Finite Group Databasebeta

← C31×#16801 #21473560

Subgroups — C31×#16801 #21473560

Order 7936.

2090 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
1C2×C31×#399C211yesmaximal, characteristic, complemented
2C2×C31×#396C212yesmaximal, complemented
3C2×C31×#394C212yesmaximal, complemented
4C2×C31×#392C211yesmaximal, characteristic
5C2×C31×#390C211yesmaximal, characteristic, complemented
6C2×C31×#388C211yesmaximal, characteristic, complemented
7C31×#1445C211yesmaximal, characteristic, complemented
8C31×#1439C212yesmaximal, complemented
9C31×#1438C212yesmaximal, complemented
10C31×#1438C211yesmaximal, characteristic, complemented
11C31×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C23×D4×C31C2212yes—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2212yes—
17C22×C4⋊C4×C31C2212yes—
18C22×C22⋊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×C31C2212yes—
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2212yes—
27C22×C42×C31C2211yescharacteristic
28C31×#399—24no—
29C31×#396—28no—
30C31×#394—28no—
31C31×#392—24no—
32C31×#390—24no—
33C31×#388—24no—
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2211yescharacteristic
39C2×C31×#95C2211yescharacteristic
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—24no—
49C22×D4×C31—22no—
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×C31C2311yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2311yescharacteristic
59C23×C4×C31C2311yescharacteristic
60C23×C4×C31C2312yes—
61C23×C4×C31C2312yes—
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C2×C4⋊C4×C31—24no—
65C2×C4⋊C4×C31—24no—
66C2×C4⋊C4×C31—24no—
67C2×C4⋊C4×C31—22no—
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31—22no—
70C2×C4⋊C4×C31—22no—
71C2×C4⋊C4×C31—42no—
72C2×C4⋊C4×C31—42no—
73C2×C4⋊C4×C31—42no—
74C2×C4⋊C4×C31D418yescomplemented
75C2×C22⋊C4×C31—22no—
76C2×C22⋊C4×C31—22no—
77C2×C22⋊C4×C31—24no—
78C2×C22⋊C4×C31—24no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—24no—
81C2×C22⋊C4×C31—24no—
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×C31D414yes—
100C2×C42×C31—42no—
101C2×C42×C31D414yescomplemented
102C31×#95—24no—
103C31×#95—22no—
104C31×#95—22no—
105C31×#95—22no—
106C31×#95—22no—
107C31×#95—24no—
108C31×#95—42no—
109C24×C31—21no—
110C24×C31—22no—
111C24×C31—22no—
112C24×C31—22no—
113C24×C31—22no—
114C24×C31—22no—
115C24×C31—21no—
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—21no—
127C24×C31—21no—
128C24×C31—22no—
129C24×C31—21no—
130C24×C31—21no—
131C24×C31—22no—
132C24×C31—22no—
133C24×C31C2×D412yes—
134C24×C31#4114yes—
135C24×C31C2411yescharacteristic
136C2×D4×C31—28no—
137C2×D4×C31—48no—
138C2×D4×C31—48no—
139C2×D4×C31—48no—
140C2×D4×C31—48no—
141C2×D4×C31—44no—
142C2×D4×C31—48no—
143C2×D4×C31—48no—
144C2×D4×C31—48no—
145C2×D4×C31—48no—
146C2×D4×C31—48no—
147C2×D4×C31—44no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—21no—
158C22×C4×C31—22no—
159C22×C4×C31—22no—
160C22×C4×C31—21no—
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—21no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
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—21no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—21no—
187C22×C4×C31—22no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31C2×D414yes—
191C22×C4×C31C2×D412yes—
192C22×C4×C31C2×D414yes—
193C22×C4×C31C2×D412yes—
