Finite Group Databasebeta

← C31×#15159 #21471918

Subgroups — C31×#15159 #21471918

Order 7936.

2578 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C31C211yesmaximal, characteristic, complemented
2C2×C31×#394C211yesmaximal, characteristic, complemented
3C2×C31×#392C211yesmaximal, characteristic
4C2×C31×#388C211yesmaximal, characteristic, complemented
5C2×C31×#386C212yesmaximal, complemented
6C31×#1441C211yesmaximal, characteristic, complemented
7C31×#1440C212yesmaximal, complemented
8C31×#1439C211yesmaximal, characteristic, complemented
9C31×#1438C212yesmaximal, complemented
10C31×#1434C211yesmaximal, characteristic, complemented
11C31×C22⋊#95C212yesmaximal, complemented
12C23×D4×C31C2211yescharacteristic
13C23×D4×C31C2212yes—
14C24×C4×C31C2212yes—
15C2×C4×D4×C31—28no—
16C2×C4×D4×C31—24no—
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2212yes—
27C22×C42×C31C2211yescharacteristic
28C31×#394—24no—
29C31×#392—24no—
30C31×#388—24no—
31C31×#386—28no—
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2212yes—
41C25×C31C2311yescharacteristic
42C25×C31C2312yes—
43C22×D4×C31—24no—
44C22×D4×C31—24no—
45C22×D4×C31—24no—
46C22×D4×C31—24no—
47C22×D4×C31—24no—
48C22×D4×C31—24no—
49C22×D4×C31—22no—
50C22×D4×C31—22no—
51C22×D4×C31—24no—
52C22×D4×C31—42no—
53C22×D4×C31—42no—
54C22×D4×C31D414yes—
55C23×C4×C31—24no—
56C23×C4×C31—24no—
57C23×C4×C31—42no—
58C23×C4×C31—42no—
59C23×C4×C31—42no—
60C23×C4×C31—42no—
61C23×C4×C31D418yescomplemented
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2312yes—
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2312yes—
67C23×C4×C31C2311yescharacteristic
68C23×C4×C31C2312yes—
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C4×D4×C31—232no—
72C2×C4⋊C4×C31—24no—
73C2×C4⋊C4×C31—22no—
74C2×C4⋊C4×C31—22no—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31—22no—
77C2×C22⋊C4×C31—24no—
78C2×C22⋊C4×C31—22no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—24no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—24no—
84C2×C22⋊C4×C31—24no—
85C2×C22⋊C4×C31—24no—
86C2×C22⋊C4×C31—24no—
87C2×C22⋊C4×C31—24no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—24no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—42no—
97C2×C22⋊C4×C31—42no—
98C2×C22⋊C4×C31—42no—
99C2×C22⋊C4×C31—42no—
100C2×C42×C31—24no—
101C2×C42×C31D414yescomplemented
102C31×#95—24no—
103C31×#95—24no—
104C31×#95—22no—
105C31×#95—22no—
106C31×#95—22no—
107C31×#95—22no—
108C31×#95—24no—
109C31×#95—42no—
110C31×#95—42no—
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—22no—
125C24×C31—21no—
126C24×C31—21no—
127C24×C31—21no—
128C24×C31—22no—
129C24×C31—22no—
130C24×C31—21no—
131C24×C31—22no—
132C24×C31—21no—
133C24×C31C2×D414yes—
134C24×C31C2×D414yes—
135C24×C31#4112yes—
136C24×C31#4114yes—
137C24×C31C2411yescharacteristic
138C2×D4×C31—28no—
139C2×D4×C31—28no—
140C2×D4×C31—216no—
141C2×D4×C31—216no—
142C2×D4×C31—216no—
143C2×D4×C31—28no—
144C2×D4×C31—48no—
145C2×D4×C31—48no—
146C2×D4×C31—48no—
147C2×D4×C31—48no—
148C2×D4×C31—48no—
149C2×D4×C31—48no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—21no—
153C22×C4×C31—22no—
154C22×C4×C31—21no—
155C22×C4×C31—22no—
156C22×C4×C31—21no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31—21no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—21no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—21no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—216no—
178C22×C4×C31—21no—
179C22×C4×C31—22no—
180C22×C4×C31—22no—
181C22×C4×C31—22no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—21no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—21no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—48no—
