Finite Group Databasebeta

← #28483972

Subgroups — #28483972

Order 15104.

618 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837749C211yesmaximal, characteristic
2#21427154C211yesmaximal, characteristic, complemented
3#21425023C211yesmaximal, characteristic
4#21425022C211yesmaximal, characteristic
5C2×#16837147C211yesmaximal, characteristic, complemented
6#21421936C211yesmaximal, characteristic, complemented
7C59×#1279C211yesmaximal, characteristic, complemented
8C2×#14273727C2211yescharacteristic
9C2×#14273724C2211yescharacteristic
10C2×#14273692—21no—
11#16837749—22no—
12#16837749C414yescomplemented
13C2×C4⋊(C59⋊C8)C2211yescharacteristic
14C2×#14273649—22no—
15C2×#14273649—21no—
16C2×#14273649—21no—
17C2×#14273647—21no—
18C2×#14273647—21no—
19#16837307—21no—
20#16837300—21no—
21#16837287—22no—
22C4×C4⋊Dic59—21no—
23C4×C4⋊Dic59C2211yescharacteristic
24#16837147—22no—
25C2×C4⋊C8×C59C2211yescharacteristic
26C2×C4×C8×C59C2211yescharacteristic
27C4×C4⋊C4×C59C2211yescharacteristic
28C22×Dic118—21no—
29C22×D236—21no—
30C22×D236—21no—
31C22×D236—21no—
32C22×C59⋊C8—21no—
33#14273727—21no—
34#14273727—21no—
35#14273727C2×C412yes—
36#14273727D412yes—
37#14273724—21no—
38#14273724—21no—
39#14273724—21no—
40#14273724C2×C412yes—
41#14273692—42no—
42#14273692—42no—
43C2×C4⋊Dic59—21no—
44C2×C4⋊Dic59D411yescharacteristic
45C2×C4⋊Dic59D412yes—
46C2×C4⋊Dic59D411yescharacteristic
47C2×Dic59⋊C4—22no—
48C2×C4×Dic59—22no—
49C2×C4×Dic59—21no—
50C4⋊(C59⋊C8)—21no—
51C4⋊(C59⋊C8)—21no—
52#14273649—28no—
53#14273649—42no—
54#14273649—42no—
55#14273647—42no—
56#14273647—42no—
57C59⋊#95—22no—
58C59⋊#95—22no—
59C59⋊#95—21no—
60C22×C8×C59—21no—
61C22×C8×C59—21no—
62C2×C4⋊C4×C59D411yescharacteristic
63C2×C4⋊C4×C59D411yescharacteristic
64C2×C42×C59—21no—
65C2×C42×C59C2311yescharacteristic
66C4⋊C8×C59—21no—
67C4⋊C8×C59—21no—
68C4×C8×C59—21no—
69C4×C8×C59C2×C412yes—
70#95×C59—21no—
71C23×D59—41no—
72C22×C4×C59—21no—
73C22×C4×C59—21no—
74C22×C4×C59C2×D411yescharacteristic
75C22×C4×C59C2×D411yescharacteristic
76C22×C4×C59C2×D411yescharacteristic
77C22×Dic59—21no—
78C22×Dic59—22no—
79C22×Dic59—21no—
80C2×D236—22no—
81C2×D236—22no—
82C2×D236—22no—
83C2×D236—42no—
84C2×D236—42no—
85C2×D236—41no—
86C2×D236—41no—
87C2×D236—41no—
88C2×D236—41no—
89C2×D236—41no—
90C2×D236—41no—
91C2×D236—41no—
92C2×D236—41no—
93C2×D236—41no—
94C2×D236—41no—
95C2×D236—41no—
96C2×Dic118—22no—
97C2×Dic118—22no—
98C2×Dic118—41no—
99C2×Dic118—41no—
100C2×Dic118—41no—
101C2×Dic118—41no—
102C2×C8×C59—22no—
103C2×C8×C59—41no—
104C2×C8×C59—41no—
105C2×C8×C59—41no—
106C2×C8×C59—41no—
107C2×C8×C59—41no—
108C4⋊C4×C59—21no—
109C4⋊C4×C59—21no—
110C4⋊C4×C59—21no—
111C4⋊C4×C59D812yes—
112C42×C59—41no—
113C42×C59—41no—
114C42×C59C22×C411yescharacteristic
115C42×C59C2×D411yescharacteristic
116C42×C59#4111yescharacteristic
117C42×C59#4111yescharacteristic
118C4⋊Dic59—22no—
119C4⋊Dic59—22no—
120C4⋊Dic59—22no—
121C4⋊Dic59—21no—
122C4⋊Dic59—21no—
123C4⋊Dic59—21no—
124C4⋊Dic59C22⋊C414yes—
125C4⋊Dic59SD1612yes—
126Dic59⋊C4—44no—
127C4×Dic59—44no—
128C4×Dic59—41no—
129C4×Dic59—41no—
130C2×C59⋊C8—41no—
131C2×C59⋊C8—41no—
132C2×C59⋊C8—41no—
133C23×C59#12011yescharacteristic
134C22×D59—42no—
135C22×D59—81no—
136C22×D59—81no—
137C22×D59—81no—
138C22×D59—81no—
139C22×D59—81no—
140C22×D59—81no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—22no—
144C2×C4×C59—41no—
145C2×C4×C59—41no—
146C2×C4×C59—41no—
147C2×C4×C59—41no—
148C2×C4×C59—41no—
149C2×C4×C59C2×C22⋊C411yescharacteristic
150C2×C4×C59C4×D411yescharacteristic
