Finite Group Databasebeta

← #28505748

Subgroups — #28505748

Order 15104.

590 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic59C211yesmaximal, characteristic, complemented
2C2×#16837203C211yesmaximal, characteristic, complemented
3C2×#16837203C211yesmaximal, characteristic, complemented
4#21424963C211yesmaximal, characteristic, complemented
5#21422188C211yesmaximal, characteristic, complemented
6#21422173C211yesmaximal, characteristic, complemented
7C22×D16×C59C211yesmaximal, characteristic
8C2×D4×Dic59—21no—
9C22×C59⋊C16C2211yescharacteristic
10D8×Dic59—22no—
11D8×Dic59—22no—
12C2×#14273661C2211yescharacteristic
13C2×#14273661C2211yescharacteristic
14C2×#14273648—21no—
15C2×#14273648—21no—
16C2×C8×Dic59C2211yescharacteristic
17#16837305—21no—
18#16837203—22no—
19#16837203—22no—
20C22×D8×C59C2211yescharacteristic
21C22×D8×C59C2211yescharacteristic
22C2×D16×C59—22no—
23C2×D16×C59—22no—
24C2×D16×C59C414yescomplemented
25C22×C16×C59C2211yescharacteristic
26C23×Dic59—41no—
27C22×C59⋊C8D411yescharacteristic
28D4×Dic59—24no—
29D4×Dic59—42no—
30C2×C4⋊Dic59—21no—
31C2×C4⋊Dic59—21no—
32C2×C22⋊Dic59—41no—
33C2×C22⋊Dic59—41no—
34C2×C22⋊Dic59—41no—
35C2×C4×Dic59D411yescharacteristic
36C2×C59⋊C16—21no—
37C2×C59⋊C16—21no—
38C2×C59⋊C16—21no—
39#14273661—21no—
40#14273661—21no—
41#14273661—21no—
42#14273661D412yes—
43#14273648—24no—
44#14273648—42no—
45C8×Dic59—21no—
46C8×Dic59—21no—
47C22×D4×C59—21no—
48C22×D4×C59—21no—
49C2×D8×C59—21no—
50C2×D8×C59—21no—
51C2×D8×C59—21no—
52C2×D8×C59—21no—
53C2×D8×C59—21no—
54C2×D8×C59—21no—
55C2×D8×C59—21no—
56C2×D8×C59—21no—
57C2×D8×C59C2×C412yes—
58C2×D8×C59C2×C412yescomplemented
59C2×D8×C59D412yes—
60C2×D8×C59D412yes—
61C22×C8×C59C2311yescharacteristic
62D16×C59—28no—
63C2×C16×C59—21no—
64C2×C16×C59—21no—
65C2×C16×C59C2×C412yescomplemented
66C24×C59—41no—
67C24×C59—41no—
68C2×D4×C59—22no—
69C2×D4×C59—22no—
70C2×D4×C59—22no—
71C2×D4×C59—22no—
72C2×D4×C59—41no—
73C2×D4×C59—41no—
74C2×D4×C59—41no—
75C2×D4×C59—41no—
76C2×D4×C59—41no—
77C2×D4×C59—41no—
78C2×D4×C59—41no—
79C2×D4×C59—41no—
80C22×C4×C59C2×D411yescharacteristic
81C22×Dic59—44no—
82C22×Dic59—41no—
83C22×Dic59—41no—
84C22×Dic59—82no—
85C22×Dic59—82no—
86C22×Dic59D811yescharacteristic
87C22×Dic59D811yescharacteristic
88D8×C59—22no—
89D8×C59—22no—
90D8×C59—22no—
91D8×C59—22no—
92D8×C59—22no—
93D8×C59—41no—
94D8×C59—41no—
95D8×C59C22⋊C414yescomplemented
96C2×C8×C59C22×C411yescharacteristic
97C2×C8×C59C2×D411yescharacteristic
98C2×C8×C59C2×D411yescharacteristic
99C2×C8×C59C2×D411yescharacteristic
100C2×C8×C59#4111yescharacteristic
101C2×C8×C59#4111yescharacteristic
102C22⋊Dic59—44no—
103C22⋊Dic59—82no—
104C22⋊Dic59—82no—
105C4⋊Dic59—22no—
106C4⋊Dic59—41no—
107C4⋊Dic59—41no—
108C4⋊Dic59—41no—
109C4×Dic59—21no—
110C4×Dic59—21no—
111C2×C59⋊C8—21no—
112C2×C59⋊C8—21no—
113C2×C59⋊C8—21no—
114C16×C59—22no—
115C59⋊C16—41no—
116C23×C59—42no—
117C23×C59—42no—
118C23×C59—42no—
119C23×C59—42no—
120C23×C59—81no—
121C23×C59—81no—
122C23×C59—81no—
123C23×C59—81no—
124C23×C59—81no—
125C23×C59—81no—
126C23×C59—81no—
127C23×C59—81no—
128C23×C59—81no—
129C23×C59—81no—
130C23×C59C2×D811yescharacteristic
131D4×C59—24no—
132D4×C59—42no—
133D4×C59—42no—
134D4×C59—42no—