196C22×C4×C31—48no—
197C22×C4×C31—48no—
198C22×C4×C31—48no—
199C22×C4×C31—48no—
200C22×C4×C31—48no—
201C22×C4×C31C2×D412yes—
202C22×C4×C31C2×D414yes—
203C22×C4×C31C2×D414yes—
204C22×C4×C31C2×D412yes—
205C22×C4×C31C2×D412yes—
206C22×C4×C31C2×D412yes—
207C22×C4×C31#4114yes—
208C22×C4×C31#4112yes—
209C22×C4×C31#4112yes—
210C4⋊C4×C31—28no—
211C4⋊C4×C31—44no—
212C22⋊C4×C31—28no—
213C22⋊C4×C31—216no—
214C22⋊C4×C31—48no—
215C22⋊C4×C31—48no—
216C22⋊C4×C31—48no—
217C22⋊C4×C31—48no—
218C22⋊C4×C31—44no—
219C22⋊C4×C31—44no—
220C42×C31—28no—
221#15159C3111yesmaximal, characteristic, direct product factor, Sylow
222C23×C31—24no—
223C23×C31—24no—
224C23×C31—24no—
225C23×C31—24no—
226C23×C31—24no—
227C23×C31—24no—
228C23×C31—24no—
229C23×C31—24no—
230C23×C31—24no—
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—24no—
244C23×C31—22no—
245C23×C31—42no—
246C23×C31—42no—
247C23×C31—42no—
248C23×C31—42no—
249C23×C31—42no—
250C23×C31—42no—
251C23×C31—42no—
252C23×C31—42no—
253C23×C31—42no—
254C23×C31—42no—
255C23×C31—42no—
256C23×C31—42no—
257C23×C31—42no—
258C23×C31—42no—
259C23×C31—42no—
260C23×C31—42no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—42no—
264C23×C31—41no—
265C23×C31—42no—
266C23×C31—42no—
267C23×C31—41no—
268C23×C31—42no—
269C23×C31—42no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—42no—
273C23×C31—41no—
274C23×C31—42no—
275C23×C31—42no—
276C23×C31—42no—
277C23×C31—41no—
278C23×C31—42no—
279C23×C31#12118yes—
280C23×C31C22×D412yes—
281C23×C31C22×D411yescharacteristic
282C23×C31C22×D411yescharacteristic
283C23×C31C2×#4112yes—
284C23×C31C2×#4111yescharacteristic
285C23×C31C2×#4111yescharacteristic
286C23×C31C2×#4112yes—
287C23×C31C2×#4111yescharacteristic
288C23×C31H(5,𝔽2)11yescharacteristic
289C23×C31H(5,𝔽2)12yes—
290C23×C31H(5,𝔽2)11yescharacteristic
291D4×C31—232no—
292D4×C31—432no—
293C2×C4×C31—22no—
294C2×C4×C31—24no—
295C2×C4×C31—22no—
296C2×C4×C31—24no—
297C2×C4×C31—24no—
298C2×C4×C31—24no—
299C2×C4×C31—22no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—24no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—24no—
306C2×C4×C31—22no—
307C2×C4×C31—24no—
308C2×C4×C31—24no—
309C2×C4×C31—22no—
310C2×C4×C31—24no—
311C2×C4×C31—24no—
312C2×C4×C31—22no—
313C2×C4×C31—432no—
314C2×C4×C31—41no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31—41no—
322C2×C4×C31—42no—
323C2×C4×C31—42no—
324C2×C4×C31—41no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—42no—
330C2×C4×C31—42no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—42no—
335C2×C4×C31—42no—
336C2×C4×C31—41no—
337C2×C4×C31—42no—
338C2×C4×C31—41no—
339C2×C4×C31—42no—
340C2×C4×C31—42no—
341C2×C4×C31—42no—
342C2×C4×C31—42no—
343C2×C4×C31—42no—
344C2×C4×C31—42no—
345C2×C4×C31#12014yes—
346C2×C4×C31#12114yes—
347C22×C4×D4C2×C3111yescharacteristic, complemented
348C2×#394C2×C3111yescharacteristic, complemented
349C2×#392C2×C3111yescharacteristic
350C2×#388C2×C3111yescharacteristic, complemented
351C2×#386C2×C3112yescomplemented
352#1441C2×C3111yescharacteristic, complemented
353#1440C2×C3112yescomplemented
354#1439C2×C3111yescharacteristic, complemented
355#1438C2×C3112yescomplemented
356#1434C2×C3111yescharacteristic, complemented
357C22⋊#95C2×C3112yescomplemented
358C22×C31—28no—
359C22×C31—28no—
360C22×C31—28no—
361C22×C31—44no—
362C22×C31—44no—
363C22×C31—44no—
364C22×C31—44no—
365C22×C31—44no—
366C22×C31—44no—
367C22×C31—44no—
368C22×C31—44no—
369C22×C31—44no—
370C22×C31—44no—
371C22×C31—44no—
372C22×C31—44no—
373C22×C31—42no—
374C22×C31—44no—
375C22×C31—42no—
