Finite Group Databasebeta

← #29687405

Subgroups — #29687405

Order 15616.

768 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#21455732C211yesmaximal, characteristic
2#21454518C211yesmaximal, characteristic
3#21454238C211yesmaximal, characteristic, complemented
4#21446465C211yesmaximal, characteristic, complemented
5#21446465C211yesmaximal, characteristic, complemented
6#21446416C211yesmaximal, characteristic, complemented
7#21446416C211yesmaximal, characteristic, complemented
8#21446119C211yesmaximal, characteristic
9#21446023C211yesmaximal, characteristic, complemented
10#21445702C211yesmaximal, characteristic, complemented
11#21445697C211yesmaximal, characteristic, complemented
12#21445660C211yesmaximal, characteristic, complemented
13#21445653C211yesmaximal, characteristic, complemented
14#21445603C211yesmaximal, characteristic, complemented
15C61×#1826C211yesmaximal, characteristic, complemented
16C2×#14519785C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19#16840273C2211yescharacteristic
20#16840103C411yescharacteristic, complemented
21#16840103C411yescharacteristic, complemented
22#16840097C411yescharacteristic, complemented
23#16840092C411yescharacteristic, complemented
24#16840086C411yescharacteristic, complemented
25#16840086C411yescharacteristic, complemented
26#16840080C411yescharacteristic, complemented
27#16840075C411yescharacteristic, complemented
28#16839837—21no—
29#16839837—21no—
30#16839836—21no—
31#16839836—21no—
32C2×#14519712C2211yescharacteristic
33C2×#14519712C2211yescharacteristic
34#16839798C2211yescharacteristic
35#16839798C2211yescharacteristic
36#16839790C2211yescharacteristic
37C2×#14519705C2211yescharacteristic
38C2×#14519705C2211yescharacteristic
39#16839756C2211yescharacteristic
40#16839756C2211yescharacteristic
41#16839730C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43#16839720C2211yescharacteristic
44#16839718—21no—
45#16839718—21no—
46#16839718C2211yescharacteristic
47#16839718C2211yescharacteristic
48#16839718C2211yescharacteristic
49#16839718C2211yescharacteristic
50C4×#11758194—21no—
51C4×#11758194—21no—
52C2×#14519688C2211yescharacteristic
53C2×C4×#92418C2211yescharacteristic
54#16839526C2211yescharacteristic
55#16839526C2211yescharacteristic
56#16839522C2211yescharacteristic
57#16839522C2211yescharacteristic
58#16839517C2211yescharacteristic
59#16839517C2211yescharacteristic
60C2×#117×C61C2211yescharacteristic
61C61×#407C2211yescharacteristic
62C4×C22⋊C4×C61C2211yescharacteristic
63C61×#339C2211yescharacteristic
64C61×#339C2211yescharacteristic
65C61×#339C2211yescharacteristic
66C61×#339C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68#14519785—22no—
69#14519785—22no—
70C2×#11758194—21no—
71C2×#11758194—22no—
72C2×#11758194—22no—
73C2×#11758194—22no—
74C2×#11758194—22no—
75C2×#11758194D411yescharacteristic
76C2×#11758194D411yescharacteristic
77C2×#11758194D411yescharacteristic
78C2×#11758194D411yescharacteristic
79C2×#11758194C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81C2×#11758189—21no—
82C22×#92418—21no—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C2×C8×D61—21no—
88#14519760—21no—
89#14519756C2×C411yescharacteristic
90#14519756C2×C411yescharacteristic
91#14519751C2×C411yescharacteristic
92#14519751C2×C411yescharacteristic
93#14519746—21no—
94C4×C22⋊D61—21no—
95C4×C22⋊D61—21no—
96#14519736C2311yescharacteristic
97#14519712—22no—
98#14519712—22no—
99#14519710C2×C411yescharacteristic
100#14519710C2×C411yescharacteristic
101#14519710C2×C411yescharacteristic
102#14519710C2×C411yescharacteristic
103#14519708C2×C411yescharacteristic
104#14519708C2×C411yescharacteristic
105#14519708C2×C411yescharacteristic
106#14519708C2×C411yescharacteristic
107#14519706—21no—
108#14519706—21no—
109#14519705—22no—
110#14519705—22no—
111#14519700C2×C411yescharacteristic
