Finite Group Databasebeta

← #29718348

Subgroups — #29718348

Order 15616.

1260 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840075C211yesmaximal, characteristic, complemented
2C22×#14519697C211yesmaximal, characteristic, complemented
3#21449456C211yesmaximal, characteristic
4#21447204C212yesmaximal, complemented
5#21447053C212yesmaximal, complemented
6#21446746C212yesmaximal, complemented
7#21446439C212yesmaximal, complemented
8#21446245C211yesmaximal, characteristic, complemented
9#21445999C211yesmaximal, characteristic, complemented
10#21445749C211yesmaximal, characteristic, complemented
11C61×#2344C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C23×#92418C2211yescharacteristic
14C2×#14519774C2212yes—
15C2×#14519751C2211yescharacteristic
16C2×#14519747—21no—
17C2×#14519747—21no—
18#16840075—24no—
19C2×#14519710C2211yescharacteristic, complemented
20C2×#14519710C2211yescharacteristic, complemented
21C2×C4⋊#92418C2212yescomplemented
22C2×#14519697—24no—
23C2×#14519697C2212yes—
24C2×#14519697C2212yes—
25C2×#14519697C2212yes—
26C2×#14519697C2212yes—
27C2×#14519697C2211yescharacteristic, complemented
28C2×#14519697C2211yescharacteristic, complemented
29C2×#14519697C2212yescomplemented
30C2×C22⋊#92418C2211yescharacteristic
31#16839672—22no—
32#16839664C2212yes—
33#16839524C2212yescomplemented
34#16839517C2212yescomplemented
35C2×#117×C61—21no—
36C22×C4⋊C4×C61C2211yescharacteristic
37C61×#389C2212yescomplemented
38C61×#387—22no—
39C61×#381—21no—
40C61×#380C2211yescharacteristic
41C4×C4⋊C4×C61C2212yescomplemented
42C4×C22⋊C4×C61C2211yescharacteristic
43C24×D61—21no—
44C22×D244—22no—
45C22×D244—24no—
46C22×D244—22no—
47C22×D244—21no—
48C22×D244—22no—
49C22×D244—22no—
50C22×D244—42no—
51C22×D244C2311yescharacteristic
52C22×D244C2312yes—
53C22×C22⋊D61—21no—
54C22×#92418—22no—
55C22×#92418—42no—
56C22×#92418C2311yescharacteristic
57C22×#92418C2311yescharacteristic
58C22×#92418C2312yes—
59#14519774—24no—
60#14519774—42no—
61#14519751—22no—
62#14519751—22no—
63#14519747—44no—
64#14519747—44no—
65C2×C4⋊Dic61C2311yescharacteristic
66C2×#11758198—22no—
67C2×#11758198—22no—
68C2×#11758198—21no—
69#14519710—22no—
70#14519710—22no—
71C4⋊#92418—42no—
72#14519697—24no—
73#14519697—24no—
74#14519697—24no—
75#14519697—22no—
76#14519697—22no—
77#14519697—42no—
78#14519697—42no—
79C22⋊#92418—22no—
80C23×C4×C61—21no—
81C23×C4×C61C2311yescharacteristic
82#117×C61—44no—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—22no—
85C2×C4⋊C4×C61—22no—
86C2×C4⋊C4×C61D414yescomplemented
87C2×C4⋊C4×C61C2312yes—
88C2×C4⋊C4×C61C2311yescharacteristic
89C2×C4⋊C4×C61C2311yescharacteristic
90C2×C22⋊C4×C61—21no—
91C2×C22⋊C4×C61D411yescharacteristic
92C2×C22⋊C4×C61D411yescharacteristic
93C2×C42×C61—22no—
94C2×C42×C61C2312yes—
95#95×C61—22no—
96#95×C61—21no—
97#95×C61—22no—
98#95×C61D412yes—
99C24×C61C2×D411yescharacteristic
100C23×D61—22no—
101C23×D61—21no—
102C23×D61—44no—
103C23×D61—42no—
104C23×D61—42no—
105C23×D61—42no—
106C23×D61—82no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—24no—
110C22×C4×C61—21no—
111C22×C4×C61—21no—
112C22×C4×C61—22no—
