Finite Group Databasebeta

← #29835136

Subgroups — #29835136

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#21456469C211yesmaximal, characteristic, complemented
2#21448004C211yesmaximal, characteristic, complemented
3#21447999C211yesmaximal, characteristic, complemented
4#21447983C211yesmaximal, characteristic, complemented
5#21447976C211yesmaximal, characteristic, complemented
6#21447859C211yesmaximal, characteristic, complemented
7#21447854C211yesmaximal, characteristic, complemented
8#21447742C211yesmaximal, characteristic, complemented
9#21447742C211yesmaximal, characteristic, complemented
10#21447693C211yesmaximal, characteristic, complemented
11#21447681C211yesmaximal, characteristic, complemented
12C4×#14519720C211yesmaximal, characteristic, complemented
13C4×#14519718C211yesmaximal, characteristic, complemented
14#21447626C211yesmaximal, characteristic, complemented
15C61×#2951C211yesmaximal, characteristic, complemented
16#16840367—21no—
17C2×#14519720C2211yescharacteristic
18C2×#14519720C2211yescharacteristic
19C2×#14519718C2211yescharacteristic
20C2×#14519718C2211yescharacteristic
21#16840164C2211yescharacteristic
22#16840139C2211yescharacteristic
23#16840127—21no—
24#16840015—21no—
25#16839998C2211yescharacteristic
26#16839998C2211yescharacteristic
27#16839875—21no—
28C4×D488C2211yescharacteristic
29C4×D488C2211yescharacteristic
30#16839589C2211yescharacteristic
31#16839589C2211yescharacteristic
32#16839587C2211yescharacteristic
33#16839587C2211yescharacteristic
34C4⋊#11758185C2211yescharacteristic
35C4⋊#11758185C2211yescharacteristic
36#16839566C2211yescharacteristic
37#16839566C2211yescharacteristic
38#16839563C2211yescharacteristic
39#16839563C2211yescharacteristic
40#16839562C2211yescharacteristic
41#16839562C2211yescharacteristic
42#16839562C2211yescharacteristic
43#16839562C2211yescharacteristic
44C22⋊#11758185C2211yescharacteristic
45C22⋊#11758185C2211yescharacteristic
46#16839538C2211yescharacteristic
47C4×#11758185C2211yescharacteristic
48C2×#135×C61C2211yescharacteristic
49C61×#520—21no—
50C61×#440—21no—
51C61×#440—21no—
52C4×Q16×C61C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic
54C4×D8×C61C2211yescharacteristic
55C4×D8×C61C2211yescharacteristic
56C2×#107×C61C2211yescharacteristic
57C61×#417—21no—
58C61×#405C2211yescharacteristic
59C2×D488—21no—
60C2×D488C2311yescharacteristic
61C2×D488C2311yescharacteristic
62#14519774—21no—
63#14519769—21no—
64#14519762—41no—
65#14519762—41no—
66#14519751—21no—
67#14519751—21no—
68#14519750—41no—
69#14519750—41no—
70C4×D244—21no—
71C4×D244—21no—
72#14519720—22no—
73#14519720—22no—
74#14519718—22no—
75#14519718—22no—
76C2×#11758185C2311yescharacteristic
77C2×#11758185C2311yescharacteristic
78C2×#11758185C2311yescharacteristic
79C2×#11758185C2311yescharacteristic
80#14519711C2311yescharacteristic
81#14519711C2311yescharacteristic
82#14519709—21no—
83#14519699—21no—
84#14519699—21no—
85#14519699—21no—
86#14519699—21no—
87C2×#41×C61—21no—
88#135×C61—22no—
89#135×C61—22no—
90C2×Q16×C61C2311yescharacteristic
91C2×SD16×C61—21no—
92C2×D8×C61C2311yescharacteristic
93C2×M16×C61D411yescharacteristic
94C22×C8×C61C2311yescharacteristic
95C4×Q8×C61—21no—
96C4×Q8×C61—21no—
97C4×D4×C61—21no—
98C4×D4×C61—21no—
99C4×D4×C61—41no—
100C4×D4×C61—41no—
101#117×C61—41no—
102#117×C61D411yescharacteristic
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61—41no—
105#107×C61—21no—
106#107×C61C2311yescharacteristic
107#107×C61C2311yescharacteristic
108#103×C61—21no—
109#103×C61—21no—
110#102×C61—21no—
111#102×C61—21no—
112#97×C61D411yescharacteristic
113#97×C61D411yescharacteristic
114C4×C8×C61C2311yescharacteristic
115C4×C8×C61C2311yescharacteristic
116#41×C61—24no—
117#41×C61—42no—
118C2×Q8×C61—21no—
119C2×D4×C61—21no—
120C2×D4×C61—41no—
121C22×C4×C61—41no—
122C22×C4×C61—41no—
123C22×C4×C61—41no—
124C22×C4×C61—41no—
125C22×C4×C61C2×D411yescharacteristic
126C2×C22⋊D61—41no—
127C2×C22⋊D61—41no—