376C22×C31—44no—
377C22×C31—42no—
378C22×C31—81no—
379C22×C31—82no—
380C22×C31—81no—
381C22×C31—81no—
382C22×C31—82no—
383C22×C31—81no—
384C22×C31C2×#12011yescharacteristic
385C22×C31C2×#12112yes—
386C22×C31C2×#12111yescharacteristic
387C22×C31#52511yescharacteristic
388C22×C31#52512yes—
389C22×C31#52511yescharacteristic
390C22×C31#52512yes—
391C22×C31#53212yes—
392C22×C31#53211yescharacteristic
393C22×C31#53412yes—
394C22×C31#53412yes—
395C22×C31#53511yescharacteristic
396C22×C31#53511yescharacteristic
397C22×C31#54611yescharacteristic
398C22×C31#54612yes—
399C22×C31#54611yescharacteristic
400C22×C31#55112yes—
401C22×C31#55112yes—
402C22×C31#55312yes—
403C22×C31#55311yescharacteristic
404C22×C31#55312yes—
405C22×C31#55311yescharacteristic
406C22×C31#55912yes—
407C4×C31—24no—
408C4×C31—24no—
409C4×C31—44no—
410C4×C31—42no—
411C4×C31—44no—
412C4×C31—42no—
413C4×C31—81no—
414C4×C31—82no—
415C4×C31—81no—
416C23×D4C22×C3111yescharacteristic
417C23×D4C22×C3112yes—
418C24×C4C22×C3112yes—
419C2×C4×D4—28no—
420C2×C4×D4—24no—
421C22×C4⋊C4C22×C3111yescharacteristic
422C22×C4⋊C4C22×C3111yescharacteristic
423C22×C22⋊C4C22×C3111yescharacteristic
424C22×C22⋊C4C22×C3112yes—
425C22×C22⋊C4C22×C3112yes—
426C22×C22⋊C4C22×C3111yescharacteristic
427C22×C22⋊C4C22×C3111yescharacteristic
428C22×C22⋊C4C22×C3112yes—
429C22×C22⋊C4C22×C3112yes—
430C22×C22⋊C4C22×C3112yes—
431C22×C42C22×C3111yescharacteristic
432#394—24no—
433#392—24no—
434#388—24no—
435#386—28no—
436C2×#95C22×C3111yescharacteristic
437C2×#95C22×C3111yescharacteristic
438C2×#95C22×C3111yescharacteristic
439C2×#95C22×C3112yes—
440C2×#95C22×C3112yes—
441C2×#95C22×C3111yescharacteristic
442C2×#95C22×C3112yes—
443C2×#95C22×C3112yes—
444C2×#95C22×C3112yes—
445C2×C31—48no—
446C2×C31—82no—
447C2×C31#238811yescharacteristic
448C2×C31#253412yes—
449C2×C31#253511yescharacteristic
450C2×C31#254312yes—
451C2×C31#254411yescharacteristic
452C2×C31#259811yescharacteristic
453C2×C31#260012yes—
454C2×C31#260212yes—
455C2×C31#260311yescharacteristic
456C2×C31#261311yescharacteristic
457C2×C31#284711yescharacteristic
458C25C23×C3111yescharacteristic
459C25C23×C3112yes—
460C22×D4—24no—
461C22×D4—24no—
462C22×D4—24no—
463C22×D4—24no—
464C22×D4—24no—
465C22×D4—24no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—24no—
469C22×D4—42no—
470C22×D4—42no—
471C22×D4D4×C3114yes—
472C23×C4—24no—
473C23×C4—24no—
474C23×C4—42no—
475C23×C4—42no—
476C23×C4—42no—
477C23×C4—42no—
478C23×C4D4×C3118yescomplemented
479C23×C4C23×C3111yescharacteristic
480C23×C4C23×C3111yescharacteristic
481C23×C4C23×C3112yes—
482C23×C4C23×C3111yescharacteristic
483C23×C4C23×C3112yes—
484C23×C4C23×C3111yescharacteristic
485C23×C4C23×C3112yes—
486C23×C4C23×C3111yescharacteristic
487C23×C4C23×C3111yescharacteristic
488C4×D4—232no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C42—24no—
518C2×C42D4×C3114yescomplemented
519#95—24no—
520#95—24no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—24no—
526#95—42no—
527#95—42no—
528C31#1515911yescharacteristic, direct product factor, Sylow
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—21no—
542C24—22no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—22no—
547C24—22no—
548C24—21no—
549C24—22no—
550C24—21no—
551C24C2×D4×C3114yes—
552C24C2×D4×C3114yes—
553C24#41×C3112yes—
554C24#41×C3114yes—
555C24C24×C3111yescharacteristic
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—216no—
559C2×D4—216no—
560C2×D4—216no—
561C2×D4—28no—
562C2×D4—48no—
563C2×D4—48no—
564C2×D4—48no—
565C2×D4—48no—
566C2×D4—48no—
