Finite Group Databasebeta

← #34060312

Subgroups — #34060312

Order 19072.

182 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 56 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#23750660C211yesmaximal, characteristic, complemented
2D4×#11924753C211yesmaximal, characteristic, complemented
3#23750487C211yesmaximal, characteristic, complemented
4D4⋊#11924753C211yesmaximal, characteristic, complemented
5D4⋊#11924753C211yesmaximal, characteristic, complemented
6#11924753⋊C8C211yesmaximal, characteristic, complemented
7D8×Dic149C211yesmaximal, characteristic
8C2×#14558745—21no—
9C22×#11924753—21no—
10C4⋊#11924753C2211yescharacteristic
11C4⋊#11924753C2211yescharacteristic
12C22⋊#11924753—21no—
13C22⋊#11924753—21no—
14C4×#11924753C2211yescharacteristic
15C4×#11924753C2211yescharacteristic
16D4×Dic149C2211yescharacteristic
17D4×Dic149C2211yescharacteristic
18#18011845C411yescharacteristic
19#18011832C411yescharacteristic
20#18011832C411yescharacteristic
21C8×Dic149C2211yescharacteristic
22C2×D8×C149C411yescharacteristic
23#14558745—42no—
24C2×#11924753—21no—
25C2×#11924753—21no—
26C2×#11924753—21no—
27C2×#11924753—42no—
28C2×#11924753D411yescharacteristic
29C2×#11924753D411yescharacteristic
30C22×Dic149—21no—
31C22×Dic149—21no—
32C2×#11924746C2×C411yescharacteristic
33C4⋊Dic149C2×C411yescharacteristic
34C4⋊Dic149C2×C411yescharacteristic
35C22⋊Dic149—21no—
36C22⋊Dic149—21no—
37C4×Dic149C2311yescharacteristic
38C2×D4×C149C2×C411yescharacteristic
39C2×D4×C149C2×C411yescharacteristic
40D8×C149—22no—
41C2×C8×C149C2×C411yescharacteristic
42#11924753—22no—
43#11924753—21no—
44#11924753—21no—
45#11924753—41no—
46#11924753—41no—
47C2×Dic149—21no—
48C2×Dic149—21no—
49C2×Dic149—41no—
50C2×Dic149—41no—
51C2×Dic149—41no—
52C2×Dic149—41no—
53C2×Dic149C2×D411yescharacteristic
54C2×Dic149#4111yescharacteristic
55#11924746—21no—
56C23×C149—21no—
57C23×C149—21no—
58D4×C149—21no—
59D4×C149—21no—
60D4×C149—21no—
61D4×C149M1612yescomplemented
62C2×C4×C149C22×C411yescharacteristic
63C8×C149—21no—
64C22×C149—22no—
65C22×C149—41no—
66C22×C149—41no—
67C22×C149—41no—
68C22×C149—41no—
69C22×C149—41no—
70C22×C149C4×D411yescharacteristic
71C4×C149C2×M1611yescharacteristic
72C4×C149#13111yescharacteristic
73Dic149—21no—
74Dic149—41no—
75Dic149—41no—
76Dic149AGL(1,ℤ/8)11yescharacteristic
77Dic149AGL(1,ℤ/8)11yescharacteristic
78C2×C149—42no—
79C2×C149—81no—
80C2×C149#43511yescharacteristic
81C2×C149#44211yescharacteristic
82C2×C149#44311yescharacteristic
83C149#158611yescharacteristic, complemented, Sylow
84#1586—1491nomaximal, Sylow
85C4×D8—1491no—
86#436—1491no—
87C8×D4—1491no—
88#334—1491no—
89D4⋊C8—1491no—
90D4⋊C8—1491no—
91#322—1491no—
92C2×D8#1059701011yescharacteristic
93C2×M16—2981no—
94C22×C8—2981no—
95C4×D4—1491no—
96C4×D4—1491no—
97#107—1491no—
98C4⋊C8—1491no—
99C4⋊C8—1491no—
100#102—1491no—
101#102—1491no—
102C22⋊C8—2981no—
103C22⋊C8—2981no—
104C4×C8—1491no—
105C4×C8—1491no—
106C4×C8—1491no—
107C2×D4C2×#1059701011yescharacteristic
108C2×D4C2×#1059701011yescharacteristic
109C22×C4—2981no—
110C22×C4—2981no—
111D8—22no—
112M16—5962no—
113C2×C8—2981no—
114C2×C8—2981no—
115C2×C8—2981no—
116C2×C8—5962no—
117C2×C8—1491no—
118C2×C8—1491no—
119C2×C8—1491no—
120C2×C8C2×#1059701011yescharacteristic
121C4⋊C4—1491no—
122C4⋊C4—1491no—
123C22⋊C4—2981no—
124C22⋊C4—2981no—
125C42—1491no—
126C23—21no—
127C23—21no—
128D4—21no—
129D4—21no—
130D4—21no—
131D4#1455874512yescomplemented
132C2×C4—2981no—
133C2×C4—2981no—
134C2×C4—5961no—
135C2×C4—5961no—
136C2×C4—5961no—
137C2×C4—5961no—
138C2×C4—1491no—
139C2×C4—1491no—
140C2×C4C22×#1059701011yescharacteristic
141C8—21no—
142C8—2982no—
143C8—2981no—
144C8—2981no—
145C8—2981no—
146C8—5961no—
147C8—5961no—
148C22—22no—
149C22—41no—
150C22—41no—
151C22—41no—
152C22—41no—
153C22—41no—
154C22D4×#1059701011yescharacteristic
155C4—2981no—
156C4—5961no—
157C4—5961no—
158C4—1491no—
159C4—1491no—
160C4C2×#1455874511yescharacteristic
161C4#1801199811yescharacteristic
162C2—42no—
163C2—81no—
164C2#2375065611yescharacteristic
165C2#2375066611yescharacteristic
166C2#2375066711yescharacteristic
subgroupG/H
centerC22D4×#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting, prime radicalC2×D8×C149C4
socleC22×C149C4×D4
cosocleC4×Dic149C23
hypercenterC2×D8#10597010
hypocenterC149#1586
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #23750660C2semidirect
2. D4×#11924753C2semidirect
3. #23750487C2semidirect
4. D4⋊#11924753C2semidirect
5. D4⋊#11924753C2semidirect
6. #11924753⋊C8C2semidirect
61. D4×C149M16semidirect
83. C149#1586semidirect
131. D4#14558745semidirect

Maximal subgroups

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

subgroupindex
#237506602
D4×#119247532
#237504872
D4⋊#119247532
#11924753⋊C82
D8×Dic1492
#1586149