Finite Group Databasebeta

← #29835133

Subgroups — #29835133

Order 15616.

558 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456466C211yesmaximal, characteristic, complemented
2#21454689C211yesmaximal, characteristic, complemented
3#21448003C211yesmaximal, characteristic, complemented
4#21447998C211yesmaximal, characteristic, complemented
5#21447984C211yesmaximal, characteristic, complemented
6#21447976C211yesmaximal, characteristic, complemented
7#21447856C211yesmaximal, characteristic, complemented
8#21447739C211yesmaximal, characteristic, complemented
9#21447739C211yesmaximal, characteristic, complemented
10#21447695C211yesmaximal, characteristic, complemented
11#21447680C211yesmaximal, characteristic, complemented
12#21447674C211yesmaximal, characteristic, complemented
13D16×Dic61C211yesmaximal, characteristic, complemented
14#21447625C211yesmaximal, characteristic, complemented
15C61×#2206C211yesmaximal, characteristic, complemented
16C2×#14519796C2211yescharacteristic
17#16840366—21no—
18#16840241—21no—
19C2×#14519721C2211yescharacteristic
20C2×#14519721C2211yescharacteristic
21#16840164C2211yescharacteristic
22#16840126—21no—
23#16840012—21no—
24#16839995C2211yescharacteristic
25#16839995C2211yescharacteristic
26#16839874—21no—
27#16839862—21no—
28#16839859—21no—
29C4×Dic244C2211yescharacteristic
30#16839856C2211yescharacteristic
31D8×Dic61C2211yescharacteristic
32D8×Dic61C2211yescharacteristic
33D8×Dic61C2211yescharacteristic
34#107×D61C2211yescharacteristic
35#16839760—21no—
36#16839716C2211yescharacteristic
37#16839590C2211yescharacteristic
38#16839589C2211yescharacteristic
39#16839588C2211yescharacteristic
40#16839587C2211yescharacteristic
41C4⋊#11758185C2211yescharacteristic
42#16839567C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839563C2211yescharacteristic
45#16839563C2211yescharacteristic
46#16839563C2211yescharacteristic
47#16839563C2211yescharacteristic
48#16839541C2211yescharacteristic
49#16839541C2211yescharacteristic
50#16839537C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C2×D16×C61C2211yescharacteristic
53C2×D16×C61C2211yescharacteristic
54C61×#493C2211yescharacteristic
55C4×D8×C61C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×#11758224—21no—
60#14519796—22no—
61#14519796—22no—
62C2×Dic244C2311yescharacteristic
63C2×#11758200—21no—
64C2×#11758189D411yescharacteristic
65C2×C8×D61C2311yescharacteristic
66#14519769—21no—
67#14519758—41no—
68#14519758—41no—
69#14519749—41no—
70#14519749—41no—
71#14519748—21no—
72#14519748—21no—
73C4×Dic122—21no—
74#14519742—21no—
75D4×Dic61—21no—
76D4×Dic61—21no—
77D4×Dic61—21no—
78C4×C22⋊D61—41no—
79#14519737—41no—
80#14519734D411yescharacteristic
81#14519733—41no—
82C2×#11758196—41no—
83C4⋊C4×D61—21no—
84#14519721—22no—
85#14519721—22no—
86C2×#11758185C2311yescharacteristic
87C2×#11758185C2311yescharacteristic
