Finite Group Databasebeta

← #34043239

Subgroups — #34043239

Order 19072.

252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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#23750175C211yesmaximal, characteristic
2#23749493C211yesmaximal, characteristic, complemented
3#23749360C214yesmaximal, complemented
4#432×C149C211yesmaximal, characteristic, complemented
5C2×#14558736—21no—
6#18011911C411yescharacteristic, complemented
7#18011908C411yescharacteristic, complemented
8#18011899—21no—
9#18011885—21no—
10#18011885C2212yes—
11C4×D596—21no—
12C4×D596C412yescomplemented
13#18011818—21no—
14#18011818—21no—
15#18011818C2212yes—
16C2×C42×C149C2211yescharacteristic
17C4⋊C8×C149—21no—
18C22⋊C8×C149C2212yes—
19#97×C149—21no—
20#14558736—44no—
21C2×Dic298—21no—
22C2×D596—21no—
23C2×D596—21no—
24C2×D596C2×C412yes—
25C2×C22⋊D149—22no—
26C22×Dic149—22no—
27C2×C4×D149—22no—
28C4⋊Dic149—21no—
29C4⋊Dic149C2×C412yes—
30#14558713—22no—
31#14558713—22no—
32C22×C4×C149D411yescharacteristic
33C22×C4×C149D411yescharacteristic
34C22×C4×C149C2311yescharacteristic
35C2×C8×C149—22no—
36C42×C149C2×C411yescharacteristic
37C42×C149C2×C411yescharacteristic
38C42×C149D411yescharacteristic
39C42×C149D411yescharacteristic
40C22×D149—22no—
41Dic298—42no—
42D596—42no—
43D596—42no—
44D596—42no—
45C22⋊D149—44no—
46C2×Dic149—22no—
47C2×Dic149—42no—
48C2×Dic149—42no—
49C2×Dic149—42no—
50C4×D149—44no—
51C23×C149C2×D411yescharacteristic
52C2×C4×C149—22no—
53C2×C4×C149—41no—
54C2×C4×C149—41no—
55C2×C4×C149C22⋊C411yescharacteristic
56C2×C4×C149C22⋊C411yescharacteristic
57C2×C4×C149C22⋊C411yescharacteristic
58C2×C4×C149C22⋊C411yescharacteristic
59C2×C4×C149C22×C411yescharacteristic
60C2×C4×C149C2×D411yescharacteristic
61C8×C149—42no—
62C22×C149—21no—
63C22×C149—21no—
64C22×C149C2×C22⋊C411yescharacteristic
65C22×C149AGL(1,ℤ/8)12yes—
66C2×D149—42no—
67C2×D149—42no—
68C2×D149—42no—
69C4×C149—21no—
70C4×C149—21no—
71C4×C149—21no—
72C4×C149—21no—
73C4×C149—21no—
74C4×C149—21no—
75Dic149—42no—
76Dic149—82no—
77C2×C149—22no—
78C2×C149#41011yescharacteristic
79C2×C149#41811yescharacteristic
80C2×C149#42111yescharacteristic
81D149—82no—
82C149#151411yescharacteristic, complemented, Sylow
83#1514—1491nomaximal, Sylow
84#532—1491no—
85#432D14911yescharacteristic, complemented
86#383—1491no—
87#327—1494no—
88C2×#41—2981no—
89C4⋊Q8—1491no—
90#127—1491no—
91#124—2981no—
92#121—2981no—
93#121—1492no—
94C4×D4—2981no—
95C4×D4—1492no—
96C2×C42C2×D14911yescharacteristic
97C4⋊C8—21no—
98C22⋊C8C2×D14912yes—
99#97—21no—
100#95—2981no—
101#95—2981no—
102#95—1492no—
103#41—5964no—
104C2×Q8—2981no—
105C2×D4—2982no—
106C2×D4—2981no—
107C2×D4—2981no—
108C2×D4—1492no—
109C22×C4—2982no—
110C22×C4—2982no—
111C22×C4D59611yescharacteristic
112C22×C4D59611yescharacteristic
113C22×C4C22×D14911yescharacteristic
114C2×C8—22no—
115C4⋊C4—2981no—
116C4⋊C4—1492no—
117C22⋊C4—2982no—
118C22⋊C4—2982no—
119C42C4×D14911yescharacteristic
120C42C4×D14911yescharacteristic
121C42C22⋊D14911yescharacteristic
122C42C22⋊D14911yescharacteristic
123C23—2982no—
124C23C2×D59611yescharacteristic
125Q8—5962no—
126D4—5962no—
127D4—5962no—
128D4—5962no—
129D4—5964no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—2982no—
134C2×C4—5964no—
135C2×C4—5962no—
136C2×C4—5962no—
137C2×C4—5962no—
138C2×C4#1455871311yescharacteristic
139C2×C4#1455871311yescharacteristic
140C2×C4#1455871311yescharacteristic
141C2×C4#1455871311yescharacteristic
142C2×C4C2×C4×D14911yescharacteristic
143C2×C4C2×C22⋊D14911yescharacteristic
144C8—42no—
145C22—21no—
146C22—21no—
147C22—5962no—
148C22—5962no—
149C22—5962no—
150C22C2×#1455871311yescharacteristic
151C22#1801193912yes—
152C4—21no—
153C4—21no—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—5962no—
159C4—11922no—
160C2—22no—
161C2—11922no—
162C2#2374959811yescharacteristic
163C2#2374963111yescharacteristic
164C2#2374964111yescharacteristic
subgroupG/H
centerC22C2×#14558713
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#432×C149C2
socleC22×C149C2×C22⋊C4
prime radical#23750175C2
cosocleC22×C4×C149C23
hypercenter#432D149
hypocenterC149#1514
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #23749493C2semidirect
3. #23749360C2semidirect
4. #432×C149C2semidirect
6. #18011911C4semidirect
7. #18011908C4semidirect
12. C4×D596C4semidirect
82. C149#1514semidirect
85. #432D149semidirect

Maximal subgroups

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

subgroupindex
#237501752
#237494932
#237493602
#432×C1492
#1514149