Finite Group Databasebeta

← #29646177

Subgroups — #29646177

Order 15616.

1012 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840363C211yesmaximal, characteristic
2#21454848C211yesmaximal, characteristic, complemented
3#21444180C212yesmaximal, complemented
4#21444178C212yesmaximal, complemented
5#21444168C212yesmaximal, complemented
6#21444165C212yesmaximal, complemented
7#21444159C212yesmaximal, complemented
8#21444151C212yesmaximal, complemented
9C61×#2973C211yesmaximal, characteristic, complemented
10#16840363—24no—
11#16840363—24no—
12C2×#14519773C411yescharacteristic
13C2×#14519768C411yescharacteristic
14C2×#14519760C2211yescharacteristic
15C2×#14519760C2211yescharacteristic
16C2×#14519759C411yescharacteristic
17C2×#14519759C411yescharacteristic
18C2×#14519752C411yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519750C411yescharacteristic
22C2×#14519750C411yescharacteristic
23C2×#14519748C411yescharacteristic
24C2×C4×D244C2211yescharacteristic
25C2×#14519734C2211yescharacteristic
26#16839834—24no—
27#16839819C2212yes—
28#16839726C2212yes—
29C2×C22⋊#92418C2212yes—
30#16839487C2214yes—
31#16839485C2214yes—
32#16839485C2214yes—
33#16839485C2214yes—
34C2×C4×D4×C61C2211yescharacteristic
35C61×#435—24no—
36C61×#432C2212yes—
37C61×#407C2212yes—
38C2×C22⋊C8×C61C2212yes—
39C22×D244C2×C411yescharacteristic
40C22×D244C2×C411yescharacteristic
41C22×D244C2×C411yescharacteristic
42C22×C22⋊D61C2×C411yescharacteristic
43C22×C22⋊D61C2×C411yescharacteristic
44C22×C22⋊D61C2×C411yescharacteristic
45C22×C22⋊D61C2×C411yescharacteristic
46C22×C22⋊D61C2×C411yescharacteristic
47C22×C22⋊D61C2×C411yescharacteristic
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C2×#11758194—22no—
52C22×#92418—22no—
53#14519773—24no—
54#14519768—24no—
55#14519760—22no—
56#14519760—22no—
57#14519760—22no—
58#14519760—22no—
59#14519759—24no—
60#14519759—24no—
61#14519752—24no—
62#14519751—22no—
63#14519751—22no—
64#14519751—22no—
65#14519751—22no—
66#14519750—24no—
67#14519750—24no—
68#14519748—24no—
69C4×D244—22no—
70C4×D244—22no—
71#14519734—22no—
72#14519734—22no—
73C2×C4⋊Dic61C2×C411yescharacteristic
74C2×C4⋊Dic61C2×C411yescharacteristic
75C2×C4⋊Dic61C2×C411yescharacteristic
76C2×#11758196C2×C411yescharacteristic
77C2×#11758196C2×C411yescharacteristic
78C2×#11758196C2×C411yescharacteristic
79C2×#11758196C2311yescharacteristic
80C2×C22⋊Dic61C2×C411yescharacteristic
81C2×C22⋊Dic61C2×C411yescharacteristic
82C2×#11758198C2×C411yescharacteristic
83C2×#11758198C2×C411yescharacteristic
84C2×#11758198C2×C411yescharacteristic
85C2×#11758198C2311yescharacteristic
86C2×#11758198C2311yescharacteristic
87C2×#11758198C2311yescharacteristic
88C2×C4×Dic61C2×C411yescharacteristic
89C4⋊#92418—22no—
90C22⋊#92418—22no—
91C22⋊#92418—22no—
92C22⋊#92418C2314yes—
93#14519688—22no—
94C22×D4×C61C2×C411yescharacteristic
95C23×C4×C61C2311yescharacteristic
96C23×C4×C61C2311yescharacteristic
97C2×M16×C61—22no—
98C22×C8×C61—22no—
99C4×D4×C61D414yes—
100C4×D4×C61D414yes—
101C2×C4⋊C4×C61C2×C411yescharacteristic
102C2×C22⋊C4×C61C2×C411yescharacteristic
103C2×C22⋊C4×C61C2×C411yescharacteristic