135D4×C59—42no—
136D4×C59—42no—
137D4×C59—81no—
138D4×C59—81no—
139C2×C4×C59C4×D411yescharacteristic
140C2×C4×C59#12011yescharacteristic
141C2×C4×C59#12111yescharacteristic
142C2×C4×C59#13511yescharacteristic
143C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
145C2×Dic59—21no—
146C2×Dic59—21no—
147C2×Dic59—21no—
148C2×Dic59—21no—
149C2×Dic59—21no—
150C2×Dic59—42no—
151C2×Dic59—88no—
152C2×Dic59—81no—
153C2×Dic59—81no—
154C2×Dic59—81no—
155C2×Dic59—81no—
156C2×Dic59—81no—
157C2×Dic59D1612yescomplemented
158C8×C59C2×C22⋊C411yescharacteristic
159C8×C59C4×D411yescharacteristic
160C8×C59#12111yescharacteristic
161C8×C59#12311yescharacteristic
162C59⋊C8—41no—
163#13012—591nomaximal, Sylow
164C22×C59—44no—
165C22×C59—82no—
166C22×C59—82no—
167C22×C59—82no—
168C22×C59—82no—
169C22×C59—82no—
170C22×C59—82no—
171C22×C59—82no—
172C22×C59—82no—
173C22×C59—82no—
174C22×C59—161no—
175C22×C59—161no—
176C22×C59—161no—
177C22×C59—161no—
178C22×C59C4×D811yescharacteristic
179C22×C59#44711yescharacteristic
180C22×C59#45911yescharacteristic
181C22×C59C2×D1611yescharacteristic
182C22×C59#50811yescharacteristic
183C22×C59#50911yescharacteristic
184C22×C59#50911yescharacteristic
185C4×C59#38611yescharacteristic
186C4×C59#44211yescharacteristic
187C4×C59#44911yescharacteristic
188C4×C59#46311yescharacteristic
189Dic59—22no—
190Dic59—41no—
191Dic59—82no—
192Dic59—161no—
193C22×D16D5911yescharacteristic
194C2×C4×D8—591no—
195C2×#357—591no—
196C2×#357—591no—
197#1970—591no—
198#1380—591no—
199#1374—591no—
200C2×C59—84no—
201C2×C59—162no—
202C2×C59#187911yescharacteristic
203C2×C59C4×D1611yescharacteristic
204C2×C59#217711yescharacteristic
205C2×C59#218411yescharacteristic
206C2×C59#218611yescharacteristic
207C2×C59#220611yescharacteristic
208C2×C59#221011yescharacteristic
209C22×D8C2×D5911yescharacteristic
210C22×D8C2×D5911yescharacteristic
211C2×C4×D4—1181no—
212C2×D16—22no—
213C2×D16—22no—
214C2×D16Dic5914yescomplemented
215C22×C16—591no—
216C22×C16C2×D5911yescharacteristic
217C4×D8—1182no—
218C4×D8—1182no—
219C2×#107—591no—
220C2×#107—591no—
221C2×#102—1181no—
222C2×#102—1181no—
223C2×C4×C8—591no—
224#390—1181no—
225#357—1182no—
226#357—1182no—
227C59#1301211yescharacteristic, complemented, Sylow
228C22×D4—21no—
229C22×D4—21no—
230C23×C4—2361no—
231C2×D8—21no—
232C2×D8—21no—
233C2×D8—21no—
234C2×D8—21no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8—21no—
238C2×D8—21no—
239C2×D8C2×Dic5912yes—
240C2×D8C2×Dic5912yescomplemented
241C2×D8C22⋊D5912yes—
242C2×D8C22⋊D5912yes—
243C22×C8—591no—
244C22×C8C22×D5911yescharacteristic
245C4×D4—1184no—
246C4×D4—2362no—
247C2×C4⋊C4—1181no—
248C2×C4⋊C4—1181no—
249C2×C22⋊C4—2361no—
250C2×C22⋊C4—2361no—
251C2×C22⋊C4—2361no—
252C2×C42—591no—
253D16—28no—
254C2×C16—21no—
255C2×C16—21no—
256C2×C16—1181no—
257C2×C16—1181no—
258C2×C16—1181no—
259C2×C16C2×Dic5912yescomplemented
260#107—592no—
261#107—1181no—
262#107—1181no—
263#107—1181no—
264#102—1184no—
265#102—2362no—
266C4×C8—1181no—
267C4×C8—1181no—
268C24—41no—
269C24—41no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C22×C4—591no—
283C22×C4—591no—
284C22×C4—4722no—
285C22×C4—4722no—
286C22×C4—2364no—
287C22×C4—2361no—
288C22×C4—2361no—
289C22×C4D4×D5911yescharacteristic
