Finite Group Databasebeta

← #34047288

Subgroups — #34047288

Order 19072.

672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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
1C22×#14558713C211yesmaximal, characteristic
2#23749517C214yesmaximal, complemented
3#23749515C214yesmaximal, complemented
4#23749485C211yesmaximal, characteristic, complemented
5#23749480C212yesmaximal
6C22⋊C4×Dic149C212yesmaximal, complemented
7#380×C149C211yesmaximal, characteristic, complemented
8C24×D149C2211yescharacteristic
9C23×Dic149C2211yescharacteristic
10C2×C4⋊Dic149C2212yescomplemented
11C2×C22⋊Dic149C2212yes—
12C2×#14558713C418yescomplemented
13C2×#14558713C2214yes—
14C2×#14558713C2214yes—
15C2×#14558713C2212yes—
16C2×#14558713C2212yes—
17C2×C4×Dic149C2214yescomplemented
18#18011818C2214yescomplemented
19#18011818C2212yescomplemented
20C23×C4×C149C2211yescharacteristic
21C2×C4⋊C4×C149C2212yescomplemented
22C2×C22⋊C4×C149C2212yes—
23#95×C149C2212yescomplemented
24C23×D149—22no—
25C23×D149—22no—
26C23×D149—42no—
27C23×D149—42no—
28C23×D149C2×C414yes—
29C23×D149C2312yes—
30C22×Dic149—42no—
31C22×Dic149C2×C414yes—
32C22×Dic149C2314yes—
33C22×Dic149C2312yes—
34C4⋊Dic149—42no—
35C22⋊Dic149—24no—
36#14558713—44no—
37#14558713—44no—
38#14558713C2×C418yes—
39#14558713C2×C418yes—
40C4×Dic149—44no—
41C24×C149C2311yescharacteristic
42C22×C4×C149—42no—
43C22×C4×C149C2×C414yes—
44C22×C4×C149C2314yes—
45C22×C4×C149C2311yescharacteristic
46C22×C4×C149C2311yescharacteristic
47C4⋊C4×C149—42no—
48C22⋊C4×C149—24no—
49C22×D149—28no—
50C22×D149—22no—
51C22×D149—22no—
52C22×D149—24no—
53C22×D149—24no—
54C22×D149—44no—
55C22×D149—44no—
56C22×D149—48no—
57C22×D149—48no—
58C22×D149C22×C414yes—
59C2×Dic149—24no—
60C2×Dic149—24no—
61C2×Dic149—24no—
62C2×Dic149—24no—
63C2×Dic149—44no—
64C2×Dic149C22×C414yes—
65C23×C149—22no—
66C23×C149—22no—
67C23×C149C22×C412yes—
68C23×C149#4112yes—
69C23×C149#4112yes—
70C23×C149C2411yescharacteristic
71C2×C4×C149—22no—
72C2×C4×C149—22no—
73C2×C4×C149—24no—
74C2×C4×C149—24no—
75C2×C4×C149—24no—
76C2×C4×C149—44no—
77C2×C4×C149C22×C412yes—
78C2×C4×C149C22×C412yes—
79C22×C149—22no—
80C22×C149—22no—
81C22×C149—24no—
82C22×C149—24no—
83C22×C149#11714yes—
84C22×C149C23×C411yescharacteristic
85C22×C149C2×#4111yescharacteristic
86C22×C149C2×#4111yescharacteristic
87C22×C149H(5,𝔽2)12yes—
88C22×C149H(5,𝔽2)12yes—
89C2×D149—24no—
90C2×D149—24no—
91C2×D149—24no—
92C2×D149—416no—
93C2×D149—44no—
94C2×D149—44no—
95C4×C149—22no—
96C4×C149—22no—
97C4×C149—44no—
98Dic149—24no—
99Dic149—44no—
100C2×C149—24no—
101C2×C149C2×#11711yescharacteristic
102C2×C149#51811yescharacteristic
103C2×C149#51811yescharacteristic
104C2×C149#53812yes—
105C2×C149#53812yes—
106D149—44no—
107C149#231211yescharacteristic, complemented, Sylow
108#2312—1491nomaximal, Sylow
109C22×C22⋊C4—1491no—
110#388—1494no—
