Finite Group Databasebeta

← #28484147

Subgroups — #28484147

Order 15104.

488 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21433181C211yesmaximal, characteristic, complemented
2C2×#16837500C211yesmaximal, characteristic
3#21422486C211yesmaximal, characteristic
4#21422416C211yesmaximal, characteristic
5#21421940C211yesmaximal, characteristic, complemented
6#21421926C211yesmaximal, characteristic, complemented
7C59×#1479C211yesmaximal, characteristic, complemented
8C22×#11745671C411yescharacteristic
9C2×C4×D236C2211yescharacteristic
10#16837533—22no—
11#16837533—22no—
12#16837500—22no—
13#16837500—22no—
14#16837459—22no—
15#16837455C2211yescharacteristic
16#16837455C2211yescharacteristic
17C2×#14273660C411yescharacteristic
18C2×#14273651C411yescharacteristic
19C2×#14273647C411yescharacteristic
20C2×#14273638C2211yescharacteristic
21#16837129—22no—
22#16837125—22no—
23C2×C4×Q8×C59C2211yescharacteristic
24C59×#431C2211yescharacteristic
25C59×#431C2211yescharacteristic
26C59×Q8⋊C8—22no—
27C22×D236C2×C411yescharacteristic
28C22×C4×D59—21no—
29C2×#11745671—22no—
30C2×#11745671—22no—
31C2×#11745671—22no—
32C22×C59⋊C8C2×C411yescharacteristic
33C22×C59⋊C8C2×C411yescharacteristic
34C4×D236—21no—
35C4×D236—21no—
36C4×D236—21no—
37C4×D236—21no—
38C2×C4⋊Dic59C2×C411yescharacteristic
39C2×(C2×D59)⋊C4—21no—
40#14273660—22no—
41C4⋊(C59⋊C8)—24no—
42C4⋊(C59⋊C8)—21no—
43C4⋊(C59⋊C8)—21no—
44#14273651—22no—
45#14273647—22no—
46C22⋊(C59⋊C8)—21no—
47C22⋊(C59⋊C8)D412yes—
48#14273638—24no—
49#14273638—21no—
50#14273638—21no—
51C4×C59⋊C8—21no—
52C4×C59⋊C8D412yes—
53C22×Q8×C59C2×C411yescharacteristic
54C4×Q8×C59—21no—
55C4×Q8×C59—21no—
56C4×Q8×C59D412yes—
57C4×Q8×C59D412yes—
58C2×C4⋊C4×C59—21no—
59C2×C4⋊C4×C59C2×C411yescharacteristic
60C2×C42×C59—21no—
61C2×C42×C59C2311yescharacteristic
62C4⋊C8×C59—21no—
63C4⋊C8×C59—21no—
64C22⋊C8×C59—21no—
65C22⋊C8×C59—21no—
66C4×C8×C59—21no—
67C4×C8×C59—21no—
68C23×D59—21no—
69C2×Q8×C59—21no—
70C2×Q8×C59—21no—
71C2×Q8×C59—21no—
72C2×Q8×C59—21no—
73C2×Q8×C59—21no—
74C2×Q8×C59C22⋊C412yes—
75C22×C4×C59—21no—
76C22×C4×C59—21no—
77C22×C4×C59C22×C411yescharacteristic
78C22×C4×C59C2×D411yescharacteristic
79C22×C4×C59#4111yescharacteristic
80C22×Dic59—21no—
81C2×D236—21no—
82C2×D236—21no—
83C2×D236—21no—
84C2×D236—21no—
85C2×D236—21no—
86C2×D236M1612yes—
87C2×C4×D59—41no—
88C2×C4×D59—41no—
89C2×C4×D59—82no—
90C2×C8×C59—41no—
91C2×C8×C59—41no—
92C4⋊C4×C59—21no—
93C4⋊C4×C59—22no—
94C4⋊C4×C59—22no—
95C4⋊C4×C59C22⋊C412yes—
96C42×C59—22no—
97C42×C59—22no—
98C42×C59C2×D411yescharacteristic
99C42×C59C2×D411yescharacteristic
100C42×C59C2×D411yescharacteristic
101C42×C59#4111yescharacteristic
102#11745671—28no—
103(C2×D59)⋊C4—41no—
104(C2×D59)⋊C4—41no—
105C4⋊Dic59—21no—
106C4⋊Dic59—21no—
107C2×C59⋊C8—21no—
108C2×C59⋊C8—21no—
109C2×C59⋊C8—21no—
110C2×C59⋊C8—22no—
111C2×C59⋊C8—22no—
112C2×C59⋊C8—21no—
113C2×C59⋊C8—21no—