194C22×C4×C31C2×D412yes—
195C22×C4×C31C2×D412yes—
196C22×C4×C31C2×D412yes—
197C22×C4×C31C2×D414yes—
198C22×C4×C31#4112yes—
199C4⋊C4×C31—48no—
200C4⋊C4×C31—48no—
201C4⋊C4×C31—44no—
202C4⋊C4×C31—44no—
203C22⋊C4×C31—28no—
204C22⋊C4×C31—48no—
205C22⋊C4×C31—48no—
206C22⋊C4×C31—48no—
207C22⋊C4×C31—44no—
208C22⋊C4×C31—48no—
209C22⋊C4×C31—48no—
210C22⋊C4×C31—48no—
211C22⋊C4×C31—44no—
212C42×C31—44no—
213#16801C3111yesmaximal, characteristic, direct product factor, Sylow
214C23×C31—22no—
215C23×C31—24no—
216C23×C31—22no—
217C23×C31—22no—
218C23×C31—24no—
219C23×C31—24no—
220C23×C31—24no—
221C23×C31—24no—
222C23×C31—24no—
223C23×C31—24no—
224C23×C31—24no—
225C23×C31—24no—
226C23×C31—42no—
227C23×C31—41no—
228C23×C31—42no—
229C23×C31—41no—
230C23×C31—42no—
231C23×C31—41no—
232C23×C31—42no—
233C23×C31—42no—
234C23×C31—42no—
235C23×C31—42no—
236C23×C31—42no—
237C23×C31—41no—
238C23×C31—42no—
239C23×C31—41no—
240C23×C31—41no—
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—41no—
251C23×C31—41no—
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×C31C22×D411yescharacteristic
273C23×C31C22×D411yescharacteristic
274C23×C31C22×D412yes—
275C23×C31C2×#4111yescharacteristic
276C23×C31C2×#4112yes—
277C23×C31H(5,𝔽2)11yescharacteristic
278C23×C31H(5,𝔽2)12yes—
279C23×C31H(5,𝔽2)11yescharacteristic
280C23×C31H(5,𝔽2)12yes—
281C23×C312−1+411yescharacteristic
282C23×C312−1+411yescharacteristic
283D4×C31—416no—
284D4×C31—432no—
285C2×C4×C31—22no—
286C2×C4×C31—22no—
287C2×C4×C31—22no—
288C2×C4×C31—24no—
289C2×C4×C31—22no—
290C2×C4×C31—24no—
291C2×C4×C31—24no—
292C2×C4×C31—24no—
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—24no—
300C2×C4×C31—24no—
301C2×C4×C31—24no—
302C2×C4×C31—24no—
303C2×C4×C31—24no—
304C2×C4×C31—41no—
305C2×C4×C31—42no—
306C2×C4×C31—41no—
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×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—42no—
321C2×C4×C31—41no—
322C2×C4×C31—42no—
323C2×C4×C31—41no—
324C2×C4×C31—42no—
325C2×C4×C31—41no—
326C2×C4×C31—42no—
327C2×C4×C31—41no—
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#12114yes—
335C2×C4×C31#12714yes—
336C2×#399C2×C3111yescharacteristic, complemented
337C2×#396C2×C3112yescomplemented
338C2×#394C2×C3112yescomplemented
339C2×#392C2×C3111yescharacteristic
340C2×#390C2×C3111yescharacteristic, complemented
341C2×#388C2×C3111yescharacteristic, complemented
342#1445C2×C3111yescharacteristic, complemented
343#1439C2×C3112yescomplemented
344#1438C2×C3112yescomplemented
345#1438C2×C3111yescharacteristic, complemented
346C4⋊#95C2×C3111yescharacteristic, complemented
347C22×C31—42no—
348C22×C31—44no—
349C22×C31—44no—
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—82no—
360C22×C31—81no—
361C22×C31—81no—
362C22×C31—82no—
363C22×C31—82no—
364C22×C31—82no—
365C22×C31—82no—
366C22×C31—82no—
367C22×C31—82no—
368C22×C31—82no—
369C22×C31—81no—
370C22×C31—82no—
371C22×C31—81no—
372C22×C31—82no—
373C22×C31C2×#12111yescharacteristic
374C22×C31#52511yescharacteristic
375C22×C31C2×#12711yescharacteristic
376C22×C31#53412yes—
377C22×C31#53411yescharacteristic
378C22×C31#53511yescharacteristic
379C22×C31#53511yescharacteristic
380C22×C31#53611yescharacteristic
381C22×C31#53711yescharacteristic
382C22×C31#53711yescharacteristic
383C22×C31#53712yes—
384C22×C31#53812yes—
