Finite Group Databasebeta

← #29721508

Subgroups — #29721508

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
1#21455641C211yesmaximal, characteristic, complemented
2C2×#16840063C211yesmaximal, characteristic, complemented
3C4×#14519802C211yesmaximal, characteristic
4#21447264C211yesmaximal, characteristic, complemented
5#21447259C211yesmaximal, characteristic, complemented
6#21447110C211yesmaximal, characteristic
7#21447110C211yesmaximal, characteristic
8#21446811C211yesmaximal, characteristic, complemented
9#21446604C211yesmaximal, characteristic, complemented
10#21446599C211yesmaximal, characteristic, complemented
11#21446595C211yesmaximal, characteristic, complemented
12#21446481C211yesmaximal, characteristic, complemented
13#21446481C211yesmaximal, characteristic, complemented
14#21445808C211yesmaximal, characteristic, complemented
15C61×#2925C211yesmaximal, characteristic, complemented
16C2×#14519802C2211yescharacteristic
17C2×#14519769C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19#16840069—21no—
20#16840069—21no—
21#16840063—21no—
22#16840063—21no—
23#16840063—21no—
24#16840063—21no—
25#16840062—21no—
26#16840062—21no—
27#16839872—21no—
28#16839860—21no—
29C4×#11758201—21no—
30C4×#11758199—21no—
31C2×#14519713C2211yescharacteristic
32C2×#14519713C2211yescharacteristic
33#16839805C2211yescharacteristic
34#16839805C2211yescharacteristic
35#16839805C2211yescharacteristic
36C2×#14519711C2211yescharacteristic
37C2×#14519709C2211yescharacteristic
38#16839786C2211yescharacteristic
39#16839766C2211yescharacteristic
40#16839763C2211yescharacteristic
41#16839763C2211yescharacteristic
42#16839763C2211yescharacteristic
43C2×#14519699C2211yescharacteristic
44C2×#14519699C2211yescharacteristic
45C2×#14519693C2211yescharacteristic
46C2×#14519693C2211yescharacteristic
47C4×#11758194C2211yescharacteristic
48#16839530C2211yescharacteristic
49#16839530C2211yescharacteristic
50#16839530C2211yescharacteristic
51#16839530C2211yescharacteristic
52#16839530C2211yescharacteristic
53#16839530C2211yescharacteristic
54#16839527C2211yescharacteristic
55#16839527C2211yescharacteristic
56C4×#41×C61C2211yescharacteristic
57C61×#433—21no—
58C61×#433—21no—
59C61×#432—21no—
60C61×#431—21no—
61C61×#423C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#408C2211yescharacteristic
64C61×#408C2211yescharacteristic
65C61×#405C2211yescharacteristic
66C61×#405C2211yescharacteristic
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
77#14519769—21no—
78#14519769—21no—
79#14519769—21no—
80#14519769—21no—
81C4×D244—21no—
82C4×D244—21no—
83C4×D244—21no—
84C4×D244—21no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×#11758198—21no—
91#14519713—22no—
92#14519713—22no—
93#14519711—21no—
94#14519711—21no—
95#14519710—21no—
96#14519710—21no—
97#14519710—21no—
98#14519709—21no—
99#14519709—21no—
100#14519708—21no—
101#14519708—21no—
102#14519708—21no—
103C4⋊#92418—21no—
104C4⋊#92418—21no—
105#14519701—21no—
106#14519701—21no—
107#14519701—21no—
108#14519699—21no—
109#14519699—21no—
110#14519699—21no—
111#14519699—21no—
112#14519698—21no—
113#14519698—21no—
114#14519698—21no—
115#14519697—21no—
116#14519697—21no—
117#14519693—22no—
118#14519693—22no—
119#14519688—21no—
120C4×#92418—21no—
121C2×#41×C61C2311yescharacteristic
122C2×M16×C61C2311yescharacteristic
123C2×M16×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
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×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61—21no—
138C4⋊C8×C61D411yescharacteristic
139C4⋊C8×C61D411yescharacteristic
140C4⋊C8×C61D411yescharacteristic
141C4⋊C8×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C22⋊C8×C61—21no—
