Finite Group Databasebeta

← #29651246

Subgroups — #29651246

Order 15616.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455870C211yesmaximal, characteristic
2#21454982C211yesmaximal, characteristic, complemented
3#21454852C211yesmaximal, characteristic, complemented
4#21444732C211yesmaximal, characteristic, complemented
5#21444719C211yesmaximal, characteristic, complemented
6#21444659C211yesmaximal, characteristic, complemented
7#21444650C211yesmaximal, characteristic, complemented
8#21444645C211yesmaximal, characteristic, complemented
9#21444641C211yesmaximal, characteristic, complemented
10SD16⋊#92418C211yesmaximal, characteristic, complemented
11#21444601C211yesmaximal, characteristic, complemented
12#21444278C211yesmaximal, characteristic, complemented
13D4⋊C8×D61C211yesmaximal, characteristic, complemented
14#21444110C211yesmaximal, characteristic, complemented
15C61×#1582C211yesmaximal, characteristic, complemented
16#16840299C2211yescharacteristic
17C4×D4×D61C2211yescharacteristic
18#16840096C411yescharacteristic
19#16840082C411yescharacteristic
20#16840061C411yescharacteristic
21#16840060C411yescharacteristic
22#16839980C411yescharacteristic
23#16839979C411yescharacteristic
24#16839911C411yescharacteristic
25#16839897C411yescharacteristic
26Q8×#92418C2211yescharacteristic, complemented
27C4×#11758201C2211yescharacteristic
28C4×D488C2211yescharacteristic
29C4×#11758199C2211yescharacteristic
30#16839841C2211yescharacteristic
31#16839839C2211yescharacteristic
32#16839839C2211yescharacteristic, complemented
33#16839835—21no—
34#16839833—21no—
35#16839830—21no—
36C8×D244C2211yescharacteristic, complemented
37D4×#92418C2211yescharacteristic
38#16839827—21no—
39#16839824—21no—
40#16839818C2211yescharacteristic
41#16839813C2211yescharacteristic
42#16839813C2211yescharacteristic
43#16839787—21no—
44C4⋊C8×D61C2211yescharacteristic
45#16839724—21no—
46C2×#14519689—21no—
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic, complemented
49#16839514C2211yescharacteristic, complemented
50#16839512C2211yescharacteristic, complemented
51Q8⋊#92418C2211yescharacteristic, complemented
52#16839491C2211yescharacteristic
53#16839491C2211yescharacteristic, complemented
54D4⋊#92418C2211yescharacteristic
55#16839489C2211yescharacteristic
56#16839489C2211yescharacteristic, complemented
57#16839484C2211yescharacteristic, complemented
58#16839484C2211yescharacteristic, complemented
59#16839483C2211yescharacteristic, complemented
60C61×#446C2211yescharacteristic, complemented
61C4×SD16×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#334C2211yescharacteristic, complemented
64C61×Q8⋊C8C2211yescharacteristic, complemented
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic, complemented
67C2×D4×D61C2×C411yescharacteristic
68C22×C4×D61—21no—
69C2×#11758201C2×C411yescharacteristic
70C2×D488C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C2×#11758189—21no—
73C2×#11758189—21no—
74C2×#11758189—21no—
75C22×#92418—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C2×C8×D61—21no—
79#14519772—21no—
80#14519768C2×C411yescharacteristic
81#14519766C2×C411yescharacteristic
82#14519762—21no—
83#14519753C2×C411yescharacteristic
84#14519752C2×C411yescharacteristic
85C4×D244—21no—
86C4×D244C2311yescharacteristic
87C4×D244C2311yescharacteristic
88D4×Dic61C2×C411yescharacteristic
89#14519739C2×C411yescharacteristic
90C4×C22⋊D61—21no—
91#14519737—21no—
92#14519734—21no—
93C4⋊C4×D61C2×C411yescharacteristic
