Finite Group Databasebeta

← #34060051

Subgroups — #34060051

Order 19072.

246 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750647C211yesmaximal, characteristic, complemented
2#23750643C211yesmaximal, characteristic, complemented
3D4⋊#11924753C214yesmaximal, complemented
4#23750173C211yesmaximal, characteristic
5#18011978—21no—
6C4⋊#11924753C2212yes—
7#18011968—21no—
8#18011968—21no—
9#18011966—21no—
10C4×#11924753C2212yes—
11C2×#14558735—21no—
12#18011911C411yescharacteristic
13#18011898—21no—
14#18011882—21no—
15#18011882C412yes—
16D4×Dic149—21no—
17D4×Dic149C2212yes—
18C42×D149C2211yescharacteristic
19#127×C149C411yescharacteristic
20C2×#11924753—22no—
21C2×#11924753—22no—
22#14558735—44no—
23C2×Dic298—21no—
24C2×C22⋊D149—22no—
25C22×Dic149—22no—
26C2×C4×D149C2×C411yescharacteristic
27C2×C4×D149D411yescharacteristic
28C2×C4×D149D411yescharacteristic
29C4⋊Dic149—21no—
30C4⋊Dic149C2×C412yes—
31C22⋊Dic149—22no—
32C22⋊Dic149—22no—
33C4×Dic149D411yescharacteristic
34C4×Dic149D411yescharacteristic
35C4×Dic149C2311yescharacteristic
36C2×D4×C149—21no—
37C2×D4×C149—21no—
38C2×D4×C149C2×C412yes—
39C42×C149C2×C411yescharacteristic
40#11924753—42no—
41#11924753—42no—
42C22×D149C22⋊C411yescharacteristic
43Dic298—42no—
44C22⋊D149—44no—
45C2×Dic149—22no—
46C2×Dic149—44no—
47C2×Dic149C22⋊C411yescharacteristic
48C2×Dic149C2×D411yescharacteristic
49C2×Dic149C2×D411yescharacteristic
50C4×D149—22no—
51C4×D149—22no—
52C4×D149—41no—
53C23×C149—22no—
54D4×C149—24no—
55D4×C149—42no—
56D4×C149—42no—
57C2×C4×C149C22⋊C411yescharacteristic
58C2×C4×C149C22⋊C411yescharacteristic
59C2×C4×C149C22×C411yescharacteristic
60C22×C149—42no—
61C22×C149—42no—
62C22×C149—42no—
63C22×C149C2×C22⋊C411yescharacteristic
64C2×D149—21no—
65C2×D149—21no—
66C2×D149—21no—
67C4×C149—21no—
68C4×C149—21no—
69C4×C149#13112yes—
70Dic149—21no—
71Dic149—21no—
72Dic149—42no—
73Dic149AGL(1,ℤ/8)12yes—
74C2×C149—82no—
75C2×C149#40811yescharacteristic
76C2×C149#41811yescharacteristic
77C2×C149#42111yescharacteristic
78D149—41no—
79C149#149611yescharacteristic, complemented, Sylow
80#1496—1491nomaximal, Sylow
81#532—1491no—
82#432—1491no—
83#431—1491no—
84D4⋊C8—1494no—
85C2×#41—2981no—
86C4⋊Q8—1491no—
87#127#1059701011yescharacteristic
88#124—2981no—
89#121—2981no—
90#121—1492no—
91C4×D4—2981no—
92C4×D4—1492no—
93C2×C42—1491no—
94C4⋊C8—2981no—
95C4⋊C8—1492no—
96C22⋊C8—2981no—
97C22⋊C8—2981no—
98#97—2981no—
99C4×C8—1492no—
100#41—5964no—
101C2×Q8—2981no—
102C2×D4—21no—
103C2×D4—21no—
104C2×D4—2982no—
105C2×D4C2×#1059701012yes—
106C22×C4—2982no—
107C22×C4—1491no—
108C22×C4—1491no—
109C22×C4—1491no—
110C2×C8—2982no—
111C2×C8—2982no—
112C4⋊C4—2981no—
113C4⋊C4—1492no—
114C22⋊C4—2982no—
115C22⋊C4—2982no—
116C42—1491no—
117C42—1491no—
118C42—1491no—
119C42C2×#1059701011yescharacteristic
120C23—22no—
121C23—1491no—
122Q8—5962no—
123D4—24no—
124D4—42no—
125D4—42no—
126D4—5964no—
127C2×C4—2982no—
128C2×C4—2982no—
129C2×C4—2982no—
130C2×C4—5961no—
131C2×C4—5964no—
132C2×C4—1491no—
133C2×C4—1491no—
134C2×C4—1491no—
135C2×C4C22⋊#1059701011yescharacteristic
136C2×C4C22⋊#1059701011yescharacteristic
137C2×C4C22×#1059701011yescharacteristic
138C8—5962no—
139C8—5962no—
140C22—42no—
141C22—42no—
142C22—42no—
143C22—2981no—
144C22—2981no—
145C22—2981no—
146C22C2×C22⋊#1059701011yescharacteristic
147C4—21no—
148C4—21no—
149C4—2981no—
150C4—2981no—
151C4—5962no—
152C4—1492no—
153C4#1801199812yes—
154C2—82no—
155C2—5961no—
156C2#2375059911yescharacteristic
157C2#2375061711yescharacteristic
158C2#2375062311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#127×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750173C2
cosocleC4×Dic149C23
hypercenter#127#10597010
hypocenterC149#1496
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #23750647C2semidirect
2. #23750643C2semidirect
3. D4⋊#11924753C2semidirect
79. C149#1496semidirect

Maximal subgroups

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

subgroupindex
#237506472
#237506432
D4⋊#119247532
#237501732
#1496149