Finite Group Databasebeta

← #29834992

Subgroups — #29834992

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#21456393C211yesmaximal, characteristic, complemented
2#21454590C211yesmaximal, characteristic, complemented
3#21448010C211yesmaximal, characteristic, complemented
4#21447970C211yesmaximal, characteristic, complemented
5#21447965C211yesmaximal, characteristic, complemented
6#21447858C211yesmaximal, characteristic, complemented
7#21447853C211yesmaximal, characteristic, complemented
8#21447744C211yesmaximal, characteristic, complemented
9#21447740C211yesmaximal, characteristic, complemented
10#21447674C211yesmaximal, characteristic, complemented
11#21447670C211yesmaximal, characteristic, complemented
12#21447665C211yesmaximal, characteristic, complemented
13#21447663C211yesmaximal, characteristic, complemented
14#21447615C211yesmaximal, characteristic, complemented
15C61×#2234C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17#16840307—21no—
18#16840230—21no—
19C2×#14519722C2211yescharacteristic
20C2×#14519721C2211yescharacteristic
21C2×D976C2211yescharacteristic
22C2×#14519718C2211yescharacteristic
23#16840166C2211yescharacteristic
24#16840137C2211yescharacteristic
25#16840107—21no—
26#16839998C2211yescharacteristic
27#16839996—21no—
28#16839856C2211yescharacteristic
29#16839856C2211yescharacteristic
30#16839849—21no—
31#16839849—21no—
32D8×Dic61C2211yescharacteristic
33#16839844C2211yescharacteristic
34#16839844C2211yescharacteristic
35#16839844C2211yescharacteristic
36#16839842—21no—
37#16839756—21no—
38C2×C8×Dic61C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839587C2211yescharacteristic
41#16839580C2211yescharacteristic
42#16839580C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839565C2211yescharacteristic
45#16839564C2211yescharacteristic
46#16839562C2211yescharacteristic
47#16839562C2211yescharacteristic
48#16839562C2211yescharacteristic
49C22⋊#11758185C2211yescharacteristic
50C16×Dic61C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#466C2211yescharacteristic
53C61×#427C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×#357C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×C22⋊C16C2211yescharacteristic
59C2×#11758222—21no—
60C2×#11758224—41no—
61#14519799—22no—
62#14519799—22no—
63C2×Dic244C2311yescharacteristic
64C2×#11758190—21no—
65C2×D488C2311yescharacteristic
66C2×D488C2311yescharacteristic
67C2×#11758199—21no—
68C22×#92418D411yescharacteristic
69#14519776—21no—
70#14519773—21no—
71#14519763—41no—
72#14519751—21no—
73#14519749—41no—
74#14519742—21no—
75#14519742—21no—
76D4×Dic61—21no—
77#14519739—21no—
78#14519739—21no—
79#14519739—21no—
80#14519737—41no—
81#14519737—41no—
82#14519737—41no—
83#14519734—41no—
84C2×C4×Dic61D411yescharacteristic
85C42×D61—41no—
86#14519722—22no—
87#14519721—22no—
88D976—22no—
89#14519718—22no—
90C2×#11758185C2311yescharacteristic
91C2×#11758185C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519710—21no—
94#14519700—21no—
95#14519700—21no—
96#14519699—21no—
97#14519698—21no—
98#14519697—21no—
99#14519697—21no—
100#14519697—21no—
101C8×Dic61D411yescharacteristic
102C8×Dic61D411yescharacteristic
103C8×Dic61C2311yescharacteristic
104C8×Dic61C2311yescharacteristic
105C2×D8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107#121×C61—21no—
108#117×C61—21no—
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#106×C61—21no—
115#102×C61—21no—
116C2×D4×C61—21no—
117C2×D4×C61—41no—
118C22×C4×C61C2×D411yescharacteristic
119C2×C22⋊D61—41no—
120C2×C22⋊D61—41no—
121C2×C22⋊D61—41no—
122C2×C22⋊D61—41no—
123C22×Dic61—41no—
124C22×Dic61D811yescharacteristic
125C22×Dic61D811yescharacteristic
126#11758224—84no—
127#11758222—24no—
128#11758222—42no—
