Finite Group Databasebeta

← #28501978

Subgroups — #28501978

Order 15104.

316 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21435448C211yesmaximal, characteristic
2#21426298C211yesmaximal, characteristic, complemented
3#21426281C211yesmaximal, characteristic
4#21422107C211yesmaximal, characteristic, complemented
5#21422104C211yesmaximal, characteristic
6#21422036C211yesmaximal, characteristic, complemented
7C59×#2087C211yesmaximal, characteristic, complemented
8#16837936—21no—
9#16837710—21no—
10#16837703—21no—
11#16837643C2211yescharacteristic
12#16837638C2211yescharacteristic
13#16837631—21no—
14#16837625—21no—
15#16837618—21no—
16#16837229—21no—
17#16837227—21no—
18#16837205—21no—
19#16837202—21no—
20C22⋊(C59⋊C16)C2211yescharacteristic
21C22⋊(C59⋊C16)C2211yescharacteristic
22C2×#107×C59C2211yescharacteristic
23C2×C4⋊C8×C59C2211yescharacteristic
24C59×#389—21no—
25C59×#340—21no—
26C59×#340C2211yescharacteristic
27C2×Dic236D411yescharacteristic
28C2×#11745660—21no—
29C2×D472D411yescharacteristic
30#14273721—41no—
31#14273719—21no—
32#14273715—21no—
33#14273710—41no—
34#14273706—21no—
35#14273701—21no—
36C4×Dic118—21no—
37C4×D236—21no—
38C4×C22⋊D59—41no—
39#14273684—41no—
40C2×C59⋊C16—21no—
41C2×C59⋊C16—21no—
42#14273661D411yescharacteristic
43#14273661D411yescharacteristic
44#14273659—21no—
45#14273652—21no—
46#14273652—21no—
47#14273649—21no—
48#14273649—21no—
49C22×C8×C59D411yescharacteristic
50C22×C8×C59C2311yescharacteristic
51C2×C4⋊C4×C59—21no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59—41no—
54C2×C42×C59D411yescharacteristic
55#107×C59—21no—
56#107×C59—21no—
57C4⋊C8×C59—21no—
58C4⋊C8×C59—21no—
59#95×C59—41no—
60C22×C4×C59—41no—
61C22×C4×C59—41no—
62C22×C4×C59D811yescharacteristic
63C22×C4×C59D811yescharacteristic
64C22×C4×C59C2×D411yescharacteristic
65C2×C22⋊D59—41no—
66C2×D236—21no—
67C2×C4×D59—41no—
68C2×Dic118—21no—
69C2×C8×C59—21no—
70C2×C8×C59—41no—
71C2×C8×C59—41no—
72C2×C8×C59C2×D411yescharacteristic
73C2×C8×C59C2×D411yescharacteristic
74C4⋊C4×C59—22no—
75C4⋊C4×C59—41no—
76C4⋊C4×C59—41no—
77C4⋊C4×C59—41no—
78C4⋊C4×C59—82no—
79C42×C59—21no—
80C42×C59—21no—
81C22⋊Dic59—41no—
82(C2×D59)⋊C4—41no—
83(C2×D59)⋊C4—41no—
84(C2×D59)⋊C4—41no—
85(C2×D59)⋊C4—41no—
86C4⋊Dic59—21no—
87C4⋊Dic59—21no—
88Dic59⋊C4—41no—
89Dic59⋊C4—41no—
90Dic59⋊C4—41no—
91Dic59⋊C4—41no—
92C4×Dic59—41no—
93Dic236—41no—
94D472—41no—
95#11745660—81no—
96C59⋊C16—41no—
97C59⋊C16—41no—
98C23×C59C2×D811yescharacteristic
99C22×D59—41no—
100C2×C4×C59—21no—
101C2×C4×C59—21no—
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—21no—
106C2×C4×C59—41no—
107C2×C4×C59—42no—
108C2×C4×C59—81no—
109C2×C4×C59—81no—
110C2×C4×C59—81no—
111C2×C4×C59—81no—
112C2×C4×C59—81no—
113C2×C4×C59#12011yescharacteristic
114C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
115C22⋊D59—81no—
116C22⋊D59—81no—
117C2×Dic59—41no—
118C2×Dic59—41no—
119C2×Dic59—41no—
120D236—41no—
121D236—41no—
122C4×D59—82no—
123Dic118—41no—
124Dic118—41no—
125C8×C59—21no—
126C8×C59—21no—
127C8×C59—41no—
128#12293—591nomaximal, Sylow
129C22×C59—21no—
130C22×C59—21no—
131C22×C59#44711yescharacteristic
132C22×C59#50811yescharacteristic
133C22×C59#51011yescharacteristic
134C2×D59—81no—
135C2×D59—81no—
136C2×D59—81no—
137C4×C59—21no—
138C4×C59—41no—
139C4×C59—41no—
140C4×C59—82no—
141C4×C59—161no—
142C4×C59#45611yescharacteristic
143C4×C59#45811yescharacteristic
144Dic59—81no—
145Dic59—81no—
146Dic59—81no—
147#3250—591no—
148#2236—591no—
149#2233—591no—
150#2087D5911yescharacteristic, complemented
