Finite Group Databasebeta

← #29837023

Subgroups — #29837023

Order 15616.

564 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457579C211yesmaximal, characteristic, complemented
2#21448062C211yesmaximal, characteristic, complemented
3#21448010C211yesmaximal, characteristic, complemented
4#21447999C211yesmaximal, characteristic, complemented
5#21447980C211yesmaximal, characteristic, complemented
6#21447920C211yesmaximal, characteristic, complemented
7#21447903C211yesmaximal, characteristic, complemented
8#21447854C211yesmaximal, characteristic, complemented
9#21447740C211yesmaximal, characteristic, complemented
10#21447740C211yesmaximal, characteristic, complemented
11#21447683C211yesmaximal, characteristic, complemented
12#21447645C211yesmaximal, characteristic, complemented
13#21447529C211yesmaximal, characteristic, complemented
14#21447524C211yesmaximal, characteristic, complemented
15C61×#3339C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17C2×#14519799C2211yescharacteristic
18#16840433—21no—
19C2×#14519721C2211yescharacteristic
20C2×#14519718C2211yescharacteristic
21C2×#14519718C2211yescharacteristic
22C2×#14519717C2211yescharacteristic
23C22×#11758185C2211yescharacteristic
24#16840139C2211yescharacteristic
25#16839998C2211yescharacteristic
26#16839998C2211yescharacteristic
27#16839963—21no—
28#16839909—21no—
29#16839909—21no—
30C4×Dic244C2211yescharacteristic
31#16839589C2211yescharacteristic
32#16839587C2211yescharacteristic
33#16839587C2211yescharacteristic
34C4⋊#11758185C2211yescharacteristic
35#16839565C2211yescharacteristic
36#16839565C2211yescharacteristic
37#16839565C2211yescharacteristic
38#16839563C2211yescharacteristic
39#16839562C2211yescharacteristic
40#16839562C2211yescharacteristic
41#16839562C2211yescharacteristic
42#16839562C2211yescharacteristic
43#16839562C2211yescharacteristic
44#16839562C2211yescharacteristic
45C22⋊#11758185C2211yescharacteristic
46C22⋊#11758185C2211yescharacteristic
47#16839538C2211yescharacteristic
48C61×#553—21no—
49C61×#499C2211yescharacteristic
50C61×#482—21no—
51C61×#481—21no—
52C61×#478—21no—
53C61×#466C2211yescharacteristic
54C61×#466C2211yescharacteristic
55C4×D8×C61C2211yescharacteristic
56C8×D4×C61C2211yescharacteristic
57C61×#427C2211yescharacteristic
58C2×#107×C61C2211yescharacteristic
59C2×#11758222—21no—
60C2×#11758222—21no—
61#14519799—22no—
62#14519799—22no—
63#14519799—41no—
64#14519799—41no—
65C2×Dic244C2311yescharacteristic
66C2×#11758190—21no—
67C2×#11758190—21no—
68C2×D488—21no—
69C2×D488C2311yescharacteristic
70C2×D488C2311yescharacteristic
71#14519774—21no—
72#14519773—41no—
73#14519751—21no—
74#14519751—21no—
75#14519750—41no—
76#14519750—41no—
77C4×Dic122—21no—
78#14519739—41no—
79#14519721—22no—
80#14519718—41no—
81#14519718—41no—
82#14519717—41no—
83C2×#11758185—41no—
84C2×#11758185C2311yescharacteristic
85C2×#11758185C2311yescharacteristic
86C2×#11758185C2311yescharacteristic
87C2×#11758185C2311yescharacteristic
88#14519711C2311yescharacteristic
89#14519702—21no—
90#14519699—21no—
91#14519699—21no—
92C2×D8×C61C2311yescharacteristic
