Finite Group Databasebeta

← #29739059

Subgroups — #29739059

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#21451049C211yesmaximal, characteristic, complemented
2#21448788C211yesmaximal, characteristic
3#21447348C211yesmaximal, characteristic
4#21447341C211yesmaximal, characteristic
5#21447192C211yesmaximal, characteristic
6#21447188C211yesmaximal, characteristic
7#21446588C211yesmaximal, characteristic, complemented
8#21446586C211yesmaximal, characteristic, complemented
9#21446534C211yesmaximal, characteristic, complemented
10#21446411C211yesmaximal, characteristic, complemented
11#21446393C211yesmaximal, characteristic, complemented
12#21445980C211yesmaximal, characteristic, complemented
13#21445828C211yesmaximal, characteristic
14#21445633C211yesmaximal, characteristic
15C61×#1948C211yesmaximal, characteristic, complemented
16C2×#14519739C2211yescharacteristic
17C2×#14519710C2211yescharacteristic
18C2×#14519710C2211yescharacteristic
19C2×#14519710C2211yescharacteristic
20C2×#14519709C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×C8×Dic61C2211yescharacteristic
28#16839700—21no—
29#16839692—21no—
30#16839664C2211yescharacteristic
31#16839663C2211yescharacteristic
32#16839661C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839653—21no—
35#16839651—21no—
36#16839648—21no—
37#16839643—21no—
38#16839627C2211yescharacteristic
39#16839627C2211yescharacteristic
40#16839627C2211yescharacteristic
41#16839624—21no—
42C4⋊C4×Dic61C2211yescharacteristic
43C4⋊C4×Dic61C2211yescharacteristic
44C4×#11758196C2211yescharacteristic
45C4×#11758198—21no—
46#16839525C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#106×C61C2211yescharacteristic
53C2×#106×C61C2211yescharacteristic
54C2×C4⋊C8×C61C2211yescharacteristic
55C61×#384C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C4×D61—21no—
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63#14519739—22no—
64#14519739Q814yes—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61C2311yescharacteristic
67C2×C4⋊Dic61C2311yescharacteristic
68C2×C4⋊Dic61C2311yescharacteristic
69C2×#11758196—21no—
70C2×#11758196D411yescharacteristic
71C2×#11758196D411yescharacteristic
72C2×#11758198—21no—
73C2×#11758198—21no—
74C2×#11758198—21no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×C4×Dic61—21no—
78C2×C4×Dic61—21no—
79C2×C4×Dic61C2311yescharacteristic
80C2×C4×Dic61C2311yescharacteristic
81#14519710—22no—
82#14519710—22no—
83#14519710—41no—
84#14519709—41no—
85#14519706—22no—
86#14519706—22no—
87#14519699—22no—
88#14519699—41no—
89#14519697—22no—
90#14519697—41no—
91C8×Dic61—22no—
92#14519684—21no—
93#14519684—21no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684D411yescharacteristic
103#14519684D411yescharacteristic
104C22×C8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C42×C61—21no—
113C2×C42×C61C2311yescharacteristic
114#106×C61—41no—
115#106×C61—41no—
116C4⋊C8×C61—22no—
117#95×C61—21no—
118C23×D61—21no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2411yescharacteristic
126C22×Dic61—21no—
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61C2×D411yescharacteristic
130C22×Dic61C2×D411yescharacteristic
131C22×Dic61C2×D411yescharacteristic
132C22×Dic61C2×D411yescharacteristic
133C2×D244—21no—
134C2×D244—21no—
135C2×D244—21no—
136C2×D244—21no—
137C2×D244—21no—
138C2×D244C2×Q812yes—
139C2×C4×D61—24no—
140C2×C4×D61—81no—
141C2×C4×D61—81no—
142C2×C8×C61—21no—
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—21no—
147C2×C8×C61#4112yes—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—42no—
156C4⋊C4×C61—81no—
157C4⋊C4×C61C2×Q812yes—
158C42×C61—21no—
159C42×C61—21no—
160C42×C61—81no—
161#11758198—24no—
162#11758198—42no—
163#11758198—42no—
164#11758198—81no—
165#11758198—81no—
166C4⋊Dic61—21no—
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—81no—
173#11758196—22no—
174#11758196—41no—
175#11758196—42no—
