Finite Group Databasebeta

← #29847357

Subgroups — #29847357

Order 15616.

1738 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451786C211yesmaximal, characteristic, complemented
2#21451783C213yesmaximal, complemented
3#21451781C211yesmaximal, characteristic, complemented
4#21451778C213yesmaximal, complemented
5#21451775C213yesmaximal, complemented
6#21451774C213yesmaximal, complemented
7#21451772C211yesmaximal, characteristic, complemented
8#21449122C211yesmaximal, characteristic, complemented
9#21449121C211yesmaximal, characteristic, complemented
10#21449118C213yesmaximal, complemented
11#21449116C213yesmaximal, complemented
12#21448304C213yesmaximal
13#21448298C213yesmaximal, complemented
14C2×#16839607C211yesmaximal, characteristic, complemented
15C61×#2643C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C2×#14519733C2213yes—
18C22×C4×Dic61C2213yes—
19C61⋊#401C2213yes—
20C61⋊#401C2213yes—
21C61⋊#401C2211yescharacteristic
22#16839704C2213yes—
23#16839704C2213yes—
24#16839703C2213yes—
25#16839703C2213yes—
26#16839702C2213yes—
27#16839701C2213yes—
28#16839700C2213yes—
29#16839691C2213yes—
30#16839691C2213yes—
31#16839690C2213yes—
32#16839690C2213yes—
33#16839689C2213yes—
34#16839688C2213yes—
35#16839687C2213yes—
36#16839686C2211yescharacteristic
37#16839685C2213yes—
38#16839684C2213yes—
39#16839666C2213yes—
40#16839666C2213yes—
41#16839662C2213yes—
42#16839662C2213yes—
43#16839659C2213yes—
44#16839659C2213yes—
45#16839657C2213yes—
46#16839657C2213yes—
47#16839642C2213yes—
48#16839641C2213yes—
49#16839639C2213yes—
50#16839637C2213yes—
51#16839635C2213yes—
52#16839634C2213yes—
53C4⋊C4×Dic61C2213yes—
54C4⋊C4×Dic61C2213yes—
55#16839613C2213yes—
56#16839613C2213yes—
57C22⋊C4×Dic61C2213yes—
58C22⋊C4×Dic61C2213yes—
59#16839609C2213yes—
60#16839609C2213yes—
61#16839607C2213yes—
62#16839607C2211yescharacteristic
63#16839607C2213yes—
64#16839607C2211yescharacteristic
65C2×#14519684C2213yes—
66C61×#401C2211yescharacteristic
67C61×#400C2213yes—
68C61×#397C2213yes—
69C61×#396C2211yescharacteristic
70C61×#386C2213yes—
71C61×#385C2213yes—
72C2×#95×C61C2211yescharacteristic
73C2×#11758224—212no—
74C22×Dic122C2311yescharacteristic
75C22×C22⋊D61C2311yescharacteristic
76C22×C22⋊D61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2313yes—
79C23×Dic61C2311yescharacteristic
80C22×C4×D61C2311yescharacteristic
81#14519733—212no—
82C2×C4⋊Dic61C2313yes—
83C2×C4⋊Dic61C2313yes—
84C2×#11758196C2313yes—
85C2×#11758196C2313yes—
86C2×#11758196C2313yes—
87C2×#11758196C2313yes—
88C2×#11758196C2313yes—
89C2×#11758196C2313yes—
90C2×C22⋊Dic61C2313yes—
91C2×C22⋊Dic61C2313yes—
92C2×C22⋊Dic61C2313yes—
93C2×#11758198C2313yes—
94C2×#11758198C2313yes—
95C2×#11758198C2313yes—
96C2×#11758198C2313yes—
97C2×C4×Dic61—212no—
98C2×C4×Dic61C2313yes—
99C2×C4×Dic61C2313yes—
100C2×C4×Dic61C2313yes—
101C2×C4×Dic61C2313yes—
102C2×C4×Dic61C2313yes—
103C2×C4×Dic61C2313yes—
104#14519684C2313yes—
105#14519684C2313yes—
106#14519684C2313yes—
