Finite Group Databasebeta

← #29684258

Subgroups — #29684258

Order 15616.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839849C211yesmaximal, characteristic
2#21448290C211yesmaximal, characteristic, complemented
3#21448277C211yesmaximal, characteristic
4#21446700C211yesmaximal, characteristic
5#21446698C211yesmaximal, characteristic
6#21446563C211yesmaximal, characteristic, complemented
7#21446517C211yesmaximal, characteristic
8#21446515C211yesmaximal, characteristic
9#21446510C211yesmaximal, characteristic, complemented
10#21446508C211yesmaximal, characteristic, complemented
11#107×Dic61C211yesmaximal, characteristic, complemented
12#21445638C211yesmaximal, characteristic, complemented
13#21445633C211yesmaximal, characteristic
14#97×Dic61C211yesmaximal, characteristic, complemented
15C61×#1944C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C2×#14519742C2211yescharacteristic
18C2×#14519739C2211yescharacteristic
19C2×#14519735—21no—
20#16839849C418yescomplemented
21C2×#14519711C2211yescharacteristic
22C2×#14519702C2211yescharacteristic
23C2×#14519700C2211yescharacteristic
24C2×#14519700C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519688C2211yescharacteristic
29C2×#14519687C2211yescharacteristic
30C2×#14519687C2211yescharacteristic
31C2×C8×Dic61C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33#16839668C2211yescharacteristic
34#16839667C2211yescharacteristic
35#16839664C2211yescharacteristic
36#16839663C2211yescharacteristic
37#16839661C2211yescharacteristic
38#16839661C2211yescharacteristic
39#16839654—21no—
40#16839652—21no—
41#16839649—21no—
42#16839643—21no—
43C4⋊C4×Dic61—21no—
44C4⋊C4×Dic61C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46#16839609—21no—
47#16839607—21no—
48C42×Dic61C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic
55C2×#97×C61C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#389C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×Dic122C2311yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C4×D61—21no—
63C2×#11758190—22no—
64C2×#11758190—22no—
65C2×#11758190C2×C414yes—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519742—22no—
69#14519742C2×C414yes—
70#14519739—22no—
71#14519739C2×C414yes—
72#14519735—44no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758196—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61D411yescharacteristic
87C2×C4×Dic61D411yescharacteristic
88C2×C4×Dic61D411yescharacteristic
89C2×C4×Dic61D411yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92#14519711—22no—
93#14519702—22no—
94#14519700—22no—
95#14519700C2×C414yes—
96#14519699—22no—
97#14519697—22no—
98#14519697C2×C414yes—
99#14519688—22no—
100#14519687—22no—
101#14519687—22no—
102C8×Dic61—22no—
103C8×Dic61C2×C414yes—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C42×C61C2311yescharacteristic
121#107×C61—22no—
122#106×C61C2×C414yes—
123#97×C61—22no—
124#95×C61—21no—
125#95×C61—21no—
126C23×D61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2411yescharacteristic
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61C2×D411yescharacteristic
138C22×Dic61C2×D411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140C22×Dic61C2×D411yescharacteristic
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244C22×C412yes—
147C2×C4×D61—24no—
148C2×C4×D61—42no—
149C2×C4×D61—42no—
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122C22×C412yes—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61C22×C412yes—
159C2×C8×C61#4112yes—
160C2×C8×C61#4112yes—
161C2×C8×C61#4112yes—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—42no—
169C4⋊C4×C61—42no—
170C4⋊C4×C61C22×C412yes—
171C4⋊C4×C61C22×C412yes—
172C42×C61—21no—
173C42×C61—21no—
174#11758198—24no—
175#11758198—42no—
176#11758198—42no—
177#11758198—42no—
178#11758198—42no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—42no—
184C4⋊Dic61—42no—
185#11758196—24no—
186C4×Dic61—21no—
187C4×Dic61—21no—
188C4×Dic61—24no—
189C4×Dic61—22no—
190C4×Dic61—22no—
191C4×Dic61—41no—
