Finite Group Databasebeta

← #29742998

Subgroups — #29742998

Order 15616.

896 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840062C211yesmaximal, characteristic, complemented
2C2×D8×Dic61C211yesmaximal, characteristic
3#21449693C211yesmaximal, characteristic, complemented
4#21448724C211yesmaximal, characteristic, complemented
5#21447342C211yesmaximal, characteristic, complemented
6#21447306C211yesmaximal, characteristic, complemented
7#21447207C211yesmaximal, characteristic, complemented
8#21447158C211yesmaximal, characteristic, complemented
9#21446551C211yesmaximal, characteristic, complemented
10#21446379C211yesmaximal, characteristic, complemented
11#21446169C211yesmaximal, characteristic
12#21446082C211yesmaximal, characteristic, complemented
13#21446078C211yesmaximal, characteristic, complemented
14#21446064C211yesmaximal, characteristic, complemented
15C61×#1879C211yesmaximal, characteristic
16C2×#14519769C2211yescharacteristic
17C2×D4×Dic61C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20#16840062—24no—
21D8×Dic61—24no—
22C2×#14519711C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519710C2211yescharacteristic
25C2×#14519709C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33#16839698—21no—
34#16839685—21no—
35#16839665C2211yescharacteristic
36#16839661C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839658C2211yescharacteristic
39#16839658C2211yescharacteristic
40#16839635—21no—
41#16839634—21no—
42#16839634—21no—
43#16839627C2211yescharacteristic
44#16839620—21no—
45#16839620—21no—
46C4×#11758196C2211yescharacteristic
47C2×#14519684—21no—
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×D8×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C61×#390C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C23×Dic61—21no—
62C23×Dic61—21no—
63C23×Dic61—21no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519769—22no—
67#14519769—41no—
68D4×Dic61—22no—
69D4×Dic61—22no—
70D4×Dic61—22no—
71D4×Dic61—22no—
72D4×Dic61—41no—
73D4×Dic61—41no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196D411yescharacteristic
85C2×#11758196D411yescharacteristic
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C4×Dic61C2311yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93#14519711—22no—
94#14519710—22no—
95#14519710—22no—
96#14519709—41no—
97#14519708—22no—
98C4⋊#92418—22no—
99#14519698—22no—
100#14519698—22no—
101#14519698—22no—
102#14519698D414yes—
103C8×Dic61—22no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684D411yescharacteristic
111#14519684D411yescharacteristic
112C22×D4×C61C2311yescharacteristic
113C22×D4×C61C2311yescharacteristic
114C23×C4×C61—21no—
115C2×D8×C61—22no—
116C2×D8×C61—22no—
117C2×D8×C61Q814yes—
118C22×C8×C61C2311yescharacteristic
119C22×C8×C61C2311yescharacteristic
120C4×D4×C61—22no—
121C4×D4×C61—41no—
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C42×C61C2311yescharacteristic
128#102×C61—22no—
129#102×C61—41no—
130C24×C61—21no—
131C24×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61C2×D412yes—
141C2×D4×C61C2×Q812yes—
142C2×D4×C61C2×Q812yes—
143C2×D4×C61#4112yes—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—42no—
147C22×C4×C61—42no—
148C22×C4×C61—81no—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2411yescharacteristic
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—24no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—42no—
158C22×Dic61—42no—
159C22×Dic61—42no—
160C22×Dic61—42no—
161C22×Dic61—81no—
162C22×Dic61—81no—
163C22×Dic61—81no—
164C22×Dic61—81no—
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169D8×C61—28no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61C2×Q812yes—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C22⋊C4×C61—42no—
181C22⋊C4×C61—81no—
182C22⋊C4×C61—81no—
183C42×C61—21no—
184C42×C61—21no—
185C22⋊Dic61—24no—
186C22⋊Dic61—42no—
187C22⋊Dic61—42no—
188C22⋊Dic61—42no—
189C22⋊Dic61—81no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—81no—
197C4⋊Dic61C2×D412yes—
198C4⋊Dic61#4112yes—
199#11758196—22no—
200#11758196—41no—
