Finite Group Databasebeta

← #29838107

Subgroups — #29838107

Order 15616.

528 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458832C211yesmaximal, characteristic, complemented
2#21448086C211yesmaximal, characteristic, complemented
3#21448083C211yesmaximal, characteristic, complemented
4#21448078C211yesmaximal, characteristic, complemented
5#21447881C211yesmaximal, characteristic, complemented
6#21447878C211yesmaximal, characteristic, complemented
7#21447874C211yesmaximal, characteristic, complemented
8#21447871C211yesmaximal, characteristic, complemented
9#21447854C211yesmaximal, characteristic, complemented
10#21447851C211yesmaximal, characteristic, complemented
11#21447728C211yesmaximal, characteristic, complemented
12#21447683C211yesmaximal, characteristic, complemented
13#21447681C211yesmaximal, characteristic, complemented
14C4×#14519718C211yesmaximal, characteristic, complemented
15C61×#3396C211yesmaximal, characteristic, complemented
16#16840497—21no—
17C2×#14519723C2211yescharacteristic
18C2×#14519721C2211yescharacteristic
19C2×#14519721C2211yescharacteristic
20C2×#14519720C2211yescharacteristic
21C2×#14519720C2211yescharacteristic
22C2×#14519718C2211yescharacteristic
23C2×#14519718C2211yescharacteristic
24C2×#14519718C2211yescharacteristic
25C2×#14519718C2211yescharacteristic
26#16840146C2211yescharacteristic
27#16840146C2211yescharacteristic
28#16840139C2211yescharacteristic
29#16839978—21no—
30#16839978—21no—
31#16839963—21no—
32C4×Dic244C2211yescharacteristic
33C4×D488C2211yescharacteristic
34C4×D488C2211yescharacteristic
35#16839587C2211yescharacteristic
36C4⋊#11758185C2211yescharacteristic
37C4⋊#11758185C2211yescharacteristic
38C4⋊#11758185C2211yescharacteristic
39#16839566C2211yescharacteristic
40#16839565C2211yescharacteristic
41#16839563C2211yescharacteristic
42#16839563C2211yescharacteristic
43#16839562C2211yescharacteristic
44#16839562C2211yescharacteristic
45#16839538C2211yescharacteristic
46#16839538C2211yescharacteristic
47C4×#11758185C2211yescharacteristic
48C61×#559—21no—
49C61×#495C2211yescharacteristic
50C61×#495C2211yescharacteristic
51C61×#493C2211yescharacteristic
52C61×#463—21no—
53C61×#463—21no—
54C61×#460—21no—
55C8×Q8×C61C2211yescharacteristic
56C4×Q16×C61C2211yescharacteristic
57C4×D8×C61C2211yescharacteristic
58C4×D8×C61C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×#11758190—21no—
61C2×#11758190—21no—
62C2×D488—21no—
63C2×D488C2311yescharacteristic
64C2×D488C2311yescharacteristic
65#14519774—21no—
66#14519766—41no—
67#14519765—21no—
68#14519765—21no—
69#14519762—41no—
70#14519762—41no—
71C4×Dic122—21no—
72C4×D244—21no—
73C4×D244—21no—
74#14519739—41no—
75#14519723—41no—
76#14519721—22no—
77#14519721—41no—
78#14519720—22no—
79#14519720—41no—
80#14519718—22no—
81#14519718—41no—
82#14519718—41no—
83#14519718—41no—
84C2×#11758185C2311yescharacteristic
85C2×#11758185C2311yescharacteristic
86C2×#11758185C2311yescharacteristic
87C2×#11758185C2311yescharacteristic
88#14519711C2311yescharacteristic
89#14519702—21no—
90#14519699—21no—
91#14519699—21no—
92C2×Q16×C61C2311yescharacteristic
