Finite Group Databasebeta

← #29699469

Subgroups — #29699469

Order 15616.

752 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454587C211yesmaximal, characteristic
2#21454483C211yesmaximal, characteristic, complemented
3#21454385C211yesmaximal, characteristic, complemented
4#21446523C211yesmaximal, characteristic, complemented
5#21446521C211yesmaximal, characteristic, complemented
6#21446418C211yesmaximal, characteristic, complemented
7#21446416C211yesmaximal, characteristic, complemented
8#21446146C211yesmaximal, characteristic
9#21446144C211yesmaximal, characteristic
10#21445955C211yesmaximal, characteristic, complemented
11#21445838C211yesmaximal, characteristic, complemented
12#21445837C211yesmaximal, characteristic, complemented
13C8×#11758196C211yesmaximal, characteristic, complemented
14#21445659C211yesmaximal, characteristic, complemented
15C61×#1764C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17C2×#14519784C2211yescharacteristic
18#41×Dic61C2211yescharacteristic
19#16840230C2211yescharacteristic
20#16839854C411yescharacteristic, complemented
21#16839854C411yescharacteristic, complemented
22#16839853C411yescharacteristic, complemented
23#16839853C411yescharacteristic, complemented
24#16839847C411yescharacteristic, complemented
25#16839847C411yescharacteristic, complemented
26#16839842C411yescharacteristic, complemented
27#16839842C411yescharacteristic, complemented
28#16839824—21no—
29#16839821—21no—
30#16839817—21no—
31#16839813—21no—
32#16839798C2211yescharacteristic
33#16839790—21no—
34#16839790C2211yescharacteristic
35#16839788—21no—
36#16839788C2211yescharacteristic
37#16839785—21no—
38#16839785C2211yescharacteristic
39#16839785C2211yescharacteristic
40C2×#14519706—21no—
41C2×#14519706C2211yescharacteristic
42C2×#14519705C2211yescharacteristic
43C2×#14519704C2211yescharacteristic
44C2×#14519703C2211yescharacteristic
45#16839759C2211yescharacteristic
46#16839730C2211yescharacteristic
47#16839728C2211yescharacteristic
48#16839718C2211yescharacteristic
49C2×C8×Dic61C2211yescharacteristic
50C2×C8×Dic61C2211yescharacteristic
51C4×#11758196C2211yescharacteristic
52#16839527C2211yescharacteristic
53#16839526C2211yescharacteristic
54#16839526C2211yescharacteristic
55#16839523C2211yescharacteristic
56#16839522C2211yescharacteristic
57#16839521C2211yescharacteristic
58#16839517C2211yescharacteristic
59#16839516C2211yescharacteristic
60C2×#131×C61C2211yescharacteristic
61C2×#104×C61C2211yescharacteristic
62C61×#416C2211yescharacteristic
63C61×#405C2211yescharacteristic
64C2×C4×C8×C61C2211yescharacteristic
65C61×#341C2211yescharacteristic
66C61×#339C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68#14519797—22no—
69#14519797—22no—
70C2×#11758202C2×C411yescharacteristic
71C2×#11758200C2×C411yescharacteristic
72C2×#11758201C2×C411yescharacteristic
73C2×#11758199C2×C411yescharacteristic
74#14519784—22no—
75#14519784—41no—
76C2×#11758194—21no—
77C2×#11758194C2311yescharacteristic
78C2×#11758194C2311yescharacteristic
79C22×#92418—21no—
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82Q8×Dic61C2×C411yescharacteristic
83Q8×Dic61C2×C411yescharacteristic
84#14519742C2×C411yescharacteristic
85#14519742C2×C411yescharacteristic
