Finite Group Databasebeta

← #29721516

Subgroups — #29721516

Order 15616.

690 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840059C211yesmaximal, characteristic, complemented
2C4×#14519802C211yesmaximal, characteristic
3#21454485C211yesmaximal, characteristic, complemented
4#21447267C211yesmaximal, characteristic, complemented
5#21447262C211yesmaximal, characteristic, complemented
6#21447109C211yesmaximal, characteristic
7#21447109C211yesmaximal, characteristic
8#21446813C211yesmaximal, characteristic, complemented
9#21446601C211yesmaximal, characteristic, complemented
10#21446596C211yesmaximal, characteristic, complemented
11#21446592C211yesmaximal, characteristic, complemented
12#21446480C211yesmaximal, characteristic, complemented
13#21446480C211yesmaximal, characteristic, complemented
14#21445808C211yesmaximal, characteristic, complemented
15C61×#3080C211yesmaximal, characteristic, complemented
16C2×#14519802C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18#16840059—21no—
19#16840059—21no—
20#16840059—21no—
21#16840059—21no—
22#16839872—21no—
23#16839860—21no—
24C4×#11758201—21no—
25C4×#11758199—21no—
26#16839823—21no—
27#16839823—21no—
28#16839819—21no—
29#16839815—21no—
30C2×#14519712C2211yescharacteristic
31C2×#14519712C2211yescharacteristic
32#16839805C2211yescharacteristic
33C2×#14519710C2211yescharacteristic
34C2×#14519708C2211yescharacteristic
35#16839786C2211yescharacteristic
36C2×C4⋊#92418C2211yescharacteristic
37#16839766C2211yescharacteristic
38#16839763C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×#14519693C2211yescharacteristic
42C2×#14519693C2211yescharacteristic
43#16839729C2211yescharacteristic
44#16839729C2211yescharacteristic
45#16839718C2211yescharacteristic
46#16839718C2211yescharacteristic
47C4×#11758194C2211yescharacteristic
48#16839531C2211yescharacteristic
49#16839531C2211yescharacteristic
50#16839531C2211yescharacteristic
51#16839531C2211yescharacteristic
52#16839530C2211yescharacteristic
53#16839530C2211yescharacteristic
54#16839526C2211yescharacteristic
55#16839526C2211yescharacteristic
56C2×#125×C61C2211yescharacteristic
57C4×#41×C61C2211yescharacteristic
58C61×#479—21no—
59C61×#479—21no—
60C61×#478—21no—
61C61×#478—21no—
62C61×#428C2211yescharacteristic
63C61×#428C2211yescharacteristic
64C61×#423C2211yescharacteristic
65C61×#417C2211yescharacteristic
66C61×#417C2211yescharacteristic
67C22×D244C2311yescharacteristic
68C22×C4×D61—21no—
69#14519802—22no—
70#14519802—22no—
71C2×#11758201—21no—
72C2×#11758199—21no—
73C2×#11758194C2311yescharacteristic
74C2×#11758194C2311yescharacteristic
75C2×#11758194C2311yescharacteristic
76C2×#11758194C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C4×D244—21no—
80C4×D244—21no—
81C4×D244—21no—
82C4×D244—21no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758198—21no—
85#14519712—22no—
86#14519712—22no—
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519708—21no—
91#14519708—21no—
92#14519708—21no—
93C4⋊#92418—21no—
94C4⋊#92418—21no—
95C4⋊#92418D411yescharacteristic
96C4⋊#92418D411yescharacteristic
97C4⋊#92418D411yescharacteristic
98C4⋊#92418D411yescharacteristic
99#14519701—21no—
100#14519698—21no—
101#14519697—21no—
102#14519697—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519693—22no—
108#14519693—22no—
109C22⋊#92418—21no—
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519688—21no—
114#14519688—21no—
115#14519688—21no—
116C4×#92418—21no—
117C4×#92418—21no—
