Finite Group Databasebeta

← #29646913

Subgroups — #29646913

Order 15616.

1216 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#41×D244C211yesmaximal, characteristic
2#21454485C211yesmaximal, characteristic, complemented
3#21444289C212yesmaximal, complemented
4#21444271C211yesmaximal, characteristic, complemented
5#21444263C212yesmaximal, complemented
6#21444245C211yesmaximal, characteristic, complemented
7#21444237C212yesmaximal, complemented
8#21444219C211yesmaximal, characteristic, complemented
9#21444211C212yesmaximal, complemented
10C2×#16839491C211yesmaximal, characteristic, complemented
11C61×#2965C211yesmaximal, characteristic, complemented
12C2×#41×D61—21no—
13#16840434C411yescharacteristic
14Q8×D244C411yescharacteristic
15#16840424—21no—
16#16840416C412yes—
17#16840416C411yescharacteristic
18#16840407—22no—
19#16840407—21no—
20D4×D244C412yes—
21D4×D244C411yescharacteristic
22#16840312C2211yescharacteristic
23#16840312C2212yes—
24#16840274—21no—
25#16840274—22no—
26C2×C4×D244C2211yescharacteristic
27C2×C4×D244C2212yes—
28#16839823—22no—
29#16839819C2212yescomplemented
30#16839815C2212yescomplemented
31#16839786C2211yescharacteristic, complemented
32C2×C4⋊#92418C2211yescharacteristic, complemented
33#16839729—21no—
34#16839718—21no—
35#16839491C2211yescharacteristic
36#16839491C2211yescharacteristic
37#16839491C2212yes—
38#16839491C2211yescharacteristic, complemented
39#16839491C2211yescharacteristic, complemented
40#16839491C2212yescomplemented
41#16839491C2212yescomplemented
42#16839491C2212yescomplemented
43#16839491C2212yescomplemented
44#16839491C2212yescomplemented
45C4×#41×C61C2211yescharacteristic
46C61×#446—21no—
47C61×#436—21no—
48C61×#435—22no—
49C61×#431C2212yescomplemented
50C61×#431C2211yescharacteristic, complemented
51C4×M16×C61C2212yescomplemented
52C2×C4×C8×C61C2211yescharacteristic, complemented
53C2×#11758226—21no—
54C2×#11758222—22no—
55C2×#11758222—21no—
56C2×#11758224—22no—
57C2×#11758224—21no—
58#41×D61—44no—
59#41×D61—44no—
60C2×Q8×D61—21no—
61C22×D244C2×C411yescharacteristic
62C22×D244C2×C412yes—
63C2×D4×D61—22no—
64C2×D4×D61—21no—
65C22×C4×D61—22no—
66C22×C4×D61—21no—
67C2×#11758194—21no—
68C22×#92418—21no—
69#14519777C2×C411yescharacteristic
70#14519777C2×C412yes—
71#14519774C2×C411yescharacteristic
72#14519774C2×C412yes—
73#14519765—21no—
74#14519765—22no—
75#14519761—22no—
76#14519761—22no—
77#14519761—22no—
78#14519757—22no—
79#14519757—21no—
80#14519757—22no—
81#14519757—21no—
82#14519752—22no—
83#14519752—21no—
84#14519752—22no—
85#14519752—21no—
86#14519751—21no—
87#14519751—22no—
88#14519751C2×C412yes—
89#14519751C2×C412yes—
90#14519751C2×C412yes—
91#14519747—22no—
92#14519747—22no—
