Finite Group Databasebeta

← #29739086

Subgroups — #29739086

Order 15616.

678 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451053C211yesmaximal, characteristic, complemented
2#21447352C211yesmaximal, characteristic
3#21447340C211yesmaximal, characteristic
4#21447207C211yesmaximal, characteristic
5#21447207C211yesmaximal, characteristic
6#21446587C211yesmaximal, characteristic, complemented
7#21446585C211yesmaximal, characteristic, complemented
8#21446577C211yesmaximal, characteristic, complemented
9#21446538C211yesmaximal, characteristic, complemented
10#21446404C211yesmaximal, characteristic, complemented
11#21446397C211yesmaximal, characteristic, complemented
12#21445981C211yesmaximal, characteristic, complemented
13#21445829C211yesmaximal, characteristic
14C4×#14519698C211yesmaximal, characteristic
15C61×#2357C211yesmaximal, characteristic
16C2×#14519710C2211yescharacteristic
17C2×#14519710C2211yescharacteristic
18C2×#14519710C2211yescharacteristic
19C2×#14519708C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C2×C4⋊#92418C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×C4×#92418C2211yescharacteristic
30#16839701—21no—
31#16839695—21no—
32#16839660C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839649—21no—
35#16839645—21no—
36#16839632C2211yescharacteristic
37#16839628C2211yescharacteristic
38#16839628C2211yescharacteristic
39C4×C4⋊Dic61C2211yescharacteristic
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×#388—21no—
52C61×#388—21no—
53C61×#382C2211yescharacteristic
54C61×#381—21no—
55C4×C4⋊C4×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C22⋊C4×C61—21no—
59C22×#92418C2311yescharacteristic
60C22×#92418C2311yescharacteristic
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61C2311yescharacteristic
66C2×C4⋊Dic61C2311yescharacteristic
67C2×C4⋊Dic61C2311yescharacteristic
68C2×C4⋊Dic61C2311yescharacteristic
69C2×#11758196—21no—
70C2×#11758196—21no—
71C2×C4×Dic61—21no—
72#14519710—41no—
73#14519710—41no—
74#14519710—41no—
75#14519708—22no—
76#14519708—22no—
77#14519708—41no—
78C4⋊#92418—22no—
79C4⋊#92418—22no—
80C4⋊#92418—22no—
81#14519698—22no—
82#14519698—22no—
83#14519698—41no—
84#14519698—41no—
85C4×#92418—22no—
86#14519684—21no—
87#14519684—21no—
88#14519684—21no—
89#14519684—21no—
90#14519684—21no—
91#14519684—21no—
92#14519684—21no—
93C22×D4×C61C2311yescharacteristic
94C23×C4×C61—21no—
95C4×D4×C61—22no—
96C4×D4×C61Q814yes—
97C2×C4⋊C4×C61D411yescharacteristic
98C2×C4⋊C4×C61D411yescharacteristic
99C2×C4⋊C4×C61C2311yescharacteristic
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—21no—
107C2×C42×C61—21no—
108C2×C42×C61—21no—
109C2×C42×C61C2311yescharacteristic
110C2×C42×C61C2311yescharacteristic
111C2×C42×C61C2311yescharacteristic
112#95×C61—21no—
113#95×C61—21no—
114#95×C61—21no—
115#95×C61—21no—
116#95×C61D411yescharacteristic
117#95×C61D411yescharacteristic
118C24×C61—21no—
119C2×D4×C61—21no—
120C2×D4×C61—21no—
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61C2×Q812yes—
125C22×C4×C61—21no—
126C22×C4×C61—24no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—81no—
130C22×C4×C61—81no—
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C4⋊C4×C61—22no—
143C4⋊C4×C61—21no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—21no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—41no—
149C4⋊C4×C61C2×Q812yes—
150C22⋊C4×C61—24no—
151C22⋊C4×C61—42no—
152C22⋊C4×C61—42no—
153C22⋊C4×C61—81no—
154C22⋊C4×C61—81no—
155C42×C61—21no—
156C42×C61—21no—
157C42×C61—21no—
158C42×C61—21no—
159C42×C61—81no—
160C42×C61—81no—
161C42×C61C2×Q812yes—
162C42×C61#4112yes—
163C4⋊Dic61—21no—
164C4⋊Dic61—21no—
165C4⋊Dic61—21no—
166C4⋊Dic61—21no—
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—42no—
172C4⋊Dic61—81no—
173#11758196—42no—
174#11758196—81no—
175C4×Dic61—81no—
176C2×#92418—21no—
177C2×#92418—21no—