113C22×C4×C61—42no—
114C22×C4×C61—42no—
115C22×C4×C61C2×D412yes—
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D412yes—
118C22×C4×C61C2×D412yes—
119C22×C4×C61#4112yes—
120C22×C4×C61C2411yescharacteristic
121C2×C22⋊D61—42no—
122C2×C22⋊D61—42no—
123C2×C22⋊D61—42no—
124C22×Dic61—21no—
125C2×D244—28no—
126C2×D244—22no—
127C2×D244—22no—
128C2×D244—22no—
129C2×D244—22no—
130C2×D244—21no—
131C2×D244—21no—
132C2×D244—22no—
133C2×D244—22no—
134C2×D244—22no—
135C2×D244—48no—
136C2×D244—44no—
137C2×D244—44no—
138C2×D244—42no—
139C2×D244—44no—
140C2×D244—44no—
141C2×D244—44no—
142C2×D244—44no—
143C2×D244—82no—
144C2×D244—82no—
145C2×D244#4114yes—
146C4⋊C4×C61—24no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—22no—
150C4⋊C4×C61—22no—
151C4⋊C4×C61—44no—
152C4⋊C4×C61C2×D412yes—
153C4⋊C4×C61C2×D412yes—
154C22⋊C4×C61—22no—
155C22⋊C4×C61—42no—
156C22⋊C4×C61D814yes—
157C42×C61—22no—
158C42×C61—22no—
159C42×C61—44no—
160#11758198—44no—
161#11758198—42no—
162#11758198—44no—
163C4⋊Dic61—21no—
164C4⋊Dic61—21no—
165C2×#92418—21no—
166C2×#92418—21no—
167C2×#92418—22no—
168C2×#92418—22no—
169C2×#92418—22no—
170C2×#92418—22no—
171C2×#92418—22no—
172C2×#92418—44no—
173C23×C61—22no—
174C23×C61—22no—
175C23×C61#12112yes—
176C23×C61C2×D812yes—
177C23×C61AGL(1,ℤ/8)12yes—
178C23×C61C22×D411yescharacteristic
179C22×D61—24no—
180C22×D61—48no—
181C22×D61—42no—
182C22×D61—42no—
183C22×D61—42no—
184C22×D61—42no—
185C22×D61—42no—
186C22×D61—42no—
187C22×D61—41no—
188C22×D61—42no—
189C22×D61—41no—
190C22×D61—41no—
191C22×D61—42no—
192C22×D61—88no—
193C22×D61—88no—
194C22×D61—84no—
195C22×D61—84no—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—22no—
201C2×C4×C61—24no—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—41no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—48no—
212C2×C4×C61—42no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61#12112yes—
216C2×C4×C61C2×D814yes—
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C2×#4112yes—
219C2×C4×C61C2×#4111yescharacteristic
220C2×C4×C61H(5,𝔽2)12yes—
221C22⋊D61—84no—
222C2×Dic61—41no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225D244—24no—
226D244—24no—
227D244—48no—
228D244—41no—
229D244—42no—
230D244—41no—
231D244—42no—
232D244—42no—
233D244—88no—
234D244—88no—
235#92418—41no—
236#92418—41no—
237#92418—42no—
238#24476—611nomaximal, Sylow
239C22×C61—22no—
240C22×C61—24no—
241C22×C61—22no—
242C22×C61—24no—
243C22×C61#45914yes—
244C22×C61C2×#12111yescharacteristic
245C22×C61#54612yes—
246C22×C61C22×D811yescharacteristic
247C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
248C22×C61#57712yes—
249C2×D61—44no—
250C2×D61—44no—
251C2×D61—44no—
252C2×D61—816no—
253C2×D61—82no—
254C2×D61—82no—
255C2×D61—82no—
256C2×D61—82no—
257C2×D61—81no—
258C2×D61—81no—
259C2×D61—82no—
260C2×D61—81no—
261C2×D61—82no—
262C4×C61—22no—
263C4×C61—24no—
264C4×C61—42no—
265C4×C61—42no—
266C4×C61—42no—
267C4×C61—82no—
268C4×C61#52511yescharacteristic
269C4×C61#53511yescharacteristic
270C4×C61#55112yes—
271Dic61—81no—
272C2×#480—611no—
273C22×#102—611no—
274#2433—611no—
275#2344D6111yescharacteristic, complemented
