Finite Group Databasebeta

← #29689274

Subgroups — #29689274

Order 15616.

1538 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840320C211yesmaximal, characteristic
2#21448416C211yesmaximal, characteristic, complemented
3#21448414C211yesmaximal, characteristic, complemented
4#21446656C211yesmaximal, characteristic, complemented
5#21446655C211yesmaximal, characteristic, complemented
6#21446654C211yesmaximal, characteristic, complemented
7#21446653C214yesmaximal, complemented
8#21445732C214yesmaximal, complemented
9C61×#1964C211yesmaximal, characteristic, complemented
10C22×D4×D61C2212yes—
11#16840320—22no—
12#16840320—22no—
13#16840320—22no—
14#16840320—22no—
15C2×#14519762C412yescomplemented
16C2×#14519759C412yescomplemented
17C2×#14519751C2211yescharacteristic
18C2×#14519749C2212yes—
19C2×#14519747C412yescomplemented
20C2×#14519745C412yescomplemented
21C22×#11758198C2211yescharacteristic
22C2×#14519692C2214yescomplemented
23C2×#14519691C2214yescomplemented
24C2×#14519691C2214yescomplemented
25#16839654—22no—
26#16839653—22no—
27#16839652—22no—
28#16839651—22no—
29#16839622C2211yescharacteristic, complemented
30#16839620C2212yescomplemented
31#16839617C2212yes—
32#16839617C2212yes—
33C22⋊C4×Dic61C2212yescomplemented
34C4×C22⋊Dic61C2211yescharacteristic, complemented
35C2×#121×C61C2211yescharacteristic
36C2×#99×C61C2214yescomplemented
37C61×#380C2211yescharacteristic, complemented
38C4×C22⋊C4×C61C2211yescharacteristic, complemented
39C24×D61C2×C412yes—
40C24×D61C2311yescharacteristic
41C22×D244C2×C412yes—
42C22×D244C2×C411yescharacteristic
43C22×C22⋊D61C2×C412yes—
44C22×C22⋊D61C2×C412yes—
45C22×C22⋊D61C2312yes—
46C2×D4×D61—24no—
47C2×D4×D61—24no—
48C2×D4×D61—44no—
49C2×D4×D61—44no—
50C23×Dic61C2311yescharacteristic
51C22×C4×D61C2×C412yes—
52#14519762—24no—
53#14519762—24no—
54#14519759—24no—
55#14519759—24no—
56#14519751—21no—
57#14519751—21no—
58#14519751—21no—
59#14519751—21no—
60#14519749—24no—
61#14519749—24no—
62#14519747—24no—
63#14519747—24no—
64#14519745—24no—
65#14519745—24no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61C2×C411yescharacteristic
68C2×#11758196—22no—
69C2×#11758196C2×C412yes—
70C2×C22⋊Dic61C2×C412yes—
71C2×C22⋊Dic61C2312yes—
72C2×C22⋊Dic61C2312yes—
73C2×#11758198—22no—
74C2×#11758198—22no—
75C2×#11758198—22no—
76C2×#11758198—22no—
77C2×#11758198C2×C412yes—
78C2×#11758198C2×C412yes—
79C2×#11758198C2×C412yes—
80C2×#11758198C2×C412yes—
81C2×#11758198D412yes—
82C2×#11758198D412yes—
83C2×#11758198D412yes—
84C2×#11758198D412yes—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—22no—
87#14519692—44no—
88#14519691—44no—
89#14519691—44no—
90#14519684—21no—
91#14519684—21no—
92#14519684—22no—
93#14519684—22no—
94C22×D4×C61C2×C411yescharacteristic
95C22×D4×C61C2312yes—
96C23×C4×C61C2311yescharacteristic
97#121×C61—21no—
98#121×C61—21no—
99#121×C61—21no—
100#121×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61C2×C411yescharacteristic
103C2×C22⋊C4×C61C2×C412yes—
104C2×C22⋊C4×C61C2312yes—
105C2×C22⋊C4×C61C2312yes—
106C2×C42×C61—21no—
107#99×C61—44no—
108#95×C61—21no—
109#95×C61—21no—
110C24×C61C22×C412yes—
111C24×C61C2411yescharacteristic
112C23×D61—22no—
113C23×D61—22no—
114C23×D61—24no—
115C23×D61—44no—
116C23×D61—81no—
117C23×D61—81no—
118C23×D61—82no—
119C23×D61—82no—
120C23×D61C22×C412yes—
121C23×D61C22×C412yes—
122C23×D61C2×D412yes—
123C23×D61C2×D412yes—
124C2×D4×C61—22no—
125C2×D4×C61—22no—
126C2×D4×C61—24no—
