Finite Group Databasebeta

← #29730734

Subgroups — #29730734

Order 15616.

1238 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839997C212yesmaximal, complemented
2C2×#16839957C211yesmaximal, characteristic, complemented
3C2×C8×D244C211yesmaximal, characteristic, complemented
4#21450761C211yesmaximal, characteristic, complemented
5#21450732C211yesmaximal, characteristic, complemented
6#21447004C212yesmaximal, complemented
7#21446816C212yesmaximal, complemented
8#21446625C211yesmaximal, characteristic, complemented
9#21446577C211yesmaximal, characteristic, complemented
10#21446246C212yesmaximal, complemented
11C4×#102×C61C211yesmaximal, characteristic, complemented
12C22×#11758199C2212yes—
13C22×C8×D61C2212yes—
14C2×#14519774—21no—
15C2×#14519774C2211yescharacteristic
16C2×#14519752C2212yes—
17C2×#14519752C2212yes—
18C2×#14519751—21no—
19C2×#14519748C2212yes—
20C2×C4×D244C2211yescharacteristic
21#16839997—28no—
22#16839957—24no—
23C8×D244—24no—
24C2×#14519710C2212yes—
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519699C2212yes—
27C2×#14519699C2212yes—
28C2×#14519697C2212yes—
29C2×#14519689C2212yes—
30#16839678—22no—
31#16839672—22no—
32#16839664—21no—
33#16839632C2211yescharacteristic
34#16839622—21no—
35#16839619C2212yes—
36#16839524C2212yes—
37C2×C4×D4×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×C4×C8×C61C2211yescharacteristic
41C4×C4⋊C4×C61C2211yescharacteristic
42C61×#340C2211yescharacteristic
43C61×#340C2211yescharacteristic
44C22×D244—21no—
45C22×D244—22no—
46C22×D244—22no—
47C22×D244—21no—
48C22×D244D411yescharacteristic
49C22×D244C2312yes—
50C22×C22⋊D61—22no—
51C22×C4×D61C2312yes—
52C2×#11758199—24no—
53C2×#11758199—24no—
54C2×#11758199—42no—
55C22×#92418C2312yes—
56C2×C8×D61—24no—
57C2×C8×D61—24no—
58C2×C8×D61—42no—
59#14519774—22no—
60#14519774—22no—
61#14519774—44no—
62#14519752—24no—
63#14519752—24no—
64#14519752—42no—
65#14519752—42no—
66#14519751—44no—
67#14519748—24no—
68#14519748—42no—
69C4×D244—22no—
70C4×D244—22no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61D411yescharacteristic
74C2×C4⋊Dic61C2312yes—
75C2×C22⋊Dic61—22no—
76C2×#11758198—22no—
77C2×#11758198—22no—
78C2×#11758198—22no—
79C2×#11758198D412yes—
80#14519710—24no—
81C4⋊#92418D414yescomplemented
82#14519699—24no—
83#14519699—42no—
84#14519697—24no—
85#14519689—24no—
86#14519684—22no—
87C22×D4×C61C2311yescharacteristic
88C23×C4×C61—21no—
89C22×C8×C61C2311yescharacteristic
90C22×C8×C61C2311yescharacteristic
91C4×D4×C61—22no—
92C4×D4×C61—22no—
93C2×C4⋊C4×C61C2311yescharacteristic
94C2×C4⋊C4×C61C2311yescharacteristic
95C2×C4⋊C4×C61C2311yescharacteristic
96C2×C22⋊C4×C61—21no—
97C2×C42×C61—21no—
98C2×C42×C61C2311yescharacteristic
99#102×C61—22no—
100#102×C61D414yescomplemented
101C4×C8×C61—22no—
102#95×C61—21no—
103C24×C61—21no—
104C23×D61—22no—
105C23×D61C2×D412yes—
106C2×D4×C61—21no—
107C2×D4×C61—21no—
108C2×D4×C61—21no—
109C2×D4×C61—21no—
110C2×D4×C61—21no—
111C2×D4×C61C2×D412yes—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
115C22×C4×C61—42no—
116C22×C4×C61—42no—
117C22×C4×C61—42no—
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2411yescharacteristic
121C2×C22⋊D61—44no—
122C2×C22⋊D61—44no—
123C2×C22⋊D61—82no—
