Finite Group Databasebeta

← #29730447

Subgroups — #29730447

Order 15616.

716 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456222C211yesmaximal, characteristic
2#21455291C211yesmaximal, characteristic
3#21454562C211yesmaximal, characteristic
4#21447265C211yesmaximal, characteristic, complemented
5#21447260C211yesmaximal, characteristic, complemented
6#21447119C211yesmaximal, characteristic, complemented
7#21447119C211yesmaximal, characteristic, complemented
8#21446813C211yesmaximal, characteristic, complemented
9#21446595C211yesmaximal, characteristic, complemented
10#21446337C211yesmaximal, characteristic, complemented
11#21446337C211yesmaximal, characteristic, complemented
12#21445884C211yesmaximal, characteristic, complemented
13#21445879C211yesmaximal, characteristic, complemented
14C4×#14519696C211yesmaximal, characteristic, complemented
15C2×C61×#479C211yesmaximal, characteristic, complemented
16C2×#14519808C2211yescharacteristic
17C2×#14519808C2211yescharacteristic
18C2×#14519783C2211yescharacteristic
19C2×#14519783C2211yescharacteristic
20#16840312C2211yescharacteristic
21#16840132—21no—
22#16840128—21no—
23#16840119—21no—
24#16840119—21no—
25#16839984—21no—
26#16839984—21no—
27#16839972—21no—
28#16839962—21no—
29#16839839—21no—
30#16839832—21no—
31#16839832—21no—
32#16839827—21no—
33C2×#14519713C2211yescharacteristic
34C2×#14519713C2211yescharacteristic
35#16839786C2211yescharacteristic
36#16839761C2211yescharacteristic
37#16839761C2211yescharacteristic
38#16839761C2211yescharacteristic
39#16839761C2211yescharacteristic
40#16839761C2211yescharacteristic
41#16839761C2211yescharacteristic
42C2×#14519696C2211yescharacteristic
43C2×#14519696C2211yescharacteristic
44#16839728C2211yescharacteristic
45#16839728C2211yescharacteristic
46C4×#11758194C2211yescharacteristic
47C4×#11758194C2211yescharacteristic
48#16839531C2211yescharacteristic
49#16839531C2211yescharacteristic
50#16839531C2211yescharacteristic
51#16839531C2211yescharacteristic
52#16839531C2211yescharacteristic
53#16839531C2211yescharacteristic
54#16839527C2211yescharacteristic
55#16839527C2211yescharacteristic
56C2×#125×C61C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C61×#479—21no—
59C61×#479—21no—
60C61×#479—21no—
61C61×#479—21no—
62C2×#107×C61C2211yescharacteristic
63C2×#106×C61C2211yescharacteristic
64C2×C4⋊C8×C61C2211yescharacteristic
65C2×#103×C61C2211yescharacteristic
66C2×#103×C61C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68C2×#11758222C2311yescharacteristic
69#14519808—22no—
70#14519808—22no—
71#14519808—41no—
72#14519808—41no—
73C2×#11758202—21no—
74C2×#11758202—21no—
75C2×#11758201—21no—
76C2×#11758201—21no—
77#14519783—22no—
78#14519783—22no—
79#14519783—41no—
80#14519783—41no—
81C2×#11758194C2311yescharacteristic
82C2×#11758194C2311yescharacteristic
83C2×#11758194C2311yescharacteristic
84C2×#11758194C2311yescharacteristic
85C2×#11758194C2311yescharacteristic
86C2×#11758194C2311yescharacteristic
87C2×#11758189—21no—
88C2×#11758189—21no—
89C2×C8×D61—21no—
90C2×C8×D61—21no—
91#14519777D411yescharacteristic
92#14519774D411yescharacteristic
93#14519765D411yescharacteristic
94#14519765D411yescharacteristic
95#14519751—21no—
96#14519751—21no—
97C4×D244—21no—
98C4×D244—21no—
99#14519713—41no—
100#14519713—41no—
101C4⋊#92418—21no—
102C4⋊#92418—21no—
103#14519700—21no—
104#14519700—21no—
105#14519700—21no—
106#14519700—21no—
107#14519700—21no—
108#14519700—21no—
109#14519697—21no—
110#14519697—21no—
111#14519697—21no—
112#14519697—21no—
113#14519697—21no—
114#14519697—21no—
115#14519696—22no—
116#14519696—22no—
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689—21no—
