Finite Group Databasebeta

← C31×#15278 #21472037

Subgroups — C31×#15278 #21472037

Order 7936.

3134 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C212yesmaximal, complemented
2C2×C31×#394C212yesmaximal, complemented
3C2×C31×#392C212yesmaximal, complemented
4C2×C31×#386C212yesmaximal, complemented
5C31×#1444C211yesmaximal, characteristic, complemented
6C31×#1439C212yesmaximal, complemented
7C31×#1438C211yesmaximal, characteristic, complemented
8C31×#1438C211yesmaximal, characteristic, complemented
9C31×C22⋊#95C212yesmaximal, complemented
10C23×D4×C31C2212yes—
11C23×D4×C31C2212yes—
12C23×D4×C31C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C24×C4×C31C2212yes—
15C2×C31×#121—28no—
16C2×C31×#121—28no—
17C2×C31×#121—28no—
18C22×C4⋊C4×C31C2212yes—
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2212yes—
27C31×#394—28no—
28C31×#392—28no—
29C31×#386—28no—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2211yescharacteristic
37C25×C31C2312yes—
38C25×C31C2312yes—
39C22×D4×C31—24no—
40C22×D4×C31—24no—
41C22×D4×C31—24no—
42C22×D4×C31—24no—
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—24no—
50C22×D4×C31—24no—
51C22×D4×C31—22no—
52C22×D4×C31—42no—
53C22×D4×C31—42no—
54C22×D4×C31—41no—
55C22×D4×C31—41no—
56C22×D4×C31—41no—
57C22×D4×C31—41no—
58C22×D4×C31—42no—
59C22×D4×C31—42no—
60C22×D4×C31—42no—
61C22×D4×C31D414yescomplemented
62C22×D4×C31D418yescomplemented
63C23×C4×C31—24no—
64C23×C4×C31—24no—
65C23×C4×C31—24no—
66C23×C4×C31—24no—
67C23×C4×C31—24no—
68C23×C4×C31—42no—
69C23×C4×C31—42no—
70C23×C4×C31C2312yes—
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2312yes—
73C23×C4×C31C2312yes—
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2312yes—
77C31×#121—264no—
78C2×C4⋊C4×C31—24no—
79C2×C4⋊C4×C31—24no—
80C2×C4⋊C4×C31—24no—
81C2×C4⋊C4×C31—24no—
82C2×C4⋊C4×C31—41no—
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—24no—
91C2×C22⋊C4×C31—24no—
92C2×C22⋊C4×C31—24no—
93C2×C22⋊C4×C31—24no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—24no—
96C2×C22⋊C4×C31—24no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—24no—
99C2×C22⋊C4×C31—42no—
100C2×C22⋊C4×C31—42no—
101C2×C22⋊C4×C31—42no—
102C2×C22⋊C4×C31—42no—
103C2×C22⋊C4×C31D418yescomplemented
104C31×#95—24no—
105C31×#95—24no—
106C31×#95—24no—
107C31×#95—41no—
108C31×#95—41no—
109C31×#95—41no—
110C31×#95D414yescomplemented
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—22no—
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—22no—
133C24×C31—22no—
134C24×C31—22no—
135C24×C31—22no—
136C24×C31—22no—
137C24×C31C2×D414yes—
138C24×C31C2×D414yes—
139C24×C31C2×D414yes—
140C24×C31C2×D414yes—
141C24×C31C2411yescharacteristic
142C2×D4×C31—216no—
143C2×D4×C31—216no—
144C2×D4×C31—216no—
145C2×D4×C31—216no—
146C2×D4×C31—48no—
147C2×D4×C31—44no—
148C2×D4×C31—48no—
149C2×D4×C31—48no—
150C2×D4×C31—48no—
151C2×D4×C31—48no—
152C2×D4×C31—48no—
153C2×D4×C31—48no—
154C2×D4×C31—48no—
155C2×D4×C31—44no—
156C2×D4×C31—44no—
157C2×D4×C31—48no—
158C2×D4×C31—44no—
159C2×D4×C31—48no—
160C2×D4×C31—48no—
161C2×D4×C31—44no—
162C2×D4×C31—48no—
163C2×D4×C31—48no—
164C2×D4×C31—44no—
165C2×D4×C31—48no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—216no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
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—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—21no—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—22no—
