Finite Group Databasebeta

← #29783227

Subgroups — #29783227

Order 15616.

674 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
1#21451784C211yesmaximal, characteristic, complemented
2#21447320C211yesmaximal, characteristic, complemented
3#21447211C211yesmaximal, characteristic, complemented
4#21447207C211yesmaximal, characteristic
5#21447136C211yesmaximal, characteristic
6#21446672C211yesmaximal, characteristic
7#21446549C211yesmaximal, characteristic, complemented
8#21446519C211yesmaximal, characteristic
9#21446508C211yesmaximal, characteristic, complemented
10#21446460C211yesmaximal, characteristic, complemented
11#21446404C211yesmaximal, characteristic, complemented
12#21446153C211yesmaximal, characteristic
13#21446066C211yesmaximal, characteristic
14#21445676C211yesmaximal, characteristic, complemented
15C61×#2319C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C2×#14519710C2211yescharacteristic
18C2×#14519710C2211yescharacteristic
19C2×#14519708C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519700C2211yescharacteristic
23C2×#14519700C2211yescharacteristic
24C2×#14519700C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519688C2211yescharacteristic
29C2×C4×#92418C2211yescharacteristic
30C61⋊#401—21no—
31#16839703—21no—
32#16839703—21no—
33#16839703—21no—
34#16839668C2211yescharacteristic
35#16839668C2211yescharacteristic
36#16839668C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839660C2211yescharacteristic
39#16839660C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×C4×D4×C61C2211yescharacteristic
49C61×#390C2211yescharacteristic
50C61×#390C2211yescharacteristic
51C61×#389C2211yescharacteristic
52C61×#389C2211yescharacteristic
53C61×#388—21no—
54C61×#388—21no—
55C61×#381—21no—
56C61×#380—21no—
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#376C2211yescharacteristic
59C22×Dic122C2311yescharacteristic
60C2×#11758200—22no—
61C2×#11758200—22no—
62C2×#11758200—41no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C2×C4⋊Dic61C2311yescharacteristic
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×#11758196—21no—
71C2×#11758196—21no—
72C2×#11758196—21no—
73#14519710—22no—
74#14519710—41no—
75#14519708—22no—
76C4⋊#92418—22no—
77C4⋊#92418—22no—
78#14519700—22no—
79#14519700—22no—
80#14519700—41no—
81#14519698—22no—
82#14519698—22no—
83#14519698—41no—
84#14519688—41no—
85C4×#92418—41no—
86#14519684—21no—
87#14519684—21no—
88#14519684—21no—
89#14519684—21no—
90#14519684—21no—
91#14519684—21no—
92#14519684—21no—
93#14519684—21no—
94#14519684—21no—
95C22×D4×C61C2311yescharacteristic
96C23×C4×C61—21no—
97C4×D4×C61—22no—
98C4×D4×C61—22no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—21no—
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—21no—
109C2×C42×C61—21no—
110C2×C42×C61C2311yescharacteristic
111C2×C42×C61C2311yescharacteristic
112C2×C42×C61C2311yescharacteristic
113#95×C61—21no—
114#95×C61—21no—
115#95×C61—21no—
116#95×C61D411yescharacteristic
117#95×C61D411yescharacteristic
118#95×C61D411yescharacteristic
119#95×C61D411yescharacteristic
120C24×C61—21no—
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61#4112yes—
127C22×C4×C61—21no—
128C22×C4×C61—24no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—81no—
132C22×C4×C61—81no—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2411yescharacteristic
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C2×Dic122—21no—
145C2×Dic122—21no—
146C2×Dic122—21no—
147C2×Dic122—21no—
148C2×Dic122—21no—
149C2×Dic122—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—81no—
156C4⋊C4×C61—81no—
157C4⋊C4×C61#4112yes—
158C22⋊C4×C61—24no—
159C22⋊C4×C61—81no—
160C22⋊C4×C61—81no—
161C22⋊C4×C61—81no—