111#388—1494no—
112#380—1491no—
113#380D14911yescharacteristic, complemented
114#379—1492no—
115C4×C22⋊C4—1492no—
116C25—1491no—
117C23×C4—1491no—
118C23×C4C2×D14911yescharacteristic
119C2×C4⋊C4—1492no—
120C2×C4⋊C4C2×D14912yescomplemented
121C2×C22⋊C4—1492no—
122C2×C22⋊C4—1494no—
123C2×C22⋊C4—1494no—
124C2×C22⋊C4—1498no—
125C2×C22⋊C4—1492no—
126C2×C22⋊C4—1492no—
127C2×C22⋊C4C2×D14912yes—
128C2×C42—1494no—
129#95—1494no—
130#95—1492no—
131#95C2×D14912yescomplemented
132C24—2982no—
133C24—2982no—
134C24—5962no—
135C24—5962no—
136C24—1492no—
137C24—1494no—
138C24C22×D14911yescharacteristic
139C22×C4—42no—
140C22×C4—5962no—
141C22×C4—1494no—
142C22×C4—1492no—
143C22×C4—1494no—
144C22×C4C4×D14914yes—
145C22×C4C22×D14914yes—
146C22×C4C22×D14911yescharacteristic
147C22×C4C22×D14911yescharacteristic
148C4⋊C4—42no—
149C4⋊C4—5962no—
150C22⋊C4—24no—
151C22⋊C4—2984no—
152C22⋊C4—5964no—
153C22⋊C4—5964no—
154C22⋊C4—1498no—
155C22⋊C4—1498no—
156C42—5964no—
157C23—22no—
158C23—22no—
159C23—2982no—
160C23—2982no—
161C23—2984no—
162C23—2984no—
163C23—2988no—
164C23—5964no—
165C23—5964no—
166C23—5968no—
167C23—5968no—
168C23—1494no—
169C23C2×C4×D14912yes—
170C23#1455873512yes—
171C23#1455873712yes—
172C23C23×D14911yescharacteristic
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—44no—
179C2×C4—2984no—
180C2×C4—2984no—
181C2×C4—2984no—
182C2×C4—2984no—
183C2×C4—5964no—
184C2×C4—1494no—
185C2×C4C2×C4×D14912yes—
186C2×C4C2×C4×D14912yes—
187C22—24no—
188C22—24no—
189C22—22no—
190C22—22no—
191C22—2984no—
192C22—2984no—
193C22—2984no—
194C22—59616no—
195C22—5964no—
196C22—5964no—
197C22#1801186914yes—
198C22C22×C4×D14911yescharacteristic
199C22C2×#1455873511yescharacteristic
200C22C2×#1455873711yescharacteristic
201C22#1801195612yes—
202C22#1801195712yes—
203C4—22no—
204C4—22no—
205C4—44no—
206C4—2984no—
207C4—5964no—
208C2—24no—
209C2—5964no—
210C2C2×#1801186911yescharacteristic
211C2#2375009811yescharacteristic
212C2#2375009911yescharacteristic
213C2#2375021212yes—
214C2#2375021512yes—
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#380×C149C2
socle, cosocleC23×C149C24
prime radicalC24×D149C22
hypercenter#380D149
hypocenterC149#2312
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #23749517C2semidirect
3. #23749515C2semidirect
4. #23749485C2semidirect
6. C22⋊C4×Dic149C2semidirect
7. #380×C149C2semidirect
10. C2×C4⋊Dic149C22semidirect
12. C2×#14558713C4semidirect
17. C2×C4×Dic149C22semidirect
18. #18011818C22semidirect
19. #18011818C22semidirect
21. C2×C4⋊C4×C149C22semidirect
23. #95×C149C22semidirect
107. C149#2312semidirect
113. #380D149semidirect
120. C2×C4⋊C4C2×D149semidirect
131. #95C2×D149semidirect

Maximal subgroups

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

subgroupindex
C22×#145587132
#237495172
#237495152
#237494852
#237494802
C22⋊C4×Dic1492
#380×C1492
#2312149