93#14519747—22no—
94C4×D244—22no—
95C4×D244—21no—
96C4×D244—21no—
97C4×D244—22no—
98C4×D244—22no—
99C4×D244—21no—
100C4×D244C2×C411yescharacteristic
101C4×D244C2×C412yes—
102C4×D244C2×C411yescharacteristic
103C4×D244C2×C412yes—
104C4×D244C2311yescharacteristic
105C4×D244C2311yescharacteristic
106C4×D244C2312yes—
107C2×C4⋊Dic61C2×C411yescharacteristic
108C2×C4⋊Dic61C2×C412yes—
109C2×#11758198—21no—
110C2×#11758198—22no—
111C4⋊#92418—21no—
112C4⋊#92418—21no—
113C4⋊#92418C2311yescharacteristic
114C4⋊#92418C2311yescharacteristic
115C4⋊#92418C2312yes—
116C22⋊#92418—22no—
117C22⋊#92418—22no—
118#14519688—22no—
119C4×#92418—22no—
120C2×#41×C61D411yescharacteristic
121C2×M16×C61—22no—
122C22×C8×C61—21no—
123C4×Q8×C61C2×C411yescharacteristic
124C4×Q8×C61D411yescharacteristic
125C4×D4×C61C2×C412yes—
126C4×D4×C61C2×C411yescharacteristic
127C4×D4×C61D412yes—
128C4×D4×C61D411yescharacteristic
129#117×C61D411yescharacteristic
130#117×C61D412yes—
131C2×C42×C61C2311yescharacteristic
132C2×C42×C61C2312yes—
133C4⋊C8×C61—22no—
134C4⋊C8×C61—21no—
135C22⋊C8×C61—21no—
136C22⋊C8×C61—22no—
137#97×C61—22no—
138C4×C8×C61—21no—
139C4×C8×C61C2311yescharacteristic
140C4×C8×C61C2311yescharacteristic
141C4×C8×C61C2312yes—
142C23×D61—22no—
143C23×D61—21no—
144#41×C61—22no—
145#41×C61—22no—
146C2×Q8×C61C22⋊C411yescharacteristic
147C2×D4×C61C22⋊C412yes—
148C2×D4×C61C22⋊C411yescharacteristic
149C22×C4×C61C22×C412yes—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C2×D412yes—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2×D411yescharacteristic
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C22×Dic61—22no—
159C22×Dic61—21no—
160#11758226—44no—
161Q8×D61—44no—
162#11758224—48no—
163#11758224—44no—
164D4×D61—48no—
165D4×D61—44no—
166#11758222—44no—
167#11758222—44no—
168#11758222—42no—
169#11758222—42no—
170C2×D244—22no—
171C2×D244—24no—
172C2×D244—22no—
173C2×D244—21no—
174C2×D244—22no—
175C2×D244—21no—
176C2×D244—22no—
177C2×D244—21no—
178C2×D244—41no—
179C2×D244—42no—
180C2×D244C22×C411yescharacteristic
181C2×D244C22×C412yes—
182C2×D244C22×C411yescharacteristic
183C2×C4×D61—22no—
184C2×C4×D61—21no—
185C2×C4×D61—22no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—22no—
189C2×C4×D61—21no—
190C2×C4×D61—44no—
191C2×C4×D61—44no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×Dic122—22no—
195C2×Dic122—21no—
196M16×C61—44no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—22no—
200C2×C8×C61—42no—
201C4⋊C4×C61C22⋊C412yes—
202C4⋊C4×C61C22⋊C411yescharacteristic
203C4⋊C4×C61C22⋊C412yes—
204C4⋊C4×C61C22⋊C411yescharacteristic
205C22⋊C4×C61C22⋊C412yes—
206C22⋊C4×C61C22⋊C412yes—
207C22⋊C4×C61C22⋊C412yes—
208C42×C61C22×C412yes—
209C42×C61C22×C411yescharacteristic
