Finite Group Databasebeta

← C31×#13971 #21470730

Subgroups — C31×#13971 #21470730

Order 7936.

3526 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C31C211yesmaximal, characteristic
2C2×C31×#388C212yesmaximal, complemented
3C2×C31×#385C211yesmaximal, characteristic, complemented
4C2×C31×#379C211yesmaximal, characteristic
5C2×C31×#379C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#1440C212yesmaximal, complemented
8C31×#1439C212yesmaximal, complemented
9C31×#1437C212yesmaximal, complemented
10C31×C22⋊#95C211yesmaximal, characteristic, complemented
11C31×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C31C2211yescharacteristic
13C24×C4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic, complemented
16C22×C4⋊C4×C31C2211yescharacteristic, complemented
17C22×C22⋊C4×C31—24no—
18C22×C22⋊C4×C31—28no—
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2212yes—
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2212yes—
29C22×C42×C31C2212yescomplemented
30C31×#388—28no—
31C31×#385—24no—
32C31×#379—24no—
33C31×#379C418yescomplemented
34C4×C22⋊C4×C31—24no—
35C2×C31×#95C2212yescomplemented
36C2×C31×#95C2212yescomplemented
37C2×C31×#95C2211yescharacteristic, complemented
38C2×C31×#95C2212yescomplemented
39C2×C31×#95C2211yescharacteristic, complemented
40C2×C31×#95C2212yescomplemented
41C2×C31×#95C2212yescomplemented
42C25×C31—24no—
43C25×C31—22no—
44C25×C31—24no—
45C25×C31—22no—
46C25×C31—22no—
47C25×C31—22no—
48C25×C31—22no—
49C25×C31—22no—
50C25×C31—42no—
51C25×C31—42no—
52C25×C31C2×C414yes—
53C25×C31C2312yes—
54C25×C31C2311yescharacteristic
55C23×C4×C31—22no—
56C23×C4×C31—22no—
57C23×C4×C31—22no—
58C23×C4×C31—24no—
59C23×C4×C31—24no—
60C23×C4×C31—22no—
61C23×C4×C31—22no—
62C23×C4×C31—42no—
63C23×C4×C31—42no—
64C23×C4×C31D414yes—
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2312yes—
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2312yes—
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2312yes—
73C23×C4×C31C2311yescharacteristic
74C2×C4⋊C4×C31—22no—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31—24no—
77C2×C4⋊C4×C31—42no—
78C2×C22⋊C4×C31—232no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—24no—
83C2×C22⋊C4×C31—22no—
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—24no—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—24no—
91C2×C22⋊C4×C31—24no—
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—22no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—24no—
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—24no—
99C2×C22⋊C4×C31—42no—
100C2×C22⋊C4×C31—42no—
101C2×C22⋊C4×C31—42no—
102C2×C22⋊C4×C31—42no—
103C2×C22⋊C4×C31C2×C414yes—
104C2×C22⋊C4×C31C2×C414yes—
105C2×C22⋊C4×C31C2×C418yescomplemented
106C2×C22⋊C4×C31C2×C418yescomplemented
107C2×C22⋊C4×C31D418yes—
108C2×C22⋊C4×C31D414yes—
109C2×C42×C31—24no—
110C2×C42×C31—24no—
