Finite Group Databasebeta

← #29650614

Subgroups — #29650614

Order 15616.

662 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#21456410C211yesmaximal, characteristic
2#21454796C211yesmaximal, characteristic, complemented
3#21454526C211yesmaximal, characteristic, complemented
4#21444710C211yesmaximal, characteristic, complemented
5#21444706C211yesmaximal, characteristic, complemented
6#21444703C211yesmaximal, characteristic, complemented
7#21444701C211yesmaximal, characteristic, complemented
8#21444644C211yesmaximal, characteristic, complemented
9#21444641C211yesmaximal, characteristic, complemented
10#21444629C211yesmaximal, characteristic, complemented
11#21444585C211yesmaximal, characteristic, complemented
12#21444286C211yesmaximal, characteristic, complemented
13#21444283C211yesmaximal, characteristic, complemented
14#21444098C211yesmaximal, characteristic, complemented
15C61×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#14519783—21no—
17#16840309C2211yescharacteristic
18#16840299C2211yescharacteristic
19#16840169C411yescharacteristic
20#16840148C411yescharacteristic
21#16840125C411yescharacteristic
22#16840123C411yescharacteristic
23#16840016C411yescharacteristic
24#16840014C411yescharacteristic
25#16840011C411yescharacteristic
26#16840005C411yescharacteristic
27#16839893C2211yescharacteristic
28C4×#11758201C2211yescharacteristic
29C4×D488C2211yescharacteristic
30C4×#11758199C2211yescharacteristic
31#16839840C2211yescharacteristic
32#16839839C2211yescharacteristic
33#16839839C2211yescharacteristic
34#16839837—21no—
35#16839832—21no—
36C8×D244—21no—
37C8×D244C2211yescharacteristic
38C8×D244C2211yescharacteristic
39C8×C22⋊D61—21no—
40#16839822—21no—
41#16839818C2211yescharacteristic
42#16839813C2211yescharacteristic
43#16839784C2211yescharacteristic
44#16839727—21no—
45#16839716—21no—
46C4×#11758189C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839513C2211yescharacteristic
50#16839512C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52#16839491C2211yescharacteristic
53#16839491C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839489C2211yescharacteristic
56#16839489C2211yescharacteristic
57#16839484C2211yescharacteristic
58C8×#92418C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C8×Q8×C61C2211yescharacteristic
61C4×SD16×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758201C2×C411yescharacteristic
69C2×D488C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71#14519783—44no—
72C2×#11758194—21no—
73C2×#11758189—21no—
74C2×#11758189—21no—
75C2×#11758189—21no—
76C2×#11758189C2×C411yescharacteristic
77C2×#11758189C2×C411yescharacteristic
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80C2×C8×D61D411yescharacteristic
81C2×C8×D61D411yescharacteristic
82#14519776C2×C411yescharacteristic
83#14519773C2×C411yescharacteristic
84#14519772—21no—
85#14519768C2×C411yescharacteristic
86#14519766C2×C411yescharacteristic
87#14519763—21no—
88#14519762—21no—
89#14519753C2×C411yescharacteristic
90#14519752C2×C411yescharacteristic
91#14519752C2×C411yescharacteristic
92#14519750—21no—
93#14519748C2×C411yescharacteristic
94C4×D244—21no—
95C4×D244C2311yescharacteristic
96C4×D244C2311yescharacteristic
97C4×C22⋊D61—21no—
98#14519734—21no—
99C42×D61C2311yescharacteristic
100#14519711C2×C411yescharacteristic
101#14519710C2×C411yescharacteristic
102#14519708C2×C411yescharacteristic
103C4⋊#92418—21no—
104C4⋊#92418C2311yescharacteristic
105C4⋊#92418C2311yescharacteristic
106#14519706—21no—
107#14519706—21no—
108#14519701C2×C411yescharacteristic
109#14519699C2×C411yescharacteristic
110#14519699C2×C411yescharacteristic
111#14519698C2×C411yescharacteristic
112#14519697C2×C411yescharacteristic
113#14519697C2×C411yescharacteristic
114C22⋊#92418—21no—
115#14519689—21no—
116#14519689—21no—
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689—21no—
121#14519688—21no—
122#14519687—21no—
123#14519687C2×C411yescharacteristic
124#14519687C2×C411yescharacteristic
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C4×#92418C2311yescharacteristic
128C8×Dic61D411yescharacteristic
129C8×Dic61D411yescharacteristic
130C2×SD16×C61C2×C411yescharacteristic
131C22×C8×C61—21no—
132C4×Q8×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134#106×C61C2×C411yescharacteristic
135C4⋊C8×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61C2×C411yescharacteristic
139#102×C61C2×C411yescharacteristic
