Finite Group Databasebeta

← #29835140

Subgroups — #29835140

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#21456465C211yesmaximal, characteristic, complemented
2#21454689C211yesmaximal, characteristic, complemented
3#21448006C211yesmaximal, characteristic, complemented
4#21447998C211yesmaximal, characteristic, complemented
5#21447986C211yesmaximal, characteristic, complemented
6#21447974C211yesmaximal, characteristic, complemented
7#21447858C211yesmaximal, characteristic, complemented
8#21447852C211yesmaximal, characteristic, complemented
9#21447743C211yesmaximal, characteristic, complemented
10#21447739C211yesmaximal, characteristic, complemented
11#21447685C211yesmaximal, characteristic, complemented
12C4×#14519721C211yesmaximal, characteristic, complemented
13C4×#14519718C211yesmaximal, characteristic, complemented
14#21447627C211yesmaximal, characteristic, complemented
15C61×#2177C211yesmaximal, characteristic, complemented
16C2×#14519796C2211yescharacteristic
17#16840363—21no—
18#16840241—21no—
19C2×#14519722C2211yescharacteristic
20C2×#14519721C2211yescharacteristic
21C2×#14519718C2211yescharacteristic
22#16840163C2211yescharacteristic
23#16840137C2211yescharacteristic
24#16840125—21no—
25#16840014—21no—
26#16839999C2211yescharacteristic
27#16839995C2211yescharacteristic
28#16839872—21no—
29#16839862—21no—
30#16839859—21no—
31C4×Dic244C2211yescharacteristic
32#16839856C2211yescharacteristic
33C4×D488C2211yescharacteristic
34D8×Dic61C2211yescharacteristic
35#107×D61C2211yescharacteristic
36#16839760—21no—
37#16839716C2211yescharacteristic
38#16839589C2211yescharacteristic
39#16839588C2211yescharacteristic
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×#367C2211yescharacteristic
56C61×#357C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×#346C2211yescharacteristic
59C2×#11758224—21no—
60#14519796—22no—
61#14519796—22no—
62C2×Dic244C2311yescharacteristic
63C2×#11758200—21no—
64C2×D488C2311yescharacteristic
65C2×#11758199—21no—
66C2×#11758189D411yescharacteristic
67C2×C8×D61C2311yescharacteristic
68#14519773—21no—
69#14519768—21no—
70#14519760—41no—
71#14519759—41no—
72#14519752—21no—
73#14519751—41no—
74#14519750—41no—
75#14519748—21no—
76C4×Dic122—21no—
77#14519742—21no—
78C4×D244—21no—
79D4×Dic61—21no—
80C4×C22⋊D61—41no—
81#14519737—41no—
82#14519734D411yescharacteristic
83#14519733—41no—
84C2×#11758196—41no—
85C4⋊C4×D61—21no—
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—
101#14519688D411yescharacteristic
102#14519687D411yescharacteristic
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—
128C2×D244—21no—
129C2×D244—41no—
130C2×C4×D61—41no—
131C2×C4×D61—41no—
132C2×C4×D61C2×D411yescharacteristic
133C2×Dic122—21no—
134D8×C61—21no—
135D8×C61—21no—
136D8×C61—21no—
137D8×C61#4112yes—
138C2×C8×C61C2×D411yescharacteristic
139C2×C8×C61C2411yescharacteristic
140C4⋊C4×C61—21no—
141C4⋊C4×C61—21no—
142C22⋊C4×C61—41no—
143C22⋊C4×C61—41no—
144C42×C61C2×D411yescharacteristic
145C22⋊Dic61—41no—
146C22⋊Dic61—41no—
147#11758200—24no—
148#11758199—42no—
149#11758198—41no—
150#11758198—41no—
151#11758198D811yescharacteristic
152#11758198D811yescharacteristic
153C4⋊Dic61—21no—
154C4⋊Dic61—21no—
155C4⋊Dic61—41no—
156#11758196—41no—
157#11758196—41no—
158#11758196—41no—
159#11758196—41no—
160#11758196D811yescharacteristic
161#11758196D811yescharacteristic
162C4×Dic61—41no—
163C4×Dic61—41no—
164C4×Dic61C2×D411yescharacteristic
165C2×#92418C2×D411yescharacteristic
166C2×#92418C2×D411yescharacteristic
167Dic244—21no—
168Dic244#4112yes—
169D488—21no—
170D488—21no—
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—
180C22×D61—41no—
181C22×D61C2×D811yescharacteristic
182D4×C61—22no—
183D4×C61—41no—
184D4×C61—41no—
185D4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—161no—
189C2×C4×C61—161no—
190C2×C4×C61C2×D811yescharacteristic
191C2×C4×C61C2×D811yescharacteristic
192C2×C4×C61C22×D411yescharacteristic
193C22⋊D61—44no—
194C22⋊D61—161no—
195C22⋊D61—161no—
196C22⋊D61—161no—
197C2×Dic61—44no—
198C2×Dic61—41no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—161no—
202C2×Dic61C2×D811yescharacteristic
203C2×Dic61C2×D811yescharacteristic
204C2×Dic61C2×D811yescharacteristic
205D244—41no—
206D244—41no—
207D244—161no—
208C4×D61—21no—
209C4×D61—21no—
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×C61—81no—