202C22×C4×C31—48no—
203C22×C4×C31—48no—
204C22×C4×C31—48no—
205C22×C4×C31—48no—
206C22×C4×C31—48no—
207C22×C4×C31—48no—
208C22×C4×C31C2×D414yes—
209C22×C4×C31C2×D412yes—
210C22×C4×C31C2×D412yes—
211C22×C4×C31C2×D414yes—
212C22×C4×C31C2×D414yes—
213C22×C4×C31C2×D414yes—
214C22×C4×C31#4112yes—
215C22×C4×C31#4114yes—
216C4⋊C4×C31—216no—
217C4⋊C4×C31—44no—
218C22⋊C4×C31—216no—
219C22⋊C4×C31—216no—
220C22⋊C4×C31—48no—
221C22⋊C4×C31—48no—
222C22⋊C4×C31—48no—
223C22⋊C4×C31—48no—
224C22⋊C4×C31—48no—
225#15278C3111yesmaximal, characteristic, direct product factor, Sylow
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—24no—
241C23×C31—24no—
242C23×C31—24no—
243C23×C31—24no—
244C23×C31—24no—
245C23×C31—24no—
246C23×C31—24no—
247C23×C31—24no—
248C23×C31—24no—
249C23×C31—24no—
250C23×C31—24no—
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×C31—42no—
281C23×C31—42no—
282C23×C31—42no—
283C23×C31—42no—
284C23×C31—42no—
285C23×C31—42no—
286C23×C31—42no—
287C23×C31—42no—
288C23×C31—42no—
289C23×C31—42no—
290C23×C31—42no—
291C23×C31—42no—
292C23×C31—42no—
293C23×C31—42no—
294C23×C31—42no—
295C23×C31#12018yes—
296C23×C31C22×D411yescharacteristic
297C23×C31C22×D412yes—
298C23×C31C22×D412yes—
299C23×C31C22×D411yescharacteristic
300C23×C31C2×#4112yes—
301C23×C31C2×#4111yescharacteristic
302C23×C31H(5,𝔽2)11yescharacteristic
303C23×C31H(5,𝔽2)11yescharacteristic
304C23×C31H(5,𝔽2)12yes—
305C23×C31H(5,𝔽2)11yescharacteristic
306C23×C312−1+411yescharacteristic
307D4×C31—432no—
308D4×C31—416no—
309D4×C31—432no—
310D4×C31—416no—
311C2×C4×C31—24no—
312C2×C4×C31—24no—
313C2×C4×C31—24no—
314C2×C4×C31—24no—
315C2×C4×C31—24no—
316C2×C4×C31—24no—
317C2×C4×C31—24no—
318C2×C4×C31—24no—
319C2×C4×C31—24no—
320C2×C4×C31—22no—
321C2×C4×C31—22no—
322C2×C4×C31—22no—
323C2×C4×C31—24no—
324C2×C4×C31—24no—
325C2×C4×C31—24no—
326C2×C4×C31—24no—
327C2×C4×C31—24no—
328C2×C4×C31—24no—
329C2×C4×C31—432no—
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—41no—
337C2×C4×C31—42no—
338C2×C4×C31—42no—
339C2×C4×C31—41no—
340C2×C4×C31—42no—
341C2×C4×C31—42no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—42no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—42no—
348C2×C4×C31—42no—
349C2×C4×C31—42no—
350C2×C4×C31—42no—
351C2×C4×C31—42no—
352C2×C4×C31—42no—
353C2×C4×C31—42no—
354C2×C4×C31#12118yescomplemented
355C22×#121C2×C3112yescomplemented
356C2×#394C2×C3112yescomplemented
357C2×#392C2×C3112yescomplemented
358C2×#386C2×C3112yescomplemented
359#1444C2×C3111yescharacteristic, complemented
360#1439C2×C3112yescomplemented
361#1438C2×C3111yescharacteristic, complemented
362#1438C2×C3111yescharacteristic, complemented
363C22⋊#95C2×C3112yescomplemented
364C22×C31—28no—
365C22×C31—28no—
366C22×C31—28no—
367C22×C31—44no—
368C22×C31—44no—
369C22×C31—44no—
370C22×C31—44no—
371C22×C31—44no—
372C22×C31—44no—
373C22×C31—44no—
374C22×C31—44no—
375C22×C31—44no—
376C22×C31—44no—
377C22×C31—44no—
378C22×C31—44no—
379C22×C31—44no—
380C22×C31—44no—
381C22×C31—44no—
382C22×C31—44no—
383C22×C31—44no—
384C22×C31—44no—
385C22×C31—44no—
386C22×C31—82no—
387C22×C31—82no—
388C22×C31—82no—
389C22×C31—82no—
390C22×C31—82no—
391C22×C31—82no—
392C22×C31—82no—
393C22×C31—82no—
394C22×C31C2×#12012yes—
395C22×C31C2×#12112yes—
396C22×C31#53212yes—
397C22×C31#53411yescharacteristic