140C22⋊C8×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151#11758222—42no—
152#11758222—42no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244C22×C411yescharacteristic
156C2×D244C22×C411yescharacteristic
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61C22×C411yescharacteristic
160C2×C4×D61C2×D411yescharacteristic
161C2×C4×D61#4111yescharacteristic
162C2×Dic122—21no—
163SD16×C61—22no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—42no—
168C2×C8×C61C22×C411yescharacteristic
169C2×C8×C61C22×C411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C4⋊C4×C61—21no—
173C4⋊C4×C61C22×C411yescharacteristic
174C4⋊C4×C61C22×C411yescharacteristic
175C22⋊C4×C61—21no—
176C42×C61—21no—
177C42×C61C2411yescharacteristic
178C22⋊Dic61—21no—
179#11758201—22no—
180#11758199—22no—
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187#11758198—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61C22×C411yescharacteristic
190C4⋊Dic61C22×C411yescharacteristic
191#11758196—21no—
192#11758196—21no—
193#11758196—21no—
194C4×Dic61C22×C411yescharacteristic
195C4×Dic61C2×D411yescharacteristic
196C4×Dic61#4111yescharacteristic
197#11758194—42no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205D488—22no—
206#11758189—22no—
207#11758189—22no—
208#11758189—42no—
209#11758189—42no—
210#11758189—42no—
211C8×D61—22no—
212C8×D61—41no—
213C8×D61—42no—
214C8×D61—42no—
215C23×C61—21no—
216C22×D61—21no—
217C22×D61—21no—
218C22×D61C4×D411yescharacteristic
219Q8×C61—21no—
220Q8×C61—21no—
221D4×C61—21no—
222D4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61C23×C411yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61C2×#4111yescharacteristic
231C22⋊D61—42no—
232C22⋊D61—42no—
233C22⋊D61—42no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61C4×D411yescharacteristic
237C2×Dic61C4×D411yescharacteristic
238C2×Dic61C4×D411yescharacteristic
239D244—21no—
240D244—21no—
241D244—21no—
242D244—21no—
243D244—42no—
244D244—42no—
245C4×D61—21no—
246C4×D61—21no—
247C4×D61—21no—
248C4×D61—21no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—41no—
252C4×D61—41no—
253C4×D61—41no—
254Dic122—42no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—41no—
259C8×C61—41no—
260C8×C61—41no—
261C8×C61#13112yescomplemented
262#92418—21no—
263#92418—21no—
264#92418—41no—
265#92418—41no—
266#92418—41no—
267#92418#13112yescomplemented
268#92418AGL(1,ℤ/8)12yes—
269#17966—611nomaximal, Sylow
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61C2×C4×D411yescharacteristic
274C2×D61—21no—
275C2×D61—21no—
276C2×D61—21no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C4×C61—21no—
284C4×C61—41no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61C2×#13111yescharacteristic
288C4×C61C2×#13111yescharacteristic
289C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
290C4×C61#57511yescharacteristic
291Dic61—21no—
292Dic61—21no—
293Dic61—21no—
294Dic61—41no—
295Dic61—41no—
296#3171—611no—
297#2966—611no—
298#2931—611no—
299#1590—611no—
300#1590—611no—
301#1589—611no—
302#1589—611no—
303#1580—611no—
304#1580—611no—
305SD16⋊C8—611no—
306SD16⋊C8D6111yescharacteristic, complemented
307#1569—611no—
308#1496—611no—
309#1495—611no—
310C8×M16—611no—
311C2×C61—81no—
312C2×C61#293111yescharacteristic
313C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
314C2×C61#295511yescharacteristic
315D61—41no—
316D61—81no—
317D61—81no—
318C2×#131—1221no—
319#532—611no—
320#529—611no—
321#501—611no—
322#496—611no—
323#490—611no—
324#489—611no—
325#469—611no—
326#469—611no—
327#468—611no—
328#468—611no—
329#446—611no—
330C8×Q8C2×D6111yescharacteristic
331C4×SD16—611no—
332C4×SD16C2×D6111yescharacteristic
333C4×D8—611no—
334C4×D8—611no—
335#436—611no—
336#436—611no—
337#436—611no—
338#436—1221no—
339#435—1221no—
340C8×D4—611no—
341C8×D4—611no—
342C8×D4—1221no—
343C8×D4—1221no—
344C8×D4C2×D6111yescharacteristic
345#433—1221no—
346#432—611no—
347#431—611no—
348#423—611no—
349#408—1221no—
350#405—1221no—
351C4×M16—611no—
352C2×C4×C8—611no—
353#335—611no—
354#335C2×D6111yescharacteristic
355#334—611no—
356#334—611no—
357Q8⋊C8—611no—
358Q8⋊C8C2×D6111yescharacteristic
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8C2×D6111yescharacteristic
365#322—611no—
366#322C2×D6111yescharacteristic
367C82—611no—
368C82—611no—
369C61#1796611yescharacteristic, complemented, Sylow
370C2×#41—1221no—
371C2×SD16—611no—
372C2×SD16C4×D6111yescharacteristic
373C2×D8—611no—
374C2×D8—611no—
375#131—2444no—
376C2×M16—611no—
