Finite Group Databasebeta

← #28491032

Subgroups — #28491032

Order 15104.

712 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837693C211yesmaximal, characteristic, complemented
2C2×#16837692C211yesmaximal, characteristic, complemented
3#21429009C211yesmaximal, characteristic
4#21424898C211yesmaximal, characteristic, complemented
5C2×#16837131C211yesmaximal, characteristic, complemented
6#21421980C211yesmaximal, characteristic, complemented
7C2×C59×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#14273727C2211yescharacteristic
9C2×#14273701—21no—
10C2×#14273698—21no—
11C2×C4×D236C2211yescharacteristic
12#16837693—22no—
13#16837693—22no—
14#16837692—22no—
15#16837692—22no—
16C2×#14273659—21no—
17C2×#14273658—21no—
18C2×C4⋊(C59⋊C8)C2211yescharacteristic
19C2×#14273652—22no—
20C2×#14273649—21no—
21C2×#14273648—21no—
22#16837318—22no—
23#16837272C2211yescharacteristic
24#16837262—21no—
25#16837259—21no—
26#16837131—22no—
27C2×C4×D4×C59C2211yescharacteristic
28C2×C4⋊C8×C59C2211yescharacteristic
29C2×C4×C8×C59C2211yescharacteristic
30C59×D4⋊C8—22no—
31C22×Dic118—21no—
32C22×D236D411yescharacteristic
33C22×C22⋊D59—22no—
34C22×C4×D59—21no—
35C22×C59⋊C8—21no—
36#14273727—21no—
37#14273727—21no—
38#14273727—21no—
39#14273727D412yescomplemented
40#14273701—42no—
41#14273701—42no—
42#14273698—42no—
43#14273698—42no—
44C4×D236—21no—
45C4×D236—21no—
46C4×D236—21no—
47C4×D236—21no—
48C2×C4⋊Dic59—21no—
49C2×C4⋊Dic59—21no—
50C2×C4⋊Dic59—21no—
51C2×C4⋊Dic59—21no—
52C2×C4⋊Dic59D411yescharacteristic
53C2×C4⋊Dic59D412yes—
54C2×C22⋊Dic59—22no—
55C2×(C2×D59)⋊C4—22no—
56C2×(C2×D59)⋊C4—21no—
57#14273659—24no—
58#14273658—24no—
59C4⋊(C59⋊C8)—21no—
60C4⋊(C59⋊C8)D412yescomplemented
61#14273652—44no—
62#14273649—24no—
63#14273648—24no—
64C59⋊#95—22no—
65C22×D4×C59D411yescharacteristic
66C23×C4×C59—21no—
67C22×C8×C59—21no—
68C22×C8×C59—21no—
69C4×D4×C59—21no—
70C4×D4×C59—21no—
71C4×D4×C59—21no—
72C4×D4×C59—21no—
73C2×C4⋊C4×C59D411yescharacteristic
74C2×C22⋊C4×C59—21no—
75C2×C42×C59C2311yescharacteristic
76C4⋊C8×C59—21no—
77C4⋊C8×C59D412yescomplemented
78C4×C8×C59—21no—
79C4×C8×C59—21no—
80C24×C59—21no—
81C23×D59—21no—
82C2×D4×C59—21no—
83C2×D4×C59—21no—
84C2×D4×C59—21no—
85C2×D4×C59—21no—
86C2×D4×C59—21no—
87C2×D4×C59SD1612yes—
88C22×C4×C59—21no—
89C22×C4×C59—41no—
90C22×C4×C59—41no—
91C22×C4×C59—41no—
92C22×C4×C59—41no—
93C22×C4×C59—41no—
94C22×C4×C59—41no—
95C22×C4×C59C2×D411yescharacteristic
96C22×C4×C59C2×D411yescharacteristic
97C22×C4×C59C2×D411yescharacteristic
98C2×C22⋊D59—44no—
99C2×C22⋊D59—44no—
100C2×C22⋊D59—82no—
101C22×Dic59—21no—
102C22×Dic59—22no—
103C22×Dic59—41no—
104C2×D236—21no—
105C2×D236—21no—
106C2×D236—21no—
107C2×D236—21no—
108C2×D236—21no—
109C2×D236SD1612yes—
110C2×C4×D59—41no—
111C2×C4×D59—41no—
112C2×C4×D59—41no—
113C2×C4×D59—41no—
114C2×C4×D59—41no—
115C2×C4×D59—41no—
116C2×Dic118—22no—
117C2×Dic118—42no—
118C2×Dic118—42no—
119C2×Dic118—41no—
120C2×C8×C59—22no—
