Finite Group Databasebeta

← #29783136

Subgroups — #29783136

Order 15616.

724 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
1#21454187C211yesmaximal, characteristic
2#21448290C211yesmaximal, characteristic, complemented
3#21447319C211yesmaximal, characteristic, complemented
4#21447209C211yesmaximal, characteristic, complemented
5#21447202C211yesmaximal, characteristic
6#21447138C211yesmaximal, characteristic
7#21446673C211yesmaximal, characteristic
8#21446501C211yesmaximal, characteristic
9#21446494C211yesmaximal, characteristic, complemented
10#21446438C211yesmaximal, characteristic
11#21446403C211yesmaximal, characteristic, complemented
12#21446175C211yesmaximal, characteristic
13#21446070C211yesmaximal, characteristic, complemented
14C4×#14519706C211yesmaximal, characteristic, complemented
15C61×#1942C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C2×#14519772—21no—
18C2×#14519742C2211yescharacteristic
19C2×#14519709C2211yescharacteristic
20C2×#14519706C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×#14519702C2211yescharacteristic
23C2×#14519700C2211yescharacteristic
24C2×#14519700C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×C4×#92418C2211yescharacteristic
29#16839668C2211yescharacteristic
30#16839667C2211yescharacteristic
31#16839664C2211yescharacteristic
32#16839663C2211yescharacteristic
33#16839663C2211yescharacteristic
34#16839661C2211yescharacteristic
35#16839661C2211yescharacteristic
36#16839658C2211yescharacteristic
37#16839654—21no—
38#16839652—21no—
39#16839651—21no—
40#16839649—21no—
41#16839643—21no—
42C4⋊C4×Dic61—21no—
43C4⋊C4×Dic61C2211yescharacteristic
44#16839607—21no—
45C42×Dic61C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#107×C61C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C2×C4×C8×C61C2211yescharacteristic
55C61×#389C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×Dic122C2311yescharacteristic
60C22×D244C2311yescharacteristic
61C2×#11758190—22no—
62C2×#11758190—22no—
63C2×#11758190—41no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519772—44no—
67#14519742—22no—
68#14519742—22no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61D411yescharacteristic
84C2×C4×Dic61D411yescharacteristic
85C2×C4×Dic61D411yescharacteristic
86C2×C4×Dic61D411yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89#14519709—22no—
90#14519706—22no—
91#14519706—22no—
92#14519702—22no—
93#14519700—22no—
94#14519700—41no—
95#14519699—22no—
96#14519697—22no—
97#14519697—41no—
98C4×#92418—41no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C42×C61C2311yescharacteristic
116#107×C61—22no—
117#107×C61—41no—
118C4×C8×C61—41no—
119#95×C61—21no—
120#95×C61—21no—
121C23×D61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2411yescharacteristic
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61C2×D411yescharacteristic
133C22×Dic61C2×D411yescharacteristic
134C22×Dic61C2×D411yescharacteristic
135C22×Dic61C2×D411yescharacteristic
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—21no—
139C2×D244—21no—
140C2×D244—21no—
141C2×D244—21no—
142C2×Dic122—21no—
143C2×Dic122—21no—
144C2×Dic122—21no—
145C2×Dic122—21no—
146C2×Dic122—21no—
147C2×Dic122#4112yes—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61#4112yes—
153C2×C8×C61#4112yes—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—42no—
162C4⋊C4×C61—42no—
163C4⋊C4×C61#4112yes—
164C42×C61—21no—
165C42×C61—21no—
166#11758198—42no—
167#11758198—42no—
168#11758198—42no—
169#11758198—42no—
170#11758198—42no—
171#11758198—42no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—42no—
177C4⋊Dic61—42no—
178#11758196—24no—
179#11758196—42no—
180C4×Dic61—24no—
181C4×Dic61—22no—
182C4×Dic61—22no—
183C4×Dic61—21no—
184C4×Dic61—21no—
185C4×Dic61—21no—
186C4×Dic61—21no—
187C4×Dic61—22no—
188C4×Dic61—22no—
189C4×Dic61—42no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196#11758190—44no—
