Finite Group Databasebeta

← #29685412

Subgroups — #29685412

Order 15616.

1138 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840363C211yesmaximal, characteristic
2#21454455C211yesmaximal, characteristic, complemented
3#21454236C211yesmaximal, characteristic, complemented
4#21446810C212yesmaximal, complemented
5#21446657C212yesmaximal, complemented
6#21446281C212yesmaximal, complemented
7#21446279C212yesmaximal, complemented
8C4×#14519693C211yesmaximal, characteristic, complemented
9C4×#14519693C211yesmaximal, characteristic, complemented
10C4×#14519694C211yesmaximal, characteristic, complemented
11C4×#100×C61C211yesmaximal, characteristic, complemented
12C2×M16×D61C2212yes—
13#16840363—22no—
14#16840363—22no—
15#16840363—22no—
16#16840363—22no—
17C2×#14519773C2211yescharacteristic
18C2×#14519768C2211yescharacteristic
19C2×#14519760C412yes—
20C2×#14519759C412yes—
21C2×#14519752C2211yescharacteristic
22C2×#14519751C412yes—
23C2×#14519750C412yes—
24C2×#14519748C2211yescharacteristic
25C2×C4×D244C2211yescharacteristic
26C2×#14519734C2211yescharacteristic
27#16839824—22no—
28#16839821—22no—
29#16839785C2212yes—
30C2×#14519694C2212yes—
31C2×#14519693C2212yes—
32C2×#14519693C2212yes—
33#16839725C2212yes—
34#16839719—22no—
35#16839716—22no—
36C4×#11758194C2211yescharacteristic
37C4×#11758194C2211yescharacteristic
38M16×Dic61C2212yes—
39#16839531C2212yes—
40#16839530C2212yes—
41#16839530C2212yes—
42C2×C4×D4×C61C2211yescharacteristic
43C2×#100×C61C2212yes—
44C4×M16×C61C2211yescharacteristic
45C4×M16×C61C2211yescharacteristic
46C61×#343C2212yes—
47C22×D244C2×C412yes—
48C22×D244C2311yescharacteristic
49C22×C22⋊D61C2×C412yes—
50C22×C22⋊D61C2×C412yes—
51C22×C22⋊D61C2×C412yes—
52C22×C4×D61C2×C412yes—
53C22×C4×D61C2311yescharacteristic
54C2×#11758194C2312yes—
55C2×#11758194C2312yes—
56C2×#11758189—22no—
57M16×D61—24no—
58M16×D61—24no—
59C2×C8×D61—22no—
60#14519773—22no—
61#14519773—22no—
62#14519768—22no—
63#14519768—22no—
64#14519760—24no—
65#14519760—24no—
66#14519759—24no—
67#14519759—24no—
68#14519752—22no—
69#14519752—22no—
70#14519751—24no—
71#14519751—24no—
72#14519750—24no—
73#14519750—24no—
74#14519748—22no—
75#14519748—22no—
76C4×D244—21no—
77C4×D244—21no—
78C4×D244—21no—
79C4×D244—21no—
80#14519734D412yes—
81#14519734D412yes—
82#14519734D412yes—
83#14519734D412yes—
84C2×C4⋊Dic61C2×C412yes—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196C2×C412yes—
87C2×#11758196C2×C411yescharacteristic
88C2×#11758196C2×C411yescharacteristic
89C2×C22⋊Dic61C2×C412yes—
90C2×#11758198C2×C412yes—
91C2×#11758198C2×C412yes—
92C2×#11758198C2×C411yescharacteristic
93C2×#11758198C2×C411yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95#14519706—24no—
96#14519694—24no—
97#14519693—24no—
98#14519693—24no—
99#14519689—24no—
100#14519688—21no—
101#14519688—21no—
102#14519687—22no—
103C4×#92418—21no—
104C4×#92418—21no—
105C8×Dic61—22no—
106C22×D4×C61C2311yescharacteristic
107C23×C4×C61C2×C412yes—
108C2×M16×C61C2312yes—
109C2×M16×C61C2312yes—
110C4×D4×C61—21no—
111C4×D4×C61—21no—
112C4×D4×C61—21no—
113C4×D4×C61—21no—
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C22⋊C4×C61C2×C412yes—
116C2×C42×C61C2311yescharacteristic
117#100×C61—24no—
118#97×C61—21no—
119#97×C61—21no—
