Finite Group Databasebeta

← #29834943

Subgroups — #29834943

Order 15616.

610 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456402C211yesmaximal, characteristic, complemented
2C4×D8×D61C211yesmaximal, characteristic
3#21448018C211yesmaximal, characteristic, complemented
4#21448015C211yesmaximal, characteristic, complemented
5#21447965C211yesmaximal, characteristic, complemented
6#21447964C211yesmaximal, characteristic, complemented
7#21447863C211yesmaximal, characteristic, complemented
8#21447862C211yesmaximal, characteristic, complemented
9#21447749C211yesmaximal, characteristic
10#21447746C211yesmaximal, characteristic
11C4×#14519722C211yesmaximal, characteristic, complemented
12C4×#14519720C211yesmaximal, characteristic, complemented
13C4×#14519721C211yesmaximal, characteristic, complemented
14#21447616C211yesmaximal, characteristic, complemented
15C4×SD32×C61C211yesmaximal, characteristic, complemented
16C2×D8×D61C2211yescharacteristic
17#16840316—21no—
18C4×D4×D61—21no—
19C2×#14519722C2211yescharacteristic
20C2×#14519721C2211yescharacteristic
21C2×#14519720C2211yescharacteristic
22#16840166C2211yescharacteristic, complemented
23#16840140C2211yescharacteristic, complemented
24#16840111—21no—
25#16840004C2211yescharacteristic
26#16840002—21no—
27#16840000C2211yescharacteristic
28C4×Dic244C2211yescharacteristic, complemented
29C4×#11758202—21no—
30C4×D488C2211yescharacteristic
31D8×Dic61C2211yescharacteristic
32#16839844C2211yescharacteristic
33C4×#11758199—21no—
34#16839842—21no—
35#107×D61C2211yescharacteristic
36#102×D61—21no—
37C4×C8×D61C2211yescharacteristic
38#16839590C2211yescharacteristic, complemented
39#16839589C2211yescharacteristic, complemented
40#16839589C2211yescharacteristic, complemented
41#16839580C2211yescharacteristic, complemented
42#16839580C2211yescharacteristic, complemented
43#16839567C2211yescharacteristic, complemented
44#16839566C2211yescharacteristic, complemented
45#16839565C2211yescharacteristic, complemented
46#16839564C2211yescharacteristic
47#16839563C2211yescharacteristic
48#16839562C2211yescharacteristic
49#16839541C2211yescharacteristic
50#16839541C2211yescharacteristic
51C4×#11758185C2211yescharacteristic, complemented
52C2×SD32×C61C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic, complemented
54C4×D8×C61C2211yescharacteristic
55C61×#367C2211yescharacteristic, complemented
56C61×#358C2211yescharacteristic, complemented
57C61×#357C2211yescharacteristic
58C4×C16×C61C2211yescharacteristic, complemented
59C2×D4×D61—21no—
60C22×C4×D61—41no—
61C2×Dic244C2311yescharacteristic
62C2×#11758202—21no—
63C2×D488C2311yescharacteristic
64C2×#11758199—21no—
65D8×D61—22no—
66D8×D61—22no—
67C2×C8×D61D411yescharacteristic
68C2×C8×D61C2311yescharacteristic
69#14519776—21no—
70#14519775—21no—
71#14519767—41no—
72#14519757—21no—
73#14519755—41no—
74#14519753—21no—
75C4×Dic122—21no—
76C4×Dic122—41no—
77C4×D244—21no—
78D4×Dic61—21no—
79#14519739—21no—
80C4×C22⋊D61—41no—
81#14519737—41no—
82#14519734—41no—
83C4⋊C4×D61—21no—
84C22⋊C4×D61—41no—
85C42×D61D411yescharacteristic
86#14519722—22no—
87#14519721—22no—
88#14519720—22no—
89C2×#11758185C2311yescharacteristic