176C4×Dic61—21no—
177C4×Dic61—21no—
178C4×Dic61—81no—
179C4×Dic61—81no—
180C4×Dic61C2×Q812yes—
181C4×Dic61#4112yes—
182C2×#92418—21no—
183C2×#92418—21no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418#4112yes—
188C23×C61C22×D411yescharacteristic
189C22×D61—22no—
190C22×D61—41no—
191C22×D61—41no—
192C22×D61—41no—
193C22×D61—41no—
194C22×D61—41no—
195C22×D61—41no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—22no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61—41no—
207C2×C4×C61—41no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61#13512yes—
214C2×C4×C61C22×Q811yescharacteristic
215C2×C4×C61C2×#4111yescharacteristic
216C2×C4×C61C2×#4111yescharacteristic
217C2×C4×C61C2×#4111yescharacteristic
218C2×C4×C61H(5,𝔽2)11yescharacteristic
219C2×C4×C612−1+411yescharacteristic
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61C22⋊Q812yes—
240C2×Dic61C22⋊Q812yes—
241D244—22no—
242D244—22no—
243D244—41no—
244D244—41no—
245C4×D61—84no—
246C8×C61—22no—
247C8×C61—41no—
248#92418—22no—
249#92418—41no—
250#26094—611nomaximal, Sylow
251C22×C61C2×C22⋊Q811yescharacteristic
252C22×C61#54711yescharacteristic
253C22×C61#55011yescharacteristic
254C22×C61C2×#13511yescharacteristic
255C22×C61#57511yescharacteristic
256C22×C61#57611yescharacteristic
257C22×C61#57711yescharacteristic
258C2×D61—42no—
259C2×D61—42no—
260C2×D61—42no—
261C2×D61—81no—
262C2×D61—81no—
263C2×D61—81no—
264C2×D61—81no—
265C4×C61—22no—
266C4×C61—42no—
267C4×C61—41no—
268C4×C61—81no—
269C4×C61—81no—
270C4×C61—81no—
271C4×C61#53311yescharacteristic
272C4×C61#54411yescharacteristic
273C4×C61#55211yescharacteristic
274C4×C61#55311yescharacteristic
275Dic61—22no—
276Dic61—22no—
277Dic61—41no—
278Dic61—41no—
279Dic61—81no—
280Dic61—81no—
281Dic61—81no—
282#2570—611no—
283#2357—611no—
284#2093—611no—
285#2092—611no—
286#2065—611no—
287#2065—611no—
288#1949—611no—
289#1949—611no—
290#1948D6111yescharacteristic, complemented
291#1939—611no—
292#1921—611no—
293#1918—611no—
294#1846—611no—
295#1804—611no—
296C4×#102—611no—
297C2×C61#244111yescharacteristic
298C2×C61#307611yescharacteristic
299C2×C61#308111yescharacteristic
300C2×C61#333711yescharacteristic
301C2×C61#335511yescharacteristic
302C2×C61#339611yescharacteristic
303C2×C61#340111yescharacteristic
304D61—82no—
305C2×C4×D4—611no—
306C2×#107—611no—
307C2×#107—611no—
308C2×#107—611no—
309C2×#106—611no—
310C2×#106C2×D6111yescharacteristic
311C2×#106C2×D6111yescharacteristic
312C2×C4⋊C8—611no—
313C2×C4⋊C8—611no—
314C2×C4⋊C8C2×D6111yescharacteristic
315C2×#102—611no—
316C2×#102—611no—
317C2×#102—611no—
318C2×#102—611no—
319C2×C4×C8—611no—
320#400—1221no—
321#398—1221no—
322#390—611no—
323#390—611no—
324#389—611no—
325#389—611no—
326#388—1221no—
327#388—1221no—
328#387—1221no—
329#387—1221no—
330#384C2×D6111yescharacteristic
331#382—611no—
332#382—611no—
333#382—611no—
334#381—1221no—
335C4×C4⋊C4—611no—
336C4×C4⋊C4—611no—
337C4×C4⋊C4—611no—
338C4×C4⋊C4C2×D6111yescharacteristic
339C4×C22⋊C4—1221no—
340#340—611no—
341#340—611no—
342#340—611no—
343#340—611no—
344#340C2×D6111yescharacteristic
345#340C2×D6111yescharacteristic
346#336—611no—
347#336—611no—
348C61#2609411yescharacteristic, complemented, Sylow
349C22×D4—611no—
350C23×C4—1221no—
351C22×C8—611no—
352C22×C8—611no—
353C22×C8C22×D6111yescharacteristic
354C22×C8C22×D6111yescharacteristic
355C4×D4—614no—
356C4×D4—1222no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—611no—
360C2×C4⋊C4—611no—
361C2×C4⋊C4—611no—
362C2×C4⋊C4—611no—
363C2×C4⋊C4—611no—
364C2×C4⋊C4—1221no—
365C2×C4⋊C4—1221no—
366C2×C4⋊C4C22×D6111yescharacteristic
367C2×C4⋊C4C22×D6111yescharacteristic
368C2×C4⋊C4C22×D6111yescharacteristic
369C2×C4⋊C4C22×D6111yescharacteristic
370C2×C22⋊C4—1221no—
371C2×C22⋊C4—1221no—
372C2×C22⋊C4—1221no—
373C2×C22⋊C4—1221no—
374C2×C22⋊C4—1221no—
375C2×C42—21no—
376C2×C42—611no—
377C2×C42—611no—
378C2×C42—1221no—