114C2×C59⋊C8M1612yes—
115C23×C59C4×D411yescharacteristic
116C22×D59—22no—
117C22×D59—41no—
118C22×D59—41no—
119C22×D59—81no—
120C22×D59—81no—
121Q8×C59—22no—
122Q8×C59—22no—
123Q8×C59—41no—
124Q8×C59—41no—
125C2×C4×C59—22no—
126C2×C4×C59—22no—
127C2×C4×C59—41no—
128C2×C4×C59—41no—
129C2×C4×C59—41no—
130C2×C4×C59—41no—
131C2×C4×C59—81no—
132C2×C4×C59C2×C22⋊C411yescharacteristic
133C2×C4×C59C4×D411yescharacteristic
134C2×C4×C59#12011yescharacteristic
135C2×C4×C59#12111yescharacteristic
136C2×C4×C59#12111yescharacteristic
137C2×C4×C59#12311yescharacteristic
138C2×C4×C59C2×M1611yescharacteristic
139C2×C4×C59C2×M1611yescharacteristic
140C2×C4×C59#13111yescharacteristic
141C2×C4×C59#13111yescharacteristic
142C2×Dic59—41no—
143C2×Dic59—81no—
144D236—22no—
145D236—22no—
146D236—41no—
147D236—41no—
148C4×D59—82no—
149C4×D59—82no—
150C8×C59—81no—
151C8×C59—81no—
152C59⋊C8—22no—
153C59⋊C8—42no—
154C59⋊C8—42no—
155C59⋊C8—41no—
156#9094—591nomaximal, Sylow
157C22×C59—21no—
158C22×C59—21no—
159C22×C59#38611yescharacteristic
160C22×C59#43511yescharacteristic
161C22×C59#43611yescharacteristic
162C2×D59—42no—
163C2×D59—82no—
164C2×D59—81no—
165C2×D59—81no—
166C2×D59—82no—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—21no—
171C4×C59—42no—
172C4×C59—42no—
173C4×C59#40711yescharacteristic
174C4×C59#40811yescharacteristic
175C4×C59#43511yescharacteristic
176C4×C59#43611yescharacteristic
177Dic59—81no—
178#2983—591no—
179C2×#440—591no—
180#1479D5911yescharacteristic, complemented
181#1478—591no—
182#1460—591no—
183#1281—591no—
184#1275—591no—
185C2×C59—21no—
186C2×C59—21no—
187C2×C59#187011yescharacteristic
188C2×C59#190311yescharacteristic
189C2×C59#190511yescharacteristic
190D59—82no—
191C22×SD16—591no—
192C2×C4×Q8C2×D5911yescharacteristic
193C2×C4×D4—591no—
194#446—1182no—
195#446—1182no—
196#440—1182no—
197#440—1182no—
198#432—1182no—
199#431—591no—
200#431—591no—
201#431C2×D5911yescharacteristic
202#431C2×D5911yescharacteristic
203C2×#107—591no—
204C2×#103—591no—
205C2×#102—591no—
206C2×#97—591no—
207Q8⋊C8—22no—
208D4⋊C8—1182no—
209#323—1182no—
210C59#909411yescharacteristic, complemented, Sylow
211C22×Q8C4×D5911yescharacteristic
212C22×D4—591no—
213C23×C4—1181no—
214C2×SD16—1182no—
215C2×SD16—1182no—
216C2×SD16—1182no—
217C22×C8—591no—
218C22×C8—591no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8D23612yes—
222C4×Q8C22⋊D5912yes—
223C4×D4—1181no—
224C4×D4—1181no—
225C4×D4—1181no—
226C4×D4—1181no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—591no—
229C2×C4⋊C4C4×D5911yescharacteristic
230C2×C22⋊C4—1181no—
231C2×C42—21no—
232C2×C42C22×D5911yescharacteristic
233#107—1182no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—1184no—
237C4⋊C8—1181no—
238C4⋊C8—1181no—
239#103—1182no—
240#102—1182no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8—592no—
244C22⋊C8—1181no—
245#97—1184no—
246#97—1181no—