398C22×C31#53412yes—
399C22×C31#53712yes—
400C22×C31#53711yescharacteristic
401C22×C31#53811yescharacteristic
402C22×C31#54012yes—
403C22×C31D4211yescharacteristic
404C22×C31D4212yes—
405C22×C31D4211yescharacteristic
406C22×C31D4211yescharacteristic
407C22×C31D4212yes—
408C22×C31#54612yes—
409C22×C31#54612yes—
410C22×C31#54612yes—
411C22×C31#54712yes—
412C22×C31#54711yescharacteristic
413C22×C31#55011yescharacteristic
414C22×C31#55511yescharacteristic
415C22×C31#56011yescharacteristic
416C22×C31#56211yescharacteristic
417C4×C31—28no—
418C4×C31—42no—
419C4×C31—44no—
420C4×C31—44no—
421C4×C31—42no—
422C4×C31—42no—
423C4×C31—82no—
424C23×D4C22×C3112yes—
425C23×D4C22×C3112yes—
426C23×D4C22×C3111yescharacteristic
427C23×D4C22×C3111yescharacteristic
428C24×C4C22×C3112yes—
429C2×#121—28no—
430C2×#121—28no—
431C2×#121—28no—
432C22×C4⋊C4C22×C3112yes—
433C22×C4⋊C4C22×C3111yescharacteristic
434C22×C22⋊C4C22×C3112yes—
435C22×C22⋊C4C22×C3112yes—
436C22×C22⋊C4C22×C3112yes—
437C22×C22⋊C4C22×C3112yes—
438C22×C22⋊C4C22×C3112yes—
439C22×C22⋊C4C22×C3112yes—
440C22×C22⋊C4C22×C3112yes—
441#394—28no—
442#392—28no—
443#386—28no—
444C2×#95C22×C3112yes—
445C2×#95C22×C3112yes—
446C2×#95C22×C3112yes—
447C2×#95C22×C3111yescharacteristic
448C2×#95C22×C3111yescharacteristic
449C2×#95C22×C3111yescharacteristic
450C2×#95C22×C3111yescharacteristic
451C2×C31—48no—
452C2×C31—84no—
453C2×C31#240311yescharacteristic
454C2×C31#241012yes—
455C2×C31#242812yes—
456C2×C31#243012yes—
457C2×C31#253711yescharacteristic
458C2×C31#255511yescharacteristic
459C2×C31#266811yescharacteristic
460C2×C31#267112yes—
461C2×C31#267511yescharacteristic
462C2×C31#268211yescharacteristic
463C2×C31#269911yescharacteristic
464C25C23×C3112yes—
465C25C23×C3112yes—
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—24no—
471C22×D4—24no—
472C22×D4—24no—
473C22×D4—24no—
474C22×D4—24no—
475C22×D4—24no—
476C22×D4—24no—
477C22×D4—24no—
478C22×D4—22no—
479C22×D4—42no—
480C22×D4—42no—
481C22×D4—41no—
482C22×D4—41no—
483C22×D4—41no—
484C22×D4—41no—
485C22×D4—42no—
486C22×D4—42no—
487C22×D4—42no—
488C22×D4D4×C3114yescomplemented
489C22×D4D4×C3118yescomplemented
490C23×C4—24no—
491C23×C4—24no—
492C23×C4—24no—
493C23×C4—24no—
494C23×C4—24no—
495C23×C4—42no—
496C23×C4—42no—
497C23×C4C23×C3112yes—
498C23×C4C23×C3111yescharacteristic
499C23×C4C23×C3112yes—
500C23×C4C23×C3112yes—
501C23×C4C23×C3111yescharacteristic
502C23×C4C23×C3111yescharacteristic
503C23×C4C23×C3112yes—
504#121—264no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—41no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4D4×C3118yescomplemented
531#95—24no—
532#95—24no—
533#95—24no—
534#95—41no—
535#95—41no—
536#95—41no—
537#95D4×C3114yescomplemented
538C31#1527811yescharacteristic, direct product factor, Sylow
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24C2×D4×C3114yes—
566C24C2×D4×C3114yes—
567C24C2×D4×C3114yes—
568C24C2×D4×C3114yes—
569C24C24×C3111yescharacteristic
570C2×D4—216no—
571C2×D4—216no—
572C2×D4—216no—
573C2×D4—216no—
574C2×D4—48no—
575C2×D4—44no—
576C2×D4—48no—
577C2×D4—48no—
578C2×D4—48no—
579C2×D4—48no—
580C2×D4—48no—
581C2×D4—48no—
582C2×D4—48no—
583C2×D4—44no—
584C2×D4—44no—
585C2×D4—48no—
586C2×D4—44no—
587C2×D4—48no—
588C2×D4—48no—
589C2×D4—44no—
590C2×D4—48no—
591C2×D4—48no—
592C2×D4—44no—
593C2×D4—48no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—216no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
