Finite Group Databasebeta

← C31×#14019 #21470778

Subgroups — C31×#14019 #21470778

Order 7936.

2538 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊C4×C31C211yesmaximal, characteristic, complemented
2C2×C31×#388C212yesmaximal, complemented
3C2×C31×#386C211yesmaximal, characteristic
4C2×C31×#386C211yesmaximal, characteristic
5C2×C31×#386C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#1442C212yesmaximal, complemented
8C31×#1439C212yesmaximal, complemented
9C31×#1436C212yesmaximal, complemented
10C31×C22⋊#95C211yesmaximal, characteristic, complemented
11C31×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C24×C4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C24×C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31—24no—
17C22×C4⋊C4×C31—28no—
18C22×C4⋊C4×C31C2212yes—
19C22×C4⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C42×C31C2212yes—
28C31×#388—28no—
29C31×#386—24no—
30C31×#386—24no—
31C31×#386C418yescomplemented
32C4×C22⋊C4×C31—24no—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2211yescharacteristic
40C2×C31×#95C2212yes—
41C2×C31×#95C2212yes—
42C25×C31C2311yescharacteristic
43C25×C31C2311yescharacteristic
44C22×D4×C31—22no—
45C22×D4×C31—22no—
46C22×D4×C31—22no—
47C22×D4×C31—22no—
48C22×D4×C31—22no—
49C22×D4×C31—22no—
50C22×D4×C31C2×C414yes—
51C23×C4×C31—22no—
52C23×C4×C31—22no—
53C23×C4×C31—24no—
54C23×C4×C31—24no—
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×C31C2×C414yes—
65C23×C4×C31D414yes—
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C23×C4×C31C2312yes—
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2312yes—
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2312yes—
73C23×C4×C31C2312yes—
74C23×C4×C31C2311yescharacteristic
75C2×C4⋊C4×C31—232no—
76C2×C4⋊C4×C31—24no—
77C2×C4⋊C4×C31—24no—
78C2×C4⋊C4×C31—24no—
79C2×C4⋊C4×C31—24no—
80C2×C4⋊C4×C31—24no—
81C2×C4⋊C4×C31D418yescomplemented
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—22no—
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31—24no—
87C2×C22⋊C4×C31—24no—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—22no—
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—42no—
97C2×C22⋊C4×C31—42no—
98C2×C22⋊C4×C31C2×C414yes—
99C2×C22⋊C4×C31C2×C418yescomplemented
100C2×C22⋊C4×C31D414yes—
101C2×C42×C31—24no—
102C2×C42×C31—24no—
103C2×C42×C31—42no—
104C31×#95—24no—
105C31×#95—24no—
106C31×#95—22no—
107C31×#95—22no—
108C31×#95—24no—
109C31×#95—24no—
110C31×#95—24no—
111C31×#95—42no—
112C31×#95C2×C418yescomplemented
113C24×C31—22no—
114C24×C31—22no—
115C24×C31—22no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—21no—
119C24×C31—21no—
120C24×C31—22no—
121C24×C31—21no—
122C24×C31—21no—
123C24×C31—21no—
124C24×C31—21no—
125C24×C31—22no—
126C24×C31—22no—
127C24×C31C22×C412yes—
128C24×C31C22×C412yes—
129C24×C31C2×D412yes—
130C24×C31C2×D412yes—
131C24×C31#4112yes—
132C24×C31#4112yes—
133C24×C31#4112yes—
134C24×C31#4112yes—
135C24×C31C2411yescharacteristic
136C2×D4×C31—28no—