151C2×C4×C59C4×D411yescharacteristic
152C2×C4×C59#12111yescharacteristic
153C2×C4×C59#12111yescharacteristic
154C2×C4×C59#12311yescharacteristic
155C2×C4×C59C2×D811yescharacteristic
156C2×C4×C59C2×SD1611yescharacteristic
157C2×C4×C59#13511yescharacteristic
158C2×C4×C59#13511yescharacteristic
159C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C59#13711yescharacteristic
163C2×Dic59—24no—
164C2×Dic59—22no—
165C2×Dic59—41no—
166C2×Dic59—42no—
167C2×Dic59—42no—
168C2×Dic59—41no—
169C2×Dic59—41no—
170C2×Dic59—41no—
171C2×Dic59—41no—
172D236—44no—
173D236—42no—
174D236—42no—
175D236—42no—
176D236—42no—
177D236—82no—
178D236—81no—
179D236—81no—
180D236—81no—
181D236—81no—
182Dic118—42no—
183Dic118—42no—
184Dic118—42no—
185Dic118—42no—
186C8×C59—42no—
187C8×C59—81no—
188C59⋊C8—81no—
189#9062—591nomaximal, Sylow
190C22×C59#38611yescharacteristic
191C22×C59#44711yescharacteristic
192C22×C59#44811yescharacteristic
193C22×C59#44911yescharacteristic
194C22×C59#44911yescharacteristic
195C22×C59#45411yescharacteristic
196C22×C59#45411yescharacteristic
197C2×D59—82no—
198C2×D59—82no—
199C2×D59—82no—
200C2×D59—161no—
201C2×D59—161no—
202C2×D59—161no—
203C2×D59—161no—
204C4×C59—21no—
205C4×C59—21no—
206C4×C59—42no—
207C4×C59—81no—
208C4×C59C4×D811yescharacteristic
209C4×C59C4×SD1611yescharacteristic
210C4×C59#44011yescharacteristic
211C4×C59#44211yescharacteristic
212C4×C59#45911yescharacteristic
213C4×C59#46011yescharacteristic
214C4×C59#46311yescharacteristic
215C4×C59#46411yescharacteristic
216Dic59—44no—
217Dic59—42no—
218Dic59—81no—
219C2×#486—591no—
220#2365—591no—
221#1982—591no—
222#1982—591no—
223C2×#332—591no—
224#1279—591no—
225#1279D5911yescharacteristic, complemented
226C2×C59#162511yescharacteristic
227C2×C59#162611yescharacteristic
228C2×C59#162711yescharacteristic
229C2×C59#162811yescharacteristic
230C2×C59#187911yescharacteristic
231C2×C59#188011yescharacteristic
232C2×C59#188811yescharacteristic
233D59—162no—
234C2×C4⋊Q8—591no—
235C2×#127—591no—
236C2×C4×Q8—1181no—
237#486—594no—
238#486—1182no—
239C2×C4⋊C8—591no—
240C2×C4⋊C8C2×D5911yescharacteristic
241C2×#102—1182no—
242C2×#102—1181no—
243C2×#102—1181no—
244C2×#102—1181no—
245C2×#102—1181no—
246C2×C4×C8C2×D5911yescharacteristic
247#391—1181no—
248#389—1181no—
249#387—1182no—
250C4×C4⋊C4—591no—
251C4×C4⋊C4—1181no—
252C4×C4⋊C4C2×D5911yescharacteristic
253#332—1182no—
254C59#906211yescharacteristic, complemented, Sylow
255C22×Q8—1181no—
256C22×D4—1181no—
257C22×D4—1181no—
258C22×D4—1181no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—1181no—
262C4⋊Q8—592no—
263C4⋊Q8—592no—
264C4⋊Q8—1181no—
265C4⋊Q8—1181no—
266#127—592no—
267#127—1181no—
268#127—1181no—
269#127—1181no—
270C4×Q8—2362no—
271C4×Q8—2362no—
272C2×C4⋊C4—592no—
273C2×C4⋊C4—591no—
274C2×C4⋊C4—591no—
275C2×C4⋊C4—1181no—
276C2×C4⋊C4—1182no—
277C2×C4⋊C4D23611yescharacteristic
278C2×C4⋊C4D23611yescharacteristic
279C2×C42—21no—
280C2×C42—1182no—
281C2×C42—1181no—
282C2×C42C22×D5911yescharacteristic
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—1181no—
286C4⋊C8—1181no—
287#102—1188no—
288#102—2362no—
289#102—2362no—
290#102—2362no—
291#102—2362no—
292C4×C8—21no—
293C4×C8C4×D5912yes—
294#95—21no—
295#95—1182no—
296#95—1182no—
297#95—1181no—
298C24—2361no—
299C2×Q8—1182no—
300C2×Q8—1182no—
301C2×Q8—2361no—
302C2×Q8—2361no—
303C2×Q8—2361no—
304C2×Q8—2361no—
305C2×D4—1182no—
306C2×D4—1182no—
307C2×D4—1182no—
308C2×D4—2362no—
309C2×D4—2362no—
310C2×D4—2361no—
311C2×D4—2361no—
312C2×D4—2361no—
313C2×D4—2361no—