201#11758196—42no—
202#11758196—42no—
203#11758196—81no—
204#11758196—81no—
205#11758196—81no—
206C4×Dic61—21no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418C2×D412yes—
216C23×C61—22no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61—41no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61C22×D411yescharacteristic
231D4×C61—22no—
232D4×C61—22no—
233D4×C61—22no—
234D4×C61—22no—
235D4×C61—22no—
236D4×C61—41no—
237D4×C61—41no—
238D4×C61C22⋊Q814yes—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—84no—
252C2×C4×C61C22×D411yescharacteristic
253C2×C4×C61C22×Q811yescharacteristic
254C2×C4×C61C2×#4111yescharacteristic
255C2×C4×C61C2×#4111yescharacteristic
256C2×C4×C61H(5,𝔽2)11yescharacteristic
257C2×C4×C612−1+411yescharacteristic
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—22no—
263C2×Dic61—21no—
264C2×Dic61—22no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—84no—
282C2×Dic61—84no—
283C2×Dic61—84no—
284C2×Dic61#13512yes—
285C8×C61—22no—
286C8×C61—41no—
287#92418—22no—
288#92418—41no—
289#26370—611nomaximal, Sylow
290C22×C61—24no—
291C22×C61—42no—
292C22×C61—42no—
293C22×C61—42no—
294C22×C61—42no—
295C22×C61—42no—
296C22×C61—42no—
297C22×C61—42no—
298C22×C61—42no—
299C22×C61—42no—
300C22×C61—81no—
301C22×C61—81no—
302C22×C61—81no—
303C22×C61—81no—
304C22×C61#52511yescharacteristic
305C22×C61D4211yescharacteristic
306C22×C61D4×Q811yescharacteristic
307C22×C61C2×#13511yescharacteristic
308C22×C61#57511yescharacteristic
309C22×C61#57611yescharacteristic
310C22×C61#57611yescharacteristic
311C4×C61—41no—
312C4×C61—41no—
313C4×C61—81no—
314C4×C61—81no—
315C4×C61C2×C22⋊Q811yescharacteristic
316C4×C61#53911yescharacteristic
317C4×C61#54711yescharacteristic
318C4×C61#55411yescharacteristic
319Dic61—22no—
320Dic61—41no—
321Dic61—41no—
322Dic61—42no—
323Dic61—41no—
324Dic61—42no—
325Dic61—81no—
326Dic61—81no—
327C2×#478—611no—
328C2×C4×D8—611no—
329#2454—611no—
330#2349—611no—
331#2092—611no—
332#2085—611no—
333#2067—611no—
334#2059—611no—
335#1942—611no—
336#1916—611no—
337#1879—611no—
338#1879D6111yescharacteristic
339#1864—611no—
340#1864—611no—
341#1862—611no—
342C2×C61—44no—
343C2×C61—82no—
344C2×C61#244911yescharacteristic
345C2×C61#310211yescharacteristic
346C2×C61#312211yescharacteristic
347C2×C61#326811yescharacteristic
348C2×C61#328011yescharacteristic
349C2×C61#338011yescharacteristic
350C2×C61#338911yescharacteristic
351C22×D8C2×D6111yescharacteristic
352C2×#125—611no—
353C2×C4×D4—611no—
354C2×C4×D4—611no—
355C2×C4×D4—611no—
356C2×C4×D4C2×D6111yescharacteristic
357#478—1224no—
358C4×D8—1224no—
359C2×#107—611no—
360C2×#107—611no—
361C2×#107—611no—
362C2×#106—611no—
363C2×#106—611no—
364C2×C4⋊C8—611no—
365C2×#102—611no—
366C2×#102—611no—
367C2×#102—611no—
368C2×#102—611no—
369C2×#102C2×D6111yescharacteristic
370C2×#102C2×D6111yescharacteristic
371C2×C4×C8—611no—
372#399—1221no—
373#396—1221no—
374#390—611no—
375#390C2×D6111yescharacteristic
376#389—611no—
377#389—611no—
378#389—611no—
379#389—611no—
380#385—1221no—
381#385—1221no—
382#385—1221no—
383#382—611no—
384#380—1221no—
385#380—1221no—
386C4×C4⋊C4—611no—
387C2×#95—1221no—
388#340—611no—
389#340—611no—
390#340—611no—
391#340C2×D6111yescharacteristic
392#336—611no—
393#336—611no—
394#336—611no—
395#336C2×D6111yescharacteristic
396C61#2637011yescharacteristic, complemented, Sylow
397C22×D4C22×D6111yescharacteristic
398C22×D4C22×D6111yescharacteristic
399C23×C4—21no—
400C23×C4—1221no—
401C23×C4—1221no—
402C23×C4—1221no—
403C2×D8—22no—
404C2×D8—22no—
405C2×D8Dic12214yes—
406C22×C8—611no—
407C22×C8—611no—
408C22×C8C22×D6111yescharacteristic
409C22×C8C22×D6111yescharacteristic
410#125—1222no—
411#125—2441no—
412C4×D4—22no—
413C4×D4—41no—
414C4×D4—1222no—
415C4×D4—1222no—
416C4×D4—1222no—
417C4×D4—1222no—
418C4×D4—2441no—
419C4×D4—2441no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—611no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4C22×D6111yescharacteristic
433C2×C4⋊C4C22×D6111yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—1221no—
438C2×C22⋊C4—1221no—
439C2×C22⋊C4—1221no—