112#14519700C2×C411yescharacteristic
113#14519700C2×C411yescharacteristic
114#14519700C2×C411yescharacteristic
115#14519697C2×C411yescharacteristic
116#14519697C2×C411yescharacteristic
117#14519697C2×C411yescharacteristic
118#14519697C2×C411yescharacteristic
119C22⋊#92418C2×C411yescharacteristic
120C22⋊#92418C2×C411yescharacteristic
121C22⋊#92418C2×C411yescharacteristic
122C22⋊#92418C2×C411yescharacteristic
123#14519689—21no—
124#14519689—21no—
125#14519688—21no—
126#14519688—21no—
127#14519688—21no—
128#14519688—21no—
129#14519688—22no—
130#14519687—21no—
131C4×#92418—21no—
132C4×#92418—21no—
133C4×#92418—21no—
134C4×#92418—21no—
135C4×#92418—22no—
136C8×Dic61—21no—
137C23×C4×C61C2311yescharacteristic
138C2×M16×C61C2311yescharacteristic
139C2×M16×C61C2311yescharacteristic
140#117×C61—21no—
141#117×C61—21no—
142#117×C61C2×C411yescharacteristic
143#117×C61C2×C411yescharacteristic
144#117×C61C2311yescharacteristic
145#117×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2×C411yescharacteristic
147C2×C4⋊C4×C61C2×C411yescharacteristic
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150C2×C42×C61—21no—
151C2×C42×C61C2311yescharacteristic
152C2×C42×C61C2311yescharacteristic
153C22⋊C8×C61—21no—
154C22⋊C8×C61—21no—
155#95×C61—21no—
156C24×C61#4111yescharacteristic
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C22×C411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61#4111yescharacteristic
170C22×C4×C61C2411yescharacteristic
171C2×C22⋊D61—21no—
172C2×C22⋊D61—21no—
173C2×C22⋊D61—21no—
174#11758222—21no—
175#11758222—21no—
176#11758222—21no—
177#11758222—21no—
178C2×D244C22×C411yescharacteristic
179C2×C4×D61—21no—
180C2×Dic122C22×C411yescharacteristic
181M16×C61—21no—
182M16×C61—21no—
183M16×C61—21no—
184M16×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61C22×C411yescharacteristic
190C4⋊C4×C61C22×C411yescharacteristic
191C4⋊C4×C61C22×C411yescharacteristic
192C4⋊C4×C61C22×C411yescharacteristic
193C22⋊C4×C61—21no—
194C22⋊C4×C61—21no—
195C22⋊C4×C61—21no—
196C22⋊C4×C61—21no—
197C22⋊C4×C61—42no—
198C42×C61—21no—
199C42×C61—21no—
200C42×C61—21no—
201C42×C61—21no—
202C42×C61—21no—
203C42×C61—21no—
204C42×C61—21no—
205C42×C61—21no—
206C22⋊Dic61—21no—
207C22⋊Dic61—21no—
208C22⋊Dic61—21no—
209#11758198—21no—
210#11758198—21no—
211C4⋊Dic61C22×C411yescharacteristic
212C4⋊Dic61C22×C411yescharacteristic
213#11758196—21no—
214#11758196—21no—
215C4×Dic61—21no—
216#11758194—24no—
217#11758194—21no—
218#11758194—21no—
219#11758194—22no—
220#11758194—22no—
221#11758194—22no—
222#11758194—22no—
223#11758194#4112yes—
224#11758194#4112yes—
225C2×#92418—24no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418C22×C411yescharacteristic
235C2×#92418C22×C411yescharacteristic
236C2×#92418C22×C411yescharacteristic
237C2×#92418C22×C411yescharacteristic
238C2×#92418C2×D411yescharacteristic
239C2×#92418C2×D411yescharacteristic
240C2×#92418C2×D411yescharacteristic
241C2×#92418C2×D411yescharacteristic
242C2×#92418#4112yes—
243C2×#92418#4112yes—
244#11758189—42no—
245C8×D61—42no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61C4×D411yescharacteristic
251C23×C61C4×D411yescharacteristic
252C23×C61C2×#4111yescharacteristic
253C22×D61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—22no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—81no—
275C2×C4×C61—81no—
276C2×C4×C61C4×D411yescharacteristic
277C2×C4×C61C4×D411yescharacteristic
278C2×C4×C61C23×C411yescharacteristic
279C2×C4×C61C22×D411yescharacteristic
280C2×C4×C61C2×#4111yescharacteristic
281C2×C4×C61C2×#4111yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C22⋊D61—41no—
285C22⋊D61—41no—
286C22⋊D61—81no—
287C22⋊D61—81no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291D244—21no—
292D244—21no—
293C4×D61—41no—
294C4×D61—41no—
295Dic122—21no—
296Dic122—21no—
297C8×C61—41no—
298C8×C61—41no—
