Finite Group Databasebeta

← #29651439

Subgroups — #29651439

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454833C211yesmaximal, characteristic, complemented
2#21454831C211yesmaximal, characteristic, complemented
3C4×#14519797C211yesmaximal, characteristic
4#21444713C212yesmaximal, complemented
5#21444658C212yesmaximal, complemented
6#21444652C212yesmaximal, complemented
7#21444611C212yesmaximal, complemented
8#21444580C211yesmaximal, characteristic, complemented
9#21444254C211yesmaximal, characteristic, complemented
10#21444100C211yesmaximal, characteristic, complemented
11C61×#1488C211yesmaximal, characteristic, complemented
12C2×#14519797C411yescharacteristic
13C4×#11758222C2211yescharacteristic
14#16839893C2212yes—
15#16839889C2212yes—
16C4×#11758202C411yescharacteristic
17C4×#11758202C2211yescharacteristic
18C4×#11758201C411yescharacteristic
19C4×#11758201C2211yescharacteristic
20C4×#11758200C411yescharacteristic
21C4×#11758200C2211yescharacteristic
22C4×#11758199C411yescharacteristic
23C4×#11758199C2211yescharacteristic
24#16839836—22no—
25#16839834—22no—
26D4×#92418C2212yes—
27#16839827C2212yes—
28#16839819—21no—
29#16839819C2211yescharacteristic
30#16839817—21no—
31#16839798C411yescharacteristic
32#16839758C411yescharacteristic
33#16839756C411yescharacteristic
34C4×#11758194C2211yescharacteristic
35C2×#14519688—21no—
36#97×D61—21no—
37C2×C4×#92418C2211yescharacteristic
38#16839514C2212yes—
39#16839512C2212yes—
40#16839494C2212yes—
41#16839491C2212yes—
42#16839484C2212yes—
43C8×#92418C2212yes—
44C4×#41×C61C2211yescharacteristic
45C61×#432C2211yescharacteristic
46C61×#431C2211yescharacteristic
47C61×Q8⋊C8C2212yes—
48C61×D4⋊C8C2212yes—
49C2×#11758222C2×C411yescharacteristic
50#14519797—24no—
51C2×#11758202C2×C411yescharacteristic
52C2×#11758200C2×C411yescharacteristic
53C2×#11758201C2×C411yescharacteristic
54C2×#11758199C2×C411yescharacteristic
55C2×#11758194D412yes—
56C22×#92418—22no—
57C22×#92418C2×C411yescharacteristic
58C22×#92418C2×C411yescharacteristic
59C2×C8×D61—22no—
60C4×Dic122C2×C411yescharacteristic
61C4×Dic122C2311yescharacteristic
62C4×D244C2×C411yescharacteristic
63C4×D244C2311yescharacteristic
64C4×C22⋊D61—21no—
65C4×C22⋊D61—21no—
66#14519736C2×C411yescharacteristic
67#14519734—21no—
68C42×D61—21no—
69#14519710C2×C411yescharacteristic
70#14519710C2×C411yescharacteristic
71#14519708C2×C411yescharacteristic
72#14519708C2×C411yescharacteristic
73C4⋊#92418—22no—
74C4⋊#92418C2312yes—
75#14519706—22no—
76#14519701C2×C411yescharacteristic
77#14519701C2×C411yescharacteristic
78#14519700C2×C411yescharacteristic
79#14519700C2×C411yescharacteristic
80#14519698C2×C411yescharacteristic
81#14519698C2×C411yescharacteristic
82#14519697C2×C411yescharacteristic
83#14519697C2×C411yescharacteristic
84C22⋊#92418—21no—
85C22⋊#92418—22no—
86#14519689—22no—
87#14519688—21no—
88#14519688—22no—
89#14519688D411yescharacteristic
90#14519688D411yescharacteristic
91#14519687—22no—
