Finite Group Databasebeta

← #29663571

Subgroups — #29663571

Order 15616.

674 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#21457126C211yesmaximal, characteristic
2#21456746C211yesmaximal, characteristic, complemented
3#21456212C211yesmaximal, characteristic, complemented
4#21454562C211yesmaximal, characteristic, complemented
5#21445379C212yesmaximal, complemented
6#21445365C212yesmaximal, complemented
7#21445255C212yesmaximal, complemented
8#21445241C212yesmaximal, complemented
9#21444572C211yesmaximal, characteristic, complemented
10C2×#16839507C211yesmaximal, characteristic, complemented
11C61×#1540C211yesmaximal, characteristic, complemented
12C2×#14519783—21no—
13#16840312C2211yescharacteristic
14C2×#14519777C2211yescharacteristic
15#16840135—21no—
16#16840121—22no—
17#16840113—21no—
18#16840112C2212yes—
19#16840108C2212yes—
20#16840042—21no—
21#16840039C2212yes—
22#16839996—22no—
23#16839968C2212yes—
24#16839968C2212yes—
25#16839957—21no—
26#16839954C2212yes—
27#16839903—22no—
28#16839839C2212yes—
29#16839832—22no—
30#16839827C2212yes—
31C2×C4⋊#92418C2211yescharacteristic
32#16839763—21no—
33#16839763—21no—
34#16839728—21no—
35C4×#11758194C2211yescharacteristic
36#16839514C2212yes—
37#16839512C2212yes—
38#16839507C2212yes—
39#16839507C2212yes—
40C61×#532C2211yescharacteristic
41C61×#431C2211yescharacteristic
42C2×C4⋊C8×C61C2211yescharacteristic
43C61×#332C2211yescharacteristic
44C61×#332C2211yescharacteristic
45C61×#331C2211yescharacteristic
46C61×#331C2211yescharacteristic
47C2×#11758222—21no—
48C22×Dic122—21no—
49C2×#11758190—22no—
50C2×#11758190—22no—
51C2×#11758199—22no—
52#14519783—44no—
53C2×#11758194D411yescharacteristic
54C2×#11758194D411yescharacteristic
55C2×#11758189—22no—
56C22×#92418—21no—
57C2×C8×D61—22no—
58#14519777—21no—
59#14519777—21no—
60#14519777—21no—
61#14519777D411yescharacteristic
62#14519777C2312yes—
63#14519774D411yescharacteristic
64#14519765—21no—
65#14519751—21no—
66#14519751D412yes—
67C4×D244—21no—
68C4×D244C2312yes—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—21no—
71#14519710—22no—
72C4⋊#92418—21no—
73C4⋊#92418C2312yes—
74#14519702—22no—
75#14519702—22no—
76#14519701—22no—
77#14519701—22no—
78#14519698—22no—
79#14519698—22no—
80#14519698—22no—
81#14519697—22no—
82#14519689—22no—
83#14519689—22no—
84#14519688D412yes—
85C4×#92418C2312yes—
86C2×#41×C61—21no—
87C22×C8×C61—21no—
88C4⋊Q8×C61C2311yescharacteristic
89#127×C61C2311yescharacteristic
90#124×C61—21no—
91#121×C61—21no—
92#121×C61—21no—
93C4×D4×C61—21no—
94C4×D4×C61—21no—
95C2×C42×C61C2311yescharacteristic
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2311yescharacteristic
98C4⋊C8×C61C2311yescharacteristic
99C4⋊C8×C61C2311yescharacteristic
100C4⋊C8×C61C2311yescharacteristic
101C22⋊C8×C61—21no—
102C4×C8×C61—21no—
103#41×C61—42no—
104#41×C61—42no—
105C2×Q8×C61—21no—
106C2×D4×C61—21no—
107C2×D4×C61—21no—
108C2×D4×C61—21no—
109C2×D4×C61—41no—
110C22×C4×C61—41no—
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C2×C22⋊D61—22no—
115C22×Dic61—41no—
116#11758222—42no—
117#11758222—42no—
118C2×D244—21no—
119C2×D244—21no—
120C2×D244C2×D412yes—
121C2×C4×D61—22no—
122C2×Dic122—21no—
123C2×Dic122—22no—
124C2×Dic122—41no—
125C2×Dic122—81no—
126C2×Dic122—81no—
127C2×C8×C61—21no—
128C2×C8×C61—21no—
129C2×C8×C61—21no—
130C2×C8×C61—21no—
131C2×C8×C61—42no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C22⋊C4×C61—41no—
135C22⋊C4×C61—41no—
136C42×C61C2×D411yescharacteristic
137C42×C61C2×D411yescharacteristic
138C42×C61#4111yescharacteristic
