Finite Group Databasebeta

← #29725166

Subgroups — #29725166

Order 15616.

706 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450740C211yesmaximal, characteristic
2#21448771C211yesmaximal, characteristic, complemented
3#21447389C211yesmaximal, characteristic, complemented
4#21447236C211yesmaximal, characteristic
5#21447233C211yesmaximal, characteristic
6#21446753C211yesmaximal, characteristic, complemented
7#21446581C211yesmaximal, characteristic, complemented
8#21446447C211yesmaximal, characteristic
9#21446444C211yesmaximal, characteristic
10#21446403C211yesmaximal, characteristic, complemented
11#21446401C211yesmaximal, characteristic, complemented
12#21445945C211yesmaximal, characteristic, complemented
13#21445818C211yesmaximal, characteristic
14#21445633C211yesmaximal, characteristic
15C61×#2101C211yesmaximal, characteristic, complemented
16C2×#14519755—21no—
17C2×C4×Dic122C2211yescharacteristic
18C2×#14519739C2211yescharacteristic
19C2×#14519709C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×#14519699C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519697C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×C8×Dic61C2211yescharacteristic
27#16839686—21no—
28#16839684—21no—
29#16839666—21no—
30#16839664C2211yescharacteristic
31#16839663C2211yescharacteristic
32#16839658C2211yescharacteristic
33#16839647—21no—
34#16839644—21no—
35#16839631C2211yescharacteristic
36#16839631C2211yescharacteristic
37#16839627C2211yescharacteristic
38#16839621—21no—
39C4⋊C4×Dic61C2211yescharacteristic
40C4⋊C4×Dic61C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
42#16839613—21no—
43#16839525C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C61×#389C2211yescharacteristic
53C61×#382C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×Dic122D411yescharacteristic
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64#14519755—44no—
65C4×Dic122—22no—
66C4×Dic122—22no—
67#14519739—22no—
68#14519739—22no—
69C2×C4⋊Dic61D411yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196D411yescharacteristic
79C2×#11758196D411yescharacteristic
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61C2311yescharacteristic
89C2×C4×Dic61C2311yescharacteristic
90#14519709—22no—
91#14519708—22no—
92#14519706—22no—
93#14519699—22no—
94#14519699—22no—
95#14519697—22no—
96#14519697—22no—
97C8×Dic61—22no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104C22×C8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C42×C61C2311yescharacteristic
112#95×C61—21no—
113#95×C61—21no—
114#95×C61—21no—
115C23×D61—21no—
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2411yescharacteristic
123C22×Dic61—21no—
124C22×Dic61—21no—
125C22×Dic61—21no—
126C22×Dic61C2×D411yescharacteristic
127C22×Dic61C2×D411yescharacteristic
128C22×Dic61C2×D411yescharacteristic
129C22×Dic61C2×D411yescharacteristic
130C2×D244—21no—
131C2×D244—21no—
132C2×D244—21no—
133C2×D244—21no—
134C2×D244—21no—
135C2×D244#4112yes—
136C2×C4×D61—42no—
137C2×C4×D61—42no—
138C2×C4×D61—42no—
139C2×Dic122—22no—
140C2×Dic122—22no—
141C2×Dic122—22no—
142C2×C8×C61—21no—
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—21no—
147C2×C8×C61—21no—
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—21no—
156C4⋊C4×C61—42no—
157C42×C61—21no—
158C42×C61—21no—
159#11758198—42no—
160#11758198—42no—
161#11758198—42no—
162#11758198—81no—
163#11758198—81no—
164C4⋊Dic61—21no—
165C4⋊Dic61—22no—
166C4⋊Dic61—21no—
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61#4112yes—
171#11758196—22no—
172#11758196—22no—
173#11758196—42no—
174#11758196—42no—
175#11758196—42no—
176#11758196—81no—
177#11758196—81no—
178C4×Dic61—21no—
179C4×Dic61—21no—
180C4×Dic61—42no—
181C4×Dic61—81no—
182C4×Dic61—81no—
