Finite Group Databasebeta

← #29721375

Subgroups — #29721375

Order 15616.

746 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×#16840056C211yesmaximal, characteristic, complemented
2C2×#16839820C211yesmaximal, characteristic
3#21451644C211yesmaximal, characteristic
4#21448497C211yesmaximal, characteristic
5#21447245C211yesmaximal, characteristic
6#21447023C211yesmaximal, characteristic
7#21447015C211yesmaximal, characteristic
8#21446769C211yesmaximal, characteristic, complemented
9#21446590C211yesmaximal, characteristic, complemented
10#21446561C211yesmaximal, characteristic, complemented
11#21446550C211yesmaximal, characteristic, complemented
12#21446507C211yesmaximal, characteristic, complemented
13#21446496C211yesmaximal, characteristic, complemented
14#21445833C211yesmaximal, characteristic, complemented
15C61×#2076C211yesmaximal, characteristic
16C2×#14519776C2211yescharacteristic
17C2×#14519756C2211yescharacteristic
18C2×#14519742C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20#16840056—24no—
21#16839820—24no—
22C2×#14519711C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×#14519687C2211yescharacteristic
33C2×C8×Dic61C2211yescharacteristic
34#16839704—21no—
35#16839698—21no—
36#16839683—21no—
37#16839674—21no—
38#16839667C2211yescharacteristic
39#16839661C2211yescharacteristic
40#16839659—21no—
41#16839658C2211yescharacteristic
42#16839658C2211yescharacteristic
43#16839656—21no—
44#16839650—21no—
45#16839649—21no—
46#16839627C2211yescharacteristic
47#16839622C2211yescharacteristic
48C4⋊C4×Dic61C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×Dic122—21no—
62C22×Dic122C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519776—22no—
66#14519776—22no—
67#14519756—22no—
68#14519756—22no—
69#14519742—22no—
70#14519742—22no—
71#14519736—22no—
72#14519736—22no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61D411yescharacteristic
75C2×C4⋊Dic61D411yescharacteristic
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×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61D411yescharacteristic
87C2×C22⋊Dic61D411yescharacteristic
88C2×C4×Dic61—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61C2311yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92#14519711—22no—
93#14519710—22no—
94#14519708—22no—
95#14519706—22no—
96#14519706D414yes—
97#14519702—22no—
98#14519702—22no—
99#14519700—22no—
100#14519700—22no—
101C22⋊#92418—22no—
102#14519687—22no—
103C8×Dic61—22no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113C23×C4×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122#107×C61—22no—
123C22⋊C8×C61—22no—
124#95×C61—21no—
125#95×C61—21no—
126C24×C61C2×D411yescharacteristic
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61C2×D411yescharacteristic
144C22×Dic61C2×D411yescharacteristic
145C22×Dic61C2×D411yescharacteristic
146C22×Dic61C2×D411yescharacteristic
147C2×Dic122—21no—
148C2×Dic122—21no—
149C2×Dic122—21no—
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122—42no—
153C2×Dic122—81no—
154C2×Dic122—81no—
155C2×Dic122#4112yes—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61C2×D412yes—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C22⋊C4×C61—81no—
171C22⋊C4×C61—81no—
172C22⋊Dic61—24no—
173C22⋊Dic61—22no—
174C22⋊Dic61—22no—
175C22⋊Dic61—81no—
176C4⋊Dic61—21no—
177C4⋊Dic61—22no—
178C4⋊Dic61—22no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—81no—
184C4⋊Dic61#4112yes—
185#11758196—24no—
186#11758196—42no—
187#11758196—42no—
188#11758196—81no—
189#11758196—81no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—42no—
193C4×Dic61—81no—
194C4×Dic61C2×D412yes—
