Finite Group Databasebeta

← #29834993

Subgroups — #29834993

Order 15616.

596 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456395C211yesmaximal, characteristic, complemented
2C4×#14519796C211yesmaximal, characteristic, complemented
3#21448013C211yesmaximal, characteristic, complemented
4#21448009C211yesmaximal, characteristic, complemented
5#21447970C211yesmaximal, characteristic, complemented
6#21447964C211yesmaximal, characteristic, complemented
7#21447858C211yesmaximal, characteristic, complemented
8#21447852C211yesmaximal, characteristic, complemented
9#21447743C211yesmaximal, characteristic, complemented
10#21447739C211yesmaximal, characteristic, complemented
11C4×#14519722C211yesmaximal, characteristic, complemented
12C4×#14519721C211yesmaximal, characteristic, complemented
13C4×#14519718C211yesmaximal, characteristic, complemented
14#21447616C211yesmaximal, characteristic, complemented
15C4×D16×C61C211yesmaximal, characteristic, complemented
16C2×#14519796C2211yescharacteristic
17#16840309—21no—
18C4×#11758224—21no—
19C2×#14519722C2211yescharacteristic
20C2×#14519721C2211yescharacteristic
21C2×#14519718C2211yescharacteristic
22#16840166C2211yescharacteristic
23#16840137C2211yescharacteristic
24#16840107—21no—
25#16839999C2211yescharacteristic
26#16839997—21no—
27#16839995C2211yescharacteristic
28C4×Dic244C2211yescharacteristic
29#16839856C2211yescharacteristic
30#16839853—21no—
31C4×#11758200—21no—
32C4×D488C2211yescharacteristic
33D8×Dic61C2211yescharacteristic
34C4×#11758199—21no—
35#16839799C2211yescharacteristic
36#16839755—21no—
37C4×C8×D61C2211yescharacteristic
38#16839590C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839587C2211yescharacteristic
41#16839580C2211yescharacteristic
42#16839580C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839565C2211yescharacteristic
45#16839564C2211yescharacteristic
46#16839563C2211yescharacteristic
47#16839563C2211yescharacteristic
48#16839562C2211yescharacteristic
49#16839541C2211yescharacteristic
50#16839541C2211yescharacteristic
51C4×#11758185C2211yescharacteristic
52C2×D16×C61C2211yescharacteristic
53C4×D8×C61C2211yescharacteristic
54C4×D8×C61C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×#357C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C4×C16×C61C2211yescharacteristic
59C2×#11758222—41no—
60C2×#11758224—21no—
61#14519796—22no—
62#14519796—22no—
63C2×Dic244C2311yescharacteristic
64C2×#11758200—21no—
65C2×D488C2311yescharacteristic
66C2×#11758199—21no—
67C2×C8×D61D411yescharacteristic
68C2×C8×D61C2311yescharacteristic
69#14519776—21no—
70#14519773—21no—
71#14519763—41no—
72#14519752—21no—
73#14519750—41no—
74#14519748—21no—
75C4×Dic122—21no—
76#14519742—21no—
77C4×D244—21no—
78D4×Dic61—21no—
79C4×C22⋊D61—41no—
80C4×C22⋊D61—41no—
81#14519737—41no—
82#14519735—21no—
83#14519733—41no—
84C2×C4×Dic61—41no—
85C42×D61D411yescharacteristic
86#14519722—22no—
87#14519721—22no—
88#14519718—22no—
89C2×#11758185C2311yescharacteristic
90C2×#11758185C2311yescharacteristic
