Finite Group Databasebeta

← #29650099

Subgroups — #29650099

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#21455873C211yesmaximal, characteristic
2#21454927C211yesmaximal, characteristic, complemented
3#21444695C211yesmaximal, characteristic, complemented
4#21444681C211yesmaximal, characteristic, complemented
5#21444660C211yesmaximal, characteristic, complemented
6#21444646C211yesmaximal, characteristic, complemented
7#21444641C211yesmaximal, characteristic, complemented
8#21444631C211yesmaximal, characteristic, complemented
9C8×#11758200C211yesmaximal, characteristic, complemented
10C8×#11758199C211yesmaximal, characteristic, complemented
11#21444605C211yesmaximal, characteristic, complemented
12#21444251C211yesmaximal, characteristic, complemented
13#21444218C211yesmaximal, characteristic, complemented
14#21444119C211yesmaximal, characteristic, complemented
15C61×#2981C211yesmaximal, characteristic, complemented
16C4×#11758222C2211yescharacteristic
17#16840083C411yescharacteristic
18#16840083C411yescharacteristic
19#16840054C411yescharacteristic
20#16840049C411yescharacteristic
21#16839959C411yescharacteristic
22#16839954C411yescharacteristic
23#16839905C411yescharacteristic
24#16839905C411yescharacteristic
25C8×Dic122C2211yescharacteristic
26C8×Dic122C2211yescharacteristic
27C4×#11758200C2211yescharacteristic
28C4×#11758200C2211yescharacteristic
29C4×#11758199C2211yescharacteristic
30C4×#11758199C2211yescharacteristic
31C8×D244C2211yescharacteristic
32C8×D244C2211yescharacteristic
33#16839825—21no—
34#16839825—21no—
35#16839815C2211yescharacteristic
36#16839815C2211yescharacteristic
37#16839814—21no—
38C2×C4⋊#92418C2211yescharacteristic
39C4⋊C8×D61—21no—
40#16839514C2211yescharacteristic
41#16839514C2211yescharacteristic
42#16839512C2211yescharacteristic
43#16839512C2211yescharacteristic
44#16839492C2211yescharacteristic
45#16839492C2211yescharacteristic
46D4⋊#92418C2211yescharacteristic
47D4⋊#92418C2211yescharacteristic
48D4⋊#92418C2211yescharacteristic
49D4⋊#92418C2211yescharacteristic
50#16839489C2211yescharacteristic
51#16839489C2211yescharacteristic
52#16839484C2211yescharacteristic
53#16839484C2211yescharacteristic
54#16839483C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#532C2211yescharacteristic
57C61×#436C2211yescharacteristic
58C61×#436C2211yescharacteristic
59C61×#435—21no—
60C61×#435—21no—
61C8×D4×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#432C2211yescharacteristic
64C61×#431C2211yescharacteristic
65C61×#408—21no—
66C61×#408—21no—
67C2×#11758222C2×C411yescharacteristic
68C2×#11758200C2×C411yescharacteristic
69C2×#11758200C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C22×#92418—21no—
73C2×C8×D61—21no—
74C2×C8×D61—21no—
75C4×Dic122C2×C411yescharacteristic
76C4×Dic122C2311yescharacteristic
77C4×D244C2×C411yescharacteristic
78C4×D244C2311yescharacteristic
79C4×C22⋊D61—21no—
80C4×C22⋊D61—21no—
81#14519736C2×C411yescharacteristic
82#14519734—21no—
83C42×D61—21no—
84#14519710C2×C411yescharacteristic
85#14519710C2×C411yescharacteristic
86#14519708C2×C411yescharacteristic
87#14519708C2×C411yescharacteristic
88C4⋊#92418—21no—
89C4⋊#92418—21no—
90C4⋊#92418C2×C411yescharacteristic
91C4⋊#92418C2×C411yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94#14519706—21no—
95#14519706—21no—
96#14519700C2×C411yescharacteristic
97#14519700C2×C411yescharacteristic
98#14519698C2×C411yescharacteristic
99#14519698C2×C411yescharacteristic
100#14519698C2×C411yescharacteristic
101#14519698C2×C411yescharacteristic
102#14519697C2×C411yescharacteristic
103#14519697C2×C411yescharacteristic
104C22⋊#92418—21no—
105C22⋊#92418C2×C411yescharacteristic
106C22⋊#92418C2×C411yescharacteristic
107#14519689—21no—
108#14519689—21no—
109C4×#92418C2311yescharacteristic
110C4×#92418C2311yescharacteristic
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C8×Dic61—21no—
114C8×Dic61—21no—
115C2×#41×C61—21no—
116C2×M16×C61—21no—
117C2×M16×C61—21no—
118C22×C8×C61—21no—
119C22×C8×C61—21no—
120C4⋊Q8×C61C2×C411yescharacteristic
121#127×C61C2×C411yescharacteristic
122#124×C61—21no—
123#121×C61—21no—
124#121×C61C2×C411yescharacteristic
125#121×C61C2×C411yescharacteristic
126C4×D4×C61—21no—
127C4×D4×C61C2311yescharacteristic
128C4×D4×C61C2311yescharacteristic
