Finite Group Databasebeta

← #30613171

Subgroups — #30613171

Order 15616.

740 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462561C211yesmaximal, characteristic, complemented
2#21462559C211yesmaximal, characteristic, complemented
3#21461468C211yesmaximal, characteristic, complemented
4#21461467C211yesmaximal, characteristic, complemented
5#21461441C211yesmaximal, characteristic, complemented
6#21461439C211yesmaximal, characteristic, complemented
7#21461439C211yesmaximal, characteristic, complemented
8#21461438C211yesmaximal, characteristic, complemented
9#21461417C211yesmaximal, characteristic, complemented
10#21461416C211yesmaximal, characteristic, complemented
11#21461386C211yesmaximal, characteristic, complemented
12#21461164C211yesmaximal, characteristic, complemented
13C2×#16840610C211yesmaximal, characteristic, complemented
14#21461030C211yesmaximal, characteristic, complemented
15#21455816C211yesmaximal, characteristic
16C2×#14519864—21no—
17C2×D61⋊M16—21no—
18#16840797C2211yescharacteristic, complemented
19#16840796C2211yescharacteristic
20#16840796C2211yescharacteristic
21#16840796C2211yescharacteristic, complemented
22#16840794—21no—
23#16840792—21no—
24#16840792—21no—
25#16840791—21no—
26#16840790C2211yescharacteristic
27#16840790C2211yescharacteristic
28#16840790C2211yescharacteristic, complemented
29D4×#92420C2211yescharacteristic, complemented
30#16840765C2211yescharacteristic
31C2×C4⋊#92420C2211yescharacteristic
32#16840735—21no—
33#16840734—21no—
34C4×#11758217C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36#16840624C2211yescharacteristic, complemented
37#16840624C2211yescharacteristic, complemented
38#16840623C2211yescharacteristic, complemented
39#16840623C2211yescharacteristic, complemented
40#16840610C2211yescharacteristic
41#16840610C2211yescharacteristic
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44#16840610C2211yescharacteristic, complemented
45#16840610C2211yescharacteristic, complemented
46D4⋊#92420C2211yescharacteristic, complemented
47D4⋊#92420C2211yescharacteristic, complemented
48#92420⋊C8C2211yescharacteristic, complemented
49#92420⋊C8C2211yescharacteristic, complemented
50#16840603C2211yescharacteristic, complemented
51#16840603C2211yescharacteristic, complemented
52#16840307C2211yescharacteristic
53C2×#14519739C2211yescharacteristic
54#16840075C411yescharacteristic
55#16840041C411yescharacteristic
56#16840041C411yescharacteristic
57#16839956C411yescharacteristic
58#16839956C411yescharacteristic
59#16839898C411yescharacteristic
60#16839895C411yescharacteristic
61#16839844C2211yescharacteristic
62#16839844C2211yescharacteristic
63#16839842C2211yescharacteristic
64#16839842C2211yescharacteristic
65#16839812C2211yescharacteristic
66C61×#480C411yescharacteristic
67#14519864—44no—
68C2×#11758213—21no—
69C2×#11758213—21no—
70C2×#11758213—21no—
71D61⋊M16—44no—
72C2×#11758217—21no—
73C2×#11758217—21no—
74C2×#11758217D411yescharacteristic
75C2×#11758217D411yescharacteristic
76C2×D61⋊C8—21no—
77C2×D61⋊C8—21no—
78C2×D61⋊C8—21no—
79C22×#92420—21no—
80C22×#92420—21no—
