Finite Group Databasebeta

← #29731748

Subgroups — #29731748

Order 15616.

764 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840172C211yesmaximal, characteristic, complemented
2C2×#16840042C211yesmaximal, characteristic
3#21448908C211yesmaximal, characteristic, complemented
4#21447301C211yesmaximal, characteristic, complemented
5#21447291C211yesmaximal, characteristic, complemented
6#21447207C211yesmaximal, characteristic
7#21447193C211yesmaximal, characteristic
8#21446777C211yesmaximal, characteristic, complemented
9#21446585C211yesmaximal, characteristic, complemented
10#21446575C211yesmaximal, characteristic, complemented
11#21446543C211yesmaximal, characteristic, complemented
12#21446443C211yesmaximal, characteristic
13#21446436C211yesmaximal, characteristic
14#21445644C211yesmaximal, characteristic
15C61×#2566C211yesmaximal, characteristic
16C2×#14519777C2211yescharacteristic
17#16840172—24no—
18#16840042—24no—
19C2×#14519710C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519688C2211yescharacteristic
33#16839666—21no—
34#16839666—21no—
35#16839660C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839658—21no—
38C4⋊C4×Dic61—21no—
39C4×C4⋊Dic61C2211yescharacteristic
40C4×C4⋊Dic61C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C2×#125×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C61×#396—21no—
53C61×#396—21no—
54C61×#390C2211yescharacteristic
55C61×#390C2211yescharacteristic
56C61×#385—21no—
57C61×#385—21no—
58C61×#384C2211yescharacteristic
59C61×#382C2211yescharacteristic
60C4×C4⋊C4×C61C2211yescharacteristic
61C22×Dic122—21no—
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519777—22no—
67#14519777D414yes—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×C4×Dic61—21no—
76C2×C4×Dic61—21no—
77C2×C4×Dic61—21no—
78#14519710—22no—
79#14519710—22no—
80#14519710—22no—
81#14519710—22no—
82#14519708—22no—
83#14519708—22no—
84C4⋊#92418—22no—
85C4⋊#92418—22no—
86C4⋊#92418—22no—
87#14519698—22no—
88#14519698—22no—
89#14519698—22no—
90#14519698Q814yescomplemented
91#14519688—22no—
92#14519684—21no—
93#14519684—21no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97C22×D4×C61C2311yescharacteristic
98C23×C4×C61—21no—
99#125×C61—22no—
100#125×C61—22no—
101C4×D4×C61—22no—
102C4×D4×C61—22no—
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61D411yescharacteristic
108C2×C4⋊C4×C61D411yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C42×C61C2311yescharacteristic
118C2×C42×C61C2311yescharacteristic
119C2×C42×C61C2311yescharacteristic
120#95×C61—21no—
121#95×C61—21no—
122#95×C61D411yescharacteristic
123#95×C61D411yescharacteristic
124C24×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61—21no—
130C2×D4×C61C2×Q812yes—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—42no—
135C22×C4×C61—81no—
136C22×C4×C61—81no—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2411yescharacteristic
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C2×Dic122—24no—
149C2×Dic122—81no—
150C2×Dic122—81no—
151C4⋊C4×C61—22no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—41no—
159C4⋊C4×C61—42no—
160C4⋊C4×C61—42no—
161C4⋊C4×C61—81no—
162C4⋊C4×C61—81no—
163C22⋊C4×C61—42no—
164C22⋊C4×C61—42no—
165C22⋊C4×C61—42no—
166C22⋊C4×C61—81no—
167C22⋊C4×C61—81no—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—21no—
171C42×C61—21no—
172C42×C61C2×D412yes—
173C42×C61#4112yes—
174C4⋊Dic61—24no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61C2×D412yes—
181C4⋊Dic61C2×D412yes—
182C4⋊Dic61C2×Q812yes—
183#11758196—81no—
184#11758196—81no—
185C4×Dic61—42no—
186C4×Dic61—81no—
187C4×Dic61—81no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418C2×Q812yes—
199C2×#92418#4112yes—
200C23×C61—22no—
201C23×C61—41no—
