Finite Group Databasebeta

← #29687397

Subgroups — #29687397

Order 15616.

782 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455730C211yesmaximal, characteristic
2#21454511C211yesmaximal, characteristic
3#405×D61C211yesmaximal, characteristic, complemented
4#21446470C211yesmaximal, characteristic, complemented
5#21446469C211yesmaximal, characteristic, complemented
6#21446417C211yesmaximal, characteristic, complemented
7#21446416C211yesmaximal, characteristic, complemented
8#21446118C211yesmaximal, characteristic
9#21446025C211yesmaximal, characteristic, complemented
10#21445917C211yesmaximal, characteristic, complemented
11#21445704C211yesmaximal, characteristic, complemented
12#21445703C211yesmaximal, characteristic, complemented
13#21445661C211yesmaximal, characteristic, complemented
14#21445596C211yesmaximal, characteristic, complemented
15C61×#1765C211yesmaximal, characteristic, complemented
16C2×M16×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18#16840269C2211yescharacteristic
19#117×D61C2211yescharacteristic
20#16840102C411yescharacteristic, complemented
21#16840101C411yescharacteristic, complemented
22#16840096C411yescharacteristic, complemented
23#16840091C411yescharacteristic, complemented
24#16840085C411yescharacteristic, complemented
25#16840084C411yescharacteristic, complemented
26#16840079C411yescharacteristic, complemented
27#16840074C411yescharacteristic, complemented
28#16839831—21no—
29#16839831—21no—
30C8×C22⋊D61—21no—
31C8×C22⋊D61—21no—
32C2×#14519713C2211yescharacteristic
33C2×#14519712C2211yescharacteristic
34#16839800C2211yescharacteristic
35#16839798C2211yescharacteristic
36#16839790C2211yescharacteristic
37C2×#14519704C2211yescharacteristic
38#16839758C2211yescharacteristic
39#16839729C2211yescharacteristic
40#16839725C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42#16839720C2211yescharacteristic
43#16839719—21no—
44#16839718C2211yescharacteristic
45#16839717C2211yescharacteristic
46#16839717C2211yescharacteristic
47#16839716—21no—
48C2×#14519687C2211yescharacteristic
49#97×D61—21no—
50C4×C8×D61—21no—
51C4×#11758198C2211yescharacteristic
52#16839526C2211yescharacteristic
53#16839523C2211yescharacteristic
54#16839523C2211yescharacteristic
55#16839522C2211yescharacteristic
56#16839522C2211yescharacteristic
57#16839521C2211yescharacteristic
58#16839517C2211yescharacteristic
59#16839516C2211yescharacteristic
60C2×#131×C61C2211yescharacteristic
61C2×#104×C61C2211yescharacteristic
62C61×#416C2211yescharacteristic
63C61×#405C2211yescharacteristic
64C2×#97×C61C2211yescharacteristic
65C61×#341C2211yescharacteristic
66C61×#339C2211yescharacteristic
67C22×C4×D61C2311yescharacteristic
68C2×#11758194C2311yescharacteristic
69C2×#11758194C2311yescharacteristic
70C2×#11758189—21no—
71M16×D61—22no—
72M16×D61—22no—
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C2×C8×D61—21no—
76C2×C8×D61—22no—
77C2×C8×D61—22no—
78C2×C8×D61D411yescharacteristic
79C2×C8×D61D411yescharacteristic
80C2×C8×D61D411yescharacteristic
81C2×C8×D61D411yescharacteristic
82#14519758—21no—
83#14519753C2×C411yescharacteristic
84#14519753C2×C411yescharacteristic