81C22×#92420—21no—
82#14519844—21no—
83C4⋊#92420—21no—
84C4⋊#92420C2311yescharacteristic
85C4⋊#92420C2311yescharacteristic
86C4⋊#92420C2311yescharacteristic
87C4⋊#92420C2311yescharacteristic
88#14519834—21no—
89#14519834—21no—
90#14519834—21no—
91#14519834—21no—
92#14519834—21no—
93#14519834—21no—
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96#14519832D411yescharacteristic
97#14519832D411yescharacteristic
98C4×#92420—21no—
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C4×#92420C2311yescharacteristic
102C4×#92420C2311yescharacteristic
103C2×#11758224—21no—
104C22×D244C2×C411yescharacteristic
105C22×C4×D61—21no—
106C2×D488C2×C411yescharacteristic
107C2×D488C2×C411yescharacteristic
108C2×#11758199C2×C411yescharacteristic
109C2×#11758199C2×C411yescharacteristic
110#14519776C2×C411yescharacteristic
111#14519773C2×C411yescharacteristic
112#14519763—21no—
113#14519751C2×C411yescharacteristic
114#14519749—21no—
115D4×Dic61C2311yescharacteristic
116#14519739—21no—
117#14519739—21no—
118#14519739C2×C411yescharacteristic
119#14519739C2×C411yescharacteristic
120#14519739C2311yescharacteristic
121#14519739C2311yescharacteristic
122#14519739C2311yescharacteristic
123#14519737—21no—
124C2×#11758198—21no—
125C2×C4×Dic61C2311yescharacteristic
126#14519710C2×C411yescharacteristic
127#14519710C2×C411yescharacteristic
128#14519706C2×C411yescharacteristic
129#14519706C2×C411yescharacteristic
130#14519699C2×C411yescharacteristic
131#14519699C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134#14519697C2×C411yescharacteristic
135#14519697C2×C411yescharacteristic
136C22⋊#92418C2×C411yescharacteristic
137C8×Dic61C2311yescharacteristic
138C8×Dic61C2311yescharacteristic
139#121×C61C2×C411yescharacteristic
140C2×C4⋊C4×C61C2×C411yescharacteristic
141#107×C61C2×C411yescharacteristic
142#107×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144#102×C61C2×C411yescharacteristic
145C22⋊C8×C61C2×C411yescharacteristic
146C23×D61—21no—
147C2×D4×C61—21no—
148C2×D4×C61C22×C411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61C22×C411yescharacteristic
151C2×C22⋊D61—21no—
152C2×C22⋊D61—21no—
153C2×C22⋊D61—21no—
154C22×Dic61—21no—
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61#4111yescharacteristic
157#11758224—42no—
158#11758224—42no—
159C2×D244—22no—
160C2×D244—21no—
161C2×D244—41no—
162C2×D244C22×C411yescharacteristic
163C2×D244C22×C411yescharacteristic
164C2×D244C22×C411yescharacteristic
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—42no—
171C2×C4×D61—42no—
172C2×Dic122—21no—
173#11758217—22no—
174#11758217—22no—
175#11758217—42no—
176#11758217—42no—
177C2×#92420—21no—
178C2×#92420—21no—
179C2×#92420—21no—
180C2×#92420—21no—
181C2×#92420—21no—
182C2×#92420—21no—
183C2×#92420—42no—
184C2×#92420—42no—
185C2×#92420—42no—
186C2×#92420C2×D411yescharacteristic
187C2×#92420C2×D411yescharacteristic
188C2×#92420C2×D411yescharacteristic
189C2×#92420C2×D411yescharacteristic
190#11758213—42no—
191#11758213—42no—
192#11758213—42no—
193D61⋊C8—42no—
194D61⋊C8—42no—
195D61⋊C8—42no—
196C2×C8×C61C22×C411yescharacteristic