385C22×C31#53912yes—
386C22×C31#54211yescharacteristic
387C22×C31#54211yescharacteristic
388C22×C31D4212yes—
389C22×C31#54612yes—
390C22×C31#54612yes—
391C22×C31#54812yes—
392C22×C31#55012yes—
393C22×C31#55112yes—
394C22×C31#56012yes—
395C22×C31#56212yes—
396C4×C31—24no—
397C4×C31—24no—
398C4×C31—44no—
399C4×C31—44no—
400C4×C31—42no—
401C4×C31—42no—
402C4×C31—81no—
403C4×C31—81no—
404C4×C31—82no—
405C23×D4C22×C3111yescharacteristic
406C23×D4C22×C3112yes—
407C22×C4⋊C4C22×C3111yescharacteristic
408C22×C4⋊C4C22×C3111yescharacteristic
409C22×C4⋊C4C22×C3112yes—
410C22×C4⋊C4C22×C3112yes—
411C22×C22⋊C4C22×C3111yescharacteristic
412C22×C22⋊C4C22×C3112yes—
413C22×C22⋊C4C22×C3112yes—
414C22×C22⋊C4C22×C3112yes—
415C22×C22⋊C4C22×C3112yes—
416C22×C22⋊C4C22×C3111yescharacteristic
417C22×C22⋊C4C22×C3112yes—
418C22×C22⋊C4C22×C3111yescharacteristic
419C22×C22⋊C4C22×C3112yes—
420C22×C42C22×C3111yescharacteristic
421#399—24no—
422#396—28no—
423#394—28no—
424#392—24no—
425#390—24no—
426#388—24no—
427C2×#95C22×C3111yescharacteristic
428C2×#95C22×C3112yes—
429C2×#95C22×C3112yes—
430C2×#95C22×C3111yescharacteristic
431C2×#95C22×C3111yescharacteristic
432C2×#95C22×C3111yescharacteristic
433C2×#95C22×C3112yes—
434C2×C31—82no—
435C2×C31—84no—
436C2×C31#253411yescharacteristic
437C2×C31#254011yescharacteristic
438C2×C31#254111yescharacteristic
439C2×C31#262011yescharacteristic
440C2×C31#263611yescharacteristic
441C2×C31#265611yescharacteristic
442C2×C31#267812yes—
443C2×C31#268112yes—
444C2×C31#270512yes—
445C2×C31#273012yes—
446C2×C31#281311yescharacteristic
447C25C23×C3111yescharacteristic
448C25C23×C3112yes—
449C22×D4—24no—
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—24no—
455C22×D4—22no—
456C22×D4—42no—
457C22×D4—42no—
458C22×D4—42no—
459C22×D4—42no—
460C22×D4—42no—
461C23×C4C23×C3112yes—
462C23×C4C23×C3111yescharacteristic
463C23×C4C23×C3111yescharacteristic
464C23×C4C23×C3111yescharacteristic
465C23×C4C23×C3112yes—
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—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4D4×C3118yescomplemented
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
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⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4D4×C3114yes—
506C2×C42—42no—
507C2×C42D4×C3114yescomplemented
508#95—22no—
509#95—22no—
510#95—22no—
511#95—24no—
512#95—24no—
513#95—22no—
514#95—42no—
515C31#1680111yescharacteristic, direct product factor, Sylow
516C24—21no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—21no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—21no—
535C24—22no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24C2×D4×C3112yes—
541C24#41×C3114yes—
542C24C24×C3111yescharacteristic
543C2×D4—28no—
544C2×D4—48no—
545C2×D4—48no—
546C2×D4—48no—
547C2×D4—48no—
548C2×D4—44no—
549C2×D4—48no—
550C2×D4—48no—
551C2×D4—48no—
552C2×D4—48no—
553C2×D4—48no—
554C2×D4—44no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
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—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4C2×D4×C3114yes—
598C22×C4C2×D4×C3112yes—
599C22×C4C2×D4×C3114yes—
600C22×C4C2×D4×C3112yes—
601C22×C4C2×D4×C3112yes—
602C22×C4C2×D4×C3112yes—
603C22×C4C2×D4×C3112yes—
604C22×C4C2×D4×C3114yes—