121#14519688—21no—
122#14519688—21no—
123C4×#92418—21no—
124C4×#92418—21no—
125C22×Q8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128#125×C61—21no—
129#125×C61—21no—
130#125×C61—21no—
131#125×C61—21no—
132C4×Q8×C61—21no—
133C4×Q8×C61—21no—
134C4×Q8×C61—21no—
135C4×Q8×C61—21no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C42×C61—21no—
143C2×C42×C61C2311yescharacteristic
144#107×C61—21no—
145#107×C61—21no—
146#106×C61—21no—
147#106×C61—21no—
148C4⋊C8×C61D411yescharacteristic
149C4⋊C8×C61D411yescharacteristic
150C4⋊C8×C61D411yescharacteristic
151C4⋊C8×C61D411yescharacteristic
152#103×C61—21no—
153#103×C61—21no—
154#103×C61—21no—
155#103×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61#4112yes—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61#4111yescharacteristic
167C22×C4×C61#4111yescharacteristic
168C22×C4×C61C2411yescharacteristic
169C2×C22⋊D61—21no—
170C2×C22⋊D61—21no—
171#11758222—21no—
172#11758222—21no—
173#11758222—21no—
174#11758222—21no—
175#11758222—21no—
176#11758222—21no—
177#11758222—21no—
178#11758222—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244C2×D411yescharacteristic
182C2×D244C2×D411yescharacteristic
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×Dic122C2×D411yescharacteristic
186C2×Dic122C2×D411yescharacteristic
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61C2×D411yescharacteristic
192C2×C8×C61C2×D411yescharacteristic
193C2×C8×C61C2×D411yescharacteristic
194C2×C8×C61C2×D411yescharacteristic
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—41no—
202C4⋊C4×C61—41no—
203C4⋊C4×C61—41no—
204C4⋊C4×C61—41no—
205C4⋊C4×C61—41no—
206C4⋊C4×C61—41no—
207C42×C61—41no—
208C42×C61—41no—
209C42×C61C2×D411yescharacteristic
210C42×C61C2×D411yescharacteristic
211C42×C61C2×D411yescharacteristic
212C42×C61C2×D411yescharacteristic
213#11758202—42no—
214#11758202—42no—
215#11758201—42no—
216#11758201—42no—
217#11758198—21no—
218#11758198—21no—
219#11758198—21no—
220#11758198—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223#11758194—21no—
224#11758194—21no—
225#11758194—21no—
226#11758194—21no—
227#11758194—21no—
228#11758194—21no—
229#11758194—21no—
230#11758194—21no—
231#11758194—21no—
232#11758194—21no—
233#11758194—21no—
234#11758194#4112yes—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241#11758189—42no—
242#11758189—42no—
243C8×D61—42no—
244C8×D61—42no—
245C23×C61C2×#4111yescharacteristic
246C22×D61—21no—
247C22×D61—21no—
248Q8×C61—22no—
249Q8×C61—22no—
250Q8×C61—41no—
251Q8×C61—41no—
252C2×C4×C61—22no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—81no—
261C2×C4×C61—81no—
262C2×C4×C61—81no—
263C2×C4×C61#12111yescharacteristic
264C2×C4×C61#12111yescharacteristic
265C2×C4×C61#12111yescharacteristic
266C2×C4×C61#12111yescharacteristic
267C2×C4×C61C22×D411yescharacteristic
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C2×#4111yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61H(5,𝔽2)11yescharacteristic
272C2×C4×C612−1+411yescharacteristic
273C22⋊D61—41no—
274C22⋊D61—41no—
275C22⋊D61—41no—
276C22⋊D61—41no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279D244—21no—
280D244—21no—
281D244—21no—
282D244—21no—
283D244—42no—
284D244—81no—
285C4×D61—41no—
286C4×D61—41no—
287C4×D61—41no—
288C4×D61—41no—
289Dic122—21no—
290Dic122—21no—
291Dic122—21no—
292Dic122—21no—
293C8×C61—21no—
294C8×C61—21no—
295C8×C61—21no—
296C8×C61—21no—
297#92418—22no—
298#92418—41no—
299#92418—41no—
300#92418—41no—
301#92418—41no—
302#92418—41no—
303#25363—611nomaximal, Sylow
304C22×C61—21no—
305C22×C61—21no—
306C22×C61C2×#12111yescharacteristic
307C22×C61#52911yescharacteristic
308C22×C61#54211yescharacteristic
