70C2×C22⋊C4×C31—24no—
71C2×C22⋊C4×C31—24no—
72C2×C22⋊C4×C31—24no—
73C2×C22⋊C4×C31—24no—
74C2×C22⋊C4×C31—24no—
75C2×C22⋊C4×C31—24no—
76C2×C22⋊C4×C31—24no—
77C2×C22⋊C4×C31—24no—
78C2×C22⋊C4×C31—24no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—24no—
81C2×C22⋊C4×C31—24no—
82C2×C22⋊C4×C31—24no—
83C2×C22⋊C4×C31—42no—
84C2×C22⋊C4×C31—42no—
85C2×C22⋊C4×C31—42no—
86C2×C22⋊C4×C31—42no—
87C2×C22⋊C4×C31—42no—
88C2×C22⋊C4×C31—42no—
89C2×C22⋊C4×C31—42no—
90C2×C22⋊C4×C31—42no—
91C2×C22⋊C4×C31—41no—
92C2×C22⋊C4×C31—42no—
93C2×C22⋊C4×C31—42no—
94C2×C22⋊C4×C31—42no—
95C2×C22⋊C4×C31—41no—
96C2×C22⋊C4×C31C2×C418yes—
97C2×C22⋊C4×C31C2×C414yes—
98C2×C22⋊C4×C31D418yes—
99C2×C22⋊C4×C31D418yescomplemented
100C2×C42×C31—24no—
101C2×C42×C31—24no—
102C2×C42×C31—42no—
103C31×#95—24no—
104C31×#95—24no—
105C31×#95—41no—
106C31×#95—42no—
107C31×#95—41no—
108C24×C31—22no—
109C24×C31—22no—
110C24×C31—22no—
111C24×C31—22no—
112C24×C31—22no—
113C24×C31—22no—
114C24×C31—22no—
115C24×C31—22no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31—22no—
122C24×C31—22no—
123C24×C31—21no—
124C24×C31—21no—
125C24×C31—22no—
126C24×C31—22no—
127C24×C31—28no—
128C24×C31—216no—
129C24×C31—22no—
130C24×C31—22no—
131C24×C31—22no—
132C24×C31—22no—
133C24×C31—22no—
134C24×C31—21no—
135C24×C31—21no—
136C24×C31—22no—
137C24×C31—44no—
138C24×C31—48no—
139C24×C31—44no—
140C24×C31—44no—
141C24×C31—48no—
142C24×C31—48no—
143C24×C31—48no—
144C24×C31—48no—
145C24×C31—48no—
146C24×C31—44no—
147C24×C31—48no—
148C24×C31—48no—
149C24×C31—48no—
150C24×C31—48no—
151C24×C31—48no—
152C24×C31—48no—
153C24×C31—48no—
154C24×C31—44no—
155C24×C31—44no—
156C24×C31C22×C412yes—
157C24×C31C22×C412yes—
158C24×C31C22×C414yes—
159C24×C31C2×D414yes—
160C24×C31C2×D414yes—
161C24×C31#4114yes—
162C24×C31C2411yescharacteristic
163C2×D4×C31—28no—
164C2×D4×C31—216no—
165C2×D4×C31—216no—
166C2×D4×C31—48no—
167C2×D4×C31—44no—
168C2×D4×C31—44no—
169C2×D4×C31—48no—
170C2×D4×C31—48no—
171C2×D4×C31—48no—
172C2×D4×C31—48no—
173C2×D4×C31—48no—
174C2×D4×C31—48no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—22no—
181C22×C4×C31—22no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
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×C31C22×C412yes—
210C22×C4×C31C22×C414yes—
211C22×C4×C31C2×D414yes—
212C22×C4×C31C2×D414yes—
213C22×C4×C31C2×D414yes—
214C22×C4×C31C2×D414yes—
215C4⋊C4×C31—48no—
216C22⋊C4×C31—216no—
217C22⋊C4×C31—48no—
218C22⋊C4×C31—44no—
219C22⋊C4×C31—48no—
220C22⋊C4×C31—48no—
221C22⋊C4×C31—48no—
222C22⋊C4×C31—48no—
223C22⋊C4×C31—48no—
224C22⋊C4×C31—48no—
225C22⋊C4×C31—44no—
226C22⋊C4×C31C22⋊C4116yescomplemented
227C42×C31—48no—
228#14358C3111yesmaximal, characteristic, direct product factor, Sylow
229C23×C31—24no—
