Finite Group Databasebeta

← C31×#14401 #21471160

Subgroups — C31×#14401 #21471160

Order 7936.

2118 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#390C211yesmaximal, characteristic
2C2×C31×#386C211yesmaximal, characteristic
3C2×C31×#386C211yesmaximal, characteristic
4C2×C31×#385C212yesmaximal, complemented
5C2×C31×#380C212yesmaximal, complemented
6C31×#1444C212yesmaximal, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1439C212yesmaximal, complemented
9C31×#1436C212yesmaximal, complemented
10C23×D4×C31C2211yescharacteristic
11C24×C4×C31C2211yescharacteristic
12C24×C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2212yes—
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2212yes—
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C42×C31C2211yescharacteristic
24C31×#390—24no—
25C31×#386—24no—
26C31×#386C418yescomplemented
27C31×#385—28no—
28C31×#380—28no—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C25×C31C2311yescharacteristic
37C25×C31C2311yescharacteristic
38C22×D4×C31—41no—
39C22×D4×C31—41no—
40C22×D4×C31—41no—
41C22×D4×C31—41no—
42C22×D4×C31C2×C414yes—
43C22×D4×C31D414yes—
44C22×D4×C31Q814yes—
45C23×C4×C31—24no—
46C23×C4×C31—24no—
47C23×C4×C31—22no—
48C23×C4×C31—24no—
49C23×C4×C31—41no—
50C23×C4×C31—41no—
51C23×C4×C31—42no—
52C23×C4×C31—41no—
53C23×C4×C31—41no—
54C23×C4×C31C2×C414yescomplemented
55C23×C4×C31C2312yes—
56C23×C4×C31C2312yes—
57C23×C4×C31C2312yes—
58C23×C4×C31C2312yes—
59C23×C4×C31C2312yes—
60C23×C4×C31C2311yescharacteristic
61C23×C4×C31C2312yes—
62C2×C4⋊C4×C31—24no—
63C2×C4⋊C4×C31—24no—
64C2×C4⋊C4×C31—24no—
65C2×C4⋊C4×C31—24no—
66C2×C4⋊C4×C31—22no—
67C2×C4⋊C4×C31—24no—
68C2×C4⋊C4×C31—42no—
69C2×C4⋊C4×C31—42no—
70C2×C4⋊C4×C31—41no—
71C2×C4⋊C4×C31—41no—
72C2×C4⋊C4×C31—42no—
73C2×C4⋊C4×C31—42no—
74C2×C22⋊C4×C31—24no—
75C2×C22⋊C4×C31—24no—
76C2×C22⋊C4×C31—24no—
77C2×C22⋊C4×C31—22no—
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—41no—
84C2×C22⋊C4×C31—41no—
85C2×C22⋊C4×C31—42no—
86C2×C22⋊C4×C31—42no—
87C2×C22⋊C4×C31—42no—
88C2×C22⋊C4×C31—41no—
89C2×C22⋊C4×C31—41no—
90C2×C22⋊C4×C31C2×C418yes—
91C2×C22⋊C4×C31C2×C414yescomplemented
92C2×C42×C31—22no—
93C2×C42×C31—41no—
94C2×C42×C31—41no—
95C31×#95—24no—
96C31×#95—24no—
97C31×#95—24no—
98C31×#95—42no—
99C31×#95—42no—
100C31×#95C2×C418yescomplemented
101C31×#95D418yescomplemented
102C24×C31—22no—
103C24×C31—22no—
104C24×C31—22no—
105C24×C31—22no—
106C24×C31—22no—
107C24×C31—22no—
108C24×C31—21no—
109C24×C31—21no—
110C24×C31—21no—
111C24×C31—21no—
112C24×C31—21no—
113C24×C31—21no—
114C24×C31—21no—
115C24×C31—21no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31C22×C412yes—
119C24×C31C22×C412yes—
120C24×C31C2×D412yes—
121C24×C31C2×D412yes—