192C4×Dic61—41no—
193C4×Dic61—42no—
194C4×Dic61—42no—
195C4×Dic61C22×C412yes—
196C4×Dic61#4112yes—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C22×C412yes—
202C2×#92418#4112yes—
203#11758190—28no—
204C23×C61C22×D411yescharacteristic
205C22×D61—22no—
206C22×D61—41no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—41no—
211C22×D61—41no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61C23×C411yescharacteristic
231C2×C4×C61C2×#4111yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—22no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61C4×D412yes—
254C2×Dic61C4×D412yes—
255C2×Dic61AGL(1,ℤ/8)12yes—
256C2×Dic61#13712yes—
257D244—22no—
258D244—22no—
259D244—41no—
260D244—41no—
261C4×D61—48no—
262Dic122—22no—
263Dic122—22no—
264Dic122—41no—
265Dic122—41no—
266C8×C61—22no—
267C8×C61#11714yescomplemented
268#92418—22no—
269#92418—22no—
270#21279—611nomaximal, Sylow
271C22×C61C2×C4×D411yescharacteristic
272C22×C61#53211yescharacteristic
273C22×C61#53211yescharacteristic
274C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C61C2×#13711yescharacteristic
276C22×C61#57511yescharacteristic
277C22×C61#57511yescharacteristic
278C2×D61—42no—
279C2×D61—42no—
280C2×D61—42no—
281C2×D61—81no—
282C2×D61—81no—
283C2×D61—81no—
284C2×D61—81no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61—42no—
288C4×C61—42no—
289C4×C61—81no—
290C4×C61—81no—
291C4×C61C2×#11711yescharacteristic
292C4×C61C4×#4111yescharacteristic
293C4×C61#52911yescharacteristic
294C4×C61#52911yescharacteristic
295Dic61—22no—
296Dic61—41no—
297Dic61—41no—
298Dic61—42no—
299Dic61—81no—
300Dic61—81no—
301Dic61#44014yes—
302C2×C4×SD16—611no—
303#2295—611no—
304#2293—611no—
305#1973—611no—
306#1973—611no—
307#1944—611no—
308#1944D6111yescharacteristic, complemented
309#1936—611no—
310#1936—611no—
311#1935—611no—
312#1935—611no—
313C4×#107—611no—
314C4×#103—611no—
315C4×#102—611no—
316C4×#97—611no—
317C2×C61#229311yescharacteristic
318C2×C61C2×#44011yescharacteristic
319C2×C61#294311yescharacteristic
320C2×C61#317111yescharacteristic
321C2×C61#317111yescharacteristic
322C2×C61#317211yescharacteristic
323C2×C61#317211yescharacteristic
324D61—82no—
325C22×SD16—611no—
326C2×C4×Q8—611no—
327C2×C4×D4—611no—
328C2×#117—1221no—
329C4×SD16—618no—
330C2×#107—611no—
331C2×#107C2×D6111yescharacteristic
332C2×#106C2×D6111yescharacteristic
333C2×#103—611no—
334C2×#103—611no—
335C2×#103—611no—
336C2×#102—611no—
337C2×#102—611no—
338C2×#102—611no—
339C2×#97—611no—
340C2×#97—611no—
341C2×#97—611no—
342C2×#97C2×D6111yescharacteristic
343C2×C4×C8—611no—
344C2×C4×C8—611no—
345#391—611no—
346#391—611no—
347#390—611no—
348#390—611no—
349#389—611no—
350#389—611no—
351#389C2×D6111yescharacteristic
352#389C2×D6111yescharacteristic
353#388—1221no—
354#388—1221no—
355#387—1221no—
356#387—1221no—
357C4×C4⋊C4—611no—
358C4×C4⋊C4—611no—
359C4×C4⋊C4—1221no—
360C4×C22⋊C4—1221no—
361#376—1221no—
362C43—611no—
363#340—611no—
364#340—611no—
365#340—611no—
366#340—611no—
367#340C2×D6111yescharacteristic
368#340C2×D6111yescharacteristic
369C61#2127911yescharacteristic, complemented, Sylow
370C22×Q8—611no—
371C22×D4—611no—
372C23×C4—1221no—
373C2×SD16—614no—
374C2×SD16—1222no—
375C2×SD16—1222no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8C22×D6111yescharacteristic
379C22×C8C22×D6111yescharacteristic
380C4×Q8—614no—
381C4×Q8—1222no—
382C4×D4—614no—
383C4×D4—1222no—
384#117—2444no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4C22×D6111yescharacteristic
393C2×C4⋊C4C22×D6111yescharacteristic
394C2×C4⋊C4C22×D6111yescharacteristic
395C2×C4⋊C4C22×D6111yescharacteristic
396C2×C22⋊C4—1221no—
397C2×C22⋊C4—1221no—
398C2×C22⋊C4—1221no—
399C2×C22⋊C4—1221no—
400C2×C22⋊C4—1221no—
401C2×C42—611no—
402C2×C42—611no—
403C2×C42—611no—
404C2×C42—611no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42—1221no—
408C2×C42—1221no—
409C2×C42—1221no—
410C2×C42C22×D6111yescharacteristic
411#107—22no—
412#107—1222no—
413#106C4×D6114yes—
414#103—614no—
415#103—1222no—
