Finite Group Databasebeta

← #29743076

Subgroups — #29743076

Order 15616.

820 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840072C211yesmaximal, characteristic, complemented
2C2×C4×#11758190C211yesmaximal, characteristic
3#21449692C211yesmaximal, characteristic
4#21448738C211yesmaximal, characteristic, complemented
5#21447341C211yesmaximal, characteristic
6#21447305C211yesmaximal, characteristic, complemented
7#21447188C211yesmaximal, characteristic
8#21447156C211yesmaximal, characteristic, complemented
9#21446376C211yesmaximal, characteristic, complemented
10#21446175C211yesmaximal, characteristic
11#21446175C211yesmaximal, characteristic
12#21446084C211yesmaximal, characteristic, complemented
13#21446072C211yesmaximal, characteristic, complemented
14#21446065C211yesmaximal, characteristic
15C61×#1941C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C2×#14519768C2211yescharacteristic
18C2×C4×Dic122C2211yescharacteristic
19C2×#14519742C2211yescharacteristic
20C2×#14519742C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22#16840072—24no—
23C4×#11758190—24no—
24C2×#14519710C2211yescharacteristic
25C2×#14519710C2211yescharacteristic
26C2×#14519709C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34#16839697—21no—
35#16839684—21no—
36#16839663C2211yescharacteristic
37#16839663C2211yescharacteristic
38#16839661C2211yescharacteristic
39#16839659—21no—
40#16839658C2211yescharacteristic
41#16839657—21no—
42#16839636—21no—
43#16839627C2211yescharacteristic
44#16839626—21no—
45#16839621—21no—
46C4⋊C4×Dic61—21no—
47C4×#11758196C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic
55C2×#106×C61C2211yescharacteristic
56C2×C4×C8×C61C2211yescharacteristic
57C61×#389C2211yescharacteristic
58C61×#389C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C4×D61—21no—
64C2×#11758190—22no—
65C2×#11758190—22no—
66C2×#11758190Q814yes—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69#14519768—22no—
70#14519768—41no—
71C4×Dic122—22no—
72C4×Dic122—41no—
73#14519742—22no—
74#14519742—22no—
75#14519742—22no—
76#14519742—41no—
77C4×D244—22no—
78C4×D244—41no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196D411yescharacteristic
89C2×#11758196D411yescharacteristic
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61C2311yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100#14519710—22no—
101#14519710—41no—
102#14519709—22no—
103#14519706—22no—
104#14519702D414yes—
105#14519700—22no—
106#14519700—22no—
107#14519699—22no—
108#14519697—22no—
109#14519697—41no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684D411yescharacteristic
115#14519684D411yescharacteristic
116C22×C8×C61C2311yescharacteristic
117C22×C8×C61C2311yescharacteristic
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C42×C61C2311yescharacteristic
125#106×C61—22no—
126#106×C61—22no—
127C4×C8×C61—22no—
128#95×C61—21no—
129#95×C61—21no—
130C23×D61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144C22×Dic61C2×D411yescharacteristic
145C2×D244—21no—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244—21no—
150C2×D244C2×Q812yes—
151C2×C4×D61—42no—
152C2×C4×D61—42no—
153C2×C4×D61—81no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122C2×D412yes—
158C2×Dic122C2×Q812yes—
159C2×Dic122#4112yes—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61C2×D412yes—
165C2×C8×C61C2×Q812yes—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—42no—
174C4⋊C4×C61—81no—
175C4⋊C4×C61#4112yes—
176C42×C61—21no—
177C42×C61—21no—
178#11758198—42no—
179#11758198—42no—
180#11758198—81no—
181#11758198—81no—
182#11758198—81no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—42no—
187C4⋊Dic61—42no—
188C4⋊Dic61C2×D412yes—
189#11758196—24no—
190#11758196—22no—
191#11758196—41no—
192#11758196—42no—
193#11758196—42no—
194#11758196—42no—
195#11758196—81no—
