Finite Group Databasebeta

← #29692134

Subgroups — #29692134

Order 15616.

836 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840050C211yesmaximal, characteristic
2C4×#14519776C211yesmaximal, characteristic, complemented
3#21448281C211yesmaximal, characteristic
4#21446765C211yesmaximal, characteristic, complemented
5#21446574C211yesmaximal, characteristic, complemented
6#21446561C211yesmaximal, characteristic, complemented
7#21446560C211yesmaximal, characteristic, complemented
8#21446518C211yesmaximal, characteristic
9#21446513C211yesmaximal, characteristic
10#21446436C211yesmaximal, characteristic
11#21446405C211yesmaximal, characteristic, complemented
12#21446404C211yesmaximal, characteristic, complemented
13#21445817C211yesmaximal, characteristic
14#21445671C211yesmaximal, characteristic, complemented
15C61×#1925C211yesmaximal, characteristic
16C2×#14519776C2211yescharacteristic
17C2×C4×Dic122—21no—
18C2×D4×Dic61C2211yescharacteristic
19C2×#14519733—21no—
20#16840050C418yescomplemented
21C2×#14519710C2211yescharacteristic
22C2×#14519709C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519687C2211yescharacteristic
29C2×#14519687C2211yescharacteristic
30#16839666—21no—
31#16839665C2211yescharacteristic
32#16839661C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839659—21no—
35#16839658C2211yescharacteristic
36#16839658C2211yescharacteristic
37#16839656—21no—
38#16839650—21no—
39#16839631C2211yescharacteristic
40C4⋊C4×Dic61C2211yescharacteristic
41C4×#11758196—21no—
42C4×C4⋊Dic61C2211yescharacteristic
43C22⋊C4×Dic61—21no—
44C42×Dic61C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839517C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C22×Dic122—21no—
61C23×Dic61—21no—
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64#14519776—22no—
65#14519776C2×C414yes—
66C4×Dic122—44no—
67D4×Dic61—22no—
68D4×Dic61C2×C414yes—
69#14519733—44no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61D411yescharacteristic
87C2×C4×Dic61D411yescharacteristic
88C2×C4×Dic61D411yescharacteristic
89C2×C4×Dic61D411yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92#14519710—41no—
93#14519709C2×C414yes—
94#14519708C2×C414yes—
95#14519706—22no—
96#14519706C2×C414yes—
97#14519698—41no—
98#14519698C2×C414yes—
99#14519687—41no—
100#14519687—41no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107C22×D4×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C42×C61—21no—
116C2×C42×C61C2311yescharacteristic
117#107×C61—41no—
118#102×C61—41no—
119#102×C61C2×C414yes—
120#95×C61—21no—
121C24×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61C22×C412yes—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2411yescharacteristic
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—24no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—42no—
140C22×Dic61—42no—
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144C22×Dic61C2×D411yescharacteristic
145C2×Dic122—24no—
146C2×Dic122—42no—
147C2×Dic122—42no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61C22×C412yes—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61C22×C412yes—
160C22⋊C4×C61—42no—
161C22⋊C4×C61—42no—
162C42×C61—21no—
163C42×C61—21no—
164C42×C61—42no—
165C22⋊Dic61—24no—
166C22⋊Dic61—42no—
167C22⋊Dic61—42no—
168C4⋊Dic61—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—42no—
175C4⋊Dic61C22×C412yes—
176C4⋊Dic61C22×C412yes—
177#11758196—24no—
178#11758196—42no—
179#11758196—42no—
180#11758196—42no—
181#11758196—42no—
182#11758196—42no—
183C4×Dic61—22no—
184C4×Dic61—21no—
185C4×Dic61—21no—
186C4×Dic61—22no—
187C4×Dic61—22no—
188C4×Dic61—41no—
189C4×Dic61—42no—
190C4×Dic61—42no—
191C4×Dic61C22×C412yes—
192C4×Dic61#4112yes—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418C22×C412yes—
199C23×C61—22no—
200C23×C61—41no—
