Finite Group Databasebeta

← #34060969

Subgroups — #34060969

Order 19072.

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

normal subgroups only

This group has 286 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
1D149⋊#99C212yesmaximal, complemented
2#23750531C212yesmaximal, complemented
3#23750530C212yesmaximal, complemented
4#23750193C211yesmaximal, characteristic
5C2×C22⋊#10597010—22no—
6#18011970C2214yes—
7#18011969—22no—
8C2×#14558737C411yescharacteristic, complemented
9C2×D4×D149C2211yescharacteristic
10#18011908C2211yescharacteristic
11#18011907C411yescharacteristic, complemented
12#18011900C2211yescharacteristic
13#18011884—22no—
14#18011881—22no—
15#18011868C411yescharacteristic, complemented
16#124×C149C411yescharacteristic, complemented
17C22×#10597010—42no—
18C22⋊#10597010—24no—
19C22⋊#10597010—42no—
20C23×D149D412yes—
21#14558737—42no—
22C2×D596—21no—
23C2×D596—22no—
24C2×D596C2×C411yescharacteristic, complemented
25C2×D596C2311yescharacteristic
26C2×C22⋊D149—22no—
27C2×C22⋊D149D412yes—
28D4×D149—42no—
29C2×C4×D149—21no—
30C2×C4×D149C2×C411yescharacteristic
31#14558715—21no—
32#14558713—21no—
33#14558713—22no—
34C4×Dic149C2×C411yescharacteristic, complemented
35C2×Q8×C149C2×C411yescharacteristic, complemented
36C2×D4×C149C2×C411yescharacteristic
37C22⋊C4×C149—22no—
38C42×C149C2×C411yescharacteristic, complemented
39C2×#10597010—44no—
40C2×#10597010—84no—
41C22×D149—22no—
42C22×D149—22no—
43C22×D149—21no—
44C22×D149—82no—
45C22×D149C22⋊C411yescharacteristic
46C22×D149C2×D412yes—
47D596—41no—
48D596—41no—
49D596—42no—
50D596—82no—
51C22⋊D149—42no—
52C22⋊D149—82no—
53C2×Dic149—21no—
54C2×Dic149C22⋊C411yescharacteristic
55C4×D149—22no—
56C4×D149—42no—
57C23×C149C22⋊C412yes—
58Q8×C149—41no—
59D4×C149—41no—
60C2×C4×C149—21no—
61C2×C4×C149—21no—
62C2×C4×C149C22×C411yescharacteristic
63C22×C149—22no—
64C22×C149—42no—
65C22×C149C2×C22⋊C411yescharacteristic
66C2×D149—22no—
67C2×D149—41no—
68C2×D149—44no—
69C2×D149—42no—
70C2×D149—42no—
71C2×D149—41no—
72C2×D149—82no—
73C2×D149#9912yes—
74#10597010—84no—
75C4×C149—21no—
76C4×C149—41no—
77C4×C149—41no—
78Dic149—21no—
79Dic149—41no—
80C2×C149—21no—
81C2×C149—42no—
82C2×C149C2×#9911yescharacteristic
83D149—22no—
84D149—42no—
85D149—81no—
86C149#212711yescharacteristic, complemented, Sylow
87#2127—1491nomaximal, Sylow
88#535—1491no—
89C2×#99—1492no—
90#354—1492no—
91#353—1492no—
92C2×#41—1491no—
93C22×D4—1491no—
94#127—1491no—
95#127—1491no—
96#124—1491no—
97#124#1059701011yescharacteristic, complemented
98#121—2982no—
99#120—2982no—
100#117—1491no—
101C2×C22⋊C4—2982no—
102#99—2982no—
103#99—1494no—
104C24—1492no—
105#41—5962no—
106C2×Q8C2×#1059701011yescharacteristic, complemented
107C2×D4—2981no—
108C2×D4—2982no—
109C2×D4—2982no—
110C2×D4—5962no—
111C2×D4—1492no—
112C2×D4—1491no—
113C2×D4—1491no—
114C2×D4C2×#1059701011yescharacteristic
115C22×C4—2981no—
116C22×C4—5962no—
117C22×C4—1491no—
118C4⋊C4—2981no—
119C22⋊C4—22no—
120C22⋊C4—2981no—
121C22⋊C4—2982no—
122C22⋊C4—2984no—
123C22⋊C4—5962no—
124C42—1491no—
125C42C2×#1059701011yescharacteristic, complemented
126C23—2982no—
127C23—2982no—
128C23—2981no—
129C23—1492no—
130C23—1491no—
131C23—11922no—
132C23C22⋊#1059701012yes—
133Q8—41no—
134D4—41no—
135D4—5961no—
136D4—5961no—
137D4—5962no—
138D4—5962no—
139D4—11922no—
140D4—11922no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—2982no—
144C2×C4—2981no—
145C2×C4—5962no—
146C2×C4—5964no—
147C2×C4—1491no—
148C2×C4—11924no—
149C2×C4C22×#1059701011yescharacteristic
150C22—22no—
151C22—42no—
152C22—2982no—
153C22—5961no—
154C22—5962no—
155C22—5962no—
156C22—5964no—
157C22—5961no—
158C22—1492no—
159C22—11922no—
160C22C2×C22⋊#1059701011yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—2981no—
165C4—5961no—
166C4—11924no—
167C2—21no—
168C2—42no—
169C2—2982no—
170C2—5962no—
171C2—11921no—
172C2D149⋊#9911yescharacteristic
subgroupG/H
centerC2D149⋊#99
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#124×C149C4
socleC2×C149C2×#99
prime radical#23750193C2
cosocleC2×D596C23
hypercenter#124#10597010
hypocenterC149#2127
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. D149⋊#99C2semidirect
2. #23750531C2semidirect
3. #23750530C2semidirect
8. C2×#14558737C4semidirect
11. #18011907C4semidirect
15. #18011868C4semidirect
16. #124×C149C4semidirect
24. C2×D596C2×C4semidirect
34. C4×Dic149C2×C4semidirect
35. C2×Q8×C149C2×C4semidirect
38. C42×C149C2×C4semidirect
86. C149#2127semidirect
97. #124#10597010semidirect
106. C2×Q8C2×#10597010semidirect
125. C42C2×#10597010semidirect

Maximal subgroups

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

subgroupindex
D149⋊#992
#237505312
#237505302
#237501932
#2127149