121C2×C8×C59—22no—
122C2×C8×C59—41no—
123C2×C8×C59—41no—
124C2×C8×C59—41no—
125C2×C8×C59—41no—
126C4⋊C4×C59—21no—
127C4⋊C4×C59—21no—
128C22⋊C4×C59—41no—
129C22⋊C4×C59—41no—
130C42×C59C2×D411yescharacteristic
131C42×C59C2×D411yescharacteristic
132C42×C59C2×D411yescharacteristic
133C42×C59#4111yescharacteristic
134C22⋊Dic59—44no—
135(C2×D59)⋊C4—44no—
136(C2×D59)⋊C4—41no—
137(C2×D59)⋊C4—41no—
138C4⋊Dic59—22no—
139C4⋊Dic59—22no—
140C4⋊Dic59—21no—
141C4⋊Dic59—21no—
142C4⋊Dic59—41no—
143C4⋊Dic59—41no—
144C4⋊Dic59—41no—
145C4⋊Dic59—41no—
146C4⋊Dic59—41no—
147C4⋊Dic59—41no—
148C4⋊Dic59—42no—
149C2×C59⋊C8—22no—
150C2×C59⋊C8—41no—
151C2×C59⋊C8—41no—
152C23×C59—22no—
153C23×C59—41no—
154C23×C59—41no—
155C23×C59—41no—
156C23×C59—41no—
157C23×C59—41no—
158C23×C59—41no—
159C23×C59#12011yescharacteristic
160C22×D59—22no—
161C22×D59—41no—
162C22×D59—41no—
163C22×D59—41no—
164C22×D59—41no—
165C22×D59—41no—
166C22×D59—41no—
167D4×C59—22no—
168D4×C59—22no—
169D4×C59—41no—
170D4×C59—41no—
171C2×C4×C59—21no—
172C2×C4×C59—21no—
173C2×C4×C59—41no—
174C2×C4×C59—41no—
175C2×C4×C59—41no—
176C2×C4×C59—81no—
177C2×C4×C59—81no—
178C2×C4×C59—81no—
179C2×C4×C59—81no—
180C2×C4×C59#12011yescharacteristic
181C2×C4×C59#12011yescharacteristic
182C2×C4×C59#12111yescharacteristic
183C2×C4×C59#12111yescharacteristic
184C2×C4×C59#12111yescharacteristic
185C2×C4×C59#12711yescharacteristic
186C2×C4×C59C2×SD1611yescharacteristic
187C2×C4×C59C2×SD1611yescharacteristic
188C2×C4×C59#13511yescharacteristic
189C2×C4×C59#13511yescharacteristic
190C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C59#13711yescharacteristic
193C2×C4×C59#13711yescharacteristic
194C22⋊D59—88no—
195C2×Dic59—42no—
196C2×Dic59—41no—
197C2×Dic59—42no—
198C2×Dic59—42no—
199C2×Dic59—41no—
200C2×Dic59—41no—
201C2×Dic59—42no—
202C2×Dic59—81no—
203C2×Dic59—81no—
204D236—22no—
205D236—22no—
206D236—41no—
207D236—41no—
208C4×D59—81no—
209C4×D59—81no—
210C4×D59—81no—
211C4×D59—81no—
212Dic118—44no—
213Dic118—82no—
214C8×C59—42no—
215C8×C59—42no—
216C59⋊C8—42no—
217#10235—591nomaximal, Sylow
218C22×C59—42no—
219C22×C59—42no—
220C22×C59—42no—
221C22×C59—81no—
222C22×C59—81no—
223C22×C59—81no—
224C22×C59—81no—
225C22×C59#39211yescharacteristic
226C22×C59#45011yescharacteristic
227C22×C59#45011yescharacteristic
228C22×C59#45211yescharacteristic
229C22×C59#45211yescharacteristic
230C22×C59#45311yescharacteristic
231C22×C59#45411yescharacteristic
232C2×D59—42no—
233C2×D59—42no—
234C2×D59—42no—
235C2×D59—81no—
236C2×D59—81no—
237C2×D59—81no—
238C2×D59—81no—
239C4×C59—21no—
240C4×C59—21no—
241C4×C59—81no—
242C4×C59#44811yescharacteristic
243C4×C59#44811yescharacteristic
244C4×C59#44911yescharacteristic
245C4×C59#44911yescharacteristic
246C4×C59#46511yescharacteristic
247C4×C59#46511yescharacteristic
248C4×C59#46811yescharacteristic
249C4×C59#46811yescharacteristic
250Dic59—82no—
251Dic59—81no—
252Dic59—82no—
253C2×#476—591no—
254C2×#476—591no—
255#2537—591no—