230C23×C31—24no—
231C23×C31—24no—
232C23×C31—22no—
233C23×C31—22no—
234C23×C31—24no—
235C23×C31—24no—
236C23×C31—24no—
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—24no—
247C23×C31—24no—
248C23×C31—24no—
249C23×C31—24no—
250C23×C31—24no—
251C23×C31—24no—
252C23×C31—24no—
253C23×C31—24no—
254C23×C31—24no—
255C23×C31—24no—
256C23×C31—24no—
257C23×C31—22no—
258C23×C31—24no—
259C23×C31—22no—
260C23×C31—22no—
261C23×C31—24no—
262C23×C31—432no—
263C23×C31—416no—
264C23×C31—416no—
265C23×C31—432no—
266C23×C31—416no—
267C23×C31—432no—
268C23×C31—432no—
269C23×C31—432no—
270C23×C31—432no—
271C23×C31—42no—
272C23×C31—42no—
273C23×C31—42no—
274C23×C31—42no—
275C23×C31—42no—
276C23×C31—42no—
277C23×C31—42no—
278C23×C31—42no—
279C23×C31—42no—
280C23×C31—42no—
281C23×C31—42no—
282C23×C31—42no—
283C23×C31—42no—
284C23×C31—42no—
285C23×C31—41no—
286C23×C31—42no—
287C23×C31—42no—
288C23×C31—42no—
289C23×C31—41no—
290C23×C31—42no—
291C23×C31—42no—
292C23×C31—42no—
293C23×C31—42no—
294C23×C31—41no—
295C23×C31—42no—
296C23×C31—41no—
297C23×C31—42no—
298C23×C31—42no—
299C23×C31—42no—
300C23×C31—42no—
301C23×C31—42no—
302C23×C31—42no—
303C23×C31—41no—
304C23×C31—42no—
305C23×C31—42no—
306C23×C31—42no—
307C23×C31—42no—
308C23×C31—42no—
309C23×C31—41no—
310C23×C31—42no—
311C23×C31—41no—
312C23×C31—41no—
313C23×C31C2×C22⋊C414yes—
314C23×C31C4×D418yes—
315C23×C31C23×C411yescharacteristic
316C23×C31C22×D412yes—
317C23×C31C22×D412yes—
318C23×C31C2×#4112yes—
319C23×C31H(5,𝔽2)12yes—
320C23×C31H(5,𝔽2)12yes—
321C23×C31H(5,𝔽2)11yescharacteristic
322C23×C31H(5,𝔽2)11yescharacteristic
323C23×C31H(5,𝔽2)12yes—
324D4×C31—432no—
325D4×C31—416no—
326C2×C4×C31—24no—
327C2×C4×C31—24no—
328C2×C4×C31—24no—
329C2×C4×C31—24no—
330C2×C4×C31—24no—
331C2×C4×C31—24no—
332C2×C4×C31—22no—
333C2×C4×C31—22no—
334C2×C4×C31—22no—
335C2×C4×C31—24no—
336C2×C4×C31—24no—
337C2×C4×C31—24no—
338C2×C4×C31—24no—
339C2×C4×C31—24no—
340C2×C4×C31—24no—
341C2×C4×C31—42no—
342C2×C4×C31—42no—
343C2×C4×C31—42no—
344C2×C4×C31—42no—
345C2×C4×C31—42no—
346C2×C4×C31—42no—
347C2×C4×C31—42no—
348C2×C4×C31—42no—
349C2×C4×C31—42no—
350C2×C4×C31—42no—
351C2×C4×C31—42no—
352C2×C4×C31—42no—
353C2×C4×C31—42no—
354C2×C4×C31—42no—
355C2×C4×C31—42no—
356C2×C4×C31—42no—
357C2×C4×C31—42no—
358C2×C4×C31—42no—
359C2×C4×C31—42no—
360C2×C4×C31—42no—
361C2×C4×C31—42no—
362C2×C4×C31—42no—
363C2×C4×C31—42no—
364C2×C4×C31—42no—
365C2×C4×C31C2×C22⋊C418yes—
366C22×#120C2×C3111yescharacteristic
367C2×#390C2×C3112yescomplemented
368C2×#388C2×C3112yescomplemented
369C2×#379C2×C3112yescomplemented
370#1439C2×C3112yescomplemented
371#1438C2×C3112yescomplemented
372#1438C2×C3111yescharacteristic, complemented
373#1438C2×C3111yescharacteristic, complemented
