Finite Group Databasebeta

← #28491038

Subgroups — #28491038

Order 15104.

628 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837697C211yesmaximal, characteristic, complemented
2C2×#16837693C211yesmaximal, characteristic
3#21429014C211yesmaximal, characteristic
4#21424898C211yesmaximal, characteristic, complemented
5C2×#16837131C211yesmaximal, characteristic
6#21421980C211yesmaximal, characteristic, complemented
7C2×C59×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#14273727C2211yescharacteristic
9C2×#14273703—21no—
10C2×C4×D236C2211yescharacteristic
11#16837697—22no—
12#16837697—22no—
13#16837693—22no—
14#16837693—22no—
15C2×#14273660—21no—
16C2×#14273659—21no—
17C2×C4⋊(C59⋊C8)C2211yescharacteristic
18C2×#14273652—22no—
19C2×#14273651—21no—
20C2×#14273649—21no—
21#16837324—22no—
22#16837304—21no—
23#16837300—21no—
24#16837272C2211yescharacteristic
25#16837259—21no—
26#16837131—22no—
27C2×C4×Q8×C59C2211yescharacteristic
28C2×C4⋊C8×C59C2211yescharacteristic
29C2×C4×C8×C59C2211yescharacteristic
30C59×Q8⋊C8—22no—
31C22×Dic118—21no—
32C22×D236D411yescharacteristic
33C22×C4×D59—21no—
34C22×C59⋊C8—21no—
35#14273727—21no—
36#14273727—21no—
37#14273727—21no—
38#14273727D412yes—
39#14273703—42no—
40#14273703—42no—
41C4×D236—21no—
42C4×D236—21no—
43C4×D236—21no—
44C4×D236—21no—
45C2×C4⋊Dic59—21no—
46C2×C4⋊Dic59—21no—
47C2×C4⋊Dic59—21no—
48C2×C4⋊Dic59—21no—
49C2×C4⋊Dic59D411yescharacteristic
50C2×C4⋊Dic59D412yes—
51C2×Dic59⋊C4—22no—
52C2×(C2×D59)⋊C4—22no—
53C2×(C2×D59)⋊C4—21no—
54C2×(C2×D59)⋊C4—22no—
55#14273660—24no—
56#14273659—24no—
57C4⋊(C59⋊C8)—21no—
58C4⋊(C59⋊C8)D412yes—
59#14273652—44no—
60#14273651—24no—
61#14273649—24no—
62C59⋊#95—22no—
63C22×Q8×C59D411yescharacteristic
64C22×C8×C59—21no—
65C22×C8×C59—21no—
66C4×Q8×C59—21no—
67C4×Q8×C59—21no—
68C4×Q8×C59—21no—
69C4×Q8×C59—21no—
70C2×C4⋊C4×C59—21no—
71C2×C4⋊C4×C59D411yescharacteristic
72C2×C42×C59—21no—
73C2×C42×C59C2311yescharacteristic
74C4⋊C8×C59—21no—
75C4⋊C8×C59D412yes—
76C4×C8×C59—21no—
77C4×C8×C59—21no—
78C23×D59—21no—
79C2×Q8×C59—21no—
80C2×Q8×C59—21no—
81C2×Q8×C59—21no—
82C2×Q8×C59—21no—
83C2×Q8×C59—21no—
84C2×Q8×C59SD1612yes—
85C22×C4×C59—21no—
86C22×C4×C59—21no—
87C22×C4×C59C2×D411yescharacteristic
88C22×C4×C59C2×D411yescharacteristic
89C22×C4×C59C2×D411yescharacteristic
90C22×Dic59—21no—
91C22×Dic59—22no—
92C22×Dic59—41no—
93C2×D236—21no—
94C2×D236—21no—
95C2×D236—21no—
96C2×D236—21no—
97C2×D236—21no—
98C2×D236Q1612yes—
99C2×C4×D59—41no—
100C2×C4×D59—41no—
101C2×C4×D59—41no—
102C2×C4×D59—41no—
103C2×C4×D59—41no—
104C2×C4×D59—41no—
105C2×Dic118—22no—
106C2×Dic118—42no—
107C2×Dic118—42no—
108C2×Dic118—41no—
109C2×C8×C59—22no—
110C2×C8×C59—22no—
111C2×C8×C59—41no—
112C2×C8×C59—41no—
113C2×C8×C59—41no—