127C2×D4×C61—24no—
128C2×D4×C61—21no—
129C2×D4×C61—21no—
130C2×D4×C61—81no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—81no—
134C22×C4×C61C22×C412yes—
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C2×C22⋊D61—22no—
142C2×C22⋊D61—22no—
143C2×C22⋊D61—24no—
144C2×C22⋊D61—24no—
145C2×C22⋊D61—24no—
146C2×C22⋊D61—24no—
147C2×C22⋊D61—44no—
148C2×C22⋊D61—82no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—81no—
152C22×Dic61C22×C412yes—
153C22×Dic61C22×C412yes—
154C22×Dic61C2×D412yes—
155C22×Dic61C2×D412yes—
156D4×D61—48no—
157D4×D61—416no—
158D4×D61—48no—
159C2×D244—24no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244—44no—
163C2×D244—81no—
164C2×C4×D61—24no—
165C2×C4×D61—44no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—81no—
169C22⋊C4×C61—22no—
170C22⋊C4×C61—22no—
171C22⋊C4×C61—22no—
172C22⋊C4×C61—24no—
173C22⋊C4×C61—22no—
174C42×C61—81no—
175C22⋊Dic61—24no—
176C22⋊Dic61—22no—
177C22⋊Dic61—24no—
178C22⋊Dic61—22no—
179#11758198—22no—
180#11758198—22no—
181#11758198—24no—
182#11758198—82no—
183#11758198—82no—
184#11758198—82no—
185#11758198—82no—
186#11758198C22⋊C414yes—
187#11758198C22⋊C414yes—
188#11758198C22⋊C414yes—
189#11758198C22⋊C414yes—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—81no—
193#11758196—24no—
194#11758196—82no—
195C4×Dic61—82no—
196C4×Dic61—81no—
197C23×C61—22no—
198C23×C61—24no—
199C23×C61—41no—
200C23×C61—41no—
201C23×C61—42no—
202C23×C61—42no—
203C23×C61C23×C411yescharacteristic
204C23×C61C22×D411yescharacteristic
205C23×C61C22×D411yescharacteristic
206C23×C61H(5,𝔽2)12yes—
207C23×C61H(5,𝔽2)12yes—
208C22×D61—24no—
209C22×D61—22no—
210C22×D61—24no—
211C22×D61—22no—
212C22×D61—22no—
213C22×D61—24no—
214C22×D61—42no—
215C22×D61—42no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—48no—
221C22×D61—42no—
222C22×D61—42no—
223C22×D61—84no—
224C22×D61—84no—
225C22×D61—84no—
226C22×D61—84no—
227C22×D61—816no—
228C22×D61C2×C22⋊C414yes—
229D4×C61—42no—
230D4×C61—44no—
231D4×C61—42no—
232D4×C61—81no—
233D4×C61—81no—
234C2×C4×C61—22no—
235C2×C4×C61—24no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61—42no—
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C2×C22⋊C411yescharacteristic
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C22⋊D61—48no—
253C22⋊D61—42no—
254C22⋊D61—44no—
255C22⋊D61—42no—
256C22⋊D61—84no—
257C2×Dic61—22no—
258C2×Dic61—24no—
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×Dic61C2×C22⋊C414yes—
269D244—48no—
270D244—81no—
271D244—81no—
272C4×D61—48no—
273#21795—611nomaximal, Sylow
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—21no—
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—42no—
281C22×C61—42no—
282C22×C61—42no—
283C22×C61—42no—
284C22×C61—42no—
285C22×C61—84no—
286C22×C61C22×C22⋊C411yescharacteristic
287C22×C61#51812yes—
288C22×C61#53511yescharacteristic
289C22×C61#53512yes—
290C22×C61#53511yescharacteristic
291C2×D61—24no—
292C2×D61—24no—
293C2×D61—24no—
294C2×D61—48no—
295C2×D61—42no—
296C2×D61—42no—
297C2×D61—42no—
298C2×D61—82no—
299C2×D61—84no—
300C2×D61—82no—
301C2×D61—816no—
302C2×D61—84no—
303C4×C61—21no—
304C4×C61—21no—
305C4×C61—21no—
306C4×C61—21no—
307C4×C61—42no—
308C4×C61—82no—
309C4×C61—82no—
310Dic61—24no—
311Dic61—42no—
312Dic61—82no—
313Dic61—82no—
314C2×#534—611no—
315#2312—611no—
316#2312—611no—
317#1964—614no—
318#1964—611no—
319#1964—611no—
320#1964—611no—
321#1964D6111yescharacteristic, complemented
322#1781—614no—