90C2×#11758185C2311yescharacteristic
91#14519711C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519710—21no—
94#14519710—21no—
95#14519702—21no—
96#14519701—21no—
97#14519700—21no—
98#14519699—21no—
99#14519698—21no—
100#14519697—21no—
101C4×#92418D411yescharacteristic
102C8×Dic61D411yescharacteristic
103C8×Dic61C2311yescharacteristic
104C2×Q16×C61C2311yescharacteristic
105C2×D8×C61C2311yescharacteristic
106C4×Q8×C61—21no—
107C4×D4×C61—21no—
108SD32×C61—22no—
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#103×C61—21no—
114#102×C61—21no—
115C4×C8×C61C2311yescharacteristic
116C23×D61—41no—
117C2×Q8×C61—21no—
118C2×D4×C61—21no—
119C22×C4×C61—41no—
120C2×C22⋊D61—41no—
121C22×Dic61—41no—
122D4×D61—24no—
123D4×D61—42no—
124C2×D244—21no—
125C2×C4×D61—41no—
126C2×C4×D61—41no—
127C2×C4×D61—41no—
128C2×C4×D61—84no—
129C2×C4×D61D811yescharacteristic
130C2×C4×D61D811yescharacteristic
131C2×C4×D61C2×D411yescharacteristic
132C2×Dic122—21no—
133C2×Dic122—41no—
134Q16×C61—21no—
135Q16×C61—21no—
136D8×C61—21no—
137D8×C61#4112yes—
138C2×C8×C61C2×D411yescharacteristic
139C2×C8×C61C2411yescharacteristic
140C4⋊C4×C61—21no—
141C4⋊C4×C61—21no—
142C4⋊C4×C61—41no—
143C22⋊C4×C61—41no—
144C42×C61—41no—
145C42×C61C2×D411yescharacteristic
146C22⋊Dic61—41no—
147#11758202—42no—
148#11758199—24no—
149#11758198—41no—
150#11758198—41no—
151#11758198—41no—
152#11758198—41no—
153C4⋊Dic61—21no—
154C4⋊Dic61—21no—
155C4⋊Dic61—41no—
156#11758196—41no—
157#11758196—41no—
158#11758196—41no—
159#11758196—41no—
160#11758196—41no—
161#11758196—41no—
162C4×Dic61—41no—
163C4×Dic61D811yescharacteristic
164C4×Dic61D811yescharacteristic
165C4×Dic61C2×D411yescharacteristic
166C2×#92418C2×D411yescharacteristic
167C2×#92418C2×D411yescharacteristic
168Dic244—21no—
169Dic244—21no—
170D488—21no—
171D488#4112yes—
172C8×D61—21no—
173C8×D61—21no—
174C8×D61—41no—
175C16×C61—21no—
176C16×C61—21no—
177#11758185—21no—
178#11758185—21no—
179C23×C61—41no—
180C22×D61—44no—
181C22×D61—41no—
182C22×D61—82no—
183C22×D61—82no—
184C22×D61C2×D811yescharacteristic
185Q8×C61—41no—
186Q8×C61—41no—
187D4×C61—22no—
188D4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—82no—
193C2×C4×C61C2×D811yescharacteristic
194C2×C4×C61C2×D811yescharacteristic
195C2×C4×C61C22×D411yescharacteristic
196C22⋊D61—44no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—41no—
200C2×Dic61—82no—
201C2×Dic61C2×D811yescharacteristic
202C2×Dic61C2×D811yescharacteristic
203C2×Dic61C2×D811yescharacteristic
204D244—22no—
205D244—41no—
206C4×D61—21no—
207C4×D61—21no—
208C4×D61—41no—
209C4×D61—82no—
210C4×D61—82no—
211C4×D61—82no—
212C4×D61SD3214yescomplemented
213Dic122—41no—
214Dic122—41no—
215Dic122—82no—
216C8×C61—21no—
217C8×C61C2×#4111yescharacteristic
218C8×C61C2×#4111yescharacteristic
219#92418—21no—
220#92418—21no—
221#33661—611nomaximal, Sylow
222C22×C61—42no—
223C22×C61—81no—
224C22×C61—81no—
225C22×C61C22×D811yescharacteristic
226C2×D61—21no—
227C2×D61—21no—
228C2×D61—42no—
229C2×D61—88no—
230C2×D61—81no—
231C2×D61—81no—
232C2×D61C2×SD3212yes—
233C4×C61—21no—
234C4×C61—81no—
235C4×C61—81no—
236C4×C61—81no—
237C4×C61C2×SD3212yes—
238C4×C61#52511yescharacteristic