247#97—1181no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8—592no—
251C4×C8—1181no—
252C24—1181no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8(C2×D59)⋊C412yes—
259C2×D4—592no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4—1181no—
263C2×D4—1181no—
264C2×D4—1181no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—1181no—
268C22×C4—4722no—
269C22×C4—2361no—
270C22×C4—2361no—
271C22×C4C2×C4×D5911yescharacteristic
272C22×C4D4×D5911yescharacteristic
273C22×C4#1174568711yescharacteristic
274SD16—1188no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—592no—
278C2×C8—1181no—
279C2×C8—1181no—
280C2×C8—1181no—
281C2×C8—1182no—
282C2×C8—1182no—
283C2×C8—1181no—
284C2×C8—1181no—
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—1181no—
289C4⋊C4—1181no—
290C4⋊C4(C2×D59)⋊C412yes—
291C22⋊C4—2361no—
292C22⋊C4—2361no—
293C42—22no—
294C42—22no—
295C42C2×D23611yescharacteristic
296C42D4×D5911yescharacteristic
297C42#1174568711yescharacteristic
298C42C2×C22⋊D5911yescharacteristic
299C23—1182no—
300C23—4721no—
301C23—4721no—
302C23—2361no—
303C23—2361no—
304C23(C22⋊D59)⋊C411yescharacteristic
305Q8—22no—
306Q8—22no—
307Q8—41no—
308Q8—41no—
309D4—1182no—
310D4—1182no—
311D4—2361no—
312D4—2361no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—4722no—
321C2×C4—4722no—
322C2×C4—4721no—
323C2×C4—2361no—
324C2×C4C2×(C2×D59)⋊C411yescharacteristic
325C2×C4(C22⋊D59)⋊C411yescharacteristic
326C2×C4#1427369711yescharacteristic
327C2×C4#1427369911yescharacteristic
328C2×C4#1427369911yescharacteristic
329C2×C4#1427371111yescharacteristic
330C2×C4M16×D5911yescharacteristic
331C2×C4M16×D5911yescharacteristic
332C2×C4#1427373311yescharacteristic
333C2×C4#1427373311yescharacteristic
334C8—81no—
335C8—81no—
336C8—1182no—
337C8—2362no—
338C8—2362no—
339C8—2361no—
340C22—21no—
341C22—21no—
342C22—4722no—
343C22—4722no—
344C22—4721no—
345C22—4721no—
346C22—2362no—
347C22#1683727911yescharacteristic
348C22#1683747611yescharacteristic
349C22#1683747711yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—42no—
355C4—42no—
356C4—4721no—
357C4#1683736511yescharacteristic
358C4#1683736811yescharacteristic
359C4#1683747611yescharacteristic
360C4#1683747711yescharacteristic
361C2—21no—
362C2—21no—
363C2—4722no—
364C2#2142439111yescharacteristic
365C2#2142457411yescharacteristic
366C2#2142458811yescharacteristic
subgroupG/H
centerC22#16837279
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1479C2
socleC22×C59#386
prime radicalC22×D236C2×C4
cosocleC2×C42×C59C23
hypercenter#1479D59
hypocenterC59#9094
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
1. #21433181C2semidirect
5. #21421940C2semidirect
6. #21421926C2semidirect
7. C59×#1479C2semidirect
180. #1479D59semidirect
210. C59#9094semidirect

Maximal subgroups

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

subgroupindex
#214331812
C2×#168375002
#214224862
#214224162
#214219402
#214219262
C59×#14792
#909459