122C24×C31C2×Q812yes—
123C24×C31C2×Q812yes—
124C24×C31C2411yescharacteristic
125C2×D4×C31—44no—
126C2×D4×C31—44no—
127C2×D4×C31—44no—
128C2×D4×C31—44no—
129C2×D4×C31—44no—
130C2×D4×C31—44no—
131C2×D4×C31C4⋊C4116yescomplemented
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—21no—
135C22×C4×C31—21no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—21no—
139C22×C4×C31—21no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—216no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—44no—
174C22×C4×C31—44no—
175C22×C4×C31—48no—
176C22×C4×C31—44no—
177C22×C4×C31—44no—
178C22×C4×C31—48no—
179C22×C4×C31—48no—
180C22×C4×C31—44no—
181C22×C4×C31—44no—
182C22×C4×C31C22×C414yes—
183C22×C4×C31C22×C412yes—
184C22×C4×C31C22×C414yes—
185C22×C4×C31C2×D414yes—
186C22×C4×C31C2×D414yes—
187C22×C4×C31C2×D412yes—
188C22×C4×C31C2×D414yes—
189C22×C4×C31C2×Q812yes—
190C22×C4×C31#4114yes—
191C4⋊C4×C31—48no—
192C4⋊C4×C31—48no—
193C4⋊C4×C31—44no—
194C4⋊C4×C31—48no—
195C22⋊C4×C31—216no—
196C22⋊C4×C31—44no—
197C22⋊C4×C31—48no—
198C22⋊C4×C31—48no—
199C22⋊C4×C31—48no—
200C22⋊C4×C31—44no—
201C42×C31—44no—
202#14401C3111yesmaximal, characteristic, direct product factor, Sylow
203C23×C31—24no—
204C23×C31—24no—
205C23×C31—22no—
206C23×C31—22no—
207C23×C31—22no—
208C23×C31—22no—
209C23×C31—24no—
210C23×C31—24no—
211C23×C31—22no—
212C23×C31—22no—
213C23×C31—22no—
214C23×C31—22no—
215C23×C31—22no—
216C23×C31—22no—
217C23×C31—22no—
218C23×C31—22no—
219C23×C31—24no—
220C23×C31—24no—
221C23×C31—24no—
222C23×C31—24no—
223C23×C31—24no—
224C23×C31—24no—
225C23×C31—24no—
226C23×C31—24no—
227C23×C31—42no—
228C23×C31—42no—
229C23×C31—42no—
230C23×C31—42no—
231C23×C31—42no—
232C23×C31—42no—
233C23×C31—42no—
234C23×C31—42no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—42no—
238C23×C31—42no—
239C23×C31—41no—
240C23×C31—41no—
241C23×C31—41no—
242C23×C31—41no—
243C23×C31—42no—
244C23×C31—42no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31C2×C4⋊C414yes—
248C23×C31C2×C4⋊C414yes—
249C23×C31C23×C411yescharacteristic
250C23×C31C22×D411yescharacteristic
251C23×C31C22×D412yes—
252C23×C31C22×Q811yescharacteristic
253C23×C31C2×#4112yes—
254C23×C31H(5,𝔽2)11yescharacteristic
255C23×C31H(5,𝔽2)11yescharacteristic
256C23×C31H(5,𝔽2)11yescharacteristic
257C23×C31H(5,𝔽2)11yescharacteristic
258C23×C31H(5,𝔽2)12yes—
259C23×C312−1+412yes—
260D4×C31—416no—
261C2×C4×C31—24no—
262C2×C4×C31—24no—
263C2×C4×C31—22no—
264C2×C4×C31—22no—
265C2×C4×C31—22no—
266C2×C4×C31—22no—
267C2×C4×C31—22no—
268C2×C4×C31—22no—
269C2×C4×C31—24no—
270C2×C4×C31—24no—
271C2×C4×C31—24no—
272C2×C4×C31—24no—
273C2×C4×C31—24no—
274C2×C4×C31—24no—
275C2×C4×C31—24no—
276C2×C4×C31—24no—
277C2×C4×C31—24no—
278C2×C4×C31—24no—