567C2×D4—48no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—216no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4C2×D4×C3112yes—
620C22×C4C2×D4×C3114yes—
621C22×C4C2×D4×C3114yes—
622C22×C4C2×D4×C3112yes—
623C22×C4C2×D4×C3112yes—
624C22×C4C2×D4×C3112yes—
625C22×C4#41×C3114yes—
626C22×C4#41×C3112yes—
627C22×C4#41×C3112yes—
628C4⋊C4—28no—
629C4⋊C4—44no—
630C22⋊C4—28no—
631C22⋊C4—216no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C42—28no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—22no—
658C23—24no—
659C23—22no—
660C23—24no—
661C23—22no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—42no—
684C23—41no—
685C23—42no—
686C23—42no—
687C23—41no—
688C23—41no—
689C23—42no—
690C23—41no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—41no—
695C23—42no—
696C23C31×#12118yes—
697C23C22×D4×C3112yes—
698C23C22×D4×C3111yescharacteristic
699C23C22×D4×C3111yescharacteristic
700C23C2×#41×C3112yes—
701C23C2×#41×C3111yescharacteristic
702C23C2×#41×C3111yescharacteristic
703C23C2×#41×C3112yes—
704C23C2×#41×C3111yescharacteristic
705C23C31×H(5,𝔽2)11yescharacteristic
706C23C31×H(5,𝔽2)12yes—
707C23C31×H(5,𝔽2)11yescharacteristic
708D4—232no—
709D4—432no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—432no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4C31×#12014yes—
763C2×C4C31×#12114yes—
764C22—28no—
765C22—28no—
766C22—28no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—42no—
780C22—44no—
781C22—42no—
782C22—44no—
783C22—42no—
784C22—81no—
785C22—82no—
786C22—81no—
787C22—81no—
788C22—82no—
789C22—81no—
790C22C2×C31×#12011yescharacteristic
791C22C2×C31×#12112yes—
792C22C2×C31×#12111yescharacteristic
793C22C31×#52511yescharacteristic
794C22C31×#52512yes—
795C22C31×#52511yescharacteristic
796C22C31×#52512yes—
797C22C31×#53212yes—
798C22C31×#53211yescharacteristic
799C22C31×#53412yes—
800C22C31×#53412yes—
801C22C31×#53511yescharacteristic
802C22C31×#53511yescharacteristic
803C22C31×#54611yescharacteristic
804C22C31×#54612yes—
805C22C31×#54611yescharacteristic
806C22C31×#55112yes—
807C22C31×#55112yes—
808C22C31×#55312yes—
809C22C31×#55311yescharacteristic
810C22C31×#55312yes—
811C22C31×#55311yescharacteristic
812C22C31×#55912yes—
813C4—24no—
814C4—24no—
815C4—44no—
816C4—42no—
817C4—44no—
818C4—42no—
819C4—81no—
820C4—82no—
821C4—81no—
822C2—48no—
823C2—82no—
824C2C31×#238811yescharacteristic
825C2C31×#253412yes—
826C2C31×#253511yescharacteristic
827C2C31×#254312yes—
828C2C31×#254411yescharacteristic
829C2C31×#259811yescharacteristic
830C2C31×#260012yes—
831C2C31×#260212yes—
832C2C31×#260311yescharacteristic
833C2C31×#261311yescharacteristic
834C2C31×#284711yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC2×C31×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×D4×C31C2semidirect
2. C2×C31×#394C2semidirect
4. C2×C31×#388C2semidirect
5. C2×C31×#386C2semidirect
6. C31×#1441C2semidirect
7. C31×#1440C2semidirect
8. C31×#1439C2semidirect
9. C31×#1438C2semidirect
10. C31×#1434C2semidirect
11. C31×C22⋊#95C2semidirect
61. C23×C4×C31D4semidirect
101. C2×C42×C31D4semidirect
221. #15159C31direct (N × H)
347. C22×C4×D4C2×C31semidirect
348. C2×#394C2×C31semidirect
350. C2×#388C2×C31semidirect
351. C2×#386C2×C31semidirect
352. #1441C2×C31semidirect
353. #1440C2×C31semidirect
354. #1439C2×C31semidirect
355. #1438C2×C31semidirect
356. #1434C2×C31semidirect
357. C22⋊#95C2×C31semidirect
478. C23×C4D4×C31semidirect
518. C2×C42D4×C31semidirect
528. C31#15159direct (N × H)

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×#3942
C2×C31×#3922
C2×C31×#3882
C2×C31×#3862
C31×#14412
C31×#14402
C31×#14392
C31×#14382
C31×#14342
C31×C22⋊#952
#1515931