309C2×D61—41no—
310C2×D61—41no—
311C2×D61—41no—
312C2×D61—41no—
313C2×D61—41no—
314C2×D61—41no—
315C4×C61—21no—
316C4×C61—21no—
317C4×C61—21no—
318C4×C61—21no—
319C4×C61—42no—
320C4×C61—81no—
321C4×C61—81no—
322C4×C61—81no—
323C4×C61#54611yescharacteristic
324C4×C61#54611yescharacteristic
325C4×C61#54711yescharacteristic
326C4×C61#54811yescharacteristic
327Dic61—41no—
328Dic61—41no—
329#3142—611no—
330C2×#479D6111yescharacteristic, complemented
331#3037—611no—
332#2935—611no—
333#2079—611no—
334#2078—611no—
335#2052—611no—
336#2052—611no—
337#1998—611no—
338#1950—611no—
339#1908—611no—
340#1908—611no—
341#1816—611no—
342#1815—611no—
343C4×#101—611no—
344C2×C61—21no—
345C2×C61—21no—
346C2×C61#242711yescharacteristic
347C2×C61#306711yescharacteristic
348C2×C61#306911yescharacteristic
349D61—81no—
350D61—81no—
351C2×#137—611no—
352C2×#137—611no—
353C2×#131—611no—
354C2×#131—611no—
355#532—611no—
356C2×#125C2×D6111yescharacteristic
357C2×C4×Q8C2×D6111yescharacteristic
358#491—1221no—
359#490—1221no—
360#488—1221no—
361#488—1221no—
362#479—21no—
363#479—21no—
364#479—21no—
365#479—21no—
366#464—1221no—
367#464—1221no—
368#462—1221no—
369#460—1221no—
370#436—1221no—
371#435—1221no—
372#435—1221no—
373C8×D4—1221no—
374C2×#108—611no—
375C2×#108—611no—
376C2×#107C2×D6111yescharacteristic
377C2×#106C2×D6111yescharacteristic
378#423—611no—
379C2×C4⋊C8C2×D6111yescharacteristic
380#417—611no—
381#417—611no—
382#417—611no—
383#417—611no—
384#417—611no—
385#417—611no—
386C2×#103C2×D6111yescharacteristic
387C2×#103C2×D6111yescharacteristic
388C2×#101—611no—
389C2×#101—611no—
390#408—611no—
391#408—611no—
392C4×M16—611no—
393C4×M16—611no—
394#343—611no—
395#343—611no—
396#343—611no—
397#343—611no—
398#343—611no—
399#343—611no—
400#341—611no—
401#341—611no—
402C61#2536311yescharacteristic, complemented, Sylow
403C2×#41—611no—
404C2×#41—611no—
405C22×Q8C22×D6111yescharacteristic
406#137—1222no—
407#137—1222no—
408#137—2441no—
409#137—2441no—
410C2×Q16—1221no—
411C2×Q16—1221no—
412C2×SD16—1221no—
413C2×SD16—1221no—
414#131—1222no—
415#131—1222no—
416#131—2441no—
417#131—2441no—
418C2×M16—611no—
419C2×M16—611no—
420C2×M16—611no—
421C2×M16—611no—
422C2×M16—611no—
423C2×M16—611no—
424C2×M16—1221no—
425C2×M16—1221no—
426C22×C8—1221no—
427C22×C8—1221no—
428C22×C8C22×D6111yescharacteristic
429C22×C8C22×D6111yescharacteristic
430C4⋊Q8—611no—
431#127—611no—
432#125—21no—
433#125—21no—
434#125—21no—
435#125—21no—
436#124—611no—
437#124—611no—
438#121—1221no—
439#121—1221no—
440C4×Q8—21no—
441C4×Q8—21no—
442C4×Q8—21no—
443C4×Q8—21no—
444C4×D4—1221no—
445C4×D4—1221no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4C22×D6111yescharacteristic
450C2×C4⋊C4C22×D6111yescharacteristic
451C2×C4⋊C4C22×D6111yescharacteristic
452C2×C42—21no—
453C2×C42C22×D6111yescharacteristic
454#108—2441no—
455#108—2441no—
456#107—21no—
457#107—21no—
458#106—21no—
459#106—21no—
460C4⋊C8—1221no—
461C4⋊C8—1221no—
462C4⋊C8C22⋊D6111yescharacteristic
463C4⋊C8C22⋊D6111yescharacteristic
464C4⋊C8C22⋊D6111yescharacteristic
465C4⋊C8C22⋊D6111yescharacteristic
466#103—21no—
467#103—21no—
468#103—21no—
469#103—21no—
470#103—1221no—
471#103—1221no—
472#103—1221no—
473#103—1221no—
474#103—1221no—
475#103—1221no—
476#102—1221no—
477#102—1221no—
478#102—1221no—
479#102—1221no—
480#102—1221no—
481#102—1221no—
482#101—1222no—
483#101—1222no—
484C22⋊C8—1221no—
485C22⋊C8—1221no—
486C22⋊C8—1221no—
487C22⋊C8—1221no—
488#97—1221no—
489#97—1221no—
490C4×C8—1221no—
491C4×C8—1221no—
492#41—1221no—
493#41—1221no—
494#41—1221no—
495#41—1221no—
496#41—1221no—
497#41—1221no—
498#41—1221no—
499#41—1221no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—611no—
