Finite Group Databasebeta

← C31×#16819 #21473578

Subgroups — C31×#16819 #21473578

Order 7936.

2006 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#394C212yesmaximal, complemented
2C2×C31×#394C211yesmaximal, characteristic, complemented
3C2×C31×#392C211yesmaximal, characteristic
4C2×C31×#390C211yesmaximal, characteristic, complemented
5C2×C31×#388C211yesmaximal, characteristic, complemented
6C31×#1441C211yesmaximal, characteristic, complemented
7C31×#1440C212yesmaximal, complemented
8C31×#1439C211yesmaximal, characteristic, complemented
9C31×#1439C212yesmaximal, complemented
10C31×#1438C212yesmaximal, complemented
11C31×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C31C2212yes—
13C23×D4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2212yes—
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C22⋊C4×C31C2211yescharacteristic
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2212yes—
26C22×C42×C31C2211yescharacteristic
27C31×#394—24no—
28C31×#394—28no—
29C31×#392—24no—
30C31×#390—24no—
31C31×#388—24no—
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2212yes—
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C25×C31C2311yescharacteristic
41C25×C31C2312yes—
42C22×D4×C31—24no—
43C22×D4×C31—24no—
44C22×D4×C31—22no—
45C22×D4×C31—22no—
46C22×D4×C31—24no—
47C22×D4×C31—42no—
48C22×D4×C31—42no—
49C22×D4×C31—42no—
50C22×D4×C31—42no—
51C22×D4×C31—42no—
52C22×D4×C31—42no—
53C22×D4×C31D414yes—
54C23×C4×C31C2312yes—
55C23×C4×C31C2312yes—
56C23×C4×C31C2311yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2311yescharacteristic
59C23×C4×C31C2311yescharacteristic
60C23×C4×C31C2312yes—
61C23×C4×C31C2311yescharacteristic
62C23×C4×C31C2311yescharacteristic
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31—22no—
65C2×C4⋊C4×C31—24no—
66C2×C4⋊C4×C31—22no—
67C2×C4⋊C4×C31—24no—
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31—42no—
70C2×C4⋊C4×C31—42no—
71C2×C22⋊C4×C31—22no—
72C2×C22⋊C4×C31—22no—
73C2×C22⋊C4×C31—24no—
74C2×C22⋊C4×C31—24no—
75C2×C22⋊C4×C31—24no—
76C2×C22⋊C4×C31—24no—
77C2×C22⋊C4×C31—22no—
78C2×C22⋊C4×C31—22no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—24no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—24no—
83C2×C22⋊C4×C31—24no—
84C2×C22⋊C4×C31—24no—
85C2×C22⋊C4×C31—24no—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—42no—
88C2×C22⋊C4×C31—42no—
89C2×C22⋊C4×C31—42no—
90C2×C22⋊C4×C31—42no—
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×C31D414yescomplemented
97C2×C42×C31—42no—
98C2×C42×C31D414yescomplemented
99C31×#95—22no—
100C31×#95—22no—
101C31×#95—22no—
102C31×#95—24no—
103C31×#95—22no—
104C31×#95—42no—
105C31×#95—42no—
106C31×#95—42no—
107C24×C31—21no—
108C24×C31—22no—
109C24×C31—22no—
110C24×C31—21no—
111C24×C31—21no—
112C24×C31—22no—
113C24×C31—21no—
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—22no—
124C24×C31—22no—
125C24×C31—22no—
126C24×C31—22no—
127C24×C31—22no—
128C24×C31—21no—
129C24×C31—22no—
130C24×C31—21no—
131C24×C31C2×D414yes—
132C24×C31C2×D412yes—
133C24×C31C2411yescharacteristic
134C2×D4×C31—28no—
135C2×D4×C31—48no—
136C2×D4×C31—48no—
137C2×D4×C31—48no—
138C2×D4×C31—44no—
139C2×D4×C31—44no—
140C2×D4×C31—48no—
141C2×D4×C31—48no—
142C2×D4×C31—48no—
143C2×D4×C31—48no—
144C2×D4×C31—48no—
145C2×D4×C31—48no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—21no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—21no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
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—21no—
