Finite Group Databasebeta

← #29685411

Subgroups — #29685411

Order 15616.

1138 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840365C211yesmaximal, characteristic
2#21454454C211yesmaximal, characteristic, complemented
3#21454237C211yesmaximal, characteristic, complemented
4#21446810C212yesmaximal, complemented
5#21446657C212yesmaximal, complemented
6#21446283C211yesmaximal, characteristic, complemented
7#21446282C211yesmaximal, characteristic, complemented
8#21446280C211yesmaximal, characteristic, complemented
9#100×Dic61C212yesmaximal, complemented
10#21445610C212yesmaximal, complemented
11C61×#1900C211yesmaximal, characteristic, complemented
12C22×#11758194C2211yescharacteristic
13#16840365—22no—
14#16840365—22no—
15#16840365—22no—
16#16840365—22no—
17C2×#14519773C2211yescharacteristic
18C2×#14519768C2211yescharacteristic
19C2×#14519761C412yes—
20C2×#14519759C412yes—
21C2×#14519751C2211yescharacteristic
22C2×#14519749C412yes—
23C2×#14519748C412yes—
24C2×D4×Dic61C2211yescharacteristic
25C2×#14519739C2211yescharacteristic
26C2×#14519736C2211yescharacteristic
27#16839820—22no—
28#16839820—22no—
29#16839785C2212yes—
30C2×#14519694C2212yes—
31C2×#14519693C2212yes—
32C2×#14519693C2212yes—
33#16839726C2211yescharacteristic
34#16839720—22no—
35#16839717—22no—
36M16×Dic61C2212yes—
37M16×Dic61C2212yes—
38M16×Dic61C2212yes—
39#16839531C2212yes—
40#16839530C2212yes—
41#16839530C2212yes—
42C22×M16×C61C2211yescharacteristic
43C2×#121×C61C2211yescharacteristic
44C2×#100×C61C2212yes—
45C61×#407C2211yescharacteristic
46C61×#343C2212yes—
47C22×D244C2311yescharacteristic
48C22×C22⋊D61C2×C412yes—
49C22×C22⋊D61C2×C412yes—
50C22×C22⋊D61C2×C412yes—
51C23×Dic61C2×C412yes—
52C22×C4×D61C2×C412yes—
53C2×#11758194—21no—
54C2×#11758194—24no—
55C2×#11758194C2312yes—
56C2×#11758194C2312yes—
57C22×#92418—21no—
58#14519773—22no—
59#14519773—22no—
60#14519768—22no—
61#14519768—22no—
62#14519761—24no—
63#14519761—24no—
64#14519759—24no—
65#14519759—24no—
66#14519751—21no—
67#14519751—21no—
68#14519751—21no—
69#14519751—21no—
70#14519749—24no—
71#14519749—24no—
72#14519748—24no—
73#14519748—24no—
74D4×Dic61—22no—
75D4×Dic61—22no—
76#14519739—22no—
77#14519739—22no—
78#14519736D412yes—
79#14519736D412yes—
80#14519736D412yes—
81#14519736D412yes—
82C2×C4⋊Dic61C2×C412yes—
83C2×C4⋊Dic61C2×C411yescharacteristic
84C2×C4⋊Dic61C2×C411yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196C2×C412yes—
87C2×C22⋊Dic61C2×C412yes—
88C2×C22⋊Dic61C2×C411yescharacteristic
89C2×C22⋊Dic61C2×C411yescharacteristic
90C2×#11758198C2×C412yes—
91C2×#11758198C2×C412yes—
92C2×C4×Dic61C2311yescharacteristic
93C2×C4×Dic61C2311yescharacteristic
94#14519706—24no—
95#14519694—24no—
96#14519693—24no—
97#14519693—24no—
98C22⋊#92418—21no—
99C22⋊#92418—21no—
100#14519687—22no—
101#14519687—22no—
102#14519687—22no—
103C8×Dic61—22no—
104C8×Dic61—22no—
105C8×Dic61—22no—
106C22×D4×C61C2×C412yes—
107C22×D4×C61C2311yescharacteristic
108C23×C4×C61C2311yescharacteristic
109C2×M16×C61—21no—
110C2×M16×C61—24no—
111C2×M16×C61C2312yes—
112C2×M16×C61C2312yes—
113C22×C8×C61—21no—
114#121×C61—21no—
