Finite Group Databasebeta

← #29730737

Subgroups — #29730737

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×#16839996C212yesmaximal, complemented
2C2×#16839954C211yesmaximal, characteristic, complemented
3C2×D4×#92418C211yesmaximal, characteristic, complemented
4#21450732C211yesmaximal, characteristic, complemented
5#21446998C212yesmaximal, complemented
6#21446815C212yesmaximal, complemented
7#21446626C211yesmaximal, characteristic, complemented
8#21446577C211yesmaximal, characteristic, complemented
9#21446248C212yesmaximal, complemented
10C4×#14519697C211yesmaximal, characteristic, complemented
11C61×#2541C211yesmaximal, characteristic, complemented
12C22×#11758199C2212yes—
13C23×#92418C2212yes—
14C2×#14519751C2212yes—
15C2×#14519748—21no—
16C2×C4×D244C2211yescharacteristic
17#16839996—28no—
18#16839954—24no—
19D4×#92418—24no—
20C2×#14519710C2212yes—
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519698C2212yes—
23C2×#14519698C2212yes—
24C2×#14519698C2212yes—
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×C22⋊#92418C2212yes—
28C2×C4×#92418C2211yescharacteristic
29#16839678—22no—
30#16839632C2211yescharacteristic
31#16839622C2212yes—
32#16839619—21no—
33#16839524C2211yescharacteristic
34#16839524C2211yescharacteristic
35#16839524C2212yes—
36C2×#127×C61—21no—
37C2×#127×C61C2211yescharacteristic
38C2×#121×C61C2212yes—
39C2×#121×C61C2212yes—
40C2×C4×D4×C61C2211yescharacteristic
41C61×#392—22no—
42C61×#390—21no—
43C4×C4⋊C4×C61C2211yescharacteristic
44C22×D244C2311yescharacteristic
45C22×C22⋊D61—22no—
46C22×C4×D61—21no—
47C2×#11758199—24no—
48C2×#11758199—24no—
49C2×#11758199—42no—
50C22×#92418—24no—
51C22×#92418—24no—
52C22×#92418—42no—
53C22×#92418C2311yescharacteristic
54C22×#92418C2311yescharacteristic
55C22×#92418C2312yes—
56#14519751—24no—
57#14519751—42no—
58#14519748—44no—
59C4×D244—22no—
60C4×D244—22no—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61C2311yescharacteristic
64C2×C4⋊Dic61C2312yes—
65C2×C22⋊Dic61—22no—
66C2×#11758198—21no—
67C2×#11758198—22no—
68#14519710—24no—
69C4⋊#92418D414yescomplemented
70#14519698—24no—
71#14519698—24no—
72#14519698—42no—
73#14519697—22no—
74#14519697D414yescomplemented
75C22⋊#92418—24no—
76C4×#92418—22no—
77#14519684—22no—
78C22×D4×C61—22no—
79C22×D4×C61—22no—
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61D411yescharacteristic
83C22×D4×C61C2312yes—
84C23×C4×C61C2312yes—
85#127×C61—22no—
86#127×C61—22no—
87#127×C61—44no—
88#121×C61—24no—
89#121×C61—24no—
90#121×C61—42no—
91#121×C61—42no—
92C4×D4×C61—22no—
93C4×D4×C61—22no—
94C2×C4⋊C4×C61D411yescharacteristic
95C2×C4⋊C4×C61C2311yescharacteristic
96C2×C4⋊C4×C61C2311yescharacteristic
97C2×C22⋊C4×C61—22no—
98C2×C22⋊C4×C61—22no—
99C2×C22⋊C4×C61D412yes—
100C2×C42×C61—21no—
101C2×C42×C61C2311yescharacteristic
102#95×C61—21no—
103C24×C61—22no—
104C24×C61C2×D412yes—
105C23×D61—21no—
106C2×D4×C61—22no—
107C2×D4×C61—22no—
108C2×D4×C61—22no—
109C2×D4×C61—22no—
110C2×D4×C61—22no—
111C2×D4×C61—22no—
112C2×D4×C61—22no—
113C2×D4×C61—22no—
114C2×D4×C61—44no—
