Finite Group Databasebeta

← #28500226

Subgroups — #28500226

Order 15104.

258 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 69 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#21434644C211yesmaximal, characteristic
2#21425907C211yesmaximal, characteristic
3#21425907C211yesmaximal, characteristic
4#21422158C211yesmaximal, characteristic, complemented
5#21422157C211yesmaximal, characteristic, complemented
6#21422156C211yesmaximal, characteristic, complemented
7C59×#1366C211yesmaximal, characteristic, complemented
8#16837958C411yescharacteristic
9#125×D59C411yescharacteristic
10#16837810—21no—
11#16837809—21no—
12#16837804C2211yescharacteristic
13#16837801C411yescharacteristic
14#16837801C411yescharacteristic
15#16837443—21no—
16#16837441—21no—
17C4×#11745659C2211yescharacteristic
18#16837223C2211yescharacteristic
19#16837223C2211yescharacteristic
20#16837183—21no—
21#16837183—21no—
22#16837179—21no—
23#16837179—21no—
24C59×#499C2211yescharacteristic
25C59×#364C2211yescharacteristic
26C59×#364C2211yescharacteristic
27C2×#11745659D411yescharacteristic
28C2×#11745659D411yescharacteristic
29#14273726—21no—
30#14273719C2×C411yescharacteristic
31#14273719C2×C411yescharacteristic
32#14273718—21no—
33#14273717—41no—
34#14273705—41no—
35#14273692—41no—
36#14273685—21no—
37C4⋊C4×D59—21no—
38C4⋊C4×D59—41no—
39C42×D59C2×C411yescharacteristic
40#14273667—21no—
41#14273667—21no—
42#14273661—21no—
43#14273660—21no—
44#14273660—21no—
45#14273659—21no—
46#14273658—21no—
47#14273658—21no—
48#14273637D411yescharacteristic
49#14273637D411yescharacteristic
50C4×C59⋊C8C2×C411yescharacteristic
51#125×C59C2×C411yescharacteristic
52#125×C59C2×C411yescharacteristic
53M32×C59—21no—
54M32×C59—21no—
55#107×C59—21no—
56#106×C59—21no—
57C4×C8×C59C2311yescharacteristic
58C2×C4×D59—21no—
59C2×C4×D59—41no—
60C2×C4×D59C22⋊C411yescharacteristic
61C2×Dic118—41no—
62C2×C8×C59C2×D411yescharacteristic
63C2×C8×C59C2×D411yescharacteristic
64C4⋊C4×C59—21no—
65C4⋊C4×C59—21no—
66C4⋊C4×C59—41no—
67C4⋊C4×C59—41no—
68C42×C59C22×C411yescharacteristic
69(C2×D59)⋊C4—41no—
70C4⋊Dic59—21no—
71C4⋊Dic59—21no—
72C4⋊Dic59—41no—
73Dic59⋊C4—41no—
74Dic59⋊C4—41no—
75Dic59⋊C4—41no—
76Dic59⋊C4—41no—
77Dic59⋊C4—41no—
78C4×Dic59—21no—
79C4×Dic59—41no—
80C4×Dic59C22⋊C411yescharacteristic
81C2×C59⋊C8C22⋊C411yescharacteristic
82C2×C59⋊C8C22⋊C411yescharacteristic
83#11745659—21no—
84#11745659—21no—
85#11745659—21no—
86#11745659—21no—
87C16×C59—41no—
88C16×C59—41no—
89C59⋊C16—41no—
90C59⋊C16—41no—
91C22×D59#10011yescharacteristic
92C2×C4×C59—21no—
93C2×C4×C59—41no—
94C2×C4×C59—41no—
95C2×C4×C59C2×C22⋊C411yescharacteristic
96C2×Dic59—21no—
97C2×Dic59—41no—
98C2×Dic59—41no—
99C2×Dic59#10011yescharacteristic
100C4×D59—21no—
101C4×D59—21no—
102C4×D59—81no—
103C4×D59—82no—
104Dic118—82no—
105C8×C59#13711yescharacteristic
106C8×C59#13711yescharacteristic
107C8×C59#13711yescharacteristic
108C8×C59#13711yescharacteristic
109C59⋊C8—21no—
110C59⋊C8—21no—
111#11994—591nomaximal, Sylow
112C22×C59C2×#10011yescharacteristic
113C2×D59—21no—
114C2×D59—41no—
115C4×C59—41no—
116C4×C59—81no—
117C4×C59—81no—
118C4×C59#41911yescharacteristic
119C4×C59#41911yescharacteristic
