Finite Group Databasebeta

← #29609193

Subgroups — #29609193

Order 15616.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839655C212yesmaximal, complemented
2#21444087C212yesmaximal, complemented
3#21444064C212yesmaximal, complemented
4#21444060C211yesmaximal, characteristic
5#21444060C211yesmaximal, characteristic
6#21444056C212yesmaximal, complemented
7#21444048C212yesmaximal, complemented
8#21444042C212yesmaximal, complemented
9C22×#123×C61C211yesmaximal, characteristic
10C22×C4⋊Dic61C2212yes—
11C22×C22⋊Dic61C2212yes—
12C22×C22⋊Dic61C2212yes—
13C22×C22⋊Dic61C2211yescharacteristic
14C22×C22⋊Dic61C2212yes—
15C22×C22⋊Dic61C2211yescharacteristic
16C22×C4×Dic61C2212yes—
17#16839655—28no—
18C2×#14519684C2212yes—
19C2×#14519684C2212yes—
20C2×#14519684C2212yes—
21C2×#14519684C2212yes—
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2211yescharacteristic
25C2×#14519684C2212yes—
26C2×#14519684C2211yescharacteristic
27C23×D4×C61C2211yescharacteristic
28C24×C4×C61C2211yescharacteristic
29C2×#123×C61—28no—
30C2×#123×C61C418yescomplemented
31C22×C4⋊C4×C61C2212yes—
32C22×C22⋊C4×C61C2212yes—
33C22×C22⋊C4×C61C2211yescharacteristic
34C23×Dic61C2312yes—
35C23×Dic61C2312yes—
36C23×Dic61C2312yes—
37C23×Dic61C2312yes—
38C2×C4⋊Dic61—24no—
39C2×C4⋊Dic61—24no—
40C2×C4⋊Dic61—42no—
41C2×C22⋊Dic61—24no—
42C2×C22⋊Dic61—24no—
43C2×C22⋊Dic61—24no—
44C2×C22⋊Dic61—24no—
45C2×C22⋊Dic61—24no—
46C2×C22⋊Dic61—24no—
47C2×C22⋊Dic61—41no—
48C2×C22⋊Dic61—42no—
49C2×C22⋊Dic61—42no—
50C2×C22⋊Dic61—42no—
51C2×C22⋊Dic61—42no—
52C2×C22⋊Dic61—41no—
53C2×C22⋊Dic61—42no—
54C2×C4×Dic61—24no—
55C2×C4×Dic61—24no—
56C2×C4×Dic61—42no—
57#14519684—24no—
58#14519684—24no—
59#14519684—41no—
60#14519684—42no—
61#14519684—42no—
62#14519684—42no—
63#14519684—42no—
64#14519684—41no—
65#14519684—42no—
66C25×C61C2311yescharacteristic
67C25×C61C2311yescharacteristic
68C22×D4×C61—24no—
69C22×D4×C61—42no—
70C22×D4×C61—41no—
71C22×D4×C61—41no—
72C22×D4×C61C2×C414yes—
73C23×C4×C61—24no—
74C23×C4×C61—42no—
75C23×C4×C61—41no—
76C23×C4×C61—41no—
77C23×C4×C61C2×C414yes—
78C23×C4×C61C2312yes—
79C23×C4×C61C2311yescharacteristic
80C23×C4×C61C2312yes—
81#123×C61—232no—
82C2×C4⋊C4×C61—24no—
83C2×C4⋊C4×C61—24no—
84C2×C4⋊C4×C61C2×C418yes—
85C2×C22⋊C4×C61—24no—
86C2×C22⋊C4×C61—24no—
87C2×C22⋊C4×C61C2×C418yes—
88C2×C22⋊C4×C61C2×C414yes—
89C2×C22⋊C4×C61D418yes—
90C24×C61—22no—
91C24×C61—22no—
92C24×C61—22no—
93C24×C61—21no—
94C24×C61—21no—
95C24×C61—22no—
96C24×C61—22no—
97C24×C61—22no—
98C24×C61—22no—
99C24×C61—22no—
100C24×C61—22no—
101C24×C61—21no—
102C24×C61—21no—
103C24×C61—22no—
104C24×C61—22no—
105C24×C61C22×C412yes—
106C24×C61C22×C412yes—
107C24×C61C2×D414yes—
108C24×C61C2411yescharacteristic
109C2×D4×C61—28no—
110C2×D4×C61—44no—
111C2×D4×C61—44no—
112C2×D4×C61—48no—
113C2×D4×C61—48no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—28no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—44no—
130C22×C4×C61—44no—
131C22×C4×C61—48no—