129C2×D244—21no—
130C2×D244—21no—
131C2×C4×D61—41no—
132C2×C4×D61—41no—
133C2×C4×D61—41no—
134C2×C4×D61—41no—
135C2×Dic122—21no—
136C2×Dic122—41no—
137D8×C61—21no—
138D8×C61—21no—
139C2×C8×C61—21no—
140C2×C8×C61—21no—
141C2×C8×C61C2×D411yescharacteristic
142C2×C8×C61C2411yescharacteristic
143C4⋊C4×C61—21no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—21no—
146C22⋊C4×C61—41no—
147C22⋊C4×C61—41no—
148C42×C61—41no—
149C22⋊Dic61—41no—
150#11758199—42no—
151#11758198—41no—
152#11758198—41no—
153#11758198—41no—
154#11758198—41no—
155C4⋊Dic61—21no—
156#11758196—41no—
157#11758196—41no—
158#11758196—41no—
159C4×Dic61—41no—
160C4×Dic61—41no—
161C4×Dic61D811yescharacteristic
162C4×Dic61D811yescharacteristic
163C4×Dic61C2×D411yescharacteristic
164C4×Dic61C2×D411yescharacteristic
165C2×#92418—41no—
166C2×#92418C2×D411yescharacteristic
167C2×#92418C2×D411yescharacteristic
168Dic244—21no—
169Dic244#4112yescomplemented
170D488—21no—
171D488—21no—
172D488—21no—
173D488#4112yescomplemented
174#11758190—24no—
175C16×C61—21no—
176C16×C61—21no—
177#11758185—21no—
178#11758185—21no—
179C23×C61—41no—
180C23×C61C2×D811yescharacteristic
181C22×D61—41no—
182C22×D61—41no—
183D4×C61—41no—
184D4×C61—41no—
185D4×C61—82no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61C2×D811yescharacteristic
192C2×C4×C61C22×D411yescharacteristic
193C22⋊D61—44no—
194C22⋊D61—82no—
195C22⋊D61—82no—
196C22⋊D61—82no—
197C2×Dic61—22no—
198C2×Dic61—22no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—82no—
202C2×Dic61C2×D811yescharacteristic
203C2×Dic61C2×D811yescharacteristic
204C2×Dic61C2×D811yescharacteristic
205C2×Dic61C2×D811yescharacteristic
206D244—22no—
207D244—41no—
208D244—41no—
209D244—41no—
210C4×D61—44no—
211C4×D61—82no—
212C4×D61—82no—
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—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—81no—
227C22×C61—81no—
228C22×C61—81no—
229C22×C61C22×D811yescharacteristic
230C2×D61—42no—
231C2×D61—81no—
232C2×D61—81no—
233C2×D61—81no—
234C2×D61—81no—
235C2×D61—81no—
236C4×C61—21no—
237C4×C61—81no—
238C4×C61—81no—
239C4×C61—81no—
240C4×C61#52511yescharacteristic
241C4×C61#57511yescharacteristic
242Dic61—21no—
243Dic61—21no—
244Dic61—42no—
245Dic61—81no—
246Dic61#50812yes—
247Dic61#50912yes—
248#3169—611no—
249C4×#135—611no—
250#2234—611no—
251#2234D6111yescharacteristic, complemented
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×D16—611no—
262#2162—611no—
263C2×C61—41no—
264C2×C61—161no—
265C2×C61#310011yescharacteristic
266C2×C61C2×#50811yescharacteristic
267C2×C61C2×#50911yescharacteristic
268D61—82no—
269D61—161no—
270C2×#135—611no—
271#532—1221no—
272C4×#41—1221no—
273C2×SD32—611no—
274C2×SD32—611no—
275C2×D16—611no—
276C2×D16—611no—
277#500—611no—
278#493—611no—
279#486—1221no—
280#466—611no—
281#466—1221no—
282#466C2×D6111yescharacteristic
283C4×Q16—611no—
284C4×Q16—611no—
285C4×SD16—1221no—
286C4×SD16—1221no—
287C4×D8—611no—
288C4×D8—611no—
289C4×D8—611no—
290C4×D8—611no—
291C4×D8—1221no—
292#427C2×D6111yescharacteristic
293#416—1221no—
294C2×C4×C8—611no—
295#367—611no—
296#367C2×D6111yescharacteristic
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⋊C16C2×D6111yescharacteristic
311C4×C16—611no—
312C4×C16—611no—
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—611no—
322C2×D8—1221no—
323C2×D8C22×D6111yescharacteristic
324C22×C8—611no—
325C22×C8C22×D6111yescharacteristic
326C4⋊Q8—1221no—
327#127—1221no—
328#124—2441no—
329#121—21no—
330#121—1221no—
331#121—2441no—
332C4×Q8—1221no—
333C4×Q8—1221no—
334C4×D4—1221no—
335C4×D4—1221no—
336C4×D4—1221no—
337C4×D4—1221no—
338C4×D4—2441no—
339C4×D4—2441no—
340C4×D4—2441no—
341#117—21no—
342#117—2441no—
343C2×C42—611no—