94C22⋊C4×D61—21no—
95C42×D61C2311yescharacteristic
96#14519711C2×C411yescharacteristic
97#14519710C2×C411yescharacteristic
98#14519708C2×C411yescharacteristic
99C4⋊#92418—21no—
100C4⋊#92418C2311yescharacteristic
101C4⋊#92418C2311yescharacteristic
102#14519706—21no—
103#14519706C2×C411yescharacteristic
104#14519706C2×C411yescharacteristic
105#14519706D411yescharacteristic
106#14519706D411yescharacteristic
107#14519701C2×C411yescharacteristic
108#14519699C2×C411yescharacteristic
109#14519699C2×C411yescharacteristic
110#14519698C2×C411yescharacteristic
111#14519697C2×C411yescharacteristic
112#14519697C2×C411yescharacteristic
113C22⋊#92418—21no—
114#14519689—21no—
115#14519689—21no—
116#14519689—21no—
117#14519689—21no—
118#14519689—21no—
119#14519689C2×C411yescharacteristic
120#14519689C2×C411yescharacteristic
121#14519689D411yescharacteristic
122#14519689D411yescharacteristic
123#14519687—21no—
124C4×#92418—21no—
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C4×#92418C2311yescharacteristic
128C8×Dic61—21no—
129C2×SD16×C61C2×C411yescharacteristic
130C22×C8×C61—21no—
131C4×Q8×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133#106×C61C2×C411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61C2×C411yescharacteristic
138#102×C61C2×C411yescharacteristic
139C22⋊C8×C61—21no—
140#97×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C23×D61—21no—
145C2×Q8×C61C22×C411yescharacteristic
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149C22×Dic61—21no—
150D4×D61—22no—
151D4×D61—41no—
152C2×D244—21no—
153C2×D244C22×C411yescharacteristic
154C2×D244C22×C411yescharacteristic
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—81no—
160C2×C4×D61—81no—
161C2×C4×D61C22×C411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61#4111yescharacteristic
164SD16×C61—22no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—81no—
169C2×C8×C61C22×C411yescharacteristic
170C2×C8×C61C22×C411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C4⋊C4×C61—21no—
174C4⋊C4×C61C22×C411yescharacteristic
175C4⋊C4×C61C22×C411yescharacteristic
176C22⋊C4×C61—21no—
177C42×C61—21no—
178C42×C61C2411yescharacteristic
179C22⋊Dic61—21no—
180#11758201—41no—
181#11758199—22no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187#11758198—21no—
188#11758198—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61C22×C411yescharacteristic
191C4⋊Dic61C22×C411yescharacteristic
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195C4×Dic61C22×C411yescharacteristic
196C4×Dic61C2×D411yescharacteristic
197C4×Dic61#4111yescharacteristic
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—81no—
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206D488—41no—
207#11758189—81no—
208#11758189—81no—
209#11758189—81no—
210C8×D61—42no—
211C8×D61—81no—
212C8×D61—81no—
213C23×C61—21no—
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61—81no—
219C22×D61C4×D411yescharacteristic
220Q8×C61—21no—
221Q8×C61—21no—
222D4×C61—21no—
223D4×C61#13112yes—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61C23×C411yescharacteristic
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61C2×#4111yescharacteristic
232C22⋊D61—42no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—81no—
236C2×Dic61C4×D411yescharacteristic
237C2×Dic61C4×D411yescharacteristic
238C2×Dic61C4×D411yescharacteristic
239D244—21no—
240D244—21no—
241D244—21no—
242D244—21no—
243D244—42no—
244C4×D61—22no—
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—81no—