183C4×Dic61#4112yes—
184C4×Dic61#4112yes—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—21no—
191C23×C61C22×D411yescharacteristic
192C22×D61—22no—
193C22×D61—41no—
194C22×D61—41no—
195C22×D61—41no—
196C22×D61—41no—
197C22×D61—41no—
198C22×D61—41no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
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—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61C2×#4111yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C2×C4×C612−1+411yescharacteristic
222C2×C4×C612−1+411yescharacteristic
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—22no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61#12312yes—
241C2×Dic61#12312yes—
242C2×Dic61#13512yes—
243C2×Dic61AGL(1,ℤ/8)12yes—
244D244—22no—
245D244—22no—
246D244—41no—
247D244—41no—
248C4×D61—84no—
249Dic122—44no—
250C8×C61—41no—
251C8×C61—41no—
252#92418—41no—
253#92418—41no—
254#24991—611nomaximal, Sylow
255C22×C61C2×#12311yescharacteristic
256C22×C61#54811yescharacteristic
257C22×C61#54811yescharacteristic
258C22×C61C2×#13511yescharacteristic
259C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C61#57711yescharacteristic
261C22×C61#57711yescharacteristic
262C2×D61—42no—
263C2×D61—42no—
264C2×D61—42no—
265C2×D61—81no—
266C2×D61—81no—
267C2×D61—81no—
268C2×D61—81no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61—81no—
272C4×C61—81no—
273C4×C61—81no—
274C4×C61—81no—
275C4×C61#52911yescharacteristic
276C4×C61#54111yescharacteristic
277C4×C61#55211yescharacteristic
278C4×C61#55611yescharacteristic
279Dic61—22no—
280Dic61—41no—
281Dic61—41no—
282Dic61—42no—
283Dic61—81no—
284Dic61—81no—
285Dic61#48214yes—
286#2538—611no—
287#2355—611no—
288#2101—611no—
289#2101D6111yescharacteristic, complemented
290#2073—611no—
291#2073—611no—
292#1984—611no—
293#1948—611no—
294#1926—611no—
295#1926—611no—
296#1920—611no—
297#1920—611no—
298#1834—611no—
299#1802—611no—
300C4×#102—611no—
301C2×C61#242111yescharacteristic
302C2×C61C2×#48211yescharacteristic
303C2×C61#309911yescharacteristic
304C2×C61#336011yescharacteristic
305C2×C61#336011yescharacteristic
306C2×C61#336811yescharacteristic
307C2×C61#337311yescharacteristic
308D61—82no—
309C2×C22⋊Q8—1221no—
310C2×C4×Q8—611no—
311C2×C4×D4—611no—
312C2×#106—611no—
313C2×#106—611no—
314C2×C4⋊C8—611no—
315C2×#102—611no—
316C2×#102—611no—
317C2×#102—611no—
318C2×#102—611no—
319C2×C4×C8—611no—
320#396—1221no—
321#396—1221no—
322#391—1221no—
323#390—611no—
324#390—611no—
325#389—611no—
326#389C2×D6111yescharacteristic
327#387—1221no—
328#387—1221no—
329#384—611no—
330#384—611no—
331#382—611no—
332#382C2×D6111yescharacteristic
333#380—1221no—
334C4×C4⋊C4—611no—
335C4×C4⋊C4—611no—
336C4×C4⋊C4—611no—
337C4×C4⋊C4—1221no—
338#340—611no—
339#340—611no—
340#340—611no—
341#340—611no—
342#340—611no—
343#340—611no—
344#340C2×D6111yescharacteristic
345#340C2×D6111yescharacteristic
346#340C2×D6111yescharacteristic
347#340C2×D6111yescharacteristic
348#336—611no—
349#336—611no—
350#336—611no—
351#336C2×D6111yescharacteristic
352C61#2499111yescharacteristic, complemented, Sylow
353C22×Q8—611no—
354C22×D4—611no—
355C23×C4—1221no—
356C22×C8—611no—
357C22×C8—611no—
358C22×C8C22×D6111yescharacteristic
359C22×C8C22×D6111yescharacteristic
360C22⋊Q8—2444no—
361C4×Q8—1222no—
362C4×Q8—1222no—
363C4×D4—1222no—
364C4×D4—1222no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—611no—
367C2×C4⋊C4—611no—
368C2×C4⋊C4—611no—
369C2×C4⋊C4—611no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—1221no—
373C2×C4⋊C4—1221no—
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×C4⋊C4C22×D6111yescharacteristic
381C2×C22⋊C4—1221no—
382C2×C22⋊C4—1221no—
383C2×C22⋊C4—1221no—
384C2×C22⋊C4—1221no—
385C2×C22⋊C4—1221no—