85#14519748C2×C411yescharacteristic
86#14519748C2×C411yescharacteristic
87#14519745—21no—
88C4×C22⋊D61—21no—
89C4×C22⋊D61—21no—
90#14519736C2311yescharacteristic
91#14519736C2311yescharacteristic
92#14519735C2×C411yescharacteristic
93#14519735C2×C411yescharacteristic
94#14519734—21no—
95#14519733—21no—
96C4⋊C4×D61C2×C411yescharacteristic
97C4⋊C4×D61C2×C411yescharacteristic
98C2×#11758198—21no—
99C22⋊C4×D61—21no—
100C2×C4×Dic61C2311yescharacteristic
101C42×D61—21no—
102#14519713—22no—
103#14519712—22no—
104#14519711C2×C411yescharacteristic
105#14519711C2×C411yescharacteristic
106#14519710C2×C411yescharacteristic
107#14519710C2×C411yescharacteristic
108#14519709C2×C411yescharacteristic
109#14519709C2×C411yescharacteristic
110#14519708C2×C411yescharacteristic
111#14519708C2×C411yescharacteristic
112#14519706—21no—
113#14519706—21no—
114#14519704—22no—
115#14519701C2×C411yescharacteristic
116#14519701C2×C411yescharacteristic
117#14519698C2×C411yescharacteristic
118#14519698C2×C411yescharacteristic
119C22⋊#92418—21no—
120C22⋊#92418—21no—
121#14519689—21no—
122#14519689—21no—
123#14519689C2×C411yescharacteristic
124#14519689C2×C411yescharacteristic
125#14519689C2×C411yescharacteristic
126#14519689C2×C411yescharacteristic
127#14519688—21no—
128#14519687—21no—
129#14519687—21no—
130#14519687—22no—
131#14519687—21no—
132C4×#92418—21no—
133C8×Dic61—21no—
134C8×Dic61—21no—
135C8×Dic61—21no—
136#14519684—21no—
137C2×#41×C61C2311yescharacteristic
138#131×C61—22no—
139#131×C61—22no—
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—
154#97×C61—22no—
155C4×C8×C61—21no—
156C23×D61#4111yescharacteristic
157#41×C61—21no—
158#41×C61—21no—
159#41×C61—21no—
160#41×C61—21no—
161C2×Q8×C61C22×C411yescharacteristic
162C2×D4×C61—21no—
163C2×D4×C61C22×C411yescharacteristic
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61C2411yescharacteristic
167C2×C22⋊D61—21no—
168C2×C22⋊D61—21no—
169C22×Dic61—21no—
170C22×Dic61#4111yescharacteristic
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61C22×C411yescharacteristic
178C2×C4×D61C22×C411yescharacteristic
179C2×C4×D61C2×D411yescharacteristic
180C2×C4×D61C2×D411yescharacteristic
181M16×C61—21no—
182M16×C61—21no—
183M16×C61—21no—
184M16×C61—42no—
185M16×C61#4112yes—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—42no—
191C2×C8×C61C22×C411yescharacteristic
192C2×C8×C61C22×C411yescharacteristic
193C2×C8×C61C2×D411yescharacteristic
194C2×C8×C61C2×D411yescharacteristic
195C2×C8×C61#4112yes—
196C2×C8×C61#4112yes—
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—
206C22⋊Dic61—21no—
207#11758198—21no—
208#11758198—21no—
209#11758198—21no—
210#11758198—21no—
211#11758198—42no—
212C4⋊Dic61C22×C411yescharacteristic
213C4⋊Dic61C22×C411yescharacteristic
214C4⋊Dic61C22×C411yescharacteristic
215C4⋊Dic61C22×C411yescharacteristic
216#11758196—21no—
217#11758196—21no—
218#11758196—21no—
219#11758196—21no—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226#11758194—21no—
227#11758194—21no—
228#11758194—21no—
229#11758194#4112yes—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418C22×C411yescharacteristic
237C2×#92418C22×C411yescharacteristic