196C4×Dic61—24no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—42no—
202C4×Dic61—42no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209#11758190—28no—
210C23×C61C22×D411yescharacteristic
211C22×D61—22no—
212C22×D61—41no—
213C22×D61—41no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—41no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—22no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61#13512yes—
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C22×Q811yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61H(5,𝔽2)11yescharacteristic
241C2×C4×C612−1+411yescharacteristic
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—22no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263D244—22no—
264D244—22no—
265D244—41no—
266D244—41no—
267C4×D61—84no—
268Dic122—22no—
269Dic122—22no—
270Dic122—22no—
271Dic122C22⋊Q814yes—
272C8×C61—22no—
273C8×C61—22no—
274#92418—41no—
275#92418—41no—
276#26375—611nomaximal, Sylow
277C22×C61#52511yescharacteristic
278C22×C61D4211yescharacteristic
279C22×C61D4×Q811yescharacteristic
280C22×C61C2×#13511yescharacteristic
281C22×C61#57511yescharacteristic
282C22×C61#57711yescharacteristic
283C22×C61#57711yescharacteristic
284C2×D61—42no—
285C2×D61—42no—
286C2×D61—42no—
287C2×D61—81no—
288C2×D61—81no—
289C2×D61—81no—
290C2×D61—81no—
291C4×C61—22no—
292C4×C61—42no—
293C4×C61—41no—
294C4×C61—81no—
295C4×C61—81no—
296C4×C61—81no—
297C4×C61C2×C22⋊Q811yescharacteristic
298C4×C61#53911yescharacteristic
299C4×C61#54711yescharacteristic
300C4×C61#55411yescharacteristic
301Dic61—24no—
302Dic61—41no—
303Dic61—41no—
304Dic61—41no—
305Dic61—42no—
306Dic61—41no—
307Dic61—81no—
308C2×#479—611no—
309C2×C4×SD16—611no—
310#2454—611no—
311#2351—611no—
312#2092—611no—
313#2085—611no—
314#2065—611no—
315#2059—611no—
316#1941D6111yescharacteristic, complemented
317#1916—611no—
318#1880—611no—
319#1880—611no—
320#1865—611no—
321#1863—611no—
322#1862—611no—
323C2×C61#244911yescharacteristic
324C2×C61#310211yescharacteristic
325C2×C61#312611yescharacteristic
326C2×C61#327111yescharacteristic
327C2×C61#328211yescharacteristic
328C2×C61#338111yescharacteristic
329C2×C61#338811yescharacteristic
330D61—82no—
331C22×SD16—611no—
332C2×#125—611no—
333C2×C4×Q8—611no—
334C2×C4×Q8—611no—
335C2×C4×Q8—611no—
336C2×C4×D4—611no—
337#479—1224no—
338C4×SD16—1224no—
339C2×#107—611no—
340C2×#107—611no—
341C2×#106—611no—
342C2×#106C2×D6111yescharacteristic
343C2×#106C2×D6111yescharacteristic
344C2×C4⋊C8—611no—
345C2×#103—611no—
346C2×#103—611no—
347C2×#103—611no—
348C2×#102—611no—
349C2×#102—611no—
350C2×#102—611no—
351C2×C4×C8C2×D6111yescharacteristic
352#399—1221no—
353#396—1221no—
354#390—611no—
355#390—611no—
356#389—611no—
357#389—611no—
358#389—1221no—
359#389—1221no—
360#389C2×D6111yescharacteristic
361#389C2×D6111yescharacteristic
362#385—1221no—
363#382—611no—
364#382—1221no—
365#380—1221no—
366C4×C4⋊C4—611no—
367C4×C4⋊C4—1221no—
368#340—611no—
369#340—611no—
370#340C2×D6111yescharacteristic
371#340C2×D6111yescharacteristic
372#336—611no—
373#336—611no—
374#336—611no—
375#336—611no—
376C61#2637511yescharacteristic, complemented, Sylow
377C22×Q8—611no—
378C22×D4—611no—
379C23×C4—1221no—
380C2×SD16—614no—
381C2×SD16—1222no—
382C2×SD16—1222no—
383C22×C8—611no—
384C22×C8—611no—
385C22×C8C22×D6111yescharacteristic
386C22×C8C22×D6111yescharacteristic
387#125—1222no—
388#125—2441no—
389C4×Q8—1222no—
390C4×Q8—1222no—
391C4×Q8—1222no—
392C4×Q8—1222no—
393C4×Q8—2441no—
394C4×Q8—2441no—
395C4×D4—1222no—
396C4×D4—2441no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4C22×D6111yescharacteristic
411C2×C4⋊C4C22×D6111yescharacteristic
412C2×C4⋊C4C22×D6111yescharacteristic
413C2×C4⋊C4C22×D6111yescharacteristic
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4—1221no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—1221no—