120C4×C8×C61—21no—
121C4×C8×C61—21no—
122C24×C61C22×C412yes—
123C23×D61C22×C412yes—
124C23×D61C22×C411yescharacteristic
125C2×D4×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61—22no—
128C2×D4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—82no—
132C22×C4×C61C22×C412yes—
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C2411yescharacteristic
136C2×C22⋊D61—24no—
137C2×C22⋊D61—24no—
138C2×C22⋊D61—24no—
139C2×C22⋊D61—82no—
140C2×C22⋊D61—82no—
141C2×C22⋊D61—82no—
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C22×C412yes—
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C2×D244—21no—
147C2×D244—21no—
148C2×D244—22no—
149C2×D244—22no—
150C2×D244—24no—
151C2×D244—82no—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—82no—
157C2×C4×D61C2×D412yes—
158C2×C4×D61C2×D412yes—
159M16×C61—22no—
160M16×C61—22no—
161M16×C61—22no—
162M16×C61#4114yes—
163C2×C8×C61—22no—
164C2×C8×C61—22no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C22⋊C4×C61—22no—
168C22⋊C4×C61—22no—
169C42×C61C2×D411yescharacteristic
170C42×C61C2×D411yescharacteristic
171C42×C61C2×D411yescharacteristic
172C42×C61C2×D411yescharacteristic
173C22⋊Dic61—24no—
174#11758198—22no—
175#11758198—22no—
176#11758198—24no—
177#11758198C22⋊C412yes—
178#11758198C22⋊C412yes—
179#11758198C22⋊C412yes—
180#11758198C22⋊C412yes—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—24no—
184#11758196—24no—
185#11758196C22⋊C412yes—
186#11758196C22⋊C412yes—
187#11758196C22⋊C412yes—
188#11758196C22⋊C412yes—
189C4×Dic61C2×D412yes—
190C4×Dic61C2×D412yes—
191#11758194—22no—
192#11758194—22no—
193#11758194—22no—
194#11758194#4114yes—
195C2×#92418—22no—
196C2×#92418—22no—
197#11758189—28no—
198C8×D61—28no—
199C23×C61—22no—
200C23×C61—22no—
201C23×C61—22no—
202C23×C61—42no—
203C23×C61—42no—
204C23×C61C23×C411yescharacteristic
205C22×D61—21no—
206C22×D61—21no—
207C22×D61—22no—
208C22×D61—22no—
209C22×D61—22no—
210C22×D61—41no—
211C22×D61—41no—
212C22×D61—42no—
213C22×D61—42no—
214C22×D61C2×C22⋊C412yes—
215D4×C61—42no—
216D4×C61—42no—
217C2×C4×C61—22no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—42no—
221C2×C4×C61—82no—
222C2×C4×C61—82no—
223C2×C4×C61C2×C22⋊C411yescharacteristic
224C2×C4×C61C2×C22⋊C411yescharacteristic
225C2×C4×C61C2×C22⋊C411yescharacteristic
226C2×C4×C61C2×C22⋊C411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C2×#4112yes—
230C2×C4×C61C2×#4112yes—
231C22⋊D61—84no—
232C22⋊D61—84no—
233C22⋊D61—84no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—22no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—42no—
240C2×Dic61C2×C22⋊C412yes—
241C2×Dic61C2×C22⋊C412yes—
242C2×Dic61C2×C22⋊C412yes—
243D244—42no—
244D244—42no—
245D244—84no—
246C4×D61—22no—
247C4×D61—22no—
248C4×D61—24no—
249C4×D61—82no—
250C4×D61—82no—
251C8×C61—24no—
252C8×C61—42no—
253#92418—24no—
254#92418—42no—
255#21428—611nomaximal, Sylow
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—42no—
259C22×C61—42no—
260C22×C61—42no—
261C22×C61—82no—
262C22×C61—82no—
263C22×C61C22×C22⋊C411yescharacteristic
264C22×C61C4×#4111yescharacteristic
265C22×C61C4×#4111yescharacteristic
266C2×D61—22no—
267C2×D61—22no—
268C2×D61—22no—
269C2×D61—42no—
270C2×D61—42no—
271C2×D61—42no—
272C2×D61—81no—
273C2×D61—81no—