107#14519684C2313yes—
108#14519684C2313yes—
109#14519684C2313yes—
110#14519684C2313yes—
111#14519684C2313yes—
112#14519684C2313yes—
113#14519684C2313yes—
114#14519684C2313yes—
115#14519684C2313yes—
116#14519684C2313yes—
117#14519684C2313yes—
118#14519684C2313yes—
119#14519684C2313yes—
120C22×D4×C61C2311yescharacteristic
121C23×C4×C61C2313yes—
122C2×C4⋊C4×C61C2313yes—
123C2×C4⋊C4×C61C2313yes—
124C2×C22⋊C4×C61C2313yes—
125C2×C22⋊C4×C61C2313yes—
126C2×C22⋊C4×C61C2313yes—
127#95×C61C2311yescharacteristic
128#95×C61C2313yes—
129#95×C61C2313yes—
130#95×C61C2313yes—
131#95×C61C2313yes—
132#95×C61C2313yes—
133C24×C61C2411yescharacteristic
134C24×C61C2411yescharacteristic
135C23×D61C2411yescharacteristic
136C2×D4×C61—26no—
137C22×C4×C61—26no—
138C22×C4×C61—43no—
139C22×C4×C61—43no—
140C22×C4×C61C2411yescharacteristic
141C22×C4×C61C2413yes—
142C22×C4×C61C2413yes—
143C22×C4×C61C2413yes—
144C22×C4×C61C2413yes—
145C2×C22⋊D61—26no—
146C2×C22⋊D61—26no—
147C22×Dic61—26no—
148C22×Dic61—26no—
149C22×Dic61—43no—
150C22×Dic61—43no—
151C22×Dic61#41112yes—
152C22×Dic61C2411yescharacteristic
153C22×Dic61C2413yes—
154C22×Dic61C2413yes—
155C22×Dic61C2413yes—
156C22×Dic61C2413yes—
157C22×Dic61C2411yescharacteristic
158C22×Dic61C2411yescharacteristic
159#11758224—416no—
160C2×C4×D61—26no—
161C2×Dic122—26no—
162C4⋊C4×C61—43no—
163C4⋊C4×C61—43no—
164C22⋊C4×C61—26no—
165C22⋊C4×C61—43no—
166C22⋊C4×C61—43no—
167C22⋊Dic61—26no—
168C22⋊Dic61—43no—
169C22⋊Dic61—43no—
170#11758198—43no—
171#11758198—43no—
172#11758198—43no—
173#11758198—43no—
174C4⋊Dic61—43no—
175C4⋊Dic61—43no—
176#11758196—26no—
177#11758196—26no—
178#11758196—43no—
179#11758196—43no—
180#11758196—43no—
181#11758196—43no—
182C4×Dic61—26no—
183C4×Dic61—26no—
184C4×Dic61—26no—
185C4×Dic61—26no—
186C4×Dic61—26no—
187C4×Dic61—26no—
188C23×C61—21no—
189C23×C61—23no—
190C23×C61—23no—
191C23×C61—21no—
192C23×C61—23no—
193C23×C61C2×#4116yes—
194C23×C61C2511yescharacteristic
195C22×D61—23no—
196C22×D61—23no—
197C22×D61—21no—
198D4×C61—44no—
199C2×C4×C61—23no—
200C2×C4×C61—23no—
201C2×C4×C61—23no—
202C2×C4×C61—23no—
203C2×C4×C61—23no—
204C2×C4×C61—23no—
205C2×C4×C61—23no—
206C2×C4×C61—23no—
207C2×C4×C61—23no—
208C2×C4×C61—23no—
209C2×C4×C61—23no—
210C2×C4×C61—23no—
211C2×C4×C61—23no—
212C2×C4×C61—412no—
213C22⋊D61—44no—
214C22⋊D61—44no—
215C2×Dic61—23no—
216C2×Dic61—23no—
217C2×Dic61—23no—
218C2×Dic61—23no—
219C2×Dic61—23no—
220C2×Dic61—23no—
221C2×Dic61—23no—
222C2×Dic61—23no—
223C2×Dic61—23no—
224C2×Dic61—23no—
225C2×Dic61—23no—
226C2×Dic61—23no—
227C2×Dic61—23no—
228C2×Dic61—412no—
229C2×Dic61—44no—
230C2×Dic61#126116yes—
231C2×Dic61C2×#4116yes—
232C2×Dic61C2×#4116yes—
233C4×D61—44no—
234Dic122—44no—
235#34639—611nomaximal, Sylow
236C22×C61—26no—
237C22×C61—26no—
238C22×C61—41no—
239C22×C61—43no—
240C22×C61—43no—
241C22×C61C2×#12614yes—
242C22×C61C22×#4113yes—
243C22×C61#58513yes—
244C22×C61#58511yescharacteristic
245C2×D61—41no—
246C2×D61—43no—
247C2×D61—43no—
