Finite Group Databasebeta

← #29650101

Subgroups — #29650101

Order 15616.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455880C211yesmaximal, characteristic
2#21454928C211yesmaximal, characteristic, complemented
3#21454897C211yesmaximal, characteristic, complemented
4#21444696C211yesmaximal, characteristic, complemented
5#21444682C211yesmaximal, characteristic, complemented
6#21444661C211yesmaximal, characteristic, complemented
7#21444647C211yesmaximal, characteristic, complemented
8#21444642C211yesmaximal, characteristic, complemented
9#21444630C211yesmaximal, characteristic, complemented
10#21444618C211yesmaximal, characteristic, complemented
11#21444613C211yesmaximal, characteristic, complemented
12#21444251C211yesmaximal, characteristic, complemented
13#21444217C211yesmaximal, characteristic, complemented
14#21444119C211yesmaximal, characteristic, complemented
15C61×#1573C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17C4×#11758222C2211yescharacteristic
18#16840087C411yescharacteristic
19#16840087C411yescharacteristic
20#16840058C411yescharacteristic
21#16840053C411yescharacteristic
22#16839963C411yescharacteristic
23#16839958C411yescharacteristic
24#16839909C411yescharacteristic
25#16839909C411yescharacteristic
26#16839886C2211yescharacteristic
27#16839886C2211yescharacteristic
28C4×#11758190C2211yescharacteristic
29C4×#11758190C2211yescharacteristic
30C4×D488C2211yescharacteristic
31C4×D488C2211yescharacteristic
32#16839839C2211yescharacteristic
33#16839839C2211yescharacteristic
34#16839835—21no—
35#16839835—21no—
36#16839827C2211yescharacteristic
37#16839827C2211yescharacteristic
38#16839827C2211yescharacteristic
39#16839827C2211yescharacteristic
40C8×C22⋊D61—21no—
41C8×C22⋊D61—21no—
42#16839815C2211yescharacteristic
43#16839815C2211yescharacteristic
44#16839814—21no—
45C4⋊C8×D61—21no—
46#16839727—21no—
47#16839727—21no—
48#16839492C2211yescharacteristic
49#16839492C2211yescharacteristic
50#16839489C2211yescharacteristic
51#16839489C2211yescharacteristic
52#16839489C2211yescharacteristic
53#16839489C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839489C2211yescharacteristic
56#16839484C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839483C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#432C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#334C2211yescharacteristic
66C61×#334C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758222C2×C411yescharacteristic
69C2×#11758190C2×C411yescharacteristic
70C2×#11758190C2×C411yescharacteristic
71C2×D488C2×C411yescharacteristic
72C2×D488C2×C411yescharacteristic
73C2×#11758189—21no—
74C2×#11758189—21no—
75C2×C8×D61—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C2×C8×D61—21no—
79#14519777C2×C411yescharacteristic
80#14519774C2×C411yescharacteristic
81#14519765—21no—
82#14519751—21no—
83#14519751C2×C411yescharacteristic
84#14519751C2×C411yescharacteristic
85C4×Dic122C2×C411yescharacteristic
86C4×Dic122C2311yescharacteristic
87C4×D244—21no—
88C4×D244C2×C411yescharacteristic
89C4×D244C2311yescharacteristic
90C4×D244C2311yescharacteristic
91C4×D244C2311yescharacteristic
92C4×C22⋊D61—21no—
93C4×C22⋊D61—21no—
94#14519736C2×C411yescharacteristic
95#14519734—21no—
96C42×D61—21no—
97#14519711C2×C411yescharacteristic
98#14519711C2×C411yescharacteristic
99#14519709C2×C411yescharacteristic
100#14519709C2×C411yescharacteristic
101C4⋊#92418—21no—
102C4⋊#92418D411yescharacteristic
103C4⋊#92418D411yescharacteristic
104#14519706—21no—
105#14519706—21no—
106#14519702C2×C411yescharacteristic
107#14519702C2×C411yescharacteristic
108#14519699C2×C411yescharacteristic
109#14519699C2×C411yescharacteristic
110#14519699C2×C411yescharacteristic
111#14519699C2×C411yescharacteristic
112#14519699C2×C411yescharacteristic
113#14519699C2×C411yescharacteristic
114C22⋊#92418—21no—
115C22⋊#92418D411yescharacteristic
116C22⋊#92418D411yescharacteristic
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689—21no—
121#14519689—21no—
122#14519689—21no—
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C8×Dic61—21no—
128C8×Dic61—21no—
129C22×C8×C61—21no—
130C2×C42×C61C2311yescharacteristic
131C4⋊C8×C61—21no—
132C4⋊C8×C61C2×C411yescharacteristic
133C4⋊C8×C61C2×C411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C22⋊C8×C61—21no—
139C22⋊C8×C61C2×C411yescharacteristic
140C22⋊C8×C61C2×C411yescharacteristic