92C4×#92418C2×C411yescharacteristic
93C4×#92418C2×C411yescharacteristic
94C4×#92418C2311yescharacteristic
95C4×#92418C2311yescharacteristic
96C4×#92418C2312yes—
97C2×#41×C61C2×C411yescharacteristic
98C4×Q8×C61C2×C411yescharacteristic
99C4×Q8×C61C2311yescharacteristic
100C4×D4×C61—21no—
101C4×D4×C61—21no—
102C4×D4×C61C2×C411yescharacteristic
103C4×D4×C61C2311yescharacteristic
104#117×C61—21no—
105#117×C61C2×C411yescharacteristic
106C2×C42×C61—21no—
107C2×C42×C61C2311yescharacteristic
108C4⋊C8×C61—21no—
109C4⋊C8×C61C2312yes—
110C22⋊C8×C61—21no—
111C22⋊C8×C61—21no—
112#97×C61—21no—
113C4×C8×C61C2312yes—
114#41×C61—22no—
115#41×C61—41no—
116C2×Q8×C61C22×C411yescharacteristic
117C2×D4×C61—21no—
118C2×D4×C61C22×C411yescharacteristic
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61#4111yescharacteristic
125C2×C22⋊D61—21no—
126#11758222—22no—
127#11758222—41no—
128C2×D244C22×C411yescharacteristic
129C2×C4×D61—21no—
130C2×C4×D61—21no—
131C2×C4×D61—21no—
132C2×Dic122C22×C411yescharacteristic
133C2×C8×C61—22no—
134C2×C8×C61—22no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61C22×C411yescharacteristic
138C4⋊C4×C61C22×C411yescharacteristic
139C22⋊C4×C61—21no—
140C22⋊C4×C61—21no—
141C22⋊C4×C61—21no—
142C42×C61—21no—
143C42×C61—21no—
144C42×C61—21no—
145C42×C61C22×C411yescharacteristic
146C42×C61C2×D411yescharacteristic
147C42×C61#4111yescharacteristic
148C42×C61C2411yescharacteristic
149C22⋊Dic61—21no—
150#11758202—22no—
151#11758201—22no—
152#11758200—22no—
153#11758199M1614yescomplemented
154#11758198—21no—
155#11758198—21no—
156C4⋊Dic61C22×C411yescharacteristic
157C4⋊Dic61C22×C411yescharacteristic
158#11758196—21no—
159#11758196—21no—
160C4×Dic61—21no—
161C4×Dic61—21no—
162C4×Dic61—21no—
163#11758194—24no—
164C2×#92418—22no—
165C2×#92418—22no—
166C2×#92418—41no—
167C2×#92418—44no—
168C2×#92418C22×C411yescharacteristic
169C2×#92418C22×C411yescharacteristic
170C2×#92418C22×C411yescharacteristic
171C2×#92418C22×C411yescharacteristic
172C2×#92418C2×D412yes—
173C2×#92418C2×D412yes—
174C8×D61—44no—
175C23×C61—21no—
176C23×C61C4×D411yescharacteristic
177C22×D61—21no—
178Q8×C61—21no—
179Q8×C61—21no—
180D4×C61—21no—
181D4×C61—42no—
182D4×C61C2×M1612yes—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—22no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—41no—
190C2×C4×C61—42no—
191C2×C4×C61—42no—
192C2×C4×C61—81no—
193C2×C4×C61C4×D411yescharacteristic
194C2×C4×C61C4×D411yescharacteristic
195C2×C4×C61C4×D411yescharacteristic
196C2×C4×C61C23×C411yescharacteristic
197C2×C4×C61C22×D411yescharacteristic
198C2×C4×C61C2×#4111yescharacteristic
199C22⋊D61—42no—
200C2×Dic61—21no—
201C2×Dic61—21no—
202C2×Dic61—21no—
203D244—21no—
204D244C2×M1612yes—
205C4×D61—42no—
206C4×D61—42no—
207C4×D61—81no—
208Dic122—21no—
209Dic122—21no—
210C8×C61—42no—
211C8×C61—42no—
212#92418—21no—
213#92418—21no—
214#92418—21no—
215#92418—22no—
216#92418—42no—
217#92418C2×M1612yes—
218#92418#13514yescomplemented
