Finite Group Databasebeta

← #28476117

Subgroups — #28476117

Order 15104.

202 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 43 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#21424310C211yesmaximal, characteristic
2#21421922C211yesmaximal, characteristic
3C59×#1319C211yesmaximal, characteristic
4#16837880C411yescharacteristic
5#16837442—21no—
6C2×#14273646C411yescharacteristic
7#16837162—21no—
8#16837157—21no—
9C59×#391C2211yescharacteristic
10C59×#324—21no—
11C2×#11745664—21no—
12C22×C59⋊C8—41no—
13Q8×Dic59—41no—
14Q8×Dic59—41no—
15#14273686—21no—
16#14273686—41no—
17#14273660—41no—
18#14273658—41no—
19#14273646—21no—
20#14273646C812yescomplemented
21C22×Q8×C59C2×C411yescharacteristic
22C2×C4⋊C4×C59D411yescharacteristic
23C2×C42×C59D411yescharacteristic
24C22⋊C8×C59—41no—
25#95×C59—41no—
26C2×Q8×C59—21no—
27C2×Q8×C59—41no—
28C2×Q8×C59—41no—
29C2×Q8×C59C2×C811yescharacteristic
30C2×Q8×C59M1611yescharacteristic
31C22×C4×C59—21no—
32C22×C4×C59—21no—
33C22×C4×C59—21no—
34C22×C4×C59C22⋊C411yescharacteristic
35C2×C8×C59—81no—
36C4⋊C4×C59—41no—
37C42×C59—41no—
38C22⋊Dic59—41no—
39C4⋊Dic59—21no—
40C4⋊Dic59—21no—
41C4⋊Dic59—41no—
42C4⋊Dic59—41no—
43C4×Dic59—41no—
44C4×Dic59—42no—
45#11745664—22no—
46#11745664—41no—
47C2×C59⋊C8—41no—
48C2×C59⋊C8—42no—
49C2×C59⋊C8—81no—
50C2×C59⋊C8—81no—
51C23×C59#9911yescharacteristic
52Q8×C59—41no—
53Q8×C59—41no—
54Q8×C59—42no—
55C2×C4×C59—21no—
56C2×C4×C59—21no—
57C2×C4×C59—21no—
58C2×C4×C59—21no—
59C2×C4×C59—21no—
60C2×C4×C59—21no—
61C2×C4×C59—41no—
62C2×C4×C59—41no—
63C2×C4×C59—41no—
64C2×C4×C59—41no—
65C2×C4×C59—41no—
66C2×C4×C59—81no—
67C2×C4×C59C22⋊C811yescharacteristic
68C2×C4×C59#10111yescharacteristic
69C2×Dic59—41no—
70C2×Dic59—41no—
71C8×C59—161no—
72C59⋊C8—42no—
73C59⋊C8—82no—
74#7376—591nomaximal, Sylow
75C22×C59—21no—
76C22×C59—21no—
77C22×C59#32411yescharacteristic
78C22×C59AΣL(1,𝔽16)11yescharacteristic
79C22×C59#35211yescharacteristic
80C4×C59—21no—
81C4×C59—21no—
82C4×C59—41no—
83C4×C59—41no—
84C4×C59—41no—
85C4×C59—41no—
86C4×C59—81no—
87Dic59—81no—
88Dic59—81no—
89#1857—591no—
90#1319D5911yescharacteristic
91#1272—591no—
92C2×C59—21no—
93C2×C59—21no—
94C2×C59#132611yescharacteristic
95C2×C59#140411yescharacteristic
96C2×C59#140511yescharacteristic
97#519—591no—
98#428—1181no—
99C2×#101—591no—
100#391C2×D5911yescharacteristic
101#339—1181no—
102#336—1181no—
103#324—21no—
104C59#737611yescharacteristic, complemented, Sylow
105C22×Q8C4×D5911yescharacteristic
106C2×M16—1181no—
107C22×C8—2361no—
108C4×Q8—2361no—
109C4×Q8—2361no—
110#117—1181no—
111#117—2361no—
112C2×C4⋊C4C22⋊D5911yescharacteristic
113C2×C42D23611yescharacteristic
114#107—2361no—
115#106—2361no—
116#101—592no—
117#101—1181no—
118C22⋊C8—41no—
119#95—41no—
120C2×Q8—21no—
121C2×Q8—41no—
122C2×Q8—41no—
123C2×Q8C8×D5911yescharacteristic
124C2×Q8#1174565911yescharacteristic
125C22×C4—21no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4(C2×D59)⋊C411yescharacteristic
129M16—1182no—
130M16—2361no—
131C2×C8—81no—
132C2×C8—4721no—
133C2×C8—4721no—
134C2×C8—2362no—
135C2×C8—2361no—
136C4⋊C4—41no—
137C4⋊C4—1181no—
138C4⋊C4—1181no—
139C4⋊C4—2361no—
140C4⋊C4—2361no—
141C22⋊C4—2361no—
142C42—41no—
143C42—2361no—
144C42—2362no—
145C23#1427364111yescharacteristic
146Q8—41no—
147Q8—41no—
148Q8—42no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—81no—
161C2×C4—2361no—
162C2×C4—2361no—
163C2×C4(C2×D59)⋊C811yescharacteristic
164C2×C4#1427364511yescharacteristic
165C8—161no—
166C8—4722no—
167C8—2362no—
168C22—21no—
169C22—21no—
170C22#1683712711yescharacteristic
171C22#1683718811yescharacteristic
172C22#1683719311yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—41no—
178C4—41no—
179C4—81no—
180C4—4721no—
181C4—4721no—
182C2—21no—
183C2—21no—
184C2#2142204311yescharacteristic
185C2#2142224611yescharacteristic
186C2#2142224911yescharacteristic
subgroupG/H
centerC22#16837188
commutatorC2×Q8×C59C2×C8
Frattini#391C2×D59
FittingC59×#1319C2
socleC22×C59AΣL(1,𝔽16)
prime radicalC23×C59#99
cosocleC59×#391C22
hypercenter#1319D59
hypocenterC59#7376
LCSG ▷ C2×Q8×C59 ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #1319

Complements

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

NH ≅ G/Ntype
20. #14273646C8semidirect
104. C59#7376semidirect

Maximal subgroups

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

subgroupindex
#214243102
#214219222
C59×#13192
#737659