Finite Group Databasebeta

← #34060812

Subgroups — #34060812

Order 19072.

396 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 118 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×C4⋊#11924753C211yesmaximal, characteristic, complemented
2C2×C22⋊#11924753C214yesmaximal, complemented
3C2×C4×#11924753C211yesmaximal, characteristic, complemented
4C2×D4×Dic149C211yesmaximal, characteristic
5C22×#11924753C2212yes—
6C22×#11924753C2212yes—
7C4⋊#11924753—22no—
8C22⋊#11924753—28no—
9C4×#11924753—22no—
10C23×Dic149C2212yes—
11D4×Dic149—22no—
12D4×Dic149—22no—
13C2×C4⋊Dic149C411yescharacteristic
14C2×C22⋊Dic149C412yes—
15C2×C4×Dic149C2211yescharacteristic
16C22×D4×C149C411yescharacteristic
17C2×#11924753—22no—
18C2×#11924753—24no—
19C2×#11924753—22no—
20C2×#11924753—22no—
21C2×#11924753D414yescomplemented
22C22×Dic149—24no—
23C22×Dic149—22no—
24C22×Dic149—22no—
25C22×Dic149—24no—
26C22×Dic149C2×C412yes—
27C22×Dic149C2×C411yescharacteristic
28C22×Dic149C2311yescharacteristic
29C4⋊Dic149—22no—
30C22⋊Dic149—24no—
31C4×Dic149D412yes—
32C4×Dic149D412yes—
33C24×C149C2×C412yes—
34C2×D4×C149—22no—
35C2×D4×C149—22no—
36C2×D4×C149C814yescomplemented
37C22×C4×C149C2×C411yescharacteristic
38#11924753—24no—
39#11924753—42no—
40C2×Dic149—22no—
41C2×Dic149—22no—
42C2×Dic149—24no—
43C2×Dic149—44no—
44C2×Dic149—42no—
45C2×Dic149—42no—
46C2×Dic149C22⋊C412yes—
47C2×Dic149C2×D411yescharacteristic
48C2×Dic149C2×D412yes—
49C2×Dic149C2×D411yescharacteristic
50C2×Dic149#4112yes—
51C23×C149—22no—
52C23×C149—24no—
53C23×C149—22no—
54C23×C149—24no—
55C23×C149C2×C814yes—
56C23×C149C22×C411yescharacteristic
57D4×C149—28no—
58C2×C4×C149C22⋊C412yes—
59C2×C4×C149C2×C812yes—
60C2×C4×C149M1612yes—
61C22×C149—24no—
62C22×C149—28no—
63C22×C149—42no—
64C22×C149—42no—
65C22×C149—44no—
66C22×C149C2×C22⋊C411yescharacteristic
67C22×C149C4×D412yes—
68C22×C149C22×C811yescharacteristic
69C22×C149C2×M1611yescharacteristic
70C22×C149#13112yes—
71C4×C149C22⋊C814yescomplemented
72Dic149—22no—
73Dic149—42no—
74Dic149#12112yes—
75Dic149#12411yescharacteristic
76Dic149#12711yescharacteristic
77C2×C149—44no—
78C2×C149#39011yescharacteristic
79C2×C149C2×C22⋊C811yescharacteristic
80C2×C149#40811yescharacteristic
81C2×C149C8×D412yes—
82C2×C149#43612yes—
83C149#195411yescharacteristic, complemented, Sylow
84#1954—1491nomaximal, Sylow
85C2×C4×D4—1491no—
86C2×C4⋊C8—1491no—
87C2×C22⋊C8—1494no—
88C2×C4×C8—1491no—
89C22×D4#1059701011yescharacteristic
90C23×C4—1492no—
91C22×C8—1492no—
92C22×C8—1492no—
93C4×D4—2982no—
94C4×D4—2982no—
95C2×C4⋊C4—1491no—
96C2×C22⋊C4—1492no—
97C2×C42—1491no—
98C4⋊C8—2982no—
99C22⋊C8—2988no—
100C4×C8—2982no—
101C24C2×#1059701012yes—
102C2×D4—22no—
103C2×D4—22no—
104C2×D4#1192475314yescomplemented
105C22×C4—2984no—
106C22×C4—2982no—
107C22×C4—2982no—
108C22×C4—2984no—
109C22×C4—1492no—
110C22×C4—1491no—
111C22×C4—1491no—
112C22×C4C2×#1059701011yescharacteristic
113C2×C8—2982no—
114C2×C8—2982no—
115C2×C8—2984no—
116C2×C8—2982no—
117C2×C8—1494no—
118C4⋊C4—2982no—
119C22⋊C4—2984no—
120C42—1492no—
121C42—1492no—
122C23—22no—
123C23—24no—
124C23—22no—
125C23—24no—
126C23C2×#1192475314yes—
127C23C22×#1059701011yescharacteristic
128D4—28no—
129C2×C4—2982no—
130C2×C4—2982no—
131C2×C4—2984no—
132C2×C4—5964no—
133C2×C4—5962no—
134C2×C4—5962no—
135C2×C4—1492no—
136C2×C4—1491no—
137C2×C4—1491no—
138C2×C4—1492no—
139C2×C4—1492no—
140C2×C4C22⋊#1059701012yes—
141C2×C4C2×#1192475312yes—
142C2×C4#1455874512yes—
143C8—2984no—
144C8—5962no—
145C22—24no—
146C22—28no—
147C22—44no—
148C22—42no—
149C22—42no—
150C22C2×C22⋊#1059701011yescharacteristic
151C22D4×#1059701012yes—
152C22C22×#1192475311yescharacteristic
153C22C2×#1455874511yescharacteristic
154C22#1801199812yes—
155C4—2982no—
156C4—5962no—
157C4—1492no—
158C4—1491no—
159C4—1491no—
160C4C22⋊#1192475314yescomplemented
161C2—44no—
162C2#2375057711yescharacteristic
163C2C2×C22⋊#1192475311yescharacteristic
164C2#2375059911yescharacteristic
165C2D4×#1192475312yes—
166C2#2375066012yes—
subgroupG/H
center, FrattiniC23C22×#10597010
commutatorC22×C149C22×C8
Fitting, prime radicalC22×D4×C149C4
socleC23×C149C22×C4
cosocleC22×Dic149C23
hypercenterC22×D4#10597010
hypocenterC149#1954
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊#11924753C2semidirect
2. C2×C22⋊#11924753C2semidirect
3. C2×C4×#11924753C2semidirect
21. C2×#11924753D4semidirect
36. C2×D4×C149C8semidirect
71. C4×C149C22⋊C8semidirect
83. C149#1954semidirect
104. C2×D4#11924753semidirect
160. C4C22⋊#11924753semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#119247532
C2×C22⋊#119247532
C2×C4×#119247532
C2×D4×Dic1492
#1954149