299#92418—21no—
300#92418—21no—
301#92418—21no—
302#92418—21no—
303#92418—21no—
304#92418—21no—
305#92418—22no—
306#92418—22no—
307#92418#12312yes—
308#92418#12312yes—
309#21594—611nomaximal, Sylow
310C22×C61—21no—
311C22×C61—21no—
312C22×C61—21no—
313C22×C61—21no—
314C22×C61—21no—
315C22×C61—21no—
316C22×C61—21no—
317C22×C61—21no—
318C22×C61—81no—
319C22×C61—81no—
320C22×C61C2×C4×D411yescharacteristic
321C22×C61#52911yescharacteristic
322C22×C61#52911yescharacteristic
323C2×D61—41no—
324C2×D61—41no—
325C2×D61—41no—
326C4×C61—21no—
327C4×C61—21no—
328C4×C61—42no—
329C4×C61—41no—
330C4×C61—41no—
331C4×C61—41no—
332C4×C61—41no—
333C4×C61—81no—
334C4×C61C4×#4111yescharacteristic
335C4×C61C4×#4111yescharacteristic
336C4×C61C2×#12311yescharacteristic
337C4×C61#52511yescharacteristic
338Dic61—41no—
339Dic61—41no—
340Dic61—41no—
341#3091—611no—
342#2930—611no—
343#2873—611no—
344#1929—611no—
345#1929—611no—
346#1922—611no—
347#1922—611no—
348#1871—611no—
349#1855—611no—
350#1826D6111yescharacteristic, complemented
351#1773—611no—
352#1772—611no—
353#1765—611no—
354#1764—611no—
355#1753—611no—
356C2×C61—21no—
357C2×C61—21no—
358C2×C61—41no—
359C2×C61—41no—
360C2×C61C4×#12311yescharacteristic
361C2×C61#295611yescharacteristic
362C2×C61#295711yescharacteristic
363D61—81no—
364C2×#131—611no—
365C22×M16—611no—
366C22×M16—611no—
367#525—611no—
368C2×#117C2×D6111yescharacteristic
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#436—1221no—
378#436—1221no—
379#435—1221no—
380#435—1221no—
381C2×#108—611no—
382C2×#108—611no—
383#427—611no—
384#427—611no—
385#424—611no—
386C2×#104—611no—
387C2×#104—611no—
388#416—611no—
389#416—611no—
390#408—611no—
391#407C2×D6111yescharacteristic
392C2×C22⋊C8—611no—
393#405—611no—
394#405—611no—
395#405—611no—
396#405—611no—
397#405—611no—
398#405—1221no—
399#405—1221no—
400C4×M16—1221no—
401C4×M16—1221no—
402C2×#97—611no—
403C2×C4×C8—611no—
404C4×C22⋊C4C2×D6111yescharacteristic
405#341—611no—
406#341—611no—
407#339—611no—
408#339—611no—
409#339C2×D6111yescharacteristic
410#339C2×D6111yescharacteristic
411#339C2×D6111yescharacteristic
412#339C2×D6111yescharacteristic
413#336—611no—
414#336—611no—
415C61#2159411yescharacteristic, complemented, Sylow
416C2×#41—611no—
417C23×C4C22×D6111yescharacteristic
418#131—1222no—
419#131—1222no—
420C2×M16—611no—
421C2×M16—611no—
422C2×M16—611no—
423C2×M16—611no—
424C2×M16—611no—
425C2×M16—611no—
426C2×M16—1221no—
427C2×M16—1222no—
428C2×M16—1222no—
429C2×M16—1222no—
430C2×M16—1222no—
431C2×M16—1221no—
432C2×M16C22×D6111yescharacteristic
433C2×M16C22×D6111yescharacteristic
434C22×C8—611no—
435C22×C8—611no—
436C22×C8—611no—
437C22×C8—611no—
438C22×C8—1221no—
439C22×C8—1221no—
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—21no—
449#117—21no—
450#117—611no—
451#117C4×D6111yescharacteristic
452#117C4×D6111yescharacteristic
453#117C22×D6111yescharacteristic
454#117C22×D6111yescharacteristic
455C2×C4⋊C4C4×D6111yescharacteristic
456C2×C4⋊C4C4×D6111yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C42—21no—
460C2×C42C22×D6111yescharacteristic
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—1222no—
475#104—1222no—
476#103—611no—
477#103—611no—
478#103—611no—
479#103—611no—
480#102—611no—
481#102—611no—
482#102—611no—
483#102—611no—
484C22⋊C8—21no—
485C22⋊C8—21no—
486C22⋊C8—611no—
487C22⋊C8—611no—
488C22⋊C8—611no—
489C22⋊C8—611no—
490C22⋊C8—1221no—
491C22⋊C8—1221no—
492#97—1222no—
493#97—1221no—
494#97—1221no—
495#97—1221no—
496#97—1221no—
497#97—1221no—
498C4×C8—1222no—
499C4×C8—1221no—
500C4×C8—1221no—
501C4×C8—1221no—
502C4×C8—1221no—
503C4×C8—1221no—
504#95—21no—
505C24#1175822411yescharacteristic
506#41—1221no—
507#41—1221no—
508#41—1221no—
509#41—1221no—
510C2×Q8—611no—
511C2×D4—611no—
512C2×D4—1221no—
513C2×D4—1221no—
514C2×D4—1221no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—1221no—