141#97×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C2×C22⋊D61—21no—
148C2×C22⋊D61—21no—
149C2×C22⋊D61—21no—
150#11758222—22no—
151#11758222—22no—
152#11758222—81no—
153#11758222—81no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244C22×C411yescharacteristic
157C2×D244C22×C411yescharacteristic
158C2×D244C22×C411yescharacteristic
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×Dic122—21no—
165C2×Dic122C22×C411yescharacteristic
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—81no—
171C2×C8×C61C22×C411yescharacteristic
172C2×C8×C61C22×C411yescharacteristic
173C2×C8×C61C22×C411yescharacteristic
174C2×C8×C61C22×C411yescharacteristic
175C42×C61C22×C411yescharacteristic
176C42×C61C2×D411yescharacteristic
177C42×C61#4111yescharacteristic
178C42×C61C2411yescharacteristic
179C22⋊Dic61—21no—
180#11758198—21no—
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61C22×C411yescharacteristic
188C4⋊Dic61C22×C411yescharacteristic
189C4⋊Dic61C22×C411yescharacteristic
190C4⋊Dic61C22×C411yescharacteristic
191#11758196—21no—
192#11758196—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418C2×D411yescharacteristic
199C2×#92418C2×D411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202D488—22no—
203D488—22no—
204#11758190—22no—
205#11758190—22no—
206#11758189—81no—
207#11758189—81no—
208C8×D61—81no—
209C8×D61—81no—
210C8×D61—81no—
211C8×D61—81no—
212C23×C61C4×D411yescharacteristic
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—41no—
221C2×C4×C61C4×D411yescharacteristic
222C2×C4×C61C4×D411yescharacteristic
223C2×C4×C61C4×D411yescharacteristic
224C2×C4×C61C23×C411yescharacteristic
225C2×C4×C61C22×D411yescharacteristic
226C2×C4×C61C2×#4111yescharacteristic
227C22⋊D61—24no—
228C22⋊D61—81no—
229C22⋊D61—81no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235D244—21no—
236D244—21no—
237D244—21no—
238D244—21no—
239D244—21no—
240D244—81no—
241D244—81no—
242D244#13112yes—
243C4×D61—24no—
244C4×D61—41no—
245C4×D61—41no—
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—81no—
251Dic122—21no—
252Dic122—81no—
253Dic122#13112yes—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—41no—
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#17920—611nomaximal, Sylow
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—21no—
272C22×C61C2×C4×D411yescharacteristic
273C2×D61—22no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C4×C61—21no—
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61C2×#13111yescharacteristic
287C4×C61C2×#13111yescharacteristic
288C4×C61#57611yescharacteristic
289C4×C61#57711yescharacteristic
290Dic61—22no—
291Dic61—41no—
292Dic61—41no—
293Dic61—41no—
294Dic61—41no—
295#3106—611no—
296#2988—611no—
297#2981—611no—
298#1588—611no—
299#1586—611no—
300#1583—611no—
301#1581—611no—
302#1580—611no—
303SD16⋊C8—611no—
304C8×SD16—611no—
305C8×D8—611no—
306#1573D6111yescharacteristic, complemented
307#1488—611no—
308#1480—611no—
309#1454—611no—
310C2×C61—41no—
311C2×C61#292911yescharacteristic
312C2×C61#294611yescharacteristic
313C2×C61#295711yescharacteristic
314D61—42no—
315D61—81no—
316D61—81no—
317#532—611no—
318C4×#41—611no—
319#482—611no—
320#482—611no—
321#477—611no—
322#476—611no—
323#460—611no—
324#459—611no—
325#449—611no—
326#449—611no—
327C8×Q8—611no—
328C8×Q8—611no—
329C4×SD16—611no—
330C4×SD16—611no—
331C4×D8—611no—
332C4×D8—611no—
333#436—611no—
334#436—611no—
335#435—1221no—
336#435—1221no—
337C8×D4—611no—
338C8×D4—611no—
339C8×D4—611no—
340C8×D4—611no—
341C8×D4—1221no—
342C8×D4—1221no—
343#432C2×D6111yescharacteristic
344#431—611no—
345#431—611no—
346#431—1221no—
347#431C2×D6111yescharacteristic
348C2×C4⋊C8—1221no—
349C2×C4⋊C8C2×D6111yescharacteristic
350#408—1221no—
351#408—1221no—
352#335C2×D6111yescharacteristic
353#335C2×D6111yescharacteristic
354#334C2×D6111yescharacteristic
355#334C2×D6111yescharacteristic
356Q8⋊C8—611no—
357Q8⋊C8—611no—
358D4⋊C8—611no—
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364#322—611no—
365#322—611no—
366#322—611no—
367C82—611no—
368C61#1792011yescharacteristic, complemented, Sylow
369C2×#41—611no—
370C2×#41—1221no—
371C2×SD16—611no—
372C2×SD16—611no—
373C2×D8—611no—
374C2×D8—611no—
375C2×M16—1221no—
376C2×M16—1221no—
377C22×C8—21no—
378C22×C8—1221no—
379C22×C8—1221no—
380C22×C8—1221no—
381C22×C8—1221no—
382C4⋊Q8—611no—
383#127—611no—
384#124—1221no—
385#121—611no—
386#121—611no—
387#121—1221no—
388C4×Q8—611no—
389C4×Q8—611no—