279C2×C4×C31—24no—
280C2×C4×C31—24no—
281C2×C4×C31—24no—
282C2×C4×C31—416no—
283C2×C4×C31—416no—
284C2×C4×C31—42no—
285C2×C4×C31—42no—
286C2×C4×C31—42no—
287C2×C4×C31—42no—
288C2×C4×C31—42no—
289C2×C4×C31—42no—
290C2×C4×C31—42no—
291C2×C4×C31—42no—
292C2×C4×C31—42no—
293C2×C4×C31—42no—
294C2×C4×C31—42no—
295C2×C4×C31—42no—
296C2×C4×C31—42no—
297C2×C4×C31—42no—
298C2×C4×C31—42no—
299C2×C4×C31—42no—
300C2×C4×C31—42no—
301C2×C4×C31—42no—
302C2×C4×C31—42no—
303C2×C4×C31—42no—
304C2×C4×C31—42no—
305C2×C4×C31—42no—
306C2×C4×C31—42no—
307C2×C4×C31—42no—
308C2×C4×C31—42no—
309C2×C4×C31—42no—
310C2×C4×C31C2×C4⋊C414yes—
311C2×C4×C31C4×D418yes—
312C2×#390C2×C3111yescharacteristic
313C2×#386C2×C3111yescharacteristic
314C2×#386C2×C3111yescharacteristic
315C2×#385C2×C3112yescomplemented
316C2×#380C2×C3112yescomplemented
317#1444C2×C3112yescomplemented
318#1439C2×C3112yescomplemented
319#1439C2×C3112yescomplemented
320#1436C2×C3112yescomplemented
321C22×C31—24no—
322C22×C31—24no—
323C22×C31—28no—
324C22×C31—28no—
325C22×C31—44no—
326C22×C31—44no—
327C22×C31—42no—
328C22×C31—42no—
329C22×C31—42no—
330C22×C31—42no—
331C22×C31—42no—
332C22×C31—42no—
333C22×C31—44no—
334C22×C31—44no—
335C22×C31—42no—
336C22×C31—42no—
337C22×C31—44no—
338C22×C31—44no—
339C22×C31—42no—
340C22×C31—42no—
341C22×C31—42no—
342C22×C31—42no—
343C22×C31C22×C4⋊C411yescharacteristic
344C22×C31C2×C4×D412yes—
345C22×C31#51811yescharacteristic
346C22×C31#51811yescharacteristic
347C22×C31#52012yes—
348C22×C31#53411yescharacteristic
349C22×C31#53411yescharacteristic
350C22×C31#53512yes—
351C22×C31#53712yes—
352C22×C31#54012yes—
353C22×C31#54212yes—
354C22×C31#54311yescharacteristic
355C22×C31#54311yescharacteristic
356C22×C31D4212yes—
357C22×C31D4211yescharacteristic
358C22×C31#54612yes—
359C22×C31#54712yes—
360C22×C31D4×Q812yes—
361C22×C31#55111yescharacteristic
362C22×C31#55412yes—
363C22×C31#56011yescharacteristic
364C22×C31#56212yes—
365C22×C31#56311yescharacteristic
366C4×C31—24no—
367C4×C31—28no—
368C4×C31—44no—
369C4×C31—44no—
370C4×C31—44no—
371C4×C31—82no—
372C4×C31—82no—
373C23×D4C22×C3111yescharacteristic
374C24×C4C22×C3111yescharacteristic
375C24×C4C22×C3111yescharacteristic
376C22×C4⋊C4C22×C3112yes—
377C22×C4⋊C4C22×C3112yes—
378C22×C4⋊C4C22×C3112yes—
379C22×C4⋊C4C22×C3111yescharacteristic
380C22×C22⋊C4C22×C3112yes—
381C22×C22⋊C4C22×C3112yes—
382C22×C22⋊C4C22×C3112yes—
383C22×C22⋊C4C22×C3112yes—
384C22×C22⋊C4C22×C3111yescharacteristic
385C22×C22⋊C4C22×C3111yescharacteristic
386C22×C42C22×C3111yescharacteristic
387#390—24no—
388#386—24no—
389#386C4×C3118yescomplemented
390#385—28no—
391#380—28no—
392C2×#95C22×C3112yes—
393C2×#95C22×C3112yes—
394C2×#95C22×C3112yes—
395C2×#95C22×C3112yes—
