Finite Group Databasebeta

← #29687995

Subgroups — #29687995

Order 15616.

858 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840118C211yesmaximal, characteristic
2#21448378C211yesmaximal, characteristic, complemented
3#21448362C211yesmaximal, characteristic
4#21446782C211yesmaximal, characteristic, complemented
5#21446627C211yesmaximal, characteristic
6#21446502C211yesmaximal, characteristic
7#21446501C211yesmaximal, characteristic
8#21446498C211yesmaximal, characteristic, complemented
9#21445948C211yesmaximal, characteristic, complemented
10#103×Dic61C211yesmaximal, characteristic, complemented
11#103×Dic61C211yesmaximal, characteristic, complemented
12#21445633C211yesmaximal, characteristic
13#21445633C211yesmaximal, characteristic
14C4×C8×Dic61C211yesmaximal, characteristic, complemented
15C61×#1933C211yesmaximal, characteristic, complemented
16C2×#14519768C2211yescharacteristic
17C2×#14519766C2211yescharacteristic
18C2×Q8×Dic61C2211yescharacteristic
19C2×#14519739C2211yescharacteristic
20#16840118C418yescomplemented
21C2×#14519701C2211yescharacteristic
22C2×#14519701C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×C4×#92418C2211yescharacteristic
28C2×C8×Dic61C2211yescharacteristic
29C2×C8×Dic61C2211yescharacteristic
30C2×C8×Dic61C2211yescharacteristic
31C2×C8×Dic61C2211yescharacteristic
32#16839664C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839654—21no—
35#16839654—21no—
36#16839647—21no—
37#16839643—21no—
38#16839627C2211yescharacteristic
39#16839627C2211yescharacteristic
40C4⋊C4×Dic61—21no—
41C4⋊C4×Dic61C2211yescharacteristic
42C4⋊C4×Dic61C2211yescharacteristic
43#16839613—21no—
44#16839609—21no—
45#16839609—21no—
46C42×Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×#103×C61C2211yescharacteristic
54C2×#103×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C61×#391C2211yescharacteristic
57C61×#389C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64#14519768—22no—
65#14519768C2×C414yescomplemented
66#14519766—22no—
67#14519766C2×C414yes—
68Q8×Dic61—22no—
69Q8×Dic61—22no—
70#14519739—22no—
71#14519739—22no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61D411yescharacteristic
88C2×C4×Dic61D411yescharacteristic
89C2×C4×Dic61D411yescharacteristic
90C2×C4×Dic61D411yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93#14519701—22no—
94#14519701C2×C414yescomplemented
95#14519699—22no—
96#14519699C2×C414yes—
97#14519697—22no—
98#14519697C2×C414yes—
99C4×#92418—22no—
100C8×Dic61—22no—
101C8×Dic61—22no—
102C8×Dic61—22no—
103C8×Dic61C2×C414yescomplemented
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111C22×Q8×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C42×C61C2311yescharacteristic
119#103×C61—22no—
120#103×C61C2×C414yescomplemented
121C4×C8×C61—22no—
122#95×C61—21no—
123#95×C61—21no—
124#95×C61—21no—
125C23×D61—21no—
126C2×Q8×C61—21no—
127C2×Q8×C61—21no—
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61C22×C412yes—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61C2×D411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144C22×Dic61C2×D411yescharacteristic
145C22×Dic61C2×D411yescharacteristic
146C2×D244—21no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244—21no—
150C2×D244—21no—
151C2×D244C22×C412yes—
152C2×C4×D61—42no—
153C2×C4×D61—42no—
154C2×C4×D61—42no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61C22×C412yes—
160C2×C8×C61#4112yes—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—42no—
167C4⋊C4×C61C22×C412yes—
168C42×C61—21no—
169C42×C61—21no—
170#11758198—24no—
171#11758198—24no—
172#11758198—42no—
173#11758198—42no—
174#11758198—42no—
175C4⋊Dic61—21no—
176C4⋊Dic61—24no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—42no—
182C4⋊Dic61C22×C412yes—
183#11758196—24no—
184#11758196—42no—
185C4×Dic61—22no—
186C4×Dic61—22no—
187C4×Dic61—22no—
188C4×Dic61—22no—
189C4×Dic61—42no—
190C4×Dic61—42no—
191C4×Dic61—42no—
192C4×Dic61C22×C412yes—
193C4×Dic61#4112yes—