377C2×M16—611no—
378C2×M16—1221no—
379C2×M16—1221no—
380C2×M16—1221no—
381C2×M16—1221no—
382C22×C8—21no—
383C22×C8—611no—
384C22×C8—611no—
385C22×C8—1221no—
386C22×C8—1221no—
387C4⋊Q8—611no—
388#127—611no—
389#126—1221no—
390#125—611no—
391#124—611no—
392#124—1221no—
393#123—1221no—
394C22⋊Q8—611no—
395#121—611no—
396#121—611no—
397#121—611no—
398#121—1221no—
399C4×Q8C22×D6111yescharacteristic
400C4×D4—611no—
401C4×D4—611no—
402C4×D4—1221no—
403C4×D4—1221no—
404C4×D4C22×D6111yescharacteristic
405#117—1221no—
406C2×C42—611no—
407#107—611no—
408#107—611no—
409#106—611no—
410#106C4×D6111yescharacteristic
411C4⋊C8—21no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416C4⋊C8—1221no—
417C4⋊C8C22×D6111yescharacteristic
418C4⋊C8C22×D6111yescharacteristic
419#103—611no—
420#103C4×D6111yescharacteristic
421#102—611no—
422#102—611no—
423#102—611no—
424#102—611no—
425#102—611no—
426#102C4×D6111yescharacteristic
427C22⋊C8—21no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435#97—611no—
436#97—611no—
437#97—1221no—
438#97—1221no—
439C4×C8—21no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—611no—
445C4×C8C22×D6111yescharacteristic
446C4×C8C22×D6111yescharacteristic
447C4×C8C22×D6111yescharacteristic
448#41—2442no—
449#41—2442no—
450C2×Q8—1221no—
451C2×Q8C2×C4×D6111yescharacteristic
452C2×D4—611no—
453C2×D4—611no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4C2×C4×D6111yescharacteristic
460C22×C4—21no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—1221no—
465C22×C4—1221no—
466SD16—22no—
467SD16—1222no—
468D8—1222no—
469D8—1222no—
470M16—1222no—
471M16—1222no—
472M16—2442no—
473M16—2442no—
474M16—2442no—
475M16—2442no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—1222no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—2441no—
489C2×C8—2442no—
490C2×C8—2442no—
491C2×C8C2×C4×D6111yescharacteristic
492C2×C8C2×C4×D6111yescharacteristic
493C2×C8D4×D6111yescharacteristic
494C2×C8D4×D6111yescharacteristic
495C4⋊C4—21no—
496C4⋊C4—611no—
497C4⋊C4—611no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4C2×C4×D6111yescharacteristic
503C4⋊C4C2×C4×D6111yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—1221no—
511C22⋊C4—1221no—
512C22⋊C4—1221no—
513C42—21no—
514C42—611no—
515C42—611no—
516C42—611no—
517C42C23×D6111yescharacteristic
518C23—21no—
519C23—611no—
520C23—1221no—
521C23—1221no—
522Q8—21no—
523Q8—21no—
524Q8—2442no—
525D4—21no—
526D4—21no—
527D4—1221no—
528D4—1221no—
529D4—1221no—
530D4—1221no—
531D4—2442no—
532D4—2442no—
533D4—2442no—
534D4—2442no—
535D4—2442no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—611no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
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—41no—
562C8—41no—
563C8—41no—
564C8—612no—
565C8—612no—
566C8—1221no—
567C8—1221no—
568C8—2441no—
569C8—2441no—
570C8—2441no—
571C8#1451978312yescomplemented
572C22—41no—
573C22—41no—
574C22—41no—
575C22—1221no—
576C22—1221no—
577C22—1221no—
578C22—2441no—
579C22—2441no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22C4×D4×D6111yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—1221no—
590C4—1221no—
591C4—1221no—
592C4—2441no—
593C4—2441no—
594C4#131×D6111yescharacteristic
595C4C2×#1451978311yescharacteristic
596C4AGL(1,ℤ/8)×D6111yescharacteristic
597C4#1684056111yescharacteristic
598C2—81no—
599C2—4881no—
600C2—4881no—
601C2—2441no—
602C2#2145452611yescharacteristic
603C2#2145462411yescharacteristic
604C2#2145471911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×SD16⋊C8C2
socleC22×C61C2×C4×D4
prime radical#21456410C2
cosocleC42×C61C24
hypercenterSD16⋊C8D61
hypocenterC61#17966
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
2. #21454796C2semidirect
3. #21454526C2semidirect
4. #21444710C2semidirect
5. #21444706C2semidirect
6. #21444703C2semidirect
7. #21444701C2semidirect
8. #21444644C2semidirect
9. #21444641C2semidirect
10. #21444629C2semidirect
11. #21444585C2semidirect
12. #21444286C2semidirect
13. #21444283C2semidirect
14. #21444098C2semidirect
15. C61×SD16⋊C8C2semidirect
261. C8×C61#131semidirect
267. #92418#131semidirect
306. SD16⋊C8D61semidirect
369. C61#17966semidirect
571. C8#14519783semidirect

Maximal subgroups

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

subgroupindex
#214564102
#214547962
#214545262
#214447102
#214447062
#214447032
#214447012
#214446442
#214446412
#214446292
#214445852
#214442862
#214442832
#214440982
C61×SD16⋊C82
#1796661