Finite Group Databasebeta

← #29651262

Subgroups — #29651262

Order 15616.

632 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455875C211yesmaximal, characteristic
2#21454942C211yesmaximal, characteristic, complemented
3#21454882C211yesmaximal, characteristic, complemented
4#21444723C211yesmaximal, characteristic, complemented
5#21444718C211yesmaximal, characteristic, complemented
6#21444655C211yesmaximal, characteristic, complemented
7#21444654C211yesmaximal, characteristic, complemented
8#21444649C211yesmaximal, characteristic, complemented
9#21444648C211yesmaximal, characteristic, complemented
10#21444640C211yesmaximal, characteristic, complemented
11#21444606C211yesmaximal, characteristic, complemented
12#21444268C211yesmaximal, characteristic, complemented
13#21444198C211yesmaximal, characteristic, complemented
14#21444110C211yesmaximal, characteristic, complemented
15C61×#1580C211yesmaximal, characteristic, complemented
16#16840309C2211yescharacteristic
17C4×#11758224C2211yescharacteristic
18#16840089C411yescharacteristic
19#16840085C411yescharacteristic
20#16840056C411yescharacteristic
21#16840050C411yescharacteristic
22#16839961C411yescharacteristic
23#16839955C411yescharacteristic
24#16839908C411yescharacteristic
25#16839904C411yescharacteristic
26#16839892C2211yescharacteristic
27#16839889C2211yescharacteristic
28C4×#11758190C2211yescharacteristic
29C4×#11758200C2211yescharacteristic
30C4×#11758199C2211yescharacteristic
31#16839841C2211yescharacteristic
32#16839840C2211yescharacteristic
33#16839837—21no—
34#16839833—21no—
35#16839830—21no—
36D4×#92418C2211yescharacteristic
37#16839827C2211yescharacteristic
38C8×C22⋊D61—21no—
39#16839816—21no—
40#16839814C2211yescharacteristic
41#16839813C2211yescharacteristic
42#16839813C2211yescharacteristic
43#16839784C2211yescharacteristic
44C2×#14519706—21no—
45#16839728—21no—
46#16839727—21no—
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839494C2211yescharacteristic
52#16839492C2211yescharacteristic
53#16839491C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55D4⋊#92418C2211yescharacteristic
56#16839489C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839484C2211yescharacteristic
59#16839483C2211yescharacteristic
60C4×D8×C61C2211yescharacteristic
61C8×D4×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#334C2211yescharacteristic
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758224C2×C411yescharacteristic
69C2×#11758190C2×C411yescharacteristic
70C2×#11758200C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C2×#11758194—21no—
73C2×#11758189—21no—
74C2×#11758189—21no—
75C22×#92418—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78#14519776C2×C411yescharacteristic
79#14519773C2×C411yescharacteristic
80#14519763—21no—
81#14519752C2×C411yescharacteristic
82#14519750—21no—
83#14519748C2×C411yescharacteristic
84C4×Dic122C2311yescharacteristic
85#14519742C2×C411yescharacteristic
86C4×D244C2311yescharacteristic
87D4×Dic61C2×C411yescharacteristic
88C4×C22⋊D61—21no—
89C4×C22⋊D61—21no—
90#14519737—21no—
91#14519735C2×C411yescharacteristic
92#14519733—21no—
93C2×C4×Dic61—21no—
94C42×D61C2311yescharacteristic
95#14519710C2×C411yescharacteristic
96#14519709C2×C411yescharacteristic
97#14519708C2×C411yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100#14519706—21no—
101#14519706—21no—
102#14519706—21no—
103#14519706C2×C411yescharacteristic
104#14519706C2×C411yescharacteristic
105#14519706D411yescharacteristic
106#14519706D411yescharacteristic
107#14519702C2×C411yescharacteristic
108#14519700C2×C411yescharacteristic
109#14519699C2×C411yescharacteristic
110#14519698C2×C411yescharacteristic
111#14519698C2×C411yescharacteristic
112#14519697C2×C411yescharacteristic
113C22⋊#92418—21no—
114C22⋊#92418—21no—
115#14519689—21no—
116#14519689—21no—
117#14519689—21no—
118#14519689C2×C411yescharacteristic
119#14519689C2×C411yescharacteristic
120#14519689D411yescharacteristic
121#14519689D411yescharacteristic
122#14519687—21no—
123#14519687—21no—
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C8×Dic61—21no—
128C8×Dic61—21no—
129C2×D8×C61C2×C411yescharacteristic
130C22×C8×C61—21no—
131C22×C8×C61—21no—
132C4×D4×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134#107×C61C2×C411yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#102×C61C2×C411yescharacteristic
138#102×C61C2×C411yescharacteristic
139C22⋊C8×C61—21no—
140C22⋊C8×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×D4×C61C22×C411yescharacteristic
145C2×D4×C61C22×C411yescharacteristic
