Finite Group Databasebeta

← #34045832

Subgroups — #34045832

Order 19072.

290 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 93 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×#18011911C211yesmaximal, characteristic
2C2×#18011835C212yesmaximal
3#23749387C212yesmaximal
4#23749380C211yesmaximal, characteristic
5#391×C149C211yesmaximal, characteristic
6C22×Dic298—21no—
7C22×#11924746C2212yes—
8#18011911—24no—
9C2×C4⋊Dic149—21no—
10C2×C4⋊Dic149C2212yes—
11#18011835—24no—
12C22×Q8×C149C2211yescharacteristic
13C2×C4⋊C4×C149C2211yescharacteristic
14C2×C42×C149C2211yescharacteristic
15#95×C149—21no—
16#95×C149—21no—
17C2×Dic298—24no—
18C2×Dic298—42no—
19C2×Dic298—42no—
20C22×Dic149—22no—
21C2×#11924746—22no—
22C2×#11924746—22no—
23C2×#11924746—22no—
24C4⋊Dic149—24no—
25C4⋊Dic149—22no—
26C4⋊Dic149D414yes—
27C2×Q8×C149—21no—
28C2×Q8×C149—22no—
29C2×Q8×C149—22no—
30C2×Q8×C149Q812yescomplemented
31C22×C4×C149—21no—
32C22×C4×C149—21no—
33C22×C4×C149D411yescharacteristic
34C22×C4×C149D411yescharacteristic
35C22×C4×C149C2311yescharacteristic
36C4⋊C4×C149—22no—
37C42×C149—22no—
38Dic298—48no—
39C2×Dic149—24no—
40C2×Dic149—42no—
41C2×Dic149—42no—
42#11924746—42no—
43C23×C149C2×D411yescharacteristic
44Q8×C149—24no—
45Q8×C149—42no—
46C2×C4×C149—21no—
47C2×C4×C149—21no—
48C2×C4×C149—21no—
49C2×C4×C149—21no—
50C2×C4×C149—22no—
51C2×C4×C149—41no—
52C2×C4×C149—41no—
53C2×C4×C149—41no—
54C2×C4×C149—41no—
55C2×C4×C149—41no—
56C2×C4×C149SD1612yes—
57C2×C4×C149Q1612yes—
58C2×C4×C149C2×D412yes—
59C2×C4×C149C2×Q811yescharacteristic
60C2×C4×C149#4112yes—
61C2×C4×C149#4111yescharacteristic
62C22×C149#12011yescharacteristic
63C22×C149C22⋊Q811yescharacteristic
64C22×C149#12411yescharacteristic
65C22×C149C2×SD1611yescharacteristic
66C22×C149C2×Q1611yescharacteristic
67C22×C149AGL(1,ℤ/8)11yescharacteristic
68C22×C149#13711yescharacteristic
69C4×C149—22no—
70C4×C149—22no—
71C4×C149—42no—
72C4×C149—81no—
73C4×C149C22⋊Q812yes—
74C4×C149#12412yes—
75Dic149—44no—
76C2×C149#39311yescharacteristic
77C2×C149#45011yescharacteristic
78C2×C149#45111yescharacteristic
79C2×C149#47511yescharacteristic
80C2×C149#47711yescharacteristic
81C2×C149#48711yescharacteristic
82C2×C149#48911yescharacteristic
83C149#202411yescharacteristic, complemented, Sylow
84#2024—1491nomaximal, Sylow
85C2×C4⋊Q8—1491no—
86C2×#103—1492no—
87#391D14911yescharacteristic
88#340—1492no—
89#336—1491no—
90C22×Q8—2981no—
91C22×Q8C2×D14911yescharacteristic
92C22×C8—1492no—
93C4⋊Q8—2984no—
94C2×C4⋊C4—2981no—
95C2×C4⋊C4—1492no—
96C2×C4⋊C4C2×D14911yescharacteristic
97C2×C42C2×D14911yescharacteristic
98#103—2984no—
99#95—21no—
100#95—21no—
101C2×Q8—21no—
102C2×Q8—22no—
103C2×Q8—22no—
104C2×Q8—2984no—
105C2×Q8—5962no—
106C2×Q8—5962no—
107C2×Q8Dic29812yescomplemented
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—2982no—
111C22×C4C22⋊D14911yescharacteristic
112C22×C4C22⋊D14911yescharacteristic
113C22×C4C22×D14911yescharacteristic
114C2×C8—2982no—
115C2×C8—2982no—
116C2×C8—2982no—
117C4⋊C4—22no—
118C4⋊C4—2984no—
119C4⋊C4—2982no—
120C4⋊C4—1494no—
121C42—22no—
122C23C2×C22⋊D14911yescharacteristic
123Q8—24no—
124Q8—42no—
125Q8—5968no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—2984no—
137C2×C4—5962no—
138C2×C4—5962no—
139C2×C4#1455872312yes—
140C2×C4#1455872612yes—
141C2×C4D4×D14912yes—
142C2×C4C2×Dic29811yescharacteristic
143C2×C4#1455873512yes—
144C2×C4#1455873611yescharacteristic
145C8—5962no—
146C22#1801187911yescharacteristic
147C22#1801189011yescharacteristic
148C22#1801189811yescharacteristic
149C22C2×#1455872311yescharacteristic
150C22C2×#1455872611yescharacteristic
151C22#1801193611yescharacteristic
152C22#1801194111yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—81no—
157C4—5964no—
158C4#1801188812yes—
159C4#1801189712yes—
160C2#2374953711yescharacteristic
161C2#2374977511yescharacteristic
162C2#2374978011yescharacteristic
163C2#2374991011yescharacteristic
164C2#2374992011yescharacteristic
165C2#2374997511yescharacteristic
166C2#2374998411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D149
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#391×C149C2
socle, prime radicalC23×C149C2×D4
hypercenter#391D149
hypocenterC149#2024
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C149Q8semidirect
83. C149#2024semidirect
107. C2×Q8Dic298semidirect

Maximal subgroups

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

subgroupindex
C2×#180119112
C2×#180118352
#237493872
#237493802
#391×C1492
#2024149