129C2×C42×C61C2311yescharacteristic
130C4⋊C8×C61D411yescharacteristic
131C4⋊C8×C61D411yescharacteristic
132C4⋊C8×C61C2311yescharacteristic
133C4⋊C8×C61C2311yescharacteristic
134C22⋊C8×C61—21no—
135C22⋊C8×C61—21no—
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61—21no—
139C22⋊C8×C61D411yescharacteristic
140C22⋊C8×C61D411yescharacteristic
141#97×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—81no—
145#41×C61—81no—
146C2×Q8×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61C22×C411yescharacteristic
152C2×D4×C61C22×C411yescharacteristic
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61#4111yescharacteristic
158C2×C22⋊D61—21no—
159#11758222—22no—
160#11758222—22no—
161C2×D244C22×C411yescharacteristic
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×Dic122C22×C411yescharacteristic
166M16×C61—81no—
167M16×C61—81no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—81no—
171C2×C8×C61—81no—
172C2×C8×C61C2×D411yescharacteristic
173C2×C8×C61C2×D411yescharacteristic
174C2×C8×C61C2×D411yescharacteristic
175C2×C8×C61C2×D411yescharacteristic
176C4⋊C4×C61—21no—
177C4⋊C4×C61C22×C411yescharacteristic
178C4⋊C4×C61C22×C411yescharacteristic
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C42×C61C22×C411yescharacteristic
184C42×C61C2×D411yescharacteristic
185C42×C61#4111yescharacteristic
186C42×C61C2411yescharacteristic
187C22⋊Dic61—21no—
188#11758200—22no—
189#11758200—22no—
190#11758199—22no—
191#11758199—22no—
192#11758198—21no—
193#11758198—21no—
194C4⋊Dic61C22×C411yescharacteristic
195C4⋊Dic61C22×C411yescharacteristic
196#11758196—21no—
197#11758196—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—81no—
206C2×#92418C22×C411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208C2×#92418C22×C411yescharacteristic
209C2×#92418C22×C411yescharacteristic
210C8×D61—81no—
211C8×D61—81no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61C4×D411yescharacteristic
215C22×D61—21no—
216Q8×C61—81no—
217D4×C61—21no—
218D4×C61—21no—
219D4×C61—21no—
220D4×C61—21no—
221D4×C61—81no—
222D4×C61—81no—
223D4×C61—81no—
224D4×C61—81no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61C4×D411yescharacteristic
238C2×C4×C61C4×D411yescharacteristic
239C2×C4×C61C23×C411yescharacteristic
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C22⋊D61—24no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246D244—21no—
247D244#13112yes—
248C4×D61—24no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—81no—
252Dic122—21no—
253Dic122#13112yes—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—41no—
259C8×C61—41no—
260#92418—21no—
261#92418—21no—
262#92418—21no—
263#92418—21no—
264#92418—41no—
265#92418—41no—
266#92418—41no—
267#92418—41no—
268#17920—611nomaximal, Sylow
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61C2×C4×D411yescharacteristic
279C2×D61—22no—
280C2×D61—41no—
281C2×D61—41no—
282C4×C61—21no—
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—41no—
287C4×C61—41no—
288C4×C61C2×#13111yescharacteristic
289C4×C61C2×#13111yescharacteristic
290C4×C61#57611yescharacteristic
291C4×C61#57711yescharacteristic
292Dic61—22no—
293Dic61—41no—
294Dic61—41no—
295#3106—611no—
296#2988—611no—
297#2981D6111yescharacteristic, complemented
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#1573—611no—
307#1488—611no—
308#1480—611no—
309#1454—611no—
310C2×C61—41no—
311C2×C61—81no—
312C2×C61—81no—
313C2×C61#292911yescharacteristic
314C2×C61#294611yescharacteristic
315C2×C61#295711yescharacteristic
316D61—42no—
317#532C2×D6111yescharacteristic
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#436C2×D6111yescharacteristic
334#436C2×D6111yescharacteristic
335#435—21no—
336#435—21no—
337C8×D4—611no—
338C8×D4—611no—
339C8×D4—1221no—
340C8×D4—1221no—
341C8×D4C2×D6111yescharacteristic
342C8×D4C2×D6111yescharacteristic
343#432C2×D6111yescharacteristic
344#431—611no—
345#431—611no—
346#431—1221no—
347#431C2×D6111yescharacteristic
348C2×C4⋊C8—611no—
349C2×C4⋊C8—1221no—
350#408—21no—
351#408—21no—
352#335—611no—
353#335—611no—
354#334—611no—
355#334—611no—
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—21no—
370C2×#41—611no—
371C2×SD16—611no—
372C2×SD16—611no—
373C2×D8—611no—
374C2×D8—611no—
375C2×M16—21no—
376C2×M16—21no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—1221no—