93C22×C8×C61C2311yescharacteristic
94C22×C8×C61C2311yescharacteristic
95#126×C61—41no—
96#125×C61—21no—
97#123×C61—41no—
98#121×C61—21no—
99#121×C61—21no—
100#121×C61—41no—
101C4×D4×C61—21no—
102C4×D4×C61—41no—
103C4×D4×C61D411yescharacteristic
104#117×C61—21no—
105C2×C4⋊C4×C61—21no—
106#107×C61—21no—
107#107×C61C2311yescharacteristic
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#106×C61—21no—
111#106×C61—21no—
112C4⋊C8×C61D411yescharacteristic
113#102×C61—21no—
114#102×C61—21no—
115#102×C61—21no—
116C22⋊C8×C61D411yescharacteristic
117C22⋊C8×C61D411yescharacteristic
118C4×C8×C61C2311yescharacteristic
119C2×D4×C61—21no—
120C2×D4×C61—41no—
121C2×D4×C61—41no—
122C2×D4×C61D811yescharacteristic
123C22×C4×C61—41no—
124C22×C4×C61—41no—
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C2×C22⋊D61—41no—
128C2×C22⋊D61—41no—
129C2×C22⋊D61—41no—
130C2×C22⋊D61—41no—
131#11758222—42no—
132#11758222—42no—
133#11758222—81no—
134#11758222—81no—
135C2×D244—21no—
136C2×D244—21no—
137C2×D244—41no—
138C2×D244—41no—
139C2×C4×D61—41no—
140C2×C4×D61—41no—
141C2×Dic122—21no—
142D8×C61—21no—
143D8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—21no—
147C2×C8×C61—21no—
148C2×C8×C61C2×D411yescharacteristic
149C2×C8×C61C2×D411yescharacteristic
150C2×C8×C61C2×D411yescharacteristic
151C2×C8×C61C2411yescharacteristic
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—41no—
156C4⋊C4×C61—41no—
157C4⋊C4×C61—41no—
158C4⋊C4×C61D811yescharacteristic
159C22⋊C4×C61—41no—
160C22⋊C4×C61—41no—
161C22⋊C4×C61—41no—
162C22⋊C4×C61—41no—
163C22⋊C4×C61D811yescharacteristic
164C22⋊C4×C61D811yescharacteristic
165C42×C61—41no—
166C42×C61C2×D411yescharacteristic
167#11758198—41no—
168#11758198—41no—
169C4⋊Dic61—21no—
170#11758196—41no—
171C4×Dic61—41no—
172Dic244—21no—
173Dic244#4112yes—
174D488—21no—
175D488—21no—
176D488—21no—
177D488—21no—
178D488—81no—
179#11758190—42no—
180#11758190—42no—
181#11758185—21no—
182#11758185—21no—
183#11758185—21no—
184#11758185—21no—
185C23×C61—41no—
186C23×C61C2×D811yescharacteristic
187C23×C61C2×D811yescharacteristic
188C22×D61—41no—
189C22×D61—41no—
190D4×C61—41no—
191D4×C61—41no—
192D4×C61—41no—
193D4×C61—82no—
194D4×C61—161no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—21no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—161no—
203C2×C4×C61—161no—
204C2×C4×C61C2×D811yescharacteristic
205C2×C4×C61C2×D811yescharacteristic
206C2×C4×C61C2×D811yescharacteristic
207C2×C4×C61C2×D811yescharacteristic
208C2×C4×C61C22×D411yescharacteristic
209C22⋊D61—82no—
210C22⋊D61—82no—
211C22⋊D61—161no—
212C22⋊D61—161no—
213C2×Dic61—41no—
214C2×Dic61—41no—
215D244—41no—
216D244—41no—
217D244—41no—
218D244—41no—
219D244—82no—
220D244—161no—
221C4×D61—82no—
222C4×D61—82no—
223Dic122—22no—
224Dic122—41no—
225C8×C61—21no—
226C8×C61—21no—
227C8×C61—21no—
228C8×C61C2×#4111yescharacteristic
229C8×C61H(5,𝔽2)11yescharacteristic
230#33876—611nomaximal, Sylow
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—81no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61C22×D811yescharacteristic
241C2×D61—81no—
242C2×D61—81no—
243C2×D61—81no—