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151C2×C22⋊D61—21no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154#11758224—22no—
155#11758224—41no—
156#11758222—81no—
157#11758222—81no—
158C2×D244—21no—
159C2×D244C22×C411yescharacteristic
160C2×C4×D61—21no—
161C2×C4×D61C22×C411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61#4111yescharacteristic
164C2×Dic122—21no—
165C2×Dic122C22×C411yescharacteristic
166D8×C61—22no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—81no—
171C2×C8×C61—81no—
172C2×C8×C61C22×C411yescharacteristic
173C2×C8×C61C22×C411yescharacteristic
174C2×C8×C61C2×D411yescharacteristic
175C2×C8×C61C2×D411yescharacteristic
176C4⋊C4×C61C22×C411yescharacteristic
177C4⋊C4×C61C22×C411yescharacteristic
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C42×C61C2411yescharacteristic
181C22⋊Dic61—21no—
182C22⋊Dic61—21no—
183#11758200—41no—
184#11758199—22no—
185#11758198—21no—
186#11758198—21no—
187#11758198—21no—
188C4⋊Dic61C22×C411yescharacteristic
189C4⋊Dic61C22×C411yescharacteristic
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61C22×C411yescharacteristic
197C4×Dic61C2×D411yescharacteristic
198C4×Dic61#4111yescharacteristic
199#11758194—81no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—81no—
204C2×#92418C22×C411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208#11758190—41no—
209#11758189—81no—
210#11758189—81no—
211C8×D61—42no—
212C8×D61—81no—
213C23×C61—21no—
214C23×C61—21no—
215C22×D61—21no—
216C22×D61C4×D411yescharacteristic
217D4×C61—21no—
218D4×C61—21no—
219D4×C61—21no—
220D4×C61#13112yes—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61C23×C411yescharacteristic
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C2×#4111yescharacteristic
230C22⋊D61—42no—
231C22⋊D61—42no—
232C22⋊D61—81no—
233C22⋊D61—81no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—42no—
238C2×Dic61—42no—
239C2×Dic61C4×D411yescharacteristic
240C2×Dic61C4×D411yescharacteristic
241C2×Dic61C4×D411yescharacteristic
242D244—21no—
243D244—21no—
244D244—81no—
245C4×D61—21no—
246C4×D61—21no—
247C4×D61—21no—
248C4×D61—21no—
249C4×D61—22no—
250C4×D61—41no—
251C4×D61—41no—
252Dic122—21no—
253Dic122—21no—
254Dic122—81no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—21no—
259C8×C61—41no—
260C8×C61—41no—
261C8×C61—41no—
262#92418—21no—
263#92418—21no—
264#92418—21no—
265#92418—21no—
266#92418—41no—
267#92418—41no—
268#92418—41no—
269#18022—611nomaximal, Sylow
270C22×C61—22no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61C2×C4×D411yescharacteristic
277C2×D61—21no—
278C2×D61—21no—
279C2×D61—21no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C4×C61—21no—
284C4×C61—41no—
285C4×C61—41no—
286C4×C61C2×#13111yescharacteristic
287C4×C61#56811yescharacteristic
288C4×C61#57611yescharacteristic
289C4×C61#57711yescharacteristic
290Dic61—21no—
291Dic61—21no—
292Dic61—41no—
293Dic61—41no—
294Dic61—41no—
295Dic61#44412yes—
296#3106—611no—
297#2990—611no—
298#2979—611no—
299#1592—611no—
300#1592—611no—
301#1582—611no—
302#1582—611no—
303#1581—611no—
304#1581—611no—
305#1580—611no—
306#1580D6111yescharacteristic, complemented
307#1574—611no—
308#1492—611no—
309#1476—611no—
310#1452—611no—
311C2×C61—42no—
312C2×C61—81no—
313C2×C61#293311yescharacteristic
314C2×C61#294611yescharacteristic
315C2×C61C2×#44411yescharacteristic
316D61—41no—
317D61—81no—
318#532—611no—
319C4×#41—611no—
320#482—611no—
321#482—611no—
322#477—611no—
323#476—611no—
324#460—611no—
325#459—611no—
326#449—611no—
327#449—611no—
328#446—611no—
329#446—611no—
330C4×SD16—611no—
331C4×SD16—611no—
332C4×D8—611no—
333C4×D8C2×D6111yescharacteristic
334#436—611no—
335#436—611no—
336#436—1221no—
337#435—1221no—
338#435—1221no—
339C8×D4—611no—
340C8×D4—611no—
341C8×D4—1221no—
342C8×D4C2×D6111yescharacteristic
343C8×D4C2×D6111yescharacteristic
344#432—1221no—
345#431—611no—
346#431—611no—
347#431—611no—
348#423—611no—
349C2×C4⋊C8—1221no—
350#408—1221no—
351#408—1221no—
352C2×C4×C8—611no—
353#335—611no—
354#335—611no—
355#334—611no—
356#334C2×D6111yescharacteristic
357Q8⋊C8—611no—
358Q8⋊C8—611no—
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8C2×D6111yescharacteristic
364D4⋊C8C2×D6111yescharacteristic
365#322—611no—
366#322—611no—
367#322—611no—
368#322C2×D6111yescharacteristic
369C61#1802211yescharacteristic, complemented, Sylow
370C2×#41—611no—
371C2×#41—1221no—
372C2×SD16—611no—
373C2×SD16—611no—
374C2×D8—611no—
375C2×D8C4×D6111yescharacteristic
376C2×M16—1221no—
377C2×M16—1221no—
378C2×M16—1221no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—1221no—
