Finite Group Databasebeta

← #29610697

Subgroups — #29610697

Order 15616.

1390 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839669C211yesmaximal, characteristic, complemented
2C2×#16839655C211yesmaximal, characteristic
3#21444090C211yesmaximal, characteristic, complemented
4#21444084C211yesmaximal, characteristic, complemented
5#21444076C212yesmaximal, complemented
6#21444076C212yesmaximal, complemented
7#21444068C212yesmaximal
8#21444064C212yesmaximal
9#21444064C211yesmaximal, characteristic
10#21444044C211yesmaximal, characteristic, complemented
11C2×C61×#393C211yesmaximal, characteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×C4⋊Dic61C2212yes—
15C22×C22⋊Dic61C2211yescharacteristic
16C22×C22⋊Dic61C2211yescharacteristic
17C22×C22⋊Dic61C2212yes—
18C22×C4×Dic61C2211yescharacteristic
19#16839669—24no—
20#16839655—24no—
21C2×#14519684C2211yescharacteristic
22C2×#14519684C2211yescharacteristic
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2211yescharacteristic
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C23×Q8×C61C2211yescharacteristic
33C22×C22⋊C4×C61C2211yescharacteristic
34C22×C22⋊C4×C61C2212yes—
35C61×#393C418yescomplemented
36C2×#95×C61C2211yescharacteristic
37C2×#95×C61C2212yes—
38C23×Dic61C2311yescharacteristic
39C23×Dic61C2312yes—
40C23×Dic61C2311yescharacteristic
41C23×Dic61C2312yes—
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2311yescharacteristic
44C2×C4⋊Dic61—22no—
45C2×C4⋊Dic61—22no—
46C2×C4⋊Dic61—42no—
47C2×C4⋊Dic61—42no—
48C2×C4⋊Dic61—42no—
49C2×C4⋊Dic61—42no—
50C2×C4⋊Dic61—42no—
51C2×C22⋊Dic61—22no—
52C2×C22⋊Dic61—22no—
53C2×C22⋊Dic61—42no—
54C2×C22⋊Dic61—42no—
55C2×C22⋊Dic61—42no—
56C2×C22⋊Dic61—42no—
57C2×C22⋊Dic61—42no—
58C2×C4×Dic61—42no—
59C2×C4×Dic61D414yes—
60#14519684—22no—
61#14519684—22no—
62#14519684—22no—
63#14519684—24no—
64#14519684—24no—
65#14519684—42no—
66#14519684—42no—
67#14519684—42no—
68#14519684—42no—
69#14519684—42no—
70#14519684—42no—
71C25×C61C2311yescharacteristic
72C22×Q8×C61—22no—
73C22×Q8×C61—22no—
74C22×Q8×C61—42no—
75C22×Q8×C61—42no—
76C22×Q8×C61C2×C414yes—
77C23×C4×C61C2311yescharacteristic
78C23×C4×C61C2312yes—
79C23×C4×C61C2312yes—
80C23×C4×C61C2311yescharacteristic
81C2×C22⋊C4×C61—22no—
82C2×C22⋊C4×C61—22no—
83C2×C22⋊C4×C61—42no—
84C2×C22⋊C4×C61—42no—
85C2×C22⋊C4×C61C2×C414yes—
86C2×C22⋊C4×C61C2×C418yes—
87#95×C61C2×C418yes—
88#95×C61C2×C414yes—
89C24×C61—21no—
90C24×C61—21no—
91C24×C61—22no—
92C24×C61—22no—
93C24×C61—22no—
94C24×C61—21no—
95C24×C61—21no—
96C24×C61—21no—
97C24×C61—21no—
98C24×C61—22no—
99C24×C61C22×C412yes—
100C24×C61C2411yescharacteristic
101C2×Q8×C61—28no—
102C2×Q8×C61—48no—
103C2×Q8×C61—44no—
104C2×Q8×C61—44no—
105C2×Q8×C61—48no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—21no—
109C22×C4×C61—22no—
110C22×C4×C61—21no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61C22×C412yes—
125C22×C4×C61C22×C414yes—
126C22×C4×C61C22×C414yes—
127C22×C4×C61C22×C412yes—
128C22×C4×C61C2×D412yes—
129C22×C4×C61#4112yes—
130C22×Dic61—21no—
131C22×Dic61—22no—
132C22×Dic61—22no—