86D4×Dic61—21no—
87D4×Dic61—21no—
88D4×Dic61C2×C411yescharacteristic
89D4×Dic61C2×C411yescharacteristic
90#14519739C2×C411yescharacteristic
91#14519739C2×C411yescharacteristic
92#14519737—21no—
93#14519737—21no—
94#14519736—21no—
95#14519736C2311yescharacteristic
96#14519734—21no—
97C2×#11758196—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61C2311yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101C42×D61—21no—
102#14519710C2×C411yescharacteristic
103#14519710C2×C411yescharacteristic
104#14519708C2×C411yescharacteristic
105#14519708C2×C411yescharacteristic
106#14519706—21no—
107#14519706—21no—
108#14519706—21no—
109#14519706—21no—
110#14519706—21no—
111#14519706—21no—
112#14519706—21no—
113#14519706—21no—
114#14519706D411yescharacteristic
115#14519706D411yescharacteristic
116#14519706D411yescharacteristic
117#14519706D411yescharacteristic
118#14519705—41no—
119#14519704—22no—
120#14519703—41no—
121#14519702C2×C411yescharacteristic
122#14519702C2×C411yescharacteristic
123#14519699C2×C411yescharacteristic
124#14519699C2×C411yescharacteristic
125#14519689—21no—
126#14519689—21no—
127#14519689—21no—
128#14519689—21no—
129#14519688—21no—
130C4×#92418—21no—
131C8×Dic61—41no—
132C8×Dic61C2×C411yescharacteristic
133C8×Dic61C2×C411yescharacteristic
134C8×Dic61C2×C411yescharacteristic
135C8×Dic61C2×C411yescharacteristic
136#14519684—21no—
137C2×#41×C61C2311yescharacteristic
138#131×C61—22no—
139#131×C61—41no—
140C2×M16×C61—21no—
141C2×M16×C61C2311yescharacteristic
142C2×M16×C61C2311yescharacteristic
143C22×C8×C61—21no—
144C22×C8×C61C2311yescharacteristic
145C22×C8×C61C2311yescharacteristic
146#117×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148#104×C61—22no—
149#103×C61C2×C411yescharacteristic
150#103×C61C2×C411yescharacteristic
151#102×C61C2×C411yescharacteristic
152#102×C61C2×C411yescharacteristic
153#97×C61—21no—
154C4×C8×C61—21no—
155C4×C8×C61—41no—
156#41×C61—21no—
157#41×C61—21no—
158#41×C61#4112yes—
159#41×C61#4112yes—
160C2×Q8×C61C22×C411yescharacteristic
161C2×D4×C61—21no—
162C2×D4×C61C22×C411yescharacteristic
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61C2411yescharacteristic
166C2×C22⋊D61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61#4111yescharacteristic
171C22×Dic61#4111yescharacteristic
172#11758222—21no—
173#11758222—21no—
174#11758222—21no—
175#11758222—21no—
176C2×D244C22×C411yescharacteristic
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×Dic122C22×C411yescharacteristic
181M16×C61—21no—
182M16×C61—21no—
183M16×C61—21no—
184M16×C61—21no—
185M16×C61—42no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—42no—
193C2×C8×C61C22×C411yescharacteristic
194C2×C8×C61C22×C411yescharacteristic
195C2×C8×C61C2×D411yescharacteristic
196C2×C8×C61C2×D411yescharacteristic
197C4⋊C4×C61C22×C411yescharacteristic
198C4⋊C4×C61C22×C411yescharacteristic
199C22⋊C4×C61—21no—
200C42×C61—21no—
201C42×C61—21no—
202C42×C61—21no—
203C22⋊Dic61—21no—
204C22⋊Dic61—21no—
205C22⋊Dic61—21no—
206#11758202—22no—
207#11758201—22no—
208#11758200—22no—
209#11758199—22no—
210#11758198—21no—
211#11758198—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61C22×C411yescharacteristic
215C4⋊Dic61C22×C411yescharacteristic
