Finite Group Databasebeta

← #29837678

Subgroups — #29837678

Order 15616.

498 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458828C211yesmaximal, characteristic, complemented
2#21458686C211yesmaximal, characteristic, complemented
3#21448052C211yesmaximal, characteristic, complemented
4#21448050C211yesmaximal, characteristic, complemented
5#21448041C211yesmaximal, characteristic, complemented
6#21447978C211yesmaximal, characteristic, complemented
7#21447977C211yesmaximal, characteristic, complemented
8#21447969C211yesmaximal, characteristic, complemented
9#21447876C211yesmaximal, characteristic, complemented
10#21447852C211yesmaximal, characteristic
11#21447721C211yesmaximal, characteristic, complemented
12SD32×Dic61C211yesmaximal, characteristic, complemented
13D16×Dic61C211yesmaximal, characteristic, complemented
14C4×#14519718C211yesmaximal, characteristic, complemented
15C61×#2210C211yesmaximal, characteristic, complemented
16#16840494—21no—
17#16840471—21no—
18C2×#14519718C2211yescharacteristic
19#16840166C2211yescharacteristic
20#16840164C2211yescharacteristic
21#16840163C2211yescharacteristic
22#16840147C2211yescharacteristic
23#16840137C2211yescharacteristic
24#16840064—21no—
25#16840062—21no—
26#16840050—21no—
27#16839979—21no—
28#16839974—21no—
29#16839960—21no—
30C8×Dic122C2211yescharacteristic
31Q16×Dic61C2211yescharacteristic
32C4×D488C2211yescharacteristic
33D8×Dic61C2211yescharacteristic
34D8×Dic61C2211yescharacteristic
35D8×Dic61C2211yescharacteristic
36#16839590C2211yescharacteristic
37#16839588C2211yescharacteristic
38#16839587C2211yescharacteristic
39#16839580C2211yescharacteristic
40#16839580C2211yescharacteristic
41#16839566C2211yescharacteristic
42#16839566C2211yescharacteristic
43#16839564C2211yescharacteristic
44#16839564C2211yescharacteristic
45#16839563C2211yescharacteristic
46#16839563C2211yescharacteristic
47#16839563C2211yescharacteristic
48#16839562C2211yescharacteristic
49C4×#11758185C2211yescharacteristic
50C16×Dic61C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C2×SD32×C61C2211yescharacteristic
53C2×D16×C61C2211yescharacteristic
54C61×#495C2211yescharacteristic
55C4×D8×C61C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×#11758201—21no—
60C2×D488C2311yescharacteristic
61C2×#11758199—21no—
62#14519776—21no—
63#14519773—21no—
64#14519769—21no—
65#14519768—21no—
66#14519766—21no—
67#14519763—41no—
68#14519761—41no—
69#14519759—41no—
70#14519756—41no—
71#14519754—41no—
72#14519754—41no—
73Q8×Dic61—21no—
74C4×Dic122D411yescharacteristic
75C4×D244—21no—
76D4×Dic61—21no—
77D4×Dic61—21no—
78D4×Dic61—21no—
79#14519737—41no—
80C2×#11758196—41no—
81#14519718—22no—
82C2×#11758185C2311yescharacteristic
83C2×#11758185C2311yescharacteristic
84#14519711C2311yescharacteristic
85#14519711C2311yescharacteristic
86#14519711C2311yescharacteristic
87#14519710—21no—
88#14519709—21no—
89#14519708—21no—
90C4⋊#92418D411yescharacteristic
91#14519706D411yescharacteristic
92#14519706D411yescharacteristic
93#14519701—21no—
94#14519699—21no—
95#14519698—21no—
96#14519698—21no—
97#14519698—21no—
98C8×Dic61C2311yescharacteristic
99C8×Dic61C2311yescharacteristic
100C2×Q16×C61C2311yescharacteristic
101C2×SD16×C61—21no—
102C2×D8×C61C2311yescharacteristic
103C2×D8×C61C2311yescharacteristic
104#124×C61—21no—
105C4×D4×C61—21no—
106SD32×C61—22no—
107D16×C61—22no—
108C2×C16×C61C2311yescharacteristic
109C2×C16×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#102×C61—21no—
112C4×C8×C61C2311yescharacteristic
113C2×Q8×C61—21no—
114C2×D4×C61—21no—
115C2×D4×C61—21no—
116C22×C4×C61—41no—
117C2×C22⋊D61—41no—
118C2×C22⋊D61—41no—
119C22×Dic61—41no—
120C22×Dic61—41no—
121C22×Dic61—41no—
122C2×D244—21no—
123C2×C4×D61—41no—
124C2×Dic122—41no—
125C2×Dic122D811yescharacteristic
126Q16×C61—21no—
127Q16×C61—21no—