422C2×C42—1221no—
423C2×C42—1221no—
424C2×C42C22×D6111yescharacteristic
425#107—1222no—
426#107—2441no—
427#106—22no—
428#106—22no—
429#106—1222no—
430C4⋊C8—1222no—
431#103—614no—
432#103—1222no—
433#103—1222no—
434#102—1222no—
435#102—1222no—
436#102—2441no—
437C4×C8—22no—
438#95—21no—
439#95—21no—
440#95—611no—
441#95—611no—
442#95—1221no—
443#95—1221no—
444#95—1221no—
445#95—1221no—
446C24—1221no—
447C2×Q8—612no—
448C2×Q8—612no—
449C2×Q8—612no—
450C2×Q8—1221no—
451C2×Q8—1221no—
452C2×Q8—1221no—
453C2×D4—612no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—4881no—
471C22×C4—2442no—
472C22×C4—2442no—
473C22×C4D4×D6111yescharacteristic
474C22×C4D4×D6111yescharacteristic
475C22×C4C23×D6111yescharacteristic
476SD16—1228no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8D4×D6112yes—
488C2×C8Q8×D6112yes—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—81no—
498C4⋊C4—612no—
499C4⋊C4—1224no—
500C4⋊C4—1221no—
501C4⋊C4—1222no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—4881no—
505C4⋊C4—2441no—
506C4⋊C4—2442no—
507C4⋊C4—2442no—
508C4⋊C4—2442no—
509C4⋊C4—2442no—
510C4⋊C4—2442no—
511C4⋊C4#1175822212yes—
512C22⋊C4—4881no—
513C22⋊C4—4881no—
514C22⋊C4—4881no—
515C22⋊C4—2442no—
516C22⋊C4—2442no—
517C42—21no—
518C42—21no—
519C42—1224no—
520C42—1221no—
521C42—1221no—
522C42—1221no—
523C42—1221no—
524C42—2442no—
525C42—2442no—
526C23—1222no—
527C23—2441no—
528C23—2441no—
529C23—2441no—
530C23—2441no—
531C23—2441no—
532C23—2441no—
533C23C2×D4×D6111yescharacteristic
534Q8—614no—
535Q8—1222no—
536Q8—1222no—
537Q8—1222no—
538D4—1222no—
539D4—1222no—
540D4—2441no—
541D4—2441no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—1222no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1222no—
575C2×C4—4884no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4#1451979812yes—
582C2×C4C2×D4×D6111yescharacteristic
583C2×C4C2×Q8×D6111yescharacteristic
584C2×C4#41×D6111yescharacteristic
585C2×C4C2×#1175822211yescharacteristic
586C2×C4#1451982311yescharacteristic
587C2×C4#1451982511yescharacteristic
588C8—22no—
589C8—22no—
590C8—2441no—
591C8—2441no—
592C22—4881no—
593C22—4881no—
594C22—4881no—
595C22—4881no—
596C22—2442no—
597C22—2442no—
598C22—2442no—
599C22#1684027111yescharacteristic
600C22#1684039611yescharacteristic
601C22#1684042711yescharacteristic
602C22C2×#1451979811yescharacteristic
603C22#1684055911yescharacteristic
604C22#1684056811yescharacteristic
605C22#1684056911yescharacteristic
606C4—22no—
607C4—42no—
608C4—41no—
609C4—81no—
610C4—81no—
611C4—81no—
612C4—1224no—
613C4—4881no—
614C4—2441no—
615C4—2442no—
616C4—2441no—
617C4—2441no—
618C4—2441no—
619C4C22⋊Q8×D6111yescharacteristic
620C4#1684036011yescharacteristic
621C4#1684041311yescharacteristic
622C4#1684047211yescharacteristic
623C2—4882no—
624C2#2144963511yescharacteristic
625C2#2145584111yescharacteristic
626C2#2145610711yescharacteristic
627C2#2145740111yescharacteristic
628C2#2145752311yescharacteristic
629C2#2145869911yescharacteristic
630C2#2145877011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1941C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#1941D61
hypocenterC61#26375
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1941

Complements

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

NH ≅ G/Ntype
1. C2×#16840072C2semidirect
4. #21448738C2semidirect
6. #21447305C2semidirect
8. #21447156C2semidirect
9. #21446376C2semidirect
12. #21446084C2semidirect
13. #21446072C2semidirect
15. C61×#1941C2semidirect
316. #1941D61semidirect
376. C61#26375semidirect

Maximal subgroups

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

subgroupindex
C2×#168400722
C2×C4×#117581902
#214496922
#214487382
#214473412
#214473052
#214471882
#214471562
#214463762
#214461752
#214460842
#214460722
#214460652
C61×#19412
#2637561