201C23×C61—41no—
202C23×C61—41no—
203C23×C61—41no—
204C23×C61—41no—
205C23×C61—41no—
206C23×C61C22×D411yescharacteristic
207D4×C61—22no—
208D4×C61—22no—
209D4×C61—41no—
210D4×C61—41no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—22no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
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×C61AGL(1,ℤ/8)12yes—
226C2×C4×C61C23×C411yescharacteristic
227C2×C4×C61C2×#4111yescharacteristic
228C2×C4×C61H(5,𝔽2)11yescharacteristic
229C2×C4×C612−1+411yescharacteristic
230C2×C4×C612−1+411yescharacteristic
231C2×C4×C612−1+411yescharacteristic
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—48no—
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×Dic61AGL(1,ℤ/8)12yes—
256C2×Dic61#13712yes—
257Dic122—48no—
258C8×C61—22no—
259C8×C61—41no—
260#92418—22no—
261#92418—41no—
262#22117—611nomaximal, Sylow
263C22×C61—42no—
264C22×C61—42no—
265C22×C61—42no—
266C22×C61—81no—
267C22×C61—81no—
268C22×C61—81no—
269C22×C61—81no—
270C22×C61C2×C4×D411yescharacteristic
271C22×C61#53611yescharacteristic
272C22×C61#53711yescharacteristic
273C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
274C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C61C2×#13711yescharacteristic
276C22×C61#57511yescharacteristic
277C4×C61—22no—
278C4×C61—42no—
279C4×C61—41no—
280C4×C61—81no—
281C4×C61—81no—
282C4×C61#51911yescharacteristic
283C4×C61#52011yescharacteristic
284C4×C61#54111yescharacteristic
285C4×C61#54211yescharacteristic
286Dic61—22no—
287Dic61—42no—
288Dic61—42no—
289Dic61—41no—
290Dic61—41no—
291Dic61—81no—
292Dic61—81no—
293Dic61#44014yes—
294C2×#476—611no—
295C4×C4⋊Q8—611no—
296#2293—611no—
297#1987—611no—
298#1947—611no—
299#1944—611no—
300#1944—611no—
301#1936—611no—
302#1936—611no—
303#1925—611no—
304#1925D6111yescharacteristic
305#1920—611no—
306#1920—611no—
307#1802—611no—
308#1767—611no—
309C2×C61—82no—
310C2×C61#232311yescharacteristic
311C2×C61C2×#44011yescharacteristic
312C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
313C2×C61#323511yescharacteristic
314C2×C61#323811yescharacteristic
315C2×C61#325211yescharacteristic
316C2×C61#325311yescharacteristic
317C2×C4⋊Q8—611no—
318C2×C4×Q8—1221no—
319C2×C4×D4—611no—
320C2×#117—1221no—
321#476—618no—
322C2×#107—611no—
323C2×#107C2×D6111yescharacteristic
324C2×#106—611no—
325C2×#106—611no—
326C2×C4⋊C8—611no—
327C2×C4⋊C8—611no—
328C2×#102—611no—
329C2×#102—611no—
330C2×#102C2×D6111yescharacteristic
331C2×#102C2×D6111yescharacteristic
332C2×#97—611no—
333C2×#97—611no—
334#391—1221no—
335#390—611no—
336#390C2×D6111yescharacteristic
337#389—611no—
338#389—611no—
339#389—611no—
340#389—611no—
341#389—1221no—
342#388—1221no—
343#388—1221no—
344#384—611no—
345C4×C4⋊C4—611no—
346C4×C4⋊C4—611no—
347C4×C4⋊C4—1221no—
348C4×C4⋊C4C2×D6111yescharacteristic
349C4×C22⋊C4—1221no—
350C43—611no—
351#340—611no—
352#340—611no—
353#340—611no—
354#340—611no—
355#340—611no—
356#340—611no—
357#340—611no—
358#340C2×D6111yescharacteristic
359#336—611no—
360#336C2×D6111yescharacteristic
361C61#2211711yescharacteristic, complemented, Sylow
362C22×Q8—1221no—
363C22×D4C22×D6111yescharacteristic
364C23×C4—1221no—
365C22×C8—611no—
366C22×C8—611no—
367C22×C8C22×D6111yescharacteristic
368C22×C8C22×D6111yescharacteristic
369C4⋊Q8—614no—
370C4⋊Q8—1222no—
371C4×Q8—2444no—
372C4×D4—614no—
373C4×D4—1222no—
374#117—2444no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4—1221no—
385C2×C4⋊C4—1221no—
386C2×C4⋊C4C22×D6111yescharacteristic
387C2×C4⋊C4C22×D6111yescharacteristic
388C2×C4⋊C4C22×D6111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—1221no—
392C2×C22⋊C4—1221no—
393C2×C22⋊C4—1221no—
394C2×C42—21no—
395C2×C42—611no—
396C2×C42—611no—
397C2×C42—611no—
398C2×C42—611no—
399C2×C42—611no—
400C2×C42—611no—
401C2×C42—1221no—
402C2×C42—1221no—