386C2×C42—611no—
387C2×C42—611no—
388C2×C42—1221no—
389C2×C42—1221no—
390C2×C42—1221no—
391C2×C42C22×D6111yescharacteristic
392#106—1222no—
393#106—1222no—
394C4⋊C8—1222no—
395#102—1222no—
396#102—1222no—
397#102—1222no—
398#102—1222no—
399C4×C8—1222no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—1221no—
404#95—1221no—
405#95—1221no—
406#95—1221no—
407#95—1221no—
408#95—1221no—
409C24—1221no—
410C2×Q8—1222no—
411C2×Q8—1222no—
412C2×Q8—1222no—
413C2×D4—612no—
414C2×D4—1221no—
415C2×D4—1221no—
416C2×D4—1221no—
417C2×D4—1221no—
418C2×D4—1221no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—1221no—
428C22×C4—1221no—
429C22×C4—1221no—
430C22×C4—2442no—
431C22×C4—2442no—
432C22×C4—2442no—
433C22×C4D4×D6111yescharacteristic
434C22×C4D4×D6111yescharacteristic
435C22×C4C23×D6111yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—1221no—
446C2×C8—1221no—
447C2×C8—1221no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—42no—
457C4⋊C4—612no—
458C4⋊C4—1222no—
459C4⋊C4—1222no—
460C4⋊C4—1222no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—4881no—
467C4⋊C4—4881no—
468C4⋊C4—2442no—
469C4⋊C4—2442no—
470C4⋊C4—2442no—
471C22⋊C4—4881no—
472C22⋊C4—4881no—
473C22⋊C4—2442no—
474C22⋊C4—2442no—
475C22⋊C4—2442no—
476C42—21no—
477C42—21no—
478C42—612no—
479C42—612no—
480C42—1221no—
481C42—1221no—
482C42—4881no—
483C42—4881no—
484C42—2442no—
485C23—1222no—
486C23—2441no—
487C23—2441no—
488C23—2441no—
489C23—2441no—
490C23—2441no—
491C23—2441no—
492C23C2×D4×D6111yescharacteristic
493Q8—2444no—
494D4—1222no—
495D4—1222no—
496D4—2441no—
497D4—2441no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
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—41no—
515C2×C4—41no—
516C2×C4—612no—
517C2×C4—612no—
518C2×C4—612no—
519C2×C4—612no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1222no—
529C2×C4—4884no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4#41×D6111yescharacteristic
539C2×C4#41×D6111yescharacteristic
540C2×C4#41×D6111yescharacteristic
541C2×C4#41×D6111yescharacteristic
542C2×C4#1451982411yescharacteristic
543C2×C4#1451982511yescharacteristic
544C8—41no—
545C8—41no—
546C8—2441no—
547C8—2441no—
548C22—4881no—
549C22—4881no—
550C22—4881no—
551C22—4881no—
552C22—2442no—
553C22—2442no—
554C22—2442no—
555C22#123×D6111yescharacteristic
556C22#1684042011yescharacteristic
557C22#1684042211yescharacteristic
558C22#135×D6111yescharacteristic
559C22AGL(1,ℤ/8)×D6111yescharacteristic
560C22#1684056911yescharacteristic
561C22#1684057111yescharacteristic
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4—614no—
569C4—1222no—
570C4—4881no—
571C4—4881no—
572C4—2442no—
573C4—2441no—
574C4—2441no—
575C4#1684029511yescharacteristic
576C4#1684037111yescharacteristic
577C4#1684044411yescharacteristic
578C4#1684047911yescharacteristic
579C2—4882no—
580C2#2144931711yescharacteristic
581C2#482×D6111yescharacteristic
582C2#2145580511yescharacteristic
583C2#2145846511yescharacteristic
584C2#2145847111yescharacteristic
585C2#2145855111yescharacteristic
586C2#2145860811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2101C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#2101D61
hypocenterC61#24991
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2101

Complements

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

NH ≅ G/Ntype
2. #21448771C2semidirect
3. #21447389C2semidirect
6. #21446753C2semidirect
7. #21446581C2semidirect
10. #21446403C2semidirect
11. #21446401C2semidirect
12. #21445945C2semidirect
15. C61×#2101C2semidirect
289. #2101D61semidirect
352. C61#24991semidirect

Maximal subgroups

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

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