91#14519711C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519710—21no—
94#14519708—21no—
95#14519702—21no—
96#14519700—21no—
97#14519699—21no—
98#14519698—21no—
99#14519698—21no—
100#14519697—21no—
101C4×#92418D411yescharacteristic
102C8×Dic61D411yescharacteristic
103C8×Dic61C2311yescharacteristic
104C2×D8×C61C2311yescharacteristic
105C2×D8×C61C2311yescharacteristic
106C4×D4×C61—21no—
107C4×D4×C61—21no—
108D16×C61—22no—
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#102×C61—21no—
114#102×C61—21no—
115C4×C8×C61C2311yescharacteristic
116C2×D4×C61—21no—
117C2×D4×C61—21no—
118C22×C4×C61—41no—
119C22×C4×C61—41no—
120C2×C22⋊D61—41no—
121C2×C22⋊D61—41no—
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124C22×Dic61—41no—
125C22×Dic61—41no—
126#11758224—24no—
127#11758224—42no—
128#11758222—84no—
129C2×D244—21no—
130C2×D244—41no—
131C2×C4×D61—41no—
132C2×C4×D61D811yescharacteristic
133C2×C4×D61D811yescharacteristic
134C2×C4×D61C2×D411yescharacteristic
135C2×Dic122—21no—
136C2×Dic122—41no—
137D8×C61—21no—
138D8×C61—21no—
139D8×C61—21no—
140D8×C61#4112yescomplemented
141C2×C8×C61C2×D411yescharacteristic
142C2×C8×C61C2411yescharacteristic
143C4⋊C4×C61—21no—
144C4⋊C4×C61—21no—
145C22⋊C4×C61—41no—
146C22⋊C4×C61—41no—
147C42×C61C2×D411yescharacteristic
148C22⋊Dic61—41no—
149C22⋊Dic61—41no—
150#11758200—24no—
151#11758199—42no—
152#11758198—41no—
153#11758198—41no—
154#11758198—41no—
155C4⋊Dic61—21no—
156C4⋊Dic61—21no—
157#11758196—41no—
158#11758196—41no—
159#11758196—41no—
160C4×Dic61—41no—
161C4×Dic61—41no—
162C4×Dic61—41no—
163C4×Dic61D811yescharacteristic
164C4×Dic61D811yescharacteristic
165C4×Dic61C2×D411yescharacteristic
166C2×#92418C2×D411yescharacteristic
167C2×#92418C2×D411yescharacteristic
168Dic244—21no—
169Dic244#4112yescomplemented
170D488—21no—
171D488—21no—
172C8×D61—21no—
173C8×D61—21no—
174C8×D61—41no—
175C16×C61—21no—
176C16×C61—21no—
177#11758185—21no—
178#11758185—21no—
179C23×C61—41no—
180C23×C61—41no—
181C22×D61—41no—
182C22×D61C2×D811yescharacteristic
183D4×C61—22no—
184D4×C61—41no—
185D4×C61—41no—
186D4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—82no—
190C2×C4×C61—82no—
191C2×C4×C61C2×D811yescharacteristic
192C2×C4×C61C2×D811yescharacteristic
193C2×C4×C61C22×D411yescharacteristic
194C22⋊D61—44no—
195C22⋊D61—82no—
196C22⋊D61—82no—
197C22⋊D61—82no—
198C2×Dic61—44no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—82no—
203C2×Dic61C2×D811yescharacteristic
204C2×Dic61C2×D811yescharacteristic
205C2×Dic61C2×D811yescharacteristic
206D244—41no—
207D244—41no—
208D244—82no—
209C4×D61—21no—
210C4×D61—21no—
211C4×D61—22no—
212C4×D61—22no—
213C4×D61—82no—
214Dic122—22no—
215Dic122—41no—
216Dic122—82no—
217C8×C61—21no—
218C8×C61C2×#4111yescharacteristic
219C8×C61C2×#4111yescharacteristic
220#92418—21no—
221#92418—21no—
222#33666—611nomaximal, Sylow
223C22×C61—42no—
224C22×C61—81no—
225C22×C61—81no—
226C22×C61—81no—
227C22×C61—81no—
228C22×C61—81no—
229C22×C61C22×D811yescharacteristic
230C2×D61—21no—
231C2×D61—21no—
232C2×D61—21no—
