Finite Group Databasebeta

← #29663511

Subgroups — #29663511

Order 15616.

726 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457126C211yesmaximal, characteristic
2#21456942C211yesmaximal, characteristic, complemented
3#21456279C211yesmaximal, characteristic, complemented
4#21454562C211yesmaximal, characteristic, complemented
5#21445307C212yesmaximal, complemented
6#21445283C212yesmaximal, complemented
7#21445183C212yesmaximal, complemented
8#21445159C212yesmaximal, complemented
9#21444572C211yesmaximal, characteristic, complemented
10C2×#16839509C211yesmaximal, characteristic, complemented
11C61×#1540C211yesmaximal, characteristic, complemented
12C2×#14519807—21no—
13C2×#14519807—21no—
14C2×#14519783—21no—
15#16840312C2211yescharacteristic
16C2×#14519777C2211yescharacteristic
17#16840167—21no—
18#16840157—22no—
19#16840141C2212yes—
20#16840134C2212yes—
21#16840109—21no—
22#16840076—22no—
23#16840043C2212yes—
24#16840043C2212yes—
25#16840042—21no—
26#16840039C2212yes—
27#16839996—22no—
28#16839957—21no—
29#16839954C2212yes—
30#16839839C2212yes—
31#16839832—22no—
32#16839827C2212yes—
33C2×C4⋊#92418C2211yescharacteristic
34#16839728—21no—
35C4×#11758194C2211yescharacteristic
36#16839514C2212yes—
37#16839512C2212yes—
38#16839509C2212yes—
39#16839509C2212yes—
40C61×#532C2211yescharacteristic
41C61×#431C2211yescharacteristic
42C2×C4⋊C8×C61C2211yescharacteristic
43C61×#332C2211yescharacteristic
44C61×#332C2211yescharacteristic
45C61×#331C2211yescharacteristic
46C61×#331C2211yescharacteristic
47C2×#11758222—21no—
48C22×Dic122—21no—
49#14519807—44no—
50#14519807—44no—
51C2×#11758202—22no—
52C2×#11758202—22no—
53C2×#11758200—22no—
54C2×#11758200—22no—
55C2×#11758199—22no—
56#14519783—44no—
57C2×#11758194D411yescharacteristic
58C2×#11758194D411yescharacteristic
59C2×#11758189—22no—
60C22×#92418—21no—
61C2×C8×D61—22no—
62#14519777—21no—
63#14519777—21no—
64#14519777—21no—
65#14519777D411yescharacteristic
66#14519777C2312yes—
67#14519774D411yescharacteristic
68#14519765—21no—
69#14519751—21no—
70#14519751D412yes—
71C4×D244—21no—
72C4×D244C2312yes—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—21no—
75#14519711—22no—
76#14519711—22no—
77#14519710—22no—
78C4⋊#92418—21no—
79C4⋊#92418C2312yes—
80#14519699—22no—
81#14519699—22no—
82#14519698—22no—
83#14519697—22no—
84#14519689—22no—
85#14519689—22no—
86#14519688D412yes—
87C4×#92418C2312yes—
88C2×#41×C61—21no—
89C22×C8×C61—21no—
90C4⋊Q8×C61C2311yescharacteristic
91#127×C61C2311yescharacteristic
92#124×C61—21no—
93#121×C61—21no—
94#121×C61—21no—
95C4×D4×C61—21no—
96C4×D4×C61—21no—
97C2×C42×C61C2311yescharacteristic
98C4⋊C8×C61—21no—
99C4⋊C8×C61C2311yescharacteristic
100C4⋊C8×C61C2311yescharacteristic
101C4⋊C8×C61C2311yescharacteristic
102C4⋊C8×C61C2311yescharacteristic
103C22⋊C8×C61—21no—
104C4×C8×C61—21no—
105#41×C61—42no—
106#41×C61—42no—
107C2×Q8×C61—21no—
108C2×D4×C61—21no—
109C2×D4×C61—21no—
110C2×D4×C61—21no—
111C2×D4×C61—41no—
112C22×C4×C61—41no—
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C2×C22⋊D61—22no—
117C22×Dic61—41no—
118#11758222—42no—
119#11758222—42no—
120C2×D244—21no—
121C2×D244—21no—
122C2×D244C2×D412yes—
123C2×C4×D61—22no—
124C2×Dic122—21no—
125C2×Dic122—22no—
126C2×Dic122—42no—
127C2×Dic122—42no—
128C2×Dic122—41no—
129C2×C8×C61—21no—
130C2×C8×C61—21no—
131C2×C8×C61—21no—
132C2×C8×C61—21no—
133C2×C8×C61—42no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—21no—
136C22⋊C4×C61—41no—
137C22⋊C4×C61—41no—
138C42×C61C2×D411yescharacteristic
139C42×C61C2×D411yescharacteristic
140C42×C61#4111yescharacteristic