114C2×C8×C59—41no—
115C4⋊C4×C59—21no—
116C4⋊C4×C59—21no—
117C4⋊C4×C59—41no—
118C4⋊C4×C59—41no—
119C42×C59—41no—
120C42×C59—41no—
121C42×C59C2×D411yescharacteristic
122C42×C59C2×D411yescharacteristic
123C42×C59C2×D411yescharacteristic
124C42×C59#4111yescharacteristic
125(C2×D59)⋊C4—44no—
126(C2×D59)⋊C4—41no—
127(C2×D59)⋊C4—41no—
128(C2×D59)⋊C4—82no—
129C4⋊Dic59—22no—
130C4⋊Dic59—22no—
131C4⋊Dic59—21no—
132C4⋊Dic59—21no—
133C4⋊Dic59—41no—
134C4⋊Dic59—41no—
135C4⋊Dic59—41no—
136C4⋊Dic59—41no—
137C4⋊Dic59—41no—
138C4⋊Dic59—41no—
139C4⋊Dic59—42no—
140Dic59⋊C4—44no—
141C2×C59⋊C8—22no—
142C2×C59⋊C8—41no—
143C2×C59⋊C8—41no—
144C23×C59#12011yescharacteristic
145C22×D59—22no—
146C22×D59—41no—
147C22×D59—41no—
148C22×D59—41no—
149C22×D59—41no—
150C22×D59—41no—
151C22×D59—41no—
152Q8×C59—22no—
153Q8×C59—22no—
154Q8×C59—41no—
155Q8×C59—41no—
156C2×C4×C59—21no—
157C2×C4×C59—21no—
158C2×C4×C59—22no—
159C2×C4×C59—41no—
160C2×C4×C59—41no—
161C2×C4×C59—41no—
162C2×C4×C59—41no—
163C2×C4×C59—41no—
164C2×C4×C59#12011yescharacteristic
165C2×C4×C59#12011yescharacteristic
166C2×C4×C59#12111yescharacteristic
167C2×C4×C59#12111yescharacteristic
168C2×C4×C59#12111yescharacteristic
169C2×C4×C59#12711yescharacteristic
170C2×C4×C59C2×SD1611yescharacteristic
171C2×C4×C59C2×Q1611yescharacteristic
172C2×C4×C59#13511yescharacteristic
173C2×C4×C59#13511yescharacteristic
174C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C59#13711yescharacteristic
176C2×C4×C59#13711yescharacteristic
177C2×C4×C59#13711yescharacteristic
178C2×Dic59—42no—
179C2×Dic59—41no—
180C2×Dic59—41no—
181C2×Dic59—42no—
182C2×Dic59—42no—
183C2×Dic59—41no—
184C2×Dic59—42no—
185C2×Dic59—81no—
186C2×Dic59—81no—
187D236—22no—
188D236—22no—
189D236—41no—
190D236—41no—
191C4×D59—81no—
192C4×D59—81no—
193C4×D59—81no—
194C4×D59—81no—
195Dic118—44no—
196Dic118—82no—
197C8×C59—42no—
198C8×C59—42no—
199C59⋊C8—42no—
200#10236—591nomaximal, Sylow
201C22×C59#39211yescharacteristic
202C22×C59#45011yescharacteristic
203C22×C59#45111yescharacteristic
204C22×C59#45211yescharacteristic
205C22×C59#45211yescharacteristic
206C22×C59#45311yescharacteristic
207C22×C59#45411yescharacteristic
208C2×D59—42no—
209C2×D59—42no—
210C2×D59—42no—
211C2×D59—81no—
212C2×D59—81no—
213C2×D59—81no—
214C2×D59—81no—
215C4×C59—21no—
216C4×C59—21no—
217C4×C59—42no—
218C4×C59—81no—
219C4×C59#44811yescharacteristic
220C4×C59#44911yescharacteristic
221C4×C59#45111yescharacteristic
222C4×C59#45211yescharacteristic
223C4×C59#46511yescharacteristic
224C4×C59#46711yescharacteristic
225C4×C59#46811yescharacteristic
226C4×C59#47011yescharacteristic
227Dic59—82no—
228Dic59—81no—
229Dic59—82no—
230C2×#477—591no—
231C2×#476—591no—
232#2538—591no—
233#1956—591no—
234C2×Q8⋊C8D5911yescharacteristic, complemented