194C4×Dic61#4112yes—
195C4×Dic61#4112yes—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418C22×C412yes—
201C2×#92418#4112yes—
202C23×C61C22×D411yescharacteristic
203C22×D61—22no—
204C22×D61—41no—
205C22×D61—41no—
206C22×D61—41no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—41no—
210Q8×C61—22no—
211Q8×C61—22no—
212Q8×C61—41no—
213Q8×C61—41no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61#13512yes—
231C2×C4×C61#13512yes—
232C2×C4×C61C23×C411yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—22no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61C4×D412yes—
254C2×Dic61C4×D412yes—
255C2×Dic61#12412yes—
256C2×Dic61#12412yes—
257C2×Dic61#13512yes—
258C2×Dic61#13512yes—
259D244—22no—
260D244—22no—
261D244—41no—
262D244—41no—
263C4×D61—84no—
264C8×C61—22no—
265C8×C61—22no—
266#92418—22no—
267#92418—22no—
268C4×#488—611nomaximal, Sylow
269C22×C61C2×C4×D411yescharacteristic
270C22×C61C2×#12411yescharacteristic
271C22×C61#53211yescharacteristic
272C22×C61C2×#13511yescharacteristic
273C22×C61C2×#13511yescharacteristic
274C22×C61C2×#13511yescharacteristic
275C22×C61C2×#13511yescharacteristic
276C2×D61—42no—
277C2×D61—42no—
278C2×D61—42no—
279C2×D61—81no—
280C2×D61—81no—
281C2×D61—81no—
282C2×D61—81no—
283C4×C61—22no—
284C4×C61—22no—
285C4×C61—42no—
286C4×C61—42no—
287C4×C61—81no—
288C4×C61—81no—
289C4×C61C4×#4111yescharacteristic
290C4×C61C4×#4111yescharacteristic
291C4×C61#52911yescharacteristic
292C4×C61#52911yescharacteristic
293Dic61—22no—
294Dic61—22no—
295Dic61—22no—
296Dic61—42no—
297Dic61—81no—
298Dic61—81no—
299Dic61#48814yescomplemented
300C2×#488—611no—
301C4×#125—611no—
302C4×#124—611no—
303#1991—611no—
304#1958—611no—
305#1934—611no—
306#1934—611no—
307#1933—611no—
308#1933D6111yescharacteristic, complemented
309#1835—611no—
310C4×#103—611no—
311C4×#103—611no—
312C4×#102—611no—
313C4×#102—611no—
314C42×C8—611no—
315C2×C61C4×#12411yescharacteristic
316C2×C61C4×#13511yescharacteristic
317C2×C61C4×#13511yescharacteristic
318C2×C61C2×#48811yescharacteristic
319C2×C61#313111yescharacteristic
320C2×C61#316811yescharacteristic
321C2×C61#316811yescharacteristic
322D61—82no—
323C2×#125—611no—
324C2×#124—611no—
325C2×C4×Q8—611no—
326C2×C4×D4—611no—
327#488—618no—
328C2×#103—611no—
329C2×#103—611no—
330C2×#103C2×D6111yescharacteristic
331C2×#103C2×D6111yescharacteristic
332C2×#102—611no—
333C2×#102—611no—
334C2×#102—611no—
335C2×#102—611no—
336C2×C4×C8—611no—
337C2×C4×C8—611no—
338C2×C4×C8—611no—
339C2×C4×C8—611no—
340C2×C4×C8—611no—
341C2×C4×C8C2×D6111yescharacteristic
342#391C2×D6111yescharacteristic
343#390—611no—
344#389—611no—
345#389C2×D6111yescharacteristic
346#388—1221no—
347#388—1221no—
348#387—1221no—
349#387—1221no—
350#382—611no—
351#382—611no—
352C4×C4⋊C4—611no—
353C4×C4⋊C4—611no—
354C4×C4⋊C4—1221no—
355C4×C4⋊C4—1221no—
356C4×C22⋊C4—1221no—
357C4×C22⋊C4—1221no—
358C43—611no—
359#340—611no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340—611no—
364#340—611no—
365#340C2×D6111yescharacteristic
366#340C2×D6111yescharacteristic
367C61C4×#48811yescharacteristic, complemented, Sylow
368C22×Q8C22×D6111yescharacteristic
369C22×D4—611no—
370C23×C4—1221no—
371C22×C8—611no—
372C22×C8—611no—
373C22×C8C22×D6111yescharacteristic
374C22×C8C22×D6111yescharacteristic
375#125—614no—
376#125—1222no—
377#124—614no—
378#124—1222no—
379C4×Q8—1222no—
380C4×Q8—1222no—
381C4×D4—1222no—
382C4×D4—1222no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4C22×D6111yescharacteristic
392C2×C4⋊C4C22×D6111yescharacteristic
393C2×C4⋊C4C22×D6111yescharacteristic
394C2×C22⋊C4—1221no—
395C2×C22⋊C4—1221no—
396C2×C22⋊C4—1221no—
397C2×C22⋊C4—1221no—
398C2×C22⋊C4—1221no—
399C2×C42—611no—
400C2×C42—611no—
401C2×C42—611no—
402C2×C42—611no—
403C2×C42—611no—
404C2×C42—611no—
405C2×C42—1221no—
406C2×C42—1221no—
407C2×C42—1221no—
408C2×C42C22×D6111yescharacteristic
409#103—22no—
410#103—614no—
411#103—1222no—
412#103C4×D6114yescomplemented
413#102—614no—
414#102—614no—