137C2×D4×C31—28no—
138C2×D4×C31—28no—
139C2×D4×C31—44no—
140C2×D4×C31—44no—
141C2×D4×C31—44no—
142C2×D4×C31—44no—
143C22×C4×C31—28no—
144C22×C4×C31—216no—
145C22×C4×C31—28no—
146C22×C4×C31—28no—
147C22×C4×C31—21no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—21no—
153C22×C4×C31—22no—
154C22×C4×C31—216no—
155C22×C4×C31—28no—
156C22×C4×C31—28no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
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—21no—
173C22×C4×C31—22no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
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—28no—
186C22×C4×C31—22no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—22no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—44no—
197C22×C4×C31—48no—
198C22×C4×C31—48no—
199C22×C4×C31—48no—
200C22×C4×C31—48no—
201C22×C4×C31—44no—
202C22×C4×C31—44no—
203C22×C4×C31C22×C412yes—
204C22×C4×C31C22×C414yes—
205C22×C4×C31C22×C414yes—
206C22×C4×C31C2×D414yes—
207C22×C4×C31C2×D412yes—
208C22×C4×C31C2×D414yes—
209C22×C4×C31C2×D414yes—
210C22×C4×C31C2×D412yes—
211C22×C4×C31C2×D414yes—
212C22×C4×C31#4114yes—
213C4⋊C4×C31—216no—
214C4⋊C4×C31—216no—
215C22⋊C4×C31—28no—
216C22⋊C4×C31—28no—
217C22⋊C4×C31—216no—
218C22⋊C4×C31—48no—
219C22⋊C4×C31—44no—
220C22⋊C4×C31—44no—
221C22⋊C4×C31—44no—
222C42×C31—48no—
223#14019C3111yesmaximal, characteristic, direct product factor, Sylow
224C23×C31—24no—
225C23×C31—24no—
226C23×C31—22no—
227C23×C31—22no—
228C23×C31—24no—
229C23×C31—22no—
230C23×C31—22no—
231C23×C31—24no—
232C23×C31—24no—
233C23×C31—24no—
234C23×C31—24no—
235C23×C31—24no—
236C23×C31—24no—
237C23×C31—24no—
238C23×C31—24no—
239C23×C31—24no—
240C23×C31—22no—
241C23×C31—24no—
242C23×C31—22no—
243C23×C31—22no—
244C23×C31—24no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31—42no—
250C23×C31—41no—
251C23×C31—41no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—42no—
255C23×C31—42no—
256C23×C31—42no—
257C23×C31—42no—
258C23×C31—42no—
259C23×C31—42no—
260C23×C31—42no—
261C23×C31—42no—
262C23×C31—42no—
263C23×C31#11714yes—
264C23×C31C4×D414yes—
265C23×C31C4×D414yes—
266C23×C31#12114yes—
267C23×C31#12314yes—
268C23×C31#12414yes—
269C23×C31#12614yes—
270C23×C31C23×C411yescharacteristic
271C23×C31C22×D411yescharacteristic
272C23×C31C22×D412yes—
273C23×C31C22×D411yescharacteristic
274C23×C31C2×#4111yescharacteristic
275C23×C31C2×#4111yescharacteristic
276C23×C31C2×#4111yescharacteristic
277C23×C31C2×#4112yes—
278C23×C31C2×#4111yescharacteristic
279C23×C31H(5,𝔽2)12yes—
280C23×C312−1+412yes—
281D4×C31—416no—
282C2×C4×C31—232no—
283C2×C4×C31—24no—
284C2×C4×C31—24no—
285C2×C4×C31—24no—
286C2×C4×C31—22no—
287C2×C4×C31—24no—
288C2×C4×C31—24no—
289C2×C4×C31—24no—
290C2×C4×C31—22no—
291C2×C4×C31—24no—
292C2×C4×C31—24no—
293C2×C4×C31—22no—
294C2×C4×C31—24no—
295C2×C4×C31—24no—
296C2×C4×C31—22no—
297C2×C4×C31—22no—
298C2×C4×C31—24no—
299C2×C4×C31—22no—
300C2×C4×C31—24no—
301C2×C4×C31—22no—
302C2×C4×C31—24no—
303C2×C4×C31—22no—
304C2×C4×C31—24no—
