Finite Group Databasebeta

← #28502887

Subgroups — #28502887

Order 15104.

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

normal subgroups only

This group has 240 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#21426147C211yesmaximal, characteristic, complemented
2#21426133C211yesmaximal, characteristic
3#21423701C211yesmaximal, characteristic
4#21422902C211yesmaximal, characteristic, complemented
5#21422165C211yesmaximal, characteristic, complemented
6#21422144C211yesmaximal, characteristic, complemented
7C59×#1361C211yesmaximal, characteristic
8C2×Dic472—21no—
9C2×#14273671—21no—
10#16837782C2211yescharacteristic
11#16837748—21no—
12#16837748—21no—
13#16837526—21no—
14C4×Dic236C2211yescharacteristic
15C4⋊(C59⋊C16)C2211yescharacteristic
16#16837207—21no—
17#16837203—21no—
18#16837132—21no—
19C8×C59⋊C8C2211yescharacteristic
20C59×#493C2211yescharacteristic
21C59×C4⋊C16C2211yescharacteristic
22C59×#335C2211yescharacteristic
23C2×Dic236—21no—
24C2×Dic236—21no—
25C2×Dic236D411yescharacteristic
26#14273727—21no—
27C4×Dic118—21no—
28Dic472—42no—
29#14273671—42no—
30C2×C59⋊C16—21no—
31#14273661D411yescharacteristic
32Dic59⋊C8—41no—
33#14273652—21no—
34#14273648—42no—
35#14273648—41no—
36#14273648—41no—
37C4×C59⋊C8D411yescharacteristic
38C4×C59⋊C8D411yescharacteristic
39C8×Dic59—41no—
40C2×D8×C59—21no—
41C2×D8×C59—21no—
42#127×C59—21no—
43C2×C16×C59—21no—
44C4⋊C8×C59—21no—
45C4×C8×C59C2311yescharacteristic
46C2×D4×C59—41no—
47C2×D4×C59—41no—
48C2×D4×C59—41no—
49C2×Dic118—21no—
50C2×Dic118—41no—
51D8×C59—41no—
52D8×C59—41no—
53D8×C59—81no—
54C2×C8×C59—41no—
55C2×C8×C59C2×D411yescharacteristic
56C2×C8×C59#4111yescharacteristic
57C42×C59C2×D411yescharacteristic
58C4⋊Dic59—21no—
59C4⋊Dic59—41no—
60C4⋊Dic59—41no—
61Dic59⋊C4—41no—
62C4×Dic59—41no—
63C2×C59⋊C8—21no—
64C2×C59⋊C8D811yescharacteristic
65C2×C59⋊C8D811yescharacteristic
66Dic236—21no—
67Dic236—41no—
68Dic236—41no—
69Dic236—81no—
70Dic236D812yes—
71C16×C59—41no—
72C59⋊C16—41no—
73C23×C59—81no—
74D4×C59—82no—
75D4×C59—81no—
76D4×C59—81no—
77D4×C59—81no—
78D4×C59—81no—
79C2×C4×C59#12111yescharacteristic
80C2×C4×C59C2×D811yescharacteristic
81C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
82C2×Dic59—41no—
83C2×Dic59—41no—
84C2×Dic59—81no—
85Dic118—22no—
86Dic118—41no—
87Dic118—81no—
88Dic118—81no—
89C8×C59—21no—
90C8×C59—81no—
91C8×C59C2×D811yescharacteristic
92C8×C59#13511yescharacteristic
93C59⋊C8—21no—
94C59⋊C8—21no—
95C59⋊C8—41no—
96#12429—591nomaximal, Sylow
97C22×C59—161no—
98C22×C59—161no—
99C22×C59—161no—
100C22×C59#45911yescharacteristic
101C4×C59—21no—
102C4×C59#46611yescharacteristic
103C4×C59#47211yescharacteristic
104C4×C59#50811yescharacteristic
105C4×C59#51011yescharacteristic
106Dic59—42no—
107Dic59—81no—
108Dic59—161no—
109#2209—591no—
110#2207—591no—