254C4×D61—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#18020—611nomaximal, Sylow
270C22×C61—22no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61C2×C4×D411yescharacteristic
274C2×D61—21no—
275C2×D61—21no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—84no—
283C2×D61#44412yes—
284C4×C61—21no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61—41no—
288C4×C61C2×#13111yescharacteristic
289C4×C61#56811yescharacteristic
290C4×C61#57611yescharacteristic
291C4×C61#57711yescharacteristic
292Dic61—21no—
293Dic61—21no—
294Dic61—21no—
295Dic61—41no—
296Dic61—41no—
297#3105—611no—
298#2994—611no—
299#2974—611no—
300#1594—611no—
301#1592—611no—
302#1583—611no—
303#1582D6111yescharacteristic, complemented
304#1581—611no—
305#1581—611no—
306#1580—611no—
307SD16⋊C8—611no—
308#1573—611no—
309#1494—611no—
310C2×D4⋊C8—611no—
311#1452—611no—
312C2×C61—42no—
313C2×C61#293311yescharacteristic
314C2×C61#294611yescharacteristic
315C2×C61C2×#44411yescharacteristic
316D61—22no—
317D61—81no—
318D61—81no—
319#529—611no—
320C2×C4×D4—611no—
321#484—611no—
322#481—611no—
323#478—611no—
324#478—611no—
325#463—611no—
326#463—611no—
327#450—611no—
328#447—611no—
329#446C2×D6111yescharacteristic, complemented
330C8×Q8—611no—
331C4×SD16—611no—
332C4×SD16C2×D6111yescharacteristic
333C4×D8—611no—
334C4×D8—611no—
335#436—611no—
336#436—611no—
337#436—611no—
338#435—1221no—
339#435—1221no—
340#435—1221no—
341C8×D4—611no—
342C8×D4—611no—
343C8×D4—1221no—
344C8×D4C2×D6111yescharacteristic
345#433—1221no—
346#432—611no—
347#431—611no—
348#431—611no—
349#424—1221no—
350C2×C4⋊C8—611no—
351#407—1221no—
352C2×C22⋊C8—1221no—
353C2×C4×C8—611no—
354#335—611no—
355#335—611no—
356#334—611no—
357#334C2×D6111yescharacteristic, complemented
358Q8⋊C8—611no—
359Q8⋊C8C2×D6111yescharacteristic, complemented
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365D4⋊C8C2×D6111yescharacteristic
366#322—611no—
367#322—611no—
368#322—611no—
369#322C2×D6111yescharacteristic, complemented
370C61#1802011yescharacteristic, complemented, Sylow
371C22×D4—611no—
372C23×C4—1221no—
373C2×SD16—611no—
374C2×SD16C4×D6111yescharacteristic
375C2×D8—611no—
376C2×D8—611no—
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C22×C8—21no—
381C22×C8—1221no—
382C22×C8—1221no—
383C22×C8—1221no—
384C22×C8—1221no—
385#126—1221no—
386#125—611no—
387#124—611no—
388#123—1221no—
389C22⋊Q8—611no—
390#121—611no—
391C4×Q8C22×D6111yescharacteristic
392C4×D4—611no—
393C4×D4—611no—
394C4×D4—611no—
395C4×D4—611no—
396C4×D4—1221no—
397C4×D4—1221no—
398C4×D4—1221no—
399C4×D4C22×D6111yescharacteristic
400#117—1221no—
401C2×C4⋊C4—611no—
402C2×C22⋊C4—1221no—
403C2×C42—611no—
404#107—611no—
405#107—611no—
406#106—611no—
407#106C4×D6111yescharacteristic
408C4⋊C8—21no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
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—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—
437C22⋊C8—1221no—
438#97—21no—
439#97—1221no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—1221no—
444C4×C8—1221no—
445C4×C8C22×D6111yescharacteristic
446C4×C8C22×D6111yescharacteristic
447C4×C8C22×D6111yescharacteristic
448C24—1221no—
449C2×Q8C2×C4×D6111yescharacteristic
450C2×D4—611no—
451C2×D4—611no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4—1222no—
455C2×D4—2441no—
456C2×D4C2×C4×D6111yescharacteristic
457C22×C4—21no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—4881no—
467C22×C4—4881no—
468SD16—22no—
469SD16—2441no—