396C2×#95C22×C3112yes—
397C2×#95C22×C3112yes—
398C2×#95C22×C3112yes—
399C2×C31—44no—
400C2×C31—44no—
401C2×C31#231511yescharacteristic
402C2×C31#232412yes—
403C2×C31D4×C4⋊C412yes—
404C2×C31#235811yescharacteristic
405C2×C31#237611yescharacteristic
406C2×C31#266911yescharacteristic
407C2×C31#267112yes—
408C2×C31#268311yescharacteristic
409C2×C31#269212yes—
410C2×C31#271711yescharacteristic
411C2×C31#274811yescharacteristic
412C25C23×C3111yescharacteristic
413C25C23×C3111yescharacteristic
414C22×D4—41no—
415C22×D4—41no—
416C22×D4—41no—
417C22×D4—41no—
418C22×D4C2×C4×C3114yes—
419C22×D4D4×C3114yes—
420C22×D4Q8×C3114yes—
421C23×C4—24no—
422C23×C4—24no—
423C23×C4—22no—
424C23×C4—24no—
425C23×C4—41no—
426C23×C4—41no—
427C23×C4—42no—
428C23×C4—41no—
429C23×C4—41no—
430C23×C4C2×C4×C3114yescomplemented
431C23×C4C23×C3112yes—
432C23×C4C23×C3112yes—
433C23×C4C23×C3112yes—
434C23×C4C23×C3112yes—
435C23×C4C23×C3112yes—
436C23×C4C23×C3111yescharacteristic
437C23×C4C23×C3112yes—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4—41no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—41no—
460C2×C22⋊C4—41no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—41no—
465C2×C22⋊C4—41no—
466C2×C22⋊C4C2×C4×C3118yes—
467C2×C22⋊C4C2×C4×C3114yescomplemented
468C2×C42—22no—
469C2×C42—41no—
470C2×C42—41no—
471#95—24no—
472#95—24no—
473#95—24no—
474#95—42no—
475#95—42no—
476#95C2×C4×C3118yescomplemented
477#95D4×C3118yescomplemented
478C31#1440111yescharacteristic, direct product factor, Sylow
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—22no—
494C24—22no—
495C24C22×C4×C3112yes—
496C24C22×C4×C3112yes—
497C24C2×D4×C3112yes—
498C24C2×D4×C3112yes—
499C24C2×Q8×C3112yes—
500C24C2×Q8×C3112yes—
501C24C24×C3111yescharacteristic
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4C4⋊C4×C31116yescomplemented
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—216no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—48no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4C22×C4×C3114yes—
560C22×C4C22×C4×C3112yes—
561C22×C4C22×C4×C3114yes—
562C22×C4C2×D4×C3114yes—
563C22×C4C2×D4×C3114yes—
564C22×C4C2×D4×C3112yes—
565C22×C4C2×D4×C3114yes—
566C22×C4C2×Q8×C3112yes—
567C22×C4#41×C3114yes—
568C4⋊C4—48no—
569C4⋊C4—48no—
570C4⋊C4—44no—
571C4⋊C4—48no—
572C22⋊C4—216no—
573C22⋊C4—44no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—44no—
578C42—44no—
579C23—24no—
580C23—24no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—24no—
586C23—24no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—41no—
612C23—41no—
613C23—42no—
614C23—42no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23C2×C4⋊C4×C3114yes—
624C23C2×C4⋊C4×C3114yes—
625C23C23×C4×C3111yescharacteristic