115C2×D4×C61—44no—
116C2×D4×C61—44no—
117C2×D4×C61—44no—
118C2×D4×C61—42no—
119C2×D4×C61—42no—
120C2×D4×C61—42no—
121C2×D4×C61—42no—
122C2×D4×C61—81no—
123C2×D4×C61—81no—
124C2×D4×C61—82no—
125C2×D4×C61—82no—
126C2×D4×C61D814yescomplemented
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61C2×D412yes—
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C2×C22⋊D61—44no—
140C2×C22⋊D61—44no—
141C2×C22⋊D61—82no—
142C22×Dic61—21no—
143C22×Dic61—22no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244C2×D412yes—
150C2×C4×D61—42no—
151C2×C4×D61—42no—
152C2×C4×D61—42no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61C2×D412yes—
157C4⋊C4×C61#4112yes—
158C22⋊C4×C61—24no—
159C22⋊C4×C61—44no—
160C22⋊C4×C61—44no—
161C42×C61—42no—
162C42×C61C2×D412yes—
163C42×C61#4112yes—
164C22⋊Dic61—44no—
165#11758199—48no—
166#11758198—44no—
167#11758198—42no—
168C4⋊Dic61—21no—
169C4⋊Dic61—22no—
170C4⋊Dic61—21no—
171C4⋊Dic61—22no—
172C4⋊Dic61—42no—
173C4⋊Dic61—81no—
174C2×#92418—21no—
175C2×#92418—22no—
176C2×#92418—21no—
177C2×#92418—22no—
178C2×#92418—21no—
179C2×#92418—21no—
180C2×#92418—21no—
181C2×#92418—48no—
182C2×#92418C2×D414yes—
183C2×#92418C2×D412yes—
184C23×C61—22no—
185C23×C61—22no—
186C23×C61—22no—
187C23×C61—22no—
188C23×C61—22no—
189C23×C61—22no—
190C23×C61—42no—
191C23×C61—42no—
192C23×C61—42no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61—42no—
196C23×C61—42no—
197C23×C61C2×D814yes—
198C23×C61C22×D411yescharacteristic
199C22×D61—22no—
200C22×D61—41no—
201C22×D61—41no—
202C22×D61—41no—
203C22×D61—41no—
204C22×D61—41no—
205C22×D61—41no—
206D4×C61—28no—
207D4×C61—42no—
208D4×C61—42no—
209D4×C61—42no—
210D4×C61—42no—
211D4×C61—84no—
212D4×C61—88no—
213D4×C61—88no—
214D4×C61—84no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61#12112yes—
231C2×C4×C61#12112yes—
232C2×C4×C61C2×D812yes—
233C2×C4×C61#13512yes—
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C2×C4×C61H(5,𝔽2)11yescharacteristic
239C2×C4×C61H(5,𝔽2)11yescharacteristic
240C22⋊D61—88no—
241C2×Dic61—41no—
242C2×Dic61—42no—
243C2×Dic61—42no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—42no—
247D244—22no—
248D244—22no—
249D244—41no—
250D244—41no—
251C4×D61—84no—
252#92418—22no—
253#92418—24no—
254#92418—41no—
255#25384—611nomaximal, Sylow
256C22×C61—24no—
257C22×C61—24no—
258C22×C61—24no—
259C22×C61—42no—
260C22×C61—42no—
261C22×C61—42no—
262C22×C61—42no—
263C22×C61—82no—
264C22×C61—82no—
265C22×C61—82no—
266C22×C61—82no—
267C22×C61—82no—
268C22×C61—82no—
269C22×C61—82no—
270C22×C61C2×#12111yescharacteristic
271C22×C61D4211yescharacteristic
272C22×C61#54611yescharacteristic
273C22×C61C22×D811yescharacteristic
274C22×C61C2×#13511yescharacteristic
275C22×C61#57611yescharacteristic
276C22×C61#57711yescharacteristic
277C2×D61—42no—
278C2×D61—42no—
279C2×D61—42no—
280C2×D61—81no—
281C2×D61—81no—
282C2×D61—81no—
283C2×D61—81no—
284C4×C61—22no—
285C4×C61—42no—
286C4×C61—42no—
287C4×C61—42no—
288C4×C61#46614yescomplemented
289C4×C61#53211yescharacteristic
290C4×C61#54011yescharacteristic