238C2×#92418C2×D411yescharacteristic
239C2×#92418C2×D411yescharacteristic
240#11758189—24no—
241C8×D61—24no—
242C8×D61—22no—
243C8×D61—22no—
244C8×D61—22no—
245C8×D61—22no—
246C23×C61—21no—
247C23×C61C2×#4111yescharacteristic
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—22no—
251C22×D61—41no—
252C22×D61C4×D411yescharacteristic
253C22×D61C4×D411yescharacteristic
254Q8×C61—21no—
255Q8×C61—21no—
256D4×C61—21no—
257D4×C61—21no—
258D4×C61—41no—
259D4×C61—41no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61C23×C411yescharacteristic
269C2×C4×C61C22×D411yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C61C2×#4111yescharacteristic
273C2×C4×C61C2×#4111yescharacteristic
274C22⋊D61—42no—
275C22⋊D61—42no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61C4×D411yescharacteristic
286C2×Dic61C4×D411yescharacteristic
287C4×D61—21no—
288C4×D61—21no—
289C4×D61—21no—
290C4×D61—21no—
291C4×D61—21no—
292C4×D61—21no—
293C4×D61—21no—
294C4×D61—21no—
295C4×D61—42no—
296C4×D61—42no—
297C8×C61—21no—
298C8×C61—21no—
299C8×C61—22no—
300C8×C61—41no—
301C8×C61#12312yes—
302C8×C61#12312yes—
303#92418—21no—
304#92418—21no—
305#92418—21no—
306#92418—21no—
307#92418—22no—
308#92418—41no—
309#21593—611nomaximal, Sylow
310C22×C61—21no—
311C22×C61—21no—
312C22×C61—41no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61C2×C4×D411yescharacteristic
316C22×C61#52911yescharacteristic
317C22×C61#52911yescharacteristic
318C2×D61—21no—
319C2×D61—21no—
320C2×D61—21no—
321C2×D61—21no—
322C2×D61—21no—
323C2×D61—42no—
324C2×D61—42no—
325C2×D61#44412yes—
326C4×C61—41no—
327C4×C61—41no—
328C4×C61—41no—
329C4×C61—81no—
330C4×C61C4×#4111yescharacteristic
331C4×C61C4×#4111yescharacteristic
332C4×C61C2×#12311yescharacteristic
333C4×C61#52511yescharacteristic
334Dic61—21no—
335Dic61—21no—
336Dic61—41no—
337Dic61—41no—
338Dic61—41no—
339Dic61—41no—
340Dic61—81no—
341#3091—611no—
342#2929—611no—
343C2×#405—611no—
344#1929—611no—
345#1929—611no—
346#1922—611no—
347#1922—611no—
348#1871—611no—
349#1855—611no—
350#1826—611no—
351#1773—611no—
352#1773—611no—
353#1765—611no—
354#1765D6111yescharacteristic, complemented
355#1752—611no—
356C2×C61—21no—
357C2×C61—21no—
358C2×C61—81no—
359C2×C61C4×#12311yescharacteristic
360C2×C61C2×#44411yescharacteristic
361C2×C61#295511yescharacteristic
362D61—22no—
363D61—41no—
364C2×#131C2×D6111yescharacteristic
365C22×M16—611no—
366C23×C8—611no—
367#525—611no—
368C2×#117—611no—
369#485—611no—
370#485—611no—
371#484—611no—
372#483—611no—
373#482—611no—
374#482—611no—
375#481—611no—
376#480—611no—
377#435—1221no—
378#435—1221no—
379C8×D4—1221no—
380C8×D4—1221no—
381C2×#108—611no—
382C2×#108—611no—
383#427—611no—
384#427—611no—
385#424—611no—
386C2×#104—611no—
387C2×#104C2×D6111yescharacteristic
388#416—611no—
389#416C2×D6111yescharacteristic
390#408—611no—
391#407—611no—
392C2×C22⋊C8—611no—
393#405—611no—
394#405—611no—
395#405—611no—
396#405—611no—
397#405—1221no—
398#405—1221no—
399#405C2×D6111yescharacteristic
400C2×#97—611no—
401C2×#97—1221no—
402C2×#97C2×D6111yescharacteristic
403C2×C4×C8—1221no—
404C4×C22⋊C4—611no—
405#341—611no—