314C2×D4—2361no—
315C2×D4—2361no—
316C2×D4—2361no—
317C2×D4—2361no—
318C2×D4—2361no—
319C2×D4—2361no—
320C2×D4—2361no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—1181no—
324C22×C4—1182no—
325C22×C4—1181no—
326C22×C4C2×D23611yescharacteristic
327C22×C4D4×D5911yescharacteristic
328C22×C4D4×D5911yescharacteristic
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—2361no—
336C2×C8—2361no—
337C2×C8—2361no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—594no—
342C4⋊C4—592no—
343C4⋊C4—1182no—
344C4⋊C4—1182no—
345C4⋊C4—1182no—
346C4⋊C4—1181no—
347C4⋊C4—1181no—
348C4⋊C4—1181no—
349C4⋊C4—2364no—
350C4⋊C4D47212yes—
351C42—41no—
352C42—41no—
353C42—2364no—
354C42—2361no—
355C42—2361no—
356C42C2×C4×D5911yescharacteristic
357C42#1174568511yescharacteristic
358C42D4×D5911yescharacteristic
359C42#1174568911yescharacteristic
360C23—4721no—
361C23—4721no—
362C23—4721no—
363C23—4721no—
364C23—4721no—
365C23—4721no—
366C23—2362no—
367C23#1427369711yescharacteristic
368Q8—2362no—
369Q8—2362no—
370Q8—2362no—
371Q8—2362no—
372D4—4722no—
373D4—4721no—
374D4—4721no—
375D4—4721no—
376D4—4721no—
377D4—2364no—
378D4—2362no—
379D4—2362no—
380D4—2362no—
381D4—2362no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—1184no—
391C2×C4—1182no—
392C2×C4—2361no—
393C2×C4—2361no—
394C2×C4—2361no—
395C2×C4—2361no—
396C2×C4—2362no—
397C2×C4—2362no—
398C2×C4—2361no—
399C2×C4C22⋊C4×D5911yescharacteristic
400C2×C4#1427368911yescharacteristic
401C2×C4C4×D23611yescharacteristic
402C2×C4#1427370011yescharacteristic
403C2×C4#1427370211yescharacteristic
404C2×C4#1427371211yescharacteristic
405C2×C4C2×D47211yescharacteristic
406C2×C4SD16×D5911yescharacteristic
407C2×C4#1427374811yescharacteristic
408C2×C4#1427374911yescharacteristic
409C2×C4#1427375111yescharacteristic
410C2×C4#1427375511yescharacteristic
411C2×C4#1427375511yescharacteristic
412C2×C4#1427375911yescharacteristic
413C8—42no—
414C8—81no—
415C8—4721no—
416C22—9441no—
417C22—9441no—
418C22—9441no—
419C22—9441no—
420C22—4722no—
421C22—4722no—
422C22—4722no—
423C22#1683728011yescharacteristic
424C22#1683753811yescharacteristic
425C22#1683754211yescharacteristic
426C22#1683754811yescharacteristic
427C22#1683754911yescharacteristic
428C22#1683757611yescharacteristic
429C22#1683757611yescharacteristic
430C4—21no—
431C4—21no—
432C4—42no—
433C4—81no—
434C4—4721no—
435C4—2364no—
436C4—2362no—
437C4C4×D47211yescharacteristic
438C4#1683748911yescharacteristic
439C4#1683750111yescharacteristic
440C4#1683751511yescharacteristic
441C4#1683759811yescharacteristic
442C4#1683760111yescharacteristic
443C4#1683761811yescharacteristic
444C4#1683762711yescharacteristic
445C2—9442no—
446C2#2142318711yescharacteristic
447C2#2142319411yescharacteristic
448C2#2142320111yescharacteristic
449C2#2142320811yescharacteristic
450C2#2142444311yescharacteristic
451C2#2142445211yescharacteristic
452C2#2142449811yescharacteristic
subgroupG/H
centerC23#14273697
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1279C2
socleC23×C59#120
prime radicalC2×#14273724C22
cosocleC2×C42×C59C23
hypercenter#1279D59
hypocenterC59#9062
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #21427154C2semidirect
5. C2×#16837147C2semidirect
6. #21421936C2semidirect
7. C59×#1279C2semidirect
12. #16837749C4semidirect
225. #1279D59semidirect
254. C59#9062semidirect

Maximal subgroups

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

subgroupindex
C2×#168377492
#214271542
#214250232
#214250222
C2×#168371472
#214219362
C59×#12792
#906259