197C23×C61C22×D411yescharacteristic
198C22×D61—41no—
199C22×D61—41no—
200C22×D61—41no—
201C22×D61—41no—
202C22×D61—41no—
203C22×D61—41no—
204C22×D61—41no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—22no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
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×C61AGL(1,ℤ/8)12yes—
222C2×C4×C61#13712yes—
223C2×C4×C61C2×#4111yescharacteristic
224C2×C4×C61C2×#4111yescharacteristic
225C2×C4×C61C2×#4111yescharacteristic
226C2×C4×C61C2×#4111yescharacteristic
227C2×C4×C61H(5,𝔽2)11yescharacteristic
228C2×C4×C612−1+411yescharacteristic
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—22no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61#13512yes—
249C2×Dic61#13512yes—
250D244—41no—
251D244—41no—
252D244—41no—
253D244—41no—
254Dic122—22no—
255Dic122—22no—
256Dic122—41no—
257Dic122—41no—
258C8×C61—22no—
259C8×C61—22no—
260#92418—41no—
261#92418—41no—
262#29435—611nomaximal, Sylow
263C22×C61#52511yescharacteristic
264C22×C61#53211yescharacteristic
265C22×C61#53711yescharacteristic
266C22×C61C2×#13511yescharacteristic
267C22×C61C2×#13511yescharacteristic
268C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
269C22×C61C2×#13711yescharacteristic
270C2×D61—81no—
271C2×D61—81no—
272C2×D61—81no—
273C2×D61—81no—
274C2×D61—81no—
275C2×D61—81no—
276C2×D61—81no—
277C4×C61—22no—
278C4×C61—22no—
279C4×C61—42no—
280C4×C61—81no—
281C4×C61—81no—
282C4×C61—81no—
283C4×C61#55111yescharacteristic
284C4×C61#55211yescharacteristic
285C4×C61#55311yescharacteristic
286C4×C61#55611yescharacteristic
287Dic61—22no—
288Dic61—22no—
289Dic61—41no—
290Dic61—42no—
291Dic61—41no—
292Dic61—81no—
293Dic61—81no—
294#2860—611no—
295#2295—611no—
296#2088—611no—
297#2068—611no—
298#2067—611no—
299#2055—611no—
300#1968—611no—
301#1942D6111yescharacteristic, complemented
302#1934—611no—
303#1933—611no—
304#1925—611no—
305#1920—611no—
306#1880—611no—
307#1863—611no—
308C4×C4⋊C8—611no—
309C2×C61#260111yescharacteristic
310C2×C61#310611yescharacteristic
311C2×C61#310811yescharacteristic
312C2×C61#316811yescharacteristic
313C2×C61#318211yescharacteristic
314C2×C61#324711yescharacteristic
315C2×C61#324811yescharacteristic
316D61—161no—
317C22×SD16—611no—
318C2×#126—1221no—
319C2×C4×Q8—611no—
320C2×#107C2×D6111yescharacteristic
321C2×#107C2×D6111yescharacteristic
322C2×#106—611no—
323C2×C4⋊C8—611no—
324C2×C4⋊C8—611no—
325C2×#103—611no—
326C2×#103—611no—
327C2×#103—611no—
328C2×#102—611no—
329C2×#102—611no—
330C2×#102—611no—
331C2×C4×C8—611no—
332C2×C4×C8C2×D6111yescharacteristic
333#391—611no—
334#391—611no—
335#390—611no—
336#390—611no—
337#390—611no—
338#389—611no—
339#389—611no—
340#389—611no—
341#389C2×D6111yescharacteristic
342#389C2×D6111yescharacteristic
343#388—1221no—
344#388—1221no—
345#388—1221no—
346#387—1221no—
347#387—1221no—
348C4×C4⋊C4—611no—
349C4×C4⋊C4—1221no—
350#376—1221no—
351C43—611no—
352#340—611no—
353#340—611no—
354#340—611no—
355#340—611no—
356#340C2×D6111yescharacteristic
357#340C2×D6111yescharacteristic
358#336—611no—
359#336—611no—
360C61#2943511yescharacteristic, complemented, Sylow
361C22×Q8—611no—
362C22×D4—611no—
363C2×SD16—1222no—
364C2×SD16—1222no—
365C2×SD16—2441no—
366C22×C8—611no—
367C22×C8—611no—
368C22×C8C22×D6111yescharacteristic
369C22×C8C22×D6111yescharacteristic
370#126—2444no—
371C4×Q8—1222no—
372C4×Q8—1222no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4C22×D6111yescharacteristic
382C2×C4⋊C4C22×D6111yescharacteristic
383C2×C4⋊C4C22×D6111yescharacteristic
384C2×C4⋊C4C22×D6111yescharacteristic
385C2×C22⋊C4—1221no—
386C2×C22⋊C4—1221no—
387C2×C22⋊C4—1221no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C42—611no—
392C2×C42—611no—
393C2×C42—611no—
394C2×C42—611no—
395C2×C42—611no—
396C2×C42—611no—
397C2×C42—1221no—
398C2×C42—1221no—
399C2×C42C22×D6111yescharacteristic
400#107—22no—
401#107—41no—
402#106—1222no—
403C4⋊C8—1222no—