202C23×C61—41no—
203C23×C61—41no—
204C23×C61—41no—
205C23×C61—41no—
206C23×C61—41no—
207C23×C61C22×D411yescharacteristic
208D4×C61—22no—
209D4×C61—22no—
210D4×C61—41no—
211D4×C61—41no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—84no—
237C2×C4×C61#12112yes—
238C2×C4×C61#12112yes—
239C2×C4×C61#13712yes—
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61C22×Q811yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C612−1+411yescharacteristic
245C2×C4×C612−1+411yescharacteristic
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—22no—
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—41no—
258Dic122—84no—
259#92418—22no—
260#92418—22no—
261#92418—41no—
262#92418—41no—
263#25462—611nomaximal, Sylow
264C22×C61—42no—
265C22×C61—42no—
266C22×C61—42no—
267C22×C61—81no—
268C22×C61—81no—
269C22×C61—81no—
270C22×C61—81no—
271C22×C61C2×#12111yescharacteristic
272C22×C61#54711yescharacteristic
273C22×C61D4×Q811yescharacteristic
274C22×C61C2×#13711yescharacteristic
275C22×C61#57511yescharacteristic
276C22×C61#57611yescharacteristic
277C22×C61#57611yescharacteristic
278C4×C61—22no—
279C4×C61—22no—
280C4×C61—22no—
281C4×C61—41no—
282C4×C61—41no—
283C4×C61—41no—
284C4×C61—81no—
285C4×C61—81no—
286C4×C61—81no—
287C4×C61#53311yescharacteristic
288C4×C61#54111yescharacteristic
289C4×C61#54811yescharacteristic
290C4×C61D4×Q811yescharacteristic
291Dic61—42no—
292Dic61—42no—
293Dic61—42no—
294Dic61—81no—
295C2×#501—611no—
296C2×#474—611no—
297#2566D6111yescharacteristic
298#2369—611no—
299#2085—611no—
300#2083—611no—
301#2067—611no—
302#2065—611no—
303#1989—611no—
304#1949—611no—
305#1947—611no—
306#1940—611no—
307#1926—611no—
308#1925—611no—
309#1762—611no—
310C2×C61—82no—
311C2×C61#242911yescharacteristic
312C2×C61#303711yescharacteristic
313C2×C61#304111yescharacteristic
314C2×C61#334611yescharacteristic
315C2×C61#334711yescharacteristic
316C2×C61#338511yescharacteristic
317C2×C61#338911yescharacteristic
318C2×C4⋊Q8—611no—
319C2×#125C2×D6111yescharacteristic
320C2×C4×D4C2×D6111yescharacteristic
321#501—1224no—
322#474—1224no—
323C2×#107—611no—
324C2×#107—611no—
325C2×#107—611no—
326C2×#107—611no—
327C2×#106—611no—
328C2×#106—611no—
329C2×C4⋊C8—611no—
330C2×C4⋊C8—611no—
331C2×C4⋊C8—611no—
332C2×#102—611no—
333C2×#102—611no—
334C2×#102—611no—
335C2×#102—611no—
336C2×#97—611no—
337#396—21no—
338#396—21no—
339#391—1221no—
340#391—1221no—
341#390C2×D6111yescharacteristic
342#390C2×D6111yescharacteristic
343#389—611no—
344#389—611no—
345#389—1221no—
346#385—21no—
347#385—21no—
348#384C2×D6111yescharacteristic
349#382C2×D6111yescharacteristic
350C4×C4⋊C4—611no—
351C4×C4⋊C4—611no—
352C4×C4⋊C4—611no—
353C4×C4⋊C4—1221no—
354C4×C4⋊C4C2×D6111yescharacteristic
355#340—611no—
356#340—611no—
357#340—611no—
358#340—611no—
359#340—611no—
360#340—611no—
361#336—611no—
362#336—611no—
363C61#2546211yescharacteristic, complemented, Sylow
364C22×Q8—1221no—
365C22×D4C22×D6111yescharacteristic
366C23×C4—21no—
367C22×C8—611no—
368C22×C8—611no—
369C22×C8—611no—
370C22×C8—611no—
371C4⋊Q8—614no—
372C4⋊Q8—1222no—
373#125—22no—
374#125—22no—
375C4×D4—22no—
376C4×D4—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—611no—
382C2×C4⋊C4—611no—
383C2×C4⋊C4—611no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—1221no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4C22⋊D6111yescharacteristic
389C2×C4⋊C4C22⋊D6111yescharacteristic
390C2×C4⋊C4C22×D6111yescharacteristic
391C2×C4⋊C4C22×D6111yescharacteristic
392C2×C4⋊C4C22×D6111yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C42—1221no—
399C2×C42—1221no—
400C2×C42—1221no—
401C2×C42C22×D6111yescharacteristic
402C2×C42C22×D6111yescharacteristic
403C2×C42C22×D6111yescharacteristic
404#107—1222no—
405#107—1222no—
