Finite Group Databasebeta

← #34077171

Subgroups — #34077171

Order 19328.

430 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#18012739C211yesmaximal, characteristic, complemented
2C2×#18012733C211yesmaximal, characteristic
3#23752152C212yesmaximal, complemented
4#23752149C212yesmaximal
5#23752144C212yesmaximal, complemented
6#23752139C212yesmaximal
7#23752133C212yesmaximal, complemented
8#23752125C212yesmaximal
9#383×C151C211yesmaximal, characteristic, complemented
10C22×Dic302C2212yes—
11#18012739—24no—
12#18012733—24no—
13C2×C4⋊Dic151C2212yes—
14C2×C4⋊Dic151C2212yes—
15C2×C4⋊Dic151C2214yes—
16C2×Dic151⋊C4C2211yescharacteristic
17C2×Dic151⋊C4C2211yescharacteristic
18C2×Dic151⋊C4C2211yescharacteristic
19C2×(C2×D151)⋊C4C2211yescharacteristic
20C2×(C2×D151)⋊C4C2211yescharacteristic
21C2×(C2×D151)⋊C4C2211yescharacteristic
22C2×(C2×D151)⋊C4C2214yes—
23C151⋊#95C2214yes—
24C151⋊#95C2214yes—
25C2×C42×C151C2211yescharacteristic
26#95×C151C2212yes—
27#95×C151C2212yes—
28#95×C151C2212yes—
29C23×D151C2311yescharacteristic
30C2×Dic302—24no—
31C2×Dic302—44no—
32C22×Dic151C2311yescharacteristic
33C22×Dic151C2311yescharacteristic
34C22×Dic151C2311yescharacteristic
35C22×Dic151C2314yes—
36C4⋊Dic151—24no—
37C4⋊Dic151—24no—
38C4⋊Dic151—44no—
39Dic151⋊C4—22no—
40Dic151⋊C4—22no—
41Dic151⋊C4—22no—
42(C2×D151)⋊C4—22no—
43(C2×D151)⋊C4—22no—
44(C2×D151)⋊C4—22no—
45(C2×D151)⋊C4—44no—
46C22×C4×C151C2314yes—
47C22×C4×C151C2311yescharacteristic
48C22×C4×C151C2311yescharacteristic
49C22×C4×C151C2311yescharacteristic
50C42×C151D414yes—
51C22×D151—21no—
52C22×D151—22no—
53C22×D151—22no—
54C22×D151—22no—
55Dic302—48no—
56C2×Dic151—21no—
57C2×Dic151—21no—
58C2×Dic151—21no—
59C2×Dic151—24no—
60C2×Dic151—24no—
61C2×Dic151—22no—
62C2×Dic151—24no—
63C2×Dic151—22no—
64C2×Dic151—22no—
65C23×C151C2411yescharacteristic
66C2×C4×C151—22no—
67C2×C4×C151—22no—
68C2×C4×C151—22no—
69C2×C4×C151—24no—
70C2×C4×C151—24no—
71C2×C4×C151—24no—
72C2×C4×C151C2×D412yes—
73C2×C4×C151C2×D412yes—
74C2×C4×C151C2×D412yes—
75C22×C151C22×D411yescharacteristic
76C22×C151H(5,𝔽2)12yes—
77C22×C1512−1+412yes—
78C22×C1512−1+412yes—
79C2×D151—41no—
80C2×D151—41no—
81C2×D151—41no—
82C2×D151—44no—
83C4×C151—22no—
84C4×C151—22no—
85C4×C151—22no—
86C4×C151—44no—
87Dic151—41no—
88Dic151—44no—
89Dic151—41no—
90Dic151—41no—
91C2×C151#53511yescharacteristic
92C2×C151#53611yescharacteristic
93C2×C151#53611yescharacteristic
94C2×C151#56314yes—
95D151—81no—
96C151#282111yescharacteristic, complemented, Sylow
97#2821—1511nomaximal, Sylow
98C2×C4⋊Q8—1511no—
99C2×#126—1511no—
100#400—1512no—
101#399—1512no—
102#398—1512no—
103#397—1512no—
104#395—1512no—
105#393—1512no—
106#383D15111yescharacteristic, complemented
107C22×Q8—1512no—
108C4⋊Q8—3024no—
109#126—3024no—
110C2×C4⋊C4—1511no—
111C2×C4⋊C4—1511no—
112C2×C4⋊C4—1511no—
113C2×C4⋊C4—1512no—
114C2×C4⋊C4—1512no—
115C2×C4⋊C4—1514no—
116C2×C22⋊C4—1511no—
117C2×C22⋊C4—1511no—
118C2×C22⋊C4—1511no—
119C2×C22⋊C4—1514no—
120C2×C42C2×D15111yescharacteristic
121#95—1514no—
122#95—1514no—
123#95C2×D15112yes—
124#95C2×D15112yes—
125#95C2×D15112yes—
126C24—1511no—
127C2×Q8—3024no—
128C2×Q8—6044no—
129C22×C4—1511no—
130C22×C4—1511no—
131C22×C4—1514no—
132C22×C4—1511no—
133C22×C4C22×D15114yes—
134C22×C4C22×D15111yescharacteristic
135C22×C4C22×D15111yescharacteristic
136C22×C4C22×D15111yescharacteristic
137C4⋊C4—3022no—
138C4⋊C4—3022no—
139C4⋊C4—3022no—
140C4⋊C4—3024no—
141C4⋊C4—3024no—
142C4⋊C4—6044no—
143C22⋊C4—3022no—
144C22⋊C4—3022no—
145C22⋊C4—3022no—
146C22⋊C4—6044no—
147C42D60414yes—
148C23—3021no—
149C23—3022no—
150C23—3022no—
151C23—3022no—
152C23C23×D15111yescharacteristic
153Q8—6048no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—3021no—
161C2×C4—3021no—
162C2×C4—3021no—
163C2×C4—3024no—
164C2×C4—3024no—
165C2×C4—3022no—
166C2×C4—3024no—
167C2×C4—3022no—
168C2×C4—3022no—
169C2×C4C2×D60412yes—
170C2×C4C2×D60412yes—
171C2×C4C2×D60412yes—
172C22—6044no—
173C22—6041no—
174C22—6041no—
175C22—6041no—
176C22C22×D60411yescharacteristic
177C22#1801278512yes—
178C22#1801278612yes—
179C22#1801278612yes—
180C4—22no—
181C4—22no—
182C4—22no—
183C4—44no—
184C4—6044no—
185C4—6041no—
186C4—6041no—
187C4—6041no—
188C2—12081no—
189C2#2375278111yescharacteristic
190C2#2375278811yescharacteristic
191C2#2375278811yescharacteristic
192C2#2375296414yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#383×C151C2
prime radicalC23×D151C23
hypercenter#383D151
hypocenterC151#2821
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
1. C2×#18012739C2semidirect
3. #23752152C2semidirect
5. #23752144C2semidirect
7. #23752133C2semidirect
9. #383×C151C2semidirect
96. C151#2821semidirect
106. #383D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127392
C2×#180127332
#237521522
#237521492
#237521442
#237521392
#237521332
#237521252
#383×C1512
#2821151