Finite Group Databasebeta

← #29651047

Subgroups — #29651047

Order 15616.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455868C211yesmaximal, characteristic
2#21454817C211yesmaximal, characteristic, complemented
3#21454554C211yesmaximal, characteristic, complemented
4#21444732C211yesmaximal, characteristic, complemented
5#21444708C211yesmaximal, characteristic, complemented
6#21444696C211yesmaximal, characteristic, complemented
7#21444682C211yesmaximal, characteristic, complemented
8#21444654C211yesmaximal, characteristic, complemented
9#21444647C211yesmaximal, characteristic, complemented
10#21444630C211yesmaximal, characteristic, complemented
11#21444613C211yesmaximal, characteristic, complemented
12#21444282C211yesmaximal, characteristic, complemented
13#21444209C211yesmaximal, characteristic, complemented
14#21444114C211yesmaximal, characteristic, complemented
15C61×#1574C211yesmaximal, characteristic, complemented
16C2×M16×D61—21no—
17#16840296C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19#16840098C411yescharacteristic
20#16840081C411yescharacteristic
21#16840063C411yescharacteristic
22#16840063C411yescharacteristic
23#16839978C411yescharacteristic
24#16839978C411yescharacteristic
25#16839915C411yescharacteristic
26#16839898C411yescharacteristic
27#16839889C2211yescharacteristic, complemented
28#16839886C2211yescharacteristic, complemented
29C4×#11758190C2211yescharacteristic
30C4×#11758190C2211yescharacteristic
31C4×D488C2211yescharacteristic
32C4×D488C2211yescharacteristic
33#16839839C2211yescharacteristic
34#16839839C2211yescharacteristic
35#16839839C2211yescharacteristic, complemented
36#16839837—21no—
37#16839836—21no—
38#16839832—21no—
39#16839832—21no—
40#16839827C2211yescharacteristic
41#16839827C2211yescharacteristic
42#16839827C2211yescharacteristic, complemented
43#16839821—21no—
44#16839815C2211yescharacteristic
45#16839725—21no—
46#16839716—21no—
47C4×#11758194C2211yescharacteristic
48#16839492C2211yescharacteristic, complemented
49#16839492C2211yescharacteristic, complemented
50#16839489C2211yescharacteristic
51#16839489C2211yescharacteristic
52#16839489C2211yescharacteristic
53#16839489C2211yescharacteristic
54#16839489C2211yescharacteristic, complemented
55#16839489C2211yescharacteristic, complemented
56#16839484C2211yescharacteristic, complemented
57#16839484C2211yescharacteristic, complemented
58#16839483C2211yescharacteristic, complemented
59C8×#92418C2211yescharacteristic, complemented
60C61×#431C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C61×#423C2211yescharacteristic
63C61×#335C2211yescharacteristic, complemented
64C61×#335C2211yescharacteristic, complemented
65C61×#334C2211yescharacteristic, complemented
66C61×#334C2211yescharacteristic, complemented
67C22×D244C2×C411yescharacteristic
68C22×C4×D61—21no—
69C2×#11758190C2×C411yescharacteristic
70C2×#11758190C2×C411yescharacteristic
71C2×D488C2×C411yescharacteristic
72C2×D488C2×C411yescharacteristic
73C2×#11758194D411yescharacteristic
74C2×#11758194D411yescharacteristic
75C2×#11758189—21no—
76C2×#11758189—21no—
77C2×#11758189—21no—
78M16×D61—44no—
79C2×C8×D61—21no—
80C2×C8×D61—21no—
81C2×C8×D61—21no—
82#14519771—21no—
83#14519769C2×C411yescharacteristic
84#14519765C2×C411yescharacteristic
85#14519760—21no—
86#14519756C2×C411yescharacteristic
87#14519751C2×C411yescharacteristic
88C4×Dic122C2311yescharacteristic
89C4×D244—21no—
90C4×D244—21no—
91C4×D244C2×C411yescharacteristic
92C4×D244C2×C411yescharacteristic
93C4×D244C2311yescharacteristic
94C4×D244C2311yescharacteristic
95C4×D244C2311yescharacteristic
96C4×C22⋊D61—21no—
97#14519734—21no—