195C4×Dic61#4112yes—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C2×D412yes—
202C23×C61—21no—
203C23×C61—21no—
204C23×C61—21no—
205C23×C61—21no—
206C23×C61—21no—
207C23×C61—21no—
208C23×C61—21no—
209C23×C61C22×D411yescharacteristic
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
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×C61C22×D411yescharacteristic
230C2×C4×C61C2×#4111yescharacteristic
231C2×C4×C61C2×#4111yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C612−1+411yescharacteristic
234C2×C4×C612−1+411yescharacteristic
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61#12112yes—
258C2×Dic61#12112yes—
259Dic122—22no—
260Dic122—22no—
261Dic122—41no—
262Dic122—41no—
263Dic122—84no—
264C8×C61—22no—
265C8×C61—41no—
266#92418—22no—
267#92418—41no—
268#24714—611nomaximal, Sylow
269C22×C61—41no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61C2×#12111yescharacteristic
277C22×C61#52511yescharacteristic
278C22×C61#53611yescharacteristic
279C22×C61#57611yescharacteristic
280C22×C61#57711yescharacteristic
281C22×C61#57811yescharacteristic
282C22×C61#57811yescharacteristic
283C4×C61—41no—
284C4×C61—81no—
285C4×C61—81no—
286C4×C61—81no—
287C4×C61—81no—
288C4×C61#54711yescharacteristic
289C4×C61#54811yescharacteristic
290C4×C61#55211yescharacteristic
291C4×C61#55611yescharacteristic
292Dic61—22no—
293Dic61—22no—
294Dic61—42no—
295Dic61—42no—
296Dic61—41no—
297Dic61—41no—
298Dic61—81no—
299Dic61—81no—
300C2×#477—611no—
301C2×#433—611no—
302#2628—611no—
303#2323—611no—
304#2076D6111yescharacteristic
305#2075—611no—
306#2036—611no—
307#2035—611no—
308#1988—611no—
309#1949—611no—
310#1944—611no—
311#1942—611no—
312#1935—611no—
313#1933—611no—
314#1805—611no—
315C2×C61—81no—
316C2×C61#241511yescharacteristic
317C2×C61#305911yescharacteristic
318C2×C61#306211yescharacteristic
319C2×C61#312111yescharacteristic
320C2×C61#312411yescharacteristic
321C2×C61#324211yescharacteristic
322C2×C61#324311yescharacteristic
323C2×C4⋊Q8—611no—
324C2×C22⋊Q8—611no—
325C2×C4×Q8—611no—
326C2×#117—611no—
327#477—1224no—
328#433—1224no—
329C2×#107—611no—
330C2×#107—611no—
331C2×#107C2×D6111yescharacteristic
332C2×#106—611no—
333C2×C4⋊C8—611no—
334C2×C4⋊C8—611no—
335C2×#103—611no—
336C2×#103—611no—
337C2×#103—611no—
338C2×#103—611no—
339C2×C22⋊C8—611no—
340C2×C22⋊C8C2×D6111yescharacteristic
341C2×#97—611no—
342C2×C4×C8—611no—
343#400—1221no—
344#399—1221no—
345#395—1221no—
346#393—1221no—
347#391—611no—
348#389—611no—
349#389—611no—
350#389—611no—
351#389—1221no—
352#388—1221no—
353#388—1221no—
354#387—1221no—
355#382—611no—
356#380—611no—
357#380C2×D6111yescharacteristic
358#380C2×D6111yescharacteristic
359C4×C4⋊C4—611no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340—611no—
364#340—611no—
365#340C2×D6111yescharacteristic
366#340C2×D6111yescharacteristic
367#340C2×D6111yescharacteristic
368C61#2471411yescharacteristic, complemented, Sylow
369C22×Q8—611no—
370C22×Q8—1221no—
371C23×C4C22×D6111yescharacteristic
372C22×C8—611no—
373C22×C8—611no—
374C22×C8C22×D6111yescharacteristic
375C22×C8C22×D6111yescharacteristic
376C4⋊Q8—1222no—
377C4⋊Q8—1222no—
378C22⋊Q8—1222no—
379C22⋊Q8—1222no—
380C4×Q8—1222no—
381C4×Q8—1222no—
382#117—1222no—
383#117—1222no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4C22×D6111yescharacteristic
396C2×C4⋊C4C22×D6111yescharacteristic
397C2×C4⋊C4C22×D6111yescharacteristic
398C2×C4⋊C4C22×D6111yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—611no—
402C2×C22⋊C4—611no—
403C2×C22⋊C4—1221no—
404C2×C22⋊C4—1221no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42—1221no—
408C2×C42—1221no—