276#2067—612no—
277#2041—612no—
278#1982—612no—
279#1925—612no—
280#1893—611no—
281#1850—611no—
282#1786—611no—
283C2×C61—24no—
284C2×C61#241111yescharacteristic
285C2×C61C2×#45911yescharacteristic
286C2×C61#304311yescharacteristic
287C2×C61#329412yes—
288C2×C61#331012yes—
289D61—84no—
290D61—161no—
291C23×D4—611no—
292C23×C8—611no—
293C2×#127—612no—
294C2×#121—611no—
295C2×#120—1221no—
296C2×#120—1221no—
297C2×#117—21no—
298C22×C4⋊C4C2×D6111yescharacteristic
299#480—1224no—
300C2×#107—611no—
301C2×#107—611no—
302C2×C4⋊C8—612no—
303C2×#102—611no—
304C2×#102—611no—
305C2×#102—612no—
306C2×#102—612no—
307C2×#102—612no—
308C2×#102—612no—
309C2×#102—612no—
310C2×#102—1224no—
311C2×C22⋊C8—611no—
312#392—1222no—
313#390—612no—
314#389C2×D6112yescomplemented
315#387—22no—
316#381—21no—
317#380C2×D6111yescharacteristic
318C4×C4⋊C4C2×D6112yescomplemented
319C4×C22⋊C4C2×D6111yescharacteristic
320#340—612no—
321#336—612no—
322C61#2447611yescharacteristic, complemented, Sylow
323C25—1221no—
324C22×D4—612no—
325C22×D4—611no—
326C22×D4—1224no—
327C22×D4—1221no—
328C22×D4—1222no—
329C22×D4—1222no—
330C22×D4—1222no—
331C22×D4—1222no—
332C22×D4—1221no—
333C22×D4—2442no—
334C23×C4—21no—
335C23×C4C22×D6111yescharacteristic
336C22×C8—612no—
337C22×C8—611no—
338C22×C8—611no—
339C22×C8—1222no—
340C22×C8—2442no—
341#127—1224no—
342#127—2442no—
343#121—1222no—
344#121—1222no—
345#120—2444no—
346#120—2444no—
347#117—44no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—611no—
352C2×C4⋊C4D24414yescomplemented
353C2×C4⋊C4C22×D6112yes—
354C2×C4⋊C4C22×D6111yescharacteristic
355C2×C4⋊C4C22×D6111yescharacteristic
356C2×C22⋊C4—21no—
357C2×C22⋊C4—1222no—
358C2×C22⋊C4—1222no—
359C2×C22⋊C4—1221no—
360C2×C22⋊C4C22⋊D6111yescharacteristic
361C2×C22⋊C4C22⋊D6111yescharacteristic
362C2×C42—22no—
363C2×C42C22×D6112yes—
364#107—1222no—
365#107—1222no—
366C4⋊C8—2442no—
367#102—1224no—
368#102—1224no—
369#102—1224no—
370#102—1222no—
371#102—1222no—
372#102—2442no—
373#102—2442no—
374C22⋊C8—1222no—
375#95—22no—
376#95—21no—
377#95—22no—
378#95C22⋊D6112yes—
379C24—1222no—
380C24—1221no—
381C24—4882no—
382C24—2444no—
383C24—2442no—
384C24—2442no—
385C24—2442no—
386C24C2×C22⋊D6111yescharacteristic
387C2×D4—614no—
388C2×D4—1228no—
389C2×D4—1222no—
390C2×D4—1221no—
391C2×D4—1222no—
392C2×D4—1222no—
393C2×D4—1222no—
394C2×D4—1221no—
395C2×D4—1222no—
396C2×D4—1222no—
397C2×D4—1222no—
398C2×D4—4882no—
399C2×D4—4882no—
400C2×D4—2448no—
401C2×D4—2444no—
402C2×D4—2444no—
403C2×D4—2444no—
404C2×D4—2444no—
405C2×D4—2444no—
406C2×D4—2442no—
407C2×D4—2442no—
408C2×D4—2442no—
409C2×D4—2442no—
410C2×D4—2444no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—1221no—
420C22×C4C2×D24412yes—
421C22×C4#1175822212yes—
422C22×C4C2×C22⋊D6112yes—
423C22×C4C2×C22⋊D6111yescharacteristic
424C22×C4C2×C22⋊D6112yes—
425C22×C4C23×D6111yescharacteristic
426C2×C8—1221no—
427C2×C8—1221no—
428C2×C8—1222no—
429C2×C8—1222no—
430C2×C8—1222no—
431C2×C8—1222no—
432C2×C8—1222no—
433C2×C8—2444no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—24no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—44no—
