Finite Group Databasebeta

← #29651462

Subgroups — #29651462

Order 15616.

654 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#21454836C211yesmaximal, characteristic, complemented
2#21454831C211yesmaximal, characteristic, complemented
3C4×#14519799C211yesmaximal, characteristic
4#21444708C212yesmaximal, complemented
5#21444668C212yesmaximal, complemented
6#21444647C212yesmaximal, complemented
7#21444618C212yesmaximal, complemented
8#21444251C211yesmaximal, characteristic, complemented
9#21444251C211yesmaximal, characteristic, complemented
10C8×#11758194C211yesmaximal, characteristic, complemented
11C61×#1568C211yesmaximal, characteristic, complemented
12C2×#14519799C411yescharacteristic
13C4×#11758222C2211yescharacteristic
14C4×#11758222C2211yescharacteristic
15#16839889C2212yes—
16#16839886C2212yes—
17C4×Dic244C411yescharacteristic
18C4×Dic244C2211yescharacteristic
19C4×#11758190C411yescharacteristic
20C4×#11758190C411yescharacteristic
21C4×#11758190C2211yescharacteristic
22C4×#11758190C2211yescharacteristic
23C4×D488C411yescharacteristic
24C4×D488C2211yescharacteristic
25#16839839C2212yes—
26#16839837—22no—
27#16839836—22no—
28#16839827C2212yes—
29#16839817—21no—
30#16839817—21no—
31#16839815C2211yescharacteristic
32#16839800C411yescharacteristic
33#16839759C411yescharacteristic
34#16839759C411yescharacteristic
35C4×#11758194C2211yescharacteristic
36#16839714—21no—
37#97×D61—21no—
38#16839492C2212yes—
39#16839492C2212yes—
40#16839489C2212yes—
41#16839489C2212yes—
42#16839484C2212yes—
43C8×#92418C2212yes—
44C61×#432C2211yescharacteristic
45C61×#432C2211yescharacteristic
46C2×C4×C8×C61C2211yescharacteristic
47C61×#335C2212yes—
48C61×#334C2212yes—
49C2×#11758222C2×C411yescharacteristic
50C2×#11758222C2×C411yescharacteristic
51#14519799—24no—
52C2×Dic244C2×C411yescharacteristic
53C2×#11758190C2×C411yescharacteristic
54C2×#11758190C2×C411yescharacteristic
55C2×D488C2×C411yescharacteristic
56C2×#11758194D412yes—
57C2×#11758189—22no—
58C2×C8×D61—22no—
59C4×Dic122C2×C411yescharacteristic
60C4×Dic122C2×C411yescharacteristic
61C4×Dic122C2311yescharacteristic
62C4×Dic122C2311yescharacteristic
63C4×D244C2×C411yescharacteristic
64C4×D244C2×C411yescharacteristic
65C4×D244C2311yescharacteristic
66C4×D244C2311yescharacteristic
67C4×C22⋊D61—21no—
68C4×C22⋊D61—21no—
69C4×C22⋊D61—21no—
70C4×C22⋊D61—21no—
71#14519736C2×C411yescharacteristic
72#14519736C2×C411yescharacteristic
73#14519734—21no—
74#14519734—21no—
75C42×D61—21no—
76C42×D61—21no—
77#14519711C2×C411yescharacteristic
78#14519711C2×C411yescharacteristic
79#14519709C2×C411yescharacteristic
80#14519709C2×C411yescharacteristic
81C4⋊#92418—21no—
82#14519706—22no—
83#14519706—22no—
84#14519702C2×C411yescharacteristic
85#14519702C2×C411yescharacteristic
86#14519702C2×C411yescharacteristic
87#14519702C2×C411yescharacteristic
88#14519699C2×C411yescharacteristic
89#14519699C2×C411yescharacteristic