239C4×C61#57511yescharacteristic
240Dic61—21no—
241Dic61—21no—
242Dic61—81no—
243Dic61—81no—
244Dic61—81no—
245Dic61C2×SD3212yes—
246#3170—611no—
247C2×C4×D8—611no—
248#2235—611no—
249#2235—611no—
250#2226—611no—
251#2226—611no—
252#2208—611no—
253#2208—611no—
254#2187—611no—
255#2187—611no—
256C4×SD32—611no—
257C4×SD32—611no—
258C4×SD32—611no—
259C4×SD32D6111yescharacteristic, complemented
260#2162—611no—
261C2×C61—82no—
262C2×C61#310011yescharacteristic
263C2×C61C22×SD3211yescharacteristic
264C2×C61#341411yescharacteristic
265D61—22no—
266D61—82no—
267C22×D8—611no—
268#533—1221no—
269C2×C4×D4—1221no—
270C2×SD32—611no—
271C2×SD32—611no—
272C2×SD32—611no—
273C2×SD32C2×D6111yescharacteristic
274#500—611no—
275#494—611no—
276#487—1221no—
277#467—611no—
278#467—611no—
279#467—1221no—
280C4×Q16—611no—
281C4×Q16—1221no—
282C4×Q16C2×D6111yescharacteristic, complemented
283C4×D8—611no—
284C4×D8—611no—
285C4×D8—611no—
286C4×D8—1221no—
287C4×D8—1221no—
288C4×D8C2×D6111yescharacteristic
289C2×#107—611no—
290C2×#102—1221no—
291C2×C4×C8—611no—
292#367—611no—
293#367—611no—
294#367—611no—
295#367C2×D6111yescharacteristic, complemented
296C4⋊C16—611no—
297C4⋊C16—611no—
298#358—611no—
299#358—611no—
300#358—611no—
301#358C2×D6111yescharacteristic, complemented
302#357—611no—
303#357—611no—
304#357—611no—
305#357C2×D6111yescharacteristic
306C22⋊C16—611no—
307C22⋊C16—611no—
308C4×C16—611no—
309C4×C16C2×D6111yescharacteristic, complemented
310C61#3366111yescharacteristic, complemented, Sylow
311C22×D4—1221no—
312C23×C4—2441no—
313C2×Q16—611no—
314C2×Q16—1221no—
315C2×Q16C22×D6111yescharacteristic
316C2×D8—611no—
317C2×D8—1221no—
318C2×D8—1222no—
319C2×D8—1222no—
320C2×D8C22×D6111yescharacteristic
321C22×C8—611no—
322C22×C8—611no—
323C4⋊Q8—1221no—
324C4⋊Q8—1221no—
325#125—2441no—
326C22⋊Q8—1221no—
327C22⋊Q8—1221no—
328C22⋊Q8—2441no—
329C4×Q8—21no—
330C4×Q8—1221no—
331C4×Q8—2441no—
332C4×D4—21no—
333C4×D4—1221no—
334C4×D4—1221no—
335C4×D4—1221no—
336C4×D4—2441no—
337C4×D4—2441no—
338#117—2441no—
339C2×C4⋊C4—1221no—
340C2×C22⋊C4—2441no—
341C2×C42—611no—
342SD32—22no—
343SD32—1222no—
344SD32—1222no—
345SD32—1222no—
346C2×C16—611no—
347C2×C16—611no—
348C2×C16C22×D6111yescharacteristic
349C2×C16C22×D6111yescharacteristic
350#107—611no—
351#107—611no—
352#107—1221no—
353#107—1221no—
354#107C22×D6111yescharacteristic
355#107C22×D6111yescharacteristic
356#103—21no—
357#103—1221no—
358#103—1221no—
359#103—1221no—
360#102—21no—
361#102—1221no—
362#102—1221no—
363#102—1221no—
364C4×C8—611no—
365C4×C8—611no—
366C4×C8—611no—
367C4×C8C22×D6111yescharacteristic
368C24—2441no—
369C2×Q8—21no—
370C2×Q8—1221no—
371C2×Q8—2441no—
372C2×D4—21no—
373C2×D4—1224no—
374C2×D4—1221no—
375C2×D4—2441no—
376C2×D4—2442no—
377C22×C4—41no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—4884no—
382C22×C4—2441no—
383C22×C4—2441no—
384C22×C4—2441no—
385C22×C4—2441no—
386Q16—21no—
387Q16—21no—
388Q16—1221no—
389Q16—1221no—
390Q16—2442no—
391D8—21no—
392D8—612no—
393D8—1224no—
394D8—1221no—
395D8#1175822212yes—
396C2×C8—611no—
397C2×C8—611no—
398C2×C8—1221no—
399C2×C8—1221no—
400C2×C8—2441no—
401C2×C8D4×D6111yescharacteristic