88#14519711C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519711C2311yescharacteristic
91#14519710—21no—
92#14519709—21no—
93#14519702—21no—
94#14519700—21no—
95#14519698—21no—
96#14519698—21no—
97#14519698—21no—
98#14519698—21no—
99#14519698—21no—
100#14519688D411yescharacteristic
101#14519687D411yescharacteristic
102C8×Dic61C2311yescharacteristic
103C2×D8×C61—21no—
104C2×D8×C61C2311yescharacteristic
105C2×D8×C61C2311yescharacteristic
106C2×D8×C61C2311yescharacteristic
107#127×C61—21no—
108C4×D4×C61—21no—
109D16×C61—22no—
110D16×C61—22no—
111C2×C16×C61C2311yescharacteristic
112C2×C16×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#102×C61—21no—
115C4×C8×C61C2311yescharacteristic
116C2×D4×C61—21no—
117C2×D4×C61—21no—
118C2×D4×C61—21no—
119C2×D4×C61—41no—
120C2×D4×C61—41no—
121C22×C4×C61—41no—
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124C2×C22⋊D61—41no—
125C22×Dic61—41no—
126C22×Dic61—41no—
127C22×Dic61—41no—
128C22×Dic61—41no—
129#11758224—24no—
130#11758224—42no—
131C2×C4×D61—41no—
132C2×C4×D61C2×D411yescharacteristic
133C2×Dic122—21no—
134D8×C61—21no—
135D8×C61—21no—
136D8×C61—21no—
137D8×C61—21no—
138D8×C61—21no—
139D8×C61—42no—
140D8×C61#4112yes—
141C2×C8×C61C2×D411yescharacteristic
142C2×C8×C61C2411yescharacteristic
143C4⋊C4×C61—21no—
144C22⋊C4×C61—41no—
145C42×C61C2×D411yescharacteristic
146C22⋊Dic61—41no—
147C22⋊Dic61—41no—
148C22⋊Dic61—41no—
149C22⋊Dic61—41no—
150C22⋊Dic61—41no—
151#11758200—24no—
152#11758198D811yescharacteristic
153#11758198D811yescharacteristic
154C4⋊Dic61—21no—
155C4⋊Dic61—21no—
156C4⋊Dic61—21no—
157#11758196—41no—
158#11758196—41no—
159#11758196—41no—
160#11758196—41no—
161#11758196—41no—
162#11758196D811yescharacteristic
163#11758196D811yescharacteristic
164C4×Dic61—41no—
165C4×Dic61—41no—
166C4×Dic61C2×D411yescharacteristic
167C2×#92418C2×D411yescharacteristic
168C2×#92418C2×D411yescharacteristic
169Dic244—21no—
170Dic244#4112yes—
171#11758189—41no—
172C8×D61—21no—
173C8×D61—21no—
174C16×C61—21no—
175C16×C61—21no—
176#11758185—21no—
177#11758185—21no—
178C23×C61—41no—
179C23×C61—41no—
180C23×C61—41no—
181C22×D61C2×D811yescharacteristic
182D4×C61—22no—
183D4×C61—41no—
184D4×C61—41no—
185D4×C61—41no—
186D4×C61—41no—
187D4×C61—41no—
188D4×C61—161no—
189D4×C61—161no—
190C2×C4×C61—41no—
191C2×C4×C61—161no—
192C2×C4×C61C2×D811yescharacteristic
193C2×C4×C61C2×D811yescharacteristic
194C2×C4×C61C22×D411yescharacteristic
195C22⋊D61—44no—
196C22⋊D61—161no—
197C22⋊D61—161no—
198C2×Dic61—44no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—41no—
203C2×Dic61—161no—
204C2×Dic61—161no—
205C2×Dic61—161no—
206C2×Dic61C2×D811yescharacteristic
207C2×Dic61C2×D811yescharacteristic
208C2×Dic61C2×D811yescharacteristic
209C4×D61—21no—
210C4×D61—21no—
211C4×D61—161no—
212Dic122—22no—
213Dic122—41no—
214C8×C61—21no—
215C8×C61C2×#4111yescharacteristic
216C8×C61C2×#4111yescharacteristic
217#92418—21no—
218#92418—21no—
219#33679—611nomaximal, Sylow
