Finite Group Databasebeta

← #29834656

Subgroups — #29834656

Order 15616.

546 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456332C211yesmaximal, characteristic, complemented
2C4×#14519796C211yesmaximal, characteristic
3#21447984C211yesmaximal, characteristic, complemented
4#21447980C211yesmaximal, characteristic, complemented
5#21447976C211yesmaximal, characteristic, complemented
6#21447970C211yesmaximal, characteristic, complemented
7#21447964C211yesmaximal, characteristic, complemented
8#21447960C211yesmaximal, characteristic, complemented
9#21447954C211yesmaximal, characteristic, complemented
10#21447602C211yesmaximal, characteristic, complemented
11#21447600C211yesmaximal, characteristic, complemented
12C4⋊C16×D61C211yesmaximal, characteristic, complemented
13#21447523C211yesmaximal, characteristic
14#21447523C211yesmaximal, characteristic
15C61×#2228C211yesmaximal, characteristic, complemented
16C2×#14519796C2211yescharacteristic
17#16840318—21no—
18C4×#11758224—21no—
19C2×C16×D61C2211yescharacteristic
20C2×C16×D61C2211yescharacteristic
21#16840166C2211yescharacteristic
22#16840166C2211yescharacteristic
23#16840164C2211yescharacteristic
24#16840161—21no—
25#16840159—21no—
26C4×Dic244C2211yescharacteristic
27#16839856C2211yescharacteristic
28#16839853—21no—
29C4×#11758200—21no—
30D8×Dic61C2211yescharacteristic
31#16839799C2211yescharacteristic
32#16839799C2211yescharacteristic
33#16839799C2211yescharacteristic
34#16839797—21no—
35#16839755—21no—
36C4×C8×D61C2211yescharacteristic
37#16839590C2211yescharacteristic
38#16839589C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839588C2211yescharacteristic
41#16839587C2211yescharacteristic
42#16839587C2211yescharacteristic
43C4⋊#11758185C2211yescharacteristic
44#16839580C2211yescharacteristic
45#16839580C2211yescharacteristic
46#16839567C2211yescharacteristic
47#16839567C2211yescharacteristic
48#16839565C2211yescharacteristic
49#16839565C2211yescharacteristic
50#16839563C2211yescharacteristic
51#16839563C2211yescharacteristic
52C61×#499C2211yescharacteristic
53C4×D8×C61C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×#11758224—21no—
60#14519796—22no—
61#14519796Q814yescomplemented
62C2×Dic244C2311yescharacteristic
63C2×#11758200—21no—
64C2×C8×D61D411yescharacteristic
65C2×C8×D61C2311yescharacteristic
66#14519776—21no—
67#14519776—21no—
68#14519769—21no—
69#14519755—41no—
70#14519755—41no—
71C4×Dic122—21no—
72#14519742—21no—
73#14519742—41no—
74#14519742—41no—
75D4×Dic61—21no—
76C4×C22⋊D61—41no—
77#14519737—41no—
78#14519735—21no—
79#14519735—21no—
80#14519735—21no—
81#14519733—41no—
82C2×C4×Dic61—41no—
83C42×D61D411yescharacteristic
84C2×#11758185C2311yescharacteristic
85C2×#11758185C2311yescharacteristic
86C16×D61—22no—
87C16×D61—22no—
88#14519711C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519711C2311yescharacteristic
91#14519710—21no—
92#14519710—21no—
93#14519709—21no—
94#14519708—21no—
95#14519708—21no—
96#14519708—21no—
97#14519702—21no—
98#14519700—21no—
99#14519698—21no—
100C4×#92418D411yescharacteristic
101C8×Dic61D411yescharacteristic
102C8×Dic61C2311yescharacteristic
103C2×D8×C61C2311yescharacteristic
104#125×C61—21no—
105C4×D4×C61—21no—
106C2×C16×C61C2311yescharacteristic
107C2×C16×C61C2311yescharacteristic
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#106×C61—21no—
112#102×C61—21no—
113C4×C8×C61C2311yescharacteristic
114C2×D4×C61—21no—
115C22×C4×C61—41no—
116C2×C22⋊D61—41no—
117C22×Dic61—41no—
118C22×Dic61—41no—
119#11758224—24no—
120#11758224—42no—
121C2×C4×D61D811yescharacteristic
122C2×C4×D61D811yescharacteristic
123C2×C4×D61C2×D411yescharacteristic
124C2×Dic122—21no—
125C2×Dic122—41no—