111C2×C42×C31—42no—
112C31×#95—24no—
113C31×#95—22no—
114C31×#95—22no—
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—28no—
124C24×C31—28no—
125C24×C31—216no—
126C24×C31—216no—
127C24×C31—28no—
128C24×C31—22no—
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—22no—
139C24×C31—22no—
140C24×C31—28no—
141C24×C31—28no—
142C24×C31—48no—
143C24×C31—48no—
144C24×C31—48no—
145C24×C31—48no—
146C24×C31—48no—
147C24×C31—48no—
148C24×C31—48no—
149C24×C31—48no—
150C24×C31—48no—
151C24×C31—44no—
152C24×C31—44no—
153C24×C31—48no—
154C24×C31—44no—
155C24×C31—44no—
156C24×C31—44no—
157C24×C31—44no—
158C24×C31C22×C414yes—
159C24×C31C22×C412yes—
160C24×C31C2×D414yes—
161C24×C31C2×D412yes—
162C24×C31C2×D412yes—
163C24×C31#4114yes—
164C24×C31#4112yes—
165C24×C31#4112yes—
166C24×C31#4112yes—
167C24×C31#4112yes—
168C24×C31C2411yescharacteristic
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—22no—
172C22×C4×C31—28no—
173C22×C4×C31—28no—
174C22×C4×C31—21no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
178C22×C4×C31—21no—
179C22×C4×C31—22no—
180C22×C4×C31—21no—
181C22×C4×C31—22no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—21no—
185C22×C4×C31—22no—
186C22×C4×C31—21no—
187C22×C4×C31—22no—
188C22×C4×C31—22no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—21no—
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—28no—
205C22×C4×C31—21no—
206C22×C4×C31—22no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—22no—
213C22×C4×C31—22no—
214C22×C4×C31—22no—
215C22×C4×C31—44no—
216C22×C4×C31—48no—
217C22×C4×C31—48no—
218C22×C4×C31—48no—
219C22×C4×C31—48no—
220C22×C4×C31—44no—
221C22×C4×C31—44no—
222C22×C4×C31C22×C412yes—
223C22×C4×C31C22×C414yes—
224C22×C4×C31C22×C412yes—
225C22×C4×C31C2×D414yes—
226C22×C4×C31C2×D414yes—
227C22×C4×C31C2×D412yes—
228C22×C4×C31C2×D412yes—
229C22×C4×C31C2×D414yes—
230C4⋊C4×C31—44no—
231C4⋊C4×C31—44no—
232C22⋊C4×C31—216no—
233C22⋊C4×C31—28no—
234C22⋊C4×C31—28no—
235C22⋊C4×C31—216no—
236C22⋊C4×C31—28no—
237C22⋊C4×C31—216no—
238C22⋊C4×C31—48no—
239C22⋊C4×C31—48no—
240C22⋊C4×C31—48no—
241C22⋊C4×C31—44no—
242C42×C31—48no—
243#13971C3111yesmaximal, characteristic, direct product factor, Sylow
244C23×C31—24no—
245C23×C31—24no—
246C23×C31—22no—
247C23×C31—22no—
248C23×C31—24no—
249C23×C31—22no—
250C23×C31—22no—
251C23×C31—24no—
252C23×C31—24no—
253C23×C31—24no—
254C23×C31—24no—
255C23×C31—24no—
256C23×C31—24no—
257C23×C31—24no—
258C23×C31—24no—
259C23×C31—24no—
260C23×C31—232no—
261C23×C31—24no—
262C23×C31—24no—
263C23×C31—24no—
264C23×C31—24no—
265C23×C31—24no—
266C23×C31—24no—
267C23×C31—24no—
268C23×C31—24no—
269C23×C31—24no—
270C23×C31—24no—
271C23×C31—24no—
272C23×C31—24no—
273C23×C31—24no—
274C23×C31—24no—
275C23×C31—24no—
276C23×C31—24no—
277C23×C31—24no—
278C23×C31—24no—
279C23×C31—432no—
280C23×C31—432no—
281C23×C31—416no—
282C23×C31—416no—
283C23×C31—416no—
