Finite Group Databasebeta

← C31×#13912 #21470671

Subgroups — C31×#13912 #21470671

Order 7936.

2314 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C31C211yesmaximal, characteristic
2C2×C31×#388C212yesmaximal, complemented
3C2×C31×#381C211yesmaximal, characteristic, complemented
4C2×C31×#380C211yesmaximal, characteristic, complemented
5C31×#1441C212yesmaximal, complemented
6C31×#1438C212yesmaximal
7C31×#1437C212yesmaximal, complemented
8C31×#1434C211yesmaximal, characteristic, complemented
9C31×C22⋊#95C211yesmaximal, characteristic, complemented
10C31×C22⋊#95C211yesmaximal, characteristic, complemented
11C4×C31×#95C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C24×C4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C2×C4×D4×C31—28no—
16C2×C4×D4×C31C418yescomplemented
17C22×C4⋊C4×C31C2212yes—
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C42×C31C2212yes—
26C22×C42×C31C2211yescharacteristic
27C31×#388—28no—
28C31×#381—24no—
29C31×#380—24no—
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2212yes—
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2211yescharacteristic
40C25×C31C2311yescharacteristic
41C25×C31C2311yescharacteristic
42C22×D4×C31—24no—
43C22×D4×C31—22no—
44C22×D4×C31—22no—
45C22×D4×C31—24no—
46C22×D4×C31C2×C414yes—
47C23×C4×C31—24no—
48C23×C4×C31—24no—
49C23×C4×C31—22no—
50C23×C4×C31—22no—
51C23×C4×C31—22no—
52C23×C4×C31—22no—
53C23×C4×C31—42no—
54C23×C4×C31—42no—
55C23×C4×C31C2×C414yes—
56C23×C4×C31C2×C414yes—
57C23×C4×C31C2312yes—
58C23×C4×C31C2312yes—
59C23×C4×C31C2311yescharacteristic
60C23×C4×C31C2312yes—
61C23×C4×C31C2312yes—
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2311yescharacteristic
66C4×D4×C31—232no—
67C2×C4⋊C4×C31—24no—
68C2×C4⋊C4×C31—24no—
69C2×C4⋊C4×C31—24no—
70C2×C4⋊C4×C31—42no—
71C2×C4⋊C4×C31C2×C414yes—
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—42no—
82C2×C22⋊C4×C31—42no—
83C2×C22⋊C4×C31—42no—
84C2×C22⋊C4×C31—42no—
85C2×C22⋊C4×C31C2×C414yes—
86C2×C22⋊C4×C31C2×C414yes—
87C2×C22⋊C4×C31D418yes—
88C2×C42×C31—24no—
89C2×C42×C31—24no—
90C2×C42×C31—24no—
91C2×C42×C31—42no—
92C2×C42×C31C2×C414yes—
93C31×#95—22no—
94C31×#95—24no—
95C31×#95—22no—
96C31×#95—24no—
97C31×#95—24no—
98C31×#95—24no—
99C31×#95—22no—
100C31×#95—24no—
101C31×#95—42no—
102C31×#95D414yescomplemented
103C24×C31—21no—
104C24×C31—21no—
105C24×C31—22no—
106C24×C31—22no—
107C24×C31—22no—
108C24×C31—21no—
109C24×C31—21no—
110C24×C31—22no—
111C24×C31—21no—
112C24×C31—21no—
113C24×C31—22no—
114C24×C31—21no—
115C24×C31—21no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—21no—
119C24×C31—21no—
120C24×C31C22×C412yes—
121C24×C31C22×C412yes—
122C24×C31C2×D414yes—
123C24×C31#4112yes—
124C24×C31#4112yes—
125C24×C31C2411yescharacteristic
126C2×D4×C31—216no—
127C2×D4×C31—216no—
128C2×D4×C31—28no—
129C2×D4×C31—28no—
130C2×D4×C31—28no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—21no—
134C22×C4×C31—22no—
135C22×C4×C31—21no—
136C22×C4×C31—21no—
137C22×C4×C31—21no—
138C22×C4×C31—21no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—21no—
142C22×C4×C31—28no—
143C22×C4×C31—21no—
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—21no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31—28no—
160C22×C4×C31—28no—
161C22×C4×C31—28no—
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—22no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—44no—
177C22×C4×C31—44no—
178C22×C4×C31—48no—
179C22×C4×C31—48no—
180C22×C4×C31—48no—
181C22×C4×C31—48no—