374#1437C2×C3112yescomplemented
375C22×C31—24no—
376C22×C31—28no—
377C22×C31—28no—
378C22×C31—28no—
379C22×C31—28no—
380C22×C31—464no—
381C22×C31—44no—
382C22×C31—44no—
383C22×C31—44no—
384C22×C31—44no—
385C22×C31—42no—
386C22×C31—42no—
387C22×C31—44no—
388C22×C31—44no—
389C22×C31—44no—
390C22×C31—44no—
391C22×C31—44no—
392C22×C31—44no—
393C22×C31—44no—
394C22×C31—44no—
395C22×C31—44no—
396C22×C31—44no—
397C22×C31—44no—
398C22×C31—44no—
399C22×C31—44no—
400C22×C31—42no—
401C22×C31—44no—
402C22×C31—44no—
403C22×C31—42no—
404C22×C31—42no—
405C22×C31—82no—
406C22×C31—82no—
407C22×C31—82no—
408C22×C31—82no—
409C22×C31C22×C22⋊C411yescharacteristic
410C22×C31C2×C4×D412yes—
411C22×C31#51811yescharacteristic
412C22×C31#51811yescharacteristic
413C22×C31#51812yes—
414C22×C31#53412yes—
415C22×C31#53512yes—
416C22×C31#53512yes—
417C22×C31#53512yes—
418C22×C31#53812yes—
419C22×C31#53812yes—
420C22×C31D4212yes—
421C22×C31D4212yes—
422C22×C31D4211yescharacteristic
423C22×C31#54612yes—
424C22×C31#54612yes—
425C22×C31#54612yes—
426C22×C31#55111yescharacteristic
427C22×C31#56012yes—
428C22×C31#56011yescharacteristic
429C22×C31H(3,𝔽4)11yescharacteristic
430C4×C31—28no—
431C4×C31—42no—
432C4×C31—44no—
433C4×C31—44no—
434C4×C31—82no—
435C4×C31—82no—
436C26C22×C3111yescharacteristic
437C23×D4C22×C3112yes—
438C23×D4C22×C3111yescharacteristic
439C2×#120—28no—
440C2×#120C4×C3118yescomplemented
441C22×C4⋊C4C22×C3112yescomplemented
442C22×C22⋊C4C22×C3112yes—
443C22×C22⋊C4C22×C3112yes—
444C22×C22⋊C4C22×C3112yes—
445C22×C22⋊C4C22×C3112yes—
446C22×C22⋊C4C22×C3112yes—
447C22×C22⋊C4C22×C3112yes—
448C22×C22⋊C4C22×C3112yes—
449C22×C22⋊C4C22×C3111yescharacteristic
450C22×C22⋊C4C22×C3111yescharacteristic, complemented
451C22×C22⋊C4C22×C3112yescomplemented
452C22×C22⋊C4C22×C3111yescharacteristic, complemented
453C22×C42C22×C3112yescomplemented
454#390—28no—
455#388—28no—
456#379—28no—
457C2×#95C22×C3112yescomplemented
458C2×#95C22×C3112yescomplemented
459C2×#95C22×C3111yescharacteristic, complemented
460C2×#95C22×C3112yescomplemented
461C2×#95C22×C3111yescharacteristic, complemented
462C2×C31—44no—
463C2×C31—48no—
464C2×C31—82no—
465C2×C31#230911yescharacteristic
466C2×C31#232112yes—
467C2×C31D4×C22⋊C412yes—
468C2×C31#235811yescharacteristic
469C2×C31#237511yescharacteristic
470C2×C31#266912yes—
471C2×C31#267012yes—
472C2×C31#267812yes—
473C2×C31#268512yes—
474C25—24no—
475C25—24no—
476C25—24no—
477C25—42no—
478C25—42no—
479C25—41no—
480C25—41no—
481C25—42no—
482C25C2×C4×C3114yes—
483C25C23×C3111yescharacteristic
484C25C23×C3111yescharacteristic
485C25C23×C3112yes—
486C22×D4—24no—
487C22×D4—24no—
488C22×D4—24no—
489C22×D4—24no—
490C22×D4—24no—
491C22×D4—42no—