284C23×C31—416no—
285C23×C31—432no—
286C23×C31—416no—
287C23×C31—432no—
288C23×C31—42no—
289C23×C31—42no—
290C23×C31—42no—
291C23×C31—42no—
292C23×C31—42no—
293C23×C31—42no—
294C23×C31—42no—
295C23×C31—42no—
296C23×C31—42no—
297C23×C31—42no—
298C23×C31—42no—
299C23×C31—42no—
300C23×C31—42no—
301C23×C31—42no—
302C23×C31—42no—
303C23×C31—42no—
304C23×C31—416no—
305C23×C31#11714yes—
306C23×C31C4×D418yes—
307C23×C31C4×D414yes—
308C23×C31C4×D414yes—
309C23×C31#12114yes—
310C23×C31#12314yes—
311C23×C31#12414yes—
312C23×C31#12614yes—
313C23×C31C23×C411yescharacteristic
314C23×C31C22×D411yescharacteristic
315C23×C31C22×D412yes—
316C23×C31C22×D411yescharacteristic
317C23×C31C2×#4111yescharacteristic
318C23×C31C2×#4111yescharacteristic
319C23×C31C2×#4111yescharacteristic
320C23×C31C2×#4112yes—
321C23×C31C2×#4111yescharacteristic
322C23×C31H(5,𝔽2)12yes—
323C23×C31H(5,𝔽2)12yes—
324C2×C4×C31—22no—
325C2×C4×C31—22no—
326C2×C4×C31—24no—
327C2×C4×C31—24no—
328C2×C4×C31—22no—
329C2×C4×C31—24no—
330C2×C4×C31—24no—
331C2×C4×C31—22no—
332C2×C4×C31—24no—
333C2×C4×C31—24no—
334C2×C4×C31—24no—
335C2×C4×C31—22no—
336C2×C4×C31—24no—
337C2×C4×C31—22no—
338C2×C4×C31—24no—
339C2×C4×C31—22no—
340C2×C4×C31—24no—
341C2×C4×C31—24no—
342C2×C4×C31—24no—
343C2×C4×C31—24no—
344C2×C4×C31—416no—
345C2×C4×C31—416no—
346C2×C4×C31—41no—
347C2×C4×C31—42no—
348C2×C4×C31—41no—
349C2×C4×C31—42no—
350C2×C4×C31—42no—
351C2×C4×C31—41no—
352C2×C4×C31—41no—
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×C31—42no—
366C2×C4×C31—41no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—41no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—42no—
373C2×C4×C31—42no—
374C2×C4×C31—42no—
375C2×C4×C31—42no—
376C2×C4×C31#12014yes—
377C23×C22⋊C4C2×C3111yescharacteristic
378C2×#388C2×C3112yescomplemented
379C2×#385C2×C3111yescharacteristic, complemented
380C2×#379C2×C3111yescharacteristic
381C2×#379C2×C3111yescharacteristic
382C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
383#1440C2×C3112yescomplemented
384#1439C2×C3112yescomplemented
385#1437C2×C3112yescomplemented
386C22⋊#95C2×C3111yescharacteristic, complemented
387C22⋊#95C2×C3111yescharacteristic, complemented
388C22×C31—24no—
389C22×C31—24no—
390C22×C31—28no—
391C22×C31—28no—
392C22×C31—24no—
393C22×C31—24no—
394C22×C31—28no—
395C22×C31—24no—
396C22×C31—28no—
397C22×C31—24no—
398C22×C31—28no—
399C22×C31—28no—
400C22×C31—28no—
401C22×C31—464no—
402C22×C31—44no—
403C22×C31—44no—
404C22×C31—44no—
405C22×C31—44no—
406C22×C31—44no—
407C22×C31—44no—
408C22×C31—44no—
409C22×C31—44no—
410C22×C31—44no—
411C22×C31—44no—
412C22×C31—44no—
413C22×C31—44no—
414C22×C31#38818yescomplemented
415C22×C31C2×#11711yescharacteristic
416C22×C31C2×C4×D411yescharacteristic
417C22×C31C2×C4×D412yes—
418C22×C31C2×C4×D411yescharacteristic
419C22×C31#51812yes—
420C22×C31C2×#12011yescharacteristic