406#107—1222no—
407#107—1222no—
408#106—1222no—
409#106—1222no—
410C4⋊C8—1222no—
411C4⋊C8—1222no—
412C4⋊C8—1222no—
413#102—614no—
414#102—1222no—
415#102—1222no—
416#102—1222no—
417#97—1222no—
418#95—21no—
419#95—21no—
420#95—1221no—
421#95—1221no—
422#95—1221no—
423#95—1221no—
424#95—1221no—
425#95C22⋊D6111yescharacteristic
426#95C22⋊D6111yescharacteristic
427C24—21no—
428C2×Q8—1224no—
429C2×Q8—4881no—
430C2×Q8—4881no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4Q8×D6112yes—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—42no—
441C22×C4—81no—
442C22×C4—81no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4C2×C22⋊D6111yescharacteristic
448C22×C4C2×C22⋊D6111yescharacteristic
449C22×C4C2×C22⋊D6111yescharacteristic
450C22×C4C2×C22⋊D6111yescharacteristic
451C22×C4C2×C22⋊D6111yescharacteristic
452C22×C4C2×C22⋊D6111yescharacteristic
453C22×C4C23×D6111yescharacteristic
454C2×C8—612no—
455C2×C8—612no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—41no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4—612no—
479C4⋊C4—612no—
480C4⋊C4—612no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1224no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—4881no—
488C4⋊C4—4881no—
489C22⋊C4—42no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—81no—
493C22⋊C4—81no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—4881no—
499C42—4881no—
500C42—2442no—
501C42D4×D6112yes—
502C42#1175822412yes—
503C23—22no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23C22×C22⋊D6111yescharacteristic
511Q8—4884no—
512D4—22no—
513D4—22no—
514D4—41no—
515D4—41no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
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—84no—
541C2×C4—1222no—
542C2×C4—1222no—
543C2×C4—1222no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4#1451974812yes—
554C2×C4#1451974812yes—
555C2×C4#1451980712yes—
556C2×C4C2×D4×D6111yescharacteristic
557C2×C4C2×Q8×D6111yescharacteristic
558C2×C4#41×D6111yescharacteristic
559C2×C4C2×#1175822411yescharacteristic
560C2×C4#1451982411yescharacteristic
561C2×C4#1451982511yescharacteristic
562C8—1222no—
563C8—1222no—
564C8—2441no—
565C8—2441no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22C2×#1451974811yescharacteristic
574C22#1684041111yescharacteristic
575C22Q8×C22⋊D6111yescharacteristic
576C22C2×#1451980711yescharacteristic
577C22#1684056011yescharacteristic
578C22#1684056511yescharacteristic
579C22#1684056511yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—4881no—
590C4—2442no—
591C4—2442no—
592C4—2442no—
593C4#1684031411yescharacteristic
594C4#1684037211yescharacteristic
595C4#1684042211yescharacteristic
596C4#1684042511yescharacteristic
597C2—82no—
598C2#2144941411yescharacteristic
599C2#2145528711yescharacteristic
600C2#2145531811yescharacteristic
601C2#2145830411yescharacteristic
602C2#2145831311yescharacteristic
603C2#2145872911yescharacteristic
604C2#2145877311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2566C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenter#2566D61
hypocenterC61#25462
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2566

Complements

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

NH ≅ G/Ntype
1. C2×#16840172C2semidirect
3. #21448908C2semidirect
4. #21447301C2semidirect
5. #21447291C2semidirect
8. #21446777C2semidirect
9. #21446585C2semidirect
10. #21446575C2semidirect
11. #21446543C2semidirect
90. #14519698Q8semidirect
363. C61#25462semidirect

Maximal subgroups

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

subgroupindex
C2×#168401722
C2×#168400422
#214489082
#214473012
#214472912
#214472072
#214471932
#214467772
#214465852
#214465752
#214465432
#214464432
#214464362
#214456442
C61×#25662
#2546261