171C22×C4×C31—22no—
172C22×C4×C31—21no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—21no—
176C22×C4×C31—22no—
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—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—22no—
189C22×C4×C31—22no—
190C22×C4×C31C2×D412yes—
191C22×C4×C31C2×D412yes—
192C22×C4×C31C2×D412yes—
193C22×C4×C31C2×D412yes—
194C22×C4×C31C2×D412yes—
195C22×C4×C31C2×D412yes—
196C22×C4×C31#4114yes—
197C22×C4×C31#4112yes—
198C22×C4×C31#4112yes—
199C4⋊C4×C31—48no—
200C4⋊C4×C31—44no—
201C4⋊C4×C31—44no—
202C22⋊C4×C31—28no—
203C22⋊C4×C31—48no—
204C22⋊C4×C31—48no—
205C22⋊C4×C31—44no—
206C22⋊C4×C31—48no—
207C22⋊C4×C31—48no—
208C22⋊C4×C31—48no—
209C22⋊C4×C31—48no—
210C22⋊C4×C31—44no—
211C42×C31—44no—
212#16819C3111yesmaximal, characteristic, direct product factor, Sylow
213C23×C31—22no—
214C23×C31—24no—
215C23×C31—24no—
216C23×C31—24no—
217C23×C31—24no—
218C23×C31—24no—
219C23×C31—22no—
220C23×C31—24no—
221C23×C31—24no—
222C23×C31—24no—
223C23×C31—24no—
224C23×C31—22no—
225C23×C31—41no—
226C23×C31—42no—
227C23×C31—41no—
228C23×C31—42no—
229C23×C31—41no—
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—41no—
239C23×C31—42no—
240C23×C31—42no—
241C23×C31—42no—
242C23×C31—42no—
243C23×C31—42no—
244C23×C31—42no—
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—41no—
256C23×C31—42no—
257C23×C31—42no—
258C23×C31—42no—
259C23×C31—42no—
260C23×C31—41no—
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×C31C22×D411yescharacteristic
272C23×C31C22×D411yescharacteristic
273C23×C31C22×D411yescharacteristic
274C23×C31C2×#4111yescharacteristic
275C23×C31C2×#4111yescharacteristic
276C23×C31C2×#4112yes—
277C23×C31H(5,𝔽2)12yes—
278C23×C31H(5,𝔽2)12yes—
279C23×C31H(5,𝔽2)12yes—
280C23×C31H(5,𝔽2)11yescharacteristic
281C23×C312−1+411yescharacteristic
282D4×C31—416no—
283D4×C31—432no—
284C2×C4×C31—22no—
285C2×C4×C31—22no—
286C2×C4×C31—22no—
287C2×C4×C31—24no—
288C2×C4×C31—22no—
289C2×C4×C31—24no—
290C2×C4×C31—24no—
291C2×C4×C31—24no—
292C2×C4×C31—22no—
293C2×C4×C31—22no—
294C2×C4×C31—22no—
295C2×C4×C31—22no—
296C2×C4×C31—24no—
297C2×C4×C31—22no—
298C2×C4×C31—24no—
299C2×C4×C31—24no—
300C2×C4×C31—22no—
301C2×C4×C31—41no—
302C2×C4×C31—42no—
303C2×C4×C31—42no—
304C2×C4×C31—41no—
305C2×C4×C31—42no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—42no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—42no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—42no—
316C2×C4×C31—41no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31—42no—
322C2×C4×C31—41no—
323C2×C4×C31—42no—
324C2×C4×C31—41no—
325C2×C4×C31—42no—
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#12114yes—
336C2×C4×C31#12114yes—
337C2×#394C2×C3112yescomplemented
338C2×#394C2×C3111yescharacteristic, complemented
339C2×#392C2×C3111yescharacteristic
340C2×#390C2×C3111yescharacteristic, complemented
341C2×#388C2×C3111yescharacteristic, complemented
342#1441C2×C3111yescharacteristic, complemented
343#1440C2×C3112yescomplemented
344#1439C2×C3111yescharacteristic, complemented
345#1439C2×C3112yescomplemented
346#1438C2×C3112yescomplemented
347C4⋊#95C2×C3111yescharacteristic, complemented
348C22×C31—44no—
349C22×C31—42no—
350C22×C31—44no—
351C22×C31—44no—
352C22×C31—44no—
353C22×C31—44no—
354C22×C31—44no—
355C22×C31—44no—
356C22×C31—42no—
357C22×C31—44no—
358C22×C31—42no—
359C22×C31—44no—
360C22×C31—81no—
361C22×C31—82no—
362C22×C31—82no—
363C22×C31—81no—
364C22×C31—82no—
365C22×C31—82no—
366C22×C31—82no—
367C22×C31—82no—