219#18035—611nomaximal, Sylow
220C22×C61—21no—
221C22×C61—22no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—41no—
225C22×C61—41no—
226C22×C61C2×C4×D411yescharacteristic
227C2×D61—22no—
228C2×D61—41no—
229C2×D61—41no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—41no—
235C4×C61—41no—
236C4×C61—41no—
237C4×C61C22×M1611yescharacteristic
238C4×C61#56811yescharacteristic
239C4×C61C2×#13512yes—
240Dic61—41no—
241Dic61—41no—
242Dic61—41no—
243#2970—611no—
244#2970—611no—
245C4×#135—611no—
246#1591—612no—
247#1582—612no—
248#1582—612no—
249C8×D8—612no—
250#1568—611no—
251#1488—611no—
252#1488D6111yescharacteristic, complemented
253C8×M16—611no—
254C2×C61—41no—
255C2×C61—42no—
256C2×C61D4×M1611yescharacteristic
257C2×C61C4×#13511yescharacteristic
258C2×C61#295711yescharacteristic
259D61—42no—
260C2×#135—611no—
261C4×#41—611no—
262C4×#41C2×D6111yescharacteristic
263#446—612no—
264#446—612no—
265C4×Q16—611no—
266C4×Q16—611no—
267C4×SD16—611no—
268C4×SD16—611no—
269C4×SD16—611no—
270C4×SD16—611no—
271C4×D8—611no—
272C4×D8—611no—
273#435—1222no—
274#435—1222no—
275C8×D4—612no—
276C8×D4—612no—
277#432—611no—
278#432—1221no—
279#432—1221no—
280#432C2×D6111yescharacteristic
281#431C2×D6111yescharacteristic
282#427—611no—
283#416—611no—
284#416—611no—
285C4×M16—611no—
286C2×#97—1221no—
287C2×#97—1221no—
288C2×C4×C8—611no—
289#335—612no—
290#334—612no—
291Q8⋊C8—612no—
292Q8⋊C8C2×D6112yes—
293D4⋊C8—612no—
294D4⋊C8C2×D6112yes—
295#322—612no—
296C82—612no—
297C61#1803511yescharacteristic, complemented, Sylow
298C2×#41—611no—
299C2×#41C4×D6111yescharacteristic
300#135—1224no—
301C2×Q16—611no—
302C2×SD16—611no—
303C2×SD16—611no—
304C2×D8—611no—
305C2×M16—612no—
306C22×C8—611no—
307C22×C8—611no—
308C22×C8—1222no—
309C22×C8—1222no—
310C4×Q8—611no—
311C4×Q8—611no—
312C4×Q8C4×D6111yescharacteristic
313C4×Q8C22×D6111yescharacteristic
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—611no—
317C4×D4—611no—
318C4×D4—1221no—
319C4×D4—1221no—
320C4×D4C4×D6111yescharacteristic
321C4×D4C22×D6111yescharacteristic
322#117—21no—
323#117—611no—
324#117—1221no—
325#117C4×D6111yescharacteristic
326C2×C42—21no—
327C2×C42—1221no—
328C2×C42C22×D6111yescharacteristic
329#107—611no—
330#107—611no—
331#106—611no—
332#106—611no—
333C4⋊C8—21no—
334C4⋊C8—612no—
335C4⋊C8—1222no—
336C4⋊C8—1222no—
337C4⋊C8C22×D6112yes—
338#103—611no—
339#103—611no—
340#103—611no—
341#103—611no—
342#102—611no—
343#102—611no—
344#102—611no—
345#102—611no—
346C22⋊C8—21no—
347C22⋊C8—21no—
348C22⋊C8—1222no—
349C22⋊C8—1222no—
350C22⋊C8—1221no—
351#97—21no—
352#97—611no—
353#97—611no—
354#97—1222no—
355#97—1222no—
356#97—1221no—
357C4×C8—611no—
358C4×C8—611no—
359C4×C8—611no—
360C4×C8—612no—
361C4×C8—611no—
362C4×C8C22×D6112yes—
363#41—22no—
364#41—41no—
365#41—1222no—
366#41—2441no—
367C2×Q8—611no—
368C2×Q8C2×C4×D6111yescharacteristic
369C2×D4—21no—
370C2×D4—611no—
371C2×D4—1221no—
372C2×D4C2×C4×D6111yescharacteristic