235C2×D4⋊C8—591no—
236#1296—591no—
237C2×C59#163111yescharacteristic
238C2×C59#163211yescharacteristic
239C2×C59#163711yescharacteristic
240C2×C59#163811yescharacteristic
241C2×C59#200011yescharacteristic
242C2×C59#200111yescharacteristic
243C2×C59#200611yescharacteristic
244D59—82no—
245C2×C4⋊Q8—591no—
246C2×C22⋊Q8—1181no—
247C2×C4×Q8C2×D5911yescharacteristic
248C2×C4×D4—591no—
249#477—1182no—
250#477—1182no—
251#476—1182no—
252#476—1182no—
253C2×#107—1181no—
254C2×#106—1181no—
255C2×C4⋊C8—591no—
256C2×C4⋊C8C2×D5911yescharacteristic
257C2×#103—1181no—
258C2×#103—1182no—
259C2×#102—1181no—
260C2×C4×C8C2×D5911yescharacteristic
261#396—1182no—
262#390—1181no—
263#389—1181no—
264#384—591no—
265#380—1181no—
266Q8⋊C8—22no—
267D4⋊C8—1182no—
268C59#1023611yescharacteristic, complemented, Sylow
269C22×Q8—1181no—
270C22×Q8D23611yescharacteristic
271C22×D4—591no—
272C23×C4—1181no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—1181no—
276C4⋊Q8—592no—
277C4⋊Q8—1181no—
278C4⋊Q8—1181no—
279C4⋊Q8—1181no—
280C22⋊Q8—2362no—
281C22⋊Q8—2362no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×Q8—21no—
285C4×Q8—21no—
286C4×D4—1181no—
287C4×D4—1181no—
288C4×D4—1181no—
289C4×D4—1181no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—591no—
292C2×C4⋊C4—592no—
293C2×C4⋊C4—1181no—
294C2×C4⋊C4—1181no—
295C2×C4⋊C4—1182no—
296C2×C4⋊C4—1181no—
297C2×C4⋊C4—1181no—
298C2×C4⋊C4D23611yescharacteristic
299C2×C22⋊C4—1182no—
300C2×C22⋊C4—1182no—
301C2×C22⋊C4—1181no—
302C2×C42—21no—
303C2×C42C22×D5911yescharacteristic
304#107—1184no—
305#106—1184no—
306C4⋊C8—21no—
307C4⋊C8—592no—
308C4⋊C8—1181no—
309C4⋊C8C22⋊D5912yes—
310#103—1184no—
311#103—2364no—
312#102—1184no—
313C4×C8—21no—
314C4×C8—21no—
315#95—1182no—
316C24—1181no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—1182no—
323C2×Q8—2362no—
324C2×Q8—2362no—
325C2×Q8—2361no—
326C2×Q8#1174566012yes—
327C2×D4—592no—
328C2×D4—1181no—
329C2×D4—1181no—
330C2×D4—1181no—
331C2×D4—1181no—
332C2×D4—1181no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—1181no—
336C22×C4—1182no—
337C22×C4—2361no—
338C22×C4—2361no—
339C22×C4—2361no—
340C22×C4—2361no—
341C22×C4—2361no—
342C22×C4—2361no—
343C22×C4—2361no—
344C22×C4C2×D23611yescharacteristic
345C22×C4D4×D5911yescharacteristic
346C22×C4D4×D5911yescharacteristic
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—1182no—
354C2×C8—2361no—
355C2×C8—2361no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—1182no—
361C4⋊C4—1181no—
362C4⋊C4—1182no—
363C4⋊C4—1181no—
364C4⋊C4—2362no—
365C4⋊C4—2364no—
366C4⋊C4—2361no—
367C4⋊C4—2361no—
368C4⋊C4—2361no—
369C4⋊C4—2361no—
370C4⋊C4—2361no—
371C4⋊C4—2361no—
372C22⋊C4—4722no—
373C22⋊C4—2364no—
374C22⋊C4—2361no—
375C22⋊C4—2361no—
376C42—41no—