128SD16×C61—81no—
129D8×C61—21no—
130D8×C61—21no—
131D8×C61—21no—
132D8×C61#4112yes—
133C2×C8×C61C2×D411yescharacteristic
134C2×C8×C61C2411yescharacteristic
135C4⋊C4×C61—21no—
136C22⋊C4×C61—41no—
137C22⋊C4×C61—41no—
138C22⋊C4×C61—41no—
139C42×C61C2×D411yescharacteristic
140C22⋊Dic61—41no—
141C22⋊Dic61—41no—
142C22⋊Dic61—41no—
143#11758201—81no—
144#11758199—81no—
145#11758198—41no—
146#11758198—41no—
147#11758198—41no—
148C4⋊Dic61—21no—
149C4⋊Dic61—21no—
150C4⋊Dic61—21no—
151C4⋊Dic61—41no—
152C4⋊Dic61—41no—
153C4⋊Dic61D811yescharacteristic
154#11758196—41no—
155#11758196—41no—
156#11758196—41no—
157#11758196—41no—
158#11758196D811yescharacteristic
159#11758196D811yescharacteristic
160C4×Dic61—41no—
161C4×Dic61C2×D411yescharacteristic
162C4×Dic61C2×D411yescharacteristic
163C2×#92418C2×D411yescharacteristic
164C2×#92418C2×D411yescharacteristic
165D488—21no—
166D488—21no—
167C16×C61—21no—
168C16×C61—21no—
169#11758185—21no—
170#11758185—21no—
171C23×C61—41no—
172C23×C61—41no—
173C22×D61—41no—
174Q8×C61—41no—
175Q8×C61—41no—
176D4×C61—22no—
177D4×C61—41no—
178D4×C61—41no—
179D4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—161no—
183C2×C4×C61C2×D811yescharacteristic
184C2×C4×C61C2×D811yescharacteristic
185C2×C4×C61C22×D411yescharacteristic
186C22⋊D61—82no—
187C22⋊D61—161no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—82no—
192C2×Dic61—161no—
193C2×Dic61—161no—
194C2×Dic61C2×D811yescharacteristic
195C2×Dic61C2×D811yescharacteristic
196C2×Dic61C2×D811yescharacteristic
197C2×Dic61C2×D811yescharacteristic
198D244—41no—
199D244—41no—
200C4×D61—161no—
201Dic122—22no—
202Dic122—161no—
203C8×C61—21no—
204C8×C61C2×#4111yescharacteristic
205C8×C612−1+411yescharacteristic
206#92418—21no—
207#92418—21no—
208#33928—611nomaximal, Sylow
209C22×C61—42no—
210C22×C61—81no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61C22×D811yescharacteristic
216C2×D61—81no—
217C2×D61—81no—
218C2×D61—81no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—81no—
222C4×C61—81no—
223C4×C61#54811yescharacteristic
224C4×C61#57711yescharacteristic
225Dic61—21no—
226Dic61—21no—
227Dic61—21no—
228Dic61—81no—
229Dic61—81no—
230Dic61—81no—
231Dic61#50812yes—
232#3396—611no—
233#3380—611no—
234#2242—611no—
235#2242—611no—
236#2240—611no—
237#2228—611no—
238#2228—611no—
239#2227—611no—
240#2210—611no—
241#2210D6111yescharacteristic, complemented
242#2206—611no—
243Q8×C16—611no—
244C4×SD32—611no—
245C4×D16—611no—
246C4×D16—611no—
247C2×C61—82no—
248C2×C61—161no—
249C2×C61#335811yescharacteristic
250C2×C61C2×#50811yescharacteristic
251C2×C61#341511yescharacteristic
252D61—161no—
253#559—1221no—
254#554—1221no—
255C2×SD32C2×D6111yescharacteristic
256C2×D16—611no—
257C2×D16C2×D6111yescharacteristic
258#500—611no—
259#499—611no—
260#499—611no—
261#495—611no—
262#495C2×D6111yescharacteristic
263#493—611no—
264#478—1221no—
265#478—1221no—
266#476—1221no—
267#463—1221no—
268#463—1221no—
269#460—1221no—
270C8×Q8—611no—
271C4×Q16—611no—
272C4×D8—611no—
273C4×D8—611no—
274C4×D8—611no—
275C4×D8—611no—
276C4×D8C2×D6111yescharacteristic
277#367—611no—
278#366—611no—
279#366—611no—
280C4⋊C16—611no—
281C4⋊C16—611no—
282C4⋊C16C2×D6111yescharacteristic
283#358—611no—
284#358—611no—
285#358C2×D6111yescharacteristic
286#357—611no—
287#357—611no—
288#357—611no—
289#357—611no—
290#357—611no—
291#357—611no—
292#357C2×D6111yescharacteristic
293C4×C16—611no—
294C4×C16—611no—
295C4×C16—611no—
296C61#3392811yescharacteristic, complemented, Sylow
297C2×Q16C22×D6111yescharacteristic
298C2×SD16—21no—
299C2×SD16—1221no—
300C2×D8—611no—
301C2×D8—1221no—
302C2×D8C22×D6111yescharacteristic
303C2×D8C22×D6111yescharacteristic
304C4⋊Q8—1221no—
305#127—1221no—
306#125—1221no—
307#125—1221no—
308#124—21no—
309#124—1221no—
310#124—2441no—
311#123—2441no—
312#123—2441no—