390C4×D4—611no—
391C4×D4—611no—
392C4×D4—611no—
393C4×D4—611no—
394C4×D4—1221no—
395C4×D4—1221no—
396C4×D4—1221no—
397#117—611no—
398#117—1221no—
399C2×C42—1221no—
400C2×C42C22×D6111yescharacteristic
401#107—611no—
402#107—611no—
403#106—611no—
404#106—611no—
405C4⋊C8—21no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—1221no—
409C4⋊C8—1221no—
410C4⋊C8—1221no—
411C4⋊C8C4×D6111yescharacteristic
412C4⋊C8C4×D6111yescharacteristic
413C4⋊C8C22×D6111yescharacteristic
414C4⋊C8C22×D6111yescharacteristic
415C4⋊C8C22×D6111yescharacteristic
416C4⋊C8C22×D6111yescharacteristic
417#103—611no—
418#103—611no—
419#102—611no—
420#102—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424#102—611no—
425C22⋊C8—21no—
426C22⋊C8—611no—
427C22⋊C8—611no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8C4×D6111yescharacteristic
436C22⋊C8C4×D6111yescharacteristic
437#97—21no—
438C4×C8—611no—
439C4×C8—611no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—1221no—
443C4×C8—1221no—
444C4×C8C22×D6111yescharacteristic
445C4×C8C22×D6111yescharacteristic
446#41—1222no—
447#41—1222no—
448#41—4881no—
449#41—4881no—
450C2×Q8—611no—
451C2×Q8—1221no—
452C2×D4—611no—
453C2×D4—611no—
454C2×D4—611no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4C2×C4×D6111yescharacteristic
466C22×C4D4×D6111yescharacteristic
467C22×C4#1175822611yescharacteristic
468SD16—1222no—
469SD16—1222no—
470D8—1222no—
471D8—1222no—
472M16—4881no—
473M16—4881no—
474C2×C8—21no—
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—4881no—
486C2×C8—4881no—
487C2×C8—4881no—
488C2×C8—4881no—
489C2×C8C2×C4×D6111yescharacteristic
490C2×C8C2×C4×D6111yescharacteristic
491C2×C8C2×C4×D6111yescharacteristic
492C2×C8C2×C4×D6111yescharacteristic
493C4⋊C4—611no—
494C4⋊C4—611no—
495C4⋊C4—611no—
496C4⋊C4—611no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C22⋊C4—1221no—
501C22⋊C4—1221no—
502C22⋊C4—1221no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C42—1221no—
508C42—1221no—
509C42—1221no—
510C42C2×C4×D6111yescharacteristic
511C42D4×D6111yescharacteristic
512C42#1175822611yescharacteristic
513C42C23×D6111yescharacteristic
514C23—1221no—
515C23—1221no—
516C23—1221no—
517C23#1451973911yescharacteristic
518Q8—612no—
519Q8—1221no—
520Q8—4881no—
521D4—612no—
522D4—1224no—
523D4—1221no—
524D4—1221no—
525D4—1221no—
526D4—1221no—
527D4—1221no—
528D4—4881no—
529D4—4881no—
530D4—4881no—
531D4—4881no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—1224no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—4881no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4#1451973911yescharacteristic
551C2×C4#1451973911yescharacteristic
552C2×C4#1451973911yescharacteristic
553C2×C4C22×C4×D6111yescharacteristic
554C2×C4C2×D4×D6111yescharacteristic
555C2×C4C2×#1175822611yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—1221no—
565C8—1221no—
566C8—1221no—
567C8—1221no—
568C8—2441no—
569C8—2441no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—1222no—
574C22—2441no—
575C22—2441no—
576C22—2441no—
577C22—2441no—
578C22—2441no—
579C22—2441no—
580C22—2441no—
581C22—2441no—
582C22C2×#1451973911yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—1222no—
588C4—2441no—
589C4—2441no—
590C4—2441no—
591C4—2441no—
592C4#131×D6111yescharacteristic
593C4#131×D6111yescharacteristic
594C4#1684056611yescharacteristic
595C4#1684057111yescharacteristic
596C2—41no—
597C2—4881no—
598C2—4881no—
599C2—2442no—
600C2#2145451211yescharacteristic
601C2#2145464911yescharacteristic
602C2#2145473511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1573C2
socleC22×C61C2×C4×D4
prime radical#21455880C2
cosocleC42×C61C24
hypercenter#1573D61
hypocenterC61#17920
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
2. #21454928C2semidirect
3. #21454897C2semidirect
4. #21444696C2semidirect
5. #21444682C2semidirect
6. #21444661C2semidirect
7. #21444647C2semidirect
8. #21444642C2semidirect
9. #21444630C2semidirect
10. #21444618C2semidirect
11. #21444613C2semidirect
12. #21444251C2semidirect
13. #21444217C2semidirect
14. #21444119C2semidirect
15. C61×#1573C2semidirect
306. #1573D61semidirect
368. C61#17920semidirect

Maximal subgroups

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

subgroupindex
#214558802
#214549282
#214548972
#214446962
#214446822
#214446612
#214446472
#214446422
#214446302
#214446182
#214446132
#214442512
#214442172
#214441192
C61×#15732
#1792061