382C22×C8—1221no—
383C22×C8—1221no—
384C4⋊Q8—611no—
385#127—611no—
386#124—1221no—
387#121—611no—
388#121—611no—
389#121—1221no—
390C4×Q8—611no—
391C4×Q8—611no—
392C4×D4—611no—
393C4×D4—611no—
394C4×D4—1221no—
395C4×D4—1221no—
396C4×D4—1221no—
397C4×D4C22×D6111yescharacteristic
398C4×D4C22×D6111yescharacteristic
399#117—611no—
400#117—1221no—
401C2×C42—611no—
402C2×C42—1221no—
403#107—611no—
404#107C4×D6111yescharacteristic
405#106—611no—
406#106—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—1221no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416C4⋊C8C22×D6111yescharacteristic
417C4⋊C8C22×D6111yescharacteristic
418#103—611no—
419#103—611no—
420#102—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424#102C4×D6111yescharacteristic
425#102C4×D6111yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—611no—
429C22⋊C8—611no—
430C22⋊C8—611no—
431C22⋊C8—611no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437#97—1221no—
438#97—1221no—
439C4×C8—611no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—1221no—
443C4×C8—1221no—
444C4×C8C22×D6111yescharacteristic
445C4×C8C22×D6111yescharacteristic
446C4×C8C22×D6111yescharacteristic
447#41—1222no—
448#41—4881no—
449#41—4881no—
450#41—2441no—
451C2×Q8—611no—
452C2×Q8—1221no—
453C2×D4—611no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4C2×C4×D6111yescharacteristic
460C2×D4C2×C4×D6111yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469SD16—2441no—
470SD16—2441no—
471D8—22no—
472D8—1222no—
473M16—4881no—
474M16—4881no—
475M16—4881no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—81no—
480C2×C8—81no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—611no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—4881no—
489C2×C8—4881no—
490C2×C8—2442no—
491C2×C8C2×C4×D6111yescharacteristic
492C2×C8C2×C4×D6111yescharacteristic
493C2×C8D4×D6111yescharacteristic
494C2×C8D4×D6111yescharacteristic
495C4⋊C4—611no—
496C4⋊C4—611no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4C2×C4×D6111yescharacteristic
501C4⋊C4C2×C4×D6111yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C42—611no—
510C42—611no—
511C42—611no—
512C42—1221no—
513C42—1221no—
514C42—1221no—
515C42C23×D6111yescharacteristic
516C23—21no—
517C23—21no—
518C23—611no—
519C23—1221no—
520Q8—1221no—
521Q8—1221no—
522Q8—4881no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—1221no—
527D4—1221no—
528D4—4881no—
529D4—4881no—
530D4—4881no—
531D4—2442no—
532D4—2442no—
533D4#1451978312yes—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—611no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—1222no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—2442no—
552C2×C4—2442no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4C22×C4×D6111yescharacteristic
556C2×C4C2×D4×D6111yescharacteristic
557C2×C4#41×D6111yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—1221no—
566C8—1221no—
567C8—1221no—
568C8—1221no—
569C8—2441no—
570C8—2441no—
571C8—2441no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—1221no—
579C22—1221no—
580C22—1221no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22C4×D4×D6111yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—612no—
589C4—1221no—
590C4—1221no—
591C4—2441no—
592C4—2441no—
593C4—2441no—
594C4C2×#1451978311yescharacteristic
595C4#1684052711yescharacteristic
596C4#1684056611yescharacteristic
597C4#1684057211yescharacteristic
598C2—42no—
599C2—81no—
600C2—4881no—
601C2—2441no—
602C2#2145453911yescharacteristic
603C2#2145464811yescharacteristic
604C2#444×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1580C2
socleC22×C61C2×C4×D4
prime radical#21455875C2
cosocleC42×C61C24
hypercenter#1580D61
hypocenterC61#18022
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1580

Complements

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

NH ≅ G/Ntype
2. #21454942C2semidirect
3. #21454882C2semidirect
4. #21444723C2semidirect
5. #21444718C2semidirect
6. #21444655C2semidirect
7. #21444654C2semidirect
8. #21444649C2semidirect
9. #21444648C2semidirect
10. #21444640C2semidirect
11. #21444606C2semidirect
12. #21444268C2semidirect
13. #21444198C2semidirect
14. #21444110C2semidirect
15. C61×#1580C2semidirect
306. #1580D61semidirect
369. C61#18022semidirect

Maximal subgroups

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

subgroupindex
#214558752
#214549422
#214548822
#214447232
#214447182
#214446552
#214446542
#214446492
#214446482
#214446402
#214446062
#214442682
#214441982
#214441102
C61×#15802
#1802261