115#121×C61—21no—
116#121×C61—21no—
117#121×C61—21no—
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61C2×C412yes—
120#100×C61—24no—
121C22⋊C8×C61—21no—
122C22⋊C8×C61—21no—
123C24×C61C22×C412yes—
124C24×C61C22×C411yescharacteristic
125C23×D61C22×C412yes—
126C2×D4×C61—22no—
127C2×D4×C61—22no—
128C2×D4×C61—21no—
129C2×D4×C61—21no—
130C2×D4×C61—22no—
131C2×D4×C61—22no—
132C2×D4×C61—82no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C412yes—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2411yescharacteristic
142C2×C22⋊D61—22no—
143C2×C22⋊D61—22no—
144C2×C22⋊D61—24no—
145C2×C22⋊D61—24no—
146C2×C22⋊D61—82no—
147C2×C22⋊D61—82no—
148C2×C22⋊D61—82no—
149C22×Dic61—24no—
150C22×Dic61—82no—
151C22×Dic61C22×C412yes—
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—22no—
159C2×D244—22no—
160C2×C4×D61—24no—
161C2×C4×D61—82no—
162M16×C61—24no—
163M16×C61—22no—
164M16×C61—22no—
165M16×C61—22no—
166M16×C61#4114yes—
167C2×C8×C61—24no—
168C2×C8×C61—22no—
169C2×C8×C61—22no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C22⋊C4×C61—22no—
173C22⋊C4×C61—22no—
174C22⋊Dic61—24no—
175C22⋊Dic61C22⋊C412yes—
176C22⋊Dic61C22⋊C412yes—
177C22⋊Dic61C22⋊C412yes—
178C22⋊Dic61C22⋊C412yes—
179#11758198—22no—
180#11758198—22no—
181#11758198—24no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—24no—
185C4⋊Dic61C22⋊C412yes—
186C4⋊Dic61C22⋊C412yes—
187C4⋊Dic61C22⋊C412yes—
188C4⋊Dic61C22⋊C412yes—
189#11758196—24no—
190C4×Dic61C2×D412yes—
191C4×Dic61C2×D412yes—
192C4×Dic61C2×D412yes—
193C4×Dic61C2×D412yes—
194#11758194—24no—
195#11758194—22no—
196#11758194—22no—
197#11758194—22no—
198#11758194#4114yes—
199C2×#92418—24no—
200C2×#92418—22no—
201C2×#92418—22no—
202C23×C61—22no—
203C23×C61—22no—
204C23×C61—24no—
205C23×C61—41no—
206C23×C61—41no—
207C23×C61—42no—
208C23×C61—42no—
209C23×C61C2×C22⋊C411yescharacteristic
210C23×C61C2×C22⋊C411yescharacteristic
211C23×C61C23×C411yescharacteristic
212C22×D61—22no—
213C22×D61—24no—
214C22×D61—42no—
215C22×D61—42no—
216D4×C61—41no—
217D4×C61—41no—
218D4×C61—42no—
219D4×C61—82no—
220D4×C61—82no—
221C2×C4×C61—22no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—42no—
230C2×C4×C61C2×C22⋊C411yescharacteristic
231C2×C4×C61C2×C22⋊C411yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C2×#4112yes—
235C2×C4×C61C2×#4112yes—
236C22⋊D61—84no—
237C22⋊D61—84no—
238C22⋊D61—82no—
239C22⋊D61—82no—
240C2×Dic61—22no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—42no—
246C2×Dic61—84no—
247C2×Dic61C2×C22⋊C412yes—
248C2×Dic61C2×C22⋊C412yes—
249C2×Dic61C2×C22⋊C412yes—
250C2×Dic61C2×C22⋊C412yes—
251D244—41no—
252D244—41no—
253D244—42no—
254C4×D61—84no—
255C8×C61—24no—
256C8×C61—42no—
257#92418—24no—
258#92418—42no—
259#21428—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—42no—
269C22×C61—42no—
270C22×C61—42no—
271C22×C61—82no—
272C22×C61—84no—
273C22×C61C22×C22⋊C411yescharacteristic
274C22×C61C4×#4112yes—
275C2×D61—42no—
276C2×D61—42no—
277C2×D61—42no—
278C2×D61—84no—
279C4×C61—21no—
280C4×C61—21no—
281C4×C61—42no—
282C4×C61#52511yescharacteristic
283C4×C61#52511yescharacteristic
284C4×C61#53212yes—