233C2×D61—81no—
234C2×D61—81no—
235C2×D61—81no—
236C4×C61—21no—
237C4×C61—81no—
238C4×C61—81no—
239C4×C61#50912yes—
240C4×C61#52511yescharacteristic
241C4×C61#57511yescharacteristic
242Dic61—21no—
243Dic61—21no—
244Dic61—42no—
245Dic61—81no—
246Dic61—81no—
247Dic61#50812yes—
248#3169—611no—
249C4×#135—611no—
250#2234—611no—
251#2234—611no—
252#2227—611no—
253#2226—611no—
254#2207—611no—
255#2206—611no—
256#2186—611no—
257#2186—611no—
258C4×SD32—611no—
259C4×SD32—611no—
260C4×D16—611no—
261C4×D16D6111yescharacteristic, complemented
262#2162—611no—
263C2×C61—82no—
264C2×C61—161no—
265C2×C61#310011yescharacteristic
266C2×C61C2×#50811yescharacteristic
267C2×C61C2×#50911yescharacteristic
268D61—41no—
269D61—161no—
270C2×#135—611no—
271#532—1221no—
272C4×#41—1221no—
273C2×SD32—611no—
274C2×SD32—611no—
275C2×D16—611no—
276C2×D16C2×D6111yescharacteristic
277#500—611no—
278#493—611no—
279#486—1221no—
280#466—611no—
281#466—611no—
282#466—1221no—
283C4×Q16—611no—
284C4×Q16—611no—
285C4×SD16—1221no—
286C4×SD16—1221no—
287C4×D8—611no—
288C4×D8—611no—
289C4×D8—1221no—
290C4×D8C2×D6111yescharacteristic
291C4×D8C2×D6111yescharacteristic
292#427—611no—
293#416—1221no—
294C2×C4×C8—611no—
295#367—611no—
296#367—611no—
297#366—611no—
298#366C2×D6111yescharacteristic
299C4⋊C16—611no—
300C4⋊C16—611no—
301#358—611no—
302#358—611no—
303#357—611no—
304#357—611no—
305#357—611no—
306#357—611no—
307#357C2×D6111yescharacteristic
308#357C2×D6111yescharacteristic
309C22⋊C16—611no—
310C22⋊C16—611no—
311C4×C16—611no—
312C4×C16C2×D6111yescharacteristic
313C61#3366611yescharacteristic, complemented, Sylow
314C2×#41—1221no—
315C2×#41—2441no—
316#135—1222no—
317#135—1222no—
318C2×Q16—611no—
319C2×SD16—1221no—
320C2×D8—611no—
321C2×D8—1221no—
322C2×D8C22×D6111yescharacteristic
323C2×D8C22×D6111yescharacteristic
324C22×C8—611no—
325C22×C8—611no—
326C4⋊Q8—1221no—
327#127—1221no—
328#124—2441no—
329#121—1221no—
330#121—1221no—
331#121—2441no—
332C4×Q8—1221no—
333C4×Q8—1221no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—1221no—
337C4×D4—1221no—
338C4×D4—2441no—
339C4×D4—2441no—
340C4×D4—2441no—
341#117—1221no—
342#117—2441no—
343C2×C42—611no—
344C2×C42—2441no—
345SD32—1222no—
346SD32—1222no—
347D16—22no—
348D16—1222no—
349C2×C16—611no—
350C2×C16—611no—
351C2×C16C22×D6111yescharacteristic
352C2×C16C22×D6111yescharacteristic
353#107—611no—
354#107—611no—
355#107—1221no—
356#107C22×D6111yescharacteristic
357#107C22×D6111yescharacteristic
358#106—1221no—
359#103—1221no—
360#103—1221no—
361#102—21no—
362#102—21no—
363#102—1221no—
364#102—1221no—
365#102—1221no—
366#102—1221no—
367C4×C8—611no—
368C4×C8—611no—
369C4×C8—611no—
370C4×C8C22×D6111yescharacteristic
371#41—1224no—
372#41—4884no—
373#41—2442no—
374C2×Q8—1221no—
375C2×Q8—2441no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—1221no—
379C2×D4—2441no—
380C2×D4—2441no—
381C2×D4—2441no—
382C2×D4—2441no—
383C2×D4—2441no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—611no—
389C22×C4—2441no—
390C22×C4—2441no—
391C22×C4—2441no—