118C4×#92418—21no—
119C2×#41×C61C2311yescharacteristic
120C2×M16×C61C2311yescharacteristic
121C2×M16×C61C2311yescharacteristic
122#125×C61—21no—
123#125×C61—21no—
124#125×C61—21no—
125#125×C61—21no—
126C4×Q8×C61D411yescharacteristic
127C4×Q8×C61D411yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61D411yescharacteristic
131C4×D4×C61D411yescharacteristic
132#117×C61—21no—
133#117×C61C2311yescharacteristic
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C42×C61—21no—
139C2×C42×C61C2311yescharacteristic
140#107×C61—21no—
141#107×C61—21no—
142#106×C61—21no—
143#106×C61—21no—
144C4⋊C8×C61—21no—
145C4⋊C8×C61—21no—
146#103×C61—21no—
147#103×C61—21no—
148#102×C61—21no—
149#102×C61—21no—
150C23×D61—21no—
151#41×C61—21no—
152#41×C61—21no—
153#41×C61—21no—
154#41×C61—21no—
155C2×Q8×C61C2×D411yescharacteristic
156C2×D4×C61—21no—
157C2×D4×C61C2×D411yescharacteristic
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61#4111yescharacteristic
164C22×C4×C61#4111yescharacteristic
165C22×C4×C61C2411yescharacteristic
166C22×Dic61—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244#4112yes—
173C2×C4×D61—41no—
174C2×C4×D61—41no—
175C2×C4×D61—82no—
176M16×C61—21no—
177M16×C61—21no—
178M16×C61—21no—
179M16×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—41no—
189C4⋊C4×C61—41no—
190C4⋊C4×C61—41no—
191C4⋊C4×C61—41no—
192C4⋊C4×C61C2×D411yescharacteristic
193C4⋊C4×C61C2×D411yescharacteristic
194C22⋊C4×C61—21no—
195C22⋊C4×C61—21no—
196C22⋊C4×C61—21no—
197C42×C61—21no—
198C42×C61—21no—
199C42×C61—21no—
200C42×C61C2×D411yescharacteristic
201C42×C61C2×D411yescharacteristic
202C42×C61C2×D411yescharacteristic
203C42×C61C2×D411yescharacteristic
204#11758201—24no—
205#11758199—24no—
206#11758198—41no—
207#11758198—41no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210#11758194—21no—
211#11758194—21no—
212#11758194—21no—
213#11758194—21no—
214#11758194—21no—
215#11758194—21no—
216#11758194—21no—
217#11758194#4112yes—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418C2×D411yescharacteristic
227C2×#92418C2×D411yescharacteristic
228C2×#92418C2×D411yescharacteristic
229C2×#92418C2×D411yescharacteristic
230C23×C61—21no—
231C23×C61C2×#4111yescharacteristic
232C22×D61—22no—
233C22×D61—41no—
234C22×D61—41no—
235C22×D61—81no—
236C22×D61—81no—
237Q8×C61—21no—
238Q8×C61—21no—
239D4×C61—21no—
240D4×C61—21no—
241D4×C61—41no—
242D4×C61—41no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—42no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—81no—
254C2×C4×C61—81no—
255C2×C4×C61—81no—
256C2×C4×C61#12111yescharacteristic
257C2×C4×C61#12111yescharacteristic
258C2×C4×C61#12111yescharacteristic
259C2×C4×C61#12111yescharacteristic
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C22×D411yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61C2×#4111yescharacteristic
264C2×C4×C612−1+411yescharacteristic
265C2×C4×C612−1+411yescharacteristic
266C2×Dic61—41no—
267C2×Dic61—81no—
268D244—22no—
269D244—22no—
270D244—41no—
271D244—41no—
272C4×D61—82no—
273C4×D61—82no—
274C8×C61—41no—
275C8×C61—41no—
276#92418—22no—
277#92418—21no—
278#92418—21no—
279#92418—21no—
280#92418—21no—
281#92418—41no—
282#92418—41no—
283#92418—41no—
284#24724—611nomaximal, Sylow
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61C2×#12111yescharacteristic
291C22×C61#55211yescharacteristic
292C22×C61#55611yescharacteristic
293C2×D61—42no—
294C2×D61—82no—
295C2×D61—81no—
296C2×D61—81no—
297C2×D61—82no—