290D8—22no—
291D8—22no—
292D8—22no—
293D8—22no—
294D8—22no—
295D8—41no—
296D8—41no—
297D8C22⋊Dic5914yescomplemented
298C2×C8—1181no—
299C2×C8—1181no—
300C2×C8—1181no—
301C2×C8D4×D5911yescharacteristic
302C2×C8#1174568711yescharacteristic
303C2×C8#1174568711yescharacteristic
304C2×C8C22×Dic5911yescharacteristic
305C2×C8C2×C22⋊D5911yescharacteristic
306C2×C8C2×C22⋊D5911yescharacteristic
307C4⋊C4—1182no—
308C4⋊C4—2361no—
309C4⋊C4—2361no—
310C4⋊C4—2361no—
311C22⋊C4—4722no—
312C22⋊C4—4722no—
313C22⋊C4—2364no—
314C42—1181no—
315C42—1181no—
316C16—22no—
317C16—2361no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—81no—
326C23—81no—
327C23—81no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23D8×D5911yescharacteristic
333D4—24no—
334D4—42no—
335D4—42no—
336D4—42no—
337D4—42no—
338D4—42no—
339D4—81no—
340D4—81no—
341C2×C4—592no—
342C2×C4—1181no—
343C2×C4—1181no—
344C2×C4—1181no—
345C2×C4—1181no—
346C2×C4—1181no—
347C2×C4—4728no—
348C2×C4—4721no—
349C2×C4—4721no—
350C2×C4—4721no—
351C2×C4—4721no—
352C2×C4—4721no—
353C2×C4—2362no—
354C2×C4D4×Dic5911yescharacteristic
355C2×C4#1427369511yescharacteristic
356C2×C4#1427369911yescharacteristic
357C2×C4#1427374611yescharacteristic
358C2×C4#1427375111yescharacteristic
359C2×C4#1427375111yescharacteristic
360C8—2361no—
361C8C2×C22⋊Dic5911yescharacteristic
362C8D4×Dic5911yescharacteristic
363C8#1427369911yescharacteristic
364C8#1427370811yescharacteristic
365C22—44no—
366C22—82no—
367C22—82no—
368C22—82no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22—82no—
373C22—82no—
374C22—82no—
375C22—161no—
376C22—161no—
377C22—161no—
378C22—161no—
379C22D8×Dic5911yescharacteristic
380C22#1683753411yescharacteristic
381C22#1683759511yescharacteristic
382C22D16×D5911yescharacteristic
383C22#1683783111yescharacteristic
384C22#1683783611yescharacteristic
385C22#1683783611yescharacteristic
386C4—1182no—
387C4—9441no—
388C4—4722no—
389C4—2361no—
390C4#1683728211yescharacteristic
391C4#1683751411yescharacteristic
392C4#1683754411yescharacteristic
393C4#1683761511yescharacteristic
394C2—84no—
395C2—162no—
396C2#2142444611yescharacteristic
397C2D16×Dic5911yescharacteristic
398C2#2142597211yescharacteristic
399C2#2142600611yescharacteristic
400C2#2142601611yescharacteristic
401C2#2142612911yescharacteristic
402C2#2142614911yescharacteristic
subgroupG/H
centerC23D8×D59
commutatorC2×C8×C59C22×C4
FrattiniC22×C8C22×D59
Fitting, prime radicalC22×D16×C59C2
socleC23×C59C2×D8
cosocleC22×C8×C59C23
hypercenterC22×D16D59
hypocenterC59#13012
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×D16

Complements

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

NH ≅ G/Ntype
1. C2×D8×Dic59C2semidirect
2. C2×#16837203C2semidirect
3. C2×#16837203C2semidirect
4. #21424963C2semidirect
5. #21422188C2semidirect
6. #21422173C2semidirect
24. C2×D16×C59C4semidirect
58. C2×D8×C59C2×C4semidirect
65. C2×C16×C59C2×C4semidirect
95. D8×C59C22⋊C4semidirect
157. C2×Dic59D16semidirect
214. C2×D16Dic59semidirect
227. C59#13012semidirect
240. C2×D8C2×Dic59semidirect
259. C2×C16C2×Dic59semidirect
297. D8C22⋊Dic59semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic592
C2×#168372032
#214249632
#214221882
#214221732
C22×D16×C592
#1301259