124C22×Dic61—22no—
125C22×Dic61C2×D412yes—
126C2×D244—22no—
127C2×D244—22no—
128C2×D244—22no—
129C2×D244—22no—
130C2×D244—22no—
131C2×D244—22no—
132C2×D244—22no—
133C2×D244—22no—
134C2×D244—44no—
135C2×D244—44no—
136C2×D244—44no—
137C2×D244—44no—
138C2×D244—42no—
139C2×D244—42no—
140C2×D244—42no—
141C2×D244—42no—
142C2×D244—81no—
143C2×D244—81no—
144C2×D244—82no—
145C2×D244—82no—
146C2×D244D814yescomplemented
147C2×C4×D61—22no—
148C2×C4×D61—22no—
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61C2×D412yes—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61C2×D412yes—
164C4⋊C4×C61#4112yes—
165C22⋊C4×C61—42no—
166C42×C61—42no—
167C42×C61C2×D412yes—
168C42×C61#4112yes—
169C22⋊Dic61—44no—
170#11758199—48no—
171#11758198—24no—
172#11758198—44no—
173#11758198—44no—
174#11758198—44no—
175C4⋊Dic61—22no—
176C4⋊Dic61—22no—
177C4⋊Dic61—22no—
178C4⋊Dic61—42no—
179C4⋊Dic61—81no—
180C2×#92418—22no—
181C2×#92418—22no—
182C2×#92418C2×D414yes—
183C8×D61—48no—
184C23×C61—22no—
185C23×C61—41no—
186C23×C61—41no—
187C23×C61—41no—
188C23×C61—41no—
189C23×C61—41no—
190C23×C61—41no—
191C23×C61C22×D411yescharacteristic
192C22×D61—22no—
193C22×D61—22no—
194C22×D61—22no—
195C22×D61—22no—
196C22×D61—22no—
197C22×D61—22no—
198C22×D61—42no—
199C22×D61—42no—
200C22×D61—42no—
201C22×D61—42no—
202C22×D61—42no—
203C22×D61—42no—
204C22×D61—42no—
205C22×D61C2×D814yes—
206D4×C61—22no—
207D4×C61—22no—
208D4×C61—41no—
209D4×C61—41no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
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×C61—84no—
222C2×C4×C61#12112yes—
223C2×C4×C61#12112yes—
224C2×C4×C61C2×D812yes—
225C2×C4×C61#13512yes—
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C2×#4111yescharacteristic
229C2×C4×C61C2×#4111yescharacteristic
230C2×C4×C61H(5,𝔽2)11yescharacteristic
231C2×C4×C61H(5,𝔽2)11yescharacteristic
232C22⋊D61—88no—
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—42no—
237C2×Dic61—42no—
238C2×Dic61—42no—
239D244—28no—
240D244—42no—
241D244—42no—
242D244—42no—
243D244—42no—
244D244—84no—
245D244—88no—
246D244—88no—
247D244—84no—
248C4×D61—42no—
249C4×D61—42no—
250C4×D61—42no—
251C4×D61—42no—
252C8×C61—22no—
253C8×C61—41no—
254#92418—24no—
255#25384—611nomaximal, Sylow
256C22×C61—42no—
257C22×C61—42no—
258C22×C61—42no—
259C22×C61—81no—
260C22×C61—81no—
261C22×C61—81no—
262C22×C61—81no—
263C22×C61C2×#12111yescharacteristic
264C22×C61D4211yescharacteristic
265C22×C61#54611yescharacteristic
266C22×C61C22×D811yescharacteristic
267C22×C61C2×#13511yescharacteristic
268C22×C61#57611yescharacteristic
269C22×C61#57711yescharacteristic
270C2×D61—24no—
271C2×D61—24no—
272C2×D61—24no—
273C2×D61—42no—
274C2×D61—42no—
275C2×D61—42no—
276C2×D61—42no—
277C2×D61—82no—
278C2×D61—82no—
279C2×D61—82no—
280C2×D61—82no—
281C2×D61—82no—
282C2×D61—82no—
283C2×D61—82no—
284C4×C61—22no—
285C4×C61—42no—
286C4×C61—42no—
287C4×C61—81no—
288C4×C61#46614yescomplemented
289C4×C61#53211yescharacteristic
290C4×C61#54011yescharacteristic
291C4×C61D4211yescharacteristic
292C4×C61#55011yescharacteristic
293Dic61—42no—
294Dic61—82no—
295C2×#466—612no—
296C2×#459—611no—
297C2×C8×D4—611no—
298#2541—611no—
299#2537—611no—
300#2033—612no—
301#1999—612no—
302#1957—611no—
