Finite Group Databasebeta

← #29663541

Subgroups — #29663541

Order 15616.

704 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457135C211yesmaximal, characteristic, complemented
2#21456734C211yesmaximal, characteristic
3#21456194C211yesmaximal, characteristic, complemented
4#21445380C212yesmaximal, complemented
5#21445352C212yesmaximal, complemented
6#21445256C212yesmaximal, complemented
7#21445228C212yesmaximal, complemented
8#21444571C211yesmaximal, characteristic, complemented
9#21444477C211yesmaximal, characteristic, complemented
10C2×#16839505C211yesmaximal, characteristic, complemented
11C61×#2935C211yesmaximal, characteristic, complemented
12#16840319C2211yescharacteristic
13C2×#14519774C2211yescharacteristic
14#16840138—21no—
15#16840127—22no—
16#16840110—21no—
17#16840109C2212yes—
18#16840109C2212yes—
19#16840052C2212yescomplemented
20#16840044—21no—
21#16839989—22no—
22#16839967C2212yescomplemented
23#16839959—21no—
24#16839957C2212yes—
25#16839957C2212yes—
26#16839895—22no—
27#16839815C2211yescharacteristic
28C2×C4⋊#92418C2211yescharacteristic
29#16839768—21no—
30#16839768—21no—
31#16839515C2212yescomplemented
32#16839513C2212yescomplemented
33#16839510C2211yescharacteristic, complemented
34#16839510C2211yescharacteristic, complemented
35#16839507C2211yescharacteristic, complemented
36#16839507C2211yescharacteristic, complemented
37#16839505C2212yes—
38#16839505C2212yes—
39C2×#131×C61—21no—
40C61×#532C2211yescharacteristic
41C61×#436C2212yescomplemented
42C61×#435—22no—
43C8×D4×C61C2212yescomplemented
44C2×C4⋊C8×C61C2211yescharacteristic
45C61×#408—21no—
46C4×M16×C61C2211yescharacteristic
47C22×D244—21no—
48C22×D244—21no—
49C22×D244—21no—
50C2×#11758200—22no—
51C2×#11758199—22no—
52C2×#11758199—22no—
53C22×#92418—21no—
54#14519777C2311yescharacteristic
55#14519777C2311yescharacteristic
56#14519774—21no—
57#14519774—21no—
58#14519774—21no—
59#14519774C2312yes—
60#14519769—21no—
61#14519756—21no—
62#14519756—21no—
63C4×Dic122—21no—
64C4×Dic122—21no—
65#14519736—21no—
66#14519708—22no—
67C4⋊#92418—21no—
68C4⋊#92418C2311yescharacteristic
69C4⋊#92418C2311yescharacteristic
70C4⋊#92418C2312yes—
71#14519700—22no—
72#14519699—22no—
73#14519699—22no—
74#14519699—22no—
75#14519699—22no—
76#14519698—22no—
77#14519697—22no—
78#14519697—22no—
79C22⋊#92418—21no—
80C4×#92418—21no—
81C2×#41×C61—21no—
82#131×C61—44no—
83C2×M16×C61—22no—
84C2×M16×C61D411yescharacteristic
85C2×M16×C61D411yescharacteristic
86C22×C8×C61—21no—
87C22×C8×C61—22no—
88C4⋊Q8×C61D411yescharacteristic
89#127×C61D411yescharacteristic
90#124×C61—21no—
91#121×C61—21no—
92#121×C61D412yes—
93C4×D4×C61—21no—
94C4×D4×C61C2312yes—
95C2×C42×C61C2311yescharacteristic
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2311yescharacteristic
98C4⋊C8×C61C2311yescharacteristic
99C22⋊C8×C61—22no—
100C22⋊C8×C61—22no—
101#97×C61D412yes—
102C4×C8×C61C2312yes—
103C23×D61—41no—
104#41×C61—42no—
105#41×C61—42no—
106C2×Q8×C61—21no—
107C2×D4×C61—22no—
108C2×D4×C61—21no—
109C2×D4×C61—21no—
110C2×D4×C61C2×D412yes—
111C22×C4×C61—22no—
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61#4111yescharacteristic
115C2×D244—22no—
116C2×D244—22no—
117C2×D244—22no—
118C2×D244—42no—
119C2×D244—42no—
120C2×D244—41no—
121C2×D244—41no—
122C2×D244—41no—
123C2×D244—81no—
124C2×D244—81no—
125C2×D244—82no—
126C2×Dic122—21no—
127C2×Dic122—21no—
128M16×C61—22no—
129M16×C61—22no—
130M16×C61—44no—
131C2×C8×C61—21no—
132C2×C8×C61—21no—
133C2×C8×C61—44no—
134C2×C8×C61—42no—
135C2×C8×C61C2×D412yes—
136C2×C8×C61C2×D412yes—
137C4⋊C4×C61—21no—
138C4⋊C4×C61C2×D412yes—
139C22⋊C4×C61—22no—
140C22⋊C4×C61—22no—
141C42×C61C2×D411yescharacteristic
142C42×C61C2×D411yescharacteristic