104C2×C42×C61C2311yescharacteristic
105C4⋊C8×C61—22no—
106C22⋊C8×C61—22no—
107C22⋊C8×C61—22no—
108C22⋊C8×C61C2314yes—
109#97×C61—22no—
110C24×C61C22×C411yescharacteristic
111C24×C61C22×C411yescharacteristic
112C23×D61C22×C411yescharacteristic
113C23×D61C22×C411yescharacteristic
114C23×D61C22×C411yescharacteristic
115C2×D4×C61—42no—
116C2×D4×C61C22⋊C414yes—
117C22×C4×C61—81no—
118C22×C4×C61—81no—
119C22×C4×C61C22×C411yescharacteristic
120C22×C4×C61C22×C411yescharacteristic
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C2×D412yes—
124C22×C4×C61C2×D412yes—
125C22×C4×C61C2×D412yes—
126C22×C4×C61C2×D412yes—
127C22×C4×C61C2411yescharacteristic
128C2×C22⋊D61—22no—
129C2×C22⋊D61—22no—
130C2×C22⋊D61—22no—
131C2×C22⋊D61—22no—
132C2×C22⋊D61—22no—
133C2×C22⋊D61—22no—
134C2×C22⋊D61—81no—
135C2×C22⋊D61—81no—
136C2×C22⋊D61—81no—
137C2×C22⋊D61—81no—
138C2×C22⋊D61—81no—
139C2×C22⋊D61—81no—
140C22×Dic61C22×C411yescharacteristic
141C22×Dic61C22×C411yescharacteristic
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C2×D244—22no—
146C2×D244—22no—
147C2×D244—22no—
148C2×D244—42no—
149C2×D244—81no—
150C2×D244—81no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—42no—
155C2×C4×D61—81no—
156C2×C4×D61—81no—
157M16×C61—82no—
158C2×C8×C61—24no—
159C2×C8×C61—82no—
160C4⋊C4×C61C22⋊C414yes—
161C22⋊C4×C61C22⋊C414yes—
162C22⋊C4×C61C22⋊C414yes—
163C42×C61C2×D412yes—
164C42×C61C2×D412yes—
165C22⋊Dic61—22no—
166C22⋊Dic61—22no—
167#11758198—22no—
168#11758198—22no—
169#11758198—22no—
170#11758198—21no—
171#11758198—21no—
172#11758198—21no—
173#11758198—21no—
174#11758198—21no—
175#11758198—21no—
176C4⋊Dic61—22no—
177C4⋊Dic61—22no—
178C4⋊Dic61—22no—
179#11758196—22no—
180#11758196—22no—
181#11758196—22no—
182#11758196—21no—
183#11758196—21no—
184C4×Dic61—22no—
185#11758194—82no—
186C2×#92418—24no—
187C2×#92418—82no—
188C23×C61—22no—
189C23×C61—22no—
190C23×C61—41no—
191C23×C61—41no—
192C23×C61—41no—
193C23×C61—41no—
194C23×C61C2×C22⋊C412yes—
195C23×C61C2×C22⋊C412yes—
196C23×C61C23×C411yescharacteristic
197C22×D61—21no—
198C22×D61—21no—
199C22×D61—21no—
200C22×D61—22no—
201C22×D61—22no—
202C22×D61—22no—
203C22×D61—41no—
204C22×D61—41no—
205C22×D61—41no—
206C22×D61—41no—
207C22×D61—41no—
208C22×D61—41no—
209D4×C61—44no—
210C2×C4×C61—22no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61C2×C22⋊C412yes—
220C2×C4×C61C2×C22⋊C412yes—
221C2×C4×C61C2×C22⋊C412yes—
222C2×C4×C61C2×C22⋊C412yes—
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C22×D411yescharacteristic
225C22⋊D61—82no—
226C22⋊D61—82no—
227C22⋊D61—82no—
228C22⋊D61—82no—
229C22⋊D61—82no—
230C22⋊D61—82no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—22no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241D244—44no—
242D244—82no—
243D244—82no—
244C4×D61—44no—
245C4×D61—82no—
246C4×D61—82no—
247C8×C61—44no—
248#92418—44no—
249#17408—611nomaximal, Sylow
250C22×C61—21no—
251C22×C61—21no—
252C22×C61—22no—
253C22×C61—22no—
254C22×C61—22no—
255C22×C61—22no—
256C22×C61—22no—
257C22×C61—22no—
258C22×C61—82no—
259C22×C61—82no—
260C22×C61C22×C22⋊C411yescharacteristic
261C22×C61#56812yes—
262C2×D61—41no—
263C2×D61—41no—