403C2×C42C22×D6111yescharacteristic
404#107—41no—
405#107—2441no—
406#106—614no—
407#106—614no—
408C4⋊C8—614no—
409C4⋊C8—1222no—
410#102—41no—
411#102—614no—
412#102—2441no—
413#102C4×D6114yes—
414#97—2441no—
415#97—2441no—
416#95—21no—
417#95—1221no—
418#95—1221no—
419#95—1221no—
420#95—1221no—
421#95—1221no—
422#95—1221no—
423C24—21no—
424C2×Q8—1224no—
425C2×Q8—2442no—
426C2×Q8—2442no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4C2×C4×D6112yes—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—1224no—
441C22×C4—1221no—
442C22×C4—1221no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—2442no—
446C22×C4—2442no—
447C22×C4D4×D6111yescharacteristic
448C22×C4D4×D6111yescharacteristic
449C22×C4C23×D6111yescharacteristic
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—612no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8C2×C4×D6112yes—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—612no—
468C4⋊C4—612no—
469C4⋊C4—1224no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—2442no—
477C4⋊C4—2442no—
478C4⋊C4—2442no—
479C4⋊C4—2442no—
480C4⋊C4—2442no—
481C4⋊C4—2442no—
482C4⋊C4C2×C4×D6112yes—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—1224no—
486C22⋊C4—2442no—
487C22⋊C4—2442no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—612no—
492C42—612no—
493C42—1222no—
494C42—1222no—
495C42—1221no—
496C42—1221no—
497C42—1222no—
498C42—2441no—
499C42—2442no—
500C42—2442no—
501C23—22no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23C2×D4×D6111yescharacteristic
509Q8—2448no—
510D4—22no—
511D4—22no—
512D4—41no—
513D4—41no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—612no—
529C2×C4—612no—
530C2×C4—612no—
531C2×C4—612no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1222no—
535C2×C4—1222no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—2448no—
543C2×C4—2441no—
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#1451980112yes—
554C2×C4C22×C4×D6111yescharacteristic
555C2×C4#41×D6111yescharacteristic
556C2×C4#1451982211yescharacteristic
557C2×C4#1451982411yescharacteristic
558C2×C4#1451982411yescharacteristic
559C2×C4#1451982411yescharacteristic
560C8—22no—
561C8—41no—
562C8—1222no—
563C8—2441no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22C4×D4×D6111yescharacteristic
572C22#1684033411yescharacteristic
573C22#1684034111yescharacteristic
574C22AGL(1,ℤ/8)×D6111yescharacteristic
575C22C2×#1451980111yescharacteristic
576C22#137×D6111yescharacteristic
577C22#1684055911yescharacteristic
578C4—22no—
579C4—42no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—614no—
584C4—1222no—
585C4—4881no—
586C4—4881no—
587C4—2442no—
588C4—2442no—
589C4—2441no—
590C4—2441no—
591C4#1684023911yescharacteristic
592C4#1684024111yescharacteristic
593C4#1684036911yescharacteristic
594C4#1684037611yescharacteristic
595C2—82no—
596C2#2144849811yescharacteristic
597C2#440×D6111yescharacteristic
598C2C4×#1451980111yescharacteristic
599C2#2145701411yescharacteristic
600C2#2145703811yescharacteristic
601C2#2145718911yescharacteristic
602C2#2145719811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1925C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
cosocleC22×C4×C61C24
hypercenter#1925D61
hypocenterC61#22117
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
2. C4×#14519776C2semidirect
4. #21446765C2semidirect
5. #21446574C2semidirect
6. #21446561C2semidirect
7. #21446560C2semidirect
11. #21446405C2semidirect
12. #21446404C2semidirect
14. #21445671C2semidirect
20. #16840050C4semidirect
361. C61#22117semidirect

Maximal subgroups

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

subgroupindex
C2×#168400502
C4×#145197762
#214482812
#214467652
#214465742
#214465612
#214465602
#214465182
#214465132
#214464362
#214464052
#214464042
#214458172
#214456712
C61×#19252
#2211761