Finite Group Databasebeta

← #34052743

Subgroups — #34052743

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
2C2×#18011899C211yesmaximal, characteristic
3#23749562C212yesmaximal, complemented
4#23749552C212yesmaximal, complemented
5#23749547C214yesmaximal, complemented
6#23749546C212yesmaximal, complemented
7#23749543C212yesmaximal
8#382×C149C211yesmaximal, characteristic, complemented
9C22×Dic298C2211yescharacteristic
10C22×D596C2211yescharacteristic
11#18011903—24no—
12#18011899—24no—
13C2×C4⋊Dic149C2211yescharacteristic
14C2×C4⋊Dic149C2211yescharacteristic
15C2×C4⋊Dic149C2214yes—
16C2×#14558715C2212yes—
17C2×#14558715C2212yes—
18C2×#14558713C2212yes—
19C2×#14558713C2212yes—
20C2×#14558713C2214yes—
21C2×#14558713C2214yes—
22#18011818C2214yes—
23C2×C4⋊C4×C149C2212yes—
24C2×C42×C149C2211yescharacteristic
25#95×C149C2212yes—
26#95×C149C2212yes—
27C23×D149C2312yes—
28C2×Dic298—22no—
29C2×Dic298—42no—
30C2×D596—22no—
31C2×D596—42no—
32C22×Dic149C2312yes—
33C22×Dic149C2312yes—
34C22×Dic149C2312yes—
35C4⋊Dic149—22no—
36C4⋊Dic149—22no—
37C4⋊Dic149—44no—
38#14558715—24no—
39#14558715—24no—
40#14558713—24no—
41#14558713—24no—
42#14558713—44no—
43#14558713—44no—
44C22×C4×C149C2314yes—
45C22×C4×C149C2311yescharacteristic
46C22×C4×C149C2311yescharacteristic
47C22×C4×C149C2311yescharacteristic
48C4⋊C4×C149—42no—
49C42×C149D414yes—
50C22×D149—22no—
51C22×D149—24no—
52C22×D149—22no—
53C22×D149—24no—
54C22×D149—22no—
55Dic298—44no—
56D596—44no—
57C2×Dic149—22no—
58C2×Dic149—22no—
59C2×Dic149—22no—
60C2×Dic149—24no—
61C2×Dic149—22no—
62C2×Dic149—24no—
63C2×Dic149—22no—
64C23×C149C2411yescharacteristic
65C2×C4×C149—22no—
66C2×C4×C149—21no—
67C2×C4×C149—22no—
68C2×C4×C149—21no—
69C2×C4×C149—24no—
70C2×C4×C149—24no—
71C2×C4×C149—24no—
72C2×C4×C149C2×D412yes—
73C2×C4×C149C2×D412yes—
74C2×C4×C149C2×D412yes—
75C22×C149C22×D411yescharacteristic
76C22×C149H(5,𝔽2)11yescharacteristic
77C22×C149H(5,𝔽2)12yes—
78C22×C1492−1+412yes—
79C22×C1492−1+411yescharacteristic
80C2×D149—42no—
81C2×D149—42no—
82C2×D149—42no—
83C2×D149—44no—
84C2×D149—44no—
85C4×C149—22no—
86C4×C149—22no—
87C4×C149—22no—
88C4×C149—44no—
89Dic149—42no—
90Dic149—42no—
91Dic149—42no—
92C2×C149#53511yescharacteristic
93C2×C149#53611yescharacteristic
94C2×C149#53711yescharacteristic
95C2×C149#56212yes—
96C2×C149#56312yes—
97D149—82no—
98C149#282011yescharacteristic, complemented, Sylow
99#2820—1491nomaximal, Sylow
100C2×#125—1491no—
101C2×#124—1491no—
102#399—1492no—
103#397—1492no—
104#396—1494no—
105#395—1492no—
106#394—1492no—
107#382D14911yescharacteristic, complemented
108C22×Q8—1491no—
109C22×D4—1491no—
110#125—2984no—
111#124—2984no—
112C2×C4⋊C4—1492no—
113C2×C4⋊C4—1492no—
114C2×C4⋊C4—1491no—
115C2×C4⋊C4—1491no—
116C2×C4⋊C4—1494no—
117C2×C4⋊C4C2×D14912yes—
118C2×C22⋊C4—1492no—
119C2×C22⋊C4—1492no—
120C2×C22⋊C4—1494no—
121C2×C22⋊C4—1494no—
122C2×C42C2×D14911yescharacteristic
123#95—1494no—
124#95C2×D14912yes—
125#95C2×D14912yes—
126C24—1492no—
127C2×Q8—2982no—
128C2×Q8—5962no—
129C2×D4—2982no—
130C2×D4—5962no—
131C22×C4—1492no—
132C22×C4—1492no—
133C22×C4—1492no—
134C22×C4C22×D14914yes—
135C22×C4C22×D14911yescharacteristic
136C22×C4C22×D14911yescharacteristic
137C22×C4C22×D14911yescharacteristic
138C4⋊C4—42no—
139C4⋊C4—2984no—
140C4⋊C4—2984no—
141C4⋊C4—2982no—
142C4⋊C4—2982no—
143C4⋊C4—5964no—
144C22⋊C4—2984no—
145C22⋊C4—2984no—
146C22⋊C4—5964no—
147C22⋊C4—5964no—
148C42D59614yes—
149C23—2982no—
150C23—2982no—
151C23—2984no—
152C23—2984no—
153C23—2982no—
154C23C23×D14911yescharacteristic
155Q8—5964no—
156D4—5964no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—2982no—
165C2×C4—2982no—
166C2×C4—2982no—
167C2×C4—2982no—
168C2×C4—2984no—
169C2×C4—2984no—
170C2×C4—2982no—
171C2×C4C2×D59612yes—
172C2×C4C2×D59612yes—
173C2×C4C2×D59612yes—
174C22—5962no—
175C22—5962no—
176C22—5962no—
177C22—5964no—
178C22—5964no—
179C22C22×D59611yescharacteristic
180C22#1801195611yescharacteristic
181C22#1801195712yes—
182C22#1801195812yes—
183C22#1801195911yescharacteristic
184C4—22no—
185C4—22no—
186C4—22no—
187C4—44no—
188C4—5962no—
189C4—5962no—
190C4—5962no—
191C2—11922no—
192C2#2375019411yescharacteristic
193C2#2375020111yescharacteristic
194C2#2375020611yescharacteristic
195C2#2375036912yes—
196C2#2375037912yes—
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#382×C149C2
prime radicalC22×D596C22
hypercenter#382D149
hypocenterC149#2820
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C2×#18011903C2semidirect
3. #23749562C2semidirect
4. #23749552C2semidirect
5. #23749547C2semidirect
6. #23749546C2semidirect
8. #382×C149C2semidirect
98. C149#2820semidirect
107. #382D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119032
C2×#180118992
#237495622
#237495522
#237495472
#237495462
#237495432
#382×C1492
#2820149