197C2×C8×C61C22×C411yescharacteristic
198C4⋊C4×C61—21no—
199C4⋊C4×C61C22×C411yescharacteristic
200C4⋊C4×C61C22×C411yescharacteristic
201C4⋊C4×C61C22×C411yescharacteristic
202C22⋊C4×C61—21no—
203C22⋊Dic61—21no—
204#11758199—22no—
205#11758199—41no—
206#11758198—21no—
207#11758198—21no—
208#11758198—21no—
209#11758198—21no—
210#11758198—21no—
211#11758198—21no—
212C4⋊Dic61C22×C411yescharacteristic
213#11758196—21no—
214C4×Dic61C22×C411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61#4111yescharacteristic
217C4×Dic61C2411yescharacteristic
218C2×#92418C22×C411yescharacteristic
219C2×#92418C22×C411yescharacteristic
220D488—22no—
221D488—41no—
222C23×C61—21no—
223C23×C61C4×D411yescharacteristic
224C22×D61—21no—
225C22×D61—21no—
226C22×D61—21no—
227C22×D61—42no—
228C22×D61—42no—
229C22×D61—81no—
230D4×C61—21no—
231D4×C61—21no—
232D4×C61—42no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—42no—
239C2×C4×C61C4×D411yescharacteristic
240C2×C4×C61C23×C411yescharacteristic
241C22⋊D61—42no—
242C22⋊D61—42no—
243C22⋊D61—81no—
244C2×Dic61—21no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61C4×D411yescharacteristic
249C2×Dic61C4×D411yescharacteristic
250C2×Dic61AGL(1,ℤ/8)12yes—
251C2×Dic61AGL(1,ℤ/8)12yes—
252C2×Dic61C22×D411yescharacteristic
253C2×Dic61C2×#4111yescharacteristic
254D244—21no—
255D244—21no—
256D244—21no—
257D244—21no—
258D244—21no—
259D244—42no—
260D244#13112yescomplemented
261C4×D61—41no—
262C4×D61—41no—
263C4×D61—41no—
264C4×D61—41no—
265C4×D61—41no—
266C4×D61—41no—
267C4×D61—42no—
268C4×D61—42no—
269Dic122—42no—
270#92420—22no—
271#92420—21no—
272#92420—21no—
273#92420—21no—
274#92420—21no—
275#92420—41no—
276#92420—41no—
277#92420—41no—
278#92420—41no—
279#92420—41no—
280C8×C61—21no—
281C8×C61—21no—
282#92418—21no—
283#92418—21no—
284#18001—611nomaximal, Sylow
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61#44212yes—
291C22×C61C2×C4×D411yescharacteristic
292C2×D61—22no—
293C2×D61—41no—
294C2×D61—41no—
295C2×D61—41no—
296C2×D61—41no—
297C2×D61—41no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—41no—
301C2×D61—84no—
302C4×C61—21no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61—41no—
306C4×C61C2×#13111yescharacteristic
307C4×C61#56811yescharacteristic
308Dic61—21no—
309Dic61—21no—
310Dic61—41no—
311Dic61#44212yes—
312Dic61C2×AGL(1,ℤ/8)11yescharacteristic
313Dic61C2×AGL(1,ℤ/8)11yescharacteristic
314#3100—611no—
315#2935—611no—
316D4×M16—611no—
317#1594—611no—
318#1594—611no—
319#1586—611no—
320#1586—611no—
321#1586—611no—
322#1586—611no—
323#1580—611no—
324#1580—611no—
325#1570—611no—
326#1492—611no—
327C2×D4⋊C8—611no—
328#1451—611no—
329C2×C61—22no—
330C2×C61—81no—
331C2×C61#293311yescharacteristic
332C2×C61C2×#44211yescharacteristic
333C2×C61#295611yescharacteristic
334D61—42no—
335D61—81no—
336D61—81no—
337C2×#131—1221no—
338C22×M16—1221no—
339#532—611no—
340C2×C4×D4—611no—
341#480—611no—
342#480#692311yescharacteristic
343#474—611no—
344#474—611no—
345#459—611no—
346#459—611no—
347#447—611no—
348#447—611no—
349C4×D8—611no—
350C4×D8—611no—
351C4×D8—611no—
352C4×D8—611no—