421C22×C31C2×#12111yescharacteristic
422C22×C31C2×#12311yescharacteristic
423C22×C31#52511yescharacteristic
424C22×C31#52512yes—
425C22×C31C2×#12411yescharacteristic
426C22×C31C2×#12611yescharacteristic
427C22×C31#53411yescharacteristic
428C22×C31#53511yescharacteristic
429C22×C31#53812yes—
430C22×C31D4212yes—
431C22×C31#54612yes—
432C22×C31#54612yes—
433C22×C31#54612yes—
434C22×C31#54612yes—
435C22×C31#55112yes—
436C22×C31#55112yes—
437C22×C31#55112yes—
438C4×C31—24no—
439C4×C31—42no—
440C4×C31—44no—
441C4×C31—42no—
442C4×C31—44no—
443C4×C31—44no—
444C4×C31—42no—
445C4×C31—81no—
446C4×C31—81no—
447C26C22×C3111yescharacteristic
448C24×C4C22×C3111yescharacteristic
449C24×C4C22×C3111yescharacteristic
450C22×C4⋊C4C22×C3111yescharacteristic, complemented
451C22×C4⋊C4C22×C3111yescharacteristic, complemented
452C22×C22⋊C4—24no—
453C22×C22⋊C4—28no—
454C22×C22⋊C4C22×C3112yes—
455C22×C22⋊C4C22×C3111yescharacteristic
456C22×C22⋊C4C22×C3112yes—
457C22×C22⋊C4C22×C3112yes—
458C22×C22⋊C4C22×C3111yescharacteristic
459C22×C22⋊C4C22×C3111yescharacteristic
460C22×C22⋊C4C22×C3112yes—
461C22×C22⋊C4C22×C3112yes—
462C22×C22⋊C4C22×C3111yescharacteristic
463C22×C22⋊C4C22×C3112yes—
464C22×C42C22×C3112yescomplemented
465#388—28no—
466#385—24no—
467#379—24no—
468#379C4×C3118yescomplemented
469C4×C22⋊C4—24no—
470C2×#95C22×C3112yescomplemented
471C2×#95C22×C3112yescomplemented
472C2×#95C22×C3111yescharacteristic, complemented
473C2×#95C22×C3112yescomplemented
474C2×#95C22×C3111yescharacteristic, complemented
475C2×#95C22×C3112yescomplemented
476C2×#95C22×C3112yescomplemented
477C2×C31—28no—
478C2×C31—48no—
479C2×C31C2×#38811yescharacteristic
480C2×C31C4×#12011yescharacteristic
481C2×C31#232111yescharacteristic
482C2×C31#234212yes—
483C2×C31#235812yes—
484C2×C31#241011yescharacteristic
485C2×C31#241111yescharacteristic
486C2×C31#241812yes—
487C2×C31#243511yescharacteristic
488C2×C31#248012yes—
489C2×C31#256111yescharacteristic
490C25—24no—
491C25—22no—
492C25—24no—
493C25—22no—
494C25—22no—
495C25—22no—
496C25—22no—
497C25—22no—
498C25—42no—
499C25—42no—
500C25C2×C4×C3114yes—
501C25C23×C3112yes—
502C25C23×C3111yescharacteristic
503C23×C4—22no—
504C23×C4—22no—
505C23×C4—22no—
506C23×C4—24no—
507C23×C4—24no—
508C23×C4—22no—
509C23×C4—22no—
510C23×C4—42no—
511C23×C4—42no—
512C23×C4D4×C3114yes—
513C23×C4C23×C3111yescharacteristic
514C23×C4C23×C3111yescharacteristic
515C23×C4C23×C3111yescharacteristic
516C23×C4C23×C3111yescharacteristic
517C23×C4C23×C3112yes—
518C23×C4C23×C3112yes—
519C23×C4C23×C3111yescharacteristic
520C23×C4C23×C3112yes—
521C23×C4C23×C3111yescharacteristic
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—24no—
525C2×C4⋊C4—42no—
526C2×C22⋊C4—232no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4C2×C4×C3114yes—
552C2×C22⋊C4C2×C4×C3114yes—
553C2×C22⋊C4C2×C4×C3118yescomplemented
554C2×C22⋊C4C2×C4×C3118yescomplemented