151#1348—591no—
152#1347—591no—
153#1322—591no—
154C2×C59—21no—
155C2×C59—21no—
156C2×C59#161011yescharacteristic
157C2×C59#218911yescharacteristic
158C2×C59#219011yescharacteristic
159D59—161no—
160#529—1181no—
161#479—1181no—
162#478—1181no—
163#467—591no—
164#466—591no—
165#465—1181no—
166#464—1181no—
167#463—1181no—
168C2×#107C2×D5911yescharacteristic
169C2×C4⋊C8C2×D5911yescharacteristic
170#389—21no—
171#367—1181no—
172#366—1181no—
173#358—1181no—
174#357—1181no—
175C22⋊C16—591no—
176C22⋊C16—591no—
177#340—21no—
178#340C2×D5911yescharacteristic
179C59#1229311yescharacteristic, complemented, Sylow
180C2×Q16—591no—
181C2×SD16—1181no—
182C2×D8—591no—
183C22×C8C22⋊D5911yescharacteristic
184C22×C8C22×D5911yescharacteristic
185#126—2361no—
186#125—1181no—
187#124—1181no—
188#123—2361no—
189C22⋊Q8—1181no—
190#121—1181no—
191C4×Q8—1181no—
192C4×D4—1181no—
193C4×D4—2361no—
194#117—2361no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—41no—
198C2×C42C22⋊D5911yescharacteristic
199C2×C16—1181no—
200C2×C16—1181no—
201#107—21no—
202#107—21no—
203#107—591no—
204#107—591no—
205#106—1181no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208#103—1181no—
209#103—1181no—
210#102—1181no—
211#102—1181no—
212#95—41no—
213C2×Q8—1181no—
214C2×D4—1181no—
215C2×D4—2361no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—2361no—
219C22×C4#1174566911yescharacteristic
220C22×C4#1174566911yescharacteristic
221C22×C4C2×C22⋊D5911yescharacteristic
222Q16—2361no—
223SD16—4721no—
224D8—2361no—
225C2×C8—21no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8D4×D5911yescharacteristic
229C2×C8D4×D5911yescharacteristic
230C4⋊C4—22no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—82no—
235C4⋊C4—1181no—
236C4⋊C4—1181no—
237C4⋊C4—2361no—
238C4⋊C4—2361no—
239C4⋊C4—2361no—
240C4⋊C4—2361no—
241C22⋊C4—2361no—
242C22⋊C4—2361no—
243C22⋊C4—2361no—
244C22⋊C4—2361no—
245C22⋊C4—2361no—
246C42—21no—
247C42—21no—
248C42—2361no—
249C16—2361no—
250C16—2361no—
251C23—2361no—
252C23C2×#1174566911yescharacteristic
253Q8—2361no—
254Q8—2361no—
255D4—4721no—
256D4—4721no—
257D4—2361no—
258D4—2361no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—4722no—
273C2×C4—2361no—
274C2×C4—2361no—
275C2×C4—2361no—
276C2×C4#1427369511yescharacteristic
277C2×C4#1427375211yescharacteristic
278C8—21no—
279C8—21no—
280C8—41no—
281C22—21no—
282C22—21no—
283C22—4721no—
284C22—4721no—
285C22—4721no—
286C22#1683753511yescharacteristic
287C22#1683783211yescharacteristic
288C22#1683784311yescharacteristic
289C4—21no—
290C4—41no—
291C4—41no—
292C4—82no—
293C4—161no—
294C4—4721no—
295C4—4721no—
296C4—4721no—
297C4#1683758411yescharacteristic
298C4#1683759111yescharacteristic
299C2—21no—
300C2—21no—
301C2—9441no—
302C2#2142309811yescharacteristic
303C2#2142603411yescharacteristic
304C2#2142604111yescharacteristic
subgroupG/H
centerC22#16837535
commutator, cosocleC22×C8×C59C23
FrattiniC22×C8C22×D59
FittingC59×#2087C2
socleC22×C59#447
prime radical#16837638C22
hypercenter#2087D59
hypocenterC59#12293
LCSG ▷ C22×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2087

Complements

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

NH ≅ G/Ntype
2. #21426298C2semidirect
4. #21422107C2semidirect
6. #21422036C2semidirect
7. C59×#2087C2semidirect
150. #2087D59semidirect
179. C59#12293semidirect

Maximal subgroups

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

subgroupindex
#214354482
#214262982
#214262812
#214221072
#214221042
#214220362
C59×#20872
#1229359