256#1956—591no—
257C2×D4⋊C8—591no—
258C2×D4⋊C8D5911yescharacteristic, complemented
259#1296—591no—
260C2×C59—82no—
261C2×C59#162911yescharacteristic
262C2×C59#163411yescharacteristic
263C2×C59#163511yescharacteristic
264C2×C59#163511yescharacteristic
265C2×C59#200011yescharacteristic
266C2×C59#200011yescharacteristic
267C2×C59#200611yescharacteristic
268D59—82no—
269C2×C4⋊Q8—591no—
270C2×#121—1181no—
271C2×#121—1181no—
272C2×C4×D4—591no—
273C2×C4×D4C2×D5911yescharacteristic
274#476—1182no—
275#476—1182no—
276#476—1182no—
277#476—1182no—
278C2×#106—1181no—
279C2×#106—1181no—
280C2×C4⋊C8—591no—
281C2×C4⋊C8C2×D5911yescharacteristic
282C2×#103—1182no—
283C2×#102—1181no—
284C2×#102—1181no—
285C2×C4×C8C2×D5911yescharacteristic
286#394—1182no—
287#384—591no—
288#380—1181no—
289#380—1181no—
290D4⋊C8—22no—
291D4⋊C8—1182no—
292C59#1023511yescharacteristic, complemented, Sylow
293C22×Q8—1181no—
294C22×D4—591no—
295C22×D4—1182no—
296C22×D4D23611yescharacteristic
297C23×C4—21no—
298C23×C4—1181no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—1181no—
302C4⋊Q8—592no—
303C4⋊Q8—1181no—
304C4⋊Q8—1181no—
305C4⋊Q8—1181no—
306#121—2362no—
307#121—2362no—
308#121—2362no—
309#121—2362no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—1181no—
315C4×D4—1181no—
316C4×D4—1181no—
317C4×D4—1181no—
318C2×C4⋊C4—591no—
319C2×C4⋊C4—592no—
320C2×C4⋊C4—1181no—
321C2×C4⋊C4—1181no—
322C2×C4⋊C4—1181no—
323C2×C4⋊C4—1181no—
324C2×C4⋊C4D23611yescharacteristic
325C2×C22⋊C4—21no—
326C2×C22⋊C4—1182no—
327C2×C22⋊C4—1182no—
328C2×C22⋊C4—1181no—
329C2×C42C22×D5911yescharacteristic
330#106—1184no—
331#106—1184no—
332C4⋊C8—21no—
333C4⋊C8—592no—
334C4⋊C8—1181no—
335C4⋊C8C22⋊D5912yescomplemented
336#103—2364no—
337#102—1184no—
338#102—1184no—
339C4×C8—21no—
340C4×C8—21no—
341#95—1182no—
342C24—21no—
343C24—1181no—
344C2×Q8—1182no—
345C2×Q8—2362no—
346C2×Q8—2362no—
347C2×Q8—2361no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—592no—
354C2×D4—1181no—
355C2×D4—1181no—
356C2×D4—1181no—
357C2×D4—1181no—
358C2×D4—1181no—
359C2×D4—4722no—
360C2×D4—2364no—
361C2×D4—2364no—
362C2×D4#1174566012yes—
363C22×C4—21no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—1181no—
371C22×C4—1182no—
372C22×C4—2361no—
373C22×C4—2361no—
374C22×C4—2361no—
375C22×C4—2361no—
376C22×C4—2361no—
377C22×C4—2361no—
378C22×C4—2361no—
379C22×C4C2×D23611yescharacteristic
380C22×C4D4×D5911yescharacteristic
381C22×C4D4×D5911yescharacteristic
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—41no—
385C2×C8—41no—
386C2×C8—41no—
387C2×C8—41no—
388C2×C8—1182no—
389C2×C8—2361no—
390C2×C8—2361no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—1182no—
394C4⋊C4—1181no—
395C4⋊C4—1182no—
396C4⋊C4—1181no—
397C4⋊C4—2362no—
398C4⋊C4—2361no—
399C4⋊C4—2361no—
400C4⋊C4—2361no—
401C4⋊C4—2361no—
402C4⋊C4—2361no—
403C4⋊C4—2361no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—2364no—
407C22⋊C4—2364no—
408C22⋊C4—2361no—
409C22⋊C4—2361no—
410C42#1174568511yescharacteristic