305C2×C4×C31—24no—
306C2×C4×C31—24no—
307C2×C4×C31—24no—
308C2×C4×C31—416no—
309C2×C4×C31—416no—
310C2×C4×C31—42no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—42no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31—42no—
322C2×C4×C31—42no—
323C2×C4×C31—42no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—42no—
335C2×C4×C31—42no—
336C2×C4×C31—42no—
337C2×C4×C31—42no—
338C2×C4×C31C4×D418yes—
339C2×C4×C31#12014yes—
340C23×C4⋊C4C2×C3111yescharacteristic, complemented
341C2×#388C2×C3112yescomplemented
342C2×#386C2×C3111yescharacteristic
343C2×#386C2×C3111yescharacteristic
344C2×#386C2×C3111yescharacteristic
345C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
346#1442C2×C3112yescomplemented
347#1439C2×C3112yescomplemented
348#1436C2×C3112yescomplemented
349C22⋊#95C2×C3111yescharacteristic, complemented
350C22⋊#95C2×C3111yescharacteristic, complemented
351C22×C31—24no—
352C22×C31—24no—
353C22×C31—28no—
354C22×C31—28no—
355C22×C31—24no—
356C22×C31—24no—
357C22×C31—24no—
358C22×C31—28no—
359C22×C31—28no—
360C22×C31—24no—
361C22×C31—42no—
362C22×C31—44no—
363C22×C31—44no—
364C22×C31—42no—
365C22×C31—42no—
366C22×C31—81no—
367C22×C31—81no—
368C22×C31—81no—
369C22×C31—81no—
370C22×C31—82no—
371C22×C31—82no—
372C22×C31#38818yescomplemented
373C22×C31C2×#11711yescharacteristic
374C22×C31C2×C4×D411yescharacteristic
375C22×C31C2×C4×D412yes—
376C22×C31C2×C4×D411yescharacteristic
377C22×C31#52012yes—
378C22×C31C2×#12011yescharacteristic
379C22×C31C2×#12111yescharacteristic
380C22×C31C2×#12311yescharacteristic
381C22×C31#52511yescharacteristic
382C22×C31#52512yes—
383C22×C31C2×#12411yescharacteristic
384C22×C31C2×#12611yescharacteristic
385C22×C31#53411yescharacteristic
386C22×C31#53611yescharacteristic
387C22×C31#53912yes—
388C22×C31D4212yes—
389C22×C31#54612yes—
390C22×C31#54712yes—
391C22×C31#54812yes—
392C22×C31#54812yes—
393C22×C31#55212yes—
394C22×C31#55312yes—
395C22×C31#55312yes—
396C4×C31—24no—
397C4×C31—28no—
398C4×C31—44no—
399C4×C31—42no—
400C4×C31—44no—
401C4×C31—44no—
402C4×C31—42no—
403C4×C31—81no—
404C4×C31—81no—
405C23×D4C22×C3111yescharacteristic
406C24×C4C22×C3111yescharacteristic
407C24×C4C22×C3111yescharacteristic
408C24×C4C22×C3111yescharacteristic
409C22×C4⋊C4—24no—
410C22×C4⋊C4—28no—
411C22×C4⋊C4C22×C3112yes—
412C22×C4⋊C4C22×C3112yes—
413C22×C22⋊C4C22×C3111yescharacteristic
414C22×C22⋊C4C22×C3111yescharacteristic
415C22×C22⋊C4C22×C3112yes—
416C22×C22⋊C4C22×C3111yescharacteristic
417C22×C22⋊C4C22×C3112yes—
418C22×C22⋊C4C22×C3111yescharacteristic
419C22×C22⋊C4C22×C3111yescharacteristic
420C22×C42C22×C3112yes—
421#388—28no—
422#386—24no—
423#386—24no—
424#386C4×C3118yescomplemented
425C4×C22⋊C4—24no—
426C2×#95C22×C3112yes—
427C2×#95C22×C3112yes—
428C2×#95C22×C3112yes—
429C2×#95C22×C3111yescharacteristic
430C2×#95C22×C3112yes—
431C2×#95C22×C3112yes—
432C2×#95C22×C3111yescharacteristic
433C2×#95C22×C3112yes—
434C2×#95C22×C3112yes—
435C2×C31—28no—
436C2×C31—82no—