344C2×C42—2441no—
345SD32—1222no—
346SD32—1222no—
347D16—1222no—
348D16—1222no—
349C2×C16—611no—
350C2×C16—611no—
351C2×C16C22×D6111yescharacteristic
352C2×C16C22×D6111yescharacteristic
353#107—611no—
354#107—1221no—
355#107C22×D6111yescharacteristic
356#107C22×D6111yescharacteristic
357#107C22×D6111yescharacteristic
358#106—21no—
359#103—1221no—
360#103—1221no—
361#102—21no—
362#102—1221no—
363#102—1221no—
364#102—1221no—
365#102—1221no—
366#102—1221no—
367C4×C8—611no—
368C4×C8—611no—
369C4×C8—611no—
370C4×C8—611no—
371#41—1224no—
372#41—4884no—
373#41—2442no—
374C2×Q8—1221no—
375C2×Q8—2441no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—1221no—
379C2×D4—1221no—
380C2×D4—2441no—
381C2×D4—2441no—
382C2×D4—2441no—
383C2×D4—2441no—
384C22×C4—611no—
385C22×C4—611no—
386C22×C4—2441no—
387C22×C4—2441no—
388C22×C4—2441no—
389C22×C4—2441no—
390C22×C4—2441no—
391C22×C4D4×D6111yescharacteristic
392Q16—612no—
393Q16—1221no—
394SD16—1224no—
395D8—21no—
396D8—21no—
397D8—612no—
398D8—1221no—
399D8—1221no—
400D8—1221no—
401D8—2442no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—611no—
405C2×C8—611no—
406C2×C8—2441no—
407C2×C8D4×D6111yescharacteristic
408C2×C8C23×D6111yescharacteristic
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
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—41no—
424C42—611no—
425C42—611no—
426C42—611no—
427C42—611no—
428C42—2441no—
429C42—2441no—
430C16—21no—
431C16—21no—
432C16—1221no—
433C16—1221no—
434C23—41no—
435C23—2441no—
436C23—2441no—
437C23D8×D6111yescharacteristic
438Q8—1222no—
439Q8—4882no—
440Q8—2441no—
441D4—41no—
442D4—41no—
443D4—82no—
444D4—1222no—
445D4—4882no—
446D4—4882no—
447D4—4882no—
448D4—2444no—
449D4—2441no—
450D4—2441no—
451D4—2441no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—611no—
458C2×C4—611no—
459C2×C4—611no—
460C2×C4—611no—
461C2×C4—1222no—
462C2×C4—1222no—
463C2×C4—4882no—
464C2×C4—4882no—
465C2×C4—4882no—
466C2×C4—4882no—
467C2×C4—2444no—
468C2×C4—2441no—
469C2×C4—2441no—
470C2×C4D8×D6111yescharacteristic
471C2×C4C2×D4×D6111yescharacteristic
472C8—21no—
473C8—1221no—
474C8—1221no—
475C8#41×D6111yescharacteristic
476C8#41×D6111yescharacteristic
477C22—21no—
478C22—21no—
479C22—21no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22—4881no—
484C22—4881no—
485C22—4881no—
486C22—4881no—
487C22—4881no—
488C22—2442no—
489C22C2×D8×D6111yescharacteristic
490C4—21no—
491C4—81no—
492C4—81no—
493C4—81no—
494C4—612no—
495C4—612no—
496C4—1221no—
497C4—1221no—
498C4—4881no—
499C4—2442no—
500C4#1684027011yescharacteristic
501C4#1684056111yescharacteristic
502C2—41no—
503C2—161no—
504C2—9761no—
505C2—4882no—
506C2#2145581611yescharacteristic
507C2#508×D6111yescharacteristic
508C2#509×D6111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2234C2
socleC22×C61C22×D8
hypercenter#2234D61
hypocenterC61#33666
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

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

NH ≅ G/Ntype
1. #21456393C2semidirect
2. #21454590C2semidirect
3. #21448010C2semidirect
4. #21447970C2semidirect
5. #21447965C2semidirect
6. #21447858C2semidirect
7. #21447853C2semidirect
8. #21447744C2semidirect
9. #21447740C2semidirect
10. #21447674C2semidirect
11. #21447670C2semidirect
12. #21447665C2semidirect
13. #21447663C2semidirect
14. #21447615C2semidirect
15. C61×#2234C2semidirect
169. Dic244#41semidirect
173. D488#41semidirect
251. #2234D61semidirect
313. C61#33666semidirect

Maximal subgroups

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

subgroupindex
#214563932
#214545902
#214480102
#214479702
#214479652
#214478582
#214478532
#214477442
#214477402
#214476742
#214476702
#214476652
#214476632
#214476152
C61×#22342
#3366661