Finite Group Databasebeta

← C31×#16655 #21473414

Subgroups — C31×#16655 #21473414

Order 7936.

2118 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#126C211yesmaximal, characteristic, complemented
2C2×C31×#394C211yesmaximal, characteristic, complemented
3C2×C31×#392C211yesmaximal, characteristic
4C2×C31×#390C211yesmaximal, characteristic, complemented
5C31×#1441C211yesmaximal, characteristic, complemented
6C31×#1439C212yesmaximal, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1439C211yesmaximal, characteristic, complemented
9C31×#1438C212yesmaximal, complemented
10C31×#1438C212yesmaximal, complemented
11C31×#1434C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C23×D4×C31C2212yes—
14C2×C31×#126—24no—
15C2×C31×#126—24no—
16C2×C31×#126—24no—
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2212yes—
27C22×C22⋊C4×C31C2212yes—
28C22×C22⋊C4×C31C2212yes—
29C22×C22⋊C4×C31C2212yes—
30C22×C42×C31C2211yescharacteristic
31C31×#394—24no—
32C31×#392—24no—
33C31×#390—24no—
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
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—22no—
47C22×D4×C31—22no—
48C22×D4×C31—22no—
49C22×D4×C31—24no—
50C22×D4×C31—42no—
51C22×D4×C31—42no—
52C22×D4×C31—42no—
53C22×D4×C31—42no—
54C22×D4×C31—42no—
55C23×C4×C31C2312yes—
56C23×C4×C31C2312yes—
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2311yescharacteristic
59C23×C4×C31C2311yescharacteristic
60C23×C4×C31C2311yescharacteristic
61C23×C4×C31C2311yescharacteristic
62C23×C4×C31C2312yes—
63C23×C4×C31C2311yescharacteristic
64C31×#126—232no—
65C2×C4⋊C4×C31—22no—
66C2×C4⋊C4×C31—22no—
67C2×C4⋊C4×C31—22no—
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31—22no—
70C2×C4⋊C4×C31—22no—
71C2×C4⋊C4×C31—22no—
72C2×C4⋊C4×C31—22no—
73C2×C4⋊C4×C31—22no—
74C2×C4⋊C4×C31—42no—
75C2×C4⋊C4×C31D414yescomplemented
76C2×C22⋊C4×C31—22no—
77C2×C22⋊C4×C31—22no—
78C2×C22⋊C4×C31—22no—
79C2×C22⋊C4×C31—22no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—22no—
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—24no—
91C2×C22⋊C4×C31—42no—
92C2×C22⋊C4×C31—42no—
93C2×C22⋊C4×C31—42no—
94C2×C22⋊C4×C31—42no—
95C2×C22⋊C4×C31—42no—
96C2×C22⋊C4×C31—42no—
97C2×C22⋊C4×C31—42no—
98C2×C22⋊C4×C31—42no—
99C2×C22⋊C4×C31—42no—
100C2×C22⋊C4×C31—42no—
101C2×C22⋊C4×C31—42no—
102C2×C22⋊C4×C31D414yes—
103C2×C42×C31—22no—
104C2×C42×C31—22no—
105C2×C42×C31D414yescomplemented
106C31×#95—22no—
107C31×#95—22no—
108C31×#95—24no—
109C31×#95—42no—
110C31×#95—42no—
111C31×#95—42no—
112C31×#95—42no—
113C24×C31—21no—
114C24×C31—21no—
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—22no—
126C24×C31—22no—
127C24×C31—22no—
128C24×C31—22no—
129C24×C31—22no—
130C24×C31—22no—
131C24×C31—22no—
132C24×C31—21no—
133C24×C31—21no—
134C24×C31—22no—
135C24×C31—21no—
136C24×C31—22no—
137C24×C31C2×D412yes—
138C24×C31#4114yes—
139C24×C31C2411yescharacteristic
140C2×D4×C31—28no—
141C2×D4×C31—48no—
142C2×D4×C31—48no—
143C2×D4×C31—48no—
144C2×D4×C31—48no—
145C2×D4×C31—44no—
146C2×D4×C31—48no—
147C2×D4×C31—48no—
148C2×D4×C31—48no—
149C2×D4×C31—48no—
150C2×D4×C31—48no—
151C2×D4×C31—44no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—22no—
181C22×C4×C31—22no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—22no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31C2×D412yes—