133C22×Dic61—22no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—22no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—22no—
140C22×Dic61—21no—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61C2×D412yes—
163C22×Dic61C2×D412yes—
164C22⋊C4×C61—28no—
165C22⋊C4×C61—48no—
166C22⋊Dic61—44no—
167C22⋊Dic61—44no—
168C22⋊Dic61—48no—
169C4⋊Dic61—44no—
170C4⋊Dic61—44no—
171C4⋊Dic61—48no—
172C4×Dic61—44no—
173C23×C61—22no—
174C23×C61—24no—
175C23×C61—22no—
176C23×C61—22no—
177C23×C61—24no—
178C23×C61—41no—
179C23×C61—41no—
180C23×C61—41no—
181C23×C61—41no—
182C23×C61—41no—
183C23×C61—41no—
184C23×C61—42no—
185C23×C61—41no—
186C23×C61—41no—
187C23×C61—42no—
188C23×C61—42no—
189C23×C61—42no—
190C23×C61—42no—
191C23×C61—42no—
192C23×C61—42no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61—42no—
196C23×C61C23×C411yescharacteristic
197C23×C61C22×D411yescharacteristic
198C23×C61C2×#4111yescharacteristic
199C23×C61H(5,𝔽2)12yes—
200C23×C61H(5,𝔽2)12yes—
201C23×C61H(5,𝔽2)12yes—
202C23×C61H(5,𝔽2)11yescharacteristic
203C23×C612−1+411yescharacteristic
204C23×C612−1+411yescharacteristic
205C23×C612−1+411yescharacteristic
206C23×C612−1+412yes—
207Q8×C61—416no—
208C2×C4×C61—24no—
209C2×C4×C61—22no—
210C2×C4×C61—22no—
211C2×C4×C61—24no—
212C2×C4×C61—22no—
213C2×C4×C61—24no—
214C2×C4×C61—24no—
215C2×C4×C61—24no—
216C2×C4×C61—24no—
217C2×C4×C61—24no—
218C2×C4×C61—24no—
219C2×C4×C61—24no—
220C2×C4×C61—42no—
221C2×C4×C61—41no—
222C2×C4×C61—42no—
223C2×C4×C61—41no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61C4×D414yes—
232C2×Dic61—22no—
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—42no—
239C2×Dic61—42no—
240C2×Dic61—42no—
241C2×Dic61—42no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—42no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—42no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—42no—
251C2×Dic61—42no—
252C2×Dic61—42no—
253C2×Dic61—42no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61—42no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61—42no—
261C2×Dic61—42no—
262C2×Dic61—42no—
263C2×Dic61—42no—
264C2×Dic61—42no—
265C2×Dic61—42no—
266#14625—611nomaximal, Sylow
267C22×C61—42no—
268C22×C61—42no—
269C22×C61—42no—
270C22×C61—44no—
271C22×C61—44no—
272C22×C61—81no—
273C22×C61—81no—
274C22×C61—81no—
275C22×C61—82no—
276C22×C61—82no—
277C22×C61—81no—
278C22×C61C2×C4×D411yescharacteristic
279C22×C61#51812yes—
280C22×C61#51911yescharacteristic
281C22×C61#52011yescharacteristic
282C22×C61#52012yes—
283C22×C61#53411yescharacteristic
284C22×C61#53511yescharacteristic
285C22×C61#53511yescharacteristic
286C22×C61#53611yescharacteristic
287C22×C61#53611yescharacteristic
288C22×C61#53711yescharacteristic
289C22×C61#53812yes—
290C22×C61#54111yescharacteristic
291C22×C61#54212yes—
292C22×C61#54211yescharacteristic
293C22×C61H(3,𝔽4)12yes—
294C22×C61#56212yes—
295C22×C61#56212yes—
296C22×C61#56212yes—
297C22×C61#56212yes—
298C22×C61#56312yes—
299C22×C61#56312yes—
300C22×C61#56312yes—
301C4×C61—24no—
302C4×C61—44no—
303C4×C61—42no—
304C4×C61—44no—
305Dic61—42no—
306Dic61—42no—
307Dic61—81no—