220C22×C61—42no—
221C22×C61—81no—
222C22×C61—81no—
223C22×C61—81no—
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—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—81no—
236C4×C61#52511yescharacteristic
237C4×C61#57511yescharacteristic
238Dic61—21no—
239Dic61—21no—
240Dic61—21no—
241Dic61—42no—
242Dic61—81no—
243Dic61—81no—
244Dic61—81no—
245#3176—611no—
246#2951—611no—
247#2233—611no—
248#2232—611no—
249#2229—611no—
250#2228—611no—
251#2207—611no—
252#2206D6111yescharacteristic, complemented
253#2186—611no—
254#2186—611no—
255#2177—611no—
256#2175—611no—
257C4×SD32—611no—
258C4×D16—611no—
259#2164—611no—
260C2×C61—82no—
261C2×C61—161no—
262C2×C61—161no—
263C2×C61#310011yescharacteristic
264C2×C61#341511yescharacteristic
265C2×C61#341611yescharacteristic
266D61—41no—
267C2×#135—611no—
268#540—1221no—
269#520—1221no—
270C2×SD32—611no—
271C2×SD32—611no—
272C2×D16C2×D6111yescharacteristic
273C2×D16C2×D6111yescharacteristic
274#499—611no—
275#493C2×D6111yescharacteristic
276#490—1221no—
277#469—1221no—
278#466—611no—
279#466—611no—
280#442—1221no—
281#440—1221no—
282#440—1221no—
283C4×Q16—611no—
284C4×Q16—611no—
285C4×D8—611no—
286C4×D8—611no—
287C4×D8—611no—
288C4×D8C2×D6111yescharacteristic
289C2×#107—611no—
290#417—1221no—
291#405—611no—
292#367—611no—
293#367—611no—
294#366—611no—
295#366—611no—
296C4⋊C16—611no—
297C4⋊C16C2×D6111yescharacteristic
298#358—611no—
299#358—611no—
300#357—611no—
301#357—611no—
302#357—611no—
303#357—611no—
304#357C2×D6111yescharacteristic
305#357C2×D6111yescharacteristic
306C22⋊C16—611no—
307C22⋊C16—611no—
308#346—611no—
309C4×C16—611no—
310C61#3367911yescharacteristic, complemented, Sylow
311C2×#41—1221no—
312#135—1222no—
313#135—1222no—
314C2×Q16—611no—
315C2×SD16—1221no—
316C2×D8—21no—
317C2×D8C22×D6111yescharacteristic
318C2×D8C22×D6111yescharacteristic
319C2×D8C22×D6111yescharacteristic
320C2×M16—611no—
321C22×C8—611no—
322#127—21no—
323#125—1221no—
324#123—2441no—
325#123—2441no—
326#121—1221no—
327#121—1221no—
328#121—2441no—
329#121—2441no—
330C4×Q8—1221no—
331C4×Q8—1221no—
332C4×D4—21no—
333C4×D4—1221no—
334C4×D4—1221no—
335C4×D4—1221no—
336C4×D4—2441no—
337C4×D4—2441no—
338#117—611no—
339#117—2441no—
340C2×C4⋊C4—1221no—
341C2×C4⋊C4—2441no—
342SD32—1222no—
343SD32—1222no—
344D16—22no—
345D16—22no—
346C2×C16—611no—
347C2×C16—611no—
348C2×C16C22×D6111yescharacteristic
349C2×C16C22×D6111yescharacteristic
350#107—611no—
351#107—611no—
352#107—611no—
353#107—1221no—
354#107C22×D6111yescharacteristic
355#106—1221no—
356#103—1221no—
357#103—1221no—
358#102—21no—
359#102—1221no—
360#102—1221no—
361#102—1221no—
362#102—1221no—
363#102—1221no—
364#97—611no—
365#97—611no—
366C4×C8—611no—
367C4×C8C22×D6111yescharacteristic
368#41—1224no—
369#41—2442no—
370C2×Q8—1221no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—2441no—
377C2×D4—2441no—
378C2×D4—2441no—
379C22×C4—41no—
380C22×C4—611no—