199C22×C4×C31C2×D412yes—
200C22×C4×C31C2×D412yes—
201C22×C4×C31C2×D412yes—
202C22×C4×C31C2×D412yes—
203C22×C4×C31C2×D412yes—
204C22×C4×C31C2×D412yes—
205C22×C4×C31C2×D412yes—
206C22×C4×C31#4114yes—
207C4⋊C4×C31—28no—
208C4⋊C4×C31—28no—
209C4⋊C4×C31—28no—
210C4⋊C4×C31—44no—
211C22⋊C4×C31—28no—
212C22⋊C4×C31—28no—
213C22⋊C4×C31—28no—
214C22⋊C4×C31—48no—
215C22⋊C4×C31—48no—
216C22⋊C4×C31—48no—
217C22⋊C4×C31—48no—
218C22⋊C4×C31—48no—
219C22⋊C4×C31—48no—
220C42×C31—28no—
221#16655C3111yesmaximal, characteristic, direct product factor, Sylow
222C23×C31—22no—
223C23×C31—24no—
224C23×C31—22no—
225C23×C31—22no—
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—42no—
235C23×C31—41no—
236C23×C31—42no—
237C23×C31—41no—
238C23×C31—42no—
239C23×C31—42no—
240C23×C31—42no—
241C23×C31—42no—
242C23×C31—42no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—41no—
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—42no—
262C23×C31—42no—
263C23×C31—42no—
264C23×C31—42no—
265C23×C31—42no—
266C23×C31—42no—
267C23×C31—42no—
268C23×C31—42no—
269C23×C31—42no—
270C23×C31—42no—
271C23×C31—42no—
272C23×C31—42no—
273C23×C31—42no—
274C23×C31—42no—
275C23×C31—42no—
276C23×C31—42no—
277C23×C31—42no—
278C23×C31—42no—
279C23×C31—42no—
280C23×C31C22×D411yescharacteristic
281C23×C31C22×D411yescharacteristic
282C23×C31C22×D411yescharacteristic
283C23×C31C2×#4112yes—
284C23×C31C2×#4112yes—
285C23×C31H(5,𝔽2)11yescharacteristic
286C23×C31H(5,𝔽2)11yescharacteristic
287C23×C31H(5,𝔽2)11yescharacteristic
288C23×C31H(5,𝔽2)12yes—
289C23×C31H(5,𝔽2)12yes—
290C23×C312−1+411yescharacteristic
291D4×C31—416no—
292D4×C31—432no—
293C2×C4×C31—22no—
294C2×C4×C31—22no—
295C2×C4×C31—24no—
296C2×C4×C31—24no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
299C2×C4×C31—22no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—22no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—24no—
309C2×C4×C31—24no—
310C2×C4×C31—24no—
311C2×C4×C31—24no—
312C2×C4×C31—24no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—42no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—42no—
331C2×C4×C31—42no—
332C2×C4×C31—42no—
333C2×C4×C31—42no—
334C2×C4×C31—42no—
335C2×C4×C31—42no—
336C2×C4×C31—42no—
337C2×C4×C31—42no—
338C2×C4×C31—42no—
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—42no—
346C2×C4×C31—42no—
347C2×C4×C31#12014yes—
348C22×#126C2×C3111yescharacteristic, complemented
349C2×#394C2×C3111yescharacteristic, complemented
350C2×#392C2×C3111yescharacteristic
351C2×#390C2×C3111yescharacteristic, complemented
352#1441C2×C3111yescharacteristic, complemented
353#1439C2×C3112yescomplemented
354#1439C2×C3112yescomplemented
355#1439C2×C3111yescharacteristic, complemented
356#1438C2×C3112yescomplemented
357#1438C2×C3112yescomplemented
358#1434C2×C3111yescharacteristic, complemented
359C22×C31—44no—
360C22×C31—42no—
361C22×C31—44no—
362C22×C31—44no—
363C22×C31—42no—
364C22×C31—44no—
365C22×C31—44no—
366C22×C31—42no—
367C22×C31—44no—
368C22×C31—44no—
369C22×C31—44no—
370C22×C31—44no—
371C22×C31—82no—
372C22×C31—81no—
373C22×C31—81no—
374C22×C31—82no—
375C22×C31—81no—
376C22×C31—82no—
377C22×C31—81no—
378C22×C31—82no—
379C22×C31—82no—
380C22×C31—82no—
381C22×C31—82no—
382C22×C31—82no—
383C22×C31—82no—
384C22×C31—82no—
385C22×C31C2×#12011yescharacteristic