415#102—1222no—
416#102—1222no—
417C4×C8—22no—
418C4×C8—614no—
419C4×C8—1222no—
420C4×C8—1222no—
421C4×C8—1222no—
422C4×C8—1222no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—1221no—
427#95—1221no—
428#95—1221no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433C24—1221no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8C2×C4×D6112yes—
440C2×D4—612no—
441C2×D4—1221no—
442C2×D4—1221no—
443C2×D4—1221no—
444C2×D4—1221no—
445C2×D4—1221no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—2442no—
458C22×C4—2442no—
459C22×C4—2442no—
460C22×C4D4×D6111yescharacteristic
461C22×C4D4×D6111yescharacteristic
462C22×C4C23×D6111yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—612no—
468C2×C8—612no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8C2×C4×D6112yes—
474C2×C8#1175822412yes—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—612no—
482C4⋊C4—1224no—
483C4⋊C4—1224no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—2442no—
490C4⋊C4—2442no—
491C4⋊C4C2×C4×D6112yes—
492C22⋊C4—1224no—
493C22⋊C4—1224no—
494C22⋊C4—2442no—
495C22⋊C4—2442no—
496C22⋊C4—2442no—
497C42—21no—
498C42—21no—
499C42—612no—
500C42—612no—
501C42—612no—
502C42—612no—
503C42—1222no—
504C42—1222no—
505C42—1222no—
506C42—1222no—
507C42—2442no—
508C42—2442no—
509C42—2442no—
510C23—1222no—
511C23—2441no—
512C23—2441no—
513C23—2441no—
514C23—2441no—
515C23—2441no—
516C23—2441no—
517C23C2×D4×D6111yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522D4—1222no—
523D4—1222no—
524D4—2441no—
525D4—2441no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—612no—
543C2×C4—612no—
544C2×C4—612no—
545C2×C4—612no—
546C2×C4—612no—
547C2×C4—612no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1222no—
555C2×C4—4884no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4#1451979812yes—
565C2×C4#1451980012yes—
566C2×C4C22×C4×D6111yescharacteristic
567C2×C4#41×D6111yescharacteristic
568C2×C4#41×D6111yescharacteristic
569C2×C4#41×D6111yescharacteristic
570C2×C4#41×D6111yescharacteristic
571C2×C4C2×#1175822411yescharacteristic
572C8—22no—
573C8—22no—
574C8—1222no—
575C8—1222no—
576C22—4881no—
577C22—4881no—
578C22—4881no—
579C22—4881no—
580C22—2442no—
581C22—2442no—
582C22—2442no—
583C22C4×D4×D6111yescharacteristic
584C22#124×D6111yescharacteristic
585C22#1684030711yescharacteristic
586C22#135×D6111yescharacteristic
587C22#135×D6111yescharacteristic
588C22C2×#1451979811yescharacteristic
589C22C2×#1451980011yescharacteristic
590C4—22no—
591C4—22no—
592C4—42no—
593C4—42no—
594C4—81no—
595C4—81no—
596C4—614no—
597C4—1222no—
598C4—1222no—
599C4—1222no—
600C4—4881no—
601C4—4881no—
602C4—2442no—
603C4C4×#1175822411yescharacteristic
604C4#1684023011yescharacteristic
605C4#1684028911yescharacteristic
606C4#1684029511yescharacteristic
607C2—4882no—
608C2#2144836011yescharacteristic
609C2C4×#1451979811yescharacteristic
610C2C4×#1451980011yescharacteristic
611C2#488×D6111yescharacteristic
612C2#2145614311yescharacteristic
613C2#2145638211yescharacteristic
614C2#2145639011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1933C2
socleC23×C61C22×D4
prime radicalC22×D244C23
cosocleC22×C4×C61C24
hypercenter#1933D61
hypocenterC61C4×#488
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1933

Complements

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

NH ≅ G/Ntype
2. #21448378C2semidirect
4. #21446782C2semidirect
8. #21446498C2semidirect
9. #21445948C2semidirect
10. #103×Dic61C2semidirect
11. #103×Dic61C2semidirect
14. C4×C8×Dic61C2semidirect
15. C61×#1933C2semidirect
20. #16840118C4semidirect
65. #14519768C2×C4semidirect
94. #14519701C2×C4semidirect
103. C8×Dic61C2×C4semidirect
120. #103×C61C2×C4semidirect
299. Dic61#488semidirect
308. #1933D61semidirect
367. C61C4×#488semidirect
412. #103C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168401182
#214483782
#214483622
#214467822
#214466272
#214465022
#214465012
#214464982
#214459482
#103×Dic612
#214456332
C4×C8×Dic612
C61×#19332
C4×#48861