126C2×Dic122—41no—
127D8×C61—21no—
128D8×C61C2×Q812yes—
129C2×C8×C61C2×D411yescharacteristic
130C2×C8×C61C2411yescharacteristic
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—41no—
135C4⋊C4×C61—41no—
136C22⋊C4×C61—41no—
137C42×C61C2×D411yescharacteristic
138C22⋊Dic61—41no—
139#11758200—24no—
140#11758198—41no—
141#11758198—41no—
142#11758198—41no—
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145C4⋊Dic61—21no—
146#11758196—41no—
147#11758196—41no—
148#11758196—41no—
149#11758196—41no—
150#11758196—41no—
151#11758196—41no—
152C4×Dic61—41no—
153C4×Dic61—41no—
154C4×Dic61—41no—
155C4×Dic61—41no—
156C4×Dic61—41no—
157C4×Dic61D811yescharacteristic
158C4×Dic61D811yescharacteristic
159C4×Dic61C2×D411yescharacteristic
160C2×#92418C2×D411yescharacteristic
161C2×#92418C2×D411yescharacteristic
162Dic244—21no—
163Dic244C2×Q812yes—
164C8×D61—22no—
165C8×D61C2×Q812yes—
166C8×D61#4112yes—
167C16×C61—21no—
168C16×C61—21no—
169#11758185—21no—
170#11758185—21no—
171C23×C61—41no—
172C22×D61C2×D811yescharacteristic
173D4×C61—22no—
174D4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—82no—
179C2×C4×C61C2×D811yescharacteristic
180C2×C4×C61C2×D811yescharacteristic
181C2×C4×C61C22×D411yescharacteristic
182C22⋊D61—44no—
183C2×Dic61—41no—
184C2×Dic61—44no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—82no—
189C2×Dic61C2×D811yescharacteristic
190C2×Dic61C2×D811yescharacteristic
191C2×Dic61C2×D811yescharacteristic
192C4×D61—22no—
193C4×D61—41no—
194C4×D61C22⋊Q812yes—
195C4×D61#13712yes—
196Dic122—22no—
197Dic122—41no—
198Dic122—82no—
199Dic122—82no—
200C8×C61—21no—
201C8×C61C22×Q811yescharacteristic
202C8×C61C2×#4111yescharacteristic
203#92418—21no—
204#92418C22⋊Q812yes—
205#33626—611nomaximal, Sylow
206C22×C61—42no—
207C22×C61—81no—
208C22×C61—81no—
209C22×C61C22×D811yescharacteristic
210C2×D61—21no—
211C2×D61—21no—
212C2×D61#47412yes—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—81no—
216C4×C61—81no—
217C4×C61—81no—
218C4×C61C2×C22⋊Q811yescharacteristic
219C4×C61C2×#13711yescharacteristic
220Dic61—21no—
221Dic61—42no—
222Dic61—81no—
223Dic61—81no—
224Dic61—81no—
225Dic61#47412yes—
226Dic61#50812yes—
227#3160—611no—
228C4×#135—611no—
229#2229—611no—
230#2229—611no—
231#2228—611no—
232#2228D6111yescharacteristic, complemented
233#2227—611no—
234#2226—611no—
235#2225—611no—
236#2224—611no—
237#2158—611no—
238#2158—611no—
239C2×C4⋊C16—611no—
240#2138—611no—
241#2138—611no—
242C2×C61—82no—
243C2×C61C2×#47411yescharacteristic
244C2×C61C2×#50811yescharacteristic
245C2×C61#341411yescharacteristic
246D61—22no—
247C2×#135—611no—
248#533—1221no—
249C4×#41—1221no—
250C22×C16—611no—
251C22×C16—611no—
252#500—611no—
253#500—611no—
254#499—611no—
255#499—1221no—
256#499C2×D6111yescharacteristic
257#498—1221no—
258C4×Q16—611no—
259C4×Q16—611no—
260C4×SD16—1221no—
261C4×SD16—1221no—
262C4×D8—611no—
263C4×D8C2×D6111yescharacteristic
264#427—611no—
265#427—611no—
266#427—611no—
267#427—1221no—
268#416—1221no—
269C2×C4×C8—611no—
270#367—611no—
271#367—611no—
272#367—611no—
273#367C2×D6111yescharacteristic
274#366—611no—
275#366—611no—
276#366—611no—
277#366C2×D6111yescharacteristic
278C4⋊C16—611no—
279C4⋊C16—611no—
280C4⋊C16—611no—
281C4⋊C16C2×D6111yescharacteristic
282#358—611no—
283#358—611no—
284#358—611no—
285#358—611no—
286#357—611no—
287#357—611no—
288#357C2×D6111yescharacteristic
289#357C2×D6111yescharacteristic
290C61#3362611yescharacteristic, complemented, Sylow
291C2×#41—1221no—
292#135—614no—
293#135—1222no—
294C2×Q16—611no—
295C2×SD16—1221no—
296C2×D8C22×D6111yescharacteristic
297C22×C8—611no—
298C22×C8—611no—
299C4⋊Q8—1221no—
300C4⋊Q8—1221no—
301#125—21no—
302#125—1221no—