216#11758196—24no—
217#11758196—21no—
218#11758196—21no—
219C4×Dic61—21no—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61C22×C411yescharacteristic
227C4×Dic61C22×C411yescharacteristic
228C4×Dic61C2×D411yescharacteristic
229C4×Dic61C2×D411yescharacteristic
230#11758194—21no—
231#11758194—21no—
232#11758194—21no—
233#11758194—21no—
234#11758194—42no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—42no—
242C2×#92418C22×C411yescharacteristic
243C2×#92418C22×C411yescharacteristic
244C2×#92418C2×D411yescharacteristic
245C2×#92418C2×D411yescharacteristic
246C23×C61—21no—
247C23×C61C2×#4111yescharacteristic
248C22×D61—21no—
249Q8×C61—21no—
250Q8×C61#11712yes—
251D4×C61—22no—
252D4×C61—22no—
253D4×C61—21no—
254D4×C61#11712yes—
255C2×C4×C61—21no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61C23×C411yescharacteristic
264C2×C4×C61C22×D411yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61C2×#4111yescharacteristic
267C2×C4×C61H(5,𝔽2)11yescharacteristic
268C2×C4×C612−1+411yescharacteristic
269C22⋊D61—41no—
270C22⋊D61—41no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—42no—
280C2×Dic61—81no—
281C2×Dic61C4×D411yescharacteristic
282C2×Dic61C4×D411yescharacteristic
283C2×Dic61C4×D411yescharacteristic
284C2×Dic61C4×D411yescharacteristic
285D244—21no—
286D244—21no—
287C4×D61—41no—
288C4×D61—41no—
289C4×D61—42no—
290C4×D61—81no—
291Dic122—21no—
292Dic122—21no—
293C8×C61—21no—
294C8×C61—21no—
295C8×C61—21no—
296C8×C61—21no—
297C8×C61—41no—
298C8×C61—41no—
299#92418—21no—
300#92418—21no—
301#92418—21no—
302#92418—21no—
303#92418—41no—
304#92418—41no—
305#22783—611nomaximal, Sylow
306C22×C61—21no—
307C22×C61—21no—
308C22×C61—22no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61C2×C4×D411yescharacteristic
312C22×C61#55211yescharacteristic
313C22×C61#55311yescharacteristic
314C2×D61—41no—
315C2×D61—41no—
316C2×D61—41no—
317C4×C61—22no—
318C4×C61—42no—
319C4×C61—41no—
320C4×C61—41no—
321C4×C61C2×#11711yescharacteristic
322C4×C61#52011yescharacteristic
323C4×C61#54611yescharacteristic
324C4×C61#54811yescharacteristic
325Dic61—21no—
326Dic61—21no—
327Dic61—21no—
328Dic61—42no—
329Dic61—41no—
330Dic61—41no—
331Dic61—41no—
332Dic61#44312yes—
333C4×#135—611no—
334#2925—611no—
335#2906—611no—
336#1937—611no—
337#1937—611no—
338#1922—611no—
339#1922—611no—
340#1876—611no—
341#1876—611no—
342#1837—611no—
343#1806—611no—
344#1806—611no—
345C8×C4⋊C4—611no—
346#1764—611no—
347#1764D6111yescharacteristic, complemented
348C2×C61—21no—
349C2×C61—21no—
350C2×C61—42no—
351C2×C61#235211yescharacteristic
352C2×C61C2×#44311yescharacteristic
353C2×C61#295711yescharacteristic
354D61—81no—
355C2×#135—611no—
356C2×#131—611no—
357C2×#131C2×D6111yescharacteristic
358C4×#41—611no—
359C4×#41—611no—
360C4×Q16—611no—
361C4×Q16—611no—
362C4×SD16—611no—
363C4×SD16—611no—
364C4×SD16—611no—
365C4×SD16—611no—
366C4×D8—611no—
367C4×D8—611no—
368#433—1221no—
369#433—1221no—
370#432—1221no—
371#431—1221no—
372#427—611no—
373#424—611no—
374#424—611no—
375#424—1221no—
376#424—1221no—
377#423—611no—
378#423—611no—
379#423—1221no—
380C2×C4⋊C8—611no—
381C2×C4⋊C8—1221no—
382C2×#104—611no—
383C2×#104—611no—
384C2×#104—611no—
385C2×#104C2×D6111yescharacteristic
386#416—611no—