248C4×C61—41no—
249C4×C61—43no—
250C4×C61—43no—
251C4×C61—43no—
252C4×C61—43no—
253Dic61—41no—
254Dic61—43no—
255Dic61—43no—
256Dic61—43no—
257Dic61—43no—
258Dic61C2×#12614yes—
259Dic61C2×#12614yes—
260#2645—611no—
261#2645—613no—
262#2644—613no—
263#2644—611no—
264#2643—613no—
265#2643—613no—
266#2643—611no—
267#2643D6111yescharacteristic, complemented
268#2401—611no—
269#2401—613no—
270#2401—613no—
271#2401—611no—
272#2297—613no—
273#2296—613no—
274C2×#376—611no—
275C2×C61—24no—
276C2×C61—81no—
277C2×C61C22×#12611yescharacteristic
278C2×C61#345513yes—
279C2×C61#345513yes—
280D61—81no—
281C22×#41—611no—
282C2×#117—613no—
283C22×C42—613no—
284#401—613no—
285#401—613no—
286#401—611no—
287#401C2×D6111yescharacteristic
288#400—613no—
289#400—613no—
290#400—613no—
291#400—613no—
292#400—613no—
293#400—613no—
294#400—613no—
295#400C2×D6113yes—
296#397—613no—
297#397—613no—
298#397—613no—
299#397—613no—
300#397—613no—
301#397—613no—
302#397—613no—
303#397C2×D6113yes—
304#396—613no—
305#396—613no—
306#396—611no—
307#396C2×D6111yescharacteristic
308#391—613no—
309#391—613no—
310#390—613no—
311#390—613no—
312#389—613no—
313#389—613no—
314#389—613no—
315#389—613no—
316#386—613no—
317#386—613no—
318#386—613no—
319#386C2×D6113yes—
320#385—613no—
321#385—613no—
322#385—613no—
323#385C2×D6113yes—
324C4×C4⋊C4—613no—
325C4×C4⋊C4—613no—
326C4×C4⋊C4—613no—
327C4×C4⋊C4—613no—
328C4×C22⋊C4—613no—
329C4×C22⋊C4—613no—
330C4×C22⋊C4—613no—
331C4×C22⋊C4—613no—
332#376—613no—
333#376—611no—
334#376—613no—
335#376—611no—
336C2×#95—613no—
337C2×#95C2×D6111yescharacteristic
338C61#3463911yescharacteristic, complemented, Sylow
339C2×#41—12212no—
340C22×Q8—611no—
341C22×D4—611no—
342C22×D4—611no—
343C22×D4C22×D6111yescharacteristic
344C23×C4—611no—
345C23×C4—611no—
346C23×C4—613no—
347C23×C4—611no—
348C23×C4C22×D6113yes—
349#117—12212no—
350C2×C4⋊C4—613no—
351C2×C4⋊C4—613no—
352C2×C4⋊C4—613no—
353C2×C4⋊C4—613no—
354C2×C4⋊C4—613no—
355C2×C4⋊C4—613no—
356C2×C4⋊C4—613no—
357C2×C4⋊C4—613no—
358C2×C4⋊C4C22×D6113yes—
359C2×C4⋊C4C22×D6113yes—
360C2×C22⋊C4—613no—
361C2×C22⋊C4—613no—
362C2×C22⋊C4—613no—
363C2×C22⋊C4—613no—
364C2×C22⋊C4—613no—
365C2×C22⋊C4—613no—
366C2×C22⋊C4—613no—
367C2×C22⋊C4C22×D6113yes—
368C2×C22⋊C4C22×D6113yes—
369C2×C22⋊C4C22×D6113yes—
370C2×C42—613no—
371C2×C42—613no—
372C2×C42—613no—
373C2×C42—613no—
374C2×C42—613no—
375C2×C42—613no—
376C2×C42—12212no—
377#95—613no—
378#95—613no—
379#95—613no—
380#95—613no—
381#95—613no—
382#95—613no—
383#95—613no—
384#95—613no—
385#95—613no—
386#95—613no—
387#95—613no—
388#95—613no—
389#95—613no—
390#95—613no—
391#95—613no—
392#95—613no—
393#95C22×D6111yescharacteristic
394#95C22×D6113yes—
395#95C22×D6113yes—
396#95C22×D6113yes—
397#95C22×D6113yes—
398#95C22×D6113yes—
399C24—611no—
400C24C23×D6111yescharacteristic
401C24C23×D6111yescharacteristic
402#41—24416no—
403C2×Q8—1226no—
404C2×D4—26no—
405C2×D4—1226no—
406C2×D4—1226no—
407C22×C4—26no—
408C22×C4—43no—
409C22×C4—43no—
410C22×C4—6112no—