244C2×D61—81no—
245C2×D61—81no—
246C2×D61—81no—
247C4×C61—21no—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61—21no—
251C4×C61—81no—
252C4×C61—81no—
253C4×C61—81no—
254C4×C61#54611yescharacteristic
255C4×C61#57711yescharacteristic
256Dic61—42no—
257Dic61—81no—
258#3339D6111yescharacteristic, complemented
259#3287—611no—
260#2244—611no—
261#2234—611no—
262#2232—611no—
263#2229—611no—
264#2218—611no—
265#2215—611no—
266#2206—611no—
267#2186—611no—
268#2186—611no—
269#2175—611no—
270#2168—611no—
271#2139—611no—
272#2138—611no—
273C2×C61—41no—
274C2×C61—41no—
275C2×C61—161no—
276C2×C61#329411yescharacteristic
277C2×C61#341411yescharacteristic
278C2×C61#341511yescharacteristic
279D61—161no—
280D61—161no—
281C2×#135—611no—
282C2×#135—611no—
283#553—21no—
284#550—1221no—
285C2×SD32—611no—
286C2×D16—611no—
287C2×D16—611no—
288C2×M32—611no—
289C22×C16—611no—
290#499C2×D6111yescharacteristic
291#493—611no—
292#482—21no—
293#481—21no—
294#478—21no—
295#466—611no—
296#466—611no—
297#466C2×D6111yescharacteristic
298#466C2×D6111yescharacteristic
299#460—1221no—
300#449—1221no—
301#449—1221no—
302C4×Q16—611no—
303C4×D8C2×D6111yescharacteristic
304C8×D4C2×D6111yescharacteristic
305#427C2×D6111yescharacteristic
306C2×#107C2×D6111yescharacteristic
307#367—611no—
308#366—611no—
309#366—611no—
310C4⋊C16—611no—
311#358—611no—
312#358—611no—
313#358—611no—
314#357—611no—
315#357—611no—
316#357—611no—
317#357—611no—
318#357—611no—
319#357—611no—
320#357—611no—
321C22⋊C16—611no—
322C22⋊C16—611no—
323#346—611no—
324C61#3387611yescharacteristic, complemented, Sylow
325C2×#41—1221no—
326C2×#41—1221no—
327#135—1222no—
328#135—1222no—
329#135—2441no—
330#135—2441no—
331C2×Q16—611no—
332C2×SD16—1221no—
333C2×SD16—1221no—
334C2×D8—611no—
335C2×D8—611no—
336C2×D8—1221no—
337C2×D8C22×D6111yescharacteristic
338C22×C8C22×D6111yescharacteristic
339C22×C8C22×D6111yescharacteristic
340#127—1221no—
341#127—2441no—
342#126—41no—
343#125—21no—
344#123—41no—
345#121—21no—
346#121—21no—
347#121—41no—
348#121—1221no—
349#121—1221no—
350#121—2441no—
351#121—2441no—
352C4×Q8—1221no—
353C4×D4—21no—
354C4×D4—41no—
355C4×D4—2441no—
356C4×D4C22⋊D6111yescharacteristic
357#117—21no—
358C2×C4⋊C4—21no—
359SD32—1222no—
360D16—2441no—
361D16—2441no—
362M32—2441no—
363C2×C16—611no—
364C2×C16—611no—
365C2×C16—611no—
366C2×C16—611no—
367C2×C16—2441no—
368#107—21no—
369#107—611no—
370#107C22×D6111yescharacteristic
371#107C22×D6111yescharacteristic
372#107C22×D6111yescharacteristic
373#106—21no—
374#106—21no—
375C4⋊C8C22⋊D6111yescharacteristic
376#103—1221no—
377#102—21no—
378#102—21no—
379#102—21no—
380#102—1221no—
381#102—1221no—
382C22⋊C8C22⋊D6111yescharacteristic
383C22⋊C8C22⋊D6111yescharacteristic
384C4×C8C22×D6111yescharacteristic
385#41—4881no—
386#41—4881no—
387#41—2442no—
388#41—2442no—
389C2×Q8—1221no—
390C2×D4—21no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—1221no—
394C2×D4—1221no—
395C2×D4—2441no—
396C2×D4—2441no—
397C2×D4—2441no—
398C2×D4—2441no—
399C2×D4—2441no—
400C2×D4—2441no—
401C2×D4#1175819911yescharacteristic
