Finite Group Databasebeta

← #34060199

Subgroups — #34060199

Order 19072.

344 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 70 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#23750643C211yesmaximal, characteristic, complemented
2#23750630C211yesmaximal, characteristic, complemented
3#23750483C214yesmaximal, complemented
4#127×D149C211yesmaximal, characteristic
5C2×#14558746—21no—
6#18011978—21no—
7#18011978C2212yescomplemented
8#18011978C2212yescomplemented
9#18011968—21no—
10C4×#11924753—21no—
11C2×D4×D149—21no—
12C2×D4×D149—21no—
13C2×D4×D149C412yes—
14#18011908C411yescharacteristic
15#18011907—21no—
16#18011907—21no—
17#18011907C2212yes—
18C42×D149C2211yescharacteristic
19#127×C149C411yescharacteristic
20#14558746—42no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23C23×D149—22no—
24C2×D596—21no—
25C2×D596—21no—
26C2×D596C2×C412yes—
27C2×C22⋊D149—22no—
28C2×C22⋊D149—22no—
29C2×C22⋊D149—22no—
30D4×D149—44no—
31D4×D149—44no—
32D4×D149—42no—
33D4×D149—42no—
34C2×C4×D149C2×C411yescharacteristic
35C2×C4×D149D411yescharacteristic
36C2×C4×D149D411yescharacteristic
37C4×Dic149D411yescharacteristic
38C4×Dic149D411yescharacteristic
39C4×Dic149C2311yescharacteristic
40C2×D4×C149—21no—
41C2×D4×C149—21no—
42C2×D4×C149C2×C412yes—
43C42×C149C2×C411yescharacteristic
44#11924753—42no—
45#11924753—42no—
46C22×D149—22no—
47C22×D149—44no—
48C22×D149—44no—
49C22×D149—44no—
50C22×D149C22⋊C411yescharacteristic
51D596—42no—
52D596—42no—
53D596—42no—
54C22⋊D149—44no—
55C22⋊D149—42no—
56C22⋊D149—42no—
57C22⋊D149—44no—
58C2×Dic149C22⋊C411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C2×Dic149C2×D411yescharacteristic
61C4×D149—22no—
62C4×D149—22no—
63C4×D149D812yes—
64C4×D149SD1612yes—
65C23×C149—22no—
66D4×C149—42no—
67D4×C149—42no—
68D4×C149—42no—
69C2×C4×C149C22⋊C411yescharacteristic
70C2×C4×C149C22⋊C411yescharacteristic
71C2×C4×C149C22×C411yescharacteristic
72C22×C149—42no—
73C22×C149—42no—
74C22×C149—42no—
75C22×C149C2×C22⋊C411yescharacteristic
76C2×D149—21no—
77C2×D149—21no—
78C2×D149—42no—
79C2×D149—42no—
80C2×D149—42no—
81C2×D149—88no—
82C2×D149#10212yes—
83C4×C149—21no—
84C4×C149—21no—
85C4×C149#10212yes—
86Dic149#10012yes—
87Dic149C2×D811yescharacteristic
88Dic149C2×SD1611yescharacteristic
89Dic149AGL(1,ℤ/8)12yes—
90C2×C149—82no—
91C2×C149C2×#10011yescharacteristic
92C2×C149C2×#10211yescharacteristic
93C2×C149#41811yescharacteristic
94D149—22no—
95D149—82no—
96C149#154511yescharacteristic, complemented, Sylow
97#1545—1491nomaximal, Sylow
98C2×#127—1491no—
99#431—1491no—
100#423—1491no—
101#331—1494no—
102C22×D4—2981no—
103C22×D4—2981no—
104C22×D4—1492no—
105C2×M16—2981no—
106#127—2981no—
107#127—2981no—
108#127—1492no—
109#127—1491no—
110#127#1059701011yescharacteristic
111C2×C42—1491no—
112C4⋊C8—2981no—
113C4⋊C8—1492no—
114C4⋊C8—1492no—
115C22⋊C8—2981no—
116C4×C8—2981no—
117C24—2982no—
118C2×D4—21no—
119C2×D4—21no—
120C2×D4—2982no—
121C2×D4—2982no—
122C2×D4—2982no—
123C2×D4—2981no—
124C2×D4—2981no—
125C2×D4—5964no—
126C2×D4—5964no—
127C2×D4—5962no—
128C2×D4—5962no—
129C2×D4—1492no—
130C2×D4C2×#1059701012yes—
131C22×C4—1491no—
132C22×C4—1491no—
133C22×C4—1491no—
134M16—5962no—
135C2×C8—2982no—
136C2×C8—2982no—
137C42—1491no—
138C42—1491no—
139C42—1491no—
140C42C2×#1059701011yescharacteristic
141C23—22no—
142C23—2982no—
143C23—5964no—
144C23—5964no—
145C23—5964no—
146C23—1491no—
147D4—42no—
148D4—42no—
149D4—42no—
150D4—5962no—
151D4—5962no—
152D4—5964no—
153D4—5962no—
154D4—5962no—
155D4—5964no—
156D4—5962no—
157C2×C4—2982no—
158C2×C4—2982no—
159C2×C4—1491no—
160C2×C4—1491no—
161C2×C4—1491no—
162C2×C4—1492no—
163C2×C4—1492no—
164C2×C4C22⋊#1059701011yescharacteristic
165C2×C4C22⋊#1059701011yescharacteristic
166C2×C4C22×#1059701011yescharacteristic
167C8—5962no—
168C8—5962no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—2981no—
173C22—2981no—
174C22—5962no—
175C22—5962no—
176C22—5962no—
177C22—1492no—
178C22—11928no—
179C22C2×C22⋊#1059701011yescharacteristic
180C4—21no—
181C4—21no—
182C4—1492no—
183C4—1491no—
184C4—1491no—
185C4—1492no—
186C4#1801197312yes—
187C2—82no—
188C2—2982no—
189C2—11922no—
190C2D149⋊#10011yescharacteristic
191C2C2×#1801197311yescharacteristic
192C2#2375061711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#127×C149C4
socleC22×C149C2×C22⋊C4
prime radical#127×D149C2
cosocleC4×Dic149C23
hypercenter#127#10597010
hypocenterC149#1545
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #23750643C2semidirect
2. #23750630C2semidirect
3. #23750483C2semidirect
7. #18011978C22semidirect
8. #18011978C22semidirect
96. C149#1545semidirect

Maximal subgroups

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

subgroupindex
#237506432
#237506302
#237504832
#127×D1492
#1545149