291C4×C61D4211yescharacteristic
292C4×C61#55011yescharacteristic
293Dic61—82no—
294Dic61—81no—
295C2×#466—612no—
296C2×#459—611no—
297C2×C8×D4—611no—
298#2541D6111yescharacteristic, complemented
299#2537—611no—
300#2033—612no—
301#1999—612no—
302#1957—611no—
303#1947—611no—
304#1893—612no—
305C4×#102—611no—
306C2×C61—44no—
307C2×C61—162no—
308C2×C61#242811yescharacteristic
309C2×C61C2×#46611yescharacteristic
310C2×C61#306211yescharacteristic
311C2×C61D4×D811yescharacteristic
312C2×C61#328411yescharacteristic
313C2×C61#329411yescharacteristic
314C2×C61#330511yescharacteristic
315D61—82no—
316C22×D8—612no—
317C23×C8—612no—
318C2×#127—21no—
319C2×#127C2×D6111yescharacteristic
320C2×#121—612no—
321C2×#121—1221no—
322C2×#121C2×D6112yes—
323C2×#121C2×D6112yes—
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—611no—
332C2×#102—612no—
333C2×#102—612no—
334C2×#102—611no—
335C2×#102—612no—
336C2×C22⋊C8—612no—
337C2×C4×C8—611no—
338#394—1222no—
339#392—22no—
340#390—21no—
341#384—611no—
342#380—612no—
343#380—1221no—
344C4×C4⋊C4C2×D6111yescharacteristic
345#340—611no—
346#340—612no—
347#340—611no—
348C61#2538411yescharacteristic, complemented, Sylow
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—611no—
354C22×D4—1222no—
355C22×D4C22⋊D6111yescharacteristic
356C22×D4C22×D6112yes—
357C23×C4—1221no—
358C23×C4C22×D6112yes—
359C2×D8—1224no—
360C2×D8—1224no—
361C2×D8—2442no—
362C22×C8—611no—
363C22×C8—612no—
364C22×C8—611no—
365C22×C8—1224no—
366C22×C8—1224no—
367C22×C8—2442no—
368#127—22no—
369#127—22no—
370#127—44no—
371#121—24no—
372#121—24no—
373#121—42no—
374#121—42no—
375#121—1224no—
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—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—1222no—
392C2×C22⋊C4—1221no—
393C2×C22⋊C4—1222no—
394C2×C22⋊C4C22⋊D6112yes—
395C2×C42—21no—
396C2×C42C22×D6111yescharacteristic
397#107—1224no—
398C4⋊C8—614no—
399#102—614no—
400#102—1224no—
401#102—1224no—
402#102—1222no—
403#102—2442no—
404C22⋊C8—1224no—
405C4×C8—1222no—
406#95—21no—
407#95—1222no—
408C24—22no—
409C24—1221no—
410C24C2×C22⋊D6112yes—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—81no—
428C2×D4—81no—
429C2×D4—82no—
430C2×D4—82no—
431C2×D4—612no—
432C2×D4—1221no—
433C2×D4—1221no—
434C2×D4—1221no—
435C2×D4—1221no—
436C2×D4—1221no—
437C2×D4—4882no—
438C2×D4—2444no—
439C2×D4—2444no—
440C2×D4#1175819914yescomplemented
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—1221no—
450C22×C4—1222no—
451C22×C4—2442no—
452C22×C4—2442no—
453C22×C4—2442no—
454C22×C4C2×C22⋊D6112yes—
455C22×C4C2×C22⋊D6111yescharacteristic
456C22×C4C2×C22⋊D6111yescharacteristic
457C22×C4C23×D6111yescharacteristic
458D8—2448no—
459C2×C8—614no—
460C2×C8—612no—
461C2×C8—1221no—
462C2×C8—1222no—
463C2×C8—1221no—
464C2×C8—1222no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—2448no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—1221no—
473C4⋊C4—1222no—
474C4⋊C4—1221no—
475C4⋊C4—1222no—
476C4⋊C4—4881no—
477C4⋊C4—2442no—
478C4⋊C4D4×D6112yes—
479C4⋊C4#1175822412yes—
480C22⋊C4—24no—