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×#11758198—21no—
100#14519711C2×C411yescharacteristic
101#14519711C2×C411yescharacteristic
102#14519709C2×C411yescharacteristic
103#14519709C2×C411yescharacteristic
104C4⋊#92418—21no—
105#14519706—21no—
106#14519706—21no—
107#14519702C2×C411yescharacteristic
108#14519702C2×C411yescharacteristic
109#14519699C2×C411yescharacteristic
110#14519699C2×C411yescharacteristic
111#14519699C2×C411yescharacteristic
112#14519699C2×C411yescharacteristic
113#14519699C2×C411yescharacteristic
114#14519699C2×C411yescharacteristic
115C22⋊#92418—21no—
116#14519689—21no—
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689—21no—
121#14519689—21no—
122#14519688D411yescharacteristic
123#14519688D411yescharacteristic
124#14519687—21no—
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C4×#92418C2311yescharacteristic
128C4×#92418C2311yescharacteristic
129C8×Dic61—21no—
130C2×M16×C61—21no—
131C2×C42×C61C2311yescharacteristic
132C4⋊C8×C61—21no—
133C4⋊C8×C61C2×C411yescharacteristic
134C4⋊C8×C61C2×C411yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C22⋊C8×C61—21no—
140C22⋊C8×C61C2×C411yescharacteristic
141C22⋊C8×C61C2×C411yescharacteristic
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C23×D61—21no—
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61#4111yescharacteristic
149C2×C22⋊D61—21no—
150C22×Dic61—21no—
151C2×D244—22no—
152C2×D244—21no—
153C2×D244—41no—
154C2×D244C22×C411yescharacteristic
155C2×D244C22×C411yescharacteristic
156C2×D244C22×C411yescharacteristic
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—42no—
163C2×C4×D61—42no—
164C2×Dic122C22×C411yescharacteristic
165M16×C61—42no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61C22×C411yescharacteristic
171C2×C8×C61C22×C411yescharacteristic
172C2×C8×C61C22×C411yescharacteristic
173C2×C8×C61C22×C411yescharacteristic
174C42×C61C22×C411yescharacteristic
175C42×C61C2×D411yescharacteristic
176C42×C61#4111yescharacteristic
177C42×C61C2411yescharacteristic
178C22⋊Dic61—21no—
179#11758198—21no—
180#11758198—21no—
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61C22×C411yescharacteristic
189C4⋊Dic61C22×C411yescharacteristic
190C4⋊Dic61C22×C411yescharacteristic
191C4⋊Dic61C22×C411yescharacteristic
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196C4×Dic61—21no—
197#11758194—22no—
198#11758194—41no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C2×D411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205D488—22no—
206D488—41no—
207#11758190—22no—
208#11758190—41no—
209#11758189—42no—
210#11758189—42no—
211#11758189—42no—
212C8×D61—42no—
213C8×D61—42no—
214C8×D61—42no—
215C23×C61C4×D411yescharacteristic
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—81no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—41no—
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C23×C411yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C22⋊D61—81no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—42no—
240D244—21no—
241D244—21no—
242D244—21no—
243D244—21no—
244D244—21no—
245D244—42no—
246D244#13112yes—
247C4×D61—42no—
248C4×D61—42no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—41no—
252C4×D61—41no—
253C4×D61—41no—
254C4×D61—41no—
255Dic122—21no—
256Dic122—21no—
257C8×C61—21no—
258C8×C61—21no—
259C8×C61—21no—
260C8×C61—21no—
261C8×C61—41no—
262C8×C61—41no—
263C8×C61—41no—
264C8×C61—41no—
265#92418—21no—
266#92418—21no—
267#92418—21no—
268#92418—41no—
269#92418—41no—
270#92418AGL(1,ℤ/8)12yes—
271#18006—611nomaximal, Sylow
272C22×C61—21no—
273C22×C61—21no—
274C22×C61—21no—
275C22×C61C2×C4×D411yescharacteristic
276C2×D61—22no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—41no—