605C22×C4#41×C3112yes—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C22⋊C4—28no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—44no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—44no—
618C22⋊C4—48no—
619C42—44no—
620C23—22no—
621C23—24no—
622C23—22no—
623C23—22no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—42no—
633C23—41no—
634C23—42no—
635C23—41no—
636C23—42no—
637C23—41no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—41no—
644C23—42no—
645C23—41no—
646C23—41no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—41no—
657C23—41no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
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—
678C23C22×D4×C3111yescharacteristic
679C23C22×D4×C3111yescharacteristic
680C23C22×D4×C3112yes—
681C23C2×#41×C3111yescharacteristic
682C23C2×#41×C3112yes—
683C23C31×H(5,𝔽2)11yescharacteristic
684C23C31×H(5,𝔽2)12yes—
685C23C31×H(5,𝔽2)11yescharacteristic
686C23C31×H(5,𝔽2)12yes—
687C23C31×2−1+411yescharacteristic
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—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4C31×#12114yes—
741C2×C4C31×#12714yes—
742C22—42no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—42no—
752C22—44no—
753C22—42no—
754C22—82no—
755C22—81no—
756C22—81no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—81no—
765C22—82no—
766C22—81no—
767C22—82no—
768C22C2×C31×#12111yescharacteristic
769C22C31×#52511yescharacteristic
770C22C2×C31×#12711yescharacteristic
771C22C31×#53412yes—
772C22C31×#53411yescharacteristic
773C22C31×#53511yescharacteristic
774C22C31×#53511yescharacteristic
775C22C31×#53611yescharacteristic
776C22C31×#53711yescharacteristic
777C22C31×#53711yescharacteristic
778C22C31×#53712yes—
779C22C31×#53812yes—
780C22C31×#53912yes—
781C22C31×#54211yescharacteristic
782C22C31×#54211yescharacteristic
783C22D42×C3112yes—
784C22C31×#54612yes—
785C22C31×#54612yes—
786C22C31×#54812yes—
787C22C31×#55012yes—
788C22C31×#55112yes—
789C22C31×#56012yes—
790C22C31×#56212yes—
791C4—24no—
792C4—24no—
793C4—44no—
794C4—44no—
795C4—42no—
796C4—42no—
797C4—81no—
798C4—81no—
799C4—82no—
800C2—82no—
801C2—84no—
802C2C31×#253411yescharacteristic
803C2C31×#254011yescharacteristic
804C2C31×#254111yescharacteristic
805C2C31×#262011yescharacteristic
806C2C31×#263611yescharacteristic
807C2C31×#265611yescharacteristic
808C2C31×#267812yes—
809C2C31×#268112yes—
810C2C31×#270512yes—
811C2C31×#273012yes—
812C2C31×#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×#399C2semidirect
2. C2×C31×#396C2semidirect
3. C2×C31×#394C2semidirect
5. C2×C31×#390C2semidirect
6. C2×C31×#388C2semidirect
7. C31×#1445C2semidirect
8. C31×#1439C2semidirect
9. C31×#1438C2semidirect
10. C31×#1438C2semidirect
11. C31×C4⋊#95C2semidirect
74. C2×C4⋊C4×C31D4semidirect
101. C2×C42×C31D4semidirect
213. #16801C31direct (N × H)
336. C2×#399C2×C31semidirect
337. C2×#396C2×C31semidirect
338. C2×#394C2×C31semidirect
340. C2×#390C2×C31semidirect
341. C2×#388C2×C31semidirect
342. #1445C2×C31semidirect
343. #1439C2×C31semidirect
344. #1438C2×C31semidirect
345. #1438C2×C31semidirect
346. C4⋊#95C2×C31semidirect
480. C2×C4⋊C4D4×C31semidirect
507. C2×C42D4×C31semidirect
515. C31#16801direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3992
C2×C31×#3962
C2×C31×#3942
C2×C31×#3922
C2×C31×#3902
C2×C31×#3882
C31×#14452
C31×#14392
C31×#14382
C31×C4⋊#952
#1680131