264C2×D61—41no—
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C2×D61—82no—
272C2×D61—82no—
273C2×D61—82no—
274C4×C61—22no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—22no—
278C4×C61—22no—
279C4×C61—22no—
280Dic61—41no—
281Dic61—41no—
282Dic61—41no—
283Dic61—41no—
284Dic61—41no—
285C2×#540—611no—
286#2973—611no—
287#2973D6111yescharacteristic, complemented
288#1471—612no—
289#1471—612no—
290#1468—612no—
291#1468—612no—
292#1466—612no—
293#1464—612no—
294C2×C61—22no—
295C2×C61—42no—
296C2×C61—42no—
297C2×C61#287911yescharacteristic
298C2×C61#288311yescharacteristic
299C2×C61#288811yescharacteristic
300D61—81no—
301D61—81no—
302D61—81no—
303#540—1224no—
304#540—1224no—
305C2×#127—611no—
306C2×#125—611no—
307C2×#123—611no—
308C2×#123—611no—
309C2×#123—611no—
310C2×#123—611no—
311C2×#121—611no—
312C2×#121—611no—
313C2×#121—611no—
314C2×#121—611no—
315C2×#121—611no—
316C2×#121—611no—
317C2×C4×D4—611no—
318C2×C4×D4C2×D6111yescharacteristic
319C2×#117—611no—
320#435—24no—
321#435—1224no—
322#432—612no—
323#432C2×D6112yes—
324#407—612no—
325#407C2×D6112yes—
326C2×C22⋊C8—612no—
327C2×C22⋊C8C2×D6112yes—
328#324—614no—
329#323—614no—
330#323—614no—
331#323—614no—
332C61#1740811yescharacteristic, complemented, Sylow
333C22×D4—611no—
334C22×D4—611no—
335C22×D4—611no—
336C22×D4—611no—
337C22×D4—611no—
338C22×D4—611no—
339C22×D4—611no—
340C22×D4—611no—
341C22×D4—611no—
342C22×D4C4×D6111yescharacteristic
343C23×C4—611no—
344C23×C4—611no—
345C23×C4—611no—
346C23×C4C22×D6111yescharacteristic
347C23×C4C22×D6111yescharacteristic
348C2×M16—22no—
349C2×M16—1222no—
350C22×C8—22no—
351C22×C8—1222no—
352#127—1224no—
353#125—1224no—
354#123—1222no—
355#123—1222no—
356#123—1222no—
357#123—1222no—
358#123—1224no—
359#123—1224no—
360#121—1224no—
361#121—1222no—
362#121—1222no—
363#121—1222no—
364#121—1222no—
365#121—1224no—
366#121—1224no—
367#121—1224no—
368C4×D4—1222no—
369C4×D4—1222no—
370C4×D4D24414yes—
371C4×D4C22⋊D6114yes—
372#117—1222no—
373#117—1222no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4—611no—
380C2×C4⋊C4—611no—
381C2×C4⋊C4C4×D6111yescharacteristic
382C2×C22⋊C4—611no—
383C2×C22⋊C4—611no—
384C2×C22⋊C4—611no—
385C2×C22⋊C4—611no—
386C2×C22⋊C4—611no—
387C2×C22⋊C4—611no—
388C2×C22⋊C4—611no—
389C2×C22⋊C4—611no—
390C2×C22⋊C4C4×D6111yescharacteristic
391C2×C22⋊C4C4×D6111yescharacteristic
392C2×C42—611no—
393C2×C42C22×D6111yescharacteristic
394C4⋊C8—22no—
395C4⋊C8—1222no—
396C22⋊C8—22no—
397C22⋊C8—22no—
398C22⋊C8—614no—
399C22⋊C8—1222no—
400C22⋊C8—1222no—
401C22⋊C8C22×D6114yes—
402#97—22no—
403#97—1222no—
404C24—611no—
405C24—611no—
406C24—611no—
407C24C2×C4×D6111yescharacteristic
408C24C2×C4×D6111yescharacteristic
409C2×D4—42no—
410C2×D4—1222no—
411C2×D4—1222no—
412C2×D4—1222no—
413C2×D4—1222no—
414C2×D4—1222no—
415C2×D4—1222no—
416C2×D4—1222no—
417C2×D4—1222no—
418C2×D4—1222no—
419C2×D4—4881no—
420C2×D4—4881no—
421C2×D4—4881no—
422C2×D4—4881no—
423C2×D4—4881no—
424C2×D4—4881no—
425C2×D4—4881no—
426C2×D4—4881no—
427C2×D4—2442no—
428C2×D4#1175819814yes—
429C22×C4—81no—
430C22×C4—81no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—1222no—
437C22×C4—1222no—