93C2×SD16×C61—21no—
94C2×SD16×C61—21no—
95C2×D8×C61—21no—
96C2×D8×C61C2311yescharacteristic
97C2×D8×C61C2311yescharacteristic
98#127×C61—21no—
99#124×C61—21no—
100#124×C61—21no—
101#124×C61—41no—
102#123×C61—41no—
103#123×C61—41no—
104C4×Q8×C61—21no—
105C4×Q8×C61D411yescharacteristic
106C4×D4×C61—21no—
107C4×D4×C61—21no—
108C4×D4×C61—41no—
109#107×C61C2311yescharacteristic
110C4⋊C8×C61D411yescharacteristic
111C4⋊C8×C61D411yescharacteristic
112C4⋊C8×C61D411yescharacteristic
113#103×C61—21no—
114#102×C61—21no—
115#102×C61—21no—
116C4×C8×C61C2311yescharacteristic
117C4×C8×C61C2311yescharacteristic
118C4×C8×C61C2311yescharacteristic
119C2×Q8×C61—21no—
120C2×Q8×C61D811yescharacteristic
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—41no—
124C2×D4×C61—41no—
125C22×C4×C61—41no—
126C22×C4×C61—41no—
127C2×D244—21no—
128C2×D244—21no—
129C2×D244—41no—
130C2×D244—41no—
131C2×C4×D61—41no—
132C2×C4×D61—41no—
133C2×Dic122—21no—
134Q16×C61—21no—
135Q16×C61—21no—
136SD16×C61—81no—
137SD16×C61—81no—
138D8×C61—21no—
139D8×C61—21no—
140D8×C61—21no—
141D8×C61—21no—
142D8×C61—81no—
143C2×C8×C61C2×D411yescharacteristic
144C2×C8×C61C2×D411yescharacteristic
145C2×C8×C61C2×D411yescharacteristic
146C2×C8×C61C2411yescharacteristic
147C4⋊C4×C61—21no—
148C4⋊C4×C61—41no—
149C4⋊C4×C61D811yescharacteristic
150C4⋊C4×C61D811yescharacteristic
151C4⋊C4×C61D811yescharacteristic
152C22⋊C4×C61—41no—
153C22⋊C4×C61—41no—
154C22⋊C4×C61—41no—
155C22⋊C4×C61—41no—
156C22⋊C4×C61—41no—
157C22⋊C4×C61—41no—
158C42×C61—41no—
159C42×C61C2×D411yescharacteristic
160C42×C61C2×D411yescharacteristic
161C42×C61C2×D411yescharacteristic
162#11758198—41no—
163#11758198—41no—
164#11758198—41no—
165#11758198—41no—
166#11758198—41no—
167#11758198—41no—
168C4⋊Dic61—21no—
169#11758196—41no—
170C4×Dic61—41no—
171Dic244—21no—
172Dic244—21no—
173D488—21no—
174D488—21no—
175D488—21no—
176D488—21no—
177D488—81no—
178#11758190—81no—
179#11758190—81no—
180#11758185—21no—
181#11758185—21no—
182#11758185—21no—
183#11758185#4112yes—
184C23×C61—41no—
185C23×C61—41no—
186C22×D61—41no—
187C22×D61—41no—
188Q8×C61—41no—
189Q8×C61—41no—
190Q8×C61—41no—
191D4×C61—41no—
192D4×C61—41no—
193D4×C61—41no—
194D4×C61—41no—
195D4×C61—82no—
196D4×C61—161no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—161no—
200C2×C4×C61—161no—
201C2×C4×C61C2×D811yescharacteristic
202C2×C4×C61C2×D811yescharacteristic
203C2×C4×C61C2×D811yescharacteristic
204C2×C4×C61C2×D811yescharacteristic
205C2×C4×C61C2×D811yescharacteristic
206C2×C4×C61C2×D811yescharacteristic
207C2×C4×C61C22×D411yescharacteristic
208C2×Dic61—41no—
209C2×Dic61—41no—
210D244—41no—
211D244—41no—
212D244—41no—
213D244—41no—
214D244—82no—
215D244—161no—
216C4×D61—161no—
217C4×D61—161no—
218Dic122—41no—
219Dic122—41no—
220C8×C61—21no—
221C8×C61—21no—
222C8×C61—21no—
223C8×C61C2×#4111yescharacteristic
224C8×C61H(5,𝔽2)11yescharacteristic
225#33970—611nomaximal, Sylow
226C22×C61—81no—
227C22×C61—81no—
228C22×C61—81no—
229C22×C61—81no—
230C22×C61—81no—
231C22×C61—81no—
232C22×C61C22×D811yescharacteristic
233C2×D61—81no—
234C2×D61—81no—
235C2×D61—81no—
236C2×D61—81no—
