Finite Group Databasebeta

← #34052742

Subgroups — #34052742

Order 19072.

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

normal subgroups only

This group has 464 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×#18011903C211yesmaximal, characteristic, complemented
2#23749561C212yesmaximal, complemented
3#23749550C212yesmaximal, complemented
4#23749548C214yesmaximal, complemented
5#23749544C212yesmaximal, complemented
6#23749539C212yesmaximal
7#23749491C211yesmaximal, characteristic, complemented
8C2×#124×C149C211yesmaximal, characteristic
9#18011903—24no—
10C2×C4⋊Dic149C2211yescharacteristic
11C2×C4⋊Dic149C2211yescharacteristic
12C2×C4⋊Dic149C2212yes—
13C2×#14558715C2212yes—
14C2×#14558715C2212yes—
15C2×#14558715C2214yes—
16C2×C22⋊Dic149C2214yes—
17C2×C22⋊Dic149C2214yes—
18#18011818C2212yes—
19#18011818C2212yes—
20#18011818C2214yes—
21C22×Q8×C149C2211yescharacteristic
22C22×D4×C149C2211yescharacteristic
23#124×C149—24no—
24C2×C22⋊C4×C149C2212yes—
25C2×C22⋊C4×C149C2212yes—
26C2×C42×C149C2211yescharacteristic
27C22×Dic149C2314yes—
28C22×Dic149C2312yes—
29C22×Dic149C2312yes—
30C4⋊Dic149—22no—
31C4⋊Dic149—22no—
32C4⋊Dic149—42no—
33#14558715—24no—
34#14558715—24no—
35#14558715—44no—
36C22⋊Dic149—44no—
37C22⋊Dic149—44no—
38C24×C149C2312yes—
39C2×Q8×C149—22no—
40C2×Q8×C149—42no—
41C2×D4×C149—22no—
42C2×D4×C149—42no—
43C22×C4×C149C2312yes—
44C22×C4×C149C2311yescharacteristic
45C22×C4×C149C2311yescharacteristic
46C22×C4×C149C2311yescharacteristic
47C22⋊C4×C149—24no—
48C22⋊C4×C149—24no—
49C42×C149D414yes—
50C2×Dic149—22no—
51C2×Dic149—22no—
52C2×Dic149—22no—
53C2×Dic149—24no—
54C2×Dic149—24no—
55C2×Dic149—24no—
56C2×Dic149—22no—
57C2×Dic149—24no—
58C23×C149—22no—
59C23×C149—24no—
60C23×C149—22no—
61C23×C149—24no—
62C23×C149—22no—
63C23×C149C2411yescharacteristic
64Q8×C149—44no—
65D4×C149—44no—
66C2×C4×C149—22no—
67C2×C4×C149—21no—
68C2×C4×C149—22no—
69C2×C4×C149—21no—
70C2×C4×C149—22no—
71C2×C4×C149—24no—
72C2×C4×C149C2×D412yes—
73C2×C4×C149C2×D412yes—
74C2×C4×C149C2×D412yes—
75C22×C149—42no—
76C22×C149—42no—
77C22×C149—42no—
78C22×C149—44no—
79C22×C149—44no—
80C22×C149C22×D411yescharacteristic
81C22×C149H(5,𝔽2)12yes—
82C22×C149H(5,𝔽2)11yescharacteristic
83C22×C1492−1+412yes—
84C22×C1492−1+411yescharacteristic
85C4×C149—22no—
86C4×C149—22no—
87C4×C149—22no—
88C4×C149—42no—
89Dic149—42no—
90Dic149—42no—
91Dic149—44no—
92C2×C149—82no—
93C2×C149#53511yescharacteristic
94C2×C149#53611yescharacteristic
95C2×C149#53711yescharacteristic
96C2×C149#56212yes—
97C2×C149#56312yes—
98C149#282011yescharacteristic, complemented, Sylow
99#2820—1491nomaximal, Sylow
100C2×#125—1491no—
101C2×#124D14911yescharacteristic
102#399—1492no—
103#397—1492no—
104#396—1494no—
105#395—1492no—
106#394—1492no—
107#382—1491no—
108C22×Q8C2×D14911yescharacteristic
109C22×D4C2×D14911yescharacteristic
110#125—2984no—
111#124—24no—
112C2×C4⋊C4—1492no—
113C2×C4⋊C4—1492no—
114C2×C4⋊C4—1491no—
115C2×C4⋊C4—1491no—
116C2×C4⋊C4—1492no—
117C2×C4⋊C4—1494no—
118C2×C22⋊C4—1494no—
119C2×C22⋊C4—1494no—
120C2×C22⋊C4C2×D14912yes—
121C2×C22⋊C4C2×D14912yes—
122C2×C42C2×D14911yescharacteristic
123#95—1492no—
124#95—1492no—
125#95—1494no—
126C24C22×D14912yes—
127C2×Q8—22no—
128C2×Q8—42no—
129C2×D4—22no—
130C2×D4—42no—
131C22×C4—1494no—
132C22×C4—1492no—
133C22×C4—1492no—
134C22×C4C22×D14912yes—
135C22×C4C22×D14911yescharacteristic
136C22×C4C22×D14911yescharacteristic
137C22×C4C22×D14911yescharacteristic
138C4⋊C4—2984no—
139C4⋊C4—2984no—
140C4⋊C4—2982no—
141C4⋊C4—2982no—
142C4⋊C4—5964no—
143C4⋊C4—5962no—
144C22⋊C4—24no—
145C22⋊C4—24no—
146C22⋊C4—5964no—
147C22⋊C4—5964no—
148C42C22⋊D14914yes—
149C23—22no—
150C23—24no—
151C23—22no—
152C23—24no—
153C23—22no—
154C23C23×D14911yescharacteristic
155Q8—44no—
156D4—44no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—24no—
163C2×C4—2982no—
164C2×C4—2982no—
165C2×C4—2984no—
166C2×C4—2984no—
167C2×C4—2982no—
168C2×C4—2984no—
169C2×C4—2982no—
170C2×C4—2984no—
171C2×C4C2×C22⋊D14912yes—
172C2×C4C2×C22⋊D14912yes—
173C2×C4C2×C22⋊D14912yes—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—44no—
178C22—44no—
179C22C22×C22⋊D14911yescharacteristic
180C22#1801195612yes—
181C22#1801195711yescharacteristic
182C22#1801195812yes—
183C22#1801195811yescharacteristic
184C4—22no—
185C4—22no—
186C4—22no—
187C4—42no—
188C4—5962no—
189C4—5962no—
190C4—5964no—
191C2—82no—
192C2#2375019211yescharacteristic
193C2#2375019611yescharacteristic
194C2#2375020311yescharacteristic
195C2#2375036912yes—
196C2#2375037512yes—
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
FittingC2×#124×C149C2
prime radicalC22×D4×C149C22
hypercenterC2×#124D149
hypocenterC149#2820
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#18011903C2semidirect
2. #23749561C2semidirect
3. #23749550C2semidirect
4. #23749548C2semidirect
5. #23749544C2semidirect
7. #23749491C2semidirect
98. C149#2820semidirect

Maximal subgroups

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

subgroupindex
C2×#180119032
#237495612
#237495502
#237495482
#237495442
#237495392
#237494912
C2×#124×C1492
#2820149