Finite Group Databasebeta

← #34070464

Subgroups — #34070464

Order 19328.

314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 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#23752838C211yesmaximal, characteristic
2#23752087C212yesmaximal
3#23752084C211yesmaximal, characteristic
4#23751978C212yesmaximal
5#342×C151C211yesmaximal, characteristic
6C23×Dic151C2211yescharacteristic
7#18012718—21no—
8#18012718—21no—
9#18012716—22no—
10#18012716—22no—
11C2×C4⋊Dic151—22no—
12C2×Dic151⋊C4—21no—
13C2×C22⋊Dic151C2212yes—
14C2×C22⋊Dic151C2211yescharacteristic
15C151⋊#95—21no—
16C151⋊#95—22no—
17C2×C22⋊C4×C151C2211yescharacteristic
18C2×C22⋊C4×C151C2212yes—
19C2×Dic302—21no—
20C2×Dic302—21no—
21C22×Dic151—21no—
22C22×Dic151—21no—
23C22×Dic151—22no—
24C22×Dic151—42no—
25C22×Dic151D412yes—
26C22×Dic151D412yes—
27C4⋊Dic151—21no—
28C4⋊Dic151—21no—
29C4⋊Dic151—44no—
30Dic151⋊C4—22no—
31Dic151⋊C4—22no—
32Dic151⋊C4—42no—
33C22⋊Dic151—22no—
34C22⋊Dic151—22no—
35C22⋊Dic151—21no—
36C22⋊Dic151Q812yescomplemented
37C24×C151C2311yescharacteristic
38C22×C4×C151—22no—
39C22×C4×C151D411yescharacteristic
40C22×C4×C151D411yescharacteristic
41C22⋊C4×C151—22no—
42C22⋊C4×C151—22no—
43C22⋊C4×C151Q814yescomplemented
44Dic302—81no—
45Dic302—81no—
46C2×Dic151—22no—
47C2×Dic151—24no—
48C2×Dic151—22no—
49C2×Dic151—22no—
50C2×Dic151—22no—
51C2×Dic151—41no—
52C2×Dic151—41no—
53C2×Dic151—41no—
54C2×Dic151—42no—
55C2×Dic151—41no—
56C2×Dic151—42no—
57C2×Dic151—42no—
58C23×C151—41no—
59C23×C151—41no—
60C23×C151C2×D412yes—
61C23×C151C2×D411yescharacteristic
62C23×C151C2×Q811yescharacteristic
63C23×C151C2×Q812yes—
64C23×C151#4111yescharacteristic
65C2×C4×C151—21no—
66C2×C4×C151—21no—
67C2×C4×C151—24no—
68C2×C4×C151—42no—
69C2×C4×C151—42no—
70C2×C4×C151—41no—
71C2×C4×C151—41no—
72C22×C151—22no—
73C22×C151—21no—
74C22×C151—22no—
75C22×C151—21no—
76C22×C151—41no—
77C22×C151—42no—
78C22×C151—41no—
79C22×C151#12011yescharacteristic
80C22×C151C22⋊Q812yes—
81C22×C151C22⋊Q811yescharacteristic
82C22×C151C4⋊Q812yes—
83C22×C151C4⋊Q811yescharacteristic
84C4×C151—44no—
85C4×C151—41no—
86C4×C151—41no—
87Dic151—42no—
88Dic151—42no—
89Dic151—42no—
90Dic151—42no—
91C2×C151—21no—
92C2×C151—22no—
93C2×C151—22no—
94C2×C151—21no—
95C2×C151#39511yescharacteristic
96C2×C151B(4,𝔽2)11yescharacteristic
97C2×C151#45811yescharacteristic
98C151#206211yescharacteristic, complemented, Sylow
99#2062—1511nomaximal, Sylow
100#543—1511no—
101#385—1511no—
102#385—1512no—
103#342—1512no—
104#342D15111yescharacteristic
105C23×C4—1511no—
106C22⋊Q8—3022no—
107C22⋊Q8—3022no—
108C22⋊Q8—3021no—
109C22⋊Q8—3021no—
110C2×C4⋊C4—3022no—
111C2×C4⋊C4—3021no—
112C2×C22⋊C4—1512no—
113C2×C22⋊C4—1511no—
114C2×C22⋊C4C2×D15111yescharacteristic
115C2×C22⋊C4C2×D15112yes—
116#95—3022no—
117#95—3021no—
118C24C22×D15111yescharacteristic
119C2×Q8—3021no—
120C2×Q8—3021no—
121C22×C4—22no—
122C22×C4—3022no—
123C22×C4—3021no—
124C22×C4—3021no—
125C22×C4—6042no—
126C22×C4—1512no—
127C22×C4—1512no—
128C22×C4D60411yescharacteristic
129C22×C4D60411yescharacteristic
130C4⋊C4—3022no—
131C4⋊C4—3022no—
132C4⋊C4—3021no—
133C4⋊C4—3021no—
134C4⋊C4—6042no—
135C4⋊C4—6044no—
136C22⋊C4—22no—
137C22⋊C4—22no—
138C22⋊C4—3022no—
139C22⋊C4—3022no—
140C22⋊C4—3021no—
141C22⋊C4—1512no—
142C22⋊C4Dic30214yescomplemented
143C23—41no—
144C23—41no—
145C23D4×D15112yes—
146C23C2×D60411yescharacteristic
147C23Q8×D15111yescharacteristic
148C23C2×Dic30212yes—
149C23#1455900311yescharacteristic
150Q8—12081no—
151Q8—12081no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—24no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—3024no—
160C2×C4—3022no—
161C2×C4—3022no—
162C2×C4—3022no—
163C2×C4—3022no—
164C2×C4—6041no—
165C2×C4—6042no—
166C2×C4—6041no—
167C2×C4—6041no—
168C2×C4—6041no—
169C2×C4—6042no—
170C2×C4—6042no—
171C22—22no—
172C22—21no—
173C22—22no—
174C22—21no—
175C22—41no—
176C22—42no—
177C22—41no—
178C22#1801270911yescharacteristic
179C22#1801271612yes—
180C22#1801271911yescharacteristic
181C22#1801273812yes—
182C22#1801273911yescharacteristic
183C4—44no—
184C4—41no—
185C4—41no—
186C4—6042no—
187C4—6042no—
188C4—6042no—
189C4—6042no—
190C2—22no—
191C2—21no—
192C2—22no—
193C2—21no—
194C2#2375213311yescharacteristic
195C2#2375240011yescharacteristic
196C2#2375240311yescharacteristic
subgroupG/H
centerC22#18012709
commutator, prime radical, cosocleC24×C151C23
FrattiniC24C22×D151
Fitting#342×C151C2
socleC22×C151#120
hypercenter#342D151
hypocenterC151#2062
LCSG ▷ C24×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
36. C22⋊Dic151Q8semidirect
43. C22⋊C4×C151Q8semidirect
98. C151#2062semidirect
142. C22⋊C4Dic302semidirect

Maximal subgroups

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

subgroupindex
#237528382
#237520872
#237520842
#237519782
#342×C1512
#2062151