437C2×C31C2×#38811yescharacteristic
438C2×C31C4×#12011yescharacteristic
439C2×C31#232211yescharacteristic
440C2×C31#235212yes—
441C2×C31#236112yes—
442C2×C31#241011yescharacteristic
443C2×C31#241311yescharacteristic
444C2×C31#243611yescharacteristic
445C2×C31#244312yes—
446C2×C31#248112yes—
447C2×C31#259111yescharacteristic
448C25C23×C3111yescharacteristic
449C25C23×C3111yescharacteristic
450C22×D4—22no—
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4C2×C4×C3114yes—
457C23×C4—22no—
458C23×C4—22no—
459C23×C4—24no—
460C23×C4—24no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—24no—
465C23×C4—24no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—42no—
469C23×C4—42no—
470C23×C4C2×C4×C3114yes—
471C23×C4D4×C3114yes—
472C23×C4C23×C3111yescharacteristic
473C23×C4C23×C3111yescharacteristic
474C23×C4C23×C3112yes—
475C23×C4C23×C3111yescharacteristic
476C23×C4C23×C3112yes—
477C23×C4C23×C3111yescharacteristic
478C23×C4C23×C3112yes—
479C23×C4C23×C3112yes—
480C23×C4C23×C3111yescharacteristic
481C2×C4⋊C4—232no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4D4×C3118yescomplemented
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4C2×C4×C3114yes—
505C2×C22⋊C4C2×C4×C3118yescomplemented
506C2×C22⋊C4D4×C3114yes—
507C2×C42—24no—
508C2×C42—24no—
509C2×C42—42no—
510#95—24no—
511#95—24no—
512#95—22no—
513#95—22no—
514#95—24no—
515#95—24no—
516#95—24no—
517#95—42no—
518#95C2×C4×C3118yescomplemented
519C31#1401911yescharacteristic, direct product factor, Sylow
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—21no—
526C24—21no—
527C24—22no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—22no—
533C24—22no—
534C24C22×C4×C3112yes—
535C24C22×C4×C3112yes—
536C24C2×D4×C3112yes—
537C24C2×D4×C3112yes—
538C24#41×C3112yes—
539C24#41×C3112yes—
540C24#41×C3112yes—
541C24#41×C3112yes—
542C24C24×C3111yescharacteristic
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—28no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C22×C4—28no—
551C22×C4—216no—
552C22×C4—28no—
553C22×C4—28no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—216no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—28no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—44no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4C22×C4×C3112yes—
611C22×C4C22×C4×C3114yes—
612C22×C4C22×C4×C3114yes—
613C22×C4C2×D4×C3114yes—
614C22×C4C2×D4×C3112yes—
615C22×C4C2×D4×C3114yes—
616C22×C4C2×D4×C3114yes—
617C22×C4C2×D4×C3112yes—
618C22×C4C2×D4×C3114yes—
619C22×C4#41×C3114yes—
620C4⋊C4—216no—
621C4⋊C4—216no—
622C22⋊C4—28no—
623C22⋊C4—28no—
624C22⋊C4—216no—
625C22⋊C4—48no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C42—48no—
630C23—24no—
631C23—24no—
632C23—22no—
633C23—22no—
634C23—24no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—42no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23C31×#11714yes—
670C23C4×D4×C3114yes—
671C23C4×D4×C3114yes—
672C23C31×#12114yes—
673C23C31×#12314yes—
674C23C31×#12414yes—
675C23C31×#12614yes—