380C22×C8—1221no—
381C22×C8—1221no—
382C4⋊Q8C4×D6111yescharacteristic
383#127C4×D6111yescharacteristic
384#124—21no—
385#121—21no—
386#121C4×D6111yescharacteristic
387#121C4×D6111yescharacteristic
388C4×Q8—611no—
389C4×Q8—611no—
390C4×D4—21no—
391C4×D4—611no—
392C4×D4—611no—
393C4×D4—1221no—
394C4×D4—1221no—
395C4×D4C22×D6111yescharacteristic
396C4×D4C22×D6111yescharacteristic
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—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—1221no—
410C4⋊C8—1221no—
411C4⋊C8—1221no—
412C4⋊C8—1221no—
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—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—611no—
431C22⋊C8—611no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8C22⋊D6111yescharacteristic
436C22⋊C8C22⋊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—81no—
447#41—81no—
448#41—1222no—
449#41—1222no—
450C2×Q8—21no—
451C2×Q8—611no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—611no—
457C2×D4—1221no—
458C2×D4C2×C4×D6111yescharacteristic
459C2×D4C2×C4×D6111yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4C2×C4×D6111yescharacteristic
466C22×C4#1175822211yescharacteristic
467C22×C4C2×C22⋊D6111yescharacteristic
468SD16—1222no—
469SD16—1222no—
470D8—1222no—
471D8—1222no—
472M16—81no—
473M16—81no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8—81no—
478C2×C8—611no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—4881no—
487C2×C8—4881no—
488C2×C8—4881no—
489C2×C8C2×C22⋊D6111yescharacteristic
490C2×C8C2×C22⋊D6111yescharacteristic
491C2×C8C2×C22⋊D6111yescharacteristic
492C2×C8C2×C22⋊D6111yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—611no—
495C4⋊C4—611no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4C2×C4×D6111yescharacteristic
499C4⋊C4C2×C4×D6111yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C42—1221no—
508C42—1221no—
509C42—1221no—
510C42C2×C4×D6111yescharacteristic
511C42#1175822211yescharacteristic
512C42C2×C22⋊D6111yescharacteristic
513C42C23×D6111yescharacteristic
514C23—21no—
515C23—21no—
516C23—1221no—
517C23C4×C22⋊D6111yescharacteristic
518Q8—81no—
519Q8—612no—
520Q8—1221no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—81no—
527D4—81no—
528D4—81no—
529D4—612no—
530D4—1224no—
531D4—1221no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—1224no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—4881no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4C4×C22⋊D6111yescharacteristic
551C2×C4C4×C22⋊D6111yescharacteristic
552C2×C4C4×C22⋊D6111yescharacteristic
553C2×C4C22×C4×D6111yescharacteristic
554C2×C4C22×C22⋊D6111yescharacteristic
555C2×C4C2×#1175822211yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—1221no—
563C8—1221no—
564C8—1221no—
565C8—1221no—
566C8—2441no—
567C8—2441no—
568C8—2441no—
569C8—2441no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—1222no—
580C22—2441no—
581C22—2441no—
582C22C2×C4×C22⋊D6111yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—1222no—
590C4—2441no—
591C4—2441no—
592C4#131×D6111yescharacteristic
593C4#131×D6111yescharacteristic
594C4#1684056511yescharacteristic
595C4#1684057311yescharacteristic
596C2—41no—
597C2—81no—
598C2—81no—
599C2—2442no—
600C2#2145451111yescharacteristic
601C2#2145465111yescharacteristic
602C2#2145473411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2981C2
socleC22×C61C2×C4×D4
prime radical#21455873C2
cosocleC42×C61C24
hypercenter#2981D61
hypocenterC61#17920
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2981

Complements

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

NH ≅ G/Ntype
2. #21454927C2semidirect
3. #21444695C2semidirect
4. #21444681C2semidirect
5. #21444660C2semidirect
6. #21444646C2semidirect
7. #21444641C2semidirect
8. #21444631C2semidirect
9. C8×#11758200C2semidirect
10. C8×#11758199C2semidirect
11. #21444605C2semidirect
12. #21444251C2semidirect
13. #21444218C2semidirect
14. #21444119C2semidirect
15. C61×#2981C2semidirect
297. #2981D61semidirect
368. C61#17920semidirect

Maximal subgroups

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

subgroupindex
#214558732
#214549272
#214446952
#214446812
#214446602
#214446462
#214446412
#214446312
C8×#117582002
C8×#117581992
#214446052
#214442512
#214442182
#214441192
C61×#29812
#1792061