90#14519699C2×C411yescharacteristic
91#14519699C2×C411yescharacteristic
92C22⋊#92418—21no—
93#14519689—22no—
94#14519689—22no—
95#14519688D411yescharacteristic
96#14519688D411yescharacteristic
97#14519687—22no—
98C4×#92418C2312yes—
99C4×#92418C2312yes—
100C8×Dic61—22no—
101C22×C8×C61C2×C411yescharacteristic
102C22×C8×C61C2×C411yescharacteristic
103C2×C42×C61C2311yescharacteristic
104C4⋊C8×C61C2312yes—
105C4⋊C8×C61C2312yes—
106C22⋊C8×C61—21no—
107C22⋊C8×C61—21no—
108#97×C61—21no—
109#97×C61—21no—
110C4×C8×C61C2×C411yescharacteristic
111C4×C8×C61C2×C411yescharacteristic
112C4×C8×C61C2311yescharacteristic
113C4×C8×C61C2311yescharacteristic
114C22×C4×C61C22×C411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61#4111yescharacteristic
117C2×C22⋊D61—21no—
118C2×C22⋊D61—21no—
119#11758222—22no—
120#11758222—22no—
121#11758222—41no—
122#11758222—41no—
123C2×D244C22×C411yescharacteristic
124C2×D244C22×C411yescharacteristic
125C2×C4×D61—21no—
126C2×C4×D61—21no—
127C2×C4×D61—21no—
128C2×C4×D61—21no—
129C2×C4×D61—21no—
130C2×C4×D61—21no—
131C2×Dic122C22×C411yescharacteristic
132C2×Dic122C22×C411yescharacteristic
133C2×C8×C61—22no—
134C2×C8×C61—22no—
135C2×C8×C61—22no—
136C2×C8×C61—41no—
137C2×C8×C61C22×C411yescharacteristic
138C2×C8×C61C22×C411yescharacteristic
139C2×C8×C61C22×C411yescharacteristic
140C2×C8×C61C22×C411yescharacteristic
141C42×C61C22×C411yescharacteristic
142C42×C61C2×D411yescharacteristic
143C42×C61#4111yescharacteristic
144C42×C61C2411yescharacteristic
145C22⋊Dic61—21no—
146C22⋊Dic61—21no—
147#11758198—21no—
148#11758198—21no—
149#11758198—21no—
150#11758198—21no—
151C4⋊Dic61C22×C411yescharacteristic
152C4⋊Dic61C22×C411yescharacteristic
153C4⋊Dic61C22×C411yescharacteristic
154C4⋊Dic61C22×C411yescharacteristic
155#11758196—21no—
156#11758196—21no—
157#11758196—21no—
158#11758196—21no—
159C4×Dic61—21no—
160C4×Dic61—21no—
161C4×Dic61—21no—
162C4×Dic61—21no—
163C4×Dic61—21no—
164C4×Dic61—21no—
165#11758194—24no—
166C2×#92418—22no—
167C2×#92418C2×D412yes—
168C2×#92418C2×D412yes—
169Dic244—22no—
170D488—22no—
171#11758190—22no—
172#11758190M1614yescomplemented
173#11758189—44no—
174C8×D61—44no—
175C23×C61C4×D411yescharacteristic
176C22×D61—21no—
177C22×D61—21no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—22no—
181C2×C4×C61—41no—
182C2×C4×C61C4×D411yescharacteristic
183C2×C4×C61C4×D411yescharacteristic
184C2×C4×C61C4×D411yescharacteristic
185C2×C4×C61C23×C411yescharacteristic
186C2×C4×C61C22×D411yescharacteristic
187C2×C4×C61C2×#4111yescharacteristic
188C22⋊D61—42no—
189C22⋊D61—42no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196D244—21no—
197D244—21no—
198D244—21no—
199D244C2×M1612yes—
200C4×D61—42no—
201C4×D61—42no—
202C4×D61—42no—
203C4×D61—42no—
204C4×D61—81no—
205C4×D61—81no—
206Dic122—21no—
207Dic122—21no—
208Dic122—21no—
209Dic122C2×M1612yes—
210C8×C61—21no—
211C8×C61—21no—
212C8×C61—21no—
213C8×C61—42no—
214C8×C61—42no—