440C4⋊C4—1221no—
441C4⋊C4—1221no—
442C4⋊C4C2×D24412yes—
443C4⋊C4C2×D24412yes—
444C22⋊C4—22no—
445C22⋊C4—42no—
446C22⋊C4—2444no—
447C22⋊C4—2442no—
448C22⋊C4—2444no—
449C22⋊C4#1175819914yes—
450C42—22no—
451C42—22no—
452C42—44no—
453C23—22no—
454C23—22no—
455C23—1224no—
456C23—4884no—
457C23—4888no—
458C23—4888no—
459C23—4884no—
460C23—2448no—
461C23—2441no—
462C23—2441no—
463C23—2441no—
464C23—2442no—
465C23—2442no—
466C23—2442no—
467C23—2442no—
468C23—2442no—
469C23—2442no—
470C23—2442no—
471C23—2442no—
472C23#1451975112yes—
473C23C2×#1175819912yes—
474C23#1451980212yes—
475C23C22×C22⋊D6111yescharacteristic
476D4—1224no—
477D4—1224no—
478D4—4888no—
479D4—4888no—
480D4—4884no—
481D4—2448no—
482D4—2441no—
483D4—2441no—
484D4—2442no—
485D4—2442no—
486D4—2442no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—48no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—2441no—
507C2×C4—2441no—
508C2×C4—2441no—
509C2×C4#1451975112yes—
510C2×C4C2×#1175819914yes—
511C2×C4C22×D24411yescharacteristic
512C2×C4#41×D6112yes—
513C2×C4C2×#1175822211yescharacteristic
514C2×C4#1451982312yes—
515C8—2441no—
516C8—2441no—
517C8—2442no—
518C22—24no—
519C22—24no—
520C22—22no—
521C22—22no—
522C22—48816no—
523C22—4881no—
524C22—4882no—
525C22—4882no—
526C22—4881no—
527C22—4881no—
528C22—4882no—
529C22—4882no—
530C22—4882no—
531C22—4882no—
532C22—2444no—
533C22—2444no—
534C22—2444no—
535C22#1683995714yes—
536C22C2×#1451975111yescharacteristic
537C22#1684040012yes—
538C22C22×#1175819911yescharacteristic
539C22C2×#1451980211yescharacteristic
540C22#1684057012yes—
541C4—24no—
542C4—22no—
543C4—42no—
544C4—42no—
545C4—42no—
546C4—82no—
547C4—4881no—
548C4#1684027411yescharacteristic
549C4#1684033111yescharacteristic
550C4#1684043612yes—
551C2—24no—
552C2—9761no—
553C2—4884no—
554C2#2144919811yescharacteristic
555C2C2×#1683995711yescharacteristic
556C2#2145534011yescharacteristic
557C2#2145762612yes—
558C2#2145783412yes—
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2344C2
socleC23×C61C22×D4
prime radical#21449456C2
hypercenter#2344D61
hypocenterC61#24476
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2344

Complements

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

NH ≅ G/Ntype
1. C2×#16840075C2semidirect
2. C22×#14519697C2semidirect
4. #21447204C2semidirect
5. #21447053C2semidirect
6. #21446746C2semidirect
7. #21446439C2semidirect
8. #21446245C2semidirect
9. #21445999C2semidirect
10. #21445749C2semidirect
11. C61×#2344C2semidirect
19. C2×#14519710C22semidirect
20. C2×#14519710C22semidirect
21. C2×C4⋊#92418C22semidirect
27. C2×#14519697C22semidirect
28. C2×#14519697C22semidirect
29. C2×#14519697C22semidirect
33. #16839524C22semidirect
34. #16839517C22semidirect
37. C61×#389C22semidirect
41. C4×C4⋊C4×C61C22semidirect
86. C2×C4⋊C4×C61D4semidirect
275. #2344D61semidirect
314. #389C2×D61semidirect
318. C4×C4⋊C4C2×D61semidirect
322. C61#24476semidirect
352. C2×C4⋊C4D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168400752
C22×#145196972
#214494562
#214472042
#214470532
#214467462
#214464392
#214462452
#214459992
#214457492
C61×#23442
#2447661