524C22×C4C2×C4×D6111yescharacteristic
525C22×C4C2×C4×D6111yescharacteristic
526C22×C4D4×D6111yescharacteristic
527C22×C4D4×D6111yescharacteristic
528C22×C4#1175822411yescharacteristic
529C22×C4C23×D6111yescharacteristic
530M16—21no—
531M16—21no—
532M16—21no—
533M16—21no—
534M16—612no—
535M16—612no—
536M16—1222no—
537M16—1222no—
538M16—1222no—
539M16—1222no—
540M16—1224no—
541M16—1221no—
542M16—1221no—
543M16—2442no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—611no—
547C2×C8—611no—
548C2×C8—612no—
549C2×C8—612no—
550C2×C8—611no—
551C2×C8—611no—
552C2×C8—611no—
553C2×C8—611no—
554C2×C8—611no—
555C2×C8—611no—
556C2×C8—1224no—
557C2×C8—1221no—
558C2×C8—1221no—
559C2×C8—1221no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8—1221no—
563C2×C8—1221no—
564C2×C8—1221no—
565C2×C8—2442no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—611no—
569C4⋊C4—611no—
570C4⋊C4—1221no—
571C4⋊C4—1221no—
572C4⋊C4C2×C4×D6111yescharacteristic
573C4⋊C4C2×C4×D6111yescharacteristic
574C4⋊C4C2×C4×D6111yescharacteristic
575C4⋊C4C2×C4×D6111yescharacteristic
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—42no—
581C22⋊C4—1221no—
582C22⋊C4—1221no—
583C22⋊C4—1221no—
584C22⋊C4—1221no—
585C22⋊C4—1221no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—1221no—
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—1221no—
600C23#1451973711yescharacteristic
601C23#1451973711yescharacteristic
602C23C2×#1175822411yescharacteristic
603Q8—1221no—
604Q8—1221no—
605D4—1221no—
606D4—1221no—
607D4—4881no—
608D4—4881no—
609D4—2441no—
610D4—2441no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—1221no—
634C2×C4—1221no—
635C2×C4—1221no—
636C2×C4—2441no—
637C2×C4—2441no—
638C2×C4#1451973711yescharacteristic
639C2×C4#1451973711yescharacteristic
640C2×C4C22×C4×D6111yescharacteristic
641C2×C4C2×D4×D6111yescharacteristic
642C2×C4#41×D6111yescharacteristic
643C2×C4#41×D6111yescharacteristic
644C2×C4#41×D6111yescharacteristic
645C2×C4#41×D6111yescharacteristic
646C8—41no—
647C8—41no—
648C8—612no—
649C8—612no—
650C8—1221no—
651C8—1221no—
652C8—1221no—
653C8—1221no—
654C8—1221no—
655C8—1221no—
656C8—1222no—
657C8—1222no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—81no—
667C22—81no—
668C22—2441no—
669C22—2441no—
670C22—2441no—
671C22C2×#1451973711yescharacteristic
672C22#1684028911yescharacteristic
673C22#1684028911yescharacteristic
674C4—21no—
675C4—21no—
676C4—42no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—81no—
682C4—2441no—
683C4—2441no—
684C4—2441no—
685C4#1684023011yescharacteristic
686C4#1684023011yescharacteristic
687C4#123×D6111yescharacteristic
688C4#1684027011yescharacteristic
689C2—21no—
690C2—21no—
691C2—41no—
692C2—41no—
693C2—4881no—
694C2#2144833611yescharacteristic
695C2#2145472511yescharacteristic
696C2#2145473211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1826C2
socleC22×C61C2×C4×D4
prime radical#16840273C22
cosocleC22×C4×C61C24
hypercenter#1826D61
hypocenterC61#21594
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
3. #21454238C2semidirect
4. #21446465C2semidirect
5. #21446465C2semidirect
6. #21446416C2semidirect
7. #21446416C2semidirect
9. #21446023C2semidirect
10. #21445702C2semidirect
11. #21445697C2semidirect
12. #21445660C2semidirect
13. #21445653C2semidirect
14. #21445603C2semidirect
15. C61×#1826C2semidirect
20. #16840103C4semidirect
21. #16840103C4semidirect
22. #16840097C4semidirect
23. #16840092C4semidirect
24. #16840086C4semidirect
25. #16840086C4semidirect
26. #16840080C4semidirect
27. #16840075C4semidirect
350. #1826D61semidirect
415. C61#21594semidirect

Maximal subgroups

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

subgroupindex
#214557322
#214545182
#214542382
#214464652
#214464162
#214461192
#214460232
#214457022
#214456972
#214456602
#214456532
#214456032
C61×#18262
#2159461