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—41no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61—81no—
306C4×C61—81no—
307C4×C61#52511yescharacteristic
308C4×C61#53611yescharacteristic
309C4×C61#54711yescharacteristic
310C4×C61#54811yescharacteristic
311Dic61—81no—
312#3080D6111yescharacteristic, complemented
313C2×#478—611no—
314C4×AGL(1,ℤ/8)—611no—
315#2925—611no—
316#2079—611no—
317#2078—611no—
318#2051—611no—
319#2051—611no—
320#1998—611no—
321#1952—611no—
322#1951—611no—
323#1950—611no—
324#1931—611no—
325#1931—611no—
326#1800—611no—
327C2×C61—21no—
328C2×C61—21no—
329C2×C61—81no—
330C2×C61#241511yescharacteristic
331C2×C61#306711yescharacteristic
332C2×C61#306811yescharacteristic
333D61—82no—
334C2×AGL(1,ℤ/8)—611no—
335C2×#125C2×D6111yescharacteristic
336C4×#41C2×D6111yescharacteristic
337C2×C4×D4—611no—
338#479—21no—
339#479—21no—
340#478—21no—
341#478—21no—
342#478—1221no—
343#478—1221no—
344#478—1221no—
345#478—1221no—
346#442—1221no—
347#440—1221no—
348C4×SD16—1221no—
349C4×D8—1221no—
350#433—1221no—
351#433—1221no—
352#432—1221no—
353#431—1221no—
354C2×#108—611no—
355C2×#108—611no—
356#428—611no—
357#428C2×D6111yescharacteristic
358#428C2×D6111yescharacteristic
359C2×#107—611no—
360C2×#106—611no—
361#423—611no—
362#423C2×D6111yescharacteristic
363C2×C4⋊C8—611no—
364#418—611no—
365#417—611no—
366#417C2×D6111yescharacteristic
367#417C2×D6111yescharacteristic
368C2×#102—611no—
369C2×#102—611no—
370C2×#100—611no—
371C2×#100—611no—
372#408—611no—
373#408—611no—
374#405—611no—
375#405—611no—
376C4×M16—611no—
377#343—611no—
378#343—611no—
379#343—611no—
380#343—611no—
381#343—611no—
382#343—611no—
383#341—611no—
384#341—611no—
385C61#2472411yescharacteristic, complemented, Sylow
386C2×#41C22×D6111yescharacteristic
387C22×D4—611no—
388C23×C4—1221no—
389AGL(1,ℤ/8)—1222no—
390AGL(1,ℤ/8)—1222no—
391C2×SD16—1221no—
392C2×D8—1221no—
393C2×M16—611no—
394C2×M16—611no—
395C2×M16—611no—
396C2×M16—611no—
397C2×M16C22×D6111yescharacteristic
398C2×M16C22×D6111yescharacteristic
399C22×C8—611no—
400C22×C8—611no—
401#125—21no—
402#125—21no—
403#125—21no—
404#125—21no—
405C4×Q8C22⋊D6111yescharacteristic
406C4×Q8C22⋊D6111yescharacteristic
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—1221no—
410C4×D4—1221no—
411C4×D4—1221no—
412C4×D4—1221no—
413C4×D4C22⋊D6111yescharacteristic
414C4×D4C22⋊D6111yescharacteristic
415#117—21no—
416#117C22×D6111yescharacteristic
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4C22×D6111yescharacteristic
421C2×C4⋊C4C22×D6111yescharacteristic
422C2×C22⋊C4—1221no—
423C2×C42—21no—
424C2×C42C22×D6111yescharacteristic
425#108—1222no—
426#108—1222no—
427#107—21no—
428#107—21no—
429#107—1221no—
430#107—1221no—
431#107—1221no—
432#106—21no—
433#106—21no—
434#106—1221no—
435#106—1221no—
436#106—1221no—
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—611no—
440C4⋊C8—611no—
441C4⋊C8—611no—
442C4⋊C8—611no—
443C4⋊C8—1221no—
444C4⋊C8—1221no—
445#103—21no—
446#103—21no—
447#103—1221no—
448#102—21no—
449#102—21no—
450#102—1221no—
451#102—1221no—
452#102—1221no—
453#102—1221no—
454#102—1221no—
455#102—1221no—
456#102—1221no—
457#100—1222no—
458#100—1222no—
459C22⋊C8—1221no—
460C22⋊C8—1221no—
461C22⋊C8—1221no—
462C22⋊C8—1221no—
463#97—1221no—
464#97—1221no—
465#97—1221no—
466C4×C8—1221no—
467C4×C8—1221no—
468C4×C8—1221no—
469C24—1221no—
470#41—21no—
471#41—21no—
472#41—21no—
473#41—21no—
474C2×Q8C2×C22⋊D6111yescharacteristic
475C2×D4—21no—
476C2×D4—612no—
