Finite Group Databasebeta

← #29651313

Subgroups — #29651313

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455815C211yesmaximal, characteristic
2#21454853C211yesmaximal, characteristic, complemented
3#21444731C211yesmaximal, characteristic, complemented
4#21444702C211yesmaximal, characteristic, complemented
5#21444683C211yesmaximal, characteristic, complemented
6#21444681C211yesmaximal, characteristic, complemented
7#21444648C211yesmaximal, characteristic, complemented
8#21444646C211yesmaximal, characteristic, complemented
9#21444641C211yesmaximal, characteristic, complemented
10C8×#11758199C211yesmaximal, characteristic, complemented
11#21444597C211yesmaximal, characteristic, complemented
12#21444288C211yesmaximal, characteristic, complemented
13#21444209C211yesmaximal, characteristic, complemented
14#21444119C211yesmaximal, characteristic, complemented
15C61×#2979C211yesmaximal, characteristic, complemented
16C2×C4×D244C2211yescharacteristic
17#16840073C411yescharacteristic
18#16840073C411yescharacteristic
19#16840039C411yescharacteristic
20#16840039C411yescharacteristic
21#16839954C411yescharacteristic
22#16839954C411yescharacteristic
23#16839895C411yescharacteristic
24#16839895C411yescharacteristic
25C4×#11758199C2211yescharacteristic
26C4×#11758199C2211yescharacteristic
27C4×#11758199C2211yescharacteristic
28C4×#11758199C2211yescharacteristic
29#16839841C2211yescharacteristic
30#16839841C2211yescharacteristic
31#16839832—21no—
32#16839832—21no—
33C8×D244C2211yescharacteristic
34C8×D244C2211yescharacteristic
35#16839819C2211yescharacteristic
36#16839815C2211yescharacteristic
37#16839815C2211yescharacteristic
38#16839724—21no—
39C22⋊C8×D61—21no—
40#16839514C2211yescharacteristic, complemented
41#16839514C2211yescharacteristic, complemented
42#16839512C2211yescharacteristic, complemented
43#16839512C2211yescharacteristic, complemented
44D4⋊#92418C2211yescharacteristic, complemented
45D4⋊#92418C2211yescharacteristic, complemented
46D4⋊#92418C2211yescharacteristic, complemented
47D4⋊#92418C2211yescharacteristic, complemented
48#16839489C2211yescharacteristic
49#16839489C2211yescharacteristic
50#16839489C2211yescharacteristic
51#16839489C2211yescharacteristic
52#16839484C2211yescharacteristic, complemented
53#16839484C2211yescharacteristic, complemented
54#16839483C2211yescharacteristic, complemented
55C8×#92418C2211yescharacteristic, complemented
56C61×#532C2211yescharacteristic
57C61×#436—21no—
58C61×#436C2211yescharacteristic, complemented
59C61×#436C2211yescharacteristic, complemented
60C8×D4×C61—21no—
61C8×D4×C61C2211yescharacteristic, complemented
62C8×D4×C61C2211yescharacteristic, complemented
63C61×#431C2211yescharacteristic
64C61×#431C2211yescharacteristic
65C61×#408—21no—
66C61×#408—21no—
67C22×D244C2×C411yescharacteristic
68C22×C4×D61—21no—
69C2×#11758199C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C2×#11758199C2×C411yescharacteristic
73C2×#11758189—21no—
74C2×#11758189—21no—
75C2×C8×D61—21no—
76C2×C8×D61—21no—
77C4×D244—21no—
78C4×D244—21no—
79C4×D244C2×C411yescharacteristic
80C4×D244C2×C411yescharacteristic
81C4×D244C2311yescharacteristic
82C4×D244C2311yescharacteristic
83C2×C4⋊Dic61C2×C411yescharacteristic
84C2×#11758198—21no—
85#14519710C2×C411yescharacteristic
86#14519710C2×C411yescharacteristic
87#14519710C2×C411yescharacteristic
88#14519710C2×C411yescharacteristic
89C4⋊#92418—21no—
90C4⋊#92418C2×C411yescharacteristic
91C4⋊#92418C2×C411yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94#14519698C2×C411yescharacteristic
95#14519698C2×C411yescharacteristic
96#14519698C2×C411yescharacteristic
97#14519698C2×C411yescharacteristic
98#14519697C2×C411yescharacteristic
99#14519697C2×C411yescharacteristic
100#14519697C2×C411yescharacteristic
101#14519697C2×C411yescharacteristic
102C22⋊#92418—21no—
103C22⋊#92418—21no—
104C22⋊#92418C2×C411yescharacteristic
105C22⋊#92418C2×C411yescharacteristic
106#14519689—21no—
107#14519689—21no—
108#14519689—21no—
109#14519689—21no—
110#14519688—21no—
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
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
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C23×D61—21no—
145#41×C61—81no—
146#41×C61—81no—
147C2×Q8×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61C22×C411yescharacteristic
153C2×D4×C61C22×C411yescharacteristic