224C22×C61—81no—
225C22×C61—81no—
226C22×C61C22×D811yescharacteristic
227C2×D61—21no—
228C2×D61—21no—
229C2×D61—21no—
230C2×D61—81no—
231C2×D61—81no—
232C2×D61—81no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—81no—
236C4×C61—81no—
237C4×C61#52511yescharacteristic
238C4×C61#57511yescharacteristic
239Dic61—21no—
240Dic61—21no—
241Dic61—21no—
242Dic61—42no—
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#2206—611no—
253#2186—611no—
254#2186—611no—
255#2177D6111yescharacteristic, complemented
256#2175—611no—
257C4×SD32—611no—
258C4×D16—611no—
259#2164—611no—
260C2×C61—82no—
261C2×C61—161no—
262C2×C61#310011yescharacteristic
263C2×C61#341511yescharacteristic
264C2×C61#341611yescharacteristic
265D61—41no—
266D61—161no—
267C2×#135—611no—
268#540—1221no—
269#520—1221no—
270C2×SD32—611no—
271C2×SD32—611no—
272C2×D16—611no—
273C2×D16C2×D6111yescharacteristic
274#499—611no—
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×D8C2×D6111yescharacteristic
288C4×D8C2×D6111yescharacteristic
289C2×#107—611no—
290#417—1221no—
291#405—611no—
292#367—611no—
293#367C2×D6111yescharacteristic
294#366—611no—
295#366—611no—
296C4⋊C16—611no—
297C4⋊C16—611no—
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#346C2×D6111yescharacteristic
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—1221no—
318C2×D8C22×D6111yescharacteristic
319C2×D8C22×D6111yescharacteristic
320C2×M16—611no—
321C22×C8—611no—
322#127—1221no—
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—21no—
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—1222no—
346C2×C16—611no—
347C2×C16—611no—
348C2×C16C22×D6111yescharacteristic
349C2×C16C22×D6111yescharacteristic
350#107—611no—
351#107—611no—
352#107—1221no—
353#107C22×D6111yescharacteristic
354#107C22×D6111yescharacteristic
355#106—1221no—
356#103—1221no—
357#103—1221no—
358#102—21no—
359#102—21no—
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—1221no—
374C2×D4—2441no—
375C2×D4—2441no—
376C2×D4—2441no—
377C2×D4—2441no—
378C2×D4—2441no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—611no—
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—1221no—
393D8—1221no—
394D8—2442no—
395D8#1175822212yes—
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—611no—
406C4⋊C4—611no—
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—41no—
416C22⋊C4—611no—
417C22⋊C4—611no—
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—611no—
433C23—2441no—
434Q8—1222no—
435Q8—2441no—
436D4—22no—
437D4—41no—
438D4—41no—
439D4—41no—
440D4—9761no—
441D4—9761no—
442D4—9761no—
443D4—9761no—
444D4—2444no—
445D4—2441no—
446D4—2441no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—161no—
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—2444no—
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×#1175822211yescharacteristic
471C22—42no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—1221no—
478C22—1221no—
479C22—1221no—
480C22—4881no—
481C22—4881no—
482C22—4881no—
483C22C2×D8×D6111yescharacteristic
484C4—21no—
485C4—21no—
486C4—81no—
487C4—81no—
488C4—1221no—
489C4—1221no—
490C4—1221no—
491C4—4881no—
492C4—4881no—
493C4—2442no—
494C4#1684027111yescharacteristic
495C4#1684055911yescharacteristic
496C2—82no—
497C2—161no—
498C2—9761no—
499C2—2441no—
500C2#2145581711yescharacteristic
501C2#2145895911yescharacteristic
502C2#2145896511yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2177C2
socleC22×C61C22×D8
hypercenter#2177D61
hypocenterC61#33679
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2177

Complements

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

NH ≅ G/Ntype
1. #21456465C2semidirect
2. #21454689C2semidirect
3. #21448006C2semidirect
4. #21447998C2semidirect
5. #21447986C2semidirect
6. #21447974C2semidirect
7. #21447858C2semidirect
8. #21447852C2semidirect
9. #21447743C2semidirect
10. #21447739C2semidirect
11. #21447685C2semidirect
12. C4×#14519721C2semidirect
13. C4×#14519718C2semidirect
14. #21447627C2semidirect
15. C61×#2177C2semidirect
255. #2177D61semidirect
310. C61#33679semidirect

Maximal subgroups

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

subgroupindex
#214564652
#214546892
#214480062
#214479982
#214479862
#214479742
#214478582
#214478522
#214477432
#214477392
#214476852
C4×#145197212
C4×#145197182
#214476272
C61×#21772
#3367961