477C2×D4—1221no—
478C2×D4—1221no—
479C2×D4—1221no—
480C2×D4—1221no—
481C2×D4—1221no—
482C2×D4C2×C22⋊D6111yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—1221no—
489C22×C4—4882no—
490C22×C4—2441no—
491C22×C4—2441no—
492C22×C4#1175822411yescharacteristic
493C22×C4#1175822411yescharacteristic
494C22×C4C23×D6111yescharacteristic
495SD16—1224no—
496D8—1224no—
497M16—21no—
498M16—21no—
499M16—21no—
500M16—21no—
501M16—612no—
502M16—1221no—
503M16—1221no—
504M16—1221no—
505M16—1221no—
506M16—1221no—
507M16—1221no—
508M16—1221no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—611no—
512C2×C8—611no—
513C2×C8—611no—
514C2×C8—611no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—1221no—
534C4⋊C4—1221no—
535C4⋊C4C2×C22⋊D6111yescharacteristic
536C4⋊C4C2×C22⋊D6111yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—2441no—
541C22⋊C4—2441no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42D4×D6111yescharacteristic
546C42D4×D6111yescharacteristic
547C42C2×C22⋊D6111yescharacteristic
548C42C2×C22⋊D6111yescharacteristic
549C23—21no—
550C23—1222no—
551C23—4881no—
552C23—4881no—
553C23—2441no—
554C23—2441no—
555C23C2×#1175822411yescharacteristic
556Q8—21no—
557Q8—21no—
558D4—21no—
559D4—21no—
560D4—41no—
561D4—41no—
562D4—1222no—
563D4—1222no—
564D4—2441no—
565D4—2441no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—81no—
577C2×C4—81no—
578C2×C4—81no—
579C2×C4—4882no—
580C2×C4—4882no—
581C2×C4—4881no—
582C2×C4—2441no—
583C2×C4#1451974911yescharacteristic
584C2×C4#1451974911yescharacteristic
585C2×C4#1451974911yescharacteristic
586C2×C4#1451974911yescharacteristic
587C2×C4C2×D4×D6111yescharacteristic
588C2×C4C22×C22⋊D6111yescharacteristic
589C2×C4#41×D6111yescharacteristic
590C2×C4#41×D6111yescharacteristic
591C2×C4#1451982511yescharacteristic
592C2×C4#1451982511yescharacteristic
593C8—41no—
594C8—41no—
595C8—1222no—
596C8—1221no—
597C8—1221no—
598C8—1221no—
599C8—1221no—
600C8—2441no—
601C8—2441no—
602C8—2441no—
603C22—21no—
604C22—21no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—4882no—
609C22—4882no—
610C22—4881no—
611C22—4881no—
612C22—2442no—
613C22C2×#1451974911yescharacteristic
614C22#1684044611yescharacteristic
615C22#1684048311yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—81no—
625C4—4881no—
626C4#1684026911yescharacteristic
627C4#1684033611yescharacteristic
628C4#1684041411yescharacteristic
629C4#1684042211yescharacteristic
630C2—21no—
631C2—21no—
632C2—81no—
633C2—4882no—
634C2#2144924911yescharacteristic
635C2#2145553611yescharacteristic
636C2#2145554911yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#3080C2
socleC22×C61C2×#121
prime radicalC2×#14519802C22
hypercenter#3080D61
hypocenterC61#24724
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3080

Complements

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

NH ≅ G/Ntype
1. C2×#16840059C2semidirect
3. #21454485C2semidirect
4. #21447267C2semidirect
5. #21447262C2semidirect
8. #21446813C2semidirect
9. #21446601C2semidirect
10. #21446596C2semidirect
11. #21446592C2semidirect
12. #21446480C2semidirect
13. #21446480C2semidirect
14. #21445808C2semidirect
15. C61×#3080C2semidirect
312. #3080D61semidirect
385. C61#24724semidirect

Maximal subgroups

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

subgroupindex
C2×#168400592
C4×#145198022
#214544852
#214472672
#214472622
#214471092
#214468132
#214466012
#214465962
#214465922
#214464802
#214458082
C61×#30802
#2472461