132C22×C4×C61—48no—
133C22×C4×C61C22×C414yes—
134C22×C4×C61C22×C412yes—
135C22×C4×C61C22×C414yes—
136C22×C4×C61C2×D414yes—
137C22×C4×C61C2×D414yes—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—22no—
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—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61#4114yes—
165C22×Dic61#4114yes—
166C4⋊C4×C61—216no—
167C22⋊C4×C61—216no—
168C22⋊C4×C61C22⋊C4116yescomplemented
169C22⋊Dic61—44no—
170C22⋊Dic61—48no—
171C22⋊Dic61—48no—
172C22⋊Dic61—48no—
173C22⋊Dic61—44no—
174C4⋊Dic61—48no—
175C4×Dic61—48no—
176C23×C61—24no—
177C23×C61—22no—
178C23×C61—22no—
179C23×C61—24no—
180C23×C61—24no—
181C23×C61—24no—
182C23×C61—24no—
183C23×C61—24no—
184C23×C61—24no—
185C23×C61—24no—
186C23×C61—22no—
187C23×C61—24no—
188C23×C61—22no—
189C23×C61—22no—
190C23×C61—24no—
191C23×C61—42no—
192C23×C61—42no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61—41no—
196C23×C61—42no—
197C23×C61—41no—
198C23×C61—41no—
199C23×C61—42no—
200C23×C61—41no—
201C23×C61—42no—
202C23×C61—42no—
203C23×C61—42no—
204C23×C61—42no—
205C23×C61—42no—
206C23×C61—42no—
207C23×C61—42no—
208C23×C61—42no—
209C23×C61—42no—
210C23×C61—42no—
211C23×C61—41no—
212C23×C61—42no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61—42no—
216C23×C61—41no—
217C23×C61C2×C22⋊C414yes—
218C23×C61C23×C411yescharacteristic
219C23×C61C22×D412yes—
220C23×C61C2×#4112yes—
221C23×C61C2×#4112yes—
222C23×C61H(5,𝔽2)12yes—
223C23×C61H(5,𝔽2)11yescharacteristic
224C23×C61H(5,𝔽2)11yescharacteristic
225C23×C61H(5,𝔽2)12yes—
226C23×C612−1+412yes—
227D4×C61—416no—
228C2×C4×C61—24no—
229C2×C4×C61—24no—
230C2×C4×C61—24no—
231C2×C4×C61—24no—
232C2×C4×C61—24no—
233C2×C4×C61—24no—
234C2×C4×C61—24no—
235C2×C4×C61—22no—
236C2×C4×C61—24no—
237C2×C4×C61—24no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—416no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61C2×C22⋊C418yes—
248C2×Dic61—24no—
249C2×Dic61—24no—
250C2×Dic61—24no—
251C2×Dic61—24no—
252C2×Dic61—24no—
253C2×Dic61—24no—
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—
266C2×Dic61—42no—
267C2×Dic61—42no—
268C2×Dic61—42no—
269C2×Dic61—42no—
270C2×Dic61—42no—
271C2×Dic61—42no—
272C2×Dic61—42no—
273C2×Dic61—42no—
274C2×Dic61—42no—
275C2×Dic61—42no—
276#14506—611nomaximal, Sylow
277C22×C61—24no—
278C22×C61—28no—
279C22×C61—44no—
280C22×C61—42no—
281C22×C61—42no—
282C22×C61—44no—
283C22×C61—44no—
284C22×C61—44no—
285C22×C61—44no—
286C22×C61—42no—
287C22×C61—44no—
288C22×C61—44no—
289C22×C61—42no—
290C22×C61—42no—
291C22×C61—82no—
292C22×C61—82no—
293C22×C61—82no—
294C22×C61—82no—
295C22×C61C22×C22⋊C411yescharacteristic
296C22×C61C4×#4112yes—
297C22×C61#51811yescharacteristic
298C22×C61#51811yescharacteristic
299C22×C61#52012yes—
300C22×C61#53512yes—
301C22×C61#53512yes—
302C22×C61#53812yes—
303C22×C61#53912yes—
304C22×C61#54012yes—
305C22×C61#54212yes—
306C22×C61#54612yes—
307C22×C61#54612yes—
308C22×C61#54712yes—
309C22×C61#54712yes—