182C22×C4×C31C22×C412yes—
183C22×C4×C31C22×C412yes—
184C22×C4×C31C22×C412yes—
185C22×C4×C31C22×C412yes—
186C22×C4×C31C22×C412yes—
187C22×C4×C31C2×D414yes—
188C22×C4×C31C2×D414yes—
189C22×C4×C31C2×D414yes—
190C22×C4×C31C2×D412yes—
191C22×C4×C31#4114yes—
192C22×C4×C31#4114yes—
193C22×C4×C31#4112yes—
194C4⋊C4×C31—28no—
195C4⋊C4×C31—48no—
196C22⋊C4×C31—28no—
197C22⋊C4×C31—48no—
198C22⋊C4×C31—48no—
199C22⋊C4×C31—48no—
200C22⋊C4×C31—48no—
201C22⋊C4×C31C22⋊C4116yescomplemented
202C42×C31—28no—
203C42×C31—48no—
204#13912C3111yesmaximal, characteristic, direct product factor, Sylow
205C23×C31—22no—
206C23×C31—22no—
207C23×C31—22no—
208C23×C31—22no—
209C23×C31—22no—
210C23×C31—22no—
211C23×C31—22no—
212C23×C31—22no—
213C23×C31—22no—
214C23×C31—22no—
215C23×C31—22no—
216C23×C31—22no—
217C23×C31—24no—
218C23×C31—24no—
219C23×C31—24no—
220C23×C31—24no—
221C23×C31—24no—
222C23×C31—22no—
223C23×C31—24no—
224C23×C31—24no—
225C23×C31—24no—
226C23×C31—22no—
227C23×C31—24no—
228C23×C31—22no—
229C23×C31—22no—
230C23×C31—24no—
231C23×C31—42no—
232C23×C31—42no—
233C23×C31—42no—
234C23×C31—42no—
235C23×C31—42no—
236C23×C31—42no—
237C23×C31—42no—
238C23×C31—42no—
239C23×C31—42no—
240C23×C31—42no—
241C23×C31—42no—
242C23×C31—41no—
243C23×C31—42no—
244C23×C31—41no—
245C23×C31—42no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—42no—
249C23×C31C2×C22⋊C414yes—
250C23×C31#11714yes—
251C23×C31C23×C411yescharacteristic
252C23×C31C22×D412yes—
253C23×C31C22×D411yescharacteristic
254C23×C31C2×#4112yes—
255C23×C31C2×#4111yescharacteristic
256C23×C31C2×#4111yescharacteristic
257C23×C31C2×#4111yescharacteristic
258C23×C31C2×#4112yes—
259C23×C31H(5,𝔽2)12yes—
260C23×C31H(5,𝔽2)11yescharacteristic
261C23×C312−1+411yescharacteristic
262D4×C31—232no—
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—22no—
270C2×C4×C31—22no—
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—22no—
280C2×C4×C31—22no—
281C2×C4×C31—22no—
282C2×C4×C31—24no—
283C2×C4×C31—24no—
284C2×C4×C31—24no—
285C2×C4×C31—24no—
286C2×C4×C31—24no—
287C2×C4×C31—24no—
288C2×C4×C31—416no—
289C2×C4×C31—416no—
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×C31—42no—
311C2×C4×C31—42no—
312C2×C4×C31—42no—
313C2×C4×C31—42no—
314C2×C4×C31C2×C22⋊C414yes—
315C2×C4×C31C2×C22⋊C414yes—
316C2×C4×C31#11714yes—
317C2×C4×C31C4×D414yes—
318C22×C4×D4C2×C3111yescharacteristic
319C2×#388C2×C3112yescomplemented
320C2×#381C2×C3111yescharacteristic, complemented
321C2×#380C2×C3111yescharacteristic, complemented
322#1441C2×C3112yescomplemented
323#1438C2×C3112yes—
324#1437C2×C3112yescomplemented
325#1434C2×C3111yescharacteristic, complemented
326C22⋊#95C2×C3111yescharacteristic, complemented
327C22⋊#95C2×C3111yescharacteristic, complemented
328C4×#95C2×C3111yescharacteristic, complemented
329C22×C31—24no—
330C22×C31—24no—
331C22×C31—24no—
332C22×C31—24no—
333C22×C31—24no—
334C22×C31—24no—
335C22×C31—42no—
336C22×C31—42no—
337C22×C31—42no—
338C22×C31—42no—
339C22×C31—42no—
340C22×C31—42no—
341C22×C31—44no—
342C22×C31—44no—
343C22×C31—44no—
344C22×C31—44no—
345C22×C31—44no—
346C22×C31—44no—
347C22×C31—44no—
348C22×C31—44no—
349C22×C31—42no—
350C22×C31—42no—
351C22×C31C22×C22⋊C411yescharacteristic
352C22×C31C2×#11711yescharacteristic
353C22×C31C2×#11711yescharacteristic
354C22×C31C2×C4×D411yescharacteristic
355C22×C31C4×#4111yescharacteristic
356C22×C31#51811yescharacteristic
357C22×C31#52011yescharacteristic
358C22×C31#52512yes—
359C22×C31#52512yes—
360C22×C31#52912yes—