144C22⋊C8×C61—21no—
145C22⋊C8×C61—21no—
146#97×C61—21no—
147#97×C61—21no—
148C4×C8×C61—21no—
149C4×C8×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#4111yescharacteristic
162C22×C4×C61#4111yescharacteristic
163C22×C4×C61C2411yescharacteristic
164C22×Dic61—21no—
165C22×Dic61—21no—
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—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61C2×D411yescharacteristic
187C2×C8×C61C2×D411yescharacteristic
188C2×C8×C61C2×D411yescharacteristic
189C2×C8×C61C2×D411yescharacteristic
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
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—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214#11758196—41no—
215#11758196—41no—
216#11758196—41no—
217#11758196—41no—
218#11758194—21no—
219#11758194—21no—
220#11758194—21no—
221#11758194—21no—
222#11758194—21no—
223#11758194—21no—
224#11758194—21no—
225#11758194#4112yes—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
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—81no—
252C2×C4×C61#12111yescharacteristic
253C2×C4×C61#12111yescharacteristic
254C2×C4×C61#12111yescharacteristic
255C2×C4×C61#12111yescharacteristic
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61C22×D411yescharacteristic
258C2×C4×C61C2×#4111yescharacteristic
259C2×C4×C61C2×#4111yescharacteristic
260C2×C4×C612−1+411yescharacteristic
261C2×C4×C612−1+411yescharacteristic
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—81no—
266C2×Dic61—81no—
267C2×Dic61—81no—
268D244—22no—
269D244—22no—
270D244—41no—
271D244—41no—
272C4×D61—82no—
273C4×D61—82no—
274C8×C61—21no—
275C8×C61—21no—
276C8×C61—21no—
277C8×C61—21no—
278C8×C61—41no—
279C8×C61—41no—
280#92418—22no—
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#52511yescharacteristic
306C4×C61#53611yescharacteristic
307C4×C61#54711yescharacteristic
308C4×C61#54811yescharacteristic
309Dic61—81no—
310Dic61—81no—
311Dic61—81no—
312#3080—611no—
313C2×#478—611no—
314C4×AGL(1,ℤ/8)—611no—
315#2925D6111yescharacteristic, complemented
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×#125—611no—
336C4×#41C2×D6111yescharacteristic
337C2×C4×D4—611no—
338#479—1221no—
339#479—1221no—
340#478—1221no—
341#478—1221no—
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—21no—
351#433—21no—
352#432—21no—
353#431—21no—
354C2×#108—611no—
355C2×#108—611no—
356#428—611no—
357#428—611no—
358#428—611no—
359C2×#107—611no—
360C2×#106—611no—
361#423—611no—
362#423C2×D6111yescharacteristic
363C2×C4⋊C8C2×D6111yescharacteristic
364#418—611no—
365#417—611no—
366#417—611no—
367#417—611no—
368C2×#102—611no—
369C2×#102—611no—
370C2×#100—611no—
371C2×#100—611no—
372#408C2×D6111yescharacteristic
373#408C2×D6111yescharacteristic
374#405C2×D6111yescharacteristic
375#405C2×D6111yescharacteristic
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×C8C22×D6111yescharacteristic
400C22×C8C22×D6111yescharacteristic
401#125—1221no—
402#125—1221no—
403#125—1221no—
404#125—1221no—
405C4×Q8D24411yescharacteristic
406C4×Q8D24411yescharacteristic
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—1221no—
410C4×D4—1221no—
411C4×D4—1221no—
412C4×D4—1221no—
413C4×D4D24411yescharacteristic
414C4×D4D24411yescharacteristic
415#117—21no—
416#117C22×D6111yescharacteristic
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4—1221no—
422C2×C22⋊C4—1221no—
423C2×C42—21no—
424C2×C42C22×D6111yescharacteristic
425#108—1222no—
426#108—1222no—
427#107—1221no—
428#107—1221no—
429#107—1221no—
430#107—1221no—
431#107—1221no—
432#106—1221no—
433#106—1221no—
434#106—1221no—
435#106—1221no—
436#106—1221no—
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—1221no—
440C4⋊C8—1221no—