387#416C2×D6111yescharacteristic
388#408—611no—
389#408—611no—
390#405—611no—
391#405C2×D6111yescharacteristic
392C2×C4×C8—611no—
393C2×C4×C8—611no—
394C2×C4×C8C2×D6111yescharacteristic
395C4×C4⋊C4—611no—
396#341—611no—
397#341—611no—
398#341—611no—
399#341C2×D6111yescharacteristic
400#339—611no—
401#339—611no—
402#339—611no—
403#339C2×D6111yescharacteristic
404#336—611no—
405#336—611no—
406C61#2278311yescharacteristic, complemented, Sylow
407C2×#41—611no—
408C2×#41C22×D6111yescharacteristic
409#135—1222no—
410#135—1222no—
411C2×Q16—611no—
412C2×SD16—611no—
413C2×SD16—611no—
414C2×D8—611no—
415#131—22no—
416#131—41no—
417#131—1222no—
418#131—2441no—
419C2×M16—21no—
420C2×M16—611no—
421C2×M16—611no—
422C2×M16—1221no—
423C2×M16C22×D6111yescharacteristic
424C2×M16C22×D6111yescharacteristic
425C22×C8—21no—
426C22×C8—611no—
427C22×C8—611no—
428C22×C8—1221no—
429C22×C8C22×D6111yescharacteristic
430C22×C8C22×D6111yescharacteristic
431C4×Q8—611no—
432C4×Q8—611no—
433C4×Q8—611no—
434C4×Q8—611no—
435C4×D4—611no—
436C4×D4—611no—
437C4×D4—611no—
438C4×D4—611no—
439C4×D4—1221no—
440C4×D4—1221no—
441C4×D4—1221no—
442C4×D4—1221no—
443#117—611no—
444#117—1221no—
445#117—1221no—
446#117C22×D6111yescharacteristic
447C2×C4⋊C4—1221no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—1221no—
451C2×C42—1221no—
452C2×C42C22×D6111yescharacteristic
453#107—611no—
454#107—611no—
455#106—611no—
456#106—611no—
457C4⋊C8—611no—
458C4⋊C8—611no—
459C4⋊C8—611no—
460C4⋊C8—611no—
461C4⋊C8—1221no—
462C4⋊C8—1221no—
463C4⋊C8—1221no—
464C4⋊C8—1221no—
465C4⋊C8—1221no—
466C4⋊C8—1221no—
467C4⋊C8—1221no—
468C4⋊C8—1221no—
469#104—22no—
470#104—1222no—
471#104—2441no—
472#104—2441no—
473#103—611no—
474#103—611no—
475#103C4×D6111yescharacteristic
476#103C4×D6111yescharacteristic
477#102—611no—
478#102—611no—
479#102C4×D6111yescharacteristic
480#102C4×D6111yescharacteristic
481C22⋊C8—1221no—
482C22⋊C8—1221no—
483C22⋊C8—1221no—
484C22⋊C8—1221no—
485#97—21no—
486#97—1221no—
487C4×C8—21no—
488C4×C8—41no—
489C4×C8—611no—
490C4×C8—611no—
491C4×C8—611no—
492C4×C8—611no—
493C4×C8—1221no—
494C4×C8—2441no—
495#95—1221no—
496#41—21no—
497#41—21no—
498#41—1221no—
499#41—1221no—
500#41—1221no—
501#41—1221no—
502#41#1175822212yes—
503#41#1175822212yes—
504C2×Q8—611no—
505C2×Q8C2×C4×D6111yescharacteristic
506C2×D4—21no—
507C2×D4—611no—
508C2×D4—1221no—
509C2×D4C2×C4×D6111yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—611no—
513C22×C4—611no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1221no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4C23×D6111yescharacteristic
521Q16—1222no—
522SD16—1222no—
523SD16—1222no—
524D8—1222no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—42no—
530M16—1221no—
531M16—1221no—
532M16—1221no—
533M16—1221no—
534M16—2442no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—42no—
542C2×C8—611no—
543C2×C8—611no—
544C2×C8—611no—
545C2×C8—611no—
546C2×C8—1221no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—2442no—
553C2×C8C2×C4×D6111yescharacteristic
554C2×C8C2×C4×D6111yescharacteristic
555C2×C8D4×D6111yescharacteristic
556C2×C8D4×D6111yescharacteristic
557C4⋊C4—611no—
558C4⋊C4—611no—
559C4⋊C4—1221no—
560C4⋊C4—1221no—
561C4⋊C4—1221no—