361C22×C31#53212yes—
362C22×C31#54012yes—
363C22×C31#54212yes—
364C22×C31D4212yes—
365C22×C31#54612yes—
366C22×C31#54612yes—
367C22×C31#54611yescharacteristic
368C22×C31#54712yes—
369C22×C31#54811yescharacteristic
370C22×C31#55112yes—
371C22×C31#55211yescharacteristic
372C22×C31#55311yescharacteristic
373C22×C31#55312yes—
374C4×C31—24no—
375C4×C31—24no—
376C4×C31—24no—
377C4×C31—24no—
378C4×C31—42no—
379C4×C31—44no—
380C4×C31—44no—
381C4×C31—82no—
382C4×C31—82no—
383C23×D4C22×C3111yescharacteristic
384C24×C4C22×C3111yescharacteristic
385C24×C4C22×C3111yescharacteristic
386C2×C4×D4—28no—
387C2×C4×D4C4×C3118yescomplemented
388C22×C4⋊C4C22×C3112yes—
389C22×C4⋊C4C22×C3111yescharacteristic
390C22×C22⋊C4C22×C3112yes—
391C22×C22⋊C4C22×C3112yes—
392C22×C22⋊C4C22×C3112yes—
393C22×C22⋊C4C22×C3112yes—
394C22×C22⋊C4C22×C3111yescharacteristic
395C22×C22⋊C4C22×C3111yescharacteristic
396C22×C42C22×C3112yes—
397C22×C42C22×C3111yescharacteristic
398#388—28no—
399#381—24no—
400#380—24no—
401C2×#95C22×C3111yescharacteristic
402C2×#95C22×C3112yes—
403C2×#95C22×C3111yescharacteristic
404C2×#95C22×C3111yescharacteristic
405C2×#95C22×C3112yes—
406C2×#95C22×C3112yes—
407C2×#95C22×C3112yes—
408C2×#95C22×C3112yes—
409C2×#95C22×C3112yes—
410C2×#95C22×C3111yescharacteristic
411C2×C31—44no—
412C2×C31—44no—
413C2×C31#228011yescharacteristic
414C2×C31#229311yescharacteristic
415C2×C31#231911yescharacteristic
416C2×C31D4×C22⋊C411yescharacteristic
417C2×C31#233911yescharacteristic
418C2×C31#235211yescharacteristic
419C2×C31#235311yescharacteristic
420C2×C31#245712yes—
421C2×C31#246112yes—
422C2×C31#246412yes—
423C2×C31#246812yes—
424C25C23×C3111yescharacteristic
425C25C23×C3111yescharacteristic
426C22×D4—24no—
427C22×D4—22no—
428C22×D4—22no—
429C22×D4—24no—
430C22×D4C2×C4×C3114yes—
431C23×C4—24no—
432C23×C4—24no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—42no—
438C23×C4—42no—
439C23×C4C2×C4×C3114yes—
440C23×C4C2×C4×C3114yes—
441C23×C4C23×C3112yes—
442C23×C4C23×C3112yes—
443C23×C4C23×C3111yescharacteristic
444C23×C4C23×C3112yes—
445C23×C4C23×C3112yes—
446C23×C4C23×C3111yescharacteristic
447C23×C4C23×C3111yescharacteristic
448C23×C4C23×C3111yescharacteristic
449C23×C4C23×C3111yescharacteristic
450C4×D4—232no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4C2×C4×C3114yes—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4C2×C4×C3114yes—
470C2×C22⋊C4C2×C4×C3114yes—
471C2×C22⋊C4D4×C3118yes—
472C2×C42—24no—
473C2×C42—24no—
474C2×C42—24no—
475C2×C42—42no—
476C2×C42C2×C4×C3114yes—
477#95—22no—
478#95—24no—
479#95—22no—
480#95—24no—
481#95—24no—
482#95—24no—
483#95—22no—
484#95—24no—
485#95—42no—
486#95D4×C3114yescomplemented
487C31#1391211yescharacteristic, direct product factor, Sylow
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—22no—
496C24—21no—
497C24—21no—
498C24—22no—
499C24—21no—
500C24—21no—
501C24—22no—
502C24—22no—
503C24—21no—
504C24—21no—
505C24C22×C4×C3112yes—
506C24C22×C4×C3112yes—
507C24C2×D4×C3114yes—
508C24#41×C3112yes—
509C24#41×C3112yes—
510C24C24×C3111yescharacteristic
511C2×D4—216no—
512C2×D4—216no—
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—28no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—28no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4C22×C4×C3112yes—
568C22×C4C22×C4×C3112yes—
569C22×C4C22×C4×C3112yes—
570C22×C4C22×C4×C3112yes—
571C22×C4C22×C4×C3112yes—
572C22×C4C2×D4×C3114yes—
573C22×C4C2×D4×C3114yes—
574C22×C4C2×D4×C3114yes—