120Dic59—21no—
121Dic59—41no—
122Dic59—81no—
123Dic59—81no—
124#3166—591no—
125#2165—591no—
126#2165—591no—
127#1366—591no—
128#1366—591no—
129#1366—591no—
130#1366D5911yescharacteristic, complemented
131C2×C59—21no—
132C2×C59#155811yescharacteristic
133D59—41no—
134#533—591no—
135C2×#125—591no—
136#501—1181no—
137#501—1181no—
138#499—591no—
139#499—591no—
140#499—591no—
141#499C2×D5911yescharacteristic
142#428—1181no—
143#428—1181no—
144C4×M16—591no—
145#364—591no—
146#364—591no—
147#364C2×D5911yescharacteristic
148#364C2×D5911yescharacteristic
149#349—1181no—
150#349—1181no—
151#347—1181no—
152#347—1181no—
153C59#1199411yescharacteristic, complemented, Sylow
154C2×M16—591no—
155C2×M16—591no—
156C4⋊Q8—1181no—
157#125—591no—
158#125—591no—
159#125—1181no—
160#125—2361no—
161#125C4×D5911yescharacteristic
162#125C4×D5911yescharacteristic
163C22⋊Q8—2361no—
164C4×Q8—2361no—
165#117—1181no—
166C2×C4⋊C4—1181no—
167C2×C4⋊C4—2361no—
168C2×C42—591no—
169M32—21no—
170M32—21no—
171M32—1181no—
172M32—1181no—
173#107—21no—
174#107—1181no—
175#107—1181no—
176#107—1181no—
177#106—21no—
178#106—1181no—
179#106—1181no—
180#106—1181no—
181#97—591no—
182#97—591no—
183C4×C8—591no—
184C4×C8C22×D5911yescharacteristic
185C2×Q8—2361no—
186C22×C4—591no—
187C22×C4—1181no—
188C22×C4—2361no—
189M16—1181no—
190M16—1181no—
191M16—1181no—
192M16—1181no—
193C2×C8—591no—
194C2×C8—591no—
195C2×C8D4×D5911yescharacteristic
196C2×C8D4×D5911yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—1181no—
202C4⋊C4—1181no—
203C4⋊C4—2361no—
204C4⋊C4—2361no—
205C4⋊C4—2361no—
206C4⋊C4—2361no—
207C4⋊C4—2361no—
208C4⋊C4—2361no—
209C22⋊C4—2361no—
210C42—591no—
211C42—1181no—
212C42—2361no—
213C42C2×C4×D5911yescharacteristic
214C16—41no—
215C16—41no—
216C16—2361no—
217C16—2361no—
218C23—591no—
219Q8—4722no—
220C2×C4—21no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—591no—
224C2×C4—1181no—
225C2×C4—1181no—
226C2×C4—1181no—
227C2×C4—4721no—
228C2×C4—4722no—
229C2×C4—2361no—
230C2×C4—2361no—
231C2×C4C22⋊C4×D5911yescharacteristic
232C8—1181no—
233C8—1181no—
234C8#1427375611yescharacteristic
235C8#1427375611yescharacteristic
236C8#1427375911yescharacteristic
237C8#1427375911yescharacteristic
238C22—1181no—
239C22—2361no—
240C22#100×D5911yescharacteristic
241C4—41no—
242C4—81no—
243C4—81no—
244C4—1181no—
245C4—4721no—
246C4—4721no—
247C4—2361no—
248C4#1683740911yescharacteristic
249C4#1683740911yescharacteristic
250C2—21no—
251C2—2361no—
252C2#2142282011yescharacteristic
subgroupG/H
centerC2#21422820
commutatorC42×C59C22×C4
FrattiniC4×C8C22×D59
FittingC59×#1366C2
socleC2×C59#1558
prime radicalC22×D59#100
cosocleC4×C8×C59C23
hypercenter#1366D59
hypocenterC59#11994
LCSG ▷ C42×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1366

Complements

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

NH ≅ G/Ntype
4. #21422158C2semidirect
5. #21422157C2semidirect
6. #21422156C2semidirect
7. C59×#1366C2semidirect
130. #1366D59semidirect
153. C59#11994semidirect

Maximal subgroups

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

subgroupindex
#214346442
#214259072
#214221582
#214221572
#214221562
C59×#13662
#1199459