481C22⋊C4—44no—
482C22⋊C4—44no—
483C22⋊C4—2444no—
484C22⋊C4—2444no—
485C22⋊C4—2442no—
486C42—42no—
487C42D4×D6112yes—
488C42#1175822412yes—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—1222no—
503C23—2441no—
504C23—2441no—
505C23—2441no—
506C23—2441no—
507C23—2441no—
508C23—2441no—
509C23C2×#1175819914yes—
510C23C22×C22⋊D6111yescharacteristic
511D4—28no—
512D4—42no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—84no—
517D4—88no—
518D4—88no—
519D4—84no—
520D4—1222no—
521D4—1222no—
522D4—4888no—
523D4—2441no—
524D4—2441no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—4884no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2442no—
544C2×C4—2441no—
545C2×C4—2442no—
546C2×C4—2442no—
547C2×C4#1451974912yes—
548C2×C4#1451974912yes—
549C2×C4C2×#1175819912yes—
550C2×C4#1451979712yes—
551C2×C4C2×D4×D6111yescharacteristic
552C2×C4C2×D4×D6111yescharacteristic
553C2×C4C2×#1175822411yescharacteristic
554C2×C4C2×#1175822411yescharacteristic
555C2×C4#1451982211yescharacteristic
556C2×C4#1451982211yescharacteristic
557C8—1222no—
558C8—1224no—
559C8—2441no—
560C22—24no—
561C22—24no—
562C22—24no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—82no—
568C22—82no—
569C22—82no—
570C22—82no—
571C22—82no—
572C22—82no—
573C22—82no—
574C22—4881no—
575C22—4881no—
576C22—4881no—
577C22—4881no—
578C22—2442no—
579C22—2442no—
580C22—2442no—
581C22C2×#1451974911yescharacteristic
582C22D4×C22⋊D6111yescharacteristic
583C22#1684040611yescharacteristic
584C22C22×#1175819911yescharacteristic
585C22C2×#1451979711yescharacteristic
586C22#1684056511yescharacteristic
587C22#1684057311yescharacteristic
588C4—22no—
589C4—42no—
590C4—42no—
591C4—42no—
592C4—4881no—
593C4—4882no—
594C4#1683999614yescomplemented
595C4#1684031011yescharacteristic
596C4#1684036611yescharacteristic
597C4#1684039711yescharacteristic
598C4#1684043211yescharacteristic
599C2—44no—
600C2—162no—
601C2—4882no—
602C2#2144941011yescharacteristic
603C2C2×#1683999611yescharacteristic
604C2#2145549511yescharacteristic
605C2D4×#1175819911yescharacteristic
606C2#2145754911yescharacteristic
607C2#2145763211yescharacteristic
608C2#2145776911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2541C2
socleC23×C61C22×D4
hypercenter#2541D61
hypocenterC61#25384
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. C2×#16839996C2semidirect
2. C2×#16839954C2semidirect
3. C2×D4×#92418C2semidirect
4. #21450732C2semidirect
5. #21446998C2semidirect
6. #21446815C2semidirect
7. #21446626C2semidirect
8. #21446577C2semidirect
9. #21446248C2semidirect
10. C4×#14519697C2semidirect
11. C61×#2541C2semidirect
69. C4⋊#92418D4semidirect
74. #14519697D4semidirect
126. C2×D4×C61D8semidirect
288. C4×C61#466semidirect
298. #2541D61semidirect
348. C61#25384semidirect
440. C2×D4#11758199semidirect
594. C4#16839996semidirect

Maximal subgroups

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

subgroupindex
C2×#168399962
C2×#168399542
C2×D4×#924182
#214507322
#214469982
#214468152
#214466262
#214465772
#214462482
C4×#145196972
C61×#25412
#2538461