562C4⋊C4—1221no—
563C4⋊C4—1224no—
564C4⋊C4C2×C4×D6111yescharacteristic
565C4⋊C4C2×C4×D6111yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—1221no—
568C22⋊C4—1221no—
569C22⋊C4—1221no—
570C22⋊C4—1221no—
571C22⋊C4—1221no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—611no—
576C42—611no—
577C42—611no—
578C42—611no—
579C42—1221no—
580C42—1221no—
581C42—1221no—
582C42—1221no—
583C42—1221no—
584C42—1221no—
585C42—1221no—
586C23—21no—
587C23—1221no—
588C23#41×D6111yescharacteristic
589Q8—21no—
590Q8—1221no—
591Q8—1221no—
592Q8#1451973412yes—
593D4—22no—
594D4—22no—
595D4—21no—
596D4—1221no—
597D4—1221no—
598D4—2441no—
599D4—2441no—
600D4#1451973412yes—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—611no—
610C2×C4—611no—
611C2×C4—611no—
612C2×C4—611no—
613C2×C4—1222no—
614C2×C4—1222no—
615C2×C4—1221no—
616C2×C4—1221no—
617C2×C4—1221no—
618C2×C4—4881no—
619C2×C4—4881no—
620C2×C4—2442no—
621C2×C4—2442no—
622C2×C4—2441no—
623C2×C4—2441no—
624C2×C4—2441no—
625C2×C4—2441no—
626C2×C4—2441no—
627C2×C4C22×C4×D6111yescharacteristic
628C2×C4C2×D4×D6111yescharacteristic
629C2×C4C2×#1175822211yescharacteristic
630C2×C4C2×#1175822211yescharacteristic
631C2×C4#1451982211yescharacteristic
632C2×C4#1451982411yescharacteristic
633C8—21no—
634C8—21no—
635C8—21no—
636C8—21no—
637C8—41no—
638C8—41no—
639C8—1221no—
640C8—1221no—
641C8—1221no—
642C8—1221no—
643C8—2441no—
644C8—2441no—
645C22—21no—
646C22—21no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—2441no—
651C22—2441no—
652C22—2441no—
653C22C4×D4×D6111yescharacteristic
654C22#1684044511yescharacteristic
655C22#1684046111yescharacteristic
656C4—22no—
657C4—42no—
658C4—41no—
659C4—41no—
660C4—612no—
661C4—1221no—
662C4—1221no—
663C4—1221no—
664C4—2442no—
665C4—2441no—
666C4—2441no—
667C4—2441no—
668C4C2×#1451973411yescharacteristic
669C4#1684024111yescharacteristic
670C4#1684040211yescharacteristic
671C4#1684042111yescharacteristic
672C2—21no—
673C2—21no—
674C2—42no—
675C2—4881no—
676C2#2144874211yescharacteristic
677C2#443×D6111yescharacteristic
678C2#2145473111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1764C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519797C22
cosocleC22×C4×C61C24
hypercenter#1764D61
hypocenterC61#22783
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1764

Complements

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

NH ≅ G/Ntype
2. #21454483C2semidirect
3. #21454385C2semidirect
4. #21446523C2semidirect
5. #21446521C2semidirect
6. #21446418C2semidirect
7. #21446416C2semidirect
10. #21445955C2semidirect
11. #21445838C2semidirect
12. #21445837C2semidirect
13. C8×#11758196C2semidirect
14. #21445659C2semidirect
15. C61×#1764C2semidirect
20. #16839854C4semidirect
21. #16839854C4semidirect
22. #16839853C4semidirect
23. #16839853C4semidirect
24. #16839847C4semidirect
25. #16839847C4semidirect
26. #16839842C4semidirect
27. #16839842C4semidirect
347. #1764D61semidirect
406. C61#22783semidirect

Maximal subgroups

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

subgroupindex
#214545872
#214544832
#214543852
#214465232
#214465212
#214464182
#214464162
#214461462
#214461442
#214459552
#214458382
#214458372
C8×#117581962
#214456592
C61×#17642
#2278361