Finite Group Databasebeta

← #34045129

Subgroups — #34045129

Order 19072.

412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 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×#18011885C211yesmaximal, characteristic
2C2×#18011833C212yesmaximal, complemented
3#23749485C211yesmaximal, characteristic, complemented
4#23749388C212yesmaximal, complemented
5C22×M16×C149C211yesmaximal, characteristic, complemented
6C22×D596C2211yescharacteristic
7C22×C22⋊D149—21no—
8#18011885—22no—
9#18011885C414yescomplemented
10C2×C4⋊Dic149C2212yes—
11C2×C4⋊Dic149C2211yescharacteristic
12C2×C22⋊Dic149—21no—
13C2×#14558713—21no—
14#18011833—24no—
15#18011818—21no—
16C23×C4×C149C2211yescharacteristic
17C2×M16×C149—22no—
18C2×M16×C149—24no—
19C22×C8×C149C2212yes—
20C23×D149—21no—
21C2×D596—22no—
22C2×D596—21no—
23C2×D596—22no—
24C2×D596C2×C412yes—
25C2×C22⋊D149—24no—
26C2×C22⋊D149—44no—
27C22×Dic149—21no—
28C22×Dic149—22no—
29C4⋊Dic149—21no—
30C4⋊Dic149—22no—
31C4⋊Dic149—22no—
32C4⋊Dic149C2×C412yes—
33C22⋊Dic149—42no—
34#14558713—24no—
35C24×C149D411yescharacteristic
36C22×C4×C149—22no—
37C22×C4×C149—22no—
38C22×C4×C149C2×C412yes—
39C22×C4×C149D411yescharacteristic
40C22×C4×C149D412yes—
41C22×C4×C149C2311yescharacteristic
42M16×C149—28no—
43C2×C8×C149—22no—
44C2×C8×C149—22no—
45C2×C8×C149D414yescomplemented
46C22×D149—22no—
47C22×D149—42no—
48C22×D149—42no—
49C22×D149—41no—
50C22×D149—41no—
51D596—24no—
52D596—41no—
53D596—41no—
54C22⋊D149—48no—
55C2×Dic149—22no—
56C2×Dic149—42no—
57C2×Dic149—42no—
58C2×Dic149—42no—
59C2×Dic149—42no—
60C23×C149—22no—
61C23×C149—22no—
62C23×C149—21no—
63C23×C149—21no—
64C23×C149C22⋊C412yes—
65C23×C149C2×D411yescharacteristic
66C2×C4×C149—22no—
67C2×C4×C149—24no—
68C2×C4×C149—22no—
69C2×C4×C149—22no—
70C2×C4×C149C22⋊C412yes—
71C2×C4×C149C22×C411yescharacteristic
72C2×C4×C149C2×D412yes—
73C2×C4×C149C2×D411yescharacteristic
74C2×C4×C149#4112yes—
75C8×C149—24no—
76C22×C149—22no—
77C22×C149—22no—
78C22×C149—22no—
79C22×C149—42no—
80C22×C149—42no—
81C22×C149C2×C22⋊C411yescharacteristic
82C22×C149#12112yes—
83C22×C149AGL(1,ℤ/8)11yescharacteristic
84C22×C149AGL(1,ℤ/8)12yes—
85C22×C149#13711yescharacteristic
86C2×D149—42no—
87C2×D149—42no—
88C2×D149—42no—
89C2×D149—82no—
90C2×D149—82no—
91C4×C149—22no—
92C4×C149C4×D412yes—
93C4×C149#12011yescharacteristic
94C4×C149#12311yescharacteristic
95Dic149—42no—
96Dic149—82no—
97C2×C149—42no—
98C2×C149#38611yescharacteristic
99C2×C149#41711yescharacteristic
100C2×C149#41811yescharacteristic
101C2×C149#46812yes—
102C2×C149#46912yes—
103D149—82no—
104C149#189511yescharacteristic, complemented, Sylow
105#1895—1491nomaximal, Sylow
106C22×M16D14911yescharacteristic, complemented
107C2×#121—1491no—
108C2×#102—1492no—
109#380—1491no—
110#340—1492no—
111C22×D4—2981no—
112C22×D4—1491no—
113C23×C4C2×D14911yescharacteristic
114C2×M16—22no—
115C2×M16—24no—
116C22×C8C2×D14912yes—
117#121—2982no—
118#121—1494no—
119C2×C4⋊C4—1492no—
120C2×C4⋊C4—1491no—
121C2×C22⋊C4—2981no—
122C2×C22⋊C4—2981no—
123#102—2984no—
124#95—2981no—
125C24—2981no—
126C24D59611yescharacteristic
127C2×D4—2984no—
128C2×D4—2982no—
129C2×D4—2981no—
130C2×D4—2982no—
131C2×D4—5964no—
132C2×D4—1492no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—2981no—
136C22×C4—2982no—
137C22×C4C4×D14912yes—
138C22×C4C22⋊D14912yes—
139C22×C4D59611yescharacteristic
140C22×C4C22×D14911yescharacteristic
141M16—28no—
142C2×C8—22no—
143C2×C8—22no—
144C2×C8C22⋊D14914yescomplemented
145C4⋊C4—2981no—
146C4⋊C4—2982no—
147C4⋊C4—2982no—
148C4⋊C4—1492no—
149C22⋊C4—2984no—
150C22⋊C4—5962no—
151C23—21no—
152C23—22no—
153C23—21no—
154C23—22no—
155C23—2982no—
156C23—5962no—
157C23—5961no—
158C23—5961no—
159C23—5962no—
160C23#1455871312yes—
161C23C2×D59611yescharacteristic
162D4—2984no—
163D4—5968no—
164D4—5961no—
165D4—5961no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—2982no—
171C2×C4—5962no—
172C2×C4—5962no—
173C2×C4—5962no—
174C2×C4—5962no—
175C2×C4#1455871312yes—
176C2×C4C2×C4×D14911yescharacteristic
177C2×C4C2×C22⋊D14912yes—
178C2×C4C2×C22⋊D14911yescharacteristic
179C2×C4#1455873612yes—
180C8—24no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—5962no—
187C22—5962no—
188C22—5962no—
189C22—11922no—
190C22—11922no—
191C22C2×#1455871311yescharacteristic
192C22#1801188512yes—
193C22#1801193912yes—
194C22#1801193911yescharacteristic
195C22#1801194411yescharacteristic
196C4—22no—
197C4—5962no—
198C4—11922no—
199C4C4×C22⋊D14912yes—
200C4#1801188011yescharacteristic
201C4#1801189411yescharacteristic
202C2—42no—
203C2—11922no—
204C2#2374950411yescharacteristic
205C2#2374962711yescharacteristic
206C2#2374963111yescharacteristic
207C2#2374987112yes—
208C2#2374987812yes—
subgroupG/H
centerC23C2×D596
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
FittingC22×M16×C149C2
socleC23×C149C2×D4
prime radicalC2×#18011885C2
cosocleC22×C4×C149C23
hypercenterC22×M16D149
hypocenterC149#1895
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#18011833C2semidirect
3. #23749485C2semidirect
4. #23749388C2semidirect
5. C22×M16×C149C2semidirect
9. #18011885C4semidirect
45. C2×C8×C149D4semidirect
104. C149#1895semidirect
106. C22×M16D149semidirect
144. C2×C8C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118852
C2×#180118332
#237494852
#237493882
C22×M16×C1492
#1895149