402C2×C8C23×D6111yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—1221no—
407C4⋊C4—1221no—
408C4⋊C4—2441no—
409C4⋊C4—2441no—
410C4⋊C4—2441no—
411C4⋊C4—2441no—
412C4⋊C4—2441no—
413C4⋊C4—2441no—
414C4⋊C4—2441no—
415C22⋊C4—41no—
416C22⋊C4—2441no—
417C22⋊C4—2441no—
418C22⋊C4—2441no—
419C22⋊C4—2441no—
420C22⋊C4—2441no—
421C42—41no—
422C42—611no—
423C42—611no—
424C42—611no—
425C42—2441no—
426C42D4×D6111yescharacteristic
427C16—21no—
428C16—21no—
429C16—1221no—
430C16—1221no—
431C23—41no—
432C23—611no—
433C23—4882no—
434C23—4882no—
435C23—2444no—
436C23—2441no—
437Q8—41no—
438Q8—41no—
439Q8—4882no—
440Q8—2441no—
441Q8—2441no—
442D4—22no—
443D4—41no—
444D4—1222no—
445D4—2444no—
446D4—2441no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—82no—
451C2×C4—611no—
452C2×C4—614no—
453C2×C4—611no—
454C2×C4—611no—
455C2×C4—1221no—
456C2×C4—1221no—
457C2×C4—4882no—
458C2×C4—4882no—
459C2×C4—4882no—
460C2×C4—4882no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4—2441no—
465C2×C4D8×D6111yescharacteristic
466C2×C4D8×D6111yescharacteristic
467C2×C4C2×D4×D6111yescharacteristic
468C8—21no—
469C8—1221no—
470C8—1221no—
471C8#41×D6111yescharacteristic
472C8C2×#1175822211yescharacteristic
473C22—42no—
474C22—81no—
475C22—81no—
476C22—612no—
477C22—1221no—
478C22—1221no—
479C22—4888no—
480C22—4881no—
481C22—4881no—
482C22—2442no—
483C22C2×D8×D6111yescharacteristic
484C4—21no—
485C4—81no—
486C4—81no—
487C4—81no—
488C4—612no—
489C4—1221no—
490C4—1221no—
491C4—4881no—
492C4—4881no—
493C4—4881no—
494C4SD32×D6112yes—
495C4#1684027111yescharacteristic
496C4#1684055911yescharacteristic
497C2—82no—
498C2—1222no—
499C2—4882no—
500C2#2145581711yescharacteristic
501C2C2×SD32×D6111yescharacteristic
502C2#2145895211yescharacteristic
subgroupG/H
centerC2×C4D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC4×SD32×C61C2
socleC22×C61C22×D8
prime radicalC2×D8×D61C22
hypercenterC4×SD32D61
hypocenterC61#33661
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
1. #21456402C2semidirect
3. #21448018C2semidirect
4. #21448015C2semidirect
5. #21447965C2semidirect
6. #21447964C2semidirect
7. #21447863C2semidirect
8. #21447862C2semidirect
11. C4×#14519722C2semidirect
12. C4×#14519720C2semidirect
13. C4×#14519721C2semidirect
14. #21447616C2semidirect
15. C4×SD32×C61C2semidirect
22. #16840166C22semidirect
23. #16840140C22semidirect
28. C4×Dic244C22semidirect
38. #16839590C22semidirect
39. #16839589C22semidirect
40. #16839589C22semidirect
41. #16839580C22semidirect
42. #16839580C22semidirect
43. #16839567C22semidirect
44. #16839566C22semidirect
45. #16839565C22semidirect
51. C4×#11758185C22semidirect
53. C4×Q16×C61C22semidirect
55. C61×#367C22semidirect
56. C61×#358C22semidirect
58. C4×C16×C61C22semidirect
212. C4×D61SD32semidirect
259. C4×SD32D61semidirect
282. C4×Q16C2×D61semidirect
295. #367C2×D61semidirect
301. #358C2×D61semidirect
309. C4×C16C2×D61semidirect
310. C61#33661semidirect

Maximal subgroups

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

subgroupindex
#214564022
C4×D8×D612
#214480182
#214480152
#214479652
#214479642
#214478632
#214478622
#214477492
#214477462
C4×#145197222
C4×#145197202
C4×#145197212
#214476162
C4×SD32×C612
#3366161