215C8×C61C2×M1612yes—
216#92418—22no—
217#92418—42no—
218#92418#13514yescomplemented
219#18037—611nomaximal, Sylow
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61C2×C4×D411yescharacteristic
224C2×D61—22no—
225C2×D61—41no—
226C2×D61—41no—
227C2×D61—41no—
228C2×D61—41no—
229C2×D61—41no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61C22×M1611yescharacteristic
235C4×C61#56811yescharacteristic
236C4×C61C2×#13512yes—
237Dic61—22no—
238Dic61—41no—
239Dic61—41no—
240Dic61—41no—
241Dic61—41no—
242Dic61—41no—
243#2971—611no—
244#2970—611no—
245C4×#135—611no—
246#1590—612no—
247#1584—612no—
248#1581—612no—
249C8×SD16—612no—
250#1568D6111yescharacteristic, complemented
251#1488—611no—
252#1488—611no—
253C8×M16—611no—
254C2×C61—41no—
255C2×C61D4×M1611yescharacteristic
256C2×C61C4×#13511yescharacteristic
257C2×C61#295711yescharacteristic
258D61—42no—
259D61—81no—
260C2×#135—611no—
261C4×#41—611no—
262C4×#41—611no—
263#446—612no—
264C8×Q8—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#436—612no—
274#436—1222no—
275#435—1222no—
276C8×D4—612no—
277#432—1221no—
278#432—1221no—
279#432C2×D6111yescharacteristic
280#432C2×D6111yescharacteristic
281#431—611no—
282#427—611no—
283#416—611no—
284#416—611no—
285C4×M16—611no—
286C4×M16—1221no—
287C2×#97—1221no—
288C2×C4×C8C2×D6111yescharacteristic
289#335C2×D6112yes—
290#334C2×D6112yes—
291Q8⋊C8—612no—
292Q8⋊C8—612no—
293D4⋊C8—612no—
294D4⋊C8—612no—
295#322—612no—
296C82—612no—
297C61#1803711yescharacteristic, complemented, Sylow
298C2×#41—611no—
299C2×#41—611no—
300#135—1224no—
301C2×Q16—611no—
302C2×SD16—611no—
303C2×SD16—611no—
304C2×D8—611no—
305C2×M16—612no—
306C2×M16—1222no—
307C22×C8—1222no—
308C22×C8C4×D6111yescharacteristic
309C22×C8C4×D6111yescharacteristic
310C4×Q8—611no—
311C4×Q8—611no—
312C4×Q8—611no—
313C4×Q8—611no—
314C4×D4—611no—
315C4×D4—611no—
316C4×D4—611no—
317C4×D4—611no—
318C4×D4—1221no—
319C4×D4—1221no—
320C4×D4—1221no—
321C4×D4—1221no—
322#117—611no—
323#117—611no—
324#117—1221no—
325#117—1221no—
326C2×C42—1221no—
327C2×C42—1221no—
328C2×C42C22×D6111yescharacteristic
329#107—611no—
330#107—611no—
331#106—611no—
332#106—611no—
333C4⋊C8—1222no—
334C4⋊C8—1222no—
335C4⋊C8—1221no—
336C4⋊C8C22×D6112yes—
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—21no—
353#97—611no—
354#97—611no—
355#97—1222no—
356C4×C8—612no—
357C4×C8—612no—
358C4×C8—1222no—
359C4×C8C4×D6111yescharacteristic
360C4×C8C4×D6111yescharacteristic
361C4×C8C22×D6111yescharacteristic
362C4×C8C22×D6111yescharacteristic
363#41—1222no—
364#41—1222no—
365#41—2441no—
366#41—2441no—
367C2×Q8—611no—
368C2×Q8—611no—
369C2×D4—611no—
370C2×D4—611no—
371C2×D4—1221no—
372C2×D4—1221no—
373C22×C4—1221no—
374C22×C4—1221no—
375C22×C4—1221no—
376C22×C4—1221no—
377C22×C4—1221no—
378C22×C4—1221no—
379C22×C4C2×C4×D6111yescharacteristic
380C22×C4D4×D6111yescharacteristic
381C22×C4#1175822611yescharacteristic
382Q16—1222no—
383SD16—614no—