111#1709—591no—
112C8×Q16—591no—
113#1370—591no—
114#1362—591no—
115#1361D5911yescharacteristic
116C2×C59—321no—
117C2×C59#166711yescharacteristic
118C2×C59#221111yescharacteristic
119C2×C59#221211yescharacteristic
120C2×Q32—1181no—
121C2×SD32—1181no—
122#494—591no—
123#493C2×D5911yescharacteristic
124#486—1181no—
125#486—1181no—
126C8×Q8—1181no—
127C4×Q16—591no—
128C4⋊C16—591no—
129C4⋊C16C2×D5911yescharacteristic
130#358—1181no—
131#357—1181no—
132#335C2×D5911yescharacteristic
133Q8⋊C8—1181no—
134C82—591no—
135C59#1242911yescharacteristic, complemented, Sylow
136C2×Q16—591no—
137C2×Q16—1181no—
138C2×Q16—1181no—
139C2×D8—21no—
140C2×D8—21no—
141C4⋊Q8—1181no—
142#127—21no—
143C4×Q8—1181no—
144Q32—2362no—
145SD32—2362no—
146C2×C16—21no—
147C2×C16—1181no—
148#107—591no—
149C4⋊C8—21no—
150C4⋊C8—2361no—
151#103—1181no—
152#102—2361no—
153#102—2361no—
154#102—2362no—
155C4×C8—591no—
156C4×C8—591no—
157C4×C8—2361no—
158C4×C8C22×D5911yescharacteristic
159C2×Q8—1181no—
160C2×Q8—2361no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—41no—
164Q16—592no—
165Q16—1181no—
166Q16—4721no—
167Q16—2361no—
168Q16—2361no—
169D8—41no—
170D8—41no—
171D8—81no—
172C2×C8—41no—
173C2×C8—591no—
174C2×C8—591no—
175C2×C8—1181no—
176C2×C8#1174568511yescharacteristic
177C2×C8D4×D5911yescharacteristic
178C4⋊C4—1181no—
179C4⋊C4—2361no—
180C4⋊C4—2361no—
181C4⋊C4—2361no—
182C42—2361no—
183C42D4×D5911yescharacteristic
184C16—41no—
185C16—2361no—
186C23—81no—
187Q8—1182no—
188Q8—4721no—
189Q8—4721no—
190Q8—2361no—
191D4—82no—
192D4—81no—
193D4—81no—
194D4—81no—
195D4—81no—
196C2×C4—4721no—
197C2×C4—2361no—
198C2×C4—2361no—
199C2×C4#1427370011yescharacteristic
200C2×C4D8×D5911yescharacteristic
201C2×C4#1427375411yescharacteristic
202C8—21no—
203C8—81no—
204C8—1181no—
205C8—1181no—
206C8—2361no—
207C8D8×D5911yescharacteristic
208C8#1427374811yescharacteristic
209C22—161no—
210C22—161no—
211C22—161no—
212C22#1683759611yescharacteristic
213C4—21no—
214C4—9441no—
215C4—4721no—
216C4—2362no—
217C4#1683763711yescharacteristic
218C4#1683767111yescharacteristic
219C4#1683783111yescharacteristic
220C4#1683784111yescharacteristic
221C2—321no—
222C2#2142345011yescharacteristic
223C2#2142615711yescharacteristic
224C2#2142616411yescharacteristic
subgroupG/H
centerC22#16837596
commutator, cosocleC4×C8×C59C23
FrattiniC4×C8C22×D59
FittingC59×#1361C2
socleC22×C59#459
prime radicalC59×#493C22
hypercenter#1361D59
hypocenterC59#12429
LCSG ▷ C4×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
1. #21426147C2semidirect
4. #21422902C2semidirect
5. #21422165C2semidirect
6. #21422144C2semidirect
135. C59#12429semidirect

Maximal subgroups

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

subgroupindex
#214261472
#214261332
#214237012
#214229022
#214221652
#214221442
C59×#13612
#1242959