141C42×C61C2411yescharacteristic
142#11758202—44no—
143#11758202—44no—
144#11758200—44no—
145#11758200—44no—
146#11758199—82no—
147#11758198—22no—
148#11758198—22no—
149C4⋊Dic61—21no—
150C4⋊Dic61—22no—
151C4⋊Dic61—22no—
152C4⋊Dic61—41no—
153C4⋊Dic61—41no—
154C4⋊Dic61C2×D412yes—
155#11758194—22no—
156#11758194D814yescomplemented
157C2×#92418—22no—
158C2×#92418—81no—
159C2×#92418C2×D412yes—
160C2×#92418C2×D412yes—
161#11758189—44no—
162C8×D61—44no—
163C23×C61—41no—
164C23×C61#12111yescharacteristic
165C22×D61—22no—
166Q8×C61—41no—
167Q8×C61—41no—
168D4×C61—41no—
169D4×C61—41no—
170D4×C61—41no—
171D4×C61—41no—
172D4×C61—81no—
173D4×C61—82no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—82no—
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#12111yescharacteristic
181C2×C4×C61#12111yescharacteristic
182C2×C4×C61C2×D812yes—
183C2×C4×C61AGL(1,ℤ/8)12yes—
184C2×C4×C61C22×D411yescharacteristic
185C2×C4×C61C22×D411yescharacteristic
186C2×C4×C61C2×#4111yescharacteristic
187C22⋊D61—44no—
188C2×Dic61—22no—
189C2×Dic61—42no—
190C2×Dic61—82no—
191D244—22no—
192D244—22no—
193D244—42no—
194D244—81no—
195C4×D61—42no—
196C4×D61—42no—
197Dic122—42no—
198Dic122—42no—
199Dic122—42no—
200Dic122—82no—
201C8×C61—41no—
202C8×C61—41no—
203C8×C61—41no—
204C8×C61—41no—
205#92418—22no—
206#92418—42no—
207#92418C2×D814yes—
208#19231—611nomaximal, Sylow
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61#45912yes—
215C22×C61C2×#12111yescharacteristic
216C2×D61—42no—
217C2×D61—42no—
218C2×D61—42no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—81no—
223C4×C61#45912yes—
224C4×C61C22×D811yescharacteristic
225C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
226C4×C61#57711yescharacteristic
227C4×C61#57811yescharacteristic
228Dic61—42no—
229Dic61—82no—
230#3245—611no—
231#3226—611no—
232#3152—611no—
233#2935—611no—
234#1689—612no—
235#1685—612no—
236#1669—612no—
237#1665—612no—
238#1565—611no—
239#1540D6111yescharacteristic, complemented
240C2×#332—611no—
241C2×C61—22no—
242C2×C61—161no—
243C2×C61C2×#45911yescharacteristic
244C2×C61#306311yescharacteristic
245C2×C61#306911yescharacteristic
246D61—82no—
247C2×#137—1221no—
248C2×#137—1221no—
249C2×#131—1221no—
250#532—611no—
251#532C2×D6111yescharacteristic
252C2×C4⋊Q8—611no—
253#500—1221no—
254#497—1222no—
255#494—612no—
256#492—612no—
257#486—1221no—
258#480—1222no—
259#474—612no—
260#474—612no—
261#474—612no—
262#474—1221no—
263#466—1222no—
264#459—612no—
265#459—1221no—
266#436—612no—
267#435—1222no—
268C8×D4—612no—
269#431C2×D6111yescharacteristic
270C2×C4⋊C8—611no—
271C2×C4⋊C8C2×D6111yescharacteristic
272#408—1221no—
273C4×M16—611no—
274#335—612no—
275#334—612no—
276#332—612no—
277#332—612no—
278#332C2×D6111yescharacteristic
279#332C2×D6111yescharacteristic
280#331C2×D6111yescharacteristic
281#331C2×D6111yescharacteristic
282C61#1923111yescharacteristic, complemented, Sylow
283C2×#41—21no—
284C2×#41—1221no—
285C22×Q8—1221no—
286#137—2444no—
287#137—2444no—
288C2×Q16—1222no—
289C2×Q16—1222no—
290C2×SD16—1222no—
291C2×SD16—1222no—
292C2×D8—1222no—
293#131—2444no—
294C2×M16—611no—
295C2×M16—611no—
296C2×M16—1222no—
297C22×C8—21no—
298C22×C8—1222no—
299C22×C8—1221no—
300C4⋊Q8—611no—
301C4⋊Q8—612no—
302C4⋊Q8—1221no—
303C4⋊Q8—1221no—
304C4⋊Q8—1221no—
305C4⋊Q8C22×D6111yescharacteristic
306#127—611no—
307#127C22×D6111yescharacteristic
308#124—21no—
309#124—1221no—
310#121—21no—
311#121—21no—
312#121—612no—
313#121—1221no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—612no—
317C4×D4—1221no—
318C2×C4⋊C4—1221no—
319C2×C4⋊C4—1221no—