440C2×C22⋊C4—1221no—
441C2×C22⋊C4—1221no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42C22×D6111yescharacteristic
445#107—1222no—
446#107—1222no—
447#107—1222no—
448#106—1222no—
449#106—2441no—
450C4⋊C8—1222no—
451#102—22no—
452#102—41no—
453#102—614no—
454#102—1222no—
455#102—1222no—
456#102—1222no—
457C4×C8—1222no—
458#95—611no—
459#95—611no—
460#95—1221no—
461#95—1221no—
462#95—1221no—
463#95—1221no—
464#95—1221no—
465#95—1221no—
466C24—21no—
467C24—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4C2×Dic12212yes—
477C2×D4C2×Dic12212yes—
478C2×D4D4×D6112yes—
479C2×D4#1175822412yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—81no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—1224no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—4881no—
495C22×C4—4881no—
496C22×C4—4881no—
497C22×C4—4881no—
498C22×C4—2442no—
499C22×C4—2442no—
500C22×C4—2442no—
501C22×C4—2442no—
502C22×C4D4×D6111yescharacteristic
503C22×C4D4×D6111yescharacteristic
504C22×C4C23×D6111yescharacteristic
505D8—28no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—612no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8C2×Dic12212yes—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—612no—
523C4⋊C4—612no—
524C4⋊C4—1222no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—4881no—
532C4⋊C4—4881no—
533C4⋊C4—4881no—
534C4⋊C4—4881no—
535C4⋊C4—2441no—
536C4⋊C4—2442no—
537C4⋊C4—2442no—
538C22⋊C4—42no—
539C22⋊C4—81no—
540C22⋊C4—81no—
541C22⋊C4—1224no—
542C22⋊C4—4881no—
543C22⋊C4—2442no—
544C22⋊C4—2442no—
545C22⋊C4—2442no—
546C42—21no—
547C42—21no—
548C42—1221no—
549C42—1221no—
550C42—1221no—
551C42—1221no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23C2×D4×D6111yescharacteristic
567D4—22no—
568D4—22no—
569D4—22no—
570D4—22no—
571D4—22no—
572D4—41no—
573D4—41no—
574D4#1451975414yes—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—84no—
588C2×C4—612no—
589C2×C4—1221no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1222no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1222no—
602C2×C4—4884no—
603C2×C4—4884no—
604C2×C4—4884no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4C2×D4×D6111yescharacteristic
616C2×C4C22×Dic12211yescharacteristic
617C2×C4#41×D6111yescharacteristic
618C2×C4C2×#1175822411yescharacteristic
619C2×C4#1451982211yescharacteristic
620C2×C4#1451982411yescharacteristic
621C8—22no—
622C8—41no—
623C8—1222no—
624C8—2441no—
625C22—24no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22#1684027211yescharacteristic
640C22#1684039411yescharacteristic
641C22D4×Dic12211yescharacteristic
642C22#135×D6111yescharacteristic
643C22#1684055811yescharacteristic
644C22#1684056311yescharacteristic
645C22#1684056611yescharacteristic
646C4—41no—
647C4—41no—
648C4—81no—
649C4—81no—
650C4—1222no—
651C4—4881no—
652C4—4881no—
653C4—2442no—
654C4—2441no—
655C4—2442no—
656C4—2441no—
657C4—2441no—
658C4C2×#1451975411yescharacteristic
659C4#1684035711yescharacteristic
660C4#1684041011yescharacteristic
661C4#1684047111yescharacteristic
662C2—44no—
663C2—82no—
664C2#2144963211yescharacteristic
665C2#2145583411yescharacteristic
666C2#2145606011yescharacteristic
667C2#2145735711yescharacteristic
668C2#2145750211yescharacteristic
669C2#2145868611yescharacteristic
670C2#2145877811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1879C2
socleC23×C61C22×D4
prime radicalC22×D8×C61C22
hypercenter#1879D61
hypocenterC61#26370
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
1. C2×#16840062C2semidirect
3. #21449693C2semidirect
4. #21448724C2semidirect
5. #21447342C2semidirect
6. #21447306C2semidirect
7. #21447207C2semidirect
8. #21447158C2semidirect
9. #21446551C2semidirect
10. #21446379C2semidirect
12. #21446082C2semidirect
13. #21446078C2semidirect
14. #21446064C2semidirect
396. C61#26370semidirect

Maximal subgroups

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

subgroupindex
C2×#168400622
C2×D8×Dic612
#214496932
#214487242
#214473422
#214473062
#214472072
#214471582
#214465512
#214463792
#214461692
#214460822
#214460782
#214460642
C61×#18792
#2637061