409#107—22no—
410#107—1222no—
411#107—1222no—
412#106—1222no—
413C4⋊C8—614no—
414C4⋊C8—1222no—
415#103—1222no—
416#103—1222no—
417#103—1222no—
418#103—1222no—
419C22⋊C8—22no—
420C22⋊C8—1222no—
421#97—1222no—
422C4×C8—1222no—
423#95—21no—
424#95—21no—
425#95—1221no—
426#95—1221no—
427#95—1221no—
428#95—1221no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433#95—1221no—
434C24D4×D6111yescharacteristic
435C2×Q8—612no—
436C2×Q8—1221no—
437C2×Q8—1221no—
438C2×Q8—1221no—
439C2×Q8—1221no—
440C2×Q8—1221no—
441C2×Q8—4881no—
442C2×Q8—4881no—
443C2×Q8—2442no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4D4×D6111yescharacteristic
463C22×C4C23×D6111yescharacteristic
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—612no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8D4×D6112yes—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—612no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—1224no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—4881no—
494C4⋊C4—4881no—
495C4⋊C4—4881no—
496C4⋊C4—2442no—
497C4⋊C4—2442no—
498C22⋊C4—81no—
499C22⋊C4—81no—
500C22⋊C4—1222no—
501C22⋊C4—1222no—
502C22⋊C4—1224no—
503C22⋊C4—4881no—
504C42—612no—
505C42—612no—
506C42—1221no—
507C42—1221no—
508C42—4881no—
509C42—2442no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23C2×D4×D6111yescharacteristic
518Q8—1222no—
519Q8—1222no—
520Q8—4884no—
521Q8—2441no—
522Q8—2441no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
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—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1222no—
551C2×C4—1222no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
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—2441no—
565C2×C4—2441no—
566C2×C4C2×D4×D6111yescharacteristic
567C2×C4#41×D6111yescharacteristic
568C2×C4#41×D6111yescharacteristic
569C2×C4#41×D6111yescharacteristic
570C2×C4#1451982411yescharacteristic
571C2×C4#1451982411yescharacteristic
572C8—22no—
573C8—41no—
574C8—1222no—
575C8—2441no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22#121×D6111yescharacteristic
584C22#1684027011yescharacteristic
585C22#1684033411yescharacteristic
586C22#1684056611yescharacteristic
587C22#1684057211yescharacteristic
588C22#1684057511yescharacteristic
589C22#1684057611yescharacteristic
590C4—41no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4—1222no—
596C4—1222no—
597C4—4881no—
598C4—4881no—
599C4—2442no—
600C4—2441no—
601C4—2441no—
602C4—2442no—
603C4#1684041011yescharacteristic
604C4#1684042011yescharacteristic
605C4#1684044811yescharacteristic
606C4#1684047911yescharacteristic
607C2—81no—
608C2#2144924311yescharacteristic
609C2#2145546911yescharacteristic
610C2#2145549611yescharacteristic
611C2#2145604311yescharacteristic
612C2#2145608411yescharacteristic
613C2#2145709111yescharacteristic
614C2#2145710011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2076C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenter#2076D61
hypocenterC61#24714
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2076

Complements

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

NH ≅ G/Ntype
1. C2×#16840056C2semidirect
8. #21446769C2semidirect
9. #21446590C2semidirect
10. #21446561C2semidirect
11. #21446550C2semidirect
12. #21446507C2semidirect
13. #21446496C2semidirect
14. #21445833C2semidirect
368. C61#24714semidirect

Maximal subgroups

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

subgroupindex
C2×#168400562
C2×#168398202
#214516442
#214484972
#214472452
#214470232
#214470152
#214467692
#214465902
#214465612
#214465502
#214465072
#214464962
#214458332
C61×#20762
#2471461