Finite Group Databasebeta

← #34077138

Subgroups — #34077138

Order 19328.

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

normal subgroups only

This group has 528 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×#18012718C211yesmaximal, characteristic, complemented
2#23752148C212yesmaximal, complemented
3#23752143C212yesmaximal, complemented
4#23752126C214yesmaximal, complemented
5#23752126C212yesmaximal, complemented
6#23752124C212yesmaximal, complemented
7#23752075C211yesmaximal, characteristic, complemented
8C2×#121×C151C211yesmaximal, characteristic
9C22×Dic302C2211yescharacteristic
10#18012718—24no—
11C2×C4⋊Dic151C2211yescharacteristic
12C2×Dic151⋊C4C2212yes—
13C2×Dic151⋊C4C2214yes—
14C2×C22⋊Dic151C2212yes—
15C2×C22⋊Dic151C2212yes—
16C2×C22⋊Dic151C2214yes—
17C2×C22⋊Dic151C2214yes—
18C151⋊#95C2212yes—
19C151⋊#95C2212yes—
20C151⋊#95C2214yes—
21C22×D4×C151C2211yescharacteristic
22C22×D4×C151C2212yes—
23C23×C4×C151C2211yescharacteristic
24#121×C151—24no—
25C2×C4⋊C4×C151C2211yescharacteristic
26C2×C22⋊C4×C151C2212yes—
27C2×Dic302—22no—
28C2×Dic302—42no—
29C22×Dic151C2312yes—
30C22×Dic151C2312yes—
31C22×Dic151C2314yes—
32C4⋊Dic151—22no—
33Dic151⋊C4—24no—
34Dic151⋊C4—44no—
35C22⋊Dic151—24no—
36C22⋊Dic151—42no—
37C22⋊Dic151—44no—
38C22⋊Dic151—44no—
39C24×C151C2312yes—
40C24×C151C2311yescharacteristic
41C2×D4×C151—24no—
42C2×D4×C151—22no—
43C2×D4×C151—42no—
44C2×D4×C151—44no—
45C22×C4×C151—42no—
46C22×C4×C151D414yes—
47C22×C4×C151C2312yes—
48C22×C4×C151C2311yescharacteristic
49C22×C4×C151C2311yescharacteristic
50C4⋊C4×C151—22no—
51C22⋊C4×C151—24no—
52Dic302—44no—
53C2×Dic151—22no—
54C2×Dic151—22no—
55C2×Dic151—22no—
56C2×Dic151—24no—
57C2×Dic151—24no—
58C2×Dic151—24no—
59C2×Dic151—22no—
60C2×Dic151—24no—
61C23×C151—22no—
62C23×C151—22no—
63C23×C151—22no—
64C23×C151—22no—
65C23×C151—24no—
66C23×C151—24no—
67C23×C151—24no—
68C23×C151C2×D412yes—
69C23×C151C2411yescharacteristic
70D4×C151—44no—
71D4×C151—48no—
72C2×C4×C151—22no—
73C2×C4×C151—22no—
74C2×C4×C151—22no—
75C2×C4×C151—24no—
76C2×C4×C151—44no—
77C2×C4×C151C2×D412yes—
78C2×C4×C151C2×D412yes—
79C22×C151—22no—
80C22×C151—22no—
81C22×C151—22no—
82C22×C151—44no—
83C22×C151—42no—
84C22×C151—42no—
85C22×C151—42no—
86C22×C151—48no—
87C22×C151C22×D411yescharacteristic
88C22×C151H(5,𝔽2)12yes—
89C22×C151H(5,𝔽2)12yes—
90C22×C1512−1+412yes—
91C4×C151—22no—
92C4×C151—22no—
93C4×C151—42no—
94Dic151—42no—
95Dic151—42no—
96Dic151—44no—
97C2×C151—42no—
98C2×C151—82no—
99C2×C151#53411yescharacteristic
100C2×C151#53511yescharacteristic
101C2×C151#53611yescharacteristic
102C2×C151#56214yes—
103C151#281611yescharacteristic, complemented, Sylow
104#2816—1511nomaximal, Sylow
105C2×C22⋊Q8—1511no—
106C2×#121D15111yescharacteristic
107#399—1512no—
108#398—1512no—
109#394—1512no—
110#394—1514no—
111#393—1512no—
112#381—1511no—
113C22×Q8—1511no—
114C22×D4C2×D15112yes—
115C22×D4C2×D15111yescharacteristic
116C23×C4C2×D15111yescharacteristic
117C22⋊Q8—3024no—
118#121—24no—
119C2×C4⋊C4—1512no—
120C2×C4⋊C4—1511no—
121C2×C4⋊C4—1514no—
122C2×C4⋊C4C2×D15111yescharacteristic
123C2×C22⋊C4—1512no—
124C2×C22⋊C4—1512no—
125C2×C22⋊C4—1514no—
126C2×C22⋊C4—1514no—
127C2×C22⋊C4C2×D15112yes—
128#95—1512no—
129#95—1512no—
130#95—1514no—
131C24C22×D15112yes—
132C24C22×D15111yescharacteristic
133C2×Q8—3022no—
134C2×Q8—6042no—
135C2×D4—24no—
136C2×D4—22no—
137C2×D4—42no—
138C2×D4—44no—
139C22×C4—42no—
140C22×C4—1514no—
141C22×C4—1512no—
142C22×C4—1512no—
143C22×C4C22⋊D15114yes—
144C22×C4C22×D15112yes—
145C22×C4C22×D15111yescharacteristic
146C22×C4C22×D15111yescharacteristic
147C4⋊C4—22no—
148C4⋊C4—3024no—
149C4⋊C4—3022no—
150C4⋊C4—6044no—
151C22⋊C4—24no—
152C22⋊C4—3024no—
153C22⋊C4—6042no—
154C22⋊C4—6044no—
155C22⋊C4—6044no—
156C23—22no—
157C23—22no—
158C23—22no—
159C23—22no—
160C23—24no—
161C23—24no—
162C23—24no—
163C23C2×C22⋊D15112yes—
164C23C23×D15111yescharacteristic
165Q8—6044no—
166D4—44no—
167D4—48no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—24no—
172C2×C4—44no—
173C2×C4—3022no—
174C2×C4—3022no—
175C2×C4—3022no—
176C2×C4—3024no—
177C2×C4—3024no—
178C2×C4—3024no—
179C2×C4—3022no—
180C2×C4—3024no—
181C2×C4C2×C22⋊D15112yes—
182C2×C4C2×C22⋊D15112yes—
183C22—22no—
184C22—22no—
185C22—22no—
186C22—44no—
187C22—42no—
188C22—42no—
189C22—42no—
190C22—48no—
191C22C22×C22⋊D15111yescharacteristic
192C22#1801278412yes—
193C22#1801278412yes—
194C22#1801278612yes—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—6042no—
199C4—6042no—
200C4—6044no—
201C2—42no—
202C2—82no—
203C2#2375277111yescharacteristic
204C2#2375277911yescharacteristic
205C2#2375278311yescharacteristic
206C2#2375295714yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting, prime radicalC2×#121×C151C2
hypercenterC2×#121D151
hypocenterC151#2816
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#18012718C2semidirect
2. #23752148C2semidirect
3. #23752143C2semidirect
4. #23752126C2semidirect
5. #23752126C2semidirect
6. #23752124C2semidirect
7. #23752075C2semidirect
103. C151#2816semidirect

Maximal subgroups

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

subgroupindex
C2×#180127182
#237521482
#237521432
#237521262
#237521242
#237520752
C2×#121×C1512
#2816151