411C42D4×D5911yescharacteristic
412C42D4×D5911yescharacteristic
413C42C2×C22⋊D5911yescharacteristic
414C23—22no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—1182no—
422C23—2361no—
423C23—2361no—
424C23—2361no—
425C23—2361no—
426C23—2361no—
427C23—2361no—
428C23#1427369711yescharacteristic
429Q8—4722no—
430Q8—2364no—
431D4—22no—
432D4—22no—
433D4—41no—
434D4—41no—
435D4—1182no—
436D4—1182no—
437D4—4728no—
438D4—2361no—
439D4—2361no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—4721no—
450C2×C4—4721no—
451C2×C4—4721no—
452C2×C4—4721no—
453C2×C4—4721no—
454C2×C4—4721no—
455C2×C4—2362no—
456C2×C4—2361no—
457C2×C4—2362no—
458C2×C4—2361no—
459C2×C4—2361no—
460C2×C4—2362no—
461C2×C4—2362no—
462C2×C4#1427369511yescharacteristic
463C2×C4#1427369711yescharacteristic
464C2×C4#1427370011yescharacteristic
465C2×C4#1427370011yescharacteristic
466C2×C4#1427370111yescharacteristic
467C2×C4#1427372311yescharacteristic
468C2×C4SD16×D5911yescharacteristic
469C2×C4C2×#1174566011yescharacteristic
470C2×C4#1427374611yescharacteristic
471C2×C4#1427374911yescharacteristic
472C2×C4#1427375111yescharacteristic
473C2×C4#1427375511yescharacteristic
474C2×C4#1427375611yescharacteristic
475C2×C4#1427376011yescharacteristic
476C8—42no—
477C8—42no—
478C8—2362no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—4721no—
487C22—4721no—
488C22—4721no—
489C22—4721no—
490C22—2362no—
491C22—2362no—
492C22—2362no—
493C22#1683731111yescharacteristic
494C22#1683755411yescharacteristic
495C22#1683755511yescharacteristic
496C22#1683756511yescharacteristic
497C22#1683756611yescharacteristic
498C22#1683757111yescharacteristic
499C22#1683757611yescharacteristic
500C4—21no—
501C4—21no—
502C4—81no—
503C4—4722no—
504C4—4721no—
505C4—4722no—
506C4#1683753911yescharacteristic
507C4#1683754311yescharacteristic
508C4#1683754411yescharacteristic
509C4#1683754911yescharacteristic
510C4#1683763011yescharacteristic
511C4#1683763111yescharacteristic
512C4#1683764711yescharacteristic
513C4#1683764811yescharacteristic
514C2—82no—
515C2—4722no—
516C2#2142321411yescharacteristic
517C2#2142324311yescharacteristic
518C2#2142324911yescharacteristic
519C2#2142325011yescharacteristic
520C2#2142510011yescharacteristic
521C2#2142510111yescharacteristic
522C2#2142513911yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC2×C59×D4⋊C8C2
socleC23×C59#120
prime radical#21429009C2
hypercenterC2×D4⋊C8D59
hypocenterC59#10235
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#16837693C2semidirect
2. C2×#16837692C2semidirect
4. #21424898C2semidirect
5. C2×#16837131C2semidirect
6. #21421980C2semidirect
7. C2×C59×D4⋊C8C2semidirect
39. #14273727D4semidirect
60. C4⋊(C59⋊C8)D4semidirect
77. C4⋊C8×C59D4semidirect
258. C2×D4⋊C8D59semidirect
292. C59#10235semidirect
335. C4⋊C8C22⋊D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168376932
C2×#168376922
#214290092
#214248982
C2×#168371312
#214219802
C2×C59×D4⋊C82
#1023559