323C2×C61—21no—
324C2×C61—22no—
325C2×C61—21no—
326C2×C61—22no—
327C2×C61—82no—
328C2×C61#230911yescharacteristic
329C2×C61#288311yescharacteristic
330C2×C61#288311yescharacteristic
331D61—44no—
332D61—82no—
333C23×D4—612no—
334#534—1222no—
335#534—1222no—
336#534—1222no—
337#534—1222no—
338C2×#123—612no—
339C2×#123—612no—
340C2×#121—612no—
341C2×#121—611no—
342C2×#121C2×D6111yescharacteristic
343C2×#120—612no—
344C2×#120—612no—
345C22×C22⋊C4—611no—
346C2×#99—614no—
347C2×#99—614no—
348C2×#99—614no—
349C2×#99C2×D6114yescomplemented
350#388—1222no—
351#388—1222no—
352#388—1222no—
353#388—1222no—
354#380—611no—
355#380—612no—
356#380C2×D6111yescharacteristic, complemented
357#379—612no—
358#379—612no—
359C4×C22⋊C4—611no—
360C4×C22⋊C4—612no—
361C4×C22⋊C4C2×D6111yescharacteristic, complemented
362C61#2179511yescharacteristic, complemented, Sylow
363C25—611no—
364C25—612no—
365C22×D4—612no—
366C22×D4—612no—
367C22×D4—612no—
368C22×D4—611no—
369C22×D4—612no—
370C22×D4—1224no—
371C22×D4—1224no—
372C22×D4—2444no—
373C22×D4—2444no—
374C22×D4C4×D6111yescharacteristic
375C22×D4C22×D6112yes—
376C23×C4—611no—
377C23×C4—612no—
378C23×C4C22×D6111yescharacteristic
379#123—1224no—
380#123—1224no—
381#123—1224no—
382#123—1224no—
383#121—21no—
384#121—21no—
385#121—21no—
386#121—21no—
387#121—1224no—
388#121—1224no—
389#121—1221no—
390#121—1221no—
391#121—1221no—
392#121—1221no—
393#120—1224no—
394#120—1224no—
395#120—1224no—
396#120—1224no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—612no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—1222no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4C4×D6111yescharacteristic
403C2×C22⋊C4—612no—
404C2×C22⋊C4—612no—
405C2×C22⋊C4—612no—
406C2×C22⋊C4—612no—
407C2×C22⋊C4—612no—
408C2×C22⋊C4—612no—
409C2×C22⋊C4—612no—
410C2×C22⋊C4—612no—
411C2×C22⋊C4—612no—
412C2×C22⋊C4—612no—
413C2×C22⋊C4—612no—
414C2×C22⋊C4—1222no—
415C2×C22⋊C4—1222no—
416C2×C22⋊C4—1222no—
417C2×C22⋊C4—1222no—
418C2×C22⋊C4C4×D6112yes—
419C2×C22⋊C4C22×D6112yes—
420C2×C22⋊C4C22×D6112yes—
421C2×C42—21no—
422C2×C42—1222no—
423C2×C42—1221no—
424#99—44no—
425#99—2444no—
426#99—2444no—
427#99—2444no—
428#95—21no—
429#95—21no—
430#95—1222no—
431#95—1222no—
432#95—1221no—
433#95—1221no—
434C24—612no—
435C24—612no—
436C24—612no—
437C24—612no—
438C24—1224no—
439C24—1222no—
440C24—1222no—
441C24—4882no—
442C24—4882no—
443C24—4881no—
444C24—4881no—
445C24—2444no—
446C24C2×C4×D6112yes—
447C24C23×D6111yescharacteristic
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—24no—
451C2×D4—24no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—81no—
455C2×D4—1224no—
456C2×D4—1224no—
457C2×D4—1224no—
458C2×D4—1222no—
459C2×D4—1222no—
460C2×D4—1224no—
461C2×D4—1224no—
462C2×D4—1221no—
463C2×D4—1221no—
464C2×D4—4881no—
465C2×D4—4882no—
466C2×D4—2444no—
467C2×D4—2444no—
468C2×D4—2448no—
469C2×D4—24416no—
470C2×D4—2448no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—81no—
474C22×C4—612no—
475C22×C4—612no—
476C22×C4—612no—
477C22×C4—612no—
478C22×C4—1224no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4—4881no—
482C22×C4—2444no—
483C22×C4C2×C4×D6112yes—
484C22×C4C2×C4×D6111yescharacteristic
485C22×C4C2×C4×D6111yescharacteristic
486C22×C4D4×D6111yescharacteristic
487C22×C4D4×D6111yescharacteristic
488C22×C4D4×D6111yescharacteristic
489C22×C4D4×D6111yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—81no—
493C4⋊C4—1224no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—4882no—