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61#4111yescharacteristic
159C22×Dic61—21no—
160C2×D244—22no—
161C2×D244—21no—
162C2×D244—41no—
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—81no—
170C2×C4×D61—81no—
171M16×C61—81no—
172M16×C61—81no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—81no—
176C2×C8×C61—81no—
177C2×C8×C61C2×D411yescharacteristic
178C2×C8×C61C2×D411yescharacteristic
179C2×C8×C61C2×D411yescharacteristic
180C2×C8×C61C2×D411yescharacteristic
181C4⋊C4×C61—21no—
182C4⋊C4×C61C22×C411yescharacteristic
183C4⋊C4×C61C22×C411yescharacteristic
184C22⋊C4×C61—21no—
185C22⋊C4×C61—21no—
186C22⋊C4×C61—21no—
187C22⋊C4×C61—21no—
188C42×C61C22×C411yescharacteristic
189C42×C61C2×D411yescharacteristic
190C42×C61#4111yescharacteristic
191C42×C61C2411yescharacteristic
192#11758199—22no—
193#11758199—22no—
194#11758199—41no—
195#11758199—41no—
196#11758198—21no—
197#11758198—21no—
198#11758198—21no—
199#11758198—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61C22×C411yescharacteristic
202C4⋊Dic61C22×C411yescharacteristic
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418C22×C411yescharacteristic
208C2×#92418C22×C411yescharacteristic
209C2×#92418C22×C411yescharacteristic
210C2×#92418C22×C411yescharacteristic
211#11758189—81no—
212#11758189—81no—
213C8×D61—81no—
214C8×D61—81no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61C4×D411yescharacteristic
218C22×D61—21no—
219C22×D61—21no—
220C22×D61—42no—
221C22×D61—42no—
222C22×D61—81no—
223Q8×C61—81no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—21no—
228D4×C61—42no—
229D4×C61—81no—
230D4×C61—81no—
231D4×C61—81no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61C4×D411yescharacteristic
244C2×C4×C61C4×D411yescharacteristic
245C2×C4×C61C4×D411yescharacteristic
246C2×C4×C61C23×C411yescharacteristic
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—81no—
252D244—21no—
253D244—21no—
254D244—21no—
255D244—42no—
256D244#13112yes—
257C4×D61—41no—
258C4×D61—41no—
259C4×D61—41no—
260C4×D61—41no—
261C4×D61—81no—
262C4×D61—81no—
263C8×C61—21no—
264C8×C61—21no—
265C8×C61—21no—
266C8×C61—21no—
267C8×C61—41no—
268C8×C61—41no—
269#92418—21no—
270#92418—21no—
271#92418—21no—
272#92418—21no—
273#92418—41no—
274#92418—41no—
275#92418—41no—
276#92418—41no—
277#18026—611nomaximal, Sylow
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—21no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61C2×C4×D411yescharacteristic
288C2×D61—22no—
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—41no—
294C2×D61—84no—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61—41no—
300C4×C61—41no—
301C4×C61C2×#13111yescharacteristic
302C4×C61#56811yescharacteristic
303C4×C61#57611yescharacteristic
304C4×C61#57611yescharacteristic
305Dic61—41no—
306Dic61—41no—
307#3100—611no—
308#2979D6111yescharacteristic, complemented
309#2974—611no—
310#1594—611no—
311#1589—611no—
312#1586—611no—
313#1586—611no—
314#1581—611no—
315#1581—611no—
316#1580—611no—
317C8×D8—611no—
318#1572—611no—
319#1496—611no—
320#1478—611no—
321#1454—611no—
322C2×C61—41no—
323C2×C61—81no—
324C2×C61—81no—
325C2×C61#293311yescharacteristic
326C2×C61#294811yescharacteristic
327C2×C61#295511yescharacteristic
328D61—42no—
329D61—81no—
330#532C2×D6111yescharacteristic
331C2×C4×D4—611no—
332#480—611no—
333#480—611no—
334#474—611no—
335#474—611no—
336#459—611no—
337#459—611no—
338#447—611no—
339#447—611no—
340C4×D8—611no—
341C4×D8—611no—
342C4×D8—611no—
343C4×D8—611no—
344#436—21no—
345#436—611no—
346#436—611no—
347#436C2×D6111yescharacteristic, complemented
348#436C2×D6111yescharacteristic, complemented
349#435—1221no—
350#435—1221no—
351C8×D4—21no—
352C8×D4—611no—
353C8×D4—611no—
354C8×D4C2×D6111yescharacteristic, complemented
355C8×D4C2×D6111yescharacteristic, complemented
356#432—611no—
357#431—611no—
358#431—611no—
359#431C2×D6111yescharacteristic
360#431C2×D6111yescharacteristic
361#408—21no—
362#408—21no—
363#407—1221no—
364C2×C22⋊C8—1221no—
365#335—611no—
366#335—611no—
367#334—611no—
368#334—611no—
369D4⋊C8—611no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375D4⋊C8—611no—
376D4⋊C8—611no—
377#322—611no—
378#322—611no—
379#322—611no—
380C82—611no—
381C61#1802611yescharacteristic, complemented, Sylow
382C2×#41—21no—
383C22×D4—611no—
384C23×C4—1221no—
385C2×D8—611no—