411C22×C4—611no—
412C22×C4—611no—
413C22×C4—611no—
414C22×C4—613no—
415C22×C4—613no—
416C22×C4—613no—
417C22×C4—613no—
418C22×C4—1226no—
419C22×C4—1226no—
420C22×C4—1226no—
421C22×C4—2443no—
422C22×C4—2443no—
423C22×C4C23×D6111yescharacteristic
424C22×C4C23×D6113yes—
425C22×C4C23×D6113yes—
426C22×C4C23×D6113yes—
427C22×C4C23×D6113yes—
428C4⋊C4—43no—
429C4⋊C4—43no—
430C4⋊C4—1226no—
431C4⋊C4—1226no—
432C4⋊C4—2443no—
433C4⋊C4—2443no—
434C4⋊C4—2443no—
435C4⋊C4—2443no—
436C4⋊C4—2443no—
437C4⋊C4—2443no—
438C22⋊C4—26no—
439C22⋊C4—43no—
440C22⋊C4—43no—
441C22⋊C4—1226no—
442C22⋊C4—2443no—
443C22⋊C4—2443no—
444C22⋊C4—2443no—
445C22⋊C4—2443no—
446C22⋊C4—2443no—
447C22⋊C4—2443no—
448C42—1226no—
449C42—1226no—
450C42—1226no—
451C42—1226no—
452C42—1226no—
453C42—1226no—
454C23—23no—
455C23—21no—
456C23—23no—
457C23—23no—
458C23—21no—
459C23—1223no—
460C23—1223no—
461C23—1221no—
462C23#41×D6116yes—
463C23C24×D6111yescharacteristic
464Q8—2444no—
465D4—44no—
466D4—2444no—
467D4—2444no—
468C2×C4—23no—
469C2×C4—23no—
470C2×C4—23no—
471C2×C4—23no—
472C2×C4—23no—
473C2×C4—23no—
474C2×C4—23no—
475C2×C4—23no—
476C2×C4—23no—
477C2×C4—23no—
478C2×C4—23no—
479C2×C4—23no—
480C2×C4—23no—
481C2×C4—412no—
482C2×C4—6116no—
483C2×C4—616no—
484C2×C4—616no—
485C2×C4—1223no—
486C2×C4—1223no—
487C2×C4—1223no—
488C2×C4—1223no—
489C2×C4—1223no—
490C2×C4—1223no—
491C2×C4—1223no—
492C2×C4—1223no—
493C2×C4—1223no—
494C2×C4—1223no—
495C2×C4—1223no—
496C2×C4—1223no—
497C2×C4—1223no—
498C2×C4—2444no—
499C2×C4—2444no—
500C2×C4—24412no—
501C22—26no—
502C22—26no—
503C22—43no—
504C22—43no—
505C22—41no—
506C22—2443no—
507C22—2443no—
508C22—2441no—
509C22#126×D6114yes—
510C22C2×#41×D6113yes—
511C22#1684059713yes—
512C22#1684059911yescharacteristic
513C4—43no—
514C4—43no—
515C4—43no—
516C4—43no—
517C4—41no—
518C4—614no—
519C4—614no—
520C4—2443no—
521C4—2443no—
522C4—2443no—
523C4—2443no—
524C4—2441no—
525C2—24no—
526C2—81no—
527C2—4881no—
528C2C2×#126×D6111yescharacteristic
529C2#2145920113yes—
530C2#2145920513yes—
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2643C2
prime radicalC22×#11758224C22
hypercenter#2643D61
hypocenterC61#34639
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2643

Complements

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

NH ≅ G/Ntype
1. #21451786C2semidirect
2. #21451783C2semidirect
3. #21451781C2semidirect
4. #21451778C2semidirect
5. #21451775C2semidirect
6. #21451774C2semidirect
7. #21451772C2semidirect
8. #21449122C2semidirect
9. #21449121C2semidirect
10. #21449118C2semidirect
11. #21449116C2semidirect
13. #21448298C2semidirect
14. C2×#16839607C2semidirect
15. C61×#2643C2semidirect
267. #2643D61semidirect
338. C61#34639semidirect

Maximal subgroups

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

subgroupindex
#214517862
#214517832
#214517812
#214517782
#214517752
#214517742
#214517722
#214491222
#214491212
#214491182
#214491162
#214483042
#214482982
C2×#168396072
C61×#26432
#3463961