381C22×C4—2441no—
382C22×C4—2441no—
383C22×C4—2441no—
384C22×C4—2441no—
385C22×C4—2441no—
386Q16—612no—
387Q16—1221no—
388SD16—1224no—
389D8—21no—
390D8—21no—
391D8—21no—
392D8—21no—
393D8—21no—
394D8—42no—
395D8#1175822412yes—
396M16—2441no—
397C2×C8—611no—
398C2×C8—611no—
399C2×C8—1221no—
400C2×C8—1221no—
401C2×C8D4×D6111yescharacteristic
402C2×C8C23×D6111yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—611no—
405C4⋊C4—611no—
406C4⋊C4—1221no—
407C4⋊C4—1221no—
408C4⋊C4—1221no—
409C4⋊C4—2441no—
410C4⋊C4—2441no—
411C4⋊C4—2441no—
412C4⋊C4—2441no—
413C4⋊C4—2441no—
414C22⋊C4—41no—
415C22⋊C4—611no—
416C22⋊C4—611no—
417C22⋊C4—2441no—
418C22⋊C4—2441no—
419C22⋊C4—2441no—
420C22⋊C4—2441no—
421C22⋊C4—2441no—
422C42—611no—
423C42—2441no—
424C42—2441no—
425C42D4×D6111yescharacteristic
426C16—21no—
427C16—21no—
428C16—1221no—
429C16—1221no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—611no—
434Q8—1222no—
435Q8—2441no—
436D4—22no—
437D4—41no—
438D4—41no—
439D4—41no—
440D4—41no—
441D4—41no—
442D4—161no—
443D4—161no—
444D4—9761no—
445D4—9761no—
446D4—2444no—
447C2×C4—41no—
448C2×C4—161no—
449C2×C4—611no—
450C2×C4—611no—
451C2×C4—611no—
452C2×C4—1221no—
453C2×C4—1221no—
454C2×C4—9761no—
455C2×C4—9761no—
456C2×C4—9761no—
457C2×C4—9761no—
458C2×C4—2444no—
459C2×C4—2441no—
460C2×C4—2441no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4D8×D6111yescharacteristic
464C2×C4D8×D6111yescharacteristic
465C2×C4C2×D4×D6111yescharacteristic
466C8—21no—
467C8—1221no—
468C8—1221no—
469C8#41×D6111yescharacteristic
470C8C2×#1175822411yescharacteristic
471C22—42no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—1221no—
481C22—1221no—
482C22—1221no—
483C22C2×D8×D6111yescharacteristic
484C4—21no—
485C4—21no—
486C4—81no—
487C4—1221no—
488C4—1221no—
489C4—1221no—
490C4—4881no—
491C4—4881no—
492C4—4881no—
493C4—2442no—
494C4#1684027211yescharacteristic
495C4#1684055811yescharacteristic
496C2—82no—
497C2—161no—
498C2—161no—
499C2—2441no—
500C2#2145581811yescharacteristic
501C2#2145895611yescharacteristic
502C2#2145896511yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2206C2
socleC22×C61C22×D8
hypercenter#2206D61
hypocenterC61#33679
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #21456466C2semidirect
2. #21454689C2semidirect
3. #21448003C2semidirect
4. #21447998C2semidirect
5. #21447984C2semidirect
6. #21447976C2semidirect
7. #21447856C2semidirect
8. #21447739C2semidirect
9. #21447739C2semidirect
10. #21447695C2semidirect
11. #21447680C2semidirect
12. #21447674C2semidirect
13. D16×Dic61C2semidirect
14. #21447625C2semidirect
15. C61×#2206C2semidirect
252. #2206D61semidirect
310. C61#33679semidirect

Maximal subgroups

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

subgroupindex
#214564662
#214546892
#214480032
#214479982
#214479842
#214479762
#214478562
#214477392
#214476952
#214476802
#214476742
D16×Dic612
#214476252
C61×#22062
#3367961