386C2×D8—611no—
387C2×D8—611no—
388C2×D8—611no—
389C2×M16—21no—
390C2×M16—21no—
391C2×M16—1221no—
392C2×M16—1221no—
393C22×C8—21no—
394C22×C8—21no—
395C22×C8—1221no—
396C22×C8—1221no—
397C4⋊Q8C4×D6111yescharacteristic
398#127C4×D6111yescharacteristic
399#124—21no—
400#121—21no—
401#121C4×D6111yescharacteristic
402#121C4×D6111yescharacteristic
403C4×D4—21no—
404C4×D4—611no—
405C4×D4—611no—
406C4×D4—611no—
407C4×D4—611no—
408C4×D4—1221no—
409C4×D4—1221no—
410C4×D4C22×D6111yescharacteristic
411C4×D4C22×D6111yescharacteristic
412C2×C4⋊C4—611no—
413C2×C22⋊C4—1221no—
414C2×C42C22×D6111yescharacteristic
415#107—611no—
416#107—611no—
417#107—611no—
418#107—611no—
419C4⋊C8—611no—
420C4⋊C8—611no—
421C4⋊C8—611no—
422C4⋊C8—611no—
423C4⋊C8—1221no—
424C4⋊C8C22⋊D6111yescharacteristic
425C4⋊C8C22⋊D6111yescharacteristic
426C4⋊C8C22×D6111yescharacteristic
427C4⋊C8C22×D6111yescharacteristic
428#102—611no—
429#102—611no—
430#102—611no—
431#102—611no—
432#102—611no—
433#102—611no—
434#102—611no—
435#102—611no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8—611no—
442C22⋊C8—611no—
443C22⋊C8—1221no—
444C22⋊C8—1221no—
445C22⋊C8—1221no—
446C22⋊C8—1221no—
447C22⋊C8—1221no—
448C22⋊C8—1221no—
449C22⋊C8C22⋊D6111yescharacteristic
450C22⋊C8C22⋊D6111yescharacteristic
451#97—1221no—
452C4×C8—21no—
453C4×C8—611no—
454C4×C8—611no—
455C4×C8—611no—
456C4×C8—611no—
457C4×C8C22×D6111yescharacteristic
458C4×C8C22×D6111yescharacteristic
459C24—1221no—
460#41—81no—
461#41—81no—
462C2×Q8—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—611no—
468C2×D4—611no—
469C2×D4—1222no—
470C2×D4—1221no—
471C2×D4—2441no—
472C2×D4C2×C4×D6111yescharacteristic
473C2×D4C2×C4×D6111yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—4881no—
482C22×C4—4881no—
483C22×C4C2×C4×D6111yescharacteristic
484C22×C4#1175822211yescharacteristic
485C22×C4C2×C22⋊D6111yescharacteristic
486D8—1222no—
487D8—1222no—
488D8—2441no—
489D8—2441no—
490M16—81no—
491M16—81no—
492M16—4881no—
493M16—4881no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—81no—
497C2×C8—81no—
498C2×C8—611no—
499C2×C8—611no—
500C2×C8—611no—
501C2×C8—611no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—4881no—
507C2×C8—4881no—
508C2×C8C2×C22⋊D6111yescharacteristic
509C2×C8C2×C22⋊D6111yescharacteristic
510C2×C8C2×C22⋊D6111yescharacteristic
511C2×C8C2×C22⋊D6111yescharacteristic
512C4⋊C4—21no—
513C4⋊C4—611no—
514C4⋊C4—611no—
515C4⋊C4—1221no—
516C4⋊C4C2×C4×D6111yescharacteristic
517C4⋊C4C2×C4×D6111yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—1221no—
523C22⋊C4—1221no—
524C22⋊C4—1221no—
525C22⋊C4—1221no—
526C42C2×C4×D6111yescharacteristic
527C42#1175822211yescharacteristic
528C42C2×C22⋊D6111yescharacteristic
529C42C23×D6111yescharacteristic
530C23—21no—
531C23—21no—
532C23—1221no—
533C23—1221no—
534C23—4881no—
535C23—2442no—
536C23—2442no—
537C23C4×C22⋊D6111yescharacteristic
538Q8—81no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—42no—
544D4—81no—
545D4—81no—
546D4—81no—
547D4—612no—
548D4—1221no—
549D4—1221no—
550D4—1221no—
551D4—2442no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—4881no—
566C2×C4—4881no—
567C2×C4—4881no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4C4×C22⋊D6111yescharacteristic
573C2×C4C4×C22⋊D6111yescharacteristic
574C2×C4C4×C22⋊D6111yescharacteristic
575C2×C4C22×C4×D6111yescharacteristic
576C2×C4C22×C22⋊D6111yescharacteristic
577C2×C4C2×#1175822211yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—1221no—
585C8—1221no—
586C8—1221no—
587C8—1221no—
588C8—2441no—
589C8—2441no—
590C8—2441no—
591C8—2441no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—1222no—
602C22—4884no—
603C22—2441no—
604C22—2441no—
605C22—2441no—
606C22—2441no—
607C22—2441no—
608C22C2×C4×C22⋊D6111yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—41no—
614C4—41no—
615C4—2441no—
616C4—2441no—
617C4#131×D6111yescharacteristic
618C4#1684052711yescharacteristic
619C4#1684056511yescharacteristic
620C4#1684056511yescharacteristic
621C2—41no—
622C2—81no—
623C2—81no—
624C2—4881no—
625C2—2442no—
626C2#2145454111yescharacteristic
627C2#2145466911yescharacteristic
628C2#2145472011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2979C2
socleC22×C61C2×C4×D4
prime radical#21455815C2
cosocleC42×C61C24
hypercenter#2979D61
hypocenterC61#18026
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2979

