Finite Group Databasebeta

← #34060991

Subgroups — #34060991

Order 19072.

262 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 52 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#23750612C212yesmaximal, complemented
2#23750534C212yesmaximal, complemented
3#23750533C212yesmaximal, complemented
4#23750188C211yesmaximal, characteristic
5C2×#14558745—22no—
6#18011972C2214yescomplemented
7#18011971—22no—
8C2×#14558735C2211yescharacteristic
9C2×D4×D149C411yescharacteristic
10#18011907C411yescharacteristic
11#18011899C2211yescharacteristic
12#18011898C2211yescharacteristic
13#18011883—22no—
14#18011879—22no—
15#18011868C411yescharacteristic
16#127×C149C411yescharacteristic
17#14558745—24no—
18#14558745—42no—
19C2×#11924753—42no—
20C23×D149—21no—
21#14558735—42no—
22C2×Dic298C2311yescharacteristic
23C2×D596C2×C411yescharacteristic
24C2×C22⋊D149—21no—
25C2×C22⋊D149—22no—
26C2×C22⋊D149D412yes—
27D4×D149—42no—
28C22×Dic149D412yes—
29C2×C4×D149C2×C411yescharacteristic
30#14558715—21no—
31C22⋊Dic149—22no—
32#14558713—21no—
33#14558713—22no—
34C4×Dic149C2×C411yescharacteristic
35C2×D4×C149—22no—
36C2×D4×C149C2×C411yescharacteristic
37C2×D4×C149C2×C411yescharacteristic
38C42×C149C2×C411yescharacteristic
39#11924753—44no—
40C22×D149—21no—
41C22×D149—42no—
42C22×D149—82no—
43C22×D149C22⋊C411yescharacteristic
44Dic298—41no—
45D596—41no—
46C22⋊D149—42no—
47C22⋊D149—42no—
48C22⋊D149—82no—
49C2×Dic149—22no—
50C2×Dic149—22no—
51C2×Dic149—21no—
52C2×Dic149C22⋊C411yescharacteristic
53C2×Dic149C2×D412yes—
54C4×D149—22no—
55C23×C149—21no—
56C23×C149C22⋊C412yes—
57D4×C149—41no—
58D4×C149—41no—
59D4×C149—82no—
60C2×C4×C149—21no—
61C2×C4×C149C22×C411yescharacteristic
62C22×C149—22no—
63C22×C149—42no—
64C22×C149—42no—
65C22×C149—41no—
66C22×C149C2×C22⋊C411yescharacteristic
67C2×D149—21no—
68C2×D149—41no—
69C2×D149—42no—
70C2×D149—41no—
71C2×D149—84no—
72C4×C149—21no—
73C4×C149—41no—
74Dic149—22no—
75Dic149—41no—
76Dic149#9912yes—
77C2×C149—21no—
78C2×C149—42no—
79C2×C149—81no—
80C2×C149C2×#9911yescharacteristic
81D149—41no—
82D149—81no—
83C149#213411yescharacteristic, complemented, Sylow
84#2134—1491nomaximal, Sylow
85#535—1491no—
86#413—1492no—
87#355—1492no—
88#355—1492no—
89C2×#41—1491no—
90C22×D4—1491no—
91C2×M16—2982no—
92#127—1491no—
93#127#1059701011yescharacteristic
94#124—1491no—
95#124—1491no—
96#121—2982no—
97#120—2982no—
98#117—1491no—
99#101—1494no—
100#100—2982no—
101C24—2981no—
102#41—5962no—
103C2×Q8—1491no—
104C2×D4—22no—
105C2×D4—2982no—
106C2×D4—2981no—
107C2×D4—5962no—
108C2×D4—1492no—
109C2×D4—1491no—
110C2×D4C2×#1059701011yescharacteristic
111C2×D4C2×#1059701011yescharacteristic
112C22×C4—1492no—
113C22×C4—1491no—
114M16—2984no—
115M16—5962no—
116C2×C8—5962no—
117C4⋊C4—2981no—
118C22⋊C4—2981no—
119C22⋊C4—2982no—
120C22⋊C4—2982no—
121C42—1491no—
122C42C2×#1059701011yescharacteristic
123C23—21no—
124C23—2981no—
125C23—5962no—
126C23—1491no—
127C23—11922no—
128C23C22⋊#1059701012yes—
129Q8—5961no—
130D4—41no—
131D4—41no—
132D4—82no—
133D4—5961no—
134D4—5962no—
135D4—5962no—
136D4—11922no—
137C2×C4—21no—
138C2×C4—2982no—
139C2×C4—2982no—
140C2×C4—2982no—
141C2×C4—2981no—
142C2×C4—1492no—
143C2×C4—1491no—
144C2×C4C22×#1059701011yescharacteristic
145C8—5964no—
146C22—22no—
147C22—42no—
148C22—42no—
149C22—41no—
150C22—2981no—
151C22—5961no—
152C22—5962no—
153C22—5961no—
154C22—11924no—
155C22C2×C22⋊#1059701011yescharacteristic
156C4—21no—
157C4—41no—
158C4—2982no—
159C4—5961no—
160C4—1492no—
161C2—21no—
162C2—42no—
163C2—81no—
164C2—5961no—
165C2—11921no—
166C2D149⋊#9911yescharacteristic
subgroupG/H
centerC2D149⋊#99
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#127×C149C4
socleC2×C149C2×#99
prime radical#23750188C2
cosocleC2×Dic298C23
hypercenter#127#10597010
hypocenterC149#2134
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #23750612C2semidirect
2. #23750534C2semidirect
3. #23750533C2semidirect
6. #18011972C22semidirect
83. C149#2134semidirect

Maximal subgroups

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

subgroupindex
#237506122
#237505342
#237505332
#237501882
#2134149