128C2×D244—21no—
129C2×D244—21no—
130C2×D244—41no—
131C2×D244—41no—
132C2×C4×D61—41no—
133C2×C4×D61—41no—
134Q16×C61—21no—
135Q16×C61#4112yes—
136SD16×C61—24no—
137D8×C61—21no—
138D8×C61#4112yes—
139M16×C61—41no—
140C2×C8×C61—21no—
141C2×C8×C61—21no—
142C2×C8×C61C2×D411yescharacteristic
143C2×C8×C61C2×D411yescharacteristic
144C2×C8×C61C2×D411yescharacteristic
145C2×C8×C61C2411yescharacteristic
146C4⋊C4×C61—21no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—41no—
149C4⋊C4×C61—41no—
150C4⋊C4×C61—41no—
151C4⋊C4×C61D811yescharacteristic
152C4⋊C4×C61D811yescharacteristic
153C22⋊C4×C61—41no—
154C22⋊C4×C61—41no—
155C22⋊C4×C61D811yescharacteristic
156C22⋊C4×C61D811yescharacteristic
157C42×C61—41no—
158C42×C61—41no—
159C42×C61C2×D411yescharacteristic
160C42×C61C2×D411yescharacteristic
161#11758198—41no—
162#11758198—41no—
163#11758198—41no—
164#11758198—41no—
165C4⋊Dic61—21no—
166C4⋊Dic61—21no—
167#11758196—41no—
168#11758196—41no—
169D488—21no—
170D488—21no—
171D488—21no—
172D488—21no—
173D488—42no—
174#11758185—21no—
175#11758185—21no—
176#11758185—21no—
177#11758185—21no—
178C23×C61—41no—
179C23×C61C2×D811yescharacteristic
180C22×D61—41no—
181C22×D61—41no—
182Q8×C61—22no—
183Q8×C61—41no—
184D4×C61—22no—
185D4×C61—44no—
186D4×C61—41no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—44no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—161no—
194C2×C4×C61—161no—
195C2×C4×C61—161no—
196C2×C4×C61C2×D811yescharacteristic
197C2×C4×C61C2×D811yescharacteristic
198C2×C4×C61C2×D811yescharacteristic
199C2×C4×C61C2×D811yescharacteristic
200C2×C4×C61C2×D811yescharacteristic
201C2×C4×C61C22×D411yescharacteristic
202C22⋊D61—161no—
203C22⋊D61—161no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206D244—41no—
207D244—41no—
208D244—41no—
209D244—41no—
210D244—161no—
211D244—161no—
212C4×D61—161no—
213C4×D61—161no—
214C8×C61—21no—
215C8×C61—21no—
216C8×C61—21no—
217C8×C61C2×#4111yescharacteristic
218C8×C61C2×#4111yescharacteristic
219#33679—611nomaximal, Sylow
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—42no—
224C22×C61—81no—
225C22×C61—81no—
226C22×C61C22×D811yescharacteristic
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—21no—
236C4×C61—21no—
237C4×C61—21no—
238C4×C61—42no—
239C4×C61—81no—
240C4×C61—81no—
241C4×C61#52511yescharacteristic
242C4×C61#57511yescharacteristic
243Dic61—81no—
244Dic61—81no—
245#3176—611no—
246#2951D6111yescharacteristic, complemented
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#2177—611no—
256#2175—611no—
257C4×SD32—611no—
258C4×D16—611no—
259#2164—611no—
260C2×C61—41no—
261C2×C61—82no—
262C2×C61#310011yescharacteristic
263C2×C61#341511yescharacteristic
264C2×C61#341611yescharacteristic
265D61—161no—
266D61—161no—
267C2×#135C2×D6111yescharacteristic
268#540—1221no—
269#520—21no—
270C2×SD32—611no—
271C2×SD32—611no—
272C2×D16—611no—
273C2×D16—611no—
274#499—611no—
275#493—611no—
276#490—1221no—
277#469—1221no—
278#466—611no—
279#466—611no—
280#442—1221no—
281#440—21no—
282#440—21no—
283C4×Q16C2×D6111yescharacteristic
284C4×Q16C2×D6111yescharacteristic
285C4×D8—611no—
286C4×D8—611no—
287C4×D8C2×D6111yescharacteristic
288C4×D8C2×D6111yescharacteristic
289C2×#107C2×D6111yescharacteristic
290#417—21no—
291#405C2×D6111yescharacteristic
292#367—611no—
293#367—611no—
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#357—611no—
305#357—611no—
306C22⋊C16—611no—
307C22⋊C16—611no—
308#346—611no—
309C4×C16—611no—
310C61#3367911yescharacteristic, complemented, Sylow
311C2×#41—21no—
312#135—22no—
313#135—22no—
314C2×Q16C22×D6111yescharacteristic
315C2×SD16—21no—
316C2×D8—611no—
317C2×D8—611no—
318C2×D8—1221no—
319C2×D8C22×D6111yescharacteristic
320C2×M16C22⋊D6111yescharacteristic
321C22×C8C22×D6111yescharacteristic
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—21no—
331C4×Q8—21no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—41no—
335C4×D4—41no—
336C4×D4—1221no—
337C4×D4—1221no—
338#117—41no—