353#436—611no—
354#436—611no—
355#436—611no—
356#436—611no—
357#435—1221no—
358#435—1221no—
359#435—1221no—
360#435—1221no—
361C8×D4—611no—
362C8×D4—611no—
363C8×D4—611no—
364C8×D4—611no—
365#431—611no—
366#423—611no—
367C2×C4⋊C8—611no—
368#408—1221no—
369#407—1221no—
370C4×M16—611no—
371C2×C4×C8—611no—
372#334—611no—
373#334—611no—
374#334—611no—
375#334—611no—
376D4⋊C8—611no—
377D4⋊C8—611no—
378D4⋊C8—611no—
379D4⋊C8—611no—
380D4⋊C8—611no—
381D4⋊C8—611no—
382D4⋊C8—611no—
383D4⋊C8—611no—
384#322—611no—
385#322—611no—
386#322—611no—
387#322—611no—
388C61#1800111yescharacteristic, complemented, Sylow
389C2×#41—1221no—
390C22×D4—611no—
391C23×C4—1221no—
392C2×D8—611no—
393C2×D8—611no—
394C2×D8—611no—
395C2×D8—611no—
396#131—2444no—
397C2×M16—611no—
398C2×M16—611no—
399C2×M16—1221no—
400C2×M16—1221no—
401C2×M16—1221no—
402C2×M16—1221no—
403C2×M16—1221no—
404C2×M16—2444no—
405C22×C8—1221no—
406C22×C8—1221no—
407C22×C8—1221no—
408C22×C8—1221no—
409C22×C8—1221no—
410C22×C8—1221no—
411C4⋊Q8—611no—
412#127—611no—
413#124—1221no—
414#121—611no—
415#121—1221no—
416#121C2×#692311yescharacteristic
417C4×D4—611no—
418C4×D4—611no—
419C4×D4—611no—
420C4×D4—611no—
421C4×D4—611no—
422C4×D4—611no—
423C4×D4—1221no—
424C4×D4—1221no—
425C4×D4—1221no—
426C2×C4⋊C4C2×#692311yescharacteristic
427C2×C22⋊C4—1221no—
428C2×C42—611no—
429#107—611no—
430#107—611no—
431#107C2×#692311yescharacteristic
432#107C2×#692311yescharacteristic
433C4⋊C8—611no—
434C4⋊C8—611no—
435C4⋊C8—611no—
436C4⋊C8—611no—
437C4⋊C8—611no—
438C4⋊C8—611no—
439C4⋊C8—1221no—
440C4⋊C8—1221no—
441#102—611no—
442#102—611no—
443#102—611no—
444#102—611no—
445#102—611no—
446#102—611no—
447#102C2×#692311yescharacteristic
448#102C2×#692311yescharacteristic
449C22⋊C8—611no—
450C22⋊C8—1221no—
451C22⋊C8—1221no—
452C22⋊C8—1221no—
453C22⋊C8—1221no—
454C22⋊C8—1221no—
455C22⋊C8—1221no—
456C22⋊C8—1221no—
457C22⋊C8—1221no—
458C22⋊C8C2×#692311yescharacteristic
459#97—611no—
460#97—611no—
461C4×C8—611no—
462C4×C8—611no—
463C4×C8—611no—
464C4×C8—611no—
465C4×C8—611no—
466C4×C8—611no—
467C4×C8—1221no—
468C24—1221no—
469#41—2442no—
470#41—2442no—
471C2×Q8—1221no—
472C2×D4—21no—
473C2×D4—611no—
474C2×D4—611no—
475C2×D4—611no—
476C2×D4—1222no—
477C2×D4—1221no—
478C2×D4—1221no—
479C2×D4—1221no—
480C2×D4—1221no—
481C2×D4—2441no—
482C2×D4C22×#692311yescharacteristic
483C22×C4—21no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—2442no—
493C22×C4—2442no—
494C22×C4C22×#692311yescharacteristic
495D8—1222no—
496D8—1222no—
497D8—2441no—
498D8—2441no—
499M16—1222no—
500M16—1222no—
501M16—2442no—
502M16—2442no—
503M16—2442no—
504M16—2442no—
505M16—2442no—
506C2×C8—611no—
507C2×C8—611no—
508C2×C8—611no—
509C2×C8—611no—
510C2×C8—611no—
511C2×C8—611no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—2442no—
519C2×C8—2442no—
520C2×C8—2442no—
521C2×C8—2442no—
522C2×C8—2442no—
523C2×C8—2442no—
524C2×C8C22×#692311yescharacteristic
525C2×C8C22×#692311yescharacteristic
526C4⋊C4—21no—
527C4⋊C4—611no—
528C4⋊C4—1221no—
529C4⋊C4C22×#692311yescharacteristic
530C4⋊C4C22×#692311yescharacteristic
