Finite Group Databasebeta

← #34046647

Subgroups — #34046647

Order 19072.

220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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#23750426C211yesmaximal, characteristic, complemented
2#23750061C211yesmaximal, characteristic, complemented
3#23749892C211yesmaximal, characteristic, complemented
4#23749438C211yesmaximal, characteristic, complemented
5#23749433C211yesmaximal, characteristic, complemented
6#23749408C211yesmaximal, characteristic, complemented
7C2×D16×C149C211yesmaximal, characteristic, complemented
8#18011956—21no—
9#18011937—21no—
10#18011937—21no—
11#18011935—22no—
12#18011933C2211yescharacteristic
13#18011930—21no—
14D8×D149—21no—
15#18011917C2211yescharacteristic
16#18011855—21no—
17#18011852—21no—
18#18011851C2211yescharacteristic, complemented
19#18011847C2211yescharacteristic, complemented
20#18011828—21no—
21C2×D8×C149C2211yescharacteristic
22C2×D8×C149C2211yescharacteristic, complemented
23D16×C149—22no—
24C2×C16×C149C2211yescharacteristic, complemented
25#14558736—21no—
26#14558736D411yescharacteristic
27#14558735—22no—
28#14558735—41no—
29C2×C22⋊D149—42no—
30D4×D149—22no—
31D4×D149—41no—
32Dic596D411yescharacteristic
33#14558725—21no—
34#14558724—22no—
35#14558724—41no—
36D1192D411yescharacteristic
37#14558721—22no—
38#14558721—41no—
39#14558720—21no—
40#14558720D411yescharacteristic
41#14558719—21no—
42C8×D149—21no—
43#14558711—21no—
44C2×D4×C149—21no—
45C2×D4×C149—21no—
46D8×C149—21no—
47D8×C149—21no—
48D8×C149—21no—
49D8×C149D412yes—
50C2×C8×C149C2311yescharacteristic
51C16×C149—21no—
52C22×D149—42no—
53Dic298—21no—
54Dic298D811yescharacteristic
55D596—21no—
56D596D811yescharacteristic
57C22⋊D149—21no—
58C22⋊D149—42no—
59C22⋊D149—42no—
60C22⋊D149—41no—
61C2×Dic149—42no—
62C4×D149—21no—
63C4×D149—41no—
64#11924746—21no—
65#11924746—41no—
66C23×C149—41no—
67C23×C149—41no—
68D4×C149—22no—
69D4×C149—41no—
70D4×C149—41no—
71D4×C149—41no—
72C2×C4×C149C2×D411yescharacteristic
73C8×C149C2×D411yescharacteristic
74C8×C149C2×D411yescharacteristic
75C22×C149—42no—
76C22×C149—81no—
77C22×C149—161no—
78C22×C149—161no—
79C22×C149AGL(1,ℤ/8)11yescharacteristic
80C2×D149—21no—
81C2×D149—41no—
82C2×D149—162no—
83C4×C149#12011yescharacteristic
84C4×C149C2×D811yescharacteristic
85Dic149—21no—
86Dic149—41no—
87C2×C149—21no—
88C2×C149—82no—
89C2×C149—161no—
90C2×C149#44711yescharacteristic
91D149—41no—
92D149—81no—
93C149#219211yescharacteristic, complemented, Sylow
94#2192—1491nomaximal, Sylow
95#576—1491no—
96#509—1491no—
97C2×D16D14911yescharacteristic, complemented
98#472—1491no—
99#361—1491no—
100#359—1491no—
101#350—1491no—
102H(5,𝔽2)—2981no—
103AGL(1,ℤ/8)—2982no—
104AGL(1,ℤ/8)—2981no—
105AGL(1,ℤ/8)—2981no—
106#135—2981no—
107#135—1491no—
108C2×D8—2981no—
109C2×D8C2×D14911yescharacteristic
110C2×D8C2×D14911yescharacteristic, complemented
111#131—1491no—
112SD32—2981no—
113D16—22no—
114D16—2981no—
115M32—1491no—
116C2×C16C2×D14911yescharacteristic, complemented
117#108—1491no—
118#100—2981no—
119#41—2982no—
120#41—2981no—
121#41—5961no—
122#41—1491no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—2982no—
126C2×D4—5961no—
127C2×D4—5962no—
128Q16—1491no—
129SD16—2982no—
130SD16—2981no—
131SD16—5961no—
132D8—21no—
133D8—21no—
134D8—21no—
135D8—2982no—
136D8—5961no—
137D8—1491no—
138D8C22⋊D14912yes—
139M16—2981no—
140M16—2981no—
141M16—1491no—
142C2×C8—2981no—
143C2×C8C22×D14911yescharacteristic
144C16—21no—
145C16—2981no—
146C23—41no—
147C23—41no—
148C23—5962no—
149Q8—2981no—
150Q8—1491no—
151D4—22no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—2981no—
156D4—2981no—
157D4—5962no—
158D4—5962no—
159D4—5961no—
160D4—1491no—
161C2×C4—2981no—
162C2×C4—5962no—
163C2×C4—5961no—
164C2×C4D4×D14911yescharacteristic
165C8—2981no—
166C8—5961no—
167C8D4×D14911yescharacteristic
168C8C2×C22⋊D14911yescharacteristic
169C22—42no—
170C22—81no—
171C22—161no—
172C22—161no—
173C22—2981no—
174C22—23842no—
175C22—5961no—
176C22#1801193511yescharacteristic
177C4—2981no—
178C4—5961no—
179C4#1801187911yescharacteristic
180C4D8×D14911yescharacteristic
181C2—21no—
182C2—82no—
183C2—161no—
184C2—5961no—
185C2—11921no—
186C2#2374975711yescharacteristic
subgroupG/H
centerC2#23749757
commutator, cosocleC2×C8×C149C23
FrattiniC2×C8C22×D149
FittingC2×D16×C149C2
socleC2×C149#447
hypercenterC2×D16D149
hypocenterC149#2192
LCSG ▷ C2×C8×C149 ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #23750426C2semidirect
2. #23750061C2semidirect
3. #23749892C2semidirect
4. #23749438C2semidirect
5. #23749433C2semidirect
6. #23749408C2semidirect
7. C2×D16×C149C2semidirect
18. #18011851C22semidirect
19. #18011847C22semidirect
22. C2×D8×C149C22semidirect
24. C2×C16×C149C22semidirect
93. C149#2192semidirect
97. C2×D16D149semidirect
110. C2×D8C2×D149semidirect
116. C2×C16C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237504262
#237500612
#237498922
#237494382
#237494332
#237494082
C2×D16×C1492
#2192149