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—1221no—
377C22×C4—1221no—
378C22×C4—1221no—
379C22×C4C2×C4×D6111yescharacteristic
380C22×C4D4×D6111yescharacteristic
381C22×C4#1175822411yescharacteristic
382Q16—1222no—
383SD16—1222no—
384SD16—1222no—
385D8—614no—
386M16—1224no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—611no—
390C2×C8—612no—
391C2×C8—611no—
392C2×C8—611no—
393C2×C8—611no—
394C2×C8—612no—
395C2×C8—1222no—
396C2×C8—1222no—
397C2×C8—2444no—
398C2×C8—2444no—
399C2×C8—2441no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—611no—
403C4⋊C4—611no—
404C4⋊C4—1221no—
405C4⋊C4—1221no—
406C4⋊C4C2×C4×D6111yescharacteristic
407C4⋊C4C2×C4×D6111yescharacteristic
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—1221no—
412C22⋊C4—1221no—
413C22⋊C4—1221no—
414C42—21no—
415C42—21no—
416C42—21no—
417C42—1221no—
418C42—1221no—
419C42—1221no—
420C42C2×C4×D6111yescharacteristic
421C42D4×D6111yescharacteristic
422C42#1175822411yescharacteristic
423C42C23×D6111yescharacteristic
424C23—21no—
425C23—1221no—
426C23#1451973711yescharacteristic
427Q8—21no—
428Q8—21no—
429Q8—1221no—
430Q8—1221no—
431D4—21no—
432D4—42no—
433D4—612no—
434D4—1221no—
435D4—2442no—
436D4M16×D6112yes—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—81no—
447C2×C4—1221no—
448C2×C4—1221no—
449C2×C4—1221no—
450C2×C4—4881no—
451C2×C4—2442no—
452C2×C4—2442no—
453C2×C4#1451973711yescharacteristic
454C2×C4#1451973711yescharacteristic
455C2×C4#1451973711yescharacteristic
456C2×C4C22×C4×D6111yescharacteristic
457C2×C4C2×D4×D6111yescharacteristic
458C2×C4C2×#1175822411yescharacteristic
459C8—42no—
460C8—42no—
461C8—612no—
462C8—614no—
463C8—1221no—
464C8—1221no—
465C8—1221no—
466C8—1222no—
467C8—2442no—
468C22—21no—
469C22—21no—
470C22—22no—
471C22—21no—
472C22—41no—
473C22—41no—
474C22—1222no—
475C22—2441no—
476C22—2441no—
477C22C2×#1451973711yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—2441no—
486C4—2441no—
487C4—2441no—
488C4C2×M16×D6111yescharacteristic
489C4#1684052811yescharacteristic
490C4#135×D6112yes—
491C2—41no—
492C2—42no—
493C2—2442no—
494C2#2145455111yescharacteristic
495C2#2145458711yescharacteristic
496C2#2145473211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1488C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519797C4
cosocleC42×C61C24
hypercenter#1488D61
hypocenterC61#18035
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
1. #21454833C2semidirect
2. #21454831C2semidirect
4. #21444713C2semidirect
5. #21444658C2semidirect
6. #21444652C2semidirect
7. #21444611C2semidirect
8. #21444580C2semidirect
9. #21444254C2semidirect
10. #21444100C2semidirect
11. C61×#1488C2semidirect
153. #11758199M16semidirect
218. #92418#135semidirect
252. #1488D61semidirect
297. C61#18035semidirect

Maximal subgroups

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

subgroupindex
#214548332
#214548312
C4×#145197972
#214447132
#214446582
#214446522
#214446112
#214445802
#214442542
#214441002
C61×#14882
#1803561