178C2×#92418—21no—
179C2×#92418—21no—
180C2×#92418—21no—
181C2×#92418—21no—
182C2×#92418—21no—
183C2×#92418—21no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418#4112yes—
187C2×#92418#4112yes—
188C23×C61—22no—
189C23×C61—41no—
190C23×C61—41no—
191C23×C61—41no—
192C23×C61—41no—
193C23×C61—41no—
194C23×C61—41no—
195C23×C61C22×D411yescharacteristic
196D4×C61—22no—
197D4×C61—22no—
198D4×C61—41no—
199D4×C61—41no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
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—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—84no—
225C2×C4×C61C22⋊Q812yes—
226C2×C4×C61C22⋊Q812yes—
227C2×C4×C61#13512yes—
228C2×C4×C61C22×Q811yescharacteristic
229C2×C4×C61C2×#4111yescharacteristic
230C2×C4×C61C2×#4111yescharacteristic
231C2×C4×C61C2×#4111yescharacteristic
232C2×C4×C61H(5,𝔽2)11yescharacteristic
233C2×C4×C612−1+411yescharacteristic
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246#92418—22no—
247#92418—22no—
248#92418—41no—
249#92418—41no—
250#26096—611nomaximal, Sylow
251C22×C61—42no—
252C22×C61—42no—
253C22×C61—42no—
254C22×C61—81no—
255C22×C61—81no—
256C22×C61—81no—
257C22×C61—81no—
258C22×C61C2×C22⋊Q811yescharacteristic
259C22×C61#54711yescharacteristic
260C22×C61#55011yescharacteristic
261C22×C61C2×#13511yescharacteristic
262C22×C61#57511yescharacteristic
263C22×C61#57611yescharacteristic
264C22×C61#57711yescharacteristic
265C4×C61—22no—
266C4×C61—22no—
267C4×C61—22no—
268C4×C61—42no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—81no—
273C4×C61—81no—
274C4×C61#53311yescharacteristic
275C4×C61#54411yescharacteristic
276C4×C61#55211yescharacteristic
277C4×C61#55311yescharacteristic
278Dic61—81no—
279Dic61—81no—
280Dic61—81no—
281Dic61—81no—
282#2570—611no—
283#2357D6111yescharacteristic
284#2094—611no—
285#2092—611no—
286#2067—611no—
287#2067—611no—
288#1949—611no—
289#1949—611no—
290#1947—611no—
291#1939—611no—
292#1920—611no—
293#1919—611no—
294#1846—611no—
295#1804—611no—
296C4×#102—611no—
297C2×C61—82no—
298C2×C61#244111yescharacteristic
299C2×C61#307611yescharacteristic
300C2×C61#308111yescharacteristic
301C2×C61#333911yescharacteristic
302C2×C61#335111yescharacteristic
303C2×C61#339411yescharacteristic
304C2×C61#340311yescharacteristic
305C2×C4×D4C2×D6111yescharacteristic
306C2×#107—611no—
307C2×#107—611no—
308C2×#107—611no—
309C2×#106—611no—
310C2×#106—611no—
311C2×#106—611no—
312C2×C4⋊C8—611no—
313C2×C4⋊C8—611no—
314C2×C4⋊C8—611no—
315C2×#102—611no—
316C2×#102—611no—
317C2×#102—611no—
318C2×#102—611no—
319C2×C4×C8—611no—
320#400—1221no—
321#398—1221no—
322#390C2×D6111yescharacteristic
323#390C2×D6111yescharacteristic
324#389—611no—
325#389—611no—
326#388—21no—
327#388—21no—
328#387—1221no—
329#387—1221no—
330#384—611no—
331#382—611no—
332#382—611no—
333#382C2×D6111yescharacteristic
334#381—21no—
335C4×C4⋊C4—611no—
336C4×C4⋊C4C2×D6111yescharacteristic
337C4×C4⋊C4C2×D6111yescharacteristic
338C4×C4⋊C4C2×D6111yescharacteristic
339C4×C22⋊C4—21no—
340#340—611no—
341#340—611no—
342#340—611no—
343#340—611no—
344#340—611no—
345#340—611no—
346#336—611no—
347#336—611no—
348C61#2609611yescharacteristic, complemented, Sylow
349C22×D4C22×D6111yescharacteristic
350C23×C4—21no—
351C22×C8—611no—
352C22×C8—611no—
353C22×C8—611no—
354C22×C8—611no—
355C4×D4—22no—
356C4×D4Dic12214yes—
357C2×C4⋊C4—611no—
358C2×C4⋊C4—611no—
359C2×C4⋊C4—611no—
360C2×C4⋊C4—611no—
361C2×C4⋊C4—1221no—
362C2×C4⋊C4—1221no—
363C2×C4⋊C4—1221no—
364C2×C4⋊C4—1221no—
365C2×C4⋊C4C22⋊D6111yescharacteristic
366C2×C4⋊C4C22⋊D6111yescharacteristic
367C2×C4⋊C4C22×D6111yescharacteristic
368C2×C4⋊C4C22×D6111yescharacteristic
369C2×C4⋊C4C22×D6111yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—1221no—
378C2×C42C22×D6111yescharacteristic
379C2×C42C22×D6111yescharacteristic
380C2×C42C22×D6111yescharacteristic
381#107—2441no—
382#107—2441no—
383#107—2441no—
