Finite Group Databasebeta

← #34060823

Subgroups — #34060823

Order 19072.

412 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 78 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
1C2×#18011973C214yesmaximal, complemented
2#23750584C211yesmaximal, characteristic, complemented
3#23750569C211yesmaximal, characteristic, complemented
4#127×D149C211yesmaximal, characteristic
5C2×D149⋊C8C2212yes—
6C2×C4⋊#10597010C2212yes—
7#18011973—28no—
8#18011966—22no—
9(C2×#10597010)⋊C4—22no—
10C2×D4×D149—22no—
11C2×D4×D149C2212yes—
12#18011908C411yescharacteristic, complemented
13#18011907—22no—
14#18011907C412yescomplemented
15C42×D149C2211yescharacteristic
16#127×C149C411yescharacteristic, complemented
17C22×#10597010—22no—
18D149⋊C8—22no—
19D149⋊C8D414yescomplemented
20C2×#11924753—22no—
21C4⋊#10597010—24no—
22C23×D149—22no—
23C2×D596—22no—
24C2×D596C2×C412yes—
25C2×C22⋊D149—24no—
26C2×C22⋊D149—22no—
27D4×D149—24no—
28D4×D149—24no—
29D4×D149—48no—
30C2×C4×D149D412yes—
31C2×C4×D149C2311yescharacteristic
32C4×Dic149C2×C411yescharacteristic
33C4×Dic149D412yes—
34C2×D4×C149—22no—
35C2×D4×C149C2×C412yes—
36C42×C149C2×C411yescharacteristic
37C2×#10597010—42no—
38C2×#10597010—44no—
39#11924753—24no—
40C22×D149—22no—
41C22×D149—42no—
42C22×D149—42no—
43C22×D149—48no—
44C22×D149C2×D411yescharacteristic
45D596—24no—
46D596—44no—
47C22⋊D149—48no—
48C22⋊D149—44no—
49C2×Dic149C22⋊C412yes—
50C2×Dic149C2×D411yescharacteristic
51C4×D149—24no—
52C4×D149C2×D412yes—
53C4×D149#4112yes—
54C23×C149—22no—
55D4×C149—24no—
56D4×C149—44no—
57C2×C4×C149C22⋊C412yes—
58C2×C4×C149C22×C411yescharacteristic
59C22×C149—42no—
60C22×C149—44no—
61C22×C149C2×C22⋊C411yescharacteristic
62C2×D149—42no—
63C2×D149—44no—
64C2×D149—84no—
65C2×D149—84no—
66C2×D149#12411yescharacteristic
67C2×D149#12711yescharacteristic
68C2×D149AGL(1,ℤ/8)14yes—
69#10597010—82no—
70C4×C149—22no—
71C4×C149C4×D412yes—
72Dic149—22no—
73Dic149#12112yes—
74C2×C149—82no—
75C2×C149#39011yescharacteristic
76C2×C149#41812yes—
77D149—82no—
78D149#49012yes—
79D149#49612yes—
80C149#196111yescharacteristic, complemented, Sylow
81#1961—1491nomaximal, Sylow
82C2×#127—1491no—
83C2×#102—1494no—
84C2×#97—1491no—
85#382—1491no—
86C22×D4—2982no—
87C22×D4—1492no—
88C22×C8—1492no—
89#127—2982no—
90#127—1492no—
91#127—1491no—
92#127#1059701011yescharacteristic, complemented
93C2×C4⋊C4—1492no—
94C2×C42—1491no—
95#102—2988no—
96#97—2982no—
97#95—2982no—
98C24—2982no—
99C2×D4—22no—
100C2×D4—2984no—
101C2×D4—2984no—
102C2×D4—2982no—
103C2×D4—2984no—
104C2×D4—2982no—
105C2×D4—5968no—
106C2×D4—1492no—
107C2×D4C2×#1059701012yes—
108C22×C4—2982no—
109C22×C4—1492no—
110C22×C4—1491no—
111C2×C8—2982no—
112C2×C8—2982no—
113C2×C8—1494no—
114C4⋊C4—2984no—
115C42—1492no—
116C42—1491no—
117C42C2×#1059701011yescharacteristic
118C23—22no—
119C23—2982no—
120C23—5962no—
121C23—5962no—
122C23—5968no—
123C23—1491no—
124D4—24no—
125D4—44no—
126D4—2984no—
127D4—5964no—
128D4—5968no—
129D4—5964no—
130C2×C4—2984no—
131C2×C4—5962no—
132C2×C4—5964no—
133C2×C4—1492no—
134C2×C4—1491no—
135C2×C4—1492no—
136C2×C4—1492no—
137C2×C4C22⋊#1059701012yes—
138C2×C4C22×#1059701011yescharacteristic
139C8—2984no—
140C22—42no—
141C22—44no—
142C22—5962no—
143C22—5964no—
144C22—1491no—
145C22—1491no—
146C22—1494no—
147C22—11924no—
148C22—11924no—
149C22C2×C22⋊#1059701011yescharacteristic
150C4—22no—
151C4—2982no—
152C4—1492no—
153C4—11922no—
154C4D4×#1059701012yes—
155C2—82no—
156C2—1492no—
157C2—1492no—
158C2—11922no—
159C2#2375057711yescharacteristic
160C2#2375061712yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#127×C149C4
socleC22×C149C2×C22⋊C4
prime radical#127×D149C2
cosocleC2×C4×D149C23
hypercenter#127#10597010
hypocenterC149#1961
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C2×#18011973C2semidirect
2. #23750584C2semidirect
3. #23750569C2semidirect
12. #18011908C4semidirect
14. #18011907C4semidirect
16. #127×C149C4semidirect
19. D149⋊C8D4semidirect
80. C149#1961semidirect
92. #127#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119732
#237505842
#237505692
#127×D1492
#1961149