492C22×D4—42no—
493C22×D4—42no—
494C22×D4—41no—
495C22×D4—41no—
496C22×D4C2×C4×C3118yes—
497C22×D4C2×C4×C3114yes—
498C23×C4C23×C3112yes—
499C23×C4C23×C3112yes—
500C23×C4C23×C3111yescharacteristic
501C23×C4C23×C3112yes—
502C23×C4C23×C3112yes—
503C23×C4C23×C3112yes—
504#120—232no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—42no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—41no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—41no—
534C2×C22⋊C4C2×C4×C3118yes—
535C2×C22⋊C4C2×C4×C3114yes—
536C2×C22⋊C4D4×C3118yes—
537C2×C22⋊C4D4×C3118yescomplemented
538C2×C42—24no—
539C2×C42—24no—
540C2×C42—42no—
541#95—24no—
542#95—24no—
543#95—41no—
544#95—42no—
545#95—41no—
546C31#1435811yescharacteristic, direct product factor, Sylow
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—21no—
563C24—21no—
564C24—22no—
565C24—22no—
566C24—28no—
567C24—216no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—21no—
574C24—21no—
575C24—22no—
576C24—44no—
577C24—48no—
578C24—44no—
579C24—44no—
580C24—48no—
581C24—48no—
582C24—48no—
583C24—48no—
584C24—48no—
585C24—44no—
586C24—48no—
587C24—48no—
588C24—48no—
589C24—48no—
590C24—48no—
591C24—48no—
592C24—48no—
593C24—44no—
594C24—44no—
595C24C22×C4×C3112yes—
596C24C22×C4×C3112yes—
597C24C22×C4×C3114yes—
598C24C2×D4×C3114yes—
599C24C2×D4×C3114yes—
600C24#41×C3114yes—
601C24C24×C3111yescharacteristic
602C2×D4—28no—
603C2×D4—216no—
604C2×D4—216no—
605C2×D4—48no—
606C2×D4—44no—
607C2×D4—44no—
608C2×D4—48no—
609C2×D4—48no—
610C2×D4—48no—
611C2×D4—48no—
612C2×D4—48no—
613C2×D4—48no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4C22×C4×C3112yes—
649C22×C4C22×C4×C3114yes—
650C22×C4C2×D4×C3114yes—
651C22×C4C2×D4×C3114yes—
652C22×C4C2×D4×C3114yes—
653C22×C4C2×D4×C3114yes—
654C4⋊C4—48no—
655C22⋊C4—216no—
656C22⋊C4—48no—
657C22⋊C4—44no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—44no—
665C22⋊C4C22⋊C4×C31116yescomplemented
666C42—48no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—22no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—22no—
696C23—24no—
697C23—22no—
698C23—22no—
699C23—24no—
700C23—432no—
701C23—416no—
702C23—416no—
703C23—432no—
704C23—416no—
705C23—432no—
706C23—432no—
707C23—432no—
708C23—432no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—41no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—41no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—41no—
748C23—42no—
749C23—41no—
750C23—41no—
751C23C2×C22⋊C4×C3114yes—
752C23C4×D4×C3118yes—
753C23C23×C4×C3111yescharacteristic
754C23C22×D4×C3112yes—
755C23C22×D4×C3112yes—
756C23C2×#41×C3112yes—
757C23C31×H(5,𝔽2)12yes—
758C23C31×H(5,𝔽2)12yes—
759C23C31×H(5,𝔽2)11yescharacteristic
760C23C31×H(5,𝔽2)11yescharacteristic
