Finite Group Databasebeta

← #29571845

Subgroups — #29571845

Order 15616.

1040 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840350C211yesmaximal, characteristic
2#21446136C211yesmaximal, characteristic, complemented
3#21446126C211yesmaximal, characteristic, complemented
4C2×#16839498C211yesmaximal, characteristic, complemented
5C2×#16839495C211yesmaximal, characteristic, complemented
6C2×#16839486C211yesmaximal, characteristic, complemented
7C61×#1439C211yesmaximal, characteristic, complemented
8#16840350—22no—
9#16840350—22no—
10#16840350—22no—
11#16840350C414yescomplemented
12C2×#14519770—21no—
13C2×#14519763—21no—
14C2×#14519759—21no—
15C2×#14519756C2211yescharacteristic
16C2×#14519751C2211yescharacteristic
17C2×#14519750—21no—
18C2×#14519746—21no—
19C2×C4×C22⋊D61—21no—
20C2×#14519700—21no—
21C2×#14519697—21no—
22C2×C22⋊#92418C2211yescharacteristic
23C2×C22⋊#92418C2211yescharacteristic
24#16839524—21no—
25#16839524—21no—
26#16839498—22no—
27#16839495—22no—
28#16839486—22no—
29C22×C4⋊C4×C61C2211yescharacteristic
30C22×C22⋊C4×C61—21no—
31C22×C22⋊C4×C61C2211yescharacteristic
32C2×#95×C61—21no—
33C2×#95×C61C2211yescharacteristic
34C22×Dic122D411yescharacteristic
35C22×D244D411yescharacteristic
36C22×C22⋊D61—21no—
37C22×C22⋊D61—21no—
38C22×C22⋊D61—21no—
39C22×C4×D61—21no—
40C22×#92418—21no—
41C22×#92418—21no—
42#14519770—24no—
43#14519770—24no—
44#14519763—24no—
45#14519763—24no—
46#14519759—24no—
47#14519759—24no—
48#14519756—21no—
49#14519756—21no—
50#14519756C2×C412yes—
51#14519756D412yes—
52#14519751—21no—
53#14519751—21no—
54#14519751C2×C412yes—
55#14519751D412yes—
56#14519750—24no—
57#14519750—24no—
58#14519746—24no—
59#14519746—24no—
60C4×C22⋊D61—24no—
61C4×C22⋊D61—24no—
62C2×C4⋊Dic61D411yescharacteristic
63C2×C4⋊Dic61D411yescharacteristic
64C2×#11758196—21no—
65C2×#11758196—21no—
66C2×C22⋊Dic61—21no—
67C2×C22⋊Dic61—21no—
68C2×C22⋊Dic61—21no—
69C2×#11758198—21no—
70C2×#11758198—21no—
71C2×C4×Dic61—21no—
72#14519700—42no—
73#14519697—42no—
74C22⋊#92418—21no—
75C22⋊#92418—21no—
76C22⋊#92418—21no—
77C22⋊#92418—21no—
78C25×C61D411yescharacteristic
79C23×C4×C61—21no—
80C23×C4×C61—21no—
81C23×C4×C61D411yescharacteristic
82C23×C4×C61C2311yescharacteristic
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61—42no—
86C2×C22⋊C4×C61—21no—
87C2×C22⋊C4×C61—21no—
88C2×C22⋊C4×C61—21no—
89C2×C22⋊C4×C61—21no—
90C2×C22⋊C4×C61—42no—
91C2×C22⋊C4×C61—42no—
92C2×C22⋊C4×C61—42no—
93C2×C22⋊C4×C61C2×C412yes—
94C2×C22⋊C4×C61D412yes—
95#95×C61—21no—
96#95×C61—21no—
97#95×C61—42no—
98C24×C61—21no—
99C24×C61—21no—
100C24×C61—21no—
101C24×C61—21no—
102C24×C61—21no—
103C24×C61—21no—
104C24×C61—41no—
105C24×C61—41no—
106C24×C61—41no—
107C24×C61—41no—
108C24×C61C22⋊C412yes—
109C24×C61C2×D411yescharacteristic
110C23×D61—21no—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—41no—
116C22×C4×C61—41no—
117C22×C4×C61—41no—
118C22×C4×C61—41no—
119C22×C4×C61—41no—
120C22×C4×C61—41no—
121C22×C4×C61—41no—
122C22×C4×C61—41no—
123C22×C4×C61—41no—
124C22×C4×C61—41no—
125C22×C4×C61—41no—
126C22×C4×C61—41no—
127C22×C4×C61—41no—
128C22×C4×C61—41no—
129C22×C4×C61—41no—
130C22×C4×C61—41no—
131C22×C4×C61C22⋊C412yes—
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C2×C22⋊D61—22no—
139C2×C22⋊D61—22no—
140C2×C22⋊D61—24no—
141C2×C22⋊D61—24no—
142C2×C22⋊D61—41no—
143C2×C22⋊D61—41no—
144C2×C22⋊D61—41no—
145C2×C22⋊D61—41no—
146C2×C22⋊D61—81no—