237C2×D61—81no—
238C2×D61—81no—
239C4×C61—21no—
240C4×C61—21no—
241C4×C61—21no—
242C4×C61—21no—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—81no—
246C4×C61—81no—
247C4×C61#55011yescharacteristic
248C4×C61#57611yescharacteristic
249Dic61—81no—
250Dic61—81no—
251#3396—611no—
252#3396D6111yescharacteristic, complemented
253#2250—611no—
254#2250—611no—
255#2249—611no—
256#2211—611no—
257#2211—611no—
258#2210—611no—
259#2210—611no—
260#2206—611no—
261#2206—611no—
262#2183—611no—
263#2175—611no—
264#2175—611no—
265C4×D16—611no—
266C2×C61—161no—
267C2×C61—161no—
268C2×C61#339111yescharacteristic
269C2×C61#341411yescharacteristic
270C2×C61#341511yescharacteristic
271D61—161no—
272D61—161no—
273#559—21no—
274#559—1221no—
275C2×Q32—611no—
276C2×SD32—611no—
277C2×SD32—611no—
278C2×SD32—611no—
279C2×SD32—611no—
280C2×D16—611no—
281C2×D16—611no—
282C2×D16—611no—
283C2×D16—611no—
284#495—611no—
285#495—611no—
286#495C2×D6111yescharacteristic
287#495C2×D6111yescharacteristic
288#493—611no—
289#493C2×D6111yescharacteristic
290#463—21no—
291#463—21no—
292#463—1221no—
293#463—1221no—
294#460—21no—
295#460—1221no—
296C8×Q8C2×D6111yescharacteristic
297C4×Q16—611no—
298C4×Q16C2×D6111yescharacteristic
299C4×D8—611no—
300C4×D8—611no—
301C4×D8C2×D6111yescharacteristic
302C4×D8C2×D6111yescharacteristic
303#366—611no—
304C4⋊C16—611no—
305C4⋊C16—611no—
306C4⋊C16—611no—
307#358—611no—
308#358—611no—
309#357—611no—
310#357—611no—
311#357—611no—
312#357—611no—
313#346—611no—
314#346—611no—
315C4×C16—611no—
316C61#3397011yescharacteristic, complemented, Sylow
317C2×Q16—611no—
318C2×Q16C22×D6111yescharacteristic
319C2×SD16—21no—
320C2×SD16—21no—
321C2×SD16—1221no—
322C2×SD16—1221no—
323C2×D8—21no—
324C2×D8—611no—
325C2×D8—611no—
326C2×D8—1221no—
327C2×D8C22×D6111yescharacteristic
328C2×D8C22×D6111yescharacteristic
329#127—21no—
330#127—1221no—
331#124—21no—
332#124—21no—
333#124—41no—
334#124—1221no—
335#124—1221no—
336#124—2441no—
337#123—41no—
338#123—41no—
339#123—2441no—
340#123—2441no—
341C4×Q8—21no—
342C4×Q8—1221no—
343C4×Q8C22⋊D6111yescharacteristic
344C4×D4—21no—
345C4×D4—21no—
346C4×D4—41no—
347C4×D4—1221no—
348C4×D4—1221no—
349C4×D4—2441no—
350Q32—2441no—
351SD32—1222no—
352SD32—1222no—
353SD32—2441no—
354SD32—2441no—
355D16—1222no—
356D16—2441no—
357D16—2441no—
358D16—2441no—
359C2×C16—611no—
360C2×C16—611no—
361C2×C16—611no—
362C2×C16—611no—
363#107—611no—
364#107C22×D6111yescharacteristic
365C4⋊C8C22⋊D6111yescharacteristic
366C4⋊C8C22⋊D6111yescharacteristic
367C4⋊C8C22⋊D6111yescharacteristic
368#103—21no—
369#103—1221no—
370#102—21no—
371#102—21no—
372#102—1221no—
373#102—1221no—
374C4×C8C22×D6111yescharacteristic
375C4×C8C22×D6111yescharacteristic
376C4×C8C22×D6111yescharacteristic
377C2×Q8—21no—
378C2×Q8—1221no—
379C2×Q8#1175819911yescharacteristic
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—1221no—
385C2×D4—1221no—
386C2×D4—2441no—
387C2×D4—2441no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—2441no—
391C22×C4—2441no—
392Q16—21no—
393Q16—21no—
394Q16—1221no—
395Q16—1221no—
396SD16—81no—
397SD16—81no—
398SD16—4881no—