386C22×C31#52511yescharacteristic
387C22×C31#53211yescharacteristic
388C22×C31#53511yescharacteristic
389C22×C31#53511yescharacteristic
390C22×C31#53511yescharacteristic
391C22×C31#53511yescharacteristic
392C22×C31#53511yescharacteristic
393C22×C31#53711yescharacteristic
394C22×C31#53711yescharacteristic
395C22×C31#53711yescharacteristic
396C22×C31#53812yes—
397C22×C31#53812yes—
398C22×C31#53912yes—
399C22×C31#54212yes—
400C22×C31#54612yes—
401C22×C31#54612yes—
402C22×C31#54612yes—
403C22×C31#55012yes—
404C22×C31#55112yes—
405C22×C31#55312yes—
406C22×C31#56012yes—
407C22×C31#56012yes—
408C4×C31—24no—
409C4×C31—42no—
410C4×C31—42no—
411C4×C31—42no—
412C4×C31—44no—
413C4×C31—42no—
414C4×C31—42no—
415C4×C31—82no—
416C4×C31—82no—
417C23×D4C22×C3111yescharacteristic
418C23×D4C22×C3112yes—
419C2×#126—24no—
420C2×#126—24no—
421C2×#126—24no—
422C22×C4⋊C4C22×C3111yescharacteristic
423C22×C4⋊C4C22×C3111yescharacteristic
424C22×C4⋊C4C22×C3111yescharacteristic
425C22×C4⋊C4C22×C3111yescharacteristic
426C22×C22⋊C4C22×C3111yescharacteristic
427C22×C22⋊C4C22×C3111yescharacteristic
428C22×C22⋊C4C22×C3112yes—
429C22×C22⋊C4C22×C3112yes—
430C22×C22⋊C4C22×C3111yescharacteristic
431C22×C22⋊C4C22×C3112yes—
432C22×C22⋊C4C22×C3112yes—
433C22×C22⋊C4C22×C3112yes—
434C22×C22⋊C4C22×C3112yes—
435C22×C42C22×C3111yescharacteristic
436#394—24no—
437#392—24no—
438#390—24no—
439C2×#95C22×C3111yescharacteristic
440C2×#95C22×C3111yescharacteristic
441C2×#95C22×C3112yes—
442C2×#95C22×C3112yes—
443C2×#95C22×C3112yes—
444C2×#95C22×C3112yes—
445C2×#95C22×C3112yes—
446C2×C31—84no—
447C2×C31—82no—
448C2×C31#240411yescharacteristic
449C2×C31#243111yescharacteristic
450C2×C31#260311yescharacteristic
451C2×C31#261511yescharacteristic
452C2×C31#263611yescharacteristic
453C2×C31#266211yescharacteristic
454C2×C31#268512yes—
455C2×C31#269112yes—
456C2×C31#270512yes—
457C2×C31#271412yes—
458C2×C31#281811yescharacteristic
459C25C23×C3111yescharacteristic
460C25C23×C3112yes—
461C22×D4—24no—
462C22×D4—24no—
463C22×D4—24no—
464C22×D4—22no—
465C22×D4—22no—
466C22×D4—22no—
467C22×D4—24no—
468C22×D4—42no—
469C22×D4—42no—
470C22×D4—42no—
471C22×D4—42no—
472C22×D4—42no—
473C23×C4C23×C3112yes—
474C23×C4C23×C3112yes—
475C23×C4C23×C3111yescharacteristic
476C23×C4C23×C3111yescharacteristic
477C23×C4C23×C3111yescharacteristic
478C23×C4C23×C3111yescharacteristic
479C23×C4C23×C3111yescharacteristic
480C23×C4C23×C3112yes—
481C23×C4C23×C3111yescharacteristic
482#126—232no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—42no—
493C2×C4⋊C4D4×C3114yescomplemented
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4D4×C3114yes—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42D4×C3114yescomplemented
524#95—22no—
525#95—22no—
526#95—24no—
527#95—42no—
528#95—42no—
529#95—42no—
530#95—42no—
531C31#1665511yescharacteristic, direct product factor, Sylow
532C24—21no—
533C24—21no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—21no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—21no—
552C24—21no—
553C24—22no—
554C24—21no—
555C24—22no—
556C24C2×D4×C3112yes—
557C24#41×C3114yes—
558C24C24×C3111yescharacteristic
559C2×D4—28no—
560C2×D4—48no—
561C2×D4—48no—
562C2×D4—48no—
563C2×D4—48no—
564C2×D4—44no—
565C2×D4—48no—
566C2×D4—48no—