Complements

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

NH ≅ G/Ntype
2. #21454853C2semidirect
3. #21444731C2semidirect
4. #21444702C2semidirect
5. #21444683C2semidirect
6. #21444681C2semidirect
7. #21444648C2semidirect
8. #21444646C2semidirect
9. #21444641C2semidirect
10. C8×#11758199C2semidirect
11. #21444597C2semidirect
12. #21444288C2semidirect
13. #21444209C2semidirect
14. #21444119C2semidirect
15. C61×#2979C2semidirect
40. #16839514C22semidirect
41. #16839514C22semidirect
42. #16839512C22semidirect
43. #16839512C22semidirect
44. D4⋊#92418C22semidirect
45. D4⋊#92418C22semidirect
46. D4⋊#92418C22semidirect
47. D4⋊#92418C22semidirect
52. #16839484C22semidirect
53. #16839484C22semidirect
54. #16839483C22semidirect
55. C8×#92418C22semidirect
58. C61×#436C22semidirect
59. C61×#436C22semidirect
61. C8×D4×C61C22semidirect
62. C8×D4×C61C22semidirect
308. #2979D61semidirect
347. #436C2×D61semidirect
348. #436C2×D61semidirect
354. C8×D4C2×D61semidirect
355. C8×D4C2×D61semidirect
381. C61#18026semidirect

Maximal subgroups

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

subgroupindex
#214558152
#214548532
#214447312
#214447022
#214446832
#214446812
#214446482
#214446462
#214446412
C8×#117581992
#214445972
#214442882
#214442092
#214441192
C61×#29792
#1802661