384#106—1222no—
385#106—1222no—
386#106—2441no—
387C4⋊C8—1222no—
388C4⋊C8—1222no—
389C4⋊C8—1222no—
390#102—1222no—
391#102—1222no—
392#102—2441no—
393#102—2441no—
394C4×C8—1222no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—1221no—
400#95—1221no—
401#95—1221no—
402#95—1221no—
403#95—1221no—
404#95—1221no—
405#95—1221no—
406#95C22⋊D6111yescharacteristic
407#95C22⋊D6111yescharacteristic
408C24—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4C2×Dic12212yes—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—81no—
420C22×C4—81no—
421C22×C4—1221no—
422C22×C4—1221no—
423C22×C4—1221no—
424C22×C4—1221no—
425C22×C4C2×C22⋊D6111yescharacteristic
426C22×C4C2×C22⋊D6111yescharacteristic
427C22×C4C2×C22⋊D6111yescharacteristic
428C22×C4C2×C22⋊D6111yescharacteristic
429C22×C4C2×C22⋊D6111yescharacteristic
430C22×C4C2×C22⋊D6111yescharacteristic
431C22×C4C23×D6111yescharacteristic
432C2×C8—612no—
433C2×C8—612no—
434C2×C8—1221no—
435C2×C8—1221no—
436C2×C8—1221no—
437C2×C8—1221no—
438C2×C8—1221no—
439C2×C8—1221no—
440C2×C8—1221no—
441C2×C8—1221no—
442C2×C8—1221no—
443C2×C8—1221no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—41no—
451C4⋊C4—1221no—
452C4⋊C4—1221no—
453C4⋊C4—1221no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C4⋊C4—1221no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—4881no—
460C4⋊C4—4881no—
461C4⋊C4—2442no—
462C4⋊C4—2442no—
463C4⋊C4C2×Dic12212yes—
464C22⋊C4—24no—
465C22⋊C4—42no—
466C22⋊C4—42no—
467C22⋊C4—81no—
468C22⋊C4—81no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—81no—
474C42—81no—
475C42—4881no—
476C42C2×Dic12212yes—
477C42#1175822212yes—
478C23—22no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23C22×C22⋊D6111yescharacteristic
486D4—22no—
487D4—22no—
488D4—41no—
489D4—41no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—84no—
515C2×C4—2441no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4#1451975612yes—
528C2×C4#1451975612yes—
529C2×C4#1451979712yes—
530C2×C4C22×Dic12211yescharacteristic
531C2×C4#41×D6111yescharacteristic
532C2×C4#41×D6111yescharacteristic
533C2×C4C2×#1175822211yescharacteristic
534C2×C4#1451982311yescharacteristic
535C2×C4#1451982411yescharacteristic
536C8—1222no—
537C8—1222no—
538C8—2441no—
539C8—2441no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22C2×#1451975611yescharacteristic
548C22#1684041111yescharacteristic
549C22#1684043111yescharacteristic
550C22C2×#1451979711yescharacteristic
551C22#1684056011yescharacteristic
552C22#1684056511yescharacteristic
553C22#1684057311yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—42no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—81no—
562C4—81no—
563C4—4881no—
564C4—4881no—
565C4—4881no—
566C4—4881no—
567C4#1684031511yescharacteristic
568C4#1684039011yescharacteristic
569C4#1684045111yescharacteristic
570C4#1684045611yescharacteristic
571C2—82no—
572C2#2144952611yescharacteristic
573C2#2145560711yescharacteristic
574C2#2145565011yescharacteristic
575C2#2145821511yescharacteristic
576C2#2145837311yescharacteristic
577C2#2145881111yescharacteristic
578C2#2145890311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2357C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenter#2357D61
hypocenterC61#26096
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2357

Complements

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

NH ≅ G/Ntype
1. #21451053C2semidirect
6. #21446587C2semidirect
7. #21446585C2semidirect
8. #21446577C2semidirect
9. #21446538C2semidirect
10. #21446404C2semidirect
11. #21446397C2semidirect
12. #21445981C2semidirect
348. C61#26096semidirect

Maximal subgroups

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

subgroupindex
#214510532
#214473522
#214473402
#214472072
#214465872
#214465852
#214465772
#214465382
#214464042
#214463972
#214459812
#214458292
C4×#145196982
C61×#23572
#2609661