Finite Group Databasebeta

← #29835141

Subgroups — #29835141

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#21456470C211yesmaximal, characteristic, complemented
2#21454689C211yesmaximal, characteristic, complemented
3#21448006C211yesmaximal, characteristic, complemented
4#21448001C211yesmaximal, characteristic, complemented
5#21447980C211yesmaximal, characteristic, complemented
6#21447860C211yesmaximal, characteristic, complemented
7#21447854C211yesmaximal, characteristic, complemented
8#21447743C211yesmaximal, characteristic, complemented
9#21447743C211yesmaximal, characteristic, complemented
10#21447692C211yesmaximal, characteristic, complemented
11#21447682C211yesmaximal, characteristic, complemented
12#21447670C211yesmaximal, characteristic, complemented
13#21447663C211yesmaximal, characteristic, complemented
14#21447625C211yesmaximal, characteristic, complemented
15C61×#2228C211yesmaximal, characteristic, complemented
16C2×#14519796C2211yescharacteristic
17#16840368—21no—
18#16840241—21no—
19C2×#14519722C2211yescharacteristic
20C2×#14519722C2211yescharacteristic
21C2×#14519718C2211yescharacteristic
22C2×#14519718C2211yescharacteristic
23#16840139C2211yescharacteristic
24#16840128—21no—
25#16840016—21no—
26#16839999C2211yescharacteristic
27#16839999C2211yescharacteristic
28#16839873—21no—
29#16839862—21no—
30#16839859—21no—
31C4×Dic244C2211yescharacteristic
32#16839856C2211yescharacteristic
33D8×Dic61C2211yescharacteristic
34#16839844C2211yescharacteristic
35#16839844C2211yescharacteristic
36#107×D61C2211yescharacteristic
37#16839760—21no—
38#16839716C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839587C2211yescharacteristic
41C4⋊#11758185C2211yescharacteristic
42#16839565C2211yescharacteristic
43#16839565C2211yescharacteristic
44#16839564C2211yescharacteristic
45#16839564C2211yescharacteristic
46#16839562C2211yescharacteristic
47#16839562C2211yescharacteristic
48#16839541C2211yescharacteristic
49#16839541C2211yescharacteristic
50#16839537C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#499C2211yescharacteristic
53C4×D8×C61C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×#11758224—21no—
60#14519796—22no—
61#14519796—22no—
62C2×Dic244C2311yescharacteristic
63C2×#11758200—21no—
64C2×D488—21no—
65C2×D488C2311yescharacteristic
66C2×D488C2311yescharacteristic
67C2×#11758189D411yescharacteristic
68C2×C8×D61C2311yescharacteristic
69#14519774—21no—
70#14519762—41no—
71#14519762—41no—
72#14519752—21no—
73#14519752—21no—
74#14519752—41no—
75#14519752—41no—
76C4×Dic122—21no—
77#14519742—21no—
78D4×Dic61—21no—
79#14519739—21no—
80#14519739—21no—
81C4×C22⋊D61—41no—
82#14519737—41no—
83#14519734D411yescharacteristic
84#14519733—41no—
85C2×#11758196—41no—
86C4⋊C4×D61—21no—
87#14519722—22no—
88#14519722—22no—
89#14519718—22no—
90#14519718—22no—
91C2×#11758185C2311yescharacteristic
92C2×#11758185C2311yescharacteristic
93#14519711C2311yescharacteristic
94#14519710—21no—
95#14519702—21no—
96#14519700—21no—
97#14519698—21no—
98#14519697—21no—
99#14519697—21no—
100#14519697—21no—
101#14519697—21no—
102#14519688D411yescharacteristic
103#14519687D411yescharacteristic
104C8×Dic61C2311yescharacteristic
105C2×D8×C61C2311yescharacteristic
106#125×C61—21no—
107C4×D4×C61—21no—
108C2×C16×C61C2311yescharacteristic
109C2×C16×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#106×C61—21no—
114#102×C61—21no—
115C4×C8×C61C2311yescharacteristic
116C2×D4×C61—21no—
117C22×C4×C61—41no—
118C2×C22⋊D61—41no—
119C22×Dic61—41no—
120C22×Dic61—41no—
121#11758224—24no—
122#11758224—42no—
123C2×D244—21no—
124C2×D244—21no—
125C2×D244—41no—
126C2×D244—41no—
127C2×D244—41no—
128C2×D244—41no—
129C2×C4×D61—41no—
130C2×C4×D61—41no—
131C2×C4×D61—41no—
132C2×C4×D61C2×D411yescharacteristic
133C2×Dic122—21no—
134D8×C61—21no—
135D8×C61#4112yes—
136C2×C8×C61C2×D411yescharacteristic
137C2×C8×C61C2411yescharacteristic
138C4⋊C4×C61—21no—
139C4⋊C4×C61—21no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—41no—
142C4⋊C4×C61—41no—
143C22⋊C4×C61—41no—
144C42×C61C2×D411yescharacteristic
145C22⋊Dic61—41no—
146#11758200—24no—
147#11758198—41no—
148#11758198—41no—
149#11758198—41no—
150#11758198—41no—
151#11758198D811yescharacteristic
152#11758198D811yescharacteristic
153C4⋊Dic61—21no—
154#11758196—41no—
155#11758196—41no—
156#11758196—41no—
157#11758196D811yescharacteristic
158#11758196D811yescharacteristic
159C4×Dic61—41no—
160C4×Dic61—41no—
161C4×Dic61C2×D411yescharacteristic
162C2×#92418C2×D411yescharacteristic
163C2×#92418C2×D411yescharacteristic
164Dic244—21no—
165Dic244#4112yes—
166D488—21no—
167D488—21no—
168D488—21no—
169D488—21no—
170D488—42no—
171#11758189—41no—
172C8×D61—21no—
173C8×D61—21no—
174C16×C61—21no—
175C16×C61—21no—
176#11758185—21no—