139C42×C61C2411yescharacteristic
140#11758199—82no—
141#11758198—22no—
142#11758198—22no—
143C4⋊Dic61—21no—
144C4⋊Dic61—22no—
145C4⋊Dic61—22no—
146C4⋊Dic61—41no—
147C4⋊Dic61—41no—
148C4⋊Dic61C2×D412yes—
149#11758194—22no—
150#11758194—22no—
151C2×#92418—22no—
152C2×#92418—81no—
153C2×#92418C2×D412yes—
154C2×#92418C2×D412yes—
155#11758190—82no—
156#11758190—82no—
157#11758189—44no—
158C8×D61—44no—
159C23×C61—41no—
160C23×C61#12111yescharacteristic
161C22×D61—22no—
162Q8×C61—41no—
163Q8×C61—41no—
164D4×C61—41no—
165D4×C61—41no—
166D4×C61—41no—
167D4×C61—41no—
168D4×C61—81no—
169D4×C61—82no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—82no—
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61#12111yescharacteristic
177C2×C4×C61#12111yescharacteristic
178C2×C4×C61#13512yes—
179C2×C4×C61AGL(1,ℤ/8)12yes—
180C2×C4×C61C22×D411yescharacteristic
181C2×C4×C61C22×D411yescharacteristic
182C2×C4×C61C2×#4111yescharacteristic
183C22⋊D61—44no—
184C2×Dic61—22no—
185C2×Dic61—42no—
186C2×Dic61—82no—
187D244—22no—
188D244—22no—
189D244—42no—
190D244—81no—
191C4×D61—42no—
192C4×D61—42no—
193Dic122—42no—
194Dic122—42no—
195Dic122—42no—
196Dic122—82no—
197C8×C61—41no—
198C8×C61—41no—
199C8×C61—41no—
200C8×C61—41no—
201#92418—22no—
202#92418—22no—
203#92418—42no—
204#19237—611nomaximal, Sylow
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—81no—
208C22×C61—81no—
209C22×C61—81no—
210C22×C61#46312yes—
211C22×C61C2×#12111yescharacteristic
212C2×D61—42no—
213C2×D61—42no—
214C2×D61—42no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—81no—
219C4×C61#46312yes—
220C4×C61C2×#13511yescharacteristic
221C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
222C4×C61#57611yescharacteristic
223C4×C61#57711yescharacteristic
224Dic61—42no—
225Dic61—82no—
226#3245—611no—
227#3206—611no—
228#3141—611no—
229#2935—611no—
230#1701—612no—
231#1699—612no—
232#1681—612no—
233#1679—612no—
234#1565—611no—
235#1540D6111yescharacteristic, complemented
236C2×#332—611no—
237C2×C61—22no—
238C2×C61—161no—
239C2×C61C2×#46311yescharacteristic
240C2×C61#306211yescharacteristic
241C2×C61#306911yescharacteristic
242D61—82no—
243C2×#131—1221no—
244#532—611no—
245#532C2×D6111yescharacteristic
246C2×C4⋊Q8—611no—
247#492—1221no—
248#489—1222no—
249#487—612no—
250#487—1221no—
251#486—612no—
252#474—612no—
253#474—1221no—
254#466—1222no—
255#461—612no—
256#461—612no—
257#459—612no—
258#459—1221no—
259#448—1222no—
260#436—612no—
261#435—1222no—
262C8×D4—612no—
263#431C2×D6111yescharacteristic
264C2×C4⋊C8—611no—
265C2×C4⋊C8C2×D6111yescharacteristic
266#417—1221no—
267#417—1221no—
268#408—1221no—
269C4×M16—611no—
270#335—612no—
271#334—612no—
272#332—612no—
273#332—612no—
274#332C2×D6111yescharacteristic
275#332C2×D6111yescharacteristic
276#331C2×D6111yescharacteristic
277#331C2×D6111yescharacteristic
278C61#1923711yescharacteristic, complemented, Sylow
279C2×#41—21no—
280C2×#41—1221no—
281C22×Q8—1221no—
282C2×SD16—1222no—
283C2×SD16—1222no—
284C2×D8—1222no—
285#131—2444no—
286C2×M16—611no—
287C2×M16—611no—
288C2×M16—1222no—
289C22×C8—21no—
290C22×C8—1222no—
291C22×C8—1221no—
292C4⋊Q8—611no—
293C4⋊Q8—612no—
294C4⋊Q8—1221no—
295C4⋊Q8—1221no—
296C4⋊Q8—1221no—
297C4⋊Q8C22×D6111yescharacteristic
298#127—611no—
299#127C22×D6111yescharacteristic
300#124—21no—
301#124—1221no—
302#121—21no—
303#121—21no—
304#121—612no—
305#121—1221no—
306C4×D4—21no—
307C4×D4—21no—
308C4×D4—612no—
309C4×D4—1221no—
310C2×C4⋊C4—1221no—
311C2×C4⋊C4—1221no—
312C2×C42C22×D6111yescharacteristic
313#107—1222no—