162C22⋊C4×C61—81no—
163C42×C61—21no—
164C42×C61—21no—
165C42×C61—21no—
166C42×C61—21no—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61—81no—
170#11758200—44no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177#11758196—81no—
178#11758196—81no—
179#11758196—81no—
180C2×#92418—21no—
181C2×#92418—21no—
182C2×#92418—21no—
183C2×#92418—21no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418#4112yes—
191C2×#92418#4112yes—
192C23×C61—22no—
193C23×C61—41no—
194C23×C61—41no—
195C23×C61—41no—
196C23×C61—41no—
197C23×C61—41no—
198C23×C61—41no—
199C23×C61C22×D411yescharacteristic
200D4×C61—22no—
201D4×C61—22no—
202D4×C61—41no—
203D4×C61—41no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—22no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
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—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
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×C61—41no—
231C2×C4×C61—84no—
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61H(5,𝔽2)11yescharacteristic
237C2×C4×C612−1+411yescharacteristic
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250Dic122—41no—
251Dic122—41no—
252Dic122—41no—
253Dic122—41no—
254#92418—22no—
255#92418—22no—
256#92418—41no—
257#92418—41no—
258#29441—611nomaximal, Sylow
259C22×C61—42no—
260C22×C61—42no—
261C22×C61—42no—
262C22×C61—81no—
263C22×C61—81no—
264C22×C61—81no—
265C22×C61—81no—
266C22×C61#52511yescharacteristic
267C22×C61#53211yescharacteristic
268C22×C61#53711yescharacteristic
269C22×C61#57611yescharacteristic
270C22×C61#57711yescharacteristic
271C22×C61#57711yescharacteristic
272C22×C61#57811yescharacteristic
273C4×C61—41no—
274C4×C61—42no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61—81no—
281C4×C61—81no—
282C4×C61#55111yescharacteristic
283C4×C61#55211yescharacteristic
284C4×C61#55311yescharacteristic
285C4×C61#55611yescharacteristic
286Dic61—81no—
287Dic61—81no—
288Dic61—81no—
289Dic61—81no—
290#2645—611no—
291#2319D6111yescharacteristic
292#2088—611no—
293#2068—611no—
294#2067—611no—
295#2055—611no—
296#1968—611no—
297#1942—611no—
298#1936—611no—
299#1935—611no—
300#1928—611no—
301#1920—611no—
302#1877—611no—
303#1862—611no—
304#1768—611no—
305C2×C61—82no—
306C2×C61#260111yescharacteristic
307C2×C61#311811yescharacteristic
308C2×C61#312011yescharacteristic
309C2×C61#317411yescharacteristic
310C2×C61#317511yescharacteristic
311C2×C61#325711yescharacteristic
312C2×C61#325811yescharacteristic
313C22×SD16—611no—
314C2×C4×D4C2×D6111yescharacteristic
315C2×#107—611no—
316C2×#107—611no—
317C2×#106—611no—
318C2×C4⋊C8—611no—
319C2×C4⋊C8—611no—
320C2×#103—611no—
321C2×#103—611no—
322C2×#103—611no—
323C2×#102—611no—
324C2×#102—611no—
325C2×#102—611no—
326C2×#97—611no—
327C2×C4×C8—611no—
328#401—1221no—
329#400—1221no—
330#400—1221no—
331#400—1221no—
332#391—611no—
333#391—611no—
334#391—611no—
335#390C2×D6111yescharacteristic
336#390C2×D6111yescharacteristic
337#389—611no—
338#389—611no—
339#389—611no—
340#389C2×D6111yescharacteristic
341#389C2×D6111yescharacteristic
342#388—21no—
343#388—21no—
344#381—21no—
345#380—21no—
346C4×C4⋊C4C2×D6111yescharacteristic
347#376C2×D6111yescharacteristic
348#340—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340—611no—
353#340—611no—
354#336—611no—
355#336—611no—
356C61#2944111yescharacteristic, complemented, Sylow
357C22×Q8—611no—
358C22×D4C22×D6111yescharacteristic
359C23×C4—21no—
360C2×SD16—1222no—
361C2×SD16—1222no—
362C2×SD16—2441no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—611no—
366C22×C8—611no—
367C4×D4—22no—
368C4×D4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4C22×D6111yescharacteristic
378C2×C4⋊C4C22×D6111yescharacteristic