143C42×C61#4111yescharacteristic
144C42×C61C2411yescharacteristic
145C22⋊Dic61—41no—
146#11758200—82no—
147#11758199—82no—
148#11758199—82no—
149C4⋊Dic61—21no—
150C4⋊Dic61—21no—
151C4⋊Dic61—21no—
152C4⋊Dic61—21no—
153#11758196—41no—
154#11758196—41no—
155C4×Dic61—41no—
156C2×#92418—21no—
157C2×#92418—21no—
158C2×#92418—22no—
159C2×#92418—81no—
160C23×C61—22no—
161C23×C61#12111yescharacteristic
162C22×D61—42no—
163C22×D61—82no—
164C22×D61—82no—
165C22×D61—82no—
166Q8×C61—42no—
167D4×C61—22no—
168D4×C61—22no—
169D4×C61—44no—
170D4×C61—42no—
171D4×C61—81no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—22no—
175C2×C4×C61—41no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61#12111yescharacteristic
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#12111yescharacteristic
181C2×C4×C61#13512yes—
182C2×C4×C61AGL(1,ℤ/8)12yes—
183C2×C4×C61C22×D411yescharacteristic
184C2×C4×C61C22×D411yescharacteristic
185C2×C4×C61C2×#4111yescharacteristic
186C2×Dic61—41no—
187C2×Dic61—41no—
188D244—42no—
189D244—42no—
190D244—42no—
191D244—42no—
192D244—82no—
193D244—82no—
194D244—82no—
195D244—82no—
196Dic122—41no—
197Dic122—41no—
198Dic122—81no—
199C8×C61—22no—
200C8×C61—22no—
201C8×C61—41no—
202C8×C61—41no—
203#92418—42no—
204#92418—41no—
205#92418—41no—
206#19234—611nomaximal, Sylow
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—42no—
210C22×C61—42no—
211C22×C61—42no—
212C22×C61#46312yes—
213C22×C61C2×#12111yescharacteristic
214C2×D61—82no—
215C2×D61—82no—
216C2×D61—82no—
217C2×D61—164no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—42no—
222C4×C61#46312yes—
223C4×C61C2×#13511yescharacteristic
224C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
225C4×C61#57611yescharacteristic
226C4×C61#57711yescharacteristic
227Dic61—81no—
228Dic61—81no—
229#3246—611no—
230#3205—611no—
231#3138—611no—
232#2935D6111yescharacteristic, complemented
233#1701—612no—
234#1697—612no—
235#1681—612no—
236#1677—612no—
237#1565—611no—
238#1542—611no—
239C2×#331—611no—
240C2×C61—22no—
241C2×C61—82no—
242C2×C61C2×#46311yescharacteristic
243C2×C61#306211yescharacteristic
244C2×C61#306811yescharacteristic
245D61—162no—
246C2×#131—21no—
247#533—611no—
248#532C2×D6111yescharacteristic
249C2×#127—611no—
250#493—1221no—
251#490—1222no—
252#486—612no—
253#486—612no—
254#486—1221no—
255#476—612no—
256#475—1221no—
257#465—1222no—
258#461—612no—
259#460—1221no—
260#459—612no—
261#459—612no—
262#447—1222no—
263#436C2×D6112yescomplemented
264#435—22no—
265C8×D4C2×D6112yescomplemented
266#431—611no—
267C2×C4⋊C8—611no—
268C2×C4⋊C8C2×D6111yescharacteristic
269#418—1221no—
270#418—1221no—
271#408—21no—
272C4×M16C2×D6111yescharacteristic
273#335—612no—
274#334—612no—
275#333—611no—
276#333—611no—
277#332—611no—
278#332—611no—
279#331—612no—
280#331—612no—
281C61#1923411yescharacteristic, complemented, Sylow
282C2×#41—21no—
283C22×D4—1221no—
284C22×D4—1221no—
285C22×D4—1221no—
286C2×SD16—1222no—
287C2×D8—1222no—
288C2×D8—1222no—
289#131—44no—
290C2×M16—22no—
291C2×M16C22⋊D6111yescharacteristic
292C2×M16C22⋊D6111yescharacteristic
293C22×C8—21no—
294C22×C8—22no—
295C22×C8—1221no—
296C4⋊Q8—611no—
297C4⋊Q8—611no—
298C4⋊Q8D24411yescharacteristic
299#127—612no—
300#127—1221no—
301#127—1221no—
302#127—1221no—
303#127D24411yescharacteristic
304#125—1221no—
305#124—21no—
306C22⋊Q8—1221no—
307C22⋊Q8—1221no—
308#121—21no—
309#121D24412yes—
310C4×Q8—1221no—
311C4×Q8—1221no—
312C4×D4—21no—
313C4×D4C22×D6112yes—
314#117—1221no—
315C2×C42C22×D6111yescharacteristic
316#106—1222no—
317C4⋊C8—21no—
318C4⋊C8—612no—
319C4⋊C8—611no—
320C4⋊C8—611no—
321C4⋊C8—1221no—
322C4⋊C8C22×D6111yescharacteristic
323C4⋊C8C22×D6111yescharacteristic
324#103—1222no—