441C4⋊C8C22⋊D6111yescharacteristic
442C4⋊C8C22⋊D6111yescharacteristic
443C4⋊C8C22⋊D6111yescharacteristic
444C4⋊C8C22⋊D6111yescharacteristic
445#103—1221no—
446#103—1221no—
447#103—1221no—
448#102—1221no—
449#102—1221no—
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—21no—
460C22⋊C8—21no—
461C22⋊C8—21no—
462C22⋊C8—21no—
463#97—21no—
464#97—21no—
465#97—1221no—
466C4×C8—21no—
467C4×C8—21no—
468C4×C8—1221no—
469C24—1221no—
470#41—21no—
471#41—21no—
472#41—21no—
473#41—21no—
474C2×Q8C2×D24411yescharacteristic
475C2×D4—21no—
476C2×D4—612no—
477C2×D4—1221no—
478C2×D4—1221no—
479C2×D4—1221no—
480C2×D4—1221no—
481C2×D4—1221no—
482C2×D4C2×D24411yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—4882no—
490C22×C4—2441no—
491C22×C4—2441no—
492C22×C4#1175822211yescharacteristic
493C22×C4#1175822211yescharacteristic
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—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8C2×C22⋊D6111yescharacteristic
520C2×C8C2×C22⋊D6111yescharacteristic
521C2×C8C2×C22⋊D6111yescharacteristic
522C2×C8C2×C22⋊D6111yescharacteristic
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—2441no—
532C4⋊C4—2441no—
533C4⋊C4—2441no—
534C4⋊C4—2441no—
535C4⋊C4C2×D24411yescharacteristic
536C4⋊C4C2×D24411yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—2441no—
541C22⋊C4—2441no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42C2×D24411yescharacteristic
546C42C2×D24411yescharacteristic
547C42C2×C22⋊D6111yescharacteristic
548C42C2×C22⋊D6111yescharacteristic
549C23—21no—
550C23—1222no—
551C23—4881no—
552C23—4881no—
553C23—2441no—
554C23—2441no—
555C23C2×#1175822211yescharacteristic
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—81no—
575C2×C4—4882no—
576C2×C4—4882no—
577C2×C4—4881no—
578C2×C4—4881no—
579C2×C4—4881no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4#1451975111yescharacteristic
584C2×C4#1451975111yescharacteristic
585C2×C4#1451975111yescharacteristic
586C2×C4#1451975111yescharacteristic
587C2×C4C22×C22⋊D6111yescharacteristic
588C2×C4C22×D24411yescharacteristic
589C2×C4#41×D6111yescharacteristic
590C2×C4#41×D6111yescharacteristic
591C2×C4#1451982411yescharacteristic
592C2×C4#1451982411yescharacteristic
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—41no—
598C8—41no—
599C8—1222no—
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×#1451975111yescharacteristic
614C22#1684045111yescharacteristic
615C22#1684048011yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—4881no—
624C4—4881no—
625C4—4881no—
626C4#1684027411yescharacteristic
627C4#1684033811yescharacteristic
628C4#1684041111yescharacteristic
629C4#1684041911yescharacteristic
630C2—21no—
631C2—21no—
632C2—81no—
633C2—4882no—
634C2#2144924211yescharacteristic
635C2#2145553911yescharacteristic
636C2#2145554711yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2925C2
socleC22×C61C2×#121
prime radicalC2×#14519802C22
hypercenter#2925D61
hypocenterC61#24724
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2925

Complements

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

NH ≅ G/Ntype
1. #21455641C2semidirect
2. C2×#16840063C2semidirect
4. #21447264C2semidirect
5. #21447259C2semidirect
8. #21446811C2semidirect
9. #21446604C2semidirect
10. #21446599C2semidirect
11. #21446595C2semidirect
12. #21446481C2semidirect
13. #21446481C2semidirect
14. #21445808C2semidirect
15. C61×#2925C2semidirect
315. #2925D61semidirect
385. C61#24724semidirect

Maximal subgroups

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

subgroupindex
#214556412
C2×#168400632
C4×#145198022
#214472642
#214472592
#214471102
#214468112
#214466042
#214465992
#214465952
#214464812
#214458082
C61×#29252
#2472461