555C2×C22⋊C4D4×C3118yes—
556C2×C22⋊C4D4×C3114yes—
557C2×C42—24no—
558C2×C42—24no—
559C2×C42—42no—
560#95—24no—
561#95—22no—
562#95—22no—
563#95—24no—
564#95—24no—
565#95—42no—
566#95—42no—
567C31#1397111yescharacteristic, direct product factor, Sylow
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—28no—
573C24—28no—
574C24—216no—
575C24—216no—
576C24—28no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—28no—
590C24—28no—
591C24—48no—
592C24—48no—
593C24—48no—
594C24—48no—
595C24—48no—
596C24—48no—
597C24—48no—
598C24—48no—
599C24—48no—
600C24—44no—
601C24—44no—
602C24—48no—
603C24—44no—
604C24—44no—
605C24—44no—
606C24—44no—
607C24C22×C4×C3114yes—
608C24C22×C4×C3112yes—
609C24C2×D4×C3114yes—
610C24C2×D4×C3112yes—
611C24C2×D4×C3112yes—
612C24#41×C3114yes—
613C24#41×C3112yes—
614C24#41×C3112yes—
615C24#41×C3112yes—
616C24#41×C3112yes—
617C24C24×C3111yescharacteristic
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—28no—
622C22×C4—28no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—21no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—28no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—44no—
665C22×C4—48no—
666C22×C4—48no—
667C22×C4—48no—
668C22×C4—48no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4C22×C4×C3112yes—
672C22×C4C22×C4×C3114yes—
673C22×C4C22×C4×C3112yes—
674C22×C4C2×D4×C3114yes—
675C22×C4C2×D4×C3114yes—
676C22×C4C2×D4×C3112yes—
677C22×C4C2×D4×C3112yes—
678C22×C4C2×D4×C3114yes—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C22⋊C4—216no—
682C22⋊C4—28no—
683C22⋊C4—28no—
684C22⋊C4—216no—
685C22⋊C4—28no—
686C22⋊C4—216no—
687C22⋊C4—48no—
688C22⋊C4—48no—
689C22⋊C4—48no—
690C22⋊C4—44no—
691C42—48no—
692C23—24no—
693C23—24no—
694C23—22no—
695C23—22no—
696C23—24no—
697C23—22no—
698C23—22no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—232no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—432no—
728C23—432no—
729C23—416no—
730C23—416no—
731C23—416no—
732C23—432no—
733C23—416no—
734C23—432no—
735C23—416no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—416no—
753C23C31×#11714yes—
754C23C4×D4×C3118yes—
755C23C4×D4×C3114yes—
756C23C4×D4×C3114yes—
757C23C31×#12114yes—
758C23C31×#12314yes—
759C23C31×#12414yes—
760C23C31×#12614yes—
761C23C23×C4×C3111yescharacteristic
762C23C22×D4×C3111yescharacteristic
763C23C22×D4×C3112yes—
764C23C22×D4×C3111yescharacteristic
765C23C2×#41×C3111yescharacteristic
766C23C2×#41×C3111yescharacteristic
767C23C2×#41×C3111yescharacteristic
768C23C2×#41×C3112yes—
769C23C2×#41×C3111yescharacteristic
770C23C31×H(5,𝔽2)12yes—
771C23C31×H(5,𝔽2)12yes—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—416no—
793C2×C4—416no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4C31×#12014yes—
825C22—24no—
826C22—28no—
827C22—28no—
828C22—24no—
829C22—24no—
830C22—28no—
831C22—24no—
832C22—28no—