284C2×D61—41no—
285C2×D61—84no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—21no—
289C4×C61—21no—
290C4×C61C2×#13111yescharacteristic
291C4×C61#56811yescharacteristic
292C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
293C4×C61#57511yescharacteristic
294Dic61—41no—
295Dic61—41no—
296Dic61—41no—
297Dic61—41no—
298Dic61—41no—
299#3105—611no—
300#2969—611no—
301D4×M16—611no—
302#1594—611no—
303#1590—611no—
304#1588—611no—
305#1586—611no—
306#1582—611no—
307#1581—611no—
308SD16⋊C8—611no—
309C8×D8—611no—
310#1574D6111yescharacteristic, complemented
311#1495—611no—
312#1478—611no—
313#1453—611no—
314C2×C61—41no—
315C2×C61#293311yescharacteristic
316C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
317C2×C61#295711yescharacteristic
318D61—42no—
319D61—81no—
320D61—81no—
321C22×M16—1221no—
322#529—611no—
323C2×C4×D4—611no—
324#484—611no—
325#481—611no—
326#478—611no—
327#478—611no—
328#463—611no—
329#463—611no—
330#450—611no—
331#447—611no—
332#446—611no—
333C8×Q8—611no—
334C4×SD16—611no—
335C4×SD16—611no—
336C4×D8—611no—
337C4×D8—611no—
338#436—611no—
339#436—611no—
340#436—611no—
341#436—1221no—
342#435—1221no—
343#435—1221no—
344#435—1221no—
345C8×D4—611no—
346C8×D4—611no—
347C8×D4—611no—
348#433—1221no—
349#431—611no—
350#431C2×D6111yescharacteristic
351#431C2×D6111yescharacteristic
352#423C2×D6111yescharacteristic
353#407—1221no—
354#405—1221no—
355C4×M16—611no—
356#335C2×D6111yescharacteristic, complemented
357#335C2×D6111yescharacteristic, complemented
358#334C2×D6111yescharacteristic, complemented
359#334C2×D6111yescharacteristic, complemented
360Q8⋊C8—611no—
361Q8⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365D4⋊C8—611no—
366D4⋊C8—611no—
367D4⋊C8—611no—
368#322—611no—
369#322—611no—
370#322—611no—
371C82—611no—
372C61#1800611yescharacteristic, complemented, Sylow
373C22×D4—611no—
374C23×C4—1221no—
375C2×SD16—611no—
376C2×SD16—611no—
377C2×D8—611no—
378C2×D8—611no—
379C2×M16—21no—
380C2×M16—611no—
381C2×M16—611no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16—1221no—
385C2×M16—2444no—
386C22×C8—1221no—
387C22×C8—1221no—
388C22×C8—1221no—
389#126—1221no—
390#125—611no—
391#124—611no—
392#123—1221no—
393C22⋊Q8—611no—
394#121—611no—
395C4×Q8—611no—
396C4×D4—611no—
397C4×D4—611no—
398C4×D4—611no—
399C4×D4—611no—
400C4×D4—611no—
401C4×D4—1221no—
402C4×D4—1221no—
403C4×D4—1221no—
404#117—1221no—
405C2×C4⋊C4—611no—
406C2×C22⋊C4—1221no—
407C2×C42C22×D6111yescharacteristic
408#107—611no—
409#107—611no—
410#106—611no—
411#106—611no—
412C4⋊C8—21no—
413C4⋊C8—1221no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416C4⋊C8C4×D6111yescharacteristic
417C4⋊C8C4×D6111yescharacteristic
418C4⋊C8C22×D6111yescharacteristic
419C4⋊C8C22×D6111yescharacteristic
420C4⋊C8C22×D6111yescharacteristic
421C4⋊C8C22×D6111yescharacteristic
422#103—611no—
423#103—611no—
424#102—611no—
425#102—611no—
426#102—611no—
427#102—611no—
428#102—611no—
429#102—611no—
430C22⋊C8—21no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438C22⋊C8C4×D6111yescharacteristic
439C22⋊C8C4×D6111yescharacteristic
440#97—611no—
441#97—611no—
442#97—1221no—
443C4×C8—21no—
444C4×C8—611no—
445C4×C8—611no—
446C4×C8—611no—
447C4×C8—611no—
448C4×C8—1221no—
449C4×C8C22×D6111yescharacteristic
450C4×C8C22×D6111yescharacteristic
451C24—1221no—
452C2×Q8—611no—
453C2×D4—611no—
454C2×D4—611no—
455C2×D4—611no—
456C2×D4—1222no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—2441no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—2442no—
467C22×C4—2442no—
468C22×C4C2×C4×D6111yescharacteristic
469C22×C4D4×D6111yescharacteristic
470C22×C4#1175822611yescharacteristic