210C42×C61C2×D412yes—
211C42×C61C2×D411yescharacteristic
212C42×C61C2×D411yescharacteristic
213C42×C61C2×D412yes—
214C42×C61C2411yescharacteristic
215#11758198—22no—
216#11758198—21no—
217#11758198—22no—
218#11758198—21no—
219#11758198—22no—
220#11758198—22no—
221#11758198—22no—
222#11758198—21no—
223#11758198—21no—
224#11758198—22no—
225C4⋊Dic61—22no—
226C4⋊Dic61—21no—
227C4⋊Dic61—22no—
228C4⋊Dic61—21no—
229C4⋊Dic61C22×C411yescharacteristic
230C4⋊Dic61C22×C411yescharacteristic
231C4⋊Dic61C22×C412yes—
232#11758194—42no—
233C2×#92418—21no—
234C2×#92418—22no—
235C2×#92418—21no—
236C2×#92418—42no—
237C23×C61C2×C22⋊C412yes—
238C23×C61C2×C22⋊C411yescharacteristic
239C22×D61—21no—
240C22×D61—22no—
241C22×D61—21no—
242C22×D61—42no—
243C22×D61—44no—
244C22×D61—44no—
245C22×D61—42no—
246C22×D61—81no—
247C22×D61—82no—
248Q8×C61—22no—
249D4×C61—24no—
250D4×C61—22no—
251C2×C4×C61—21no—
252C2×C4×C61—22no—
253C2×C4×C61—21no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—41no—
258C2×C4×C61—42no—
259C2×C4×C61C2×C22⋊C412yes—
260C2×C4×C61C2×C22⋊C411yescharacteristic
261C2×C4×C61C2×C22⋊C412yes—
262C2×C4×C61C2×C22⋊C411yescharacteristic
263C2×C4×C61C2×C22⋊C412yes—
264C2×C4×C61C2×C22⋊C411yescharacteristic
265C2×C4×C61AGL(1,ℤ/8)12yes—
266C2×C4×C61AGL(1,ℤ/8)12yes—
267C2×C4×C61C23×C411yescharacteristic
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C22×D411yescharacteristic
270C22⋊D61—44no—
271C22⋊D61—44no—
272C22⋊D61—44no—
273C2×Dic61—21no—
274C2×Dic61—22no—
275C2×Dic61—21no—
276C2×Dic61—44no—
277C2×Dic61—42no—
278D244—21no—
279D244—22no—
280D244—21no—
281D244—21no—
282D244—22no—
283D244—42no—
284D244—44no—
285D244—44no—
286D244—42no—
287D244—81no—
288D244—82no—
289D244#13112yes—
290C4×D61—44no—
291C4×D61—44no—
292C4×D61—41no—
293C4×D61—41no—
294C4×D61—42no—
295C4×D61—42no—
296C4×D61—41no—
297C4×D61—41no—
298C4×D61—42no—
299C4×D61—42no—
300Dic122—44no—
301Dic122—42no—
302C8×C61—22no—
303C8×C61—41no—
304C8×C61—42no—
305#92418—41no—
306#92418—41no—
307#92418—42no—
308#17511—611nomaximal, Sylow
309C22×C61—21no—
310C22×C61—21no—
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—22no—
314C22×C61#41812yes—
315C22×C61C22×C22⋊C411yescharacteristic
316C2×D61—22no—
317C2×D61—41no—
318C2×D61—41no—
319C2×D61—41no—
320C2×D61—42no—
321C2×D61—42no—
322C2×D61—41no—
323C2×D61—41no—
324C2×D61—42no—
325C2×D61—84no—
326C2×D61—88no—
327C4×C61—21no—
328C4×C61—22no—
329C4×C61—22no—
330C4×C61—21no—
331C4×C61—21no—
332C4×C61—22no—
333C4×C61#41812yes—
334C4×C61C2×#13111yescharacteristic
335C4×C61#56811yescharacteristic
336C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
337C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
338Dic61—41no—
339Dic61—42no—
