Finite Group Databasebeta

← #34044886

Subgroups — #34044886

Order 19072.

360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4⋊Dic149C211yesmaximal, characteristic
2C2×#18011843C212yesmaximal, complemented
3#23749485C211yesmaximal, characteristic
4#23749388C212yesmaximal, complemented
5C2×C22⋊C8×C149C211yesmaximal, characteristic
6C23×Dic149—21no—
7C2×C4⋊Dic149—24no—
8C2×C4⋊Dic149—21no—
9C2×C4⋊Dic149C2211yescharacteristic
10C2×C4⋊Dic149C2211yescharacteristic
11C2×C4⋊Dic149C2212yes—
12C2×C22⋊Dic149—21no—
13#18011843—24no—
14#18011818—21no—
15C23×C4×C149C2211yescharacteristic
16C22×C8×C149C2212yes—
17C22⋊C8×C149C414yescomplemented
18C22×Dic149—24no—
19C22×Dic149—22no—
20C22×Dic149—21no—
21C22×Dic149—21no—
22C22×Dic149—42no—
23C22×Dic149—42no—
24C4⋊Dic149—24no—
25C4⋊Dic149—22no—
26C4⋊Dic149—22no—
27C4⋊Dic149—22no—
28C4⋊Dic149D414yes—
29C22⋊Dic149—42no—
30C24×C149D411yescharacteristic
31C22×C4×C149—22no—
32C22×C4×C149—22no—
33C22×C4×C149C2×C412yes—
34C22×C4×C149D411yescharacteristic
35C22×C4×C149Q812yes—
36C22×C4×C149C2311yescharacteristic
37C2×C8×C149—22no—
38C2×C8×C149—22no—
39C2×C8×C149C2×C414yescomplemented
40C2×Dic149—24no—
41C2×Dic149—48no—
42C2×Dic149—42no—
43C2×Dic149—42no—
44C2×Dic149—41no—
45C2×Dic149—41no—
46C2×Dic149—41no—
47C2×Dic149—41no—
48C2×Dic149—41no—
49C2×Dic149—41no—
50C23×C149—21no—
51C23×C149—21no—
52C23×C149—21no—
53C23×C149—21no—
54C23×C149C4⋊C412yes—
55C23×C149SD1612yes—
56C23×C149SD1612yes—
57C23×C149C2×D411yescharacteristic
58C2×C4×C149—21no—
59C2×C4×C149—21no—
60C2×C4×C149—24no—
61C2×C4×C149—24no—
62C2×C4×C149C4⋊C412yes—
63C2×C4×C149C22×C411yescharacteristic
64C2×C4×C149C2×D412yes—
65C2×C4×C149C2×Q811yescharacteristic
66C2×C4×C149#4112yes—
67C8×C149—24no—
68C22×C149—22no—
69C22×C149—22no—
70C22×C149—22no—
71C22×C149—22no—
72C22×C149—22no—
73C22×C149—22no—
74C22×C149#10614yescomplemented
75C22×C149C2×C4⋊C411yescharacteristic
76C22×C149#12011yescharacteristic
77C22×C149#12311yescharacteristic
78C22×C149C2×SD1611yescharacteristic
79C22×C149C2×SD1611yescharacteristic
80C22×C149AGL(1,ℤ/8)11yescharacteristic
81C22×C149#13711yescharacteristic
82C4×C149—22no—
83C4×C149C4×D412yes—
84C4×C149C22⋊Q812yes—
85Dic149—44no—
86Dic149—81no—
87Dic149—81no—
88C2×C149—24no—
89C2×C149#38511yescharacteristic
90C2×C149C2×#10611yescharacteristic
91C2×C149#42811yescharacteristic
92C2×C149#44811yescharacteristic
93C2×C149#45011yescharacteristic
94C2×C149#48111yescharacteristic
95C2×C149#48311yescharacteristic
96C149#185311yescharacteristic, complemented, Sylow
97#1853—1491nomaximal, Sylow
98C22×C4⋊C4—1491no—
99C2×#106—1492no—
100C2×C22⋊C8D14911yescharacteristic
101#380—1491no—
102#340—1492no—
103C23×C4—2981no—
104C23×C4C2×D14911yescharacteristic
105C22×C8C2×D14912yes—
106C2×C4⋊C4—2981no—
107C2×C4⋊C4—2984no—
108C2×C4⋊C4—1491no—
109C2×C4⋊C4—1491no—
110C2×C4⋊C4—1492no—
111C2×C22⋊C4—2981no—
112#106—2984no—
113C22⋊C8Dic14914yescomplemented
114#95—2981no—
115C24D59611yescharacteristic
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—2984no—
119C22×C4—2982no—
120C22×C4—2981no—
121C22×C4—2981no—
122C22×C4—5962no—
123C22×C4—5962no—
124C22×C4C2×Dic14912yes—
125C22×C4D59611yescharacteristic
126C22×C4Dic29812yes—
127C22×C4C22×D14911yescharacteristic
128C2×C8—22no—
129C2×C8—22no—
130C2×C8C2×Dic14914yescomplemented
131C4⋊C4—2984no—
132C4⋊C4—2982no—
133C4⋊C4—2982no—
134C4⋊C4—2982no—
135C4⋊C4—1494no—
136C22⋊C4—5962no—
137C23—21no—
138C23—21no—
139C23—21no—
140C23—21no—
141C23C4⋊Dic14912yes—
142C23#1455872512yes—
143C23#1455872512yes—
144C23C2×D59611yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—24no—
148C2×C4—24no—
149C2×C4—2984no—
150C2×C4—5968no—
151C2×C4—5962no—
152C2×C4—5962no—
153C2×C4—5961no—
154C2×C4—5961no—
155C2×C4—5961no—
156C2×C4—5961no—
157C2×C4—5961no—
158C2×C4—5961no—
159C2×C4C4⋊Dic14912yes—
160C2×C4C22×Dic14911yescharacteristic
161C2×C4D4×D14912yes—
162C2×C4C2×Dic29811yescharacteristic
163C2×C4#1455873512yes—
164C8—24no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22#1801184314yescomplemented
172C22C2×C4⋊Dic14911yescharacteristic
173C22#1801188111yescharacteristic
174C22#1801189511yescharacteristic
175C22C2×#1455872511yescharacteristic
176C22C2×#1455872511yescharacteristic
177C22#1801193911yescharacteristic
178C22#1801194411yescharacteristic
179C4—22no—
180C4—5964no—
181C4—11921no—
182C4—11921no—
183C4D4×Dic14912yes—
184C4#1801188812yes—
185C2—24no—
186C2#2374950011yescharacteristic
187C2C2×#1801184311yescharacteristic
188C2#2374966711yescharacteristic
189C2#2374976611yescharacteristic
190C2#2374977811yescharacteristic
191C2#2374994411yescharacteristic
192C2#2374995611yescharacteristic
subgroupG/H
centerC23C2×D596
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
FittingC2×C22⋊C8×C149C2
socleC23×C149C2×D4
prime radicalC24×C149D4
cosocleC22×C4×C149C23
hypercenterC2×C22⋊C8D149
hypocenterC149#1853
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#18011843C2semidirect
4. #23749388C2semidirect
17. C22⋊C8×C149C4semidirect
39. C2×C8×C149C2×C4semidirect
74. C22×C149#106semidirect
96. C149#1853semidirect
113. C22⋊C8Dic149semidirect
130. C2×C8C2×Dic149semidirect
171. C22#18011843semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic1492
C2×#180118432
#237494852
#237493882
C2×C22⋊C8×C1492
#1853149