Finite Group Databasebeta

← #34060120

Subgroups — #34060120

Order 19072.

264 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 66 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#23750569C211yesmaximal, characteristic, complemented
3#23750476C214yesmaximal, complemented
4#23750173C211yesmaximal, characteristic
5C2×C4⋊#10597010—21no—
6#18011978—21no—
7#18011968C2212yes—
8C4×#11924753—21no—
9(C2×#10597010)⋊C4—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—42no—
23#14558735—42no—
24#14558735—42no—
25C2×Dic298—21no—
26C2×C22⋊D149—22no—
27C22×Dic149—22no—
28C2×C4×D149D411yescharacteristic
29C2×C4×D149D411yescharacteristic
30C2×C4×D149C2311yescharacteristic
31C4⋊Dic149—21no—
32C4⋊Dic149C2×C412yes—
33C22⋊Dic149—22no—
34C22⋊Dic149—22no—
35C4×Dic149C2×C411yescharacteristic
36C4×Dic149D411yescharacteristic
37C4×Dic149D411yescharacteristic
38C2×D4×C149—21no—
39C2×D4×C149—21no—
40C2×D4×C149C2×C412yes—
41C42×C149C2×C411yescharacteristic
42C2×#10597010—42no—
43C2×#10597010—42no—
44C2×#10597010—42no—
45#11924753—42no—
46C22×D149C2×D411yescharacteristic
47Dic298—42no—
48C22⋊D149—42no—
49C22⋊D149—42no—
50C2×Dic149—22no—
51C2×Dic149—44no—
52C2×Dic149C22⋊C411yescharacteristic
53C2×Dic149C22⋊C411yescharacteristic
54C2×Dic149C2×D411yescharacteristic
55C4×D149—41no—
56C4×D149—41no—
57C4×D149D812yes—
58C4×D149SD1612yes—
59C23×C149—22no—
60D4×C149—42no—
61D4×C149—42no—
62D4×C149—42no—
63C2×C4×C149C22⋊C411yescharacteristic
64C2×C4×C149C22⋊C411yescharacteristic
65C2×C4×C149C22×C411yescharacteristic
66C22×C149—42no—
67C22×C149—42no—
68C22×C149—42no—
69C22×C149C2×C22⋊C411yescharacteristic
70C2×D149—21no—
71C2×D149—21no—
72C2×D149C2×D811yescharacteristic
73C2×D149C2×SD1611yescharacteristic
74#10597010—82no—
75C4×C149—21no—
76C4×C149—21no—
77C4×C149#10212yes—
78Dic149—21no—
79Dic149—21no—
80Dic149—42no—
81Dic149#10212yes—
82C2×C149—82no—
83C2×C149#41011yescharacteristic
84C2×C149C2×#10211yescharacteristic
85C2×C149#42111yescharacteristic
86D149—21no—
87D149—21no—
88C149#151711yescharacteristic, complemented, Sylow
89#1517—1491nomaximal, Sylow
90#532—1491no—
91#431—1491no—
92#382—1491no—
93#327—1494no—
94C2×#41—2981no—
95C4⋊Q8—1491no—
96#127#1059701011yescharacteristic, complemented
97#124—2981no—
98#121—2981no—
99#121—1492no—
100C4×D4—2981no—
101C4×D4—1492no—
102C2×C4⋊C4—2981no—
103C2×C42—1491no—
104C4⋊C8—2981no—
105C22⋊C8—1492no—
106C4×C8—2981no—
107#95—2981no—
108#95—1492no—
109#41—5962no—
110#41—5962no—
111C2×Q8—2981no—
112C2×D4—21no—
113C2×D4—21no—
114C2×D4—2982no—
115C2×D4C2×#1059701012yes—
116C22×C4—2982no—
117C22×C4—2982no—
118C22×C4—1491no—
119C22×C4—1491no—
120C22×C4—1491no—
121C2×C8—2982no—
122C4⋊C4—2981no—
123C4⋊C4—5962no—
124C4⋊C4—1492no—
125C22⋊C4—2982no—
126C22⋊C4—2982no—
127C42—1491no—
128C42—1491no—
129C42—1491no—
130C42C2×#1059701011yescharacteristic
131C23—22no—
132C23—1491no—
133Q8—5962no—
134D4—42no—
135D4—42no—
136D4—42no—
137D4—5962no—
138D4—5962no—
139C2×C4—2982no—
140C2×C4—5961no—
141C2×C4—5961no—
142C2×C4—5964no—
143C2×C4—5962no—
144C2×C4—5962no—
145C2×C4—5962no—
146C2×C4—1491no—
147C2×C4—1491no—
148C2×C4—1491no—
149C2×C4—1492no—
150C2×C4—1492no—
151C2×C4C22⋊#1059701011yescharacteristic
152C2×C4C22⋊#1059701011yescharacteristic
153C2×C4C22×#1059701011yescharacteristic
154C8—5962no—
155C22—42no—
156C22—42no—
157C22—42no—
158C22—2981no—
159C22—2981no—
160C22—1491no—
161C22—1491no—
162C22C2×C22⋊#1059701011yescharacteristic
163C4—21no—
164C4—21no—
165C4—2981no—
166C4—2981no—
167C4—5962no—
168C4—1492no—
169C4—11922no—
170C4#1801197312yes—
171C2—82no—
172C2—2981no—
173C2—2981no—
174C2#2375060511yescharacteristic
175C2C2×#1801197311yescharacteristic
176C2#2375062311yescharacteristic
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#1517
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. #23750569C2semidirect
3. #23750476C2semidirect
12. #18011911C4semidirect
17. D4×Dic149C4semidirect
19. #127×C149C4semidirect
88. C149#1517semidirect
96. #127#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506432
#237505692
#237504762
#237501732
#1517149