340Dic61—41no—
341D4×#41—611no—
342#2965D6111yescharacteristic, complemented
343#2925—611no—
344#1496—612no—
345#1492—611no—
346#1490—612no—
347#1486—611no—
348#1484—612no—
349#1480—611no—
350#1478—612no—
351C2×D4⋊C8—611no—
352C2×C61—22no—
353C2×C61—42no—
354C2×C61#288011yescharacteristic
355C2×C61C2×#41811yescharacteristic
356C2×C61#290111yescharacteristic
357D61—42no—
358D61—81no—
359D61—82no—
360C22×#41—1221no—
361#550—611no—
362D4×Q8—611no—
363#548—1221no—
364#547—612no—
365#547—611no—
366#546—1222no—
367#546—1221no—
368D42—611no—
369D42—612no—
370#532—611no—
371#532—612no—
372#525—1221no—
373#525—1222no—
374C4×#41C2×D6111yescharacteristic
375C2×C4×D4—611no—
376C2×C4×D4—612no—
377#446—21no—
378#436—21no—
379#435—22no—
380#433—1222no—
381#432—612no—
382#431—612no—
383#431C2×D6112yescomplemented
384#431C2×D6111yescharacteristic, complemented
385#423—611no—
386C2×C4⋊C8—611no—
387#408—1221no—
388#405—1221no—
389C4×M16C2×D6112yescomplemented
390C2×C4×C8C2×D6111yescharacteristic, complemented
391D4⋊C8—611no—
392D4⋊C8—611no—
393D4⋊C8—612no—
394D4⋊C8—611no—
395D4⋊C8—611no—
396D4⋊C8—612no—
397D4⋊C8—612no—
398D4⋊C8—612no—
399D4⋊C8—612no—
400D4⋊C8—612no—
401C61#1751111yescharacteristic, complemented, Sylow
402C2×#41—1221no—
403C2×#41—1221no—
404C2×#41—1222no—
405C2×#41—1222no—
406C2×#41—1221no—
407C2×#41—2444no—
408C2×#41—2444no—
409C2×#41D24411yescharacteristic
410C22×Q8—1221no—
411C22×D4—611no—
412C22×D4—612no—
413C22×D4—1222no—
414C22×D4—1221no—
415C23×C4—1222no—
416C23×C4—1221no—
417C2×M16—22no—
418C2×M16—1221no—
419C22×C8—21no—
420C22×C8—1221no—
421C4⋊Q8—611no—
422C4⋊Q8—612no—
423#127—611no—
424#127—612no—
425#124—1221no—
426#124—1222no—
427#123—1222no—
428#123—1222no—
429#123—1222no—
430C22⋊Q8—1222no—
431C22⋊Q8—1221no—
432C22⋊Q8—1222no—
433C22⋊Q8—1221no—
434#121—612no—
435#121—612no—
436#121—612no—
437#121—1221no—
438#121—1222no—
439#121—1222no—
440#121—1221no—
441#121—1222no—
442#121—1221no—
443#120—1222no—
444#120—1222no—
445#120—1222no—
446C4×Q8C4×D6111yescharacteristic
447C4×Q8C22⋊D6111yescharacteristic
448C4×D4—611no—
449C4×D4—612no—
450C4×D4—611no—
451C4×D4—612no—
452C4×D4—611no—
453C4×D4—611no—
454C4×D4—612no—
455C4×D4—1222no—
456C4×D4—1221no—
457C4×D4—1222no—
458C4×D4—1221no—
459C4×D4—1221no—
460C4×D4—1222no—
461C4×D4C4×D6112yes—
462C4×D4C4×D6111yescharacteristic
463C4×D4C22⋊D6112yes—
464C4×D4C22⋊D6111yescharacteristic
465#117D24411yescharacteristic
466#117D24412yes—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—612no—
469C2×C22⋊C4—1221no—
470C2×C22⋊C4—1222no—
471C2×C42C22×D6111yescharacteristic
472C2×C42C22×D6112yes—
473C4⋊C8—22no—
474C4⋊C8—21no—
475C4⋊C8—611no—
476C4⋊C8—611no—
477C4⋊C8—612no—
478C4⋊C8—1221no—
479C4⋊C8—1221no—