303#1947—611no—
304#1893—612no—
305C4×#102D6111yescharacteristic, complemented
306C2×C61—82no—
307C2×C61#242811yescharacteristic
308C2×C61C2×#46611yescharacteristic
309C2×C61#306211yescharacteristic
310C2×C61D4×D811yescharacteristic
311C2×C61#328411yescharacteristic
312C2×C61#329411yescharacteristic
313C2×C61#330511yescharacteristic
314D61—44no—
315D61—162no—
316C22×D8—612no—
317C23×C8—612no—
318C2×#127—611no—
319C2×#127—1221no—
320C2×#121—612no—
321C2×#121—612no—
322C2×#121—612no—
323C2×#121—1221no—
324C2×C4×D4—611no—
325C2×C4×D4C2×D6111yescharacteristic
326#466—1228no—
327#459—1224no—
328C8×D4—1224no—
329C2×#107—612no—
330C2×C4⋊C8—611no—
331C2×#102—612no—
332C2×#102—612no—
333C2×#102—612no—
334C2×#102C2×D6111yescharacteristic
335C2×#102C2×D6111yescharacteristic
336C2×C22⋊C8—612no—
337C2×C4×C8C2×D6111yescharacteristic
338#394—1222no—
339#392—1222no—
340#390—1221no—
341#384—611no—
342#380—612no—
343#380—1221no—
344C4×C4⋊C4C2×D6111yescharacteristic
345#340—612no—
346#340C2×D6111yescharacteristic
347#340C2×D6111yescharacteristic
348C61#2538411yescharacteristic, complemented, Sylow
349C22×D4—611no—
350C22×D4—612no—
351C22×D4—1222no—
352C22×D4—1222no—
353C22×D4—1222no—
354C22×D4—1221no—
355C22×D4—1221no—
356C22×D4C22×D6111yescharacteristic
357C23×C4—21no—
358C23×C4—612no—
359C2×D8—1224no—
360C2×D8—1224no—
361C2×D8—2442no—
362C22×C8—612no—
363C22×C8—1224no—
364C22×C8—1224no—
365C22×C8—2442no—
366C22×C8C22×D6111yescharacteristic
367C22×C8C22×D6111yescharacteristic
368#127—1222no—
369#127—1222no—
370#127—2444no—
371#121—1224no—
372#121—1224no—
373#121—1224no—
374#121—2442no—
375#121—2442no—
376#121—2442no—
377#121—2444no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—1222no—
381C4×D4—1222no—
382C2×C4⋊C4—611no—
383C2×C4⋊C4—612no—
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—612no—
391C2×C22⋊C4—1222no—
392C2×C22⋊C4—1222no—
393C2×C22⋊C4—1222no—
394C2×C22⋊C4—1222no—
395C2×C42—21no—
396C2×C42C22×D6111yescharacteristic
397#107—1224no—
398C4⋊C8—614no—
399#102—22no—
400#102—1224no—
401#102—1224no—
402#102—2442no—
403#102D24414yescomplemented
404C22⋊C8—1224no—
405C4×C8—22no—
406#95—21no—
407#95—1222no—
408C24—21no—
409C24—612no—
410C24—1222no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—614no—
417C2×D4—1222no—
418C2×D4—1222no—
419C2×D4—1222no—
420C2×D4—1222no—
421C2×D4—1222no—
422C2×D4—1222no—
423C2×D4—1222no—
424C2×D4—1222no—
425C2×D4—4881no—
426C2×D4—4881no—
427C2×D4—4882no—
428C2×D4—4882no—
429C2×D4—4882no—
430C2×D4—2444no—
431C2×D4—2444no—
432C2×D4—2444no—
433C2×D4—2444no—
434C2×D4—2444no—
435C2×D4—2444no—
436C2×D4—2442no—
437C2×D4—2442no—
438C2×D4—2442no—
439C2×D4—2442no—
440C2×D4C2×D24412yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—612no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—1222no—
452C22×C4—1222no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4D4×D6111yescharacteristic
456C22×C4D4×D6111yescharacteristic
457C22×C4C23×D6111yescharacteristic
458D8—2448no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—614no—
465C2×C8—1222no—
466C2×C8—1222no—
467C2×C8—2448no—
468C2×C8C2×D24412yes—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—1222no—
474C4⋊C4—1222no—
475C4⋊C4—1222no—
476C4⋊C4—4881no—