147C2×C22⋊D61—81no—
148C2×C22⋊D61—81no—
149C2×C22⋊D61—81no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C2×D244—21no—
154C2×D244—41no—
155C2×D244—41no—
156C2×D244C22⋊C412yescomplemented
157C2×C4×D61—24no—
158C2×C4×D61—81no—
159C2×C4×D61—81no—
160C2×Dic122—21no—
161C2×Dic122—41no—
162C2×Dic122—41no—
163C2×Dic122C22⋊C412yescomplemented
164C4⋊C4×C61—22no—
165C4⋊C4×C61—22no—
166C4⋊C4×C61—41no—
167C4⋊C4×C61—41no—
168C22⋊C4×C61—22no—
169C22⋊C4×C61—22no—
170C22⋊C4×C61—22no—
171C22⋊C4×C61—22no—
172C22⋊C4×C61—48no—
173C22⋊Dic61—24no—
174C22⋊Dic61—24no—
175C22⋊Dic61—22no—
176C22⋊Dic61—22no—
177#11758198—24no—
178#11758198—22no—
179#11758198—22no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61C22⋊C412yescomplemented
183C4⋊Dic61C22⋊C412yescomplemented
184#11758196—24no—
185#11758196—22no—
186#11758196—22no—
187C4×Dic61—24no—
188C2×#92418—41no—
189C2×#92418—41no—
190C2×#92418—41no—
191C2×#92418—41no—
192C2×#92418—41no—
193C2×#92418—41no—
194C23×C61—21no—
195C23×C61—21no—
196C23×C61—21no—
197C23×C61—21no—
198C23×C61—22no—
199C23×C61—22no—
200C23×C61—22no—
201C23×C61—42no—
202C23×C61—42no—
203C23×C61—42no—
204C23×C61—42no—
205C23×C61—42no—
206C23×C61—42no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61—41no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61—81no—
216C23×C61—81no—
217C23×C61—81no—
218C23×C61—81no—
219C23×C61—81no—
220C23×C61—81no—
221C23×C61C2×C22⋊C411yescharacteristic
222C23×C61#12011yescharacteristic
223C23×C61#12011yescharacteristic
224C23×C61#13511yescharacteristic
225C23×C61#13511yescharacteristic
226C23×C61AGL(1,ℤ/8)11yescharacteristic
227C23×C61#13711yescharacteristic
228C22×D61—22no—
229C22×D61—41no—
230C22×D61—41no—
231C22×D61—41no—
232C22×D61—41no—
233C22×D61—41no—
234C22×D61—41no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—22no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—42no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61—81no—
254C2×C4×C61—81no—
255C2×C4×C61—81no—
256C2×C4×C61—81no—
257C2×C4×C61—81no—
258C2×C4×C61—81no—
259C2×C4×C61—81no—
260C2×C4×C61—81no—
261C2×C4×C61—81no—
262C2×C4×C61C2×C22⋊C411yescharacteristic
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61#12011yescharacteristic
265C2×C4×C61#12011yescharacteristic
266C22⋊D61—42no—
267C22⋊D61—42no—
268C22⋊D61—42no—
269C22⋊D61—42no—
270C22⋊D61—84no—
271C22⋊D61—84no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—22no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281D244—42no—
282D244—81no—
283C4×D61—84no—
284Dic122—42no—
285Dic122—81no—
286#92418—81no—
287#92418—81no—
288#8408—611nomaximal, Sylow
289C22×C61—21no—
290C22×C61—21no—
291C22×C61—21no—
292C22×C61—21no—
293C22×C61—21no—
294C22×C61—21no—
295C22×C61—21no—
296C22×C61—21no—
297C22×C61—21no—
298C22×C61—21no—
299C22×C61—21no—
300C22×C61—21no—
301C22×C61—44no—
302C22×C61—42no—
303C22×C61—42no—
304C22×C61—42no—
305C22×C61—82no—
306C22×C61—82no—
307C22×C61—82no—
308C22×C61—81no—
309C22×C61—81no—
310C22×C61—81no—
311C22×C61—81no—
312C22×C61#37911yescharacteristic
313C22×C61#41611yescharacteristic
314C22×C61#41711yescharacteristic
315C22×C61#44911yescharacteristic
316C22×C61#44911yescharacteristic
317C22×C61#45211yescharacteristic
318C22×C61#45211yescharacteristic
319C22×C61#45311yescharacteristic
320C22×C61#45511yescharacteristic
321C22×C61B(4,𝔽2)11yescharacteristic
322C22×C61#45811yescharacteristic
323C2×D61—42no—