480C22⋊C8—21no—
481C22⋊C8—22no—
482C22⋊C8—1222no—
483C22⋊C8—1222no—
484#97—22no—
485#97—1222no—
486C4×C8—21no—
487C4×C8—1222no—
488C4×C8C22×D6111yescharacteristic
489C4×C8C22×D6111yescharacteristic
490C4×C8C22×D6112yes—
491C24—1222no—
492C24—1221no—
493#41—22no—
494#41—22no—
495#41—2444no—
496#41—2444no—
497#41—2448no—
498#41—2444no—
499#41—2444no—
500#41—2442no—
501#41—2442no—
502C2×Q8—1222no—
503C2×Q8—1221no—
504C2×Q8—2444no—
505C2×Q8#1175819811yescharacteristic
506C2×D4—611no—
507C2×D4—611no—
508C2×D4—612no—
509C2×D4—1222no—
510C2×D4—1224no—
511C2×D4—1222no—
512C2×D4—1222no—
513C2×D4—1222no—
514C2×D4—1222no—
515C2×D4—1221no—
516C2×D4—1222no—
517C2×D4—1221no—
518C2×D4—1222no—
519C2×D4—1221no—
520C2×D4—2441no—
521C2×D4—2442no—
522C2×D4—2448no—
523C2×D4—2444no—
524C2×D4#1175819812yes—
525C2×D4#1175819811yescharacteristic
526C22×C4—1222no—
527C22×C4—1221no—
528C22×C4—1221no—
529C22×C4—1222no—
530C22×C4—1221no—
531C22×C4—1222no—
532C22×C4—1221no—
533C22×C4—1222no—
534C22×C4—1221no—
535C22×C4—2444no—
536C22×C4—2444no—
537C22×C4—2442no—
538C22×C4—2442no—
539C22×C4C2×C4×D6112yes—
540C22×C4C2×C4×D6111yescharacteristic
541C22×C4C2×D24412yes—
542C22×C4C2×D24411yescharacteristic
543C22×C4C2×C22⋊D6111yescharacteristic
544C22×C4C2×C22⋊D6112yes—
545M16—44no—
546M16—2442no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—22no—
550C2×C8—42no—
551C2×C8—1221no—
552C2×C8—1222no—
553C2×C8—1221no—
554C2×C8—2442no—
555C4⋊C4—611no—
556C4⋊C4—611no—
557C4⋊C4—612no—
558C4⋊C4—1222no—
559C4⋊C4—1221no—
560C4⋊C4—1222no—
561C4⋊C4—1221no—
562C4⋊C4#1175819812yes—
563C4⋊C4#1175819811yescharacteristic
564C4⋊C4#1175819812yes—
565C4⋊C4#1175819811yescharacteristic
566C22⋊C4—1221no—
567C22⋊C4—1221no—
568C22⋊C4—1222no—
569C22⋊C4—1222no—
570C22⋊C4—1221no—
571C22⋊C4—1222no—
572C22⋊C4—1221no—
573C22⋊C4—1222no—
574C22⋊C4—1222no—
575C22⋊C4—1222no—
576C22⋊C4#1175819812yes—
577C22⋊C4#1175819812yes—
578C22⋊C4#1175819812yes—
579C42C2×C4×D6112yes—
580C42C2×C4×D6111yescharacteristic
581C42C2×D24412yes—
582C42C2×D24411yescharacteristic
583C42C2×C22⋊D6111yescharacteristic
584C42C2×C22⋊D6112yes—
585C42C23×D6111yescharacteristic
586C23—1221no—
587C23—1222no—
588C23—1221no—
589C23—4881no—
590C23—4882no—
591C23—2442no—
592C23—2444no—
593C23—2444no—
594C23—2442no—
595C23C2×#1175819812yes—
596C23C2×#1175819811yescharacteristic
597Q8—22no—
598Q8—2444no—
599Q8—2442no—
600D4—24no—
601D4—22no—
602D4—612no—
603D4—1221no—
604D4—1222no—
605D4—1221no—
606D4—1221no—
607D4—1222no—
608D4—4881no—
609D4—4882no—
610D4—2442no—
611D4—2444no—
612D4—2444no—
613D4—2444no—
614D4—2444no—
615D4—2444no—
616D4—2442no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—1221no—
626C2×C4—1222no—
627C2×C4—1221no—