531C4⋊C4C22×#692311yescharacteristic
532C22⋊C4—21no—
533C22⋊C4—1221no—
534C22⋊C4—1221no—
535C22⋊C4—1221no—
536C22⋊C4—1221no—
537C22⋊C4—1221no—
538C22⋊C4—1221no—
539C22⋊C4—1221no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—611no—
544C23—21no—
545C23—1221no—
546C23—1221no—
547C23—1221no—
548C23—4881no—
549C23—2442no—
550C23—2442no—
551C23D4×#692311yescharacteristic
552Q8—2442no—
553D4—21no—
554D4—21no—
555D4—42no—
556D4—612no—
557D4—1221no—
558D4—1221no—
559D4—1221no—
560D4—1221no—
561D4—1221no—
562D4—4881no—
563D4—2442no—
564D4—2442no—
565D4—2442no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—42no—
572C2×C4—612no—
573C2×C4—612no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—611no—
577C2×C4—611no—
578C2×C4—1221no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2442no—
585C2×C4—2442no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4D4×#692311yescharacteristic
591C2×C4C23×#692311yescharacteristic
592C8—21no—
593C8—21no—
594C8—1221no—
595C8—1221no—
596C8—1221no—
597C8—1221no—
598C8—1222no—
599C8—1221no—
600C8—1221no—
601C8—2441no—
602C8—2441no—
603C8—2441no—
604C8—2441no—
605C8—2441no—
606C22—21no—
607C22—21no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—1222no—
612C22—4884no—
613C22—2441no—
614C22—2441no—
615C22—2441no—
616C22—2441no—
617C22—2441no—
618C22—2441no—
619C22—2441no—
620C22—2441no—
621C22#1684080312yes—
622C22C2×D4×#692311yescharacteristic
623C4—21no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—611no—
628C4—611no—
629C4—612no—
630C4—1221no—
631C4—1221no—
632C4—2441no—
633C4D61⋊#13111yescharacteristic
634C4#1684084111yescharacteristic
635C2—22no—
636C2—81no—
637C2—4881no—
638C2—4881no—
639C2—2442no—
640C2#2146255311yescharacteristic
641C2C2×#1684080311yescharacteristic
642C2#2146259411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#480C4
socleC22×C61C2×C4×D4
prime radical#21455816C2
cosocleC4×Dic61C24
hypercenter#480#6923
hypocenterC61#18001
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #21462561C2semidirect
2. #21462559C2semidirect
3. #21461468C2semidirect
4. #21461467C2semidirect
5. #21461441C2semidirect
6. #21461439C2semidirect
7. #21461439C2semidirect
8. #21461438C2semidirect
9. #21461417C2semidirect
10. #21461416C2semidirect
11. #21461386C2semidirect
12. #21461164C2semidirect
13. C2×#16840610C2semidirect
14. #21461030C2semidirect
18. #16840797C22semidirect
21. #16840796C22semidirect
28. #16840790C22semidirect
29. D4×#92420C22semidirect
36. #16840624C22semidirect
37. #16840624C22semidirect
38. #16840623C22semidirect
39. #16840623C22semidirect
44. #16840610C22semidirect
45. #16840610C22semidirect
46. D4⋊#92420C22semidirect
47. D4⋊#92420C22semidirect
48. #92420⋊C8C22semidirect
49. #92420⋊C8C22semidirect
50. #16840603C22semidirect
51. #16840603C22semidirect
260. D244#131semidirect
388. C61#18001semidirect

Maximal subgroups

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

subgroupindex
#214625612
#214625592
#214614682
#214614672
#214614412
#214614392
#214614382
#214614172
#214614162
#214613862
#214611642
C2×#168406102
#214610302
#214558162
#1800161