506C2×Q8—611no—
507C2×Q8#1175822612yes—
508C2×D4—611no—
509C2×D4—611no—
510C2×D4—1221no—
511C2×D4—1221no—
512C2×D4—1221no—
513C2×D4—1221no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4#1175822411yescharacteristic
521C22×C4#1175822411yescharacteristic
522C22×C4C23×D6111yescharacteristic
523Q16—2442no—
524Q16—2442no—
525SD16—2442no—
526SD16—2442no—
527M16—612no—
528M16—1221no—
529M16—1221no—
530M16—1221no—
531M16—1221no—
532M16—1221no—
533M16—1221no—
534M16—1221no—
535M16—1221no—
536M16—1221no—
537M16—1221no—
538M16—1221no—
539M16—2442no—
540M16—2442no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—1221no—
546C2×C8—1221no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—2442no—
552C2×C8—2442no—
553C2×C8C2×C22⋊D6111yescharacteristic
554C2×C8C2×C22⋊D6111yescharacteristic
555C2×C8C2×C22⋊D6111yescharacteristic
556C2×C8C2×C22⋊D6111yescharacteristic
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—1221no—
570C4⋊C4—1221no—
571C22⋊C4—1221no—
572C22⋊C4—1221no—
573C22⋊C4—1221no—
574C22⋊C4—1221no—
575C42—41no—
576C42—41no—
577C42D4×D6111yescharacteristic
578C42D4×D6111yescharacteristic
579C42C2×C22⋊D6111yescharacteristic
580C42C2×C22⋊D6111yescharacteristic
581C23—1221no—
582C23—1221no—
583C23C2×#1175822411yescharacteristic
584Q8—22no—
585Q8—22no—
586Q8—41no—
587Q8—41no—
588Q8—1221no—
589Q8—1221no—
590Q8—1221no—
591Q8—1221no—
592D4—1221no—
593D4—1221no—
594D4—1221no—
595D4—1221no—
596D4—4881no—
597D4—2442no—
598D4—2441no—
599D4—2441no—
600D4—2441no—
601D4—2441no—
602C2×C4—22no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—81no—
611C2×C4—81no—
612C2×C4—81no—
613C2×C4—1221no—
614C2×C4—1221no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4#1451974811yescharacteristic
620C2×C4#1451974811yescharacteristic
621C2×C4#1451974811yescharacteristic
622C2×C4#1451974811yescharacteristic
623C2×C4C2×D4×D6111yescharacteristic
624C2×C4C22×C22⋊D6111yescharacteristic
625C2×C4#41×D6111yescharacteristic
626C2×C4C2×#1175822611yescharacteristic
627C2×C4#1451982311yescharacteristic
628C2×C4#1451982511yescharacteristic
629C8—21no—
630C8—21no—
631C8—21no—
632C8—21no—
633C8—1222no—
634C8—2441no—
635C8—2441no—
636C8—2441no—
637C8—2441no—
638C8—2441no—
639C22—21no—
640C22—21no—
641C22—2441no—
642C22—2441no—
643C22—2441no—
644C22—2441no—
645C22—2441no—
646C22—2441no—
647C22C2×#1451974811yescharacteristic
648C22#1684029811yescharacteristic
649C22#1684038511yescharacteristic
650C4—21no—
651C4—21no—
652C4—21no—
653C4—21no—
654C4—42no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4—2441no—
659C4—2441no—
660C4#1684040011yescharacteristic
661C4#1684040311yescharacteristic
662C4#1684041411yescharacteristic
663C4#1684042311yescharacteristic
664C2—21no—
665C2—21no—
666C2—4881no—
667C2—4881no—
668C2#2144939211yescharacteristic
669C2#2145553511yescharacteristic
670C2#2145555211yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#479C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenterC2×#479D61
hypocenterC61#25363
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
4. #21447265C2semidirect
5. #21447260C2semidirect
6. #21447119C2semidirect
7. #21447119C2semidirect
8. #21446813C2semidirect
9. #21446595C2semidirect
10. #21446337C2semidirect
11. #21446337C2semidirect
12. #21445884C2semidirect
13. #21445879C2semidirect
14. C4×#14519696C2semidirect
15. C2×C61×#479C2semidirect
330. C2×#479D61semidirect
402. C61#25363semidirect

Maximal subgroups

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

subgroupindex
#214562222
#214552912
#214545622
#214472652
#214472602
#214471192
#214468132
#214465952
#214463372
#214458842
#214458792
C4×#145196962
C2×C61×#4792
#2536361