379C2×C4⋊C4C22×D6111yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C42—21no—
386C2×C42C22×D6111yescharacteristic
387C2×C42C22×D6111yescharacteristic
388C2×C42C22×D6111yescharacteristic
389#107—1222no—
390#107—2441no—
391#106—1222no—
392C4⋊C8—1222no—
393C4⋊C8—1222no—
394#103—1222no—
395#103—1222no—
396#103—2441no—
397#102—1222no—
398#102—1222no—
399#102—2441no—
400#97—2441no—
401C4×C8—2441no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—1221no—
406#95—1221no—
407#95—1221no—
408#95—1221no—
409#95—1221no—
410#95—1221no—
411#95—1221no—
412#95—1221no—
413#95—1221no—
414#95C22⋊D6111yescharacteristic
415#95C22⋊D6111yescharacteristic
416#95C22⋊D6111yescharacteristic
417#95C22⋊D6111yescharacteristic
418C24—21no—
419C2×Q8—1221no—
420C2×Q8—1221no—
421C2×Q8—1221no—
422C2×Q8—1221no—
423C2×Q8—1221no—
424C2×Q8—1221no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4#1175822212yes—
431C22×C4—21no—
432C22×C4—24no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—81no—
436C22×C4—81no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4C2×C22⋊D6111yescharacteristic
442C22×C4C2×C22⋊D6111yescharacteristic
443C22×C4C2×C22⋊D6111yescharacteristic
444C22×C4C2×C22⋊D6111yescharacteristic
445C22×C4C2×C22⋊D6111yescharacteristic
446C22×C4C2×C22⋊D6111yescharacteristic
447C22×C4C23×D6111yescharacteristic
448SD16—2444no—
449C2×C8—612no—
450C2×C8—612no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—4881no—
475C4⋊C4—4881no—
476C4⋊C4—4881no—
477C4⋊C4#1175822212yes—
478C22⋊C4—24no—
479C22⋊C4—81no—
480C22⋊C4—81no—
481C22⋊C4—81no—
482C22⋊C4—81no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—81no—
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23C22×C22⋊D6111yescharacteristic
498Q8—2441no—
499Q8—2441no—
500Q8—2441no—
501Q8—2441no—
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—84no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4#41×D6111yescharacteristic
547C2×C4#41×D6111yescharacteristic
548C2×C4C2×#1175822211yescharacteristic
549C2×C4C2×#1175822211yescharacteristic
550C2×C4#1451982311yescharacteristic
551C2×C4#1451982411yescharacteristic
552C8—1222no—
553C8—1222no—
554C8—2441no—
555C8—2441no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22#1684027311yescharacteristic
564C22#1684030811yescharacteristic
565C22#1684034011yescharacteristic
566C22#1684056511yescharacteristic
567C22#1684057311yescharacteristic
568C22#1684057311yescharacteristic
569C22#1684057711yescharacteristic
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—42no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—4881no—
580C4—4881no—
581C4—4881no—
582C4—4881no—
583C4#1684043611yescharacteristic
584C4#1684044511yescharacteristic
585C4#1684045611yescharacteristic
586C4#1684048011yescharacteristic
587C2—82no—
588C2#2145141611yescharacteristic
589C2#2145600311yescharacteristic
590C2#2145603311yescharacteristic
591C2#2145644111yescharacteristic
592C2#2145645211yescharacteristic
593C2#2145722411yescharacteristic
594C2#2145724511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2319C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenter#2319D61
hypocenterC61#29441
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
1. #21451784C2semidirect
2. #21447320C2semidirect
3. #21447211C2semidirect
7. #21446549C2semidirect
9. #21446508C2semidirect
10. #21446460C2semidirect
11. #21446404C2semidirect
14. #21445676C2semidirect
356. C61#29441semidirect

Maximal subgroups

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

subgroupindex
#214517842
#214473202
#214472112
#214472072
#214471362
#214466722
#214465492
#214465192
#214465082
#214464602
#214464042
#214461532
#214460662
#214456762
C61×#23192
#2944161