567C2×D4—48no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—44no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4C2×D4×C3112yes—
618C22×C4C2×D4×C3112yes—
619C22×C4C2×D4×C3112yes—
620C22×C4C2×D4×C3112yes—
621C22×C4C2×D4×C3112yes—
622C22×C4C2×D4×C3112yes—
623C22×C4C2×D4×C3112yes—
624C22×C4C2×D4×C3112yes—
625C22×C4#41×C3114yes—
626C4⋊C4—28no—
627C4⋊C4—28no—
628C4⋊C4—28no—
629C4⋊C4—44no—
630C22⋊C4—28no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C42—28no—
640C23—22no—
641C23—24no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—42no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23C22×D4×C3111yescharacteristic
699C23C22×D4×C3111yescharacteristic
700C23C22×D4×C3111yescharacteristic
701C23C2×#41×C3112yes—
702C23C2×#41×C3112yes—
703C23C31×H(5,𝔽2)11yescharacteristic
704C23C31×H(5,𝔽2)11yescharacteristic
705C23C31×H(5,𝔽2)11yescharacteristic
706C23C31×H(5,𝔽2)12yes—
707C23C31×H(5,𝔽2)12yes—
708C23C31×2−1+411yescharacteristic
709D4—416no—
710D4—432no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4C31×#12014yes—
766C22—44no—
767C22—42no—
768C22—44no—
769C22—44no—
770C22—42no—
771C22—44no—
772C22—44no—
773C22—42no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—81no—
779C22—82no—
780C22—81no—
781C22—82no—
782C22—81no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—81no—
792C22C2×C31×#12011yescharacteristic
793C22C31×#52511yescharacteristic
794C22C31×#53211yescharacteristic
795C22C31×#53511yescharacteristic
796C22C31×#53511yescharacteristic
797C22C31×#53511yescharacteristic
798C22C31×#53511yescharacteristic
799C22C31×#53511yescharacteristic
800C22C31×#53711yescharacteristic
801C22C31×#53711yescharacteristic
802C22C31×#53711yescharacteristic
803C22C31×#53812yes—
804C22C31×#53812yes—
805C22C31×#53912yes—
806C22C31×#54212yes—
807C22C31×#54612yes—
808C22C31×#54612yes—
809C22C31×#54612yes—
810C22C31×#55012yes—
811C22C31×#55112yes—
812C22C31×#55312yes—
813C22C31×#56012yes—
814C22C31×#56012yes—
815C4—24no—
816C4—42no—
817C4—42no—
818C4—42no—
819C4—44no—
820C4—42no—
821C4—42no—
822C4—82no—
823C4—82no—
824C2—84no—
825C2—82no—
826C2C31×#240411yescharacteristic
827C2C31×#243111yescharacteristic
828C2C31×#260311yescharacteristic
829C2C31×#261511yescharacteristic
830C2C31×#263611yescharacteristic
831C2C31×#266211yescharacteristic
832C2C31×#268512yes—
833C2C31×#269112yes—
834C2C31×#270512yes—
835C2C31×#271412yes—
836C2C31×#281811yescharacteristic
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×C31×#126C2semidirect
2. C2×C31×#394C2semidirect
4. C2×C31×#390C2semidirect
5. C31×#1441C2semidirect
6. C31×#1439C2semidirect
7. C31×#1439C2semidirect
8. C31×#1439C2semidirect
9. C31×#1438C2semidirect
10. C31×#1438C2semidirect
11. C31×#1434C2semidirect
75. C2×C4⋊C4×C31D4semidirect
105. C2×C42×C31D4semidirect
221. #16655C31direct (N × H)
348. C22×#126C2×C31semidirect
349. C2×#394C2×C31semidirect
351. C2×#390C2×C31semidirect
352. #1441C2×C31semidirect
353. #1439C2×C31semidirect
354. #1439C2×C31semidirect
355. #1439C2×C31semidirect
356. #1438C2×C31semidirect
357. #1438C2×C31semidirect
358. #1434C2×C31semidirect
493. C2×C4⋊C4D4×C31semidirect
523. C2×C42D4×C31semidirect
531. C31#16655direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1262
C2×C31×#3942
C2×C31×#3922
C2×C31×#3902
C31×#14412
C31×#14392
C31×#14382
C31×#14342
#1665531