313C22⋊Q8—2441no—
314C22⋊Q8—2441no—
315C22⋊Q8—2441no—
316C4×Q8—611no—
317C4×Q8—1221no—
318C4×D4—21no—
319C4×D4—1221no—
320C4×D4—1221no—
321C4×D4—1221no—
322C4×D4—1221no—
323C4×D4—2441no—
324C2×C4⋊C4—2441no—
325SD32—22no—
326D16—22no—
327D16—1222no—
328C2×C16—611no—
329C2×C16—611no—
330C2×C16C22×D6111yescharacteristic
331C2×C16C22×D6111yescharacteristic
332#107—611no—
333#107—611no—
334#107—611no—
335#107—1221no—
336#107C22×D6111yescharacteristic
337#106—1221no—
338#106—1221no—
339C4⋊C8—611no—
340C4⋊C8—611no—
341C4⋊C8—611no—
342#103—1221no—
343#102—21no—
344#102—1221no—
345#102—1221no—
346#102—1221no—
347#102—1221no—
348C4×C8—611no—
349C4×C8—611no—
350C4×C8C22×D6111yescharacteristic
351C2×Q8—21no—
352C2×Q8—611no—
353C2×Q8—2441no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—1221no—
357C2×D4—2441no—
358C2×D4—2441no—
359C22×C4—41no—
360C22×C4—2441no—
361C22×C4—2441no—
362C22×C4—2441no—
363C22×C4—2441no—
364Q16—21no—
365Q16—21no—
366SD16—81no—
367SD16—4881no—
368D8—21no—
369D8—21no—
370D8—21no—
371D8—1221no—
372D8—1221no—
373D8—4881no—
374D8#1175822412yes—
375C2×C8—611no—
376C2×C8—611no—
377C2×C8D4×D6111yescharacteristic
378C2×C8C23×D6111yescharacteristic
379C4⋊C4—21no—
380C4⋊C4—611no—
381C4⋊C4—611no—
382C4⋊C4—611no—
383C4⋊C4—1221no—
384C4⋊C4—1221no—
385C4⋊C4—1221no—
386C4⋊C4—2441no—
387C4⋊C4—2441no—
388C4⋊C4—2441no—
389C4⋊C4—2441no—
390C4⋊C4—2441no—
391C4⋊C4—2441no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—2441no—
396C22⋊C4—2441no—
397C22⋊C4—2441no—
398C22⋊C4—2441no—
399C22⋊C4—2441no—
400C22⋊C4—2441no—
401C42—611no—
402C42—611no—
403C42—2441no—
404C42D4×D6111yescharacteristic
405C16—21no—
406C16—21no—
407C16—1221no—
408C16—1221no—
409C23—41no—
410C23—41no—
411C23—2441no—
412Q8—41no—
413Q8—41no—
414Q8—1222no—
415Q8—9761no—
416D4—22no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—9761no—
421D4—4882no—
422D4—2441no—
423D4—2441no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—161no—
427C2×C4—611no—
428C2×C4—611no—
429C2×C4—611no—
430C2×C4—611no—
431C2×C4—9761no—
432C2×C4—9761no—
433C2×C4—9761no—
434C2×C4—4882no—
435C2×C4—2441no—
436C2×C4—2441no—
437C2×C4—2441no—
438C2×C4D8×D6111yescharacteristic
439C2×C4D8×D6111yescharacteristic
440C2×C4C2×D4×D6111yescharacteristic
441C8—21no—
442C8—1221no—
443C8—1221no—
444C8C2×#1175822411yescharacteristic
445C8#1451982411yescharacteristic
446C22—42no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—4881no—
453C22—4881no—
454C22—4881no—
455C22C2×D8×D6111yescharacteristic
456C4—21no—
457C4—21no—
458C4—81no—
459C4—81no—
460C4—612no—
461C4—1221no—
462C4—1221no—
463C4—1221no—
464C4—4881no—
465C4—4881no—
466C4—4881no—
467C4#1684041811yescharacteristic
468C4#1684057211yescharacteristic
469C2—82no—
470C2—161no—
471C2—9761no—
472C2#2145844911yescharacteristic
473C2#508×D6111yescharacteristic
474C2#2145895911yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2210C2
socleC22×C61C22×D8
prime radical#21447852C2
hypercenter#2210D61
hypocenterC61#33928
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2210

Complements

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

NH ≅ G/Ntype
1. #21458828C2semidirect
2. #21458686C2semidirect
3. #21448052C2semidirect
4. #21448050C2semidirect
5. #21448041C2semidirect
6. #21447978C2semidirect
7. #21447977C2semidirect
8. #21447969C2semidirect
9. #21447876C2semidirect
11. #21447721C2semidirect
12. SD32×Dic61C2semidirect
13. D16×Dic61C2semidirect
14. C4×#14519718C2semidirect
15. C61×#2210C2semidirect
241. #2210D61semidirect
296. C61#33928semidirect

Maximal subgroups

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

subgroupindex
#214588282
#214586862
#214480522
#214480502
#214480412
#214479782
#214479772
#214479692
#214478762
#214478522
#214477212
SD32×Dic612
D16×Dic612
C4×#145197182
C61×#22102
#3392861