324C2×D61—42no—
325C2×D61—42no—
326C2×D61—81no—
327C2×D61—81no—
328C2×D61—81no—
329C2×D61—81no—
330C4×C61—21no—
331C4×C61—21no—
332C4×C61—21no—
333C4×C61—21no—
334C4×C61—42no—
335C4×C61—82no—
336C4×C61—82no—
337Dic61—42no—
338Dic61—42no—
339Dic61—42no—
340C2×#538—611no—
341#1874—611no—
342#1872—611no—
343C2×#328—611no—
344C2×#327—611no—
345C2×#323—611no—
346#1439D6111yescharacteristic, complemented
347C2×C61—21no—
348C2×C61—21no—
349C2×C61—21no—
350C2×C61—21no—
351C2×C61—82no—
352C2×C61#160011yescharacteristic
353C2×C61#160611yescharacteristic
354C2×C61#161211yescharacteristic
355C2×C61#161811yescharacteristic
356C2×C61#178811yescharacteristic
357C2×C61#179011yescharacteristic
358C2×C61#179211yescharacteristic
359D61—82no—
360#538—614no—
361#538—1222no—
362#538—1222no—
363#538—1222no—
364C2×#126—1221no—
365C2×#124—1221no—
366C2×#123—1221no—
367C2×C22⋊Q8—611no—
368C2×#121—611no—
369C2×#121—1221no—
370C2×#120—1221no—
371C2×C4×D4—1221no—
372C22×C4⋊C4C2×D6111yescharacteristic
373C22×C22⋊C4—21no—
374C22×C22⋊C4C2×D6111yescharacteristic
375C2×#103—1221no—
376C2×#102—1221no—
377C2×C22⋊C8—611no—
378C2×C22⋊C8—611no—
379C2×#95—21no—
380C2×#95C2×D6111yescharacteristic
381#340—1221no—
382#340—1221no—
383#328—1222no—
384#327—1222no—
385#323—1222no—
386C61#840811yescharacteristic, complemented, Sylow
387C25C22⋊D6111yescharacteristic
388C22×Q8—611no—
389C22×D4—611no—
390C22×D4—1221no—
391C22×D4—1221no—
392C22×D4—1221no—
393C23×C4—21no—
394C23×C4—21no—
395C23×C4—1221no—
396C23×C4C22⋊D6111yescharacteristic
397C23×C4C22×D6111yescharacteristic
398C22×C8—1221no—
399C22×C8—1221no—
400#126—1224no—
401#126—1224no—
402#124—1224no—
403#124—1224no—
404#123—1224no—
405#123—1224no—
406C22⋊Q8—612no—
407C22⋊Q8—612no—
408C22⋊Q8—1221no—
409C22⋊Q8—1221no—
410#121—612no—
411#121—612no—
412#121—1224no—
413#121—1224no—
414#121—1221no—
415#121—1221no—
416#120—1224no—
417#120—1224no—
418C4×D4—1224no—
419C4×D4—1224no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4—1221no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4—42no—
434C2×C22⋊C4—1221no—
435C2×C22⋊C4—1221no—
436C2×C22⋊C4—1221no—
437C2×C22⋊C4—1221no—
438C2×C22⋊C4—1221no—
439C2×C22⋊C4C4×D6112yes—
440C2×C22⋊C4D24412yes—
441C2×C42—1221no—
442#103—2442no—
443#102—2442no—
444C22⋊C8—1221no—
445C22⋊C8—1221no—
446C22⋊C8—1221no—
447C22⋊C8—1221no—
448#95—21no—
449#95—21no—
450#95—42no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—41no—
458C24—41no—
459C24—41no—
460C24—41no—
461C24—1221no—
462C24#1175819812yes—
463C24C2×C22⋊D6111yescharacteristic
464C2×Q8—612no—
465C2×Q8—1221no—
466C2×Q8—2441no—
467C2×Q8—2441no—
468C2×D4—612no—
469C2×D4—1224no—
470C2×D4—1224no—
471C2×D4—1222no—
472C2×D4—1222no—
473C2×D4—1221no—
474C2×D4—4881no—
475C2×D4—4881no—
476C2×D4—4881no—
477C2×D4—4881no—
478C2×D4—2441no—
479C2×D4—2441no—
480C2×D4—2441no—
481C2×D4—2441no—
482C2×D4—2441no—
483C2×D4—2441no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—1224no—
505C22×C4—1221no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4—4881no—
509C22×C4—4881no—
510C22×C4#1175819812yes—
511C22×C4C2×C4×D6111yescharacteristic
512C22×C4C2×D24411yescharacteristic
513C22×C4D4×D6111yescharacteristic
514C22×C4D4×D6111yescharacteristic
515C22×C4D4×D6111yescharacteristic
516C22×C4D4×D6111yescharacteristic
517C2×C8—2441no—
518C2×C8—2441no—
519C2×C8—2441no—
520C2×C8—2441no—
521C2×C8—2441no—