404C4⋊C8—1222no—
405#103—1222no—
406#103—1222no—
407#103—2441no—
408#102—1222no—
409#102—1222no—
410#102—2441no—
411C4×C8—41no—
412C4×C8—2441no—
413#95—21no—
414#95—21no—
415#95—1221no—
416#95—1221no—
417#95—1221no—
418#95—1221no—
419#95—1221no—
420#95—1221no—
421#95—1221no—
422#95—1221no—
423C24—1221no—
424C2×Q8—612no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×Q8—1221no—
428C2×Q8—1221no—
429C2×Q8—1221no—
430C2×D4—1221no—
431C2×D4—1221no—
432C2×D4—1221no—
433C2×D4—1221no—
434C2×D4—1221no—
435C2×D4—1221no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4D4×D6111yescharacteristic
448C22×C4D4×D6111yescharacteristic
449C22×C4C23×D6111yescharacteristic
450SD16—2444no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8#1175822612yes—
462C2×C8#1175822612yes—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—1224no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—2442no—
478C4⋊C4—2442no—
479C4⋊C4—2442no—
480C4⋊C4#1175822212yes—
481C22⋊C4—2442no—
482C22⋊C4—2442no—
483C22⋊C4—2442no—
484C22⋊C4—2442no—
485C22⋊C4—2442no—
486C22⋊C4—2442no—
487C42—21no—
488C42—21no—
489C42—1222no—
490C42—1222no—
491C42—1224no—
492C42—1222no—
493C42—1221no—
494C42—1221no—
495C42—1221no—
496C42—1221no—
497C42—1222no—
498C42—2442no—
499C23—2441no—
500C23—2441no—
501C23—2441no—
502C23—2441no—
503C23—2441no—
504C23—2441no—
505C23—2441no—
506C23C2×D4×D6111yescharacteristic
507Q8—1222no—
508Q8—1222no—
509Q8—2441no—
510Q8—2441no—
511D4—2441no—
512D4—2441no—
513D4—2441no—
514D4—2441no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
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—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—612no—
532C2×C4—612no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1222no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
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#1451980112yes—
553C2×C4#1451980912yes—
554C2×C4#41×D6111yescharacteristic
555C2×C4C2×#1175822211yescharacteristic
556C2×C4C2×#1175822611yescharacteristic
557C2×C4C2×#1175822611yescharacteristic
558C2×C4#1451982211yescharacteristic
559C2×C4#1451982411yescharacteristic
560C8—22no—
561C8—22no—
562C8—2441no—
563C8—2441no—
564C22—4881no—
565C22—4881no—
566C22—4881no—
567C22—4881no—
568C22—4881no—
569C22—4881no—
570C22—4881no—
571C22#1684027111yescharacteristic
572C22#1684031311yescharacteristic
573C22#1684033911yescharacteristic
574C22#135×D6111yescharacteristic
575C22#135×D6111yescharacteristic
576C22C2×#1451980111yescharacteristic
577C22C2×#1451980911yescharacteristic
578C4—22no—
579C4—22no—
580C4—42no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—1222no—
585C4—1222no—
586C4—4881no—
587C4—4881no—
588C4—2441no—
589C4—2442no—
590C4—2441no—
591C4#1684043911yescharacteristic
592C4#1684045011yescharacteristic
593C4#1684046011yescharacteristic
594C4#1684048511yescharacteristic
595C2—9761no—
596C2#2145141511yescharacteristic
597C2#2145587511yescharacteristic
598C2#2145590311yescharacteristic
599C2#2145639111yescharacteristic
600C2#2145653911yescharacteristic
601C2#2145713811yescharacteristic
602C2#2145715111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1942C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#1942D61
hypocenterC61#29435
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1942

Complements

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

NH ≅ G/Ntype
2. #21448290C2semidirect
3. #21447319C2semidirect
4. #21447209C2semidirect
9. #21446494C2semidirect
11. #21446403C2semidirect
13. #21446070C2semidirect
14. C4×#14519706C2semidirect
15. C61×#1942C2semidirect
301. #1942D61semidirect
360. C61#29435semidirect

Maximal subgroups

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

subgroupindex
#214541872
#214482902
#214473192
#214472092
#214472022
#214471382
#214466732
#214465012
#214464942
#214464382
#214464032
#214461752
#214460702
C4×#145197062
C61×#19422
#2943561