384SD16—1222no—
385D8—1222no—
386M16—1224no—
387M16—2444no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—41no—
392C2×C8—612no—
393C2×C8—612no—
394C2×C8—1222no—
395C2×C8—2444no—
396C2×C8C2×C4×D6111yescharacteristic
397C2×C8C2×C4×D6111yescharacteristic
398C2×C8C2×C4×D6111yescharacteristic
399C2×C8C2×C4×D6111yescharacteristic
400C4⋊C4—611no—
401C4⋊C4—611no—
402C4⋊C4—611no—
403C4⋊C4—611no—
404C4⋊C4—1221no—
405C4⋊C4—1221no—
406C4⋊C4—1221no—
407C4⋊C4—1221no—
408C22⋊C4—1221no—
409C22⋊C4—1221no—
410C22⋊C4—1221no—
411C22⋊C4—1221no—
412C22⋊C4—1221no—
413C22⋊C4—1221no—
414C42—1221no—
415C42—1221no—
416C42—1221no—
417C42—1221no—
418C42—1221no—
419C42—1221no—
420C42C2×C4×D6111yescharacteristic
421C42D4×D6111yescharacteristic
422C42#1175822611yescharacteristic
423C42C23×D6111yescharacteristic
424C23—1221no—
425C23—1221no—
426C23#1451973911yescharacteristic
427Q8—612no—
428Q8—1221no—
429Q8—1221no—
430Q8—1221no—
431D4—612no—
432D4—1221no—
433D4—1221no—
434D4—1221no—
435D4—2442no—
436D4—2442no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—1221no—
442C2×C4—1221no—
443C2×C4—1221no—
444C2×C4—1221no—
445C2×C4—1221no—
446C2×C4—1221no—
447C2×C4—4881no—
448C2×C4—4881no—
449C2×C4—2442no—
450C2×C4—2442no—
451C2×C4—2442no—
452C2×C4—2442no—
453C2×C4#1451973911yescharacteristic
454C2×C4#1451973911yescharacteristic
455C2×C4#1451973911yescharacteristic
456C2×C4C22×C4×D6111yescharacteristic
457C2×C4C2×D4×D6111yescharacteristic
458C2×C4C2×#1175822611yescharacteristic
459C8—21no—
460C8—21no—
461C8—21no—
462C8—42no—
463C8—42no—
464C8—614no—
465C8—1222no—
466C8—2442no—
467C8M16×D6112yes—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—1222no—
472C22—2441no—
473C22—2441no—
474C22—2441no—
475C22—2441no—
476C22—2441no—
477C22C2×#1451973911yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—1222no—
483C4—2441no—
484C4—2441no—
485C4—2441no—
486C4—2441no—
487C4—2441no—
488C4C2×M16×D6111yescharacteristic
489C4#1684052811yescharacteristic
490C4#135×D6112yes—
491C2—41no—
492C2—4881no—
493C2—2442no—
494C2#2145455411yescharacteristic
495C2#2145459011yescharacteristic
496C2#2145473511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1568C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519799C4
cosocleC42×C61C24
hypercenter#1568D61
hypocenterC61#18037
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
1. #21454836C2semidirect
2. #21454831C2semidirect
4. #21444708C2semidirect
5. #21444668C2semidirect
6. #21444647C2semidirect
7. #21444618C2semidirect
8. #21444251C2semidirect
9. #21444251C2semidirect
10. C8×#11758194C2semidirect
11. C61×#1568C2semidirect
172. #11758190M16semidirect
218. #92418#135semidirect
250. #1568D61semidirect
297. C61#18037semidirect

Maximal subgroups

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

subgroupindex
#214548362
#214548312
C4×#145197992
#214447082
#214446682
#214446472
#214446182
#214442512
C8×#117581942
C61×#15682
#1803761