308Dic61—82no—
309Dic61—81no—
310Dic61—82no—
311C2×#393D6111yescharacteristic
312C2×#391—611no—
313C2×#388—611no—
314#1446—611no—
315#1444—611no—
316#1442—612no—
317#1442—612no—
318#1440—612no—
319#1439—612no—
320#1439—611no—
321#1434—611no—
322C2×C61—82no—
323C2×C61#232111yescharacteristic
324C2×C61#232311yescharacteristic
325C2×C61#232611yescharacteristic
326C2×C61#237812yes—
327C2×C61#237912yes—
328C2×C61#281411yescharacteristic
329C2×C61#281611yescharacteristic
330C2×C61#281911yescharacteristic
331C2×C61#282111yescharacteristic
332C2×C61#283112yes—
333C2×C61#283212yes—
334C23×Q8C2×D6111yescharacteristic
335C22×C4⋊C4—611no—
336C22×C4⋊C4—611no—
337C22×C4⋊C4—612no—
338C22×C22⋊C4—611no—
339C22×C22⋊C4—611no—
340C22×C22⋊C4—612no—
341C22×C22⋊C4C2×D6111yescharacteristic
342C22×C22⋊C4C2×D6112yes—
343C22×C42—611no—
344#393Dic6118yescomplemented
345#391—1224no—
346#388—1224no—
347C2×#95—611no—
348C2×#95—612no—
349C2×#95—612no—
350C2×#95—611no—
351C2×#95—611no—
352C2×#95—612no—
353C2×#95—612no—
354C2×#95—612no—
355C2×#95—612no—
356C2×#95—612no—
357C2×#95—612no—
358C2×#95C2×D6111yescharacteristic
359C2×#95C2×D6112yes—
360C61#1462511yescharacteristic, complemented, Sylow
361C25C22×D6111yescharacteristic
362C22×Q8—22no—
363C22×Q8—22no—
364C22×Q8—42no—
365C22×Q8—42no—
366C22×Q8C2×Dic6114yes—
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—611no—
370C23×C4—612no—
371C23×C4—611no—
372C23×C4—612no—
373C23×C4C22×D6111yescharacteristic
374C23×C4C22×D6112yes—
375C23×C4C22×D6112yes—
376C23×C4C22×D6111yescharacteristic
377C2×C4⋊C4—1222no—
378C2×C4⋊C4—1222no—
379C2×C4⋊C4—2442no—
380C2×C4⋊C4—2442no—
381C2×C4⋊C4—2442no—
382C2×C4⋊C4—2442no—
383C2×C4⋊C4—2442no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—1222no—
389C2×C22⋊C4—1222no—
390C2×C22⋊C4—2442no—
391C2×C22⋊C4—2442no—
392C2×C22⋊C4—2442no—
393C2×C22⋊C4—2442no—
394C2×C22⋊C4—2442no—
395C2×C22⋊C4C2×Dic6114yes—
396C2×C22⋊C4C2×Dic6118yes—
397C2×C42—614no—
398C2×C42—2442no—
399#95—1222no—
400#95—1224no—
401#95—1224no—
402#95—1222no—
403#95—1222no—
404#95—2442no—
405#95—2442no—
406#95—2442no—
407#95—2442no—
408#95—2442no—
409#95—2442no—
410#95C2×Dic6118yes—
411#95C2×Dic6114yes—
412C24—21no—
413C24—21no—
414C24—22no—
415C24—22no—
416C24—21no—
417C24—22no—
418C24—21no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24C22×Dic6112yes—
423C24C23×D6111yescharacteristic
424C2×Q8—28no—
425C2×Q8—48no—
426C2×Q8—44no—
427C2×Q8—44no—
428C2×Q8—48no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—612no—
448C22×C4—612no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—1221no—
452C22×C4—1222no—
453C22×C4—1222no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1222no—
459C22×C4—1221no—
460C22×C4—1222no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—1222no—
464C22×C4—1222no—
465C22×C4—1222no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1222no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4D4×D6112yes—
482C22×C4#1175822412yes—
483C22×C4C22×Dic6112yes—
484C22×C4C22×Dic6114yes—
485C22×C4C22×Dic6114yes—
486C22×C4C22×Dic6112yes—
487C4⋊C4—2444no—
488C4⋊C4—2444no—