628C2×C4—2444no—
629C2×C4—2444no—
630C2×C4—2444no—
631C2×C4—2442no—
632C2×C4—2442no—
633C2×C4—2442no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4—2442no—
637C2×C4—2442no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4C2×#1175819812yes—
641C2×C4C2×#1175819811yescharacteristic
642C2×C4C2×#1175819812yes—
643C2×C4C2×#1175819812yes—
644C2×C4C2×#1175819811yescharacteristic
645C2×C4C2×#1175819811yescharacteristic
646C2×C4#1451980512yes—
647C2×C4#1451980512yes—
648C2×C4C22×C4×D6111yescharacteristic
649C2×C4C22×C22⋊D6111yescharacteristic
650C2×C4C22×D24411yescharacteristic
651C8—22no—
652C8—41no—
653C8—42no—
654C8—2441no—
655C8—2441no—
656C8—2442no—
657C22—21no—
658C22—21no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—1222no—
663C22—4884no—
664C22—4888no—
665C22—2441no—
666C22—2442no—
667C22—2441no—
668C22—2442no—
669C22—2442no—
670C22—2441no—
671C22—2441no—
672C22—2441no—
673C22#1683976812yes—
674C22C22×#1175819811yescharacteristic
675C4—21no—
676C4—21no—
677C4—22no—
678C4—21no—
679C4—22no—
680C4—22no—
681C4—2441no—
682C4—2442no—
683C4—2441no—
684C4#1683976812yes—
685C4#131×D6111yescharacteristic
686C4#1684052711yescharacteristic
687C4C2×#1451980511yescharacteristic
688C4C2×#1451980511yescharacteristic
689C2—22no—
690C2—42no—
691C2—4881no—
692C2—4882no—
693C2—2442no—
694C2#2145426611yescharacteristic
695C2C2×#1683976811yescharacteristic
696C2#2145436711yescharacteristic
subgroupG/H
centerC2×C4C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2965C2
socleC22×C61C22×C22⋊C4
prime radical#41×D244C2
cosocleC42×C61C24
hypercenter#2965D61
hypocenterC61#17511
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #21454485C2semidirect
3. #21444289C2semidirect
4. #21444271C2semidirect
5. #21444263C2semidirect
6. #21444245C2semidirect
7. #21444237C2semidirect
8. #21444219C2semidirect
9. #21444211C2semidirect
10. C2×#16839491C2semidirect
11. C61×#2965C2semidirect
29. #16839819C22semidirect
30. #16839815C22semidirect
31. #16839786C22semidirect
32. C2×C4⋊#92418C22semidirect
38. #16839491C22semidirect
39. #16839491C22semidirect
40. #16839491C22semidirect
41. #16839491C22semidirect
42. #16839491C22semidirect
43. #16839491C22semidirect
44. #16839491C22semidirect
49. C61×#431C22semidirect
50. C61×#431C22semidirect
51. C4×M16×C61C22semidirect
52. C2×C4×C8×C61C22semidirect
342. #2965D61semidirect
383. #431C2×D61semidirect
384. #431C2×D61semidirect
389. C4×M16C2×D61semidirect
390. C2×C4×C8C2×D61semidirect
401. C61#17511semidirect

Maximal subgroups

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

subgroupindex
#41×D2442
#214544852
#214442892
#214442712
#214442632
#214442452
#214442372
#214442192
#214442112
C2×#168394912
C61×#29652
#1751161