497C4⋊C4—4881no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—24no—
502C22⋊C4—22no—
503C22⋊C4—614no—
504C22⋊C4—614no—
505C22⋊C4—614no—
506C22⋊C4—614no—
507C22⋊C4—1224no—
508C22⋊C4—1224no—
509C22⋊C4—1222no—
510C22⋊C4—1222no—
511C22⋊C4—1222no—
512C22⋊C4—1222no—
513C22⋊C4—1224no—
514C22⋊C4—4882no—
515C22⋊C4—4882no—
516C22⋊C4—4882no—
517C22⋊C4—4882no—
518C42—81no—
519C42—4881no—
520C42—4882no—
521C23—22no—
522C23—24no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23—42no—
527C23—614no—
528C23—1222no—
529C23—1224no—
530C23—1222no—
531C23—1224no—
532C23—1224no—
533C23—1222no—
534C23—4884no—
535C23—4884no—
536C23—4884no—
537C23—4884no—
538C23—48816no—
539C23—2442no—
540C23—2442no—
541C23—2442no—
542C23—2442no—
543C23—2442no—
544C23—2442no—
545C23—2442no—
546C23—2442no—
547C23—2448no—
548C23C22×C4×D6111yescharacteristic
549C23C2×D4×D6111yescharacteristic
550C23C2×D4×D6111yescharacteristic
551C23#1451982212yes—
552C23#1451982312yes—
553D4—42no—
554D4—44no—
555D4—42no—
556D4—81no—
557D4—81no—
558D4—4881no—
559D4—4881no—
560D4—4884no—
561D4—2448no—
562D4—2448no—
563D4—2442no—
564D4—2444no—
565D4—2442no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—614no—
581C2×C4—1222no—
582C2×C4—1224no—
583C2×C4—2448no—
584C2×C4—2442no—
585C2×C4—2442no—
586C2×C4—2442no—
587C2×C4—2442no—
588C2×C4—2442no—
589C2×C4—2442no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4C22⋊C4×D6111yescharacteristic
594C2×C4C22⋊C4×D6111yescharacteristic
595C2×C4C22⋊C4×D6111yescharacteristic
596C2×C4C22⋊C4×D6111yescharacteristic
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—84no—
609C22—1224no—
610C22—1224no—
611C22—1224no—
612C22—4884no—
613C22—4882no—
614C22—4884no—
615C22—4882no—
616C22—48816no—
617C22—2448no—
618C22—2442no—
619C22—2442no—
620C22—2442no—
621C22C2×C22⋊C4×D6111yescharacteristic
622C22#1684023412yes—
623C22#1684032511yescharacteristic
624C22#1684032812yes—
625C22#1684033011yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—42no—
631C4—82no—
632C4—82no—
633C4—1224no—
634C4—4882no—
635C4—4882no—
636C4—2442no—
637C2—21no—
638C2—22no—
639C2—21no—
640C2—22no—
641C2—82no—
642C2—4882no—
643C2—2444no—
644C2#2144839811yescharacteristic
645C2#2145427711yescharacteristic
646C2#2145427811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1964C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840320C2
cosocleC24×C61C24
hypercenter#1964D61
hypocenterC61#21795
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #21448416C2semidirect
3. #21448414C2semidirect
4. #21446656C2semidirect
5. #21446655C2semidirect
6. #21446654C2semidirect
7. #21446653C2semidirect
8. #21445732C2semidirect
9. C61×#1964C2semidirect
15. C2×#14519762C4semidirect
16. C2×#14519759C4semidirect
19. C2×#14519747C4semidirect
20. C2×#14519745C4semidirect
22. C2×#14519692C22semidirect
23. C2×#14519691C22semidirect
24. C2×#14519691C22semidirect
29. #16839622C22semidirect
30. #16839620C22semidirect
33. C22⋊C4×Dic61C22semidirect
34. C4×C22⋊Dic61C22semidirect
36. C2×#99×C61C22semidirect
37. C61×#380C22semidirect
38. C4×C22⋊C4×C61C22semidirect
321. #1964D61semidirect
349. C2×#99C2×D61semidirect
356. #380C2×D61semidirect
361. C4×C22⋊C4C2×D61semidirect
362. C61#21795semidirect

Maximal subgroups

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

subgroupindex
C2×#168403202
#214484162
#214484142
#214466562
#214466552
#214466542
#214466532
#214457322
C61×#19642
#2179561