285Dic61—22no—
286Dic61—22no—
287Dic61—22no—
288Dic61—22no—
289Dic61—42no—
290C2×#540—611no—
291#2921—611no—
292#2873—611no—
293#1998—612no—
294#1965—612no—
295#1900—611no—
296#1900—611no—
297#1900—611no—
298#1900D6111yescharacteristic, complemented
299C4×#100—612no—
300C4×#100—612no—
301C2×C61—22no—
302C2×C61—41no—
303C2×C61—41no—
304C2×C61—82no—
305C2×C61#229711yescharacteristic
306C2×C61#288811yescharacteristic
307C2×C61#288811yescharacteristic
308D61—82no—
309C22×M16—611no—
310C22×M16C2×D6111yescharacteristic
311#540—1222no—
312#540—1222no—
313#540—1222no—
314#540—1222no—
315C2×#127—611no—
316C2×#125—611no—
317C2×#123—612no—
318C2×#123—612no—
319C2×#121—612no—
320C2×#121—612no—
321C2×#121—611no—
322C2×#121C2×D6111yescharacteristic
323C2×C4×D4—611no—
324C2×C4×D4—611no—
325C2×#117—611no—
326#433—1222no—
327#433—1222no—
328#423—612no—
329C2×#100—612no—
330C2×#100—612no—
331C2×#100—612no—
332C2×#100C2×D6112yes—
333#407—611no—
334#407C2×D6111yescharacteristic
335#405—1222no—
336#405—1222no—
337C4×M16—612no—
338C4×M16—612no—
339C4×M16—612no—
340#343—612no—
341#343—612no—
342#343—612no—
343#343C2×D6112yes—
344C61#2142811yescharacteristic, complemented, Sylow
345C22×D4—612no—
346C22×D4—612no—
347C22×D4—612no—
348C22×D4—611no—
349C22×D4C4×D6112yes—
350C22×D4C22×D6111yescharacteristic
351C23×C4—612no—
352C23×C4—612no—
353C23×C4C22×D6111yescharacteristic
354C2×M16—21no—
355C2×M16—24no—
356C2×M16—612no—
357C2×M16—612no—
358C2×M16—1224no—
359C2×M16—1221no—
360C2×M16C22×D6112yes—
361C2×M16C22×D6112yes—
362C22×C8—21no—
363C22×C8—1221no—
364#127—1222no—
365#127—1222no—
366#125—1222no—
367#125—1222no—
368#123—1224no—
369#123—1224no—
370#123—1224no—
371#123—1224no—
372#121—21no—
373#121—21no—
374#121—21no—
375#121—21no—
376#121—1224no—
377#121—1224no—
378#121—1224no—
379#121—1224no—
380#121—1221no—
381#121—1221no—
382#121—1221no—
383#121—1221no—
384C4×D4—1222no—
385C4×D4—1222no—
386C4×D4—1222no—
387C4×D4—1222no—
388#117—612no—
389#117—612no—
390#117—612no—
391#117—612no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—612no—
395C2×C4⋊C4—612no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4C22×D6111yescharacteristic
398C2×C22⋊C4—611no—
399C2×C22⋊C4—611no—
400C2×C22⋊C4—612no—
401C2×C22⋊C4—612no—
402C2×C22⋊C4—612no—
403C2×C22⋊C4C4×D6112yes—
404C2×C42—611no—
405C2×C42—611no—
406C4⋊C8—1224no—
407#100—24no—
408#100—1224no—
409#100—1224no—
410#100—1224no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—1221no—
414C22⋊C8—1221no—
415#97—1222no—
416#97—1222no—
417#97—1222no—
418C4×C8—1222no—
419C4×C8—1222no—
420C4×C8—1222no—
421C24—612no—
422C24C2×C4×D6112yes—
423C24C2×C4×D6111yescharacteristic
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—82no—
431C2×D4—1224no—
432C2×D4—1224no—
433C2×D4—1222no—
434C2×D4—1222no—
435C2×D4—1221no—
436C2×D4—1221no—
437C2×D4—1222no—
438C2×D4—1222no—
439C2×D4—4882no—
440C2×D4—4882no—
441C2×D4—4882no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—612no—
449C22×C4—1224no—
450C22×C4—1224no—
451C22×C4—4882no—
452C22×C4—4882no—
453C22×C4C2×C4×D6111yescharacteristic
454C22×C4C2×C4×D6112yes—