438C22×C4—1222no—
439C22×C4—4881no—
440C22×C4—4881no—
441C22×C4—2442no—
442C22×C4C2×C4×D6111yescharacteristic
443C22×C4C2×C4×D6111yescharacteristic
444C22×C4C2×C4×D6111yescharacteristic
445C22×C4C2×C4×D6111yescharacteristic
446C22×C4C2×D24412yes—
447C22×C4C2×D24412yes—
448C22×C4C2×C22⋊D6112yes—
449C22×C4C2×C22⋊D6112yes—
450C22×C4C23×D6111yescharacteristic
451M16—82no—
452M16—4882no—
453C2×C8—24no—
454C2×C8—82no—
455C2×C8—1224no—
456C2×C8—4882no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1222no—
460C4⋊C4—1222no—
461C4⋊C4—1222no—
462C4⋊C4—1222no—
463C4⋊C4—1222no—
464C4⋊C4—1222no—
465C4⋊C4#1175819814yes—
466C22⋊C4—1222no—
467C22⋊C4—1222no—
468C22⋊C4—1221no—
469C22⋊C4—1221no—
470C22⋊C4—1221no—
471C22⋊C4—1221no—
472C22⋊C4—1221no—
473C22⋊C4—1221no—
474C22⋊C4—1222no—
475C22⋊C4—1222no—
476C22⋊C4—1222no—
477C22⋊C4#1175819814yes—
478C22⋊C4#1175819814yes—
479C42—1222no—
480C42C2×D24412yes—
481C42C2×C22⋊D6112yes—
482C23—22no—
483C23—22no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—1222no—
489C23—1222no—
490C23—1222no—
491C23—1221no—
492C23—1221no—
493C23—1221no—
494C23—2441no—
495C23—2441no—
496C23—2441no—
497C23—2441no—
498C23—2441no—
499C23—2441no—
500C23C2×#1175819812yes—
501C23C2×#1175819812yes—
502C23C22×C4×D6111yescharacteristic
503D4—44no—
504D4—4882no—
505D4—4882no—
506D4—4882no—
507D4—4882no—
508D4—4882no—
509D4—4882no—
510D4—4882no—
511D4—4882no—
512D4—2444no—
513C2×C4—22no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1222no—
528C2×C4—4882no—
529C2×C4—4882no—
530C2×C4—2444no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4C2×#1175819812yes—
536C2×C4C2×#1175819812yes—
537C2×C4C2×#1175819812yes—
538C2×C4C2×#1175819812yes—
539C2×C4C22×C22⋊D6111yescharacteristic
540C2×C4C22×D24411yescharacteristic
541C8—44no—
542C8—2444no—
543C22—21no—
544C22—21no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—82no—
552C22—82no—
553C22—4882no—
554C22—4882no—
555C22—4882no—
556C22—2441no—
557C22—2441no—
558C22—2441no—
559C22—2441no—
560C22—2441no—
561C22—2441no—
562C22—2441no—
563C22—2441no—
564C22—2441no—
565C22C22×#1175819811yescharacteristic
566C22#1684052812yes—
567C4—22no—
568C4—21no—
569C4—21no—
570C4—22no—
571C4—22no—
572C4—22no—
573C4—2441no—
574C4—2441no—
575C4—2441no—
576C4—2441no—
577C4—2441no—
578C2—22no—
579C2—42no—
580C2—42no—
581C2—4881no—
582C2—4881no—
583C2—4881no—
584C2#2145426311yescharacteristic
585C2#2145427911yescharacteristic
586C2#2145429711yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2973C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840363C2
cosocleC22×C4×C61C24
hypercenter#2973D61
hypocenterC61#17408
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #21454848C2semidirect
3. #21444180C2semidirect
4. #21444178C2semidirect
5. #21444168C2semidirect
6. #21444165C2semidirect
7. #21444159C2semidirect
8. #21444151C2semidirect
9. C61×#2973C2semidirect
287. #2973D61semidirect
332. C61#17408semidirect

Maximal subgroups

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

subgroupindex
C2×#168403632
#214548482
#214441802
#214441782
#214441682
#214441652
#214441592
#214441512
C61×#29732
#1740861