406#341C2×D6111yescharacteristic
407#339—611no—
408#339—611no—
409#339—611no—
410#339—611no—
411#339—611no—
412#339C2×D6111yescharacteristic
413#336—611no—
414#336—611no—
415C61#2159311yescharacteristic, complemented, Sylow
416C2×#41C22×D6111yescharacteristic
417C23×C4—611no—
418#131—22no—
419#131—22no—
420C2×M16—21no—
421C2×M16—611no—
422C2×M16—611no—
423C2×M16—1221no—
424C2×M16—1222no—
425C2×M16—1222no—
426C2×M16C22×D6111yescharacteristic
427C2×M16C22×D6111yescharacteristic
428C22×C8—21no—
429C22×C8—611no—
430C22×C8—611no—
431C22×C8—611no—
432C22×C8—611no—
433C22×C8—611no—
434C22×C8—611no—
435C22×C8—1221no—
436C22×C8—1222no—
437C22×C8—1222no—
438C22×C8C22×D6111yescharacteristic
439C22×C8C22×D6111yescharacteristic
440#123—1221no—
441C22⋊Q8—611no—
442C22⋊Q8—611no—
443#121—611no—
444#121—611no—
445#120—1221no—
446C4×D4—1221no—
447C4×D4—1221no—
448#117—611no—
449#117—611no—
450#117—611no—
451#117—611no—
452#117—1221no—
453#117—1221no—
454#117C22×D6111yescharacteristic
455C2×C4⋊C4—611no—
456C2×C4⋊C4—611no—
457C2×C22⋊C4—1221no—
458C2×C22⋊C4—1221no—
459C2×C42—611no—
460C2×C42—1221no—
461C2×C42C22×D6111yescharacteristic
462#108—1222no—
463#108—1222no—
464#107—611no—
465#107—611no—
466#107—611no—
467#107—611no—
468#106—611no—
469#106—611no—
470#106—611no—
471#106—611no—
472C4⋊C8—1221no—
473C4⋊C8—1221no—
474#104—22no—
475#104—1222no—
476#103—611no—
477#103—611no—
478#103C4×D6111yescharacteristic
479#103C4×D6111yescharacteristic
480#102—611no—
481#102—611no—
482#102C4×D6111yescharacteristic
483#102C4×D6111yescharacteristic
484C22⋊C8—611no—
485C22⋊C8—611no—
486C22⋊C8—611no—
487C22⋊C8—611no—
488C22⋊C8—1221no—
489C22⋊C8—1221no—
490C22⋊C8—1221no—
491C22⋊C8—1221no—
492#97—21no—
493#97—22no—
494#97—1221no—
495#97—1221no—
496#97—1222no—
497#97—1221no—
498#97—1221no—
499C4×C8—21no—
500C4×C8—1221no—
501C4×C8—1221no—
502C4×C8—1221no—
503C4×C8—1221no—
504#95—1221no—
505C24—611no—
506#41—21no—
507#41—21no—
508#41—21no—
509#41—21no—
510C2×Q8C2×C4×D6111yescharacteristic
511C2×D4—21no—
512C2×D4—1221no—
513C2×D4—1221no—
514C2×D4C2×C4×D6111yescharacteristic
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—1221no—
528C22×C4—1221no—
529C22×C4C23×D6111yescharacteristic
530M16—21no—
531M16—21no—
532M16—21no—
533M16—42no—
534M16—612no—
535M16—1224no—
536M16—1221no—
537M16—1221no—
538M16—1221no—
539M16#1175822212yes—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—42no—
545C2×C8—611no—
546C2×C8—611no—
547C2×C8—611no—
548C2×C8—611no—
549C2×C8—1224no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1221no—
554C2×C8—1221no—
555C2×C8—1222no—
556C2×C8—1222no—
557C2×C8—1222no—
558C2×C8—1222no—
559C2×C8—1221no—
560C2×C8C2×C4×D6111yescharacteristic
561C2×C8C2×C4×D6111yescharacteristic
562C2×C8#1175822212yes—
563C2×C8D4×D6111yescharacteristic
564C2×C8D4×D6111yescharacteristic
565C2×C8#1175822412yes—
566C4⋊C4—611no—
567C4⋊C4—611no—
568C4⋊C4—611no—
569C4⋊C4—611no—
570C4⋊C4—1221no—
571C4⋊C4—1221no—
572C4⋊C4—1221no—
573C4⋊C4—1221no—
574C4⋊C4C2×C4×D6111yescharacteristic
575C4⋊C4C2×C4×D6111yescharacteristic
576C22⋊C4—21no—
577C22⋊C4—1221no—
578C22⋊C4—1221no—
579C22⋊C4—1221no—
580C22⋊C4—1221no—
581C22⋊C4—1221no—