274C2×D61—82no—
275C2×D61—82no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—21no—
280C4×C61—42no—
281C4×C61#52512yes—
282C4×C61#53212yes—
283Dic61—22no—
284Dic61—22no—
285Dic61—22no—
286Dic61—42no—
287C2×#540—611no—
288#2921—611no—
289#2873—611no—
290#1998—612no—
291#1965—612no—
292#1900—612no—
293#1900—612no—
294C4×#100—611no—
295C4×#100—611no—
296C4×#100—611no—
297C4×#100D6111yescharacteristic, complemented
298C2×C61—21no—
299C2×C61—21no—
300C2×C61—82no—
301C2×C61#229711yescharacteristic
302C2×C61#288811yescharacteristic
303C2×C61#288811yescharacteristic
304D61—42no—
305D61—82no—
306C22×M16—612no—
307#540—1222no—
308#540—1222no—
309#540—1222no—
310#540—1222no—
311C2×#127—611no—
312C2×#125—611no—
313C2×#123—612no—
314C2×#123—612no—
315C2×#121—611no—
316C2×#121—612no—
317C2×#121—611no—
318C2×#121—612no—
319C2×C4×D4—611no—
320C2×C4×D4C2×D6111yescharacteristic
321C2×#117—611no—
322#433—1222no—
323#433—1222no—
324#423—612no—
325C2×#100—612no—
326C2×#100—612no—
327C2×#100—612no—
328C2×#100C2×D6112yes—
329#407—612no—
330#405—1222no—
331#405—1222no—
332C4×M16—612no—
333C4×M16—611no—
334C4×M16—611no—
335C4×M16C2×D6111yescharacteristic
336C4×M16C2×D6111yescharacteristic
337#343—612no—
338#343—612no—
339#343—612no—
340#343C2×D6112yes—
341C61#2142811yescharacteristic, complemented, Sylow
342C22×D4—612no—
343C22×D4—612no—
344C22×D4—612no—
345C22×D4—612no—
346C22×D4—611no—
347C22×D4C22×D6111yescharacteristic
348C23×C4—611no—
349C23×C4—612no—
350C23×C4C4×D6112yes—
351C2×M16—612no—
352C2×M16—612no—
353C2×M16—1222no—
354C2×M16—1224no—
355C2×M16—1224no—
356C2×M16C22×D6112yes—
357C2×M16C22×D6112yes—
358C22×C8—1222no—
359#127—1222no—
360#127—1222no—
361#125—1222no—
362#125—1222no—
363#123—1224no—
364#123—1224no—
365#123—1224no—
366#123—1224no—
367#121—1224no—
368#121—1224no—
369#121—1224no—
370#121—1224no—
371#121—1222no—
372#121—1222no—
373#121—1222no—
374#121—1222no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—1221no—
380C4×D4—1221no—
381C4×D4—1221no—
382C4×D4—1221no—
383#117—612no—
384#117—612no—
385#117—612no—
386#117—612no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—612no—
390C2×C4⋊C4—612no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4C22×D6111yescharacteristic
393C2×C22⋊C4—611no—
394C2×C22⋊C4—611no—
395C2×C22⋊C4—612no—
396C2×C22⋊C4—612no—
397C2×C22⋊C4—612no—
398C2×C22⋊C4C4×D6112yes—
399C2×C42—611no—
400C2×C42C22×D6111yescharacteristic
401C4⋊C8—1224no—
402#100—24no—
403#100—1224no—
404#100—1224no—
405#100—1224no—
406C22⋊C8—1224no—
407#97—21no—
408#97—21no—
409#97—1222no—
410#97—1221no—
411#97—1221no—
412C4×C8—21no—
413C4×C8—21no—
414C4×C8—1222no—
415C4×C8—1221no—
416C4×C8—1221no—
417C24—611no—
418C24—612no—
419C24C2×C4×D6112yes—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—1224no—
425C2×D4—1224no—
426C2×D4—1224no—
427C2×D4—1224no—
428C2×D4—1221no—
429C2×D4—1221no—
430C2×D4—1222no—
431C2×D4—1222no—
432C2×D4—4882no—
433C2×D4—4882no—
434C2×D4—4882no—
435C2×D4—4882no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—82no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—612no—
443C22×C4—612no—
444C22×C4—612no—
445C22×C4—1222no—
446C22×C4—1222no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—4882no—
450C22×C4C2×C4×D6112yes—
