Finite Group Databasebeta

← #34047876

Subgroups — #34047876

Order 19072.

408 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 173 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
2#23749522C212yesmaximal
3#23749520C212yesmaximal
4#23749512C212yesmaximal
5#23749510C212yesmaximal
6#23749508C212yesmaximal
7#23749506C212yesmaximal
8#23749491C211yesmaximal, characteristic
9#382×C149C211yesmaximal, characteristic
10#18011903C418yescomplemented
11C2×C4⋊Dic149C2211yescharacteristic
12C2×C4⋊Dic149C2211yescharacteristic
13C2×C4⋊Dic149C2211yescharacteristic
14C2×C4⋊Dic149C2211yescharacteristic
15C2×#14558715C2212yes—
16C2×#14558715C2212yes—
17C2×#14558715C2212yes—
18C2×#14558715C2212yes—
19C2×C4×Dic149C2212yes—
20C2×C4×Dic149C2212yes—
21#18011818C2212yes—
22#18011818C2212yes—
23#18011818C2212yes—
24#18011818C2212yes—
25#18011818C2212yes—
26#18011818C2212yes—
27C2×C4⋊C4×C149C2211yescharacteristic
28C2×C4⋊C4×C149C2211yescharacteristic
29C2×C42×C149C2211yescharacteristic
30#95×C149C2212yes—
31#95×C149C2212yes—
32C22×Dic149C2312yes—
33C22×Dic149C2312yes—
34C22×Dic149C2312yes—
35C22×Dic149C2312yes—
36C4⋊Dic149—41no—
37C4⋊Dic149—41no—
38C4⋊Dic149C2×C414yes—
39C4⋊Dic149C2×C414yes—
40#14558715—42no—
41#14558715—42no—
42#14558715C2×C418yes—
43#14558715C2×C418yes—
44C4×Dic149—42no—
45C4×Dic149—42no—
46C22×C4×C149C2312yes—
47C22×C4×C149C2312yes—
48C22×C4×C149C2311yescharacteristic
49C22×C4×C149C2311yescharacteristic
50C22×C4×C149C2311yescharacteristic
51C4⋊C4×C149—41no—
52C4⋊C4×C149—41no—
53C42×C149C2×C414yes—
54C2×Dic149—22no—
55C2×Dic149—22no—
56C2×Dic149—22no—
57C2×Dic149—22no—
58C2×Dic149—22no—
59C2×Dic149—22no—
60C2×Dic149—22no—
61C2×Dic149—22no—
62C2×Dic149—22no—
63C2×Dic149—22no—
64C2×Dic149C22×C414yes—
65C2×Dic149C22×C414yes—
66C23×C149C2411yescharacteristic
67C2×C4×C149—21no—
68C2×C4×C149—21no—
69C2×C4×C149—21no—
70C2×C4×C149—21no—
71C2×C4×C149—21no—
72C2×C4×C149—21no—
73C2×C4×C149—22no—
74C2×C4×C149—22no—
75C2×C4×C149—22no—
76C2×C4×C149—22no—
77C2×C4×C149—22no—
78C2×C4×C149—22no—
79C2×C4×C149C22×C412yes—
80C2×C4×C149C22×C412yes—
81C2×C4×C149C22×C412yes—
82C22×C149C23×C411yescharacteristic
83C22×C149H(5,𝔽2)11yescharacteristic
84C22×C149H(5,𝔽2)11yescharacteristic
85C22×C1492−1+411yescharacteristic
86C22×C1492−1+411yescharacteristic
87C22×C1492−1+411yescharacteristic
88C22×C1492−1+411yescharacteristic
89C4×C149—22no—
90C4×C149—22no—
91C4×C149—22no—
92C4×C149—42no—
93C4×C149—42no—
94Dic149—24no—
95Dic149—24no—
96Dic149—42no—
97Dic149—42no—
98C2×C149#51911yescharacteristic
99C2×C149#52011yescharacteristic
100C2×C149#52011yescharacteristic
101C2×C149#56211yescharacteristic
102C2×C149#56311yescharacteristic
103C2×C149#56311yescharacteristic
104C2×C149#56411yescharacteristic
105C149#238211yescharacteristic, complemented, Sylow
106#2382—1491nomaximal, Sylow
107C2×#125—1491no—
108#389—1492no—
109#389—1492no—
110#387—1492no—
111#387—1492no—
112#387—1492no—
113#387—1492no—
114#382—1491no—
115#382D14911yescharacteristic
116#125—1498no—
117C2×C4⋊C4—1491no—
118C2×C4⋊C4—1491no—
119C2×C4⋊C4—1492no—
120C2×C4⋊C4—1492no—
121C2×C4⋊C4—1491no—
122C2×C4⋊C4—1491no—
123C2×C4⋊C4—1492no—
124C2×C4⋊C4—1492no—
125C2×C4⋊C4C2×D14911yescharacteristic
126C2×C4⋊C4C2×D14911yescharacteristic
127C2×C42—1492no—
128C2×C42—1492no—
129C2×C42C2×D14911yescharacteristic
130#95—1492no—
131#95—1492no—
132#95—1492no—
133#95—1492no—
134#95—1492no—
135#95—1492no—
136#95C2×D14912yes—
137#95C2×D14912yes—
138C22×C4—1492no—
139C22×C4—1492no—
140C22×C4—1492no—
141C22×C4—1492no—
142C22×C4C22×D14912yes—
143C22×C4C22×D14912yes—
144C22×C4C22×D14911yescharacteristic
145C22×C4C22×D14911yescharacteristic
146C22×C4C22×D14911yescharacteristic
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—5962no—
150C4⋊C4—5962no—
151C4⋊C4—5961no—
152C4⋊C4—5961no—
153C4⋊C4—1498no—
154C4⋊C4—1498no—
155C4⋊C4—1494no—
156C4⋊C4—1494no—
157C42—5962no—
158C42—5962no—
159C42C4×D14914yes—
160C23C23×D14911yescharacteristic
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—2982no—
174C2×C4—2982no—
175C2×C4—2982no—
176C2×C4—2982no—
177C2×C4—2982no—
178C2×C4—2982no—
179C2×C4—2982no—
180C2×C4—2982no—
181C2×C4—2982no—
182C2×C4—2982no—
183C2×C4—1494no—
184C2×C4—1494no—
185C2×C4C2×C4×D14912yes—
186C2×C4C2×C4×D14912yes—
187C2×C4C2×C4×D14912yes—
188C22C22×C4×D14911yescharacteristic
189C22#1801195611yescharacteristic
190C22#1801195711yescharacteristic
191C22#1801195811yescharacteristic
192C22#1801195811yescharacteristic
193C22#1801195811yescharacteristic
194C22#1801195911yescharacteristic
195C4—22no—
196C4—22no—
197C4—22no—
198C4—42no—
199C4—42no—
200C4—2984no—
201C4—2984no—
202C4—5962no—
203C4—5962no—
204C2#2375010211yescharacteristic
205C2#2375010511yescharacteristic
206C2#2375010611yescharacteristic
207C2#2375036911yescharacteristic
208C2#2375037511yescharacteristic
209C2#2375037911yescharacteristic
210C2C149⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#382×C149C2
socle, prime radical, cosocleC23×C149C24
hypercenter#382D149
hypocenterC149#2382
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
10. #18011903C4semidirect
105. C149#2382semidirect

Maximal subgroups

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

subgroupindex
C2×#180119032
#237495222
#237495202
#237495122
#237495102
#237495082
#237495062
#237494912
#382×C1492
#2382149