368C22×C31—81no—
369C22×C31—82no—
370C22×C31—82no—
371C22×C31—82no—
372C22×C31—81no—
373C22×C31—82no—
374C22×C31C2×#12111yescharacteristic
375C22×C31C2×#12111yescharacteristic
376C22×C31#53211yescharacteristic
377C22×C31#53412yes—
378C22×C31#53411yescharacteristic
379C22×C31#53511yescharacteristic
380C22×C31#53512yes—
381C22×C31#53511yescharacteristic
382C22×C31#53711yescharacteristic
383C22×C31#53812yes—
384C22×C31#53812yes—
385C22×C31#54012yes—
386C22×C31#54212yes—
387C22×C31D4211yescharacteristic
388C22×C31#54612yes—
389C22×C31#54612yes—
390C22×C31#54711yescharacteristic
391C22×C31#54711yescharacteristic
392C22×C31#55312yes—
393C22×C31#55511yescharacteristic
394C22×C31#55912yes—
395C22×C31#56012yes—
396C22×C31#56212yes—
397C4×C31—24no—
398C4×C31—24no—
399C4×C31—44no—
400C4×C31—42no—
401C4×C31—42no—
402C4×C31—81no—
403C4×C31—82no—
404C4×C31—82no—
405C4×C31—81no—
406C23×D4C22×C3112yes—
407C23×D4C22×C3111yescharacteristic
408C22×C4⋊C4C22×C3111yescharacteristic
409C22×C4⋊C4C22×C3112yes—
410C22×C4⋊C4C22×C3111yescharacteristic
411C22×C22⋊C4C22×C3111yescharacteristic
412C22×C22⋊C4C22×C3112yes—
413C22×C22⋊C4C22×C3112yes—
414C22×C22⋊C4C22×C3112yes—
415C22×C22⋊C4C22×C3111yescharacteristic
416C22×C22⋊C4C22×C3112yes—
417C22×C22⋊C4C22×C3112yes—
418C22×C22⋊C4C22×C3111yescharacteristic
419C22×C22⋊C4C22×C3112yes—
420C22×C42C22×C3111yescharacteristic
421#394—24no—
422#394—28no—
423#392—24no—
424#390—24no—
425#388—24no—
426C2×#95C22×C3111yescharacteristic
427C2×#95C22×C3111yescharacteristic
428C2×#95C22×C3112yes—
429C2×#95C22×C3111yescharacteristic
430C2×#95C22×C3111yescharacteristic
431C2×#95C22×C3112yes—
432C2×#95C22×C3112yes—
433C2×#95C22×C3112yes—
434C2×C31—84no—
435C2×C31—82no—
436C2×C31#253711yescharacteristic
437C2×C31#254311yescharacteristic
438C2×C31#254411yescharacteristic
439C2×C31#261711yescharacteristic
440C2×C31#261911yescharacteristic
441C2×C31#266211yescharacteristic
442C2×C31#267812yes—
443C2×C31#270112yes—
444C2×C31#271012yes—
445C2×C31#280312yes—
446C2×C31#281311yescharacteristic
447C25C23×C3111yescharacteristic
448C25C23×C3112yes—
449C22×D4—24no—
450C22×D4—24no—
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—24no—
454C22×D4—42no—
455C22×D4—42no—
456C22×D4—42no—
457C22×D4—42no—
458C22×D4—42no—
459C22×D4—42no—
460C22×D4D4×C3114yes—
461C23×C4C23×C3112yes—
462C23×C4C23×C3112yes—
463C23×C4C23×C3111yescharacteristic
464C23×C4C23×C3111yescharacteristic
465C23×C4C23×C3111yescharacteristic
466C23×C4C23×C3111yescharacteristic
467C23×C4C23×C3112yes—
468C23×C4C23×C3111yescharacteristic
469C23×C4C23×C3111yescharacteristic
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4D4×C3114yescomplemented
504C2×C42—42no—
505C2×C42D4×C3114yescomplemented
506#95—22no—
507#95—22no—
508#95—22no—
509#95—24no—
510#95—22no—
511#95—42no—
512#95—42no—
513#95—42no—
514C31#1681911yescharacteristic, direct product factor, Sylow
515C24—21no—
516C24—22no—
517C24—22no—
518C24—21no—
519C24—21no—
520C24—22no—
521C24—21no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—21no—
537C24—22no—
538C24—21no—
539C24C2×D4×C3114yes—
540C24C2×D4×C3112yes—
541C24C24×C3111yescharacteristic
542C2×D4—28no—
543C2×D4—48no—
544C2×D4—48no—
545C2×D4—48no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—48no—
549C2×D4—48no—
550C2×D4—48no—
551C2×D4—48no—
552C2×D4—48no—
553C2×D4—48no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4C2×D4×C3112yes—
599C22×C4C2×D4×C3112yes—
600C22×C4C2×D4×C3112yes—
601C22×C4C2×D4×C3112yes—
602C22×C4C2×D4×C3112yes—