339#117C22⋊D6111yescharacteristic
340C2×C4⋊C4—21no—
341C2×C4⋊C4—41no—
342SD32—1222no—
343SD32—1222no—
344D16—1222no—
345D16—1222no—
346C2×C16—611no—
347C2×C16—611no—
348C2×C16—611no—
349C2×C16—611no—
350#107—21no—
351#107—611no—
352#107—611no—
353#107C22×D6111yescharacteristic
354#107C22×D6111yescharacteristic
355#106—1221no—
356#103—21no—
357#103—21no—
358#102—21no—
359#102—21no—
360#102—1221no—
361#102—1221no—
362#102—1221no—
363#102—1221no—
364#97C22⋊D6111yescharacteristic
365#97C22⋊D6111yescharacteristic
366C4×C8C22×D6111yescharacteristic
367C4×C8C22×D6111yescharacteristic
368#41—24no—
369#41—42no—
370C2×Q8—21no—
371C2×D4—21no—
372C2×D4—41no—
373C2×D4—1221no—
374C2×D4—1221no—
375C2×D4—2441no—
376C2×D4—2441no—
377C2×D4—2441no—
378C2×D4—2441no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—2441no—
384C22×C4—2441no—
385C22×C4C2×C22⋊D6111yescharacteristic
386Q16—21no—
387Q16#1175822212yes—
388SD16—24no—
389D8—21no—
390D8—1221no—
391D8—1221no—
392D8—1221no—
393D8—1221no—
394D8—2442no—
395D8#1175822212yes—
396M16—41no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8C2×C22⋊D6111yescharacteristic
400C2×C8C2×C22⋊D6111yescharacteristic
401C2×C8C2×C22⋊D6111yescharacteristic
402C2×C8C23×D6111yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—1221no—
409C4⋊C4—1221no—
410C4⋊C4—2441no—
411C4⋊C4—2441no—
412C4⋊C4#1175819911yescharacteristic
413C4⋊C4#1175819911yescharacteristic
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—2441no—
417C22⋊C4—2441no—
418C22⋊C4—2441no—
419C22⋊C4—2441no—
420C22⋊C4#1175819911yescharacteristic
421C22⋊C4#1175819911yescharacteristic
422C42—41no—
423C42—41no—
424C42C2×C22⋊D6111yescharacteristic
425C42C2×C22⋊D6111yescharacteristic
426C16—1221no—
427C16—1221no—
428C16—1221no—
429C16—1221no—
430C23—41no—
431C23—2441no—
432C23—2441no—
433C23C2×#1175819911yescharacteristic
434Q8—22no—
435Q8—41no—
436D4—22no—
437D4—44no—
438D4—41no—
439D4—9761no—
440D4—9761no—
441D4—9761no—
442D4—9761no—
443D4—2441no—
444D4—2441no—
445D4—2441no—
446D4—2441no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—44no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—161no—
454C2×C4—161no—
455C2×C4—161no—
456C2×C4—9761no—
457C2×C4—9761no—
458C2×C4—2441no—
459C2×C4—2441no—
460C2×C4C2×#1175819911yescharacteristic
461C2×C4C2×#1175819911yescharacteristic
462C2×C4C2×#1175819911yescharacteristic
463C2×C4C2×#1175819911yescharacteristic
464C2×C4C2×#1175819911yescharacteristic
465C2×C4C22×C22⋊D6111yescharacteristic
466C8—21no—
467C8—21no—
468C8—21no—
469C8C2×#1175822211yescharacteristic
470C8C2×#1175822211yescharacteristic
471C22—21no—
472C22—21no—
473C22—21no—
474C22—42no—
475C22—81no—
476C22—81no—
477C22—4881no—
478C22—4881no—
479C22—4881no—
480C22—4881no—
481C22—4881no—
482C22—4881no—
483C22C22×#1175819911yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—42no—
490C4—81no—
491C4—81no—
492C4—4881no—
493C4—4881no—
494C4#1684027311yescharacteristic
495C4#1684056011yescharacteristic
496C2—41no—
497C2—82no—
498C2—9761no—
499C2—9761no—
500C2#2145581911yescharacteristic
501C2#2145895811yescharacteristic
502C2#2145896311yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2951C2
socleC22×C61C22×D8
hypercenter#2951D61
hypocenterC61#33679
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
1. #21456469C2semidirect
2. #21448004C2semidirect
3. #21447999C2semidirect
4. #21447983C2semidirect
5. #21447976C2semidirect
6. #21447859C2semidirect
7. #21447854C2semidirect
8. #21447742C2semidirect
9. #21447742C2semidirect
10. #21447693C2semidirect
11. #21447681C2semidirect
12. C4×#14519720C2semidirect
13. C4×#14519718C2semidirect
14. #21447626C2semidirect
15. C61×#2951C2semidirect
246. #2951D61semidirect
310. C61#33679semidirect

Maximal subgroups

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

subgroupindex
#214564692
#214480042
#214479992
#214479832
#214479762
#214478592
#214478542
#214477422
#214476932
#214476812
C4×#145197202
C4×#145197182
#214476262
C61×#29512
#3367961