303C22⋊Q8—2441no—
304C22⋊Q8—2441no—
305C4×Q8—1221no—
306C4×Q8—1221no—
307C4×Q8—2441no—
308C4×Q8—2441no—
309C4×D4—21no—
310C4×D4—1221no—
311C4×D4—2441no—
312C4×D4—2441no—
313#117—1221no—
314#117—1221no—
315#117—1221no—
316#117—2441no—
317C2×C42—611no—
318C2×C42—2441no—
319C2×C16—611no—
320C2×C16—611no—
321C2×C16—1222no—
322C2×C16—1222no—
323C2×C16C22×D6111yescharacteristic
324C2×C16C22×D6111yescharacteristic
325#107—611no—
326#107—611no—
327#107—611no—
328#107—1221no—
329#107—1221no—
330#107C22×D6111yescharacteristic
331#107C22×D6111yescharacteristic
332#107C22×D6111yescharacteristic
333#106—21no—
334#106—1221no—
335#106—1221no—
336#106—1221no—
337#106—1221no—
338#103—1221no—
339#103—1221no—
340#102—21no—
341#102—1221no—
342C4×C8—611no—
343C4×C8—611no—
344C4×C8—611no—
345C4×C8C22×D6111yescharacteristic
346#41—1224no—
347#41—2442no—
348C2×Q8—1221no—
349C2×Q8—2441no—
350C2×Q8—2441no—
351C2×D4—21no—
352C2×D4—2441no—
353C22×C4—41no—
354C22×C4—611no—
355C22×C4—611no—
356C22×C4—611no—
357C22×C4—2441no—
358C22×C4—2441no—
359Q16—612no—
360Q16—1221no—
361SD16—1224no—
362D8—21no—
363D8Q8×D6112yes—
364C2×C8—611no—
365C2×C8—612no—
366C2×C8—612no—
367C2×C8—611no—
368C2×C8—1222no—
369C2×C8D4×D6111yescharacteristic
370C2×C8C23×D6111yescharacteristic
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—1221no—
377C4⋊C4—1221no—
378C4⋊C4—1221no—
379C4⋊C4—2441no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C4⋊C4—2441no—
383C4⋊C4—2441no—
384C4⋊C4—2441no—
385C22⋊C4—41no—
386C22⋊C4—2441no—
387C22⋊C4—2441no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C42—611no—
391C42—611no—
392C42—611no—
393C42—2441no—
394C42—2441no—
395C42—2441no—
396C42—2441no—
397C42—2441no—
398C42D4×D6111yescharacteristic
399C16—21no—
400C16—21no—
401C16—1221no—
402C16—1221no—
403C23—41no—
404C23—611no—
405Q8—1222no—
406Q8—4882no—
407Q8—4882no—
408Q8—2441no—
409D4—22no—
410D4—41no—
411D4—2444no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—82no—
416C2×C4—611no—
417C2×C4—611no—
418C2×C4—612no—
419C2×C4—612no—
420C2×C4—611no—
421C2×C4—1222no—
422C2×C4—4882no—
423C2×C4—2441no—
424C2×C4—2444no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4—2441no—
428C2×C4—2441no—
429C2×C4D8×D6111yescharacteristic
430C2×C4D8×D6111yescharacteristic
431C2×C4C2×D4×D6111yescharacteristic
432C8—21no—
433C8—612no—
434C8—1221no—
435C8C2×Q8×D6111yescharacteristic
436C8#41×D6111yescharacteristic
437C22—42no—
438C22—81no—
439C22—81no—
440C22—612no—
441C22—1221no—
442C22—1221no—
443C22C2×D8×D6111yescharacteristic
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—612no—
450C4—612no—
451C4—1221no—
452C4—4881no—
453C4—4881no—
454C4—4881no—
455C4—2442no—
456C4C22⋊Q8×D6111yescharacteristic
457C4#137×D6111yescharacteristic
458C2—82no—
459C2—1222no—
460C2#474×D6111yescharacteristic
461C2#508×D6111yescharacteristic
462C2#2145895111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2228C2
socleC22×C61C22×D8
prime radicalC2×#14519796C22
hypercenter#2228D61
hypocenterC61#33626
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #21456332C2semidirect
3. #21447984C2semidirect
4. #21447980C2semidirect
5. #21447976C2semidirect
6. #21447970C2semidirect
7. #21447964C2semidirect
8. #21447960C2semidirect
9. #21447954C2semidirect
10. #21447602C2semidirect
11. #21447600C2semidirect
12. C4⋊C16×D61C2semidirect
15. C61×#2228C2semidirect
61. #14519796Q8semidirect
232. #2228D61semidirect
290. C61#33626semidirect

Maximal subgroups

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

subgroupindex
#214563322
C4×#145197962
#214479842
#214479802
#214479762
#214479702
#214479642
#214479602
#214479542
#214476022
#214476002
C4⋊C16×D612
#214475232
C61×#22282
#3362661