177#11758185—21no—
178C23×C61—41no—
179C22×D61—41no—
180C22×D61—41no—
181C22×D61C2×D811yescharacteristic
182D4×C61—22no—
183D4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—161no—
188C2×C4×C61C2×D811yescharacteristic
189C2×C4×C61C2×D811yescharacteristic
190C2×C4×C61C22×D411yescharacteristic
191C22⋊D61—44no—
192C2×Dic61—44no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—161no—
196C2×Dic61C2×D811yescharacteristic
197C2×Dic61C2×D811yescharacteristic
198C2×Dic61C2×D811yescharacteristic
199D244—41no—
200D244—41no—
201D244—41no—
202D244—41no—
203D244—161no—
204D244—161no—
205D244—161no—
206D244—161no—
207C4×D61—21no—
208C4×D61—21no—
209C4×D61—161no—
210C4×D61—161no—
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×C61C22×D811yescharacteristic
224C2×D61—21no—
225C2×D61—21no—
226C2×D61—21no—
227C2×D61—81no—
228C2×D61—81no—
229C2×D61—81no—
230C2×D61—81no—
231C2×D61—81no—
232C2×D61—81no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—81no—
236C4×C61—81no—
237C4×C61—81no—
238C4×C61#52511yescharacteristic
239C4×C61#57511yescharacteristic
240Dic61—21no—
241Dic61—21no—
242Dic61—21no—
243Dic61—42no—
244Dic61—81no—
245#3176—611no—
246#2951—611no—
247#2233—611no—
248#2232—611no—
249#2229—611no—
250#2228D6111yescharacteristic, complemented
251#2207—611no—
252#2206—611no—
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#310011yescharacteristic
262C2×C61#341511yescharacteristic
263C2×C61#341611yescharacteristic
264D61—41no—
265D61—161no—
266D61—161no—
267C2×#135—611no—
268#540—1221no—
269#520—1221no—
270C2×SD32—611no—
271C2×SD32—611no—
272C2×D16—611no—
273C2×D16—611no—
274#499C2×D6111yescharacteristic
275#493—611no—
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#367C2×D6111yescharacteristic
294#366—611no—
295#366C2×D6111yescharacteristic
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—611no—
317C2×D8—611no—
318C2×D8—1221no—
319C2×D8C22×D6111yescharacteristic
320C2×M16—611no—
321C22×C8—611no—
322#127—1221no—
323#125—21no—
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—1222no—
345D16—1222no—
346C2×C16—611no—
347C2×C16—611no—
348C2×C16C22×D6111yescharacteristic
349C2×C16C22×D6111yescharacteristic
350#107—611no—
351#107—1221no—
352#107C22×D6111yescharacteristic
353#107C22×D6111yescharacteristic
354#107C22×D6111yescharacteristic
355#106—21no—
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—1221no—
373C2×D4—1221no—
374C2×D4—2441no—
375C2×D4—2441no—
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—1221no—
391D8—1221no—
392D8—1221no—
393D8—1221no—
394D8—2442no—
395D8#1175822612yes—
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—21no—
405C4⋊C4—21no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—611no—
409C4⋊C4—611no—
410C4⋊C4—1221no—
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—611no—
432C23—2441no—
433C23—2441no—
434Q8—1222no—
435Q8—2441no—
436D4—22no—
437D4—41no—
438D4—9761no—
439D4—9761no—
440D4—9761no—
441D4—9761no—
442D4—2444no—
443D4—2441no—
444D4—2441no—
445D4—2441no—
446D4—2441no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—161no—
451C2×C4—611no—
452C2×C4—611no—
453C2×C4—611no—
454C2×C4—1221no—
455C2×C4—1221no—
456C2×C4—9761no—
457C2×C4—9761no—
458C2×C4—9761no—
459C2×C4—9761no—
460C2×C4—2444no—
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×#1175822611yescharacteristic
471C22—42no—
472C22—81no—
473C22—81no—
474C22—1221no—
475C22—1221no—
476C22—1221no—
477C22—4881no—
478C22—4881no—
479C22—4881no—
480C22—4881no—
481C22—4881no—
482C22—4881no—
483C22C2×D8×D6111yescharacteristic
484C4—21no—
485C4—21no—
486C4—81no—
487C4—81no—
488C4—81no—
489C4—1221no—
490C4—1221no—
491C4—1221no—
492C4—4881no—
493C4—2442no—
494C4#1684027511yescharacteristic
495C4#1684056111yescharacteristic
496C2—82no—
497C2—9761no—
498C2—9761no—
499C2—2441no—
500C2#2145582111yescharacteristic
501C2#2145895911yescharacteristic
502C2#2145896211yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2228C2
socleC22×C61C22×D8
hypercenter#2228D61
hypocenterC61#33679
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #21456470C2semidirect
2. #21454689C2semidirect
3. #21448006C2semidirect
4. #21448001C2semidirect
5. #21447980C2semidirect
6. #21447860C2semidirect
7. #21447854C2semidirect
8. #21447743C2semidirect
9. #21447743C2semidirect
10. #21447692C2semidirect
11. #21447682C2semidirect
12. #21447670C2semidirect
13. #21447663C2semidirect
14. #21447625C2semidirect
15. C61×#2228C2semidirect
250. #2228D61semidirect
310. C61#33679semidirect

Maximal subgroups

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

subgroupindex
#214564702
#214546892
#214480062
#214480012
#214479802
#214478602
#214478542
#214477432
#214476922
#214476822
#214476702
#214476632
#214476252
C61×#22282
#3367961