320C2×C42C22×D6111yescharacteristic
321#107—1222no—
322#107—1222no—
323#107—1222no—
324C4⋊C8—21no—
325C4⋊C8—612no—
326C4⋊C8—1221no—
327C4⋊C8C22×D6111yescharacteristic
328C4⋊C8C22×D6111yescharacteristic
329C4⋊C8C22×D6111yescharacteristic
330C4⋊C8C22×D6111yescharacteristic
331#102—1222no—
332#102—1222no—
333#102—1222no—
334#102—1222no—
335C22⋊C8—21no—
336C22⋊C8—1222no—
337C22⋊C8—1222no—
338#97—612no—
339C4×C8—21no—
340C4×C8—612no—
341#41—42no—
342#41—42no—
343#41—2442no—
344#41—2442no—
345C2×Q8—21no—
346C2×Q8—1221no—
347C2×Q8—1222no—
348C2×Q8—2442no—
349C2×Q8—2442no—
350C2×Q8—2441no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—41no—
355C2×D4—612no—
356C2×D4—1222no—
357C2×D4—1221no—
358C2×D4—1221no—
359C22×C4—41no—
360C22×C4—1222no—
361C22×C4—2441no—
362C22×C4#1175822211yescharacteristic
363C22×C4D4×D6111yescharacteristic
364C22×C4D4×D6111yescharacteristic
365Q16—2444no—
366Q16—2444no—
367SD16—2444no—
368SD16—2444no—
369D8—4882no—
370M16—614no—
371M16—1222no—
372M16—2444no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—42no—
378C2×C8—612no—
379C2×C8—612no—
380C2×C8—1222no—
381C2×C8—4881no—
382C2×C8—2444no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—612no—
386C4⋊C4—1221no—
387C4⋊C4—1222no—
388C4⋊C4—1222no—
389C4⋊C4—2441no—
390C4⋊C4—2441no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—1222no—
394C22⋊C4—1222no—
395C42#1175822211yescharacteristic
396C42D4×D6111yescharacteristic
397C42D4×D6111yescharacteristic
398C42C23×D6111yescharacteristic
399C23—41no—
400C23—1222no—
401C23#1451975011yescharacteristic
402Q8—41no—
403Q8—41no—
404Q8—4882no—
405Q8—2442no—
406Q8—2442no—
407Q8—2442no—
408D4—41no—
409D4—41no—
410D4—41no—
411D4—41no—
412D4—81no—
413D4—82no—
414D4—1222no—
415D4—1222no—
416D4—4881no—
417D4—2444no—
418D4—2442no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—82no—
424C2×C4—1222no—
425C2×C4—4882no—
426C2×C4—2442no—
427C2×C4—2442no—
428C2×C4—2442no—
429C2×C4#1451975011yescharacteristic
430C2×C4#1451975011yescharacteristic
431C2×C4#1451975011yescharacteristic
432C2×C4D8×D6112yes—
433C2×C4#1451980412yes—
434C2×C4C2×D4×D6111yescharacteristic
435C2×C4C2×D4×D6111yescharacteristic
436C2×C4C2×#1175822211yescharacteristic
437C8—41no—
438C8—41no—
439C8—41no—
440C8—41no—
441C8—614no—
442C8—1222no—
443C8—2442no—
444C22—21no—
445C22—21no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—2442no—
450C22—2442no—
451C22—2442no—
452C22#1683995612yes—
453C22C2×#1451975011yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—81no—
458C4—4882no—
459C4—2442no—
460C4#1683995612yes—
461C4C2×D8×D6111yescharacteristic
462C4C2×#1451980411yescharacteristic
463C4#1684056911yescharacteristic
464C4#1684057611yescharacteristic
465C2—22no—
466C2—161no—
467C2—4882no—
468C2C2×#1683995611yescharacteristic
469C2#2145551311yescharacteristic
470C2#2145555911yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1540C2
socleC22×C61C2×#121
prime radical#21457126C2
hypercenter#1540D61
hypocenterC61#19231
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. #21456942C2semidirect
3. #21456279C2semidirect
4. #21454562C2semidirect
5. #21445307C2semidirect
6. #21445283C2semidirect
7. #21445183C2semidirect
8. #21445159C2semidirect
9. #21444572C2semidirect
10. C2×#16839509C2semidirect
11. C61×#1540C2semidirect
156. #11758194D8semidirect
239. #1540D61semidirect
282. C61#19231semidirect

Maximal subgroups

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

subgroupindex
#214571262
#214569422
#214562792
#214545622
#214453072
#214452832
#214451832
#214451592
#214445722
C2×#168395092
C61×#15402
#1923161