Finite Group Databasebeta

← #34077169

Subgroups — #34077169

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×#18012733C211yesmaximal, characteristic
2#23752150C212yesmaximal, complemented
3#23752147C212yesmaximal
4#23752143C212yesmaximal, complemented
5#23752138C212yesmaximal
6#23752131C212yesmaximal, complemented
7#23752123C212yesmaximal
8#23752080C211yesmaximal, characteristic, complemented
9C2×C4⋊Q8×C151C211yesmaximal, characteristic, complemented
10#18012733—24no—
11C2×Dic151⋊C4C2211yescharacteristic
12C2×Dic151⋊C4C2211yescharacteristic
13C2×Dic151⋊C4C2211yescharacteristic
14C2×Dic151⋊C4C2214yes—
15C2×(C2×D151)⋊C4C2211yescharacteristic
16C2×(C2×D151)⋊C4C2211yescharacteristic
17C2×(C2×D151)⋊C4C2211yescharacteristic
18C2×(C2×D151)⋊C4C2214yes—
19C151⋊#95C2212yes—
20C151⋊#95C2212yes—
21C151⋊#95C2212yes—
22C151⋊#95C2214yes—
23C151⋊#95C2214yes—
24C22×Q8×C151C2212yes—
25C4⋊Q8×C151—24no—
26C2×C4⋊C4×C151C2212yes—
27C2×C4⋊C4×C151C2212yes—
28C2×C42×C151C2211yescharacteristic
29C23×D151C2311yescharacteristic
30C22×Dic151C2311yescharacteristic
31C22×Dic151C2311yescharacteristic
32C22×Dic151C2311yescharacteristic
33C22×Dic151C2314yes—
34Dic151⋊C4—22no—
35Dic151⋊C4—22no—
36Dic151⋊C4—22no—
37Dic151⋊C4—44no—
38(C2×D151)⋊C4—22no—
39(C2×D151)⋊C4—22no—
40(C2×D151)⋊C4—22no—
41(C2×D151)⋊C4—44no—
42C2×Q8×C151—24no—
43C2×Q8×C151—44no—
44C22×C4×C151C2314yes—
45C22×C4×C151C2311yescharacteristic
46C22×C4×C151C2311yescharacteristic
47C22×C4×C151C2311yescharacteristic
48C4⋊C4×C151—24no—
49C4⋊C4×C151—24no—
50C42×C151D414yes—
51C22×D151—21no—
52C22×D151—22no—
53C22×D151—22no—
54C22×D151—22no—
55C2×Dic151—21no—
56C2×Dic151—21no—
57C2×Dic151—21no—
58C2×Dic151—24no—
59C2×Dic151—22no—
60C2×Dic151—22no—
61C2×Dic151—22no—
62C2×Dic151—24no—
63C2×Dic151—24no—
64C23×C151C2411yescharacteristic
65Q8×C151—48no—
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—41no—
89Dic151—41no—
90Dic151—44no—
91C2×C151#53511yescharacteristic
92C2×C151#53611yescharacteristic
93C2×C151#53611yescharacteristic
94C2×C151#56314yes—
95D151—81no—
96C151#282111yescharacteristic, complemented, Sylow
97#2821—1511nomaximal, Sylow
98C2×C4⋊Q8D15111yescharacteristic, complemented
99C2×#126—1511no—
100#400—1512no—
101#399—1512no—
102#398—1512no—
103#397—1512no—
104#395—1512no—
105#393—1512no—
106#383—1511no—
107C22×Q8C2×D15112yes—
108C4⋊Q8—24no—
109#126—3024no—
110C2×C4⋊C4—1511no—
111C2×C4⋊C4—1511no—
112C2×C4⋊C4—1511no—
113C2×C4⋊C4—1514no—
114C2×C4⋊C4C2×D15112yes—
115C2×C4⋊C4C2×D15112yes—
116C2×C22⋊C4—1511no—
117C2×C22⋊C4—1511no—
118C2×C22⋊C4—1511no—
119C2×C22⋊C4—1514no—
120C2×C42C2×D15111yescharacteristic
121#95—1512no—
122#95—1512no—
123#95—1512no—
124#95—1514no—
125#95—1514no—
126C24—1511no—
127C2×Q8—24no—
128C2×Q8—44no—
129C22×C4—1514no—
130C22×C4—1511no—
131C22×C4—1511no—
132C22×C4—1511no—
133C22×C4C22×D15114yes—
134C22×C4C22×D15111yescharacteristic
135C22×C4C22×D15111yescharacteristic
136C22×C4C22×D15111yescharacteristic
137C4⋊C4—24no—
138C4⋊C4—24no—
139C4⋊C4—3022no—
140C4⋊C4—3022no—
141C4⋊C4—3022no—
142C4⋊C4—6044no—
143C22⋊C4—3022no—
144C22⋊C4—3022no—
145C22⋊C4—3022no—
146C22⋊C4—6044no—
147C42C22⋊D15114yes—
148C23—3021no—
149C23—3022no—
150C23—3022no—
151C23—3022no—
152C23C23×D15111yescharacteristic
153Q8—48no—
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—3022no—
165C2×C4—3024no—
166C2×C4—3024no—
167C2×C4—3022no—
168C2×C4—3022no—
169C2×C4C2×C22⋊D15112yes—
170C2×C4C2×C22⋊D15112yes—
171C2×C4C2×C22⋊D15112yes—
172C22—6044no—
173C22—6041no—
174C22—6041no—
175C22—6041no—
176C22C22×C22⋊D15111yescharacteristic
177C22#1801278412yes—
178C22#1801278712yes—
179C22#1801278712yes—
180C4—22no—
181C4—22no—
182C4—22no—
183C4—44no—
184C4—6044no—
185C4—6041no—
186C4—6041no—
187C4—6041no—
188C2—12081no—
189C2#2375277911yescharacteristic
190C2#2375278611yescharacteristic
191C2#2375278611yescharacteristic
192C2#2375296114yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
FittingC2×C4⋊Q8×C151C2
prime radicalC23×D151C23
hypercenterC2×C4⋊Q8D151
hypocenterC151#2821
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #23752150C2semidirect
4. #23752143C2semidirect
6. #23752131C2semidirect
8. #23752080C2semidirect
9. C2×C4⋊Q8×C151C2semidirect
96. C151#2821semidirect
98. C2×C4⋊Q8D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127332
#237521502
#237521472
#237521432
#237521382
#237521312
#237521232
#237520802
C2×C4⋊Q8×C1512
#2821151