582C22⋊C4—1221no—
583C22⋊C4—1221no—
584C22⋊C4—1221no—
585C22⋊C4—2442no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—1221no—
590C42—1221no—
591C42—1221no—
592C42—1221no—
593C42—1221no—
594C42—1221no—
595C23—21no—
596C23—611no—
597C23—611no—
598C23—1222no—
599C23—1221no—
600C23—1221no—
601C23—2441no—
602C23#41×D6111yescharacteristic
603Q8—21no—
604Q8—21no—
605D4—21no—
606D4—21no—
607D4—41no—
608D4—41no—
609D4—2442no—
610D4—2442no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—611no—
620C2×C4—611no—
621C2×C4—1221no—
622C2×C4—1221no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—1221no—
626C2×C4—1221no—
627C2×C4—1221no—
628C2×C4—1221no—
629C2×C4—1221no—
630C2×C4—1221no—
631C2×C4—1221no—
632C2×C4—1221no—
633C2×C4—1221no—
634C2×C4—1221no—
635C2×C4—2442no—
636C2×C4—2442no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4C22×C4×D6111yescharacteristic
641C2×C4C2×D4×D6111yescharacteristic
642C2×C4#41×D6111yescharacteristic
643C2×C4C2×#1175822411yescharacteristic
644C2×C4C2×#1175822211yescharacteristic
645C2×C4C2×#1175822211yescharacteristic
646C8—21no—
647C8—21no—
648C8—22no—
649C8—41no—
650C8—1221no—
651C8—1221no—
652C8—1221no—
653C8—1221no—
654C8—1222no—
655C8—2441no—
656C8#1451975912yes—
657C8#1451975912yes—
658C22—21no—
659C22—21no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—612no—
664C22—1221no—
665C22—1221no—
666C22—1221no—
667C22—1221no—
668C22—1221no—
669C22—2442no—
670C22—2442no—
671C22C4×D4×D6111yescharacteristic
672C22#1684029011yescharacteristic
673C22#1684029411yescharacteristic
674C4—41no—
675C4—41no—
676C4—41no—
677C4—81no—
678C4—1221no—
679C4—1221no—
680C4—4881no—
681C4—2441no—
682C4—2441no—
683C4—2441no—
684C4—2441no—
685C4C4×#1175822411yescharacteristic
686C4C4×#1175822211yescharacteristic
687C4C2×#1451975911yescharacteristic
688C4#1684027111yescharacteristic
689C2—21no—
690C2—21no—
691C2—81no—
692C2—1222no—
693C2—2441no—
694C2C4×#1451975911yescharacteristic
695C2#444×D6111yescharacteristic
696C2#2145471911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1765C2
socleC22×C61C2×C4×D4
prime radical#16840269C22
cosocleC22×C4×C61C24
hypercenter#1765D61
hypocenterC61#21593
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1765

Complements

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

NH ≅ G/Ntype
3. #405×D61C2semidirect
4. #21446470C2semidirect
5. #21446469C2semidirect
6. #21446417C2semidirect
7. #21446416C2semidirect
9. #21446025C2semidirect
10. #21445917C2semidirect
11. #21445704C2semidirect
12. #21445703C2semidirect
13. #21445661C2semidirect
14. #21445596C2semidirect
15. C61×#1765C2semidirect
20. #16840102C4semidirect
21. #16840101C4semidirect
22. #16840096C4semidirect
23. #16840091C4semidirect
24. #16840085C4semidirect
25. #16840084C4semidirect
26. #16840079C4semidirect
27. #16840074C4semidirect
354. #1765D61semidirect
415. C61#21593semidirect

Maximal subgroups

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

subgroupindex
#214557302
#214545112
#405×D612
#214464702
#214464692
#214464172
#214464162
#214461182
#214460252
#214459172
#214457042
#214457032
#214456612
#214455962
C61×#17652
#2159361