379C2×C42—1221no—
380C2×C42C22×D6111yescharacteristic
381#107—1222no—
382#107—1222no—
383#107—2441no—
384#106—41no—
385#106—41no—
386#106—2441no—
387C4⋊C8—22no—
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—611no—
397#95—611no—
398#95—1221no—
399#95—1221no—
400#95—1221no—
401#95—1221no—
402#95—1221no—
403#95—1221no—
404#95—1221no—
405#95—1221no—
406#95—1221no—
407#95—1221no—
408C24—1221no—
409C2×D4—612no—
410C2×D4—1221no—
411C2×D4—1221no—
412C2×D4—1221no—
413C2×D4—1221no—
414C2×D4—1221no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—611no—
420C22×C4—611no—
421C22×C4—611no—
422C22×C4—611no—
423C22×C4—1224no—
424C22×C4—1221no—
425C22×C4—1221no—
426C22×C4—1221no—
427C22×C4—4881no—
428C22×C4—4881no—
429C22×C4D4×D6111yescharacteristic
430C22×C4D4×D6111yescharacteristic
431C22×C4C23×D6111yescharacteristic
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—612no—
438C2×C8—1221no—
439C2×C8—1221no—
440C2×C8—1221no—
441C2×C8—1221no—
442C2×C8—1221no—
443C2×C8#1175822212yes—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—42no—
452C4⋊C4—81no—
453C4⋊C4—1222no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C4⋊C4—1221no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—4881no—
461C4⋊C4—2441no—
462C4⋊C4—2442no—
463C4⋊C4Q8×D6112yes—
464C22⋊C4—1224no—
465C22⋊C4—4881no—
466C22⋊C4—4881no—
467C22⋊C4—2442no—
468C22⋊C4—2442no—
469C42—21no—
470C42—21no—
471C42—81no—
472C42—612no—
473C42—612no—
474C42—1221no—
475C42—1221no—
476C42—4881no—
477C42—4881no—
478C23—1222no—
479C23—2441no—
480C23—2441no—
481C23—2441no—
482C23—2441no—
483C23—2441no—
484C23—2441no—
485C23C2×D4×D6111yescharacteristic
486D4—1222no—
487D4—1222no—
488D4—2441no—
489D4—2441no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—612no—
508C2×C4—612no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1221no—
517C2×C4—1221no—
518C2×C4—1221no—
519C2×C4—4884no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4#1451979812yes—
530C2×C4C2×Q8×D6111yescharacteristic
531C2×C4#41×D6111yescharacteristic
532C2×C4#41×D6111yescharacteristic
533C2×C4C2×#1175822211yescharacteristic
534C2×C4#1451982211yescharacteristic
535C2×C4#1451982511yescharacteristic
536C8—22no—
537C8—41no—
538C8—1222no—
539C8—2441no—
540C22—4881no—
541C22—4881no—
542C22—4881no—
543C22—4881no—
544C22—2442no—
545C22—2442no—
546C22—2442no—
547C22C22⋊Q8×D6111yescharacteristic
548C22#1684041311yescharacteristic
549C22#1684043011yescharacteristic
550C22C2×#1451979811yescharacteristic
551C22#1684056111yescharacteristic
552C22#1684056611yescharacteristic
553C22#1684056811yescharacteristic
554C4—22no—
555C4—42no—
556C4—41no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4—1222no—
561C4—1222no—
562C4—4881no—
563C4—4881no—
564C4—4881no—
565C4—2441no—
566C4—2441no—
567C4#1684031611yescharacteristic
568C4#1684038911yescharacteristic
569C4#1684044411yescharacteristic
570C4#1684046111yescharacteristic
571C2—4882no—
572C2#2144952911yescharacteristic
573C2#2145560211yescharacteristic
574C2#2145564511yescharacteristic
575C2#2145819411yescharacteristic
576C2#2145842111yescharacteristic
577C2#2145883011yescharacteristic
578C2#2145889211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1948C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#1948D61
hypocenterC61#26094
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
1. #21451049C2semidirect
7. #21446588C2semidirect
8. #21446586C2semidirect
9. #21446534C2semidirect
10. #21446411C2semidirect
11. #21446393C2semidirect
12. #21445980C2semidirect
15. C61×#1948C2semidirect
290. #1948D61semidirect
348. C61#26094semidirect

Maximal subgroups

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

subgroupindex
#214510492
#214487882
#214473482
#214473412
#214471922
#214471882
#214465882
#214465862
#214465342
#214464112
#214463932
#214459802
#214458282
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