455C22×C4D4×D6111yescharacteristic
456C22×C4D4×D6111yescharacteristic
457C22×C4D4×D6111yescharacteristic
458C22×C4D4×D6111yescharacteristic
459C22×C4C23×D6111yescharacteristic
460M16—24no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—614no—
465M16—1224no—
466M16—1222no—
467M16—1222no—
468M16—1222no—
469M16#1175822414yes—
470C2×C8—24no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—1224no—
474C2×C8—1222no—
475C2×C8—1222no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—612no—
479C4⋊C4—612no—
480C4⋊C4—612no—
481C4⋊C4—612no—
482C4⋊C4—1224no—
483C4⋊C4—1224no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—612no—
489C22⋊C4—612no—
490C22⋊C4—612no—
491C22⋊C4—612no—
492C22⋊C4—1224no—
493C22⋊C4—1224no—
494C22⋊C4—1222no—
495C22⋊C4—1222no—
496C42—612no—
497C42—612no—
498C42—612no—
499C42—612no—
500C23—22no—
501C23—22no—
502C23—24no—
503C23—41no—
504C23—41no—
505C23—42no—
506C23—42no—
507C23—1224no—
508C23—1222no—
509C23—2442no—
510C23—2442no—
511C23C22⋊C4×D6111yescharacteristic
512C23C22⋊C4×D6111yescharacteristic
513C23C22×C4×D6111yescharacteristic
514D4—41no—
515D4—41no—
516D4—42no—
517D4—82no—
518D4—82no—
519D4—4884no—
520D4—4884no—
521D4—4882no—
522D4—4882no—
523D4—2441no—
524D4—2441no—
525D4—2442no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—42no—
535C2×C4—612no—
536C2×C4—612no—
537C2×C4—612no—
538C2×C4—612no—
539C2×C4—1222no—
540C2×C4—4884no—
541C2×C4—4884no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2442no—
547C2×C4C22⋊C4×D6111yescharacteristic
548C2×C4C22⋊C4×D6111yescharacteristic
549C2×C4C2×D4×D6111yescharacteristic
550C2×C4C2×D4×D6111yescharacteristic
551C2×C4#41×D6112yes—
552C2×C4C2×#1175822412yes—
553C8—24no—
554C8—42no—
555C8—1224no—
556C8—2442no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—82no—
569C22—84no—
570C22—4884no—
571C22—2442no—
572C22—2442no—
573C22—2442no—
574C22C2×C22⋊C4×D6111yescharacteristic
575C22C4×#1175822412yes—
576C4—21no—
577C4—21no—
578C4—42no—
579C4—1222no—
580C4—1222no—
581C4—1222no—
582C4—1222no—
583C4—2442no—
584C4#1684026811yescharacteristic
585C4#1684027011yescharacteristic
586C4#1684030712yes—
587C2—22no—
588C2—41no—
589C2—41no—
590C2—82no—
591C2—4882no—
592C2#2144830411yescharacteristic
593C2#2145429511yescharacteristic
594C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1900C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840365C2
cosocleC22×C4×C61C24
hypercenter#1900D61
hypocenterC61#21428
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1900

Complements

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

NH ≅ G/Ntype
2. #21454454C2semidirect
3. #21454237C2semidirect
4. #21446810C2semidirect
5. #21446657C2semidirect
6. #21446283C2semidirect
7. #21446282C2semidirect
8. #21446280C2semidirect
9. #100×Dic61C2semidirect
10. #21445610C2semidirect
11. C61×#1900C2semidirect
298. #1900D61semidirect
344. C61#21428semidirect

Maximal subgroups

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

subgroupindex
C2×#168403652
#214544542
#214542372
#214468102
#214466572
#214462832
#214462822
#214462802
#100×Dic612
#214456102
C61×#19002
#2142861