Finite Group Databasebeta

← #34046766

Subgroups — #34046766

Order 19072.

170 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 43 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
1#23750063C211yesmaximal, characteristic, complemented
2#23750061C211yesmaximal, characteristic, complemented
3#23750000C211yesmaximal, characteristic, complemented
4#23749741C211yesmaximal, characteristic, complemented
5#23749445C211yesmaximal, characteristic, complemented
6#23749437C211yesmaximal, characteristic, complemented
7#361×C149C211yesmaximal, characteristic, complemented
8#18011933C2211yescharacteristic
9C2×D1192C2211yescharacteristic
10C2×#14558721—21no—
11#18011919—21no—
12#18011907—21no—
13#18011856—21no—
14#18011855—21no—
15D2384—21no—
16#18011852—21no—
17#18011851C2211yescharacteristic
18#18011837—21no—
19C8×Dic149C2211yescharacteristic
20C2×D8×C149C2211yescharacteristic
21M32×C149C2211yescharacteristic
22#108×C149C2211yescharacteristic
23#14558736—21no—
24C2×D596—21no—
25C2×C22⋊D149—42no—
26Dic596D411yescharacteristic, complemented
27#14558725—21no—
28D1192—21no—
29D1192—21no—
30D1192D411yescharacteristic, complemented
31#14558721—41no—
32#14558721—41no—
33#14558719—41no—
34C2×#11924746D411yescharacteristic
35C8×D149—41no—
36C4×Dic149D411yescharacteristic
37#14558711—21no—
38C2×D4×C149—21no—
39D8×C149—21no—
40D8×C149—21no—
41M16×C149—21no—
42C2×C8×C149C2311yescharacteristic
43C16×C149—21no—
44C22×D149—41no—
45Dic298—21no—
46D596—21no—
47D596—41no—
48D596—41no—
49C22⋊D149—41no—
50C22⋊D149—84no—
51C2×Dic149—21no—
52C4×D149—41no—
53#11924746D811yescharacteristic
54#11924746D811yescharacteristic
55C23×C149—41no—
56D4×C149—41no—
57D4×C149—41no—
58C2×C4×C149C2×D411yescharacteristic
59C8×C149—41no—
60C8×C149C2×D411yescharacteristic
61C8×C149#4111yescharacteristic
62C22×C149—82no—
63C22×C149—81no—
64C22×C149AGL(1,ℤ/8)11yescharacteristic
65C2×D149—41no—
66C2×D149—82no—
67C2×D149—81no—
68C4×C149#12111yescharacteristic
69C4×C149C2×D811yescharacteristic
70Dic149—22no—
71Dic149—41no—
72C2×C149—21no—
73C2×C149—161no—
74C2×C149#45911yescharacteristic
75D149—81no—
76D149—161no—
77C149#221311yescharacteristic, complemented, Sylow
78#2213—1491nomaximal, Sylow
79#509—1491no—
80#509—1491no—
81#493—1491no—
82#443—1491no—
83#364—1491no—
84#361—1491no—
85#361D14911yescharacteristic, complemented
86#135—1491no—
87C2×D8—2981no—
88C2×D8—1491no—
89C2×D8C2×D14911yescharacteristic
90#131—2981no—
91#127—2981no—
92SD32—2981no—
93SD32—2981no—
94D16—2981no—
95D16—2981no—
96M32—1491no—
97M32C2×D14911yescharacteristic
98#108C2×D14911yescharacteristic
99#104—2981no—
100C4×C8—1491no—
101#41—2981no—
102C2×D4—21no—
103C2×D4—2981no—
104C2×D4—5962no—
105Q16—1491no—
106SD16—2981no—
107D8—21no—
108D8—21no—
109D8—2981no—
110D8—2981no—
111D8—5961no—
112D8—5961no—
113D8—1491no—
114M16—21no—
115M16—5961no—
116C2×C8—5961no—
117C2×C8—1491no—
118C2×C8C22×D14911yescharacteristic
119C42—1491no—
120C16—21no—
121C16—2981no—
122C23—41no—
123C23—5961no—
124Q8—2981no—
125D4—41no—
126D4—41no—
127D4—2981no—
128D4—5961no—
129D4—5961no—
130D4—5961no—
131D4—11924no—
132C2×C4—2981no—
133C2×C4—5961no—
134C2×C4D4×D14911yescharacteristic
135C8—41no—
136C8—1491no—
137C8—1491no—
138C8D4×D14911yescharacteristic
139C8#1455873611yescharacteristic
140C22—82no—
141C22—81no—
142C22—5961no—
143C22—11922no—
144C22—11921no—
145C22#1801193811yescharacteristic
146C4—2982no—
147C4—5961no—
148C4#1801188411yescharacteristic
149C4D8×D14911yescharacteristic
150C2—21no—
151C2—161no—
152C2—23841no—
153C2—11921no—
154C2#2374981911yescharacteristic
subgroupG/H
centerC2#23749819
commutator, cosocleC2×C8×C149C23
FrattiniC2×C8C22×D149
Fitting#361×C149C2
socleC2×C149#459
hypercenter#361D149
hypocenterC149#2213
LCSG ▷ C2×C8×C149 ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #23750063C2semidirect
2. #23750061C2semidirect
3. #23750000C2semidirect
4. #23749741C2semidirect
5. #23749445C2semidirect
6. #23749437C2semidirect
7. #361×C149C2semidirect
26. Dic596D4semidirect
30. D1192D4semidirect
77. C149#2213semidirect
85. #361D149semidirect

Maximal subgroups

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

subgroupindex
#237500632
#237500612
#237500002
#237497412
#237494452
#237494372
#361×C1492
#2213149