522C2×C8—2441no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—612no—
528C4⋊C4—612no—
529C4⋊C4—1224no—
530C4⋊C4—1222no—
531C4⋊C4—1221no—
532C4⋊C4—1221no—
533C4⋊C4—1222no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—48no—
539C22⋊C4—1224no—
540C22⋊C4—1224no—
541C22⋊C4—1224no—
542C22⋊C4—1222no—
543C22⋊C4—1222no—
544C22⋊C4—1222no—
545C22⋊C4—1222no—
546C42—1224no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—81no—
569C23—81no—
570C23—81no—
571C23—81no—
572C23—81no—
573C23—81no—
574C23—1222no—
575C23—2441no—
576C23—2441no—
577C23—2441no—
578C23—2441no—
579C23—2441no—
580C23—2441no—
581C23C2×#1175819811yescharacteristic
582C23#1451974511yescharacteristic
583C23#1451974511yescharacteristic
584C23#1451979711yescharacteristic
585C23#1451979711yescharacteristic
586C23#1451980311yescharacteristic
587C23#1451980811yescharacteristic
588Q8—4881no—
589Q8—2442no—
590D4—4881no—
591D4—4884no—
592D4—4884no—
593D4—2442no—
594D4—2442no—
595D4—2442no—
596D4—2442no—
597D4—2442no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—81no—
617C2×C4—81no—
618C2×C4—81no—
619C2×C4—81no—
620C2×C4—81no—
621C2×C4—81no—
622C2×C4—81no—
623C2×C4—81no—
624C2×C4—81no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—1222no—
628C2×C4—4884no—
629C2×C4—2441no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4C22⋊C4×D6111yescharacteristic
636C2×C4C22⋊C4×D6111yescharacteristic
637C2×C4#1451974711yescharacteristic
638C2×C4#1451974711yescharacteristic
639C8—4881no—
640C8—4881no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—21no—
649C22—21no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—44no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—82no—
658C22—82no—
659C22—82no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—4881no—
665C22—4881no—
666C22—4881no—
667C22—4881no—
668C22—2442no—
669C22—2442no—
670C22—2442no—
671C22#1683961711yescharacteristic
672C22#1683975611yescharacteristic
673C22#1683976111yescharacteristic
674C22#1683990511yescharacteristic
675C22#1683990511yescharacteristic
676C22#1683992211yescharacteristic
677C22#1683992211yescharacteristic
678C22#1683992911yescharacteristic
679C22#1683993911yescharacteristic
680C22#1683994811yescharacteristic
681C22#1683995111yescharacteristic
682C4—21no—
683C4—21no—
684C4—21no—
685C4—21no—
686C4—42no—
687C4—82no—
688C4—82no—
689C4—2442no—
690C4—2442no—
691C4—2442no—
692C2—21no—
693C2—21no—
694C2—21no—
695C2—21no—
696C2—82no—
697C2—4882no—
698C2#2144476311yescharacteristic
699C2#2144479711yescharacteristic
700C2#2144483111yescharacteristic
701C2#2144486511yescharacteristic
702C2#2144575711yescharacteristic
703C2#2144576611yescharacteristic
704C2#2144577211yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1439C2
socleC23×C61#120
prime radicalC2×#16840350C2
cosocleC23×C4×C61C23
hypercenter#1439D61
hypocenterC61#8408
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #21446136C2semidirect
3. #21446126C2semidirect
4. C2×#16839498C2semidirect
5. C2×#16839495C2semidirect
6. C2×#16839486C2semidirect
7. C61×#1439C2semidirect
11. #16840350C4semidirect
156. C2×D244C22⋊C4semidirect
163. C2×Dic122C22⋊C4semidirect
182. C4⋊Dic61C22⋊C4semidirect
183. C4⋊Dic61C22⋊C4semidirect
346. #1439D61semidirect
386. C61#8408semidirect

Maximal subgroups

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

subgroupindex
C2×#168403502
#214461362
#214461262
C2×#168394982
C2×#168394952
C2×#168394862
C61×#14392
#840861