626C23C22×D4×C3111yescharacteristic
627C23C22×D4×C3112yes—
628C23C22×Q8×C3111yescharacteristic
629C23C2×#41×C3112yes—
630C23C31×H(5,𝔽2)11yescharacteristic
631C23C31×H(5,𝔽2)11yescharacteristic
632C23C31×H(5,𝔽2)11yescharacteristic
633C23C31×H(5,𝔽2)11yescharacteristic
634C23C31×H(5,𝔽2)12yes—
635C23C31×2−1+412yes—
636D4—416no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—416no—
659C2×C4—416no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4C2×C4⋊C4×C3114yes—
687C2×C4C4×D4×C3118yes—
688C22—24no—
689C22—24no—
690C22—28no—
691C22—28no—
692C22—44no—
693C22—44no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—44no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—44no—
705C22—44no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22C22×C4⋊C4×C3111yescharacteristic
711C22C2×C4×D4×C3112yes—
712C22C31×#51811yescharacteristic
713C22C31×#51811yescharacteristic
714C22C31×#52012yes—
715C22C31×#53411yescharacteristic
716C22C31×#53411yescharacteristic
717C22C31×#53512yes—
718C22C31×#53712yes—
719C22C31×#54012yes—
720C22C31×#54212yes—
721C22C31×#54311yescharacteristic
722C22C31×#54311yescharacteristic
723C22D42×C3112yes—
724C22D42×C3111yescharacteristic
725C22C31×#54612yes—
726C22C31×#54712yes—
727C22D4×Q8×C3112yes—
728C22C31×#55111yescharacteristic
729C22C31×#55412yes—
730C22C31×#56011yescharacteristic
731C22C31×#56212yes—
732C22C31×#56311yescharacteristic
733C4—24no—
734C4—28no—
735C4—44no—
736C4—44no—
737C4—44no—
738C4—82no—
739C4—82no—
740C2—44no—
741C2—44no—
742C2C31×#231511yescharacteristic
743C2C31×#232412yes—
744C2D4×C4⋊C4×C3112yes—
745C2C31×#235811yescharacteristic
746C2C31×#237611yescharacteristic
747C2C31×#266911yescharacteristic
748C2C31×#267112yes—
749C2C31×#268311yescharacteristic
750C2C31×#269212yes—
751C2C31×#271711yescharacteristic
752C2C31×#274811yescharacteristic
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×#380C2semidirect
6. C31×#1444C2semidirect
7. C31×#1439C2semidirect
8. C31×#1439C2semidirect
9. C31×#1436C2semidirect
26. C31×#386C4semidirect
54. C23×C4×C31C2×C4semidirect
91. C2×C22⋊C4×C31C2×C4semidirect
100. C31×#95C2×C4semidirect
101. C31×#95D4semidirect
131. C2×D4×C31C4⋊C4semidirect
202. #14401C31direct (N × H)
315. C2×#385C2×C31semidirect
316. C2×#380C2×C31semidirect
317. #1444C2×C31semidirect
318. #1439C2×C31semidirect
319. #1439C2×C31semidirect
320. #1436C2×C31semidirect
389. #386C4×C31semidirect
430. C23×C4C2×C4×C31semidirect
467. C2×C22⋊C4C2×C4×C31semidirect
476. #95C2×C4×C31semidirect
477. #95D4×C31semidirect
478. C31#14401direct (N × H)
508. C2×D4C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3902
C2×C31×#3862
C2×C31×#3852
C2×C31×#3802
C31×#14442
C31×#14392
C31×#14362
#1440131