325#102—1222no—
326#102—1222no—
327#102—1222no—
328#102—1222no—
329#102—1222no—
330#102—1222no—
331#102—1222no—
332C22⋊C8—22no—
333C22⋊C8—22no—
334C22⋊C8—1221no—
335#97C22⋊D6112yes—
336C4×C8—1221no—
337C4×C8C22×D6112yes—
338C24—2441no—
339#41—42no—
340#41—42no—
341C2×Q8—21no—
342C2×Q8—1221no—
343C2×Q8—1221no—
344C2×D4—22no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—1222no—
348C2×D4—1222no—
349C2×D4—1222no—
350C2×D4—4881no—
351C2×D4—4881no—
352C2×D4—4882no—
353C2×D4—2441no—
354C2×D4—2441no—
355C2×D4—2441no—
356C2×D4—2442no—
357C2×D4—2442no—
358C2×D4C2×D24412yes—
359C22×C4—22no—
360C22×C4C2×D24411yescharacteristic
361C22×C4#1175822211yescharacteristic
362C22×C4C2×C22⋊D6111yescharacteristic
363SD16—4882no—
364D8—4882no—
365D8—4882no—
366M16—22no—
367M16—22no—
368M16—44no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—44no—
372C2×C8—42no—
373C2×C8—1221no—
374C2×C8—1221no—
375C2×C8—1222no—
376C2×C8—4881no—
377C2×C8C2×C22⋊D6112yes—
378C2×C8C2×C22⋊D6112yes—
379C4⋊C4—21no—
380C4⋊C4—1221no—
381C4⋊C4—1221no—
382C4⋊C4—1221no—
383C4⋊C4—1221no—
384C4⋊C4—2441no—
385C4⋊C4—2441no—
386C4⋊C4C2×D24412yes—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—2441no—
390C42—2441no—
391C42C2×D24411yescharacteristic
392C42#1175822211yescharacteristic
393C42C2×C22⋊D6111yescharacteristic
394C42C23×D6111yescharacteristic
395C23—22no—
396C23—4882no—
397C23—4882no—
398C23—4882no—
399C23—2442no—
400C23#1451975111yescharacteristic
401Q8—42no—
402Q8—4881no—
403Q8—2441no—
404Q8—2441no—
405D4—22no—
406D4—22no—
407D4—44no—
408D4—42no—
409D4—81no—
410D4—4882no—
411D4—4882no—
412D4—4882no—
413D4—4882no—
414D4—2442no—
415D4—2442no—
416D4—2442no—
417D4—2442no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4#1451975111yescharacteristic
427C2×C4#1451975111yescharacteristic
428C2×C4#1451975111yescharacteristic
429C2×C4#1451979712yes—
430C2×C4#1451980312yes—
431C2×C4C22×C22⋊D6111yescharacteristic
432C2×C4C22×D24411yescharacteristic
433C2×C4C2×#1175822211yescharacteristic
434C8—22no—
435C8—22no—
436C8—41no—
437C8—41no—
438C8—2442no—
439C8—2441no—
440C8—2441no—
441C22—21no—
442C22—21no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—9764no—
447C22—4882no—
448C22—4882no—
449C22—4882no—
450C22#1683997712yes—
451C22C2×#1451975111yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—42no—
456C4—4881no—
457C4—4881no—
458C4#1683997712yes—
459C4C2×#1451979711yescharacteristic
460C4C2×#1451980311yescharacteristic
461C4#1684056711yescharacteristic
462C4#1684057411yescharacteristic
463C2—22no—
464C2—82no—
465C2—9762no—
466C2C2×#1683997711yescharacteristic
467C2#2145549911yescharacteristic
468C2#2145554711yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2935C2
socleC22×C61C2×#121
prime radical#21456734C2
hypercenter#2935D61
hypocenterC61#19234
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
1. #21457135C2semidirect
3. #21456194C2semidirect
4. #21445380C2semidirect
5. #21445352C2semidirect
6. #21445256C2semidirect
7. #21445228C2semidirect
8. #21444571C2semidirect
9. #21444477C2semidirect
10. C2×#16839505C2semidirect
11. C61×#2935C2semidirect
19. #16840052C22semidirect
22. #16839967C22semidirect
31. #16839515C22semidirect
32. #16839513C22semidirect
33. #16839510C22semidirect
34. #16839510C22semidirect
35. #16839507C22semidirect
36. #16839507C22semidirect
41. C61×#436C22semidirect
43. C8×D4×C61C22semidirect
232. #2935D61semidirect
263. #436C2×D61semidirect
265. C8×D4C2×D61semidirect
281. C61#19234semidirect

Maximal subgroups

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

subgroupindex
#214571352
#214567342
#214561942
#214453802
#214453522
#214452562
#214452282
#214445712
#214444772
C2×#168395052
C61×#29352
#1923461