477C4⋊C4—2442no—
478C4⋊C4C2×D24412yes—
479C4⋊C4#1175822212yes—
480C22⋊C4—42no—
481C22⋊C4—1224no—
482C22⋊C4—2444no—
483C22⋊C4—2444no—
484C22⋊C4—2444no—
485C22⋊C4—2444no—
486C42—42no—
487C42#1175822212yes—
488C42D4×D6112yes—
489C23—22no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—614no—
497C23—1222no—
498C23—1222no—
499C23—1222no—
500C23—1222no—
501C23—1222no—
502C23—1222no—
503C23—2442no—
504C23—2442no—
505C23—2442no—
506C23—2442no—
507C23—2442no—
508C23—2442no—
509C23—2442no—
510C23C2×D4×D6111yescharacteristic
511D4—22no—
512D4—22no—
513D4—41no—
514D4—41no—
515D4—1228no—
516D4—4884no—
517D4—4888no—
518D4—4888no—
519D4—4888no—
520D4—4884no—
521D4—2442no—
522D4—2442no—
523D4—2442no—
524D4—2442no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—84no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—2442no—
541C2×C4—2442no—
542C2×C4—2442no—
543C2×C4—2442no—
544C2×C4—2442no—
545C2×C4—2442no—
546C2×C4—2442no—
547C2×C4#1451975012yes—
548C2×C4#1451975012yes—
549C2×C4D8×D6112yes—
550C2×C4#1451979812yes—
551C2×C4C2×D4×D6111yescharacteristic
552C2×C4C22×D24411yescharacteristic
553C2×C4C2×#1175822211yescharacteristic
554C2×C4C2×#1175822211yescharacteristic
555C2×C4#1451982311yescharacteristic
556C2×C4#1451982311yescharacteristic
557C8—22no—
558C8—41no—
559C8—1224no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—1224no—
568C22—1224no—
569C22—1224no—
570C22—4882no—
571C22—4882no—
572C22—4882no—
573C22—4882no—
574C22—4882no—
575C22—4882no—
576C22—4882no—
577C22—2442no—
578C22—2442no—
579C22—2442no—
580C22—2442no—
581C22C2×#1451975011yescharacteristic
582C22D4×D24411yescharacteristic
583C22#1684040811yescharacteristic
584C22C2×D8×D6111yescharacteristic
585C22C2×#1451979811yescharacteristic
586C22#1684056411yescharacteristic
587C22#1684056911yescharacteristic
588C4—22no—
589C4—42no—
590C4—42no—
591C4—81no—
592C4—4882no—
593C4—2442no—
594C4#1683999714yescomplemented
595C4#1684031211yescharacteristic
596C4#1684036711yescharacteristic
597C4D4×D24411yescharacteristic
598C4#1684043311yescharacteristic
599C2—82no—
600C2—9762no—
601C2—2444no—
602C2#2144940711yescharacteristic
603C2C2×#1683999711yescharacteristic
604C2#2145550211yescharacteristic
605C2D8×D24411yescharacteristic
606C2#2145755011yescharacteristic
607C2#2145763411yescharacteristic
608C2#2145777111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC4×#102×C61C2
socleC23×C61C22×D4
hypercenterC4×#102D61
hypocenterC61#25384
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. C2×#16839997C2semidirect
2. C2×#16839957C2semidirect
3. C2×C8×D244C2semidirect
4. #21450761C2semidirect
5. #21450732C2semidirect
6. #21447004C2semidirect
7. #21446816C2semidirect
8. #21446625C2semidirect
9. #21446577C2semidirect
10. #21446246C2semidirect
11. C4×#102×C61C2semidirect
81. C4⋊#92418D4semidirect
100. #102×C61D4semidirect
146. C2×D244D8semidirect
288. C4×C61#466semidirect
305. C4×#102D61semidirect
348. C61#25384semidirect
403. #102D244semidirect
594. C4#16839997semidirect

Maximal subgroups

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

subgroupindex
C2×#168399972
C2×#168399572
C2×C8×D2442
#214507612
#214507322
#214470042
#214468162
#214466252
#214465772
#214462462
C4×#102×C612
#2538461