489C4⋊C4—2448no—
490C22⋊C4—28no—
491C22⋊C4—48no—
492C22⋊C4—2444no—
493C22⋊C4—2444no—
494C22⋊C4—2448no—
495C42—2444no—
496C23—22no—
497C23—24no—
498C23—22no—
499C23—24no—
500C23—22no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—42no—
516C23—41no—
517C23—42no—
518C23—41no—
519C23C23×Dic6111yescharacteristic
520C23C2×D4×D6111yescharacteristic
521C23C2×#1175822411yescharacteristic
522C23#1451982212yes—
523C23#1451982212yes—
524C23#1451982311yescharacteristic
525C23#1451982312yes—
526C23#1451982411yescharacteristic
527C23#1451982412yes—
528C23#1451982511yescharacteristic
529C23#1451982511yescharacteristic
530Q8—416no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—2442no—
561C2×C4—2442no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2442no—
565C2×C4—2442no—
566C2×C4—2442no—
567C2×C4—2442no—
568C2×C4—2442no—
569C2×C4—2442no—
570C2×C4—2442no—
571C2×C4—2442no—
572C2×C4—2441no—
573C2×C4—2442no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4—2442no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2442no—
581C2×C4—2442no—
582C2×C4—2442no—
583C2×C4—2442no—
584C2×C4—2442no—
585C2×C4—2442no—
586C2×C4—2442no—
587C2×C4—2442no—
588C2×C4D4×Dic6114yes—
589C22—44no—
590C22—42no—
591C22—44no—
592C22—42no—
593C22—42no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—82no—
599C22—82no—
600C22C2×D4×Dic6111yescharacteristic
601C22#1684023712yes—
602C22#1684024011yescharacteristic
603C22#1684024512yes—
604C22#1684024511yescharacteristic
605C22#1684032211yescharacteristic
606C22#1684032711yescharacteristic
607C22#1684033011yescharacteristic
608C22#1684033211yescharacteristic
609C22#1684033511yescharacteristic
610C22#1684034211yescharacteristic
611C22#1684034712yes—
612C22#1684037211yescharacteristic
613C22#1684038112yes—
614C22#1684038511yescharacteristic
615C22#1684050412yes—
616C22#1684050612yes—
617C22#1684050612yes—
618C22#1684050812yes—
619C22#1684050812yes—
620C22#1684051212yes—
621C22#1684051312yes—
622C22#1684051312yes—
623C4—24no—
624C4—44no—
625C4—44no—
626C4—42no—
627C4—4881no—
628C4—4882no—
629C4—4881no—
630C4—4882no—
631C4—2442no—
632C4—2442no—
633C2—82no—
634C2#2144848011yescharacteristic
635C2#2144850311yescharacteristic
636C2#2144853211yescharacteristic
637C2#2144898512yes—
638C2#2144899312yes—
639C2#2145382911yescharacteristic
640C2#2145384511yescharacteristic
641C2#2145386711yescharacteristic
642C2#2145388111yescharacteristic
643C2#2145397512yes—
644C2#2145398912yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#393C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#393D61
hypocenterC61#14625
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C2×#16839669C2semidirect
3. #21444090C2semidirect
4. #21444084C2semidirect
5. #21444076C2semidirect
6. #21444076C2semidirect
10. #21444044C2semidirect
35. C61×#393C4semidirect
344. #393Dic61semidirect
360. C61#14625semidirect

Maximal subgroups

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

subgroupindex
C2×#168396692
C2×#168396552
#214440902
#214440842
#214440762
#214440682
#214440642
#214440442
C2×C61×#3932
#1462561