314C4⋊C8—21no—
315C4⋊C8—612no—
316C4⋊C8—1221no—
317C4⋊C8C22×D6111yescharacteristic
318C4⋊C8C22×D6111yescharacteristic
319C4⋊C8C22×D6111yescharacteristic
320C4⋊C8C22×D6111yescharacteristic
321#103—1222no—
322#103—1222no—
323#103—1222no—
324#103—1222no—
325#102—1222no—
326#102—1222no—
327#102—1222no—
328#102—1222no—
329C22⋊C8—21no—
330C22⋊C8—1222no—
331C22⋊C8—1222no—
332#97—612no—
333C4×C8—21no—
334C4×C8—612no—
335#41—42no—
336#41—42no—
337#41—2442no—
338#41—2442no—
339C2×Q8—21no—
340C2×Q8—1221no—
341C2×Q8—1222no—
342C2×Q8—4881no—
343C2×Q8—4881no—
344C2×Q8—2441no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—41no—
349C2×D4—612no—
350C2×D4—1222no—
351C2×D4—1221no—
352C2×D4—1221no—
353C22×C4—41no—
354C22×C4—1222no—
355C22×C4—2441no—
356C22×C4#1175822211yescharacteristic
357C22×C4D4×D6111yescharacteristic
358C22×C4D4×D6111yescharacteristic
359SD16—4882no—
360SD16—4882no—
361D8—4882no—
362M16—1222no—
363M16—1222no—
364M16—2444no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—42no—
370C2×C8—612no—
371C2×C8—612no—
372C2×C8—1222no—
373C2×C8—4881no—
374C2×C8—2444no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—612no—
378C4⋊C4—1221no—
379C4⋊C4—1222no—
380C4⋊C4—1222no—
381C4⋊C4—2441no—
382C4⋊C4—2441no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—1222no—
386C22⋊C4—1222no—
387C42#1175822211yescharacteristic
388C42D4×D6111yescharacteristic
389C42D4×D6111yescharacteristic
390C42C23×D6111yescharacteristic
391C23—41no—
392C23—1222no—
393C23#1451975011yescharacteristic
394Q8—41no—
395Q8—41no—
396Q8—4882no—
397Q8—2442no—
398Q8—2442no—
399Q8—2442no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—41no—
404D4—81no—
405D4—82no—
406D4—1222no—
407D4—1222no—
408D4—4881no—
409D4—2444no—
410D4—2442no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—82no—
416C2×C4—1222no—
417C2×C4—4882no—
418C2×C4—2442no—
419C2×C4—2442no—
420C2×C4—2442no—
421C2×C4#1451975011yescharacteristic
422C2×C4#1451975011yescharacteristic
423C2×C4#1451975011yescharacteristic
424C2×C4#1451979812yes—
425C2×C4#1451980112yes—
426C2×C4C2×D4×D6111yescharacteristic
427C2×C4C2×D4×D6111yescharacteristic
428C2×C4C2×#1175822211yescharacteristic
429C8—41no—
430C8—41no—
431C8—41no—
432C8—41no—
433C8—1222no—
434C8—1222no—
435C8—2442no—
436C22—21no—
437C22—21no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—2442no—
442C22—2442no—
443C22—2442no—
444C22#1683997612yes—
445C22C2×#1451975011yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—81no—
450C4—4882no—
451C4—2442no—
452C4#1683997612yes—
453C4C2×#1451979811yescharacteristic
454C4C2×#1451980111yescharacteristic
455C4#1684056411yescharacteristic
456C4#1684056911yescharacteristic
457C2—22no—
458C2—161no—
459C2—4882no—
460C2C2×#1683997611yescharacteristic
461C2#2145550211yescharacteristic
462C2#2145555911yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1540C2
socleC22×C61C2×#121
prime radical#21457126C2
hypercenter#1540D61
hypocenterC61#19237
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
2. #21456746C2semidirect
3. #21456212C2semidirect
4. #21454562C2semidirect
5. #21445379C2semidirect
6. #21445365C2semidirect
7. #21445255C2semidirect
8. #21445241C2semidirect
9. #21444572C2semidirect
10. C2×#16839507C2semidirect
11. C61×#1540C2semidirect
235. #1540D61semidirect
278. C61#19237semidirect

Maximal subgroups

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

subgroupindex
#214571262
#214567462
#214562122
#214545622
#214453792
#214453652
#214452552
#214452412
#214445722
C2×#168395072
C61×#15402
#1923761