833C22—24no—
834C22—24no—
835C22—28no—
836C22—28no—
837C22—28no—
838C22—464no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22C31×#38818yescomplemented
852C22C2×C31×#11711yescharacteristic
853C22C2×C4×D4×C3111yescharacteristic
854C22C2×C4×D4×C3112yes—
855C22C2×C4×D4×C3111yescharacteristic
856C22C31×#51812yes—
857C22C2×C31×#12011yescharacteristic
858C22C2×C31×#12111yescharacteristic
859C22C2×C31×#12311yescharacteristic
860C22C31×#52511yescharacteristic
861C22C31×#52512yes—
862C22C2×C31×#12411yescharacteristic
863C22C2×C31×#12611yescharacteristic
864C22C31×#53411yescharacteristic
865C22C31×#53511yescharacteristic
866C22C31×#53812yes—
867C22D42×C3112yes—
868C22C31×#54612yes—
869C22C31×#54612yes—
870C22C31×#54612yes—
871C22C31×#54612yes—
872C22C31×#55112yes—
873C22C31×#55112yes—
874C22C31×#55112yes—
875C4—24no—
876C4—42no—
877C4—44no—
878C4—42no—
879C4—44no—
880C4—44no—
881C4—42no—
882C4—81no—
883C4—81no—
884C2—28no—
885C2—48no—
886C2C2×C31×#38811yescharacteristic
887C2C4×C31×#12011yescharacteristic
888C2C31×#232111yescharacteristic
889C2C31×#234212yes—
890C2C31×#235812yes—
891C2C31×#241011yescharacteristic
892C2C31×#241111yescharacteristic
893C2C31×#241812yes—
894C2C31×#243511yescharacteristic
895C2C31×#248012yes—
896C2C31×#256111yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC26×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#388C2semidirect
3. C2×C31×#385C2semidirect
6. C2×C4×C22⋊C4×C31C2semidirect
7. C31×#1440C2semidirect
8. C31×#1439C2semidirect
9. C31×#1437C2semidirect
10. C31×C22⋊#95C2semidirect
11. C31×C22⋊#95C2semidirect
15. C22×C4⋊C4×C31C22semidirect
16. C22×C4⋊C4×C31C22semidirect
29. C22×C42×C31C22semidirect
33. C31×#379C4semidirect
35. C2×C31×#95C22semidirect
36. C2×C31×#95C22semidirect
37. C2×C31×#95C22semidirect
38. C2×C31×#95C22semidirect
39. C2×C31×#95C22semidirect
40. C2×C31×#95C22semidirect
41. C2×C31×#95C22semidirect
105. C2×C22⋊C4×C31C2×C4semidirect
106. C2×C22⋊C4×C31C2×C4semidirect
243. #13971C31direct (N × H)
378. C2×#388C2×C31semidirect
379. C2×#385C2×C31semidirect
382. C2×C4×C22⋊C4C2×C31semidirect
383. #1440C2×C31semidirect
384. #1439C2×C31semidirect
385. #1437C2×C31semidirect
386. C22⋊#95C2×C31semidirect
387. C22⋊#95C2×C31semidirect
414. C22×C31#388semidirect
450. C22×C4⋊C4C22×C31semidirect
451. C22×C4⋊C4C22×C31semidirect
464. C22×C42C22×C31semidirect
468. #379C4×C31semidirect
470. C2×#95C22×C31semidirect
471. C2×#95C22×C31semidirect
472. C2×#95C22×C31semidirect
473. C2×#95C22×C31semidirect
474. C2×#95C22×C31semidirect
475. C2×#95C22×C31semidirect
476. C2×#95C22×C31semidirect
553. C2×C22⋊C4C2×C4×C31semidirect
554. C2×C22⋊C4C2×C4×C31semidirect
567. C31#13971direct (N × H)
851. C22C31×#388semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C312
C2×C31×#3882
C2×C31×#3852
C2×C31×#3792
C2×C4×C22⋊C4×C312
C31×#14402
C31×#14392
C31×#14372
C31×C22⋊#952
#1397131