399SD16—4881no—
400D8—21no—
401D8—21no—
402D8—21no—
403D8—21no—
404D8—81no—
405D8—1221no—
406D8—1221no—
407D8—1221no—
408D8—1221no—
409D8—4881no—
410C2×C8C2×C22⋊D6111yescharacteristic
411C2×C8C2×C22⋊D6111yescharacteristic
412C2×C8C2×C22⋊D6111yescharacteristic
413C2×C8C23×D6111yescharacteristic
414C4⋊C4—21no—
415C4⋊C4—41no—
416C4⋊C4—1221no—
417C4⋊C4—2441no—
418C4⋊C4#1175819911yescharacteristic
419C4⋊C4#1175819911yescharacteristic
420C4⋊C4#1175819911yescharacteristic
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—2441no—
428C22⋊C4—2441no—
429C22⋊C4—2441no—
430C22⋊C4—2441no—
431C22⋊C4—2441no—
432C22⋊C4—2441no—
433C42—41no—
434C42—2441no—
435C42C2×C22⋊D6111yescharacteristic
436C42C2×C22⋊D6111yescharacteristic
437C42C2×C22⋊D6111yescharacteristic
438C16—612no—
439C16—1221no—
440C16—1221no—
441C16—1221no—
442C23—41no—
443C23—41no—
444C23—2441no—
445C23—2441no—
446Q8—41no—
447Q8—41no—
448Q8—41no—
449Q8—2441no—
450Q8—2441no—
451D4—41no—
452D4—41no—
453D4—41no—
454D4—41no—
455D4—82no—
456D4—161no—
457D4—9761no—
458D4—4882no—
459D4—2441no—
460D4—2441no—
461D4—2441no—
462D4—2441no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—161no—
466C2×C4—161no—
467C2×C4—9761no—
468C2×C4—9761no—
469C2×C4—2441no—
470C2×C4—2441no—
471C2×C4C2×#1175819911yescharacteristic
472C2×C4C2×#1175819911yescharacteristic
473C2×C4C2×#1175819911yescharacteristic
474C2×C4C2×#1175819911yescharacteristic
475C2×C4C2×#1175819911yescharacteristic
476C2×C4C2×#1175819911yescharacteristic
477C2×C4C22×C22⋊D6111yescharacteristic
478C8—21no—
479C8—21no—
480C8—21no—
481C8#41×D6111yescharacteristic
482C8#1451982311yescharacteristic
483C22—81no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—4881no—
490C22—4881no—
491C22—4881no—
492C22—4881no—
493C22—4881no—
494C22—4881no—
495C22C22×#1175819911yescharacteristic
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—21no—
501C4—21no—
502C4—81no—
503C4—81no—
504C4—4881no—
505C4—4881no—
506C4#1684043111yescharacteristic
507C4#1684056511yescharacteristic
508C2—161no—
509C2—161no—
510C2—9761no—
511C2—9761no—
512C2#2145879111yescharacteristic
513C2#2145895311yescharacteristic
514C2#2145895811yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3396C2
socleC22×C61C22×D8
hypercenter#3396D61
hypocenterC61#33970
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3396

Complements

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

NH ≅ G/Ntype
1. #21458832C2semidirect
2. #21448086C2semidirect
3. #21448083C2semidirect
4. #21448078C2semidirect
5. #21447881C2semidirect
6. #21447878C2semidirect
7. #21447874C2semidirect
8. #21447871C2semidirect
9. #21447854C2semidirect
10. #21447851C2semidirect
11. #21447728C2semidirect
12. #21447683C2semidirect
13. #21447681C2semidirect
14. C4×#14519718C2semidirect
15. C61×#3396C2semidirect
252. #3396D61semidirect
316. C61#33970semidirect

Maximal subgroups

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

subgroupindex
#214588322
#214480862
#214480832
#214480782
#214478812
#214478782
#214478742
#214478712
#214478542
#214478512
#214477282
#214476832
#214476812
C4×#145197182
C61×#33962
#3397061