310C22×C61#55111yescharacteristic
311C22×C61#55312yes—
312C22×C61#55911yescharacteristic
313C22×C61#56011yescharacteristic
314C22×C61#56212yes—
315C22×C61#56311yescharacteristic
316C4×C61—28no—
317C4×C61—44no—
318C4×C61—42no—
319Dic61—44no—
320Dic61—44no—
321Dic61—82no—
322Dic61—82no—
323C22×#123D6111yescharacteristic
324C2×#388—612no—
325#1445—612no—
326#1439—612no—
327#1438—611no—
328#1438—611no—
329#1437—612no—
330C4⋊#95—612no—
331C22⋊#95—612no—
332C2×C61—44no—
333C2×C61—82no—
334C2×C61#230911yescharacteristic
335C2×C61#233512yes—
336C2×C61#233912yes—
337C2×C61#237411yescharacteristic
338C2×C61#237611yescharacteristic
339C2×C61#270312yes—
340C2×C61#270612yes—
341C2×C61#271012yes—
342C2×C61#271812yes—
343C23×D4C2×D6111yescharacteristic
344C24×C4C2×D6111yescharacteristic
345C2×#123—28no—
346C2×#123Dic6118yescomplemented
347C22×C4⋊C4—612no—
348C22×C4⋊C4C2×D6112yes—
349C22×C22⋊C4—612no—
350C22×C22⋊C4—612no—
351C22×C22⋊C4—611no—
352C22×C22⋊C4—612no—
353C22×C22⋊C4—611no—
354C22×C22⋊C4C2×D6112yes—
355C22×C22⋊C4C2×D6111yescharacteristic
356C22×C42—612no—
357#388—1228no—
358C2×#95—612no—
359C2×#95—612no—
360C2×#95—612no—
361C2×#95—612no—
362C2×#95—612no—
363C2×#95—612no—
364C2×#95—611no—
365C2×#95—612no—
366C2×#95—611no—
367C61#1450611yescharacteristic, complemented, Sylow
368C25C22×D6111yescharacteristic
369C25C22×D6111yescharacteristic
370C22×D4—24no—
371C22×D4—41no—
372C22×D4—41no—
373C22×D4—42no—
374C22×D4C2×Dic6114yes—
375C23×C4—24no—
376C23×C4—41no—
377C23×C4—41no—
378C23×C4—42no—
379C23×C4—612no—
380C23×C4—612no—
381C23×C4—612no—
382C23×C4—612no—
383C23×C4C2×Dic6114yes—
384C23×C4C22×D6112yes—
385C23×C4C22×D6111yescharacteristic
386C23×C4C22×D6112yes—
387#123—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—1224no—
391C2×C4⋊C4—1224no—
392C2×C4⋊C4—2442no—
393C2×C4⋊C4C2×Dic6118yes—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—1224no—
397C2×C22⋊C4—1224no—
398C2×C22⋊C4—1224no—
399C2×C22⋊C4—1224no—
400C2×C22⋊C4—1224no—
401C2×C22⋊C4—1224no—
402C2×C22⋊C4—2441no—
403C2×C22⋊C4—2442no—
404C2×C22⋊C4—2442no—
405C2×C22⋊C4—2442no—
406C2×C22⋊C4—2442no—
407C2×C22⋊C4—2441no—
408C2×C22⋊C4—2442no—
409C2×C22⋊C4C2×Dic6118yes—
410C2×C22⋊C4C2×Dic6114yes—
411C2×C22⋊C4C22⋊D6118yes—
412C2×C42—1224no—
413C2×C42—1224no—
414C2×C42—2442no—
415#95—1224no—
416#95—1224no—
417#95—2442no—
418#95—2442no—
419#95—2442no—
420#95—2442no—
421#95—2441no—
422#95—2442no—
423#95—2441no—
424C24—22no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24C22×Dic6112yes—
440C24C22×Dic6112yes—
441C24C2×C22⋊D6114yes—
442C24C23×D6111yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—28no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4—48no—
466C22×C4—48no—
467C22×C4—614no—
468C22×C4—614no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4C22×Dic6114yes—
496C22×C4C22×Dic6112yes—
497C22×C4C22×Dic6114yes—
498C22×C4C2×C22⋊D6114yes—
499C22×C4C2×C22⋊D6114yes—
500C4⋊C4—216no—
501C4⋊C4—2448no—
