Finite Group Databasebeta

← #34060071

Subgroups — #34060071

Order 19072.

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

normal subgroups only

This group has 284 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#23750644C211yesmaximal, characteristic, complemented
2C4×C4⋊#10597010C211yesmaximal, characteristic, complemented
3#23750476C214yesmaximal, complemented
4#23750173C211yesmaximal, characteristic
5C2×C4⋊#10597010—21no—
6C2×C4×#10597010—21no—
7C4⋊#11924753—21no—
8#18011968C2212yes—
9C4×#11924753—21no—
10(C2×#10597010)⋊C4C2212yes—
11C2×#14558735—21no—
12#18011911C411yescharacteristic, complemented
13#18011898—21no—
14#18011882—21no—
15#18011882C2212yes—
16D4×Dic149—21no—
17D4×Dic149C412yescomplemented
18C42×D149C2211yescharacteristic
19#127×C149C411yescharacteristic, complemented
20C22×#10597010—22no—
21C2×#11924753—22no—
22C4⋊#10597010—24no—
23C4×#10597010—42no—
24#14558735—42no—
25#14558735—42no—
26C2×Dic298—21no—
27C2×C22⋊D149—22no—
28C22×Dic149—22no—
29C2×C4×D149D411yescharacteristic
30C2×C4×D149D411yescharacteristic
31C2×C4×D149C2311yescharacteristic
32C4⋊Dic149—21no—
33C4⋊Dic149C2×C412yes—
34C22⋊Dic149—22no—
35C22⋊Dic149—22no—
36C4×Dic149C2×C411yescharacteristic
37C4×Dic149D411yescharacteristic
38C4×Dic149D411yescharacteristic
39C2×D4×C149—21no—
40C2×D4×C149—21no—
41C2×D4×C149C2×C412yes—
42C42×C149C2×C411yescharacteristic
43C2×#10597010—24no—
44C2×#10597010—42no—
45C2×#10597010—42no—
46#11924753—42no—
47C22×D149C2×D411yescharacteristic
48Dic298—42no—
49C22⋊D149—42no—
50C22⋊D149—42no—
51C2×Dic149—22no—
52C2×Dic149—44no—
53C2×Dic149C22⋊C411yescharacteristic
54C2×Dic149C22⋊C411yescharacteristic
55C2×Dic149C2×D411yescharacteristic
56C4×D149—22no—
57C4×D149—41no—
58C4×D149D812yes—
59C4×D149SD1612yes—
60C23×C149—22no—
61D4×C149—42no—
62D4×C149—42no—
63D4×C149—42no—
64C2×C4×C149C22⋊C411yescharacteristic
65C2×C4×C149C22⋊C411yescharacteristic
66C2×C4×C149C22×C411yescharacteristic
67C22×C149—42no—
68C22×C149—42no—
69C22×C149—42no—
70C22×C149C2×C22⋊C411yescharacteristic
71C2×D149—21no—
72C2×D149—21no—
73C2×D149C2×D811yescharacteristic
74C2×D149C2×SD1611yescharacteristic
75#10597010—44no—
76C4×C149—21no—
77C4×C149#10212yes—
78C4×C149#10412yes—
79Dic149—21no—
80Dic149—21no—
81Dic149—42no—
82Dic149#10212yes—
83C2×C149—82no—
84C2×C149#41011yescharacteristic
85C2×C149C2×#10211yescharacteristic
86C2×C149C2×#10411yescharacteristic
87D149—21no—
88D149—21no—
89C149#150211yescharacteristic, complemented, Sylow
90#1502—1491nomaximal, Sylow
91#532—1491no—
92#431—1491no—
93C4×C4⋊C4—1491no—
94#327—1494no—
95C2×#41—2981no—
96C4⋊Q8—1491no—
97#127#1059701011yescharacteristic, complemented
98#124—2981no—
99#121—2981no—
100#121—1492no—
101C4×D4—2981no—
102C4×D4—1492no—
103C2×C4⋊C4—2981no—
104C2×C42—2981no—
105C2×C42—1491no—
106C4⋊C8—2981no—
107C22⋊C8—1492no—
108C4×C8—2981no—
109#95—1492no—
110#41—5962no—
111#41—5962no—
112C2×Q8—2981no—
113C2×D4—21no—
114C2×D4—21no—
115C2×D4—2982no—
116C2×D4C2×#1059701012yes—
117C22×C4—2982no—
118C22×C4—2982no—
119C22×C4—1491no—
120C22×C4—1491no—
121C22×C4—1491no—
122C2×C8—2982no—
123C4⋊C4—2984no—
124C4⋊C4—2981no—
125C4⋊C4—1492no—
126C22⋊C4—2982no—
127C22⋊C4—2982no—
128C42—5962no—
129C42—1491no—
130C42—1491no—
131C42—1491no—
132C42C2×#1059701011yescharacteristic
133C23—22no—
134C23—1491no—
135Q8—5962no—
136D4—42no—
137D4—42no—
138D4—42no—
139D4—5962no—
140D4—5962no—
141C2×C4—2982no—
142C2×C4—2984no—
143C2×C4—2982no—
144C2×C4—5961no—
145C2×C4—5962no—
146C2×C4—5962no—
147C2×C4—5964no—
148C2×C4—1491no—
149C2×C4—1491no—
150C2×C4—1491no—
151C2×C4—1492no—
152C2×C4—1492no—
153C2×C4C22⋊#1059701011yescharacteristic
154C2×C4C22⋊#1059701011yescharacteristic
155C2×C4C22×#1059701011yescharacteristic
156C8—5962no—
157C22—42no—
158C22—42no—
159C22—42no—
160C22—2981no—
161C22—2981no—
162C22—1491no—
163C22—1491no—
164C22C2×C22⋊#1059701011yescharacteristic
165C4—21no—
166C4—2981no—
167C4—2981no—
168C4—5964no—
169C4—5962no—
170C4—1492no—
171C4#1801197312yes—
172C4#1801197512yes—
173C2—82no—
174C2—2981no—
175C2—2981no—
176C2#2375060511yescharacteristic
177C2C2×#1801197311yescharacteristic
178C2C2×#1801197511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#127×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750173C2
cosocleC2×C4×D149C23
hypercenter#127#10597010
hypocenterC149#1502
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. #23750644C2semidirect
2. C4×C4⋊#10597010C2semidirect
3. #23750476C2semidirect
12. #18011911C4semidirect
17. D4×Dic149C4semidirect
19. #127×C149C4semidirect
89. C149#1502semidirect
97. #127#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506442
C4×C4⋊#105970102
#237504762
#237501732
#1502149