575C22×C4C2×D4×C3112yes—
576C22×C4#41×C3114yes—
577C22×C4#41×C3114yes—
578C22×C4#41×C3112yes—
579C4⋊C4—28no—
580C4⋊C4—48no—
581C22⋊C4—28no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4C22⋊C4×C31116yescomplemented
587C42—28no—
588C42—48no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—22no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—22no—
611C23—24no—
612C23—22no—
613C23—22no—
614C23—24no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—41no—
627C23—42no—
628C23—41no—
629C23—42no—
630C23—41no—
631C23—41no—
632C23—42no—
633C23C2×C22⋊C4×C3114yes—
634C23C31×#11714yes—
635C23C23×C4×C3111yescharacteristic
636C23C22×D4×C3112yes—
637C23C22×D4×C3111yescharacteristic
638C23C2×#41×C3112yes—
639C23C2×#41×C3111yescharacteristic
640C23C2×#41×C3111yescharacteristic
641C23C2×#41×C3111yescharacteristic
642C23C2×#41×C3112yes—
643C23C31×H(5,𝔽2)12yes—
644C23C31×H(5,𝔽2)11yescharacteristic
645C23C31×2−1+411yescharacteristic
646D4—232no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—416no—
673C2×C4—416no—
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×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4C2×C22⋊C4×C3114yes—
699C2×C4C2×C22⋊C4×C3114yes—
700C2×C4C31×#11714yes—
701C2×C4C4×D4×C3114yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—44no—
715C22—44no—
716C22—44no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—44no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22C22×C22⋊C4×C3111yescharacteristic
725C22C2×C31×#11711yescharacteristic
726C22C2×C31×#11711yescharacteristic
727C22C2×C4×D4×C3111yescharacteristic
728C22C4×#41×C3111yescharacteristic
729C22C31×#51811yescharacteristic
730C22C31×#52011yescharacteristic
731C22C31×#52512yes—
732C22C31×#52512yes—
733C22C31×#52912yes—
734C22C31×#53212yes—
735C22C31×#54012yes—
736C22C31×#54212yes—
737C22D42×C3112yes—
738C22C31×#54612yes—
739C22C31×#54612yes—
740C22C31×#54611yescharacteristic
741C22C31×#54712yes—
742C22C31×#54811yescharacteristic
743C22C31×#55112yes—
744C22C31×#55211yescharacteristic
745C22C31×#55311yescharacteristic
746C22C31×#55312yes—
747C4—24no—
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—44no—
753C4—44no—
754C4—82no—
755C4—82no—
756C2—44no—
757C2—44no—
758C2C31×#228011yescharacteristic
759C2C31×#229311yescharacteristic
760C2C31×#231911yescharacteristic
761C2D4×C22⋊C4×C3111yescharacteristic
762C2C31×#233911yescharacteristic
763C2C31×#235211yescharacteristic
764C2C31×#235311yescharacteristic
765C2C31×#245712yes—
766C2C31×#246112yes—
767C2C31×#246412yes—
768C2C31×#246812yes—
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
2. C2×C31×#388C2semidirect
3. C2×C31×#381C2semidirect
4. C2×C31×#380C2semidirect
5. C31×#1441C2semidirect
7. C31×#1437C2semidirect
8. C31×#1434C2semidirect
9. C31×C22⋊#95C2semidirect
10. C31×C22⋊#95C2semidirect
11. C4×C31×#95C2semidirect
16. C2×C4×D4×C31C4semidirect
102. C31×#95D4semidirect
201. C22⋊C4×C31C22⋊C4semidirect
204. #13912C31direct (N × H)
319. C2×#388C2×C31semidirect
320. C2×#381C2×C31semidirect
321. C2×#380C2×C31semidirect
322. #1441C2×C31semidirect
324. #1437C2×C31semidirect
325. #1434C2×C31semidirect
326. C22⋊#95C2×C31semidirect
327. C22⋊#95C2×C31semidirect
328. C4×#95C2×C31semidirect
387. C2×C4×D4C4×C31semidirect
486. #95D4×C31semidirect
487. C31#13912direct (N × H)
586. 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×C4×D4×C312
C2×C31×#3882
C2×C31×#3812
C2×C31×#3802
C31×#14412
C31×#14382
C31×#14372
C31×#14342
C31×C22⋊#952
C4×C31×#952
#1391231