471SD16—1222no—
472SD16—2441no—
473D8—1222no—
474D8—2441no—
475M16—42no—
476M16—1222no—
477M16—2442no—
478M16—2442no—
479M16—2442no—
480M16—2441no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—611no—
486C2×C8—611no—
487C2×C8—611no—
488C2×C8—611no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—2442no—
492C2×C8—2442no—
493C2×C8—2442no—
494C2×C8C2×C4×D6111yescharacteristic
495C2×C8C2×C4×D6111yescharacteristic
496C2×C8C2×C4×D6111yescharacteristic
497C2×C8C2×C4×D6111yescharacteristic
498C4⋊C4—611no—
499C4⋊C4—611no—
500C4⋊C4—611no—
501C4⋊C4—611no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—1221no—
511C22⋊C4—1221no—
512C22⋊C4—1221no—
513C22⋊C4—1221no—
514C22⋊C4—1221no—
515C22⋊C4—1221no—
516C42—1221no—
517C42C2×C4×D6111yescharacteristic
518C42D4×D6111yescharacteristic
519C42#1175822611yescharacteristic
520C42C23×D6111yescharacteristic
521C23—1221no—
522C23—1221no—
523C23—1221no—
524C23—4881no—
525C23—2442no—
526C23—2442no—
527C23#1451973911yescharacteristic
528Q8—1221no—
529Q8—1221no—
530D4—612no—
531D4—1221no—
532D4—1221no—
533D4—1221no—
534D4—1221no—
535D4—1221no—
536D4—4881no—
537D4—2442no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—2442no—
549C2×C4—2442no—
550C2×C4—2442no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4#1451973911yescharacteristic
558C2×C4#1451973911yescharacteristic
559C2×C4#1451973911yescharacteristic
560C2×C4C22×C4×D6111yescharacteristic
561C2×C4C2×D4×D6111yescharacteristic
562C2×C4C2×#1175822611yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—612no—
572C8—1221no—
573C8—1221no—
574C8—1221no—
575C8—2441no—
576C8—2441no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—1222no—
581C22—4884no—
582C22—2441no—
583C22—2441no—
584C22—2441no—
585C22—2441no—
586C22—2441no—
587C22—2441no—
588C22—2441no—
589C22—2441no—
590C22C2×#1451973911yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—2441no—
596C4—2441no—
597C4—2441no—
598C4—2441no—
599C4—2441no—
600C4#131×D6111yescharacteristic
601C4#1684052711yescharacteristic
602C4AGL(1,ℤ/8)×D6111yescharacteristic
603C4#1684056111yescharacteristic
604C2—41no—
605C2—4881no—
606C2—4881no—
607C2—2442no—
608C2#2145454311yescharacteristic
609C2#2145462611yescharacteristic
610C2#2145473511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1574C2
socleC22×C61C2×C4×D4
prime radical#16839898C4
cosocleC42×C61C24
hypercenter#1574D61
hypocenterC61#18006
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
2. #21454817C2semidirect
3. #21454554C2semidirect
4. #21444732C2semidirect
5. #21444708C2semidirect
6. #21444696C2semidirect
7. #21444682C2semidirect
8. #21444654C2semidirect
9. #21444647C2semidirect
10. #21444630C2semidirect
11. #21444613C2semidirect
12. #21444282C2semidirect
13. #21444209C2semidirect
14. #21444114C2semidirect
15. C61×#1574C2semidirect
27. #16839889C22semidirect
28. #16839886C22semidirect
35. #16839839C22semidirect
42. #16839827C22semidirect
48. #16839492C22semidirect
49. #16839492C22semidirect
54. #16839489C22semidirect
55. #16839489C22semidirect
56. #16839484C22semidirect
57. #16839484C22semidirect
58. #16839483C22semidirect
59. C8×#92418C22semidirect
63. C61×#335C22semidirect
64. C61×#335C22semidirect
65. C61×#334C22semidirect
66. C61×#334C22semidirect
310. #1574D61semidirect
356. #335C2×D61semidirect
357. #335C2×D61semidirect
358. #334C2×D61semidirect
359. #334C2×D61semidirect
372. C61#18006semidirect

Maximal subgroups

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

subgroupindex
#214558682
#214548172
#214545542
#214447322
#214447082
#214446962
#214446822
#214446542
#214446472
#214446302
#214446132
#214442822
#214442092
#214441142
C61×#15742
#1800661