676C23C23×C4×C3111yescharacteristic
677C23C22×D4×C3111yescharacteristic
678C23C22×D4×C3112yes—
679C23C22×D4×C3111yescharacteristic
680C23C2×#41×C3111yescharacteristic
681C23C2×#41×C3111yescharacteristic
682C23C2×#41×C3111yescharacteristic
683C23C2×#41×C3112yes—
684C23C2×#41×C3111yescharacteristic
685C23C31×H(5,𝔽2)12yes—
686C23C31×2−1+412yes—
687D4—416no—
688C2×C4—232no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—416no—
715C2×C4—416no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4C4×D4×C3118yes—
745C2×C4C31×#12014yes—
746C22—24no—
747C22—24no—
748C22—28no—
749C22—28no—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—28no—
754C22—28no—
755C22—24no—
756C22—42no—
757C22—44no—
758C22—44no—
759C22—42no—
760C22—42no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—82no—
766C22—82no—
767C22C31×#38818yescomplemented
768C22C2×C31×#11711yescharacteristic
769C22C2×C4×D4×C3111yescharacteristic
770C22C2×C4×D4×C3112yes—
771C22C2×C4×D4×C3111yescharacteristic
772C22C31×#52012yes—
773C22C2×C31×#12011yescharacteristic
774C22C2×C31×#12111yescharacteristic
775C22C2×C31×#12311yescharacteristic
776C22C31×#52511yescharacteristic
777C22C31×#52512yes—
778C22C2×C31×#12411yescharacteristic
779C22C2×C31×#12611yescharacteristic
780C22C31×#53411yescharacteristic
781C22C31×#53611yescharacteristic
782C22C31×#53912yes—
783C22D42×C3112yes—
784C22C31×#54612yes—
785C22C31×#54712yes—
786C22C31×#54812yes—
787C22C31×#54812yes—
788C22C31×#55212yes—
789C22C31×#55312yes—
790C22C31×#55312yes—
791C4—24no—
792C4—28no—
793C4—44no—
794C4—42no—
795C4—44no—
796C4—44no—
797C4—42no—
798C4—81no—
799C4—81no—
800C2—28no—
801C2—82no—
802C2C2×C31×#38811yescharacteristic
803C2C4×C31×#12011yescharacteristic
804C2C31×#232211yescharacteristic
805C2C31×#235212yes—
806C2C31×#236112yes—
807C2C31×#241011yescharacteristic
808C2C31×#241311yescharacteristic
809C2C31×#243611yescharacteristic
810C2C31×#244312yes—
811C2C31×#248112yes—
812C2C31×#259111yescharacteristic
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
1. C23×C4⋊C4×C31C2semidirect
2. C2×C31×#388C2semidirect
6. C2×C4×C22⋊C4×C31C2semidirect
7. C31×#1442C2semidirect
8. C31×#1439C2semidirect
9. C31×#1436C2semidirect
10. C31×C22⋊#95C2semidirect
11. C31×C22⋊#95C2semidirect
31. C31×#386C4semidirect
81. C2×C4⋊C4×C31D4semidirect
99. C2×C22⋊C4×C31C2×C4semidirect
112. C31×#95C2×C4semidirect
223. #14019C31direct (N × H)
340. C23×C4⋊C4C2×C31semidirect
341. C2×#388C2×C31semidirect
345. C2×C4×C22⋊C4C2×C31semidirect
346. #1442C2×C31semidirect
347. #1439C2×C31semidirect
348. #1436C2×C31semidirect
349. C22⋊#95C2×C31semidirect
350. C22⋊#95C2×C31semidirect
372. C22×C31#388semidirect
424. #386C4×C31semidirect
487. C2×C4⋊C4D4×C31semidirect
505. C2×C22⋊C4C2×C4×C31semidirect
518. #95C2×C4×C31semidirect
519. C31#14019direct (N × H)
767. C22C31×#388semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊C4×C312
C2×C31×#3882
C2×C31×#3862
C2×C4×C22⋊C4×C312
C31×#14422
C31×#14392
C31×#14362
C31×C22⋊#952
#1401931