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—21no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4C2×D4×C3114yes—
637C22×C4C2×D4×C3112yes—
638C22×C4C2×D4×C3112yes—
639C22×C4C2×D4×C3114yes—
640C22×C4C2×D4×C3114yes—
641C22×C4C2×D4×C3114yes—
642C22×C4#41×C3112yes—
643C22×C4#41×C3114yes—
644C4⋊C4—216no—
645C4⋊C4—44no—
646C22⋊C4—216no—
647C22⋊C4—216no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
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—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23C31×#12018yes—
723C23C22×D4×C3111yescharacteristic
724C23C22×D4×C3112yes—
725C23C22×D4×C3112yes—
726C23C22×D4×C3111yescharacteristic
727C23C2×#41×C3112yes—
728C23C2×#41×C3111yescharacteristic
729C23C31×H(5,𝔽2)11yescharacteristic
730C23C31×H(5,𝔽2)11yescharacteristic
731C23C31×H(5,𝔽2)12yes—
732C23C31×H(5,𝔽2)11yescharacteristic
733C23C31×2−1+411yescharacteristic
734D4—432no—
735D4—416no—
736D4—432no—
737D4—416no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—432no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4C31×#12118yescomplemented
782C22—28no—
783C22—28no—
784C22—28no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—44no—
803C22—44no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22C2×C31×#12012yes—
813C22C2×C31×#12112yes—
814C22C31×#53212yes—
815C22C31×#53411yescharacteristic
816C22C31×#53412yes—
817C22C31×#53712yes—
818C22C31×#53711yescharacteristic
819C22C31×#53811yescharacteristic
820C22C31×#54012yes—
821C22D42×C3111yescharacteristic
822C22D42×C3112yes—
823C22D42×C3111yescharacteristic
824C22D42×C3111yescharacteristic
825C22D42×C3112yes—
826C22C31×#54612yes—
827C22C31×#54612yes—
828C22C31×#54612yes—
829C22C31×#54712yes—
830C22C31×#54711yescharacteristic
831C22C31×#55011yescharacteristic
832C22C31×#55511yescharacteristic
833C22C31×#56011yescharacteristic
834C22C31×#56211yescharacteristic
835C4—28no—
836C4—42no—
837C4—44no—
838C4—44no—
839C4—42no—
840C4—42no—
841C4—82no—
842C2—48no—
843C2—84no—
844C2C31×#240311yescharacteristic
845C2C31×#241012yes—
846C2C31×#242812yes—
847C2C31×#243012yes—
848C2C31×#253711yescharacteristic
849C2C31×#255511yescharacteristic
850C2C31×#266811yescharacteristic
851C2C31×#267112yes—
852C2C31×#267511yescharacteristic
853C2C31×#268211yescharacteristic
854C2C31×#269911yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#121C2semidirect
2. C2×C31×#394C2semidirect
3. C2×C31×#392C2semidirect
4. C2×C31×#386C2semidirect
5. C31×#1444C2semidirect
6. C31×#1439C2semidirect
7. C31×#1438C2semidirect
8. C31×#1438C2semidirect
9. C31×C22⋊#95C2semidirect
61. C22×D4×C31D4semidirect
62. C22×D4×C31D4semidirect
103. C2×C22⋊C4×C31D4semidirect
110. C31×#95D4semidirect
225. #15278C31direct (N × H)
354. C2×C4×C31#121semidirect
355. C22×#121C2×C31semidirect
356. C2×#394C2×C31semidirect
357. C2×#392C2×C31semidirect
358. C2×#386C2×C31semidirect
359. #1444C2×C31semidirect
360. #1439C2×C31semidirect
361. #1438C2×C31semidirect
362. #1438C2×C31semidirect
363. C22⋊#95C2×C31semidirect
488. C22×D4D4×C31semidirect
489. C22×D4D4×C31semidirect
530. C2×C22⋊C4D4×C31semidirect
537. #95D4×C31semidirect
538. C31#15278direct (N × H)
781. C2×C4C31×#121semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C2×C31×#3942
C2×C31×#3922
C2×C31×#3862
C31×#14442
C31×#14392
C31×#14382
C31×C22⋊#952
#1527831