Finite Group Databasebeta

← #34060018

Subgroups — #34060018

Order 19072.

312 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 74 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#23750642C211yesmaximal, characteristic, complemented
2#23750628C211yesmaximal, characteristic, complemented
3#23750473C214yesmaximal, complemented
4C2×#18011873C211yesmaximal, characteristic
5C2×#14558745—21no—
6#18011978—21no—
7#18011978—21no—
8C4⋊#11924753C2212yescomplemented
9C22⋊#11924753—21no—
10C4×#11924753C2212yescomplemented
11C22×D596C411yescharacteristic
12C22×C4×D149—21no—
13#18011873—21no—
14#18011873—21no—
15#18011873C412yes—
16#18011873C2212yes—
17C2×#14558713—21no—
18C2×C4×Dic149C2211yescharacteristic
19C2×C4⋊C4×C149C411yescharacteristic
20#14558745—42no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23C23×D149—21no—
24C2×D596—24no—
25C2×D596—21no—
26C2×D596C2×C412yes—
27C22×Dic149D411yescharacteristic
28C22×Dic149D411yescharacteristic
29C2×C4×D149—22no—
30C2×C4×D149—22no—
31C2×C4×D149—42no—
32C2×C4×D149—42no—
33#14558713—22no—
34#14558713—22no—
35C4×Dic149C2×C411yescharacteristic
36C4×Dic149D411yescharacteristic
37C4×Dic149D411yescharacteristic
38C4×Dic149C2311yescharacteristic
39C22×C4×C149—21no—
40C22×C4×C149C2×C411yescharacteristic
41C4⋊C4×C149—21no—
42C4⋊C4×C149C2×C412yes—
43#11924753—42no—
44#11924753—42no—
45C22×D149—24no—
46C22×D149—22no—
47C22×D149—42no—
48C22×D149—42no—
49D596—24no—
50D596—22no—
51D596M1614yescomplemented
52C2×Dic149—41no—
53C2×Dic149C22⋊C411yescharacteristic
54C2×Dic149C22⋊C411yescharacteristic
55C2×Dic149D812yes—
56C2×Dic149SD1612yes—
57C2×Dic149C2×D411yescharacteristic
58C2×Dic149C2×D411yescharacteristic
59C4×D149—44no—
60C4×D149—42no—
61C4×D149—42no—
62C23×C149C22⋊C411yescharacteristic
63C2×C4×C149—22no—
64C2×C4×C149—22no—
65C2×C4×C149—42no—
66C2×C4×C149C22⋊C411yescharacteristic
67C2×C4×C149C22×C411yescharacteristic
68C22×C149—21no—
69C22×C149—21no—
70C22×C149#10212yes—
71C22×C149C2×C22⋊C411yescharacteristic
72C2×D149—24no—
73C2×D149—48no—
74C2×D149—42no—
75C2×D149—42no—
76C4×C149—21no—
77C4×C149—42no—
78C4×C149C2×M1612yes—
79Dic149—21no—
80Dic149—21no—
81Dic149#10212yes—
82Dic149C2×D811yescharacteristic
83Dic149C2×SD1611yescharacteristic
84C2×C149—22no—
85C2×C149#40711yescharacteristic
86C2×C149C2×#10211yescharacteristic
87C2×C149#42111yescharacteristic
88D149—44no—
89C149#148611yescharacteristic, complemented, Sylow
90#1486—1491nomaximal, Sylow
91C2×C4×D4—1491no—
92#431—1491no—
93#423—1491no—
94D4⋊C8—1494no—
95C22×D4—1491no—
96C23×C4—2981no—
97C2×M16—2981no—
98C4×D4—2981no—
99C4×D4—2981no—
100C4×D4—1492no—
101C4×D4—1492no—
102C2×C4⋊C4#1059701011yescharacteristic
103C2×C22⋊C4—2981no—
104C2×C42—1491no—
105C4⋊C8—2981no—
106C4⋊C8—2981no—
107C4⋊C8—1492no—
108C22⋊C8—2981no—
109C4×C8—1492no—
110C24—2981no—
111C2×D4—2984no—
112C2×D4—2981no—
113C2×D4—1492no—
114C22×C4—21no—
115C22×C4—2982no—
116C22×C4—2982no—
117C22×C4—5962no—
118C22×C4—5962no—
119C22×C4—1491no—
120C22×C4—1491no—
121C22×C4C2×#1059701011yescharacteristic
122M16—5962no—
123C2×C8—2982no—
124C2×C8—2982no—
125C4⋊C4—21no—
126C4⋊C4C2×#1059701012yes—
127C22⋊C4—2982no—
128C22⋊C4—2982no—
129C42—1491no—
130C42—1491no—
131C42—1491no—
132C42—1491no—
133C23—2984no—
134C23—2982no—
135C23—5962no—
136C23—5962no—
137C23C22⋊#1059701011yescharacteristic
138D4—2984no—
139D4—2982no—
140D4—1494no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—5962no—
145C2×C4—5964no—
146C2×C4—5962no—
147C2×C4—5961no—
148C2×C4—1491no—
149C2×C4—1491no—
150C2×C4—1492no—
151C2×C4—1492no—
152C2×C4—1491no—
153C2×C4—1491no—
154C2×C4C22⋊#1059701011yescharacteristic
155C2×C4C22×#1059701011yescharacteristic
156C8—5962no—
157C8—5962no—
158C22—21no—
159C22—21no—
160C22—2984no—
161C22—5968no—
162C22—5962no—
163C22—5962no—
164C22#1801197312yes—
165C22C2×C22⋊#1059701011yescharacteristic
166C4—21no—
167C4—42no—
168C4—2981no—
169C4—2981no—
170C4—1491no—
171C4—1492no—
172C4—1491no—
173C4D149⋊M1612yes—
174C2—22no—
175C2—5964no—
176C2#2375059711yescharacteristic
177C2C2×#1801197311yescharacteristic
178C2#2375062411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D596C4
cosocleC4×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1486
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #23750642C2semidirect
2. #23750628C2semidirect
3. #23750473C2semidirect
8. C4⋊#11924753C22semidirect
10. C4×#11924753C22semidirect
51. D596M16semidirect
89. C149#1486semidirect

Maximal subgroups

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

subgroupindex
#237506422
#237506282
#237504732
C2×#180118732
#1486149