502C22⋊C4—216no—
503C22⋊C4—2444no—
504C22⋊C4—2448no—
505C22⋊C4—2448no—
506C22⋊C4—2448no—
507C22⋊C4—2444no—
508C22⋊C4C22⋊Dic61116yescomplemented
509C42—2448no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—42no—
526C23—41no—
527C23—41no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—41no—
537C23—41no—
538C23—42no—
539C23—41no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—41no—
551C23C2×C22⋊Dic6114yes—
552C23C23×Dic6111yescharacteristic
553C23C22×C22⋊D6112yes—
554C23#41×D6112yes—
555C23#41×D6112yes—
556C23#1451982211yescharacteristic
557C23#1451982211yescharacteristic
558C23#1451982212yes—
559C23#1451982312yes—
560C23#1451982412yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—416no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—1224no—
582C2×C4—1224no—
583C2×C4—1224no—
584C2×C4—1224no—
585C2×C4—1224no—
586C2×C4—1224no—
587C2×C4—2442no—
588C2×C4—2442no—
589C2×C4—2442no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4—2442no—
596C2×C4—2442no—
597C2×C4—2442no—
598C2×C4—2442no—
599C2×C4—2442no—
600C2×C4—2442no—
601C2×C4—2442no—
602C2×C4—2442no—
603C2×C4—2442no—
604C2×C4—2442no—
605C2×C4—2442no—
606C2×C4—2442no—
607C2×C4—2442no—
608C2×C4—2442no—
609C2×C4C2×C22⋊Dic6118yes—
610C22—28no—
611C22—24no—
612C22—42no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—42no—
619C22—42no—
620C22—44no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C22×C22⋊Dic6111yescharacteristic
629C22#41×Dic6112yes—
630C22#1684023711yescharacteristic
631C22#1684023711yescharacteristic
632C22#1684024512yes—
633C22#1684032912yes—
634C22#1684032912yes—
635C22#1684034812yes—
636C22#1684035512yes—
637C22#1684036412yes—
638C22#1684038012yes—
639C22#1684040012yes—
640C22#1684040012yes—
641C22#1684041112yes—
642C22#1684041112yes—
643C22#1684044011yescharacteristic
644C22#1684045712yes—
645C22#1684049611yescharacteristic
646C22#1684050211yescharacteristic
647C22#1684050912yes—
648C22#1684051511yescharacteristic
649C4—28no—
650C4—44no—
651C4—42no—
652C4—4882no—
653C4—4882no—
654C4—2444no—
655C4—2444no—
656C2—44no—
657C2—82no—
658C2#2144840111yescharacteristic
659C2#2144861312yes—
660C2#2144864912yes—
661C2#2144895511yescharacteristic
662C2#2144896711yescharacteristic
663C2#2145245612yes—
664C2#2145250112yes—
665C2#2145255712yes—
666C2#2145266512yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC22×#123×C61C2
socle, cosocleC24×C61C24
prime radicalC23×D4×C61C22
hypercenterC22×#123D61
hypocenterC61#14506
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C2×#16839655C2semidirect
2. #21444087C2semidirect
3. #21444064C2semidirect
6. #21444056C2semidirect
7. #21444048C2semidirect
8. #21444042C2semidirect
30. C2×#123×C61C4semidirect
168. C22⋊C4×C61C22⋊C4semidirect
346. C2×#123Dic61semidirect
367. C61#14506semidirect
508. C22⋊C4C22⋊Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396552
#214440872
#214440642
#214440602
#214440562
#214440482
#214440422
C22×#123×C612
#1450661