392Q16—612no—
393Q16—1221no—
394SD16—1224no—
395D8—21no—
396D8—21no—
397D8—21no—
398D8—1221no—
399D8—1221no—
400D8—2442no—
401D8#1175822212yescomplemented
402C2×C8—611no—
403C2×C8—611no—
404C2×C8—1221no—
405C2×C8—1221no—
406C2×C8—2441no—
407C2×C8D4×D6111yescharacteristic
408C2×C8C23×D6111yescharacteristic
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—1221no—
412C4⋊C4—1221no—
413C4⋊C4—2441no—
414C4⋊C4—2441no—
415C4⋊C4—2441no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—2441no—
419C22⋊C4—2441no—
420C22⋊C4—2441no—
421C22⋊C4—2441no—
422C22⋊C4—2441no—
423C42—611no—
424C42—611no—
425C42—611no—
426C42—2441no—
427C42—2441no—
428C42—2441no—
429C42D4×D6111yescharacteristic
430C16—21no—
431C16—21no—
432C16—1221no—
433C16—1221no—
434C23—41no—
435C23—41no—
436C23—611no—
437C23—2441no—
438Q8—1222no—
439Q8—4882no—
440Q8—2441no—
441D4—22no—
442D4—41no—
443D4—41no—
444D4—41no—
445D4—4882no—
446D4—4882no—
447D4—4882no—
448D4—4882no—
449D4—2444no—
450D4—2441no—
451D4—2441no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—611no—
457C2×C4—611no—
458C2×C4—611no—
459C2×C4—1222no—
460C2×C4—1222no—
461C2×C4—1221no—
462C2×C4—1221no—
463C2×C4—4882no—
464C2×C4—4882no—
465C2×C4—2444no—
466C2×C4—2441no—
467C2×C4—2441no—
468C2×C4—2441no—
469C2×C4D8×D6111yescharacteristic
470C2×C4D8×D6111yescharacteristic
471C2×C4C2×D4×D6111yescharacteristic
472C8—21no—
473C8—1221no—
474C8—1221no—
475C8#41×D6111yescharacteristic
476C8C2×#1175822211yescharacteristic
477C22—42no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22—1221no—
484C22—1221no—
485C22—1221no—
486C22—4881no—
487C22—4881no—
488C22—4881no—
489C22C2×D8×D6111yescharacteristic
490C4—21no—
491C4—81no—
492C4—81no—
493C4—612no—
494C4—1221no—
495C4—1221no—
496C4—4881no—
497C4—4881no—
498C4—2442no—
499C4#1684019612yes—
500C4#1684027111yescharacteristic
501C4#1684055911yescharacteristic
502C2—82no—
503C2—161no—
504C2—9761no—
505C2—2441no—
506C2#2145581711yescharacteristic
507C2#508×D6111yescharacteristic
508C2C2×#1684019611yescharacteristic
subgroupG/H
centerC2×C4D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC4×D16×C61C2
socleC22×C61C22×D8
hypercenterC4×D16D61
hypocenterC61#33666
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. #21456395C2semidirect
2. C4×#14519796C2semidirect
3. #21448013C2semidirect
4. #21448009C2semidirect
5. #21447970C2semidirect
6. #21447964C2semidirect
7. #21447858C2semidirect
8. #21447852C2semidirect
9. #21447743C2semidirect
10. #21447739C2semidirect
11. C4×#14519722C2semidirect
12. C4×#14519721C2semidirect
13. C4×#14519718C2semidirect
14. #21447616C2semidirect
15. C4×D16×C61C2semidirect
140. D8×C61#41semidirect
169. Dic244#41semidirect
261. C4×D16D61semidirect
313. C61#33666semidirect
401. D8#11758222semidirect

Maximal subgroups

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

subgroupindex
#214563952
C4×#145197962
#214480132
#214480092
#214479702
#214479642
#214478582
#214478522
#214477432
#214477392
C4×#145197222
C4×#145197212
C4×#145197182
#214476162
C4×D16×C612
#3366661