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—2441no—
405C22×C4—2441no—
406C22×C4C2×C22⋊D6111yescharacteristic
407C22×C4C2×C22⋊D6111yescharacteristic
408Q16—612no—
409Q16—1221no—
410SD16—2442no—
411SD16—2442no—
412D8—21no—
413D8—21no—
414D8—1221no—
415D8—1221no—
416D8—1221no—
417D8—1221no—
418D8—4881no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8C2×C22⋊D6111yescharacteristic
424C2×C8C2×C22⋊D6111yescharacteristic
425C2×C8C2×C22⋊D6111yescharacteristic
426C2×C8C23×D6111yescharacteristic
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—1221no—
434C4⋊C4—2441no—
435C4⋊C4#1175819911yescharacteristic
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—2441no—
441C22⋊C4—2441no—
442C22⋊C4#1175819911yescharacteristic
443C22⋊C4#1175819911yescharacteristic
444C42—41no—
445C42—2441no—
446C42C2×C22⋊D6111yescharacteristic
447C16—1221no—
448C16—1221no—
449C16—1221no—
450C16—1221no—
451C23—41no—
452C23—2441no—
453C23—2441no—
454C23C2×#1175819911yescharacteristic
455C23C2×#1175819911yescharacteristic
456Q8—1222no—
457Q8—2441no—
458D4—41no—
459D4—41no—
460D4—41no—
461D4—82no—
462D4—161no—
463D4—9761no—
464D4—9761no—
465D4—9761no—
466D4—4882no—
467D4—4882no—
468D4—4882no—
469D4—2441no—
470D4—2441no—
471D4—2441no—
472D4—2441no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—161no—
481C2×C4—161no—
482C2×C4—4882no—
483C2×C4—4882no—
484C2×C4—2441no—
485C2×C4—2441no—
486C2×C4C2×#1175819911yescharacteristic
487C2×C4C2×#1175819911yescharacteristic
488C2×C4C2×#1175819911yescharacteristic
489C2×C4C2×#1175819911yescharacteristic
490C2×C4C22×C22⋊D6111yescharacteristic
491C8—21no—
492C8—21no—
493C8—21no—
494C8#41×D6111yescharacteristic
495C8#1451982311yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—4881no—
506C22—4881no—
507C22—4881no—
508C22—4881no—
509C22—4881no—
510C22—4881no—
511C22C22×#1175819911yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—81no—
517C4—81no—
518C4—81no—
519C4—4881no—
520C4—2442no—
521C4#1684040011yescharacteristic
522C4#1684057011yescharacteristic
523C2—41no—
524C2—41no—
525C2—161no—
526C2—9761no—
527C2—9761no—
528C2#2145762611yescharacteristic
529C2#2145895311yescharacteristic
530C2#2145895811yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3339C2
socleC22×C61C22×D8
hypercenter#3339D61
hypocenterC61#33876
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3339

Complements

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

NH ≅ G/Ntype
1. #21457579C2semidirect
2. #21448062C2semidirect
3. #21448010C2semidirect
4. #21447999C2semidirect
5. #21447980C2semidirect
6. #21447920C2semidirect
7. #21447903C2semidirect
8. #21447854C2semidirect
9. #21447740C2semidirect
10. #21447740C2semidirect
11. #21447683C2semidirect
12. #21447645C2semidirect
13. #21447529C2semidirect
14. #21447524C2semidirect
15. C61×#3339C2semidirect
258. #3339D61semidirect
324. C61#33876semidirect

Maximal subgroups

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

subgroupindex
#214575792
#214480622
#214480102
#214479992
#214479802
#214479202
#214479032
#214478542
#214477402
#214476832
#214476452
#214475292
#214475242
C61×#33392
#3387661