416#103—1222no—
417#102—614no—
418#102—1222no—
419#102—1222no—
420#97—22no—
421#97—1222no—
422#97—1222no—
423#97—1222no—
424C4×C8—614no—
425C4×C8—1222no—
426#95—21no—
427#95—21no—
428#95—1221no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433#95—1221no—
434#95—1221no—
435#95—1221no—
436C24—1221no—
437C2×Q8—612no—
438C2×Q8—1221no—
439C2×Q8—1221no—
440C2×Q8—1221no—
441C2×Q8—1221no—
442C2×Q8—1221no—
443C2×D4—612no—
444C2×D4—1221no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—1221no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—1224no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—2442no—
462C22×C4—2442no—
463C22×C4D4×D6111yescharacteristic
464C22×C4D4×D6111yescharacteristic
465C22×C4C23×D6111yescharacteristic
466SD16—1228no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—612no—
470C2×C8—612no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8C2×C4×D6112yes—
476C2×C8#1175822412yes—
477C2×C8#1175822612yes—
478C2×C8#1175822612yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—1224no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—2442no—
493C4⋊C4—2442no—
494C4⋊C4C2×C4×D6112yes—
495C4⋊C4C2×C4×D6112yes—
496C22⋊C4—1224no—
497C22⋊C4—2442no—
498C22⋊C4—2442no—
499C22⋊C4—2442no—
500C22⋊C4—2442no—
501C42—21no—
502C42—21no—
503C42—612no—
504C42—612no—
505C42—1222no—
506C42—1222no—
507C42—1224no—
508C42—1221no—
509C42—1221no—
510C42—2441no—
511C42—2441no—
512C42—2442no—
513C42—2442no—
514C23—1222no—
515C23—2441no—
516C23—2441no—
517C23—2441no—
518C23—2441no—
519C23—2441no—
520C23—2441no—
521C23C2×D4×D6111yescharacteristic
522Q8—1222no—
523Q8—1222no—
524Q8—2441no—
525Q8—2441no—
526D4—1222no—
527D4—1222no—
528D4—2441no—
529D4—2441no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—612no—
549C2×C4—612no—
550C2×C4—612no—
551C2×C4—612no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1222no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—2448no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4C22×C4×D6111yescharacteristic
571C2×C4#41×D6111yescharacteristic
572C2×C4#41×D6111yescharacteristic
573C2×C4C2×#1175822411yescharacteristic
574C2×C4C2×#1175822611yescharacteristic
575C2×C4C2×#1175822611yescharacteristic
576C8—22no—
577C8—1222no—
578C8—1222no—
579C8#1451973514yescomplemented
580C22—4881no—
581C22—4881no—
582C22—4881no—
583C22—4881no—
584C22—2442no—
585C22—2442no—
586C22—2442no—
587C22C4×D4×D6111yescharacteristic
588C22#1684030711yescharacteristic
589C22#1684031311yescharacteristic
590C22AGL(1,ℤ/8)×D6111yescharacteristic
591C22#137×D6111yescharacteristic
592C22#1684055811yescharacteristic
593C22#1684056111yescharacteristic
594C4—42no—
595C4—42no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4—614no—
601C4—1222no—
602C4—4881no—
603C4—4881no—
604C4—2441no—
605C4—2441no—
606C4—2442no—
607C4C2×#1451973511yescharacteristic
608C4C4×#1175822611yescharacteristic
609C4#1684029711yescharacteristic
610C4#1684029811yescharacteristic
611C2—4882no—
612C2#2144827711yescharacteristic
613C2#440×D6111yescharacteristic
614C2#2145461411yescharacteristic
615C2#2145640911yescharacteristic
616C2#2145641611yescharacteristic
617C2#2145642011yescharacteristic
618C2#2145642711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1944C2
socleC23×C61C22×D4
prime radicalC22×D244C23
cosocleC22×C4×C61C24
hypercenter#1944D61
hypocenterC61#21279
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
2. #21448290C2semidirect
6. #21446563C2semidirect
9. #21446510C2semidirect
10. #21446508C2semidirect
11. #107×Dic61C2semidirect
12. #21445638C2semidirect
14. #97×Dic61C2semidirect
15. C61×#1944C2semidirect
20. #16839849C4semidirect
267. C8×C61#117semidirect
308. #1944D61semidirect
369. C61#21279semidirect
579. C8#14519735semidirect

Maximal subgroups

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

subgroupindex
C2×#168398492
#214482902
#214482772
#214467002
#214466982
#214465632
#214465172
#214465152
#214465102
#214465082
#107×Dic612
#214456382
#214456332
#97×Dic612
C61×#19442
#2127961