761C23C31×H(5,𝔽2)12yes—
762D4—432no—
763D4—416no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4C2×C22⋊C4×C3118yes—
804C22—24no—
805C22—28no—
806C22—28no—
807C22—28no—
808C22—28no—
809C22—464no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—42no—
815C22—42no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—42no—
830C22—44no—
831C22—44no—
832C22—42no—
833C22—42no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22C22×C22⋊C4×C3111yescharacteristic
839C22C2×C4×D4×C3112yes—
840C22C31×#51811yescharacteristic
841C22C31×#51811yescharacteristic
842C22C31×#51812yes—
843C22C31×#53412yes—
844C22C31×#53512yes—
845C22C31×#53512yes—
846C22C31×#53512yes—
847C22C31×#53812yes—
848C22C31×#53812yes—
849C22D42×C3112yes—
850C22D42×C3112yes—
851C22D42×C3111yescharacteristic
852C22C31×#54612yes—
853C22C31×#54612yes—
854C22C31×#54612yes—
855C22C31×#55111yescharacteristic
856C22C31×#56012yes—
857C22C31×#56011yescharacteristic
858C22C31×H(3,𝔽4)11yescharacteristic
859C4—28no—
860C4—42no—
861C4—44no—
862C4—44no—
863C4—82no—
864C4—82no—
865C2—44no—
866C2—48no—
867C2—82no—
868C2C31×#230911yescharacteristic
869C2C31×#232112yes—
870C2D4×C22⋊C4×C3112yes—
871C2C31×#235811yescharacteristic
872C2C31×#237511yescharacteristic
873C2C31×#266912yes—
874C2C31×#267012yes—
875C2C31×#267812yes—
876C2C31×#268512yes—
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×#388C2semidirect
4. C2×C31×#379C2semidirect
5. C31×#1439C2semidirect
6. C31×#1438C2semidirect
7. C31×#1438C2semidirect
8. C31×#1438C2semidirect
9. C31×#1437C2semidirect
14. C2×C31×#120C4semidirect
15. C22×C4⋊C4×C31C22semidirect
24. C22×C22⋊C4×C31C22semidirect
25. C22×C22⋊C4×C31C22semidirect
26. C22×C22⋊C4×C31C22semidirect
27. C22×C42×C31C22semidirect
31. C2×C31×#95C22semidirect
32. C2×C31×#95C22semidirect
33. C2×C31×#95C22semidirect
34. C2×C31×#95C22semidirect
35. C2×C31×#95C22semidirect
99. C2×C22⋊C4×C31D4semidirect
226. C22⋊C4×C31C22⋊C4semidirect
228. #14358C31direct (N × H)
367. C2×#390C2×C31semidirect
368. C2×#388C2×C31semidirect
369. C2×#379C2×C31semidirect
370. #1439C2×C31semidirect
371. #1438C2×C31semidirect
372. #1438C2×C31semidirect
373. #1438C2×C31semidirect
374. #1437C2×C31semidirect
440. C2×#120C4×C31semidirect
441. C22×C4⋊C4C22×C31semidirect
450. C22×C22⋊C4C22×C31semidirect
451. C22×C22⋊C4C22×C31semidirect
452. C22×C22⋊C4C22×C31semidirect
453. C22×C42C22×C31semidirect
457. C2×#95C22×C31semidirect
458. C2×#95C22×C31semidirect
459. C2×#95C22×C31semidirect
460. C2×#95C22×C31semidirect
461. C2×#95C22×C31semidirect
537. C2×C22⋊C4D4×C31semidirect
546. C31#14358direct (N × H)
665. C22⋊C4C22⋊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×#3882
C2×C31×#3792
C31×#14392
C31×#14382
C31×#14372
#1435831