603C22×C4C2×D4×C3112yes—
604C22×C4#41×C3114yes—
605C22×C4#41×C3112yes—
606C22×C4#41×C3112yes—
607C4⋊C4—48no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C22⋊C4—28no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—44no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—44no—
619C42—44no—
620C23—22no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—22no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—22no—
632C23—41no—
633C23—42no—
634C23—41no—
635C23—42no—
636C23—41no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—41no—
643C23—41no—
644C23—42no—
645C23—41no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—41no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23C22×D4×C3111yescharacteristic
679C23C22×D4×C3111yescharacteristic
680C23C22×D4×C3111yescharacteristic
681C23C2×#41×C3111yescharacteristic
682C23C2×#41×C3111yescharacteristic
683C23C2×#41×C3112yes—
684C23C31×H(5,𝔽2)12yes—
685C23C31×H(5,𝔽2)12yes—
686C23C31×H(5,𝔽2)12yes—
687C23C31×H(5,𝔽2)11yescharacteristic
688C23C31×2−1+411yescharacteristic
689D4—416no—
690D4—432no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4C31×#12114yes—
743C2×C4C31×#12114yes—
744C22—44no—
745C22—42no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—42no—
753C22—44no—
754C22—42no—
755C22—44no—
756C22—81no—
757C22—82no—
758C22—82no—
759C22—81no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—81no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—81no—
769C22—82no—
770C22C2×C31×#12111yescharacteristic
771C22C2×C31×#12111yescharacteristic
772C22C31×#53211yescharacteristic
773C22C31×#53412yes—
774C22C31×#53411yescharacteristic
775C22C31×#53511yescharacteristic
776C22C31×#53512yes—
777C22C31×#53511yescharacteristic
778C22C31×#53711yescharacteristic
779C22C31×#53812yes—
780C22C31×#53812yes—
781C22C31×#54012yes—
782C22C31×#54212yes—
783C22D42×C3111yescharacteristic
784C22C31×#54612yes—
785C22C31×#54612yes—
786C22C31×#54711yescharacteristic
787C22C31×#54711yescharacteristic
788C22C31×#55312yes—
789C22C31×#55511yescharacteristic
790C22C31×#55912yes—
791C22C31×#56012yes—
792C22C31×#56212yes—
793C4—24no—
794C4—24no—
795C4—44no—
796C4—42no—
797C4—42no—
798C4—81no—
799C4—82no—
800C4—82no—
801C4—81no—
802C2—84no—
803C2—82no—
804C2C31×#253711yescharacteristic
805C2C31×#254311yescharacteristic
806C2C31×#254411yescharacteristic
807C2C31×#261711yescharacteristic
808C2C31×#261911yescharacteristic
809C2C31×#266211yescharacteristic
810C2C31×#267812yes—
811C2C31×#270112yes—
812C2C31×#271012yes—
813C2C31×#280312yes—
814C2C31×#281311yescharacteristic
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. C2×C31×#394C2semidirect
2. C2×C31×#394C2semidirect
4. C2×C31×#390C2semidirect
5. C2×C31×#388C2semidirect
6. C31×#1441C2semidirect
7. C31×#1440C2semidirect
8. C31×#1439C2semidirect
9. C31×#1439C2semidirect
10. C31×#1438C2semidirect
11. C31×C4⋊#95C2semidirect
96. C2×C22⋊C4×C31D4semidirect
98. C2×C42×C31D4semidirect
212. #16819C31direct (N × H)
337. C2×#394C2×C31semidirect
338. C2×#394C2×C31semidirect
340. C2×#390C2×C31semidirect
341. C2×#388C2×C31semidirect
342. #1441C2×C31semidirect
343. #1440C2×C31semidirect
344. #1439C2×C31semidirect
345. #1439C2×C31semidirect
346. #1438C2×C31semidirect
347. C4⋊#95C2×C31semidirect
503. C2×C22⋊C4D4×C31semidirect
505. C2×C42D4×C31semidirect
514. C31#16819direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3942
C2×C31×#3922
C2×C31×#3902
C2×C31×#3882
C31×#14412
C31×#14402
C31×#14392
C31×#14382
C31×C4⋊#952
#1681931