377C42—41no—
378C42#1174568511yescharacteristic
379C42D4×D5911yescharacteristic
380C42D4×D5911yescharacteristic
381C42C2×C22⋊D5911yescharacteristic
382C23—1182no—
383C23—2361no—
384C23—2361no—
385C23—2361no—
386C23—2361no—
387C23—2361no—
388C23—2361no—
389C23#1427369711yescharacteristic
390Q8—22no—
391Q8—22no—
392Q8—41no—
393Q8—41no—
394Q8—4722no—
395Q8—2364no—
396D4—1182no—
397D4—1182no—
398D4—2361no—
399D4—2361no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—4721no—
409C2×C4—4721no—
410C2×C4—4721no—
411C2×C4—4721no—
412C2×C4—4721no—
413C2×C4—4721no—
414C2×C4—2362no—
415C2×C4—2361no—
416C2×C4—2361no—
417C2×C4—2361no—
418C2×C4—2362no—
419C2×C4—2362no—
420C2×C4—2362no—
421C2×C4#1427369511yescharacteristic
422C2×C4#1427369711yescharacteristic
423C2×C4#1427370011yescharacteristic
424C2×C4#1427370011yescharacteristic
425C2×C4#1427370111yescharacteristic
426C2×C4#1427372311yescharacteristic
427C2×C4C2×#1174566011yescharacteristic
428C2×C4Q16×D5911yescharacteristic
429C2×C4#1427374811yescharacteristic
430C2×C4#1427374911yescharacteristic
431C2×C4#1427375511yescharacteristic
432C2×C4#1427375611yescharacteristic
433C2×C4#1427375911yescharacteristic
434C2×C4#1427376011yescharacteristic
435C8—42no—
436C8—42no—
437C8—2362no—
438C22—4721no—
439C22—4721no—
440C22—4721no—
441C22—4721no—
442C22—2362no—
443C22—2362no—
444C22—2362no—
445C22#1683731111yescharacteristic
446C22#1683755511yescharacteristic
447C22#1683755911yescharacteristic
448C22#1683756611yescharacteristic
449C22#1683756711yescharacteristic
450C22#1683757111yescharacteristic
451C22#1683757611yescharacteristic
452C4—21no—
453C4—21no—
454C4—42no—
455C4—81no—
456C4—4722no—
457C4—4721no—
458C4—4722no—
459C4#1683754311yescharacteristic
460C4#1683754911yescharacteristic
461C4#1683755611yescharacteristic
462C4#1683756111yescharacteristic
463C4#1683763111yescharacteristic
464C4#1683764211yescharacteristic
465C4#1683764811yescharacteristic
466C4#1683765911yescharacteristic
467C2—4722no—
468C2#2142322511yescharacteristic
469C2#2142323311yescharacteristic
470C2#2142326311yescharacteristic
471C2#2142327111yescharacteristic
472C2#2142510111yescharacteristic
473C2#2142510511yescharacteristic
474C2#2142513911yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC2×C59×Q8⋊C8C2
socleC23×C59#120
prime radicalC22×D236D4
hypercenterC2×Q8⋊C8D59
hypocenterC59#10236
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#16837697C2semidirect
4. #21424898C2semidirect
6. #21421980C2semidirect
7. C2×C59×Q8⋊C8C2semidirect
234. C2×Q8⋊C8D59semidirect
268. C59#10236semidirect

Maximal subgroups

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

subgroupindex
C2×#168376972
C2×#168376932
#214290142
#214248982
C2×#168371312
#214219802
C2×C59×Q8⋊C82
#1023659