451C22×C4C2×C4×D6111yescharacteristic
452C22×C4C2×C4×D6111yescharacteristic
453C22×C4C23×D6111yescharacteristic
454M16—22no—
455M16—22no—
456M16—22no—
457M16—614no—
458M16—1228no—
459M16—1222no—
460M16—1222no—
461M16—1222no—
462M16#1175822214yes—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—1228no—
466C2×C8—1222no—
467C2×C8—1222no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—612no—
471C4⋊C4—612no—
472C4⋊C4—612no—
473C4⋊C4—612no—
474C4⋊C4—1224no—
475C4⋊C4—1224no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—612no—
481C22⋊C4—612no—
482C22⋊C4—612no—
483C22⋊C4—612no—
484C22⋊C4—1224no—
485C22⋊C4—1224no—
486C22⋊C4—1222no—
487C22⋊C4—1222no—
488C42—612no—
489C42—612no—
490C42D4×D6111yescharacteristic
491C42D4×D6111yescharacteristic
492C42D4×D6111yescharacteristic
493C42D4×D6111yescharacteristic
494C23—22no—
495C23—22no—
496C23—22no—
497C23—42no—
498C23—42no—
499C23—612no—
500C23—1221no—
501C23—1221no—
502C23—1222no—
503C23—1222no—
504C23—1222no—
505C23—2441no—
506C23—2441no—
507C23—2442no—
508C23—2442no—
509C23C22×C4×D6111yescharacteristic
510D4—42no—
511D4—42no—
512D4—4884no—
513D4—4884no—
514D4—4884no—
515D4—4884no—
516D4—2442no—
517D4—2442no—
518C2×C4—22no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4—612no—
525C2×C4—612no—
526C2×C4—612no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1222no—
530C2×C4—1222no—
531C2×C4—1224no—
532C2×C4—1222no—
533C2×C4—4882no—
534C2×C4—4882no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2442no—
538C2×C4C22⋊C4×D6111yescharacteristic
539C2×C4C22⋊C4×D6111yescharacteristic
540C2×C4C22⋊C4×D6111yescharacteristic
541C2×C4C22⋊C4×D6111yescharacteristic
542C2×C4C2×D4×D6111yescharacteristic
543C2×C4C2×D4×D6111yescharacteristic
544C2×C4#41×D6112yes—
545C2×C4C2×#1175822212yes—
546C8—24no—
547C8—42no—
548C8—1224no—
549C8—2442no—
550C22—21no—
551C22—21no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—82no—
556C22—82no—
557C22—1222no—
558C22—1222no—
559C22—1222no—
560C22—4882no—
561C22—4882no—
562C22—4881no—
563C22—4881no—
564C22—2442no—
565C22—2442no—
566C22—2442no—
567C22C2×C22⋊C4×D6111yescharacteristic
568C22#1684023011yescharacteristic
569C22C4×#1175822211yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—42no—
575C4—1222no—
576C4—1222no—
577C4—1222no—
578C4—2442no—
579C4#1684027112yes—
580C4#1684030912yes—
581C2—21no—
582C2—21no—
583C2—82no—
584C2—4882no—
585C2—2442no—
586C2#2144830511yescharacteristic
587C2#2145429511yescharacteristic
588C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#100×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840363C2
cosocleC22×C4×C61C24
hypercenterC4×#100D61
hypocenterC61#21428
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
2. #21454455C2semidirect
3. #21454236C2semidirect
4. #21446810C2semidirect
5. #21446657C2semidirect
6. #21446281C2semidirect
7. #21446279C2semidirect
8. C4×#14519693C2semidirect
9. C4×#14519693C2semidirect
10. C4×#14519694C2semidirect
11. C4×#100×C61C2semidirect
297. C4×#100D61semidirect
341. C61#21428semidirect

Maximal subgroups

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

subgroupindex
C2×#168403632
#214544552
#214542362
#214468102
#214466572
#214462812
#214462792
C4×#145196932
C4×#145196942
C4×#100×C612
#2142861