470D8—1222no—
471D8—2441no—
472M16—4881no—
473M16—4881no—
474M16—4881no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—81no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—4881no—
487C2×C8—4881no—
488C2×C8—4881no—
489C2×C8—2442no—
490C2×C8C2×C4×D6111yescharacteristic
491C2×C8C2×C4×D6111yescharacteristic
492C2×C8D4×D6111yescharacteristic
493C2×C8D4×D6111yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—611no—
496C4⋊C4—611no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4C2×C4×D6111yescharacteristic
502C4⋊C4C2×C4×D6111yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—1221no—
511C22⋊C4—1221no—
512C42—21no—
513C42—611no—
514C42—611no—
515C42—611no—
516C42C23×D6111yescharacteristic
517C23—21no—
518C23—611no—
519C23—1221no—
520C23—1221no—
521C23—4881no—
522C23—2442no—
523C23—2442no—
524Q8—21no—
525Q8—21no—
526D4—21no—
527D4—1221no—
528D4—1221no—
529D4—1221no—
530D4—1221no—
531D4—2442no—
532D4—2442no—
533D4#1451978512yes—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—611no—
540C2×C4—611no—
541C2×C4—611no—
542C2×C4—1222no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—4881no—
550C2×C4—4881no—
551C2×C4—4881no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4C22×C4×D6111yescharacteristic
557C2×C4C2×D4×D6111yescharacteristic
558C2×C4#41×D6111yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—1221no—
567C8—1221no—
568C8—1221no—
569C8—1221no—
570C8—2441no—
571C8—2441no—
572C8—2441no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—612no—
577C22—1221no—
578C22—1221no—
579C22—4884no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22—2441no—
585C22—2441no—
586C22C4×D4×D6111yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—1221no—
592C4—1221no—
593C4—1221no—
594C4—2441no—
595C4—2441no—
596C4C2×#1451978511yescharacteristic
597C4#1684052711yescharacteristic
598C4#1684056411yescharacteristic
599C4#1684056811yescharacteristic
600C2—42no—
601C2—1222no—
602C2—4881no—
603C2—4881no—
604C2#2145454511yescharacteristic
605C2#2145464611yescharacteristic
606C2#444×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1582C2
socleC22×C61C2×C4×D4
prime radical#16839897C4
cosocleC42×C61C24
hypercenter#1582D61
hypocenterC61#18020
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
2. #21454982C2semidirect
3. #21454852C2semidirect
4. #21444732C2semidirect
5. #21444719C2semidirect
6. #21444659C2semidirect
7. #21444650C2semidirect
8. #21444645C2semidirect
9. #21444641C2semidirect
10. SD16⋊#92418C2semidirect
11. #21444601C2semidirect
12. #21444278C2semidirect
13. D4⋊C8×D61C2semidirect
14. #21444110C2semidirect
15. C61×#1582C2semidirect
26. Q8×#92418C22semidirect
32. #16839839C22semidirect
36. C8×D244C22semidirect
48. #16839515C22semidirect
49. #16839514C22semidirect
50. #16839512C22semidirect
51. Q8⋊#92418C22semidirect
53. #16839491C22semidirect
56. #16839489C22semidirect
57. #16839484C22semidirect
58. #16839484C22semidirect
59. #16839483C22semidirect
60. C61×#446C22semidirect
63. C61×#334C22semidirect
64. C61×Q8⋊C8C22semidirect
66. C61×#322C22semidirect
303. #1582D61semidirect
329. #446C2×D61semidirect
357. #334C2×D61semidirect
359. Q8⋊C8C2×D61semidirect
369. #322C2×D61semidirect
370. C61#18020semidirect

Maximal subgroups

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

subgroupindex
#214558702
#214549822
#214548522
#214447322
#214447192
#214446592
#214446502
#214446452
#214446412
SD16⋊#924182
#214446012
#214442782
D4⋊C8×D612
#214441102
C61×#15822
#1802061