Finite Group Databasebeta

← #23750162

Subgroups — #23750162

Order 9536.

234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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#18011906C212yesmaximal, complemented
2#18011902C211yesmaximal, characteristic, complemented
3#18011900C211yesmaximal, characteristic, complemented
4#18011896C212yesmaximal, complemented
5#18011887C211yesmaximal, characteristic, complemented
6#18011886C211yesmaximal, characteristic
7C4×D596C212yesmaximal, complemented
8C4×D596C211yesmaximal, characteristic, complemented
9#18011868C212yesmaximal, complemented
10C42×D149C211yesmaximal, characteristic, complemented
11C4×Q8×C149C211yesmaximal, characteristic, complemented
12C2×D596C2212yes—
13C2×D596C2211yescharacteristic
14C2×C4×D149C2211yescharacteristic
15C2×C4×D149C2211yescharacteristic
16C2×C4×D149C2211yescharacteristic
17C2×C4×D149C2212yes—
18C4⋊Dic149C2212yes—
19C4⋊Dic149C2211yescharacteristic
20#14558715C2212yes—
21#14558715C2212yes—
22#14558713C2212yes—
23#14558713C2212yes—
24#14558713C2212yes—
25#14558713C2212yes—
26#14558713C2212yes—
27C4×Dic149C2211yescharacteristic
28C4×Dic149C2211yescharacteristic
29C4×Dic149C2211yescharacteristic
30C2×Q8×C149C2211yescharacteristic
31C4⋊C4×C149C2212yes—
32C4⋊C4×C149C2211yescharacteristic
33C42×C149C2211yescharacteristic
34C42×C149C2212yes—
35C22×D149C2312yes—
36C22×D149C2311yescharacteristic
37D596—24no—
38D596—22no—
39C2×Dic149C2311yescharacteristic
40C2×Dic149C2311yescharacteristic
41C2×Dic149C2311yescharacteristic
42C2×Dic149C2312yes—
43C4×D149—22no—
44C4×D149—22no—
45C4×D149—22no—
46C4×D149—24no—
47Q8×C149—22no—
48C2×C4×C149C2311yescharacteristic
49C2×C4×C149C2312yes—
50C2×C4×C149C2312yes—
51C2×C4×C149C2311yescharacteristic
52C2×C4×C149C2311yescharacteristic
53C22×C149C2411yescharacteristic
54C2×D149—21no—
55C2×D149—21no—
56C2×D149—22no—
57C2×D149—22no—
58C2×D149—22no—
59C2×D149#4112yes—
60C4×C149—22no—
61C4×C149—21no—
62C4×C149—22no—
63C4×C149#4112yes—
64C4×C149#4112yes—
65Dic149—21no—
66Dic149—21no—
67Dic149—21no—
68Dic149—22no—
69C2×C149C2×#4111yescharacteristic
70C2×C149C2×#4111yescharacteristic
71C2×C149C2×#4111yescharacteristic
72D149—22no—
73D149—42no—
74C149#52911yescharacteristic, complemented, Sylow
75#529—1491nomaximal, Sylow
76#126—1492no—
77#125—1491no—
78#124—1491no—
79#123—1492no—
80C22⋊Q8—1491no—
81#121—1491no—
82C4×Q8D14911yescharacteristic, complemented
83C4×D4—1491no—
84C4×D4—1492no—
85#117—1492no—
86C2×C42—1491no—
87C2×Q8C2×D14911yescharacteristic
88C2×D4—1492no—
89C2×D4—1491no—
90C22×C4—1491no—
91C22×C4—1491no—
92C22×C4—1491no—
93C22×C4—1492no—
94C4⋊C4—1492no—
95C4⋊C4—1492no—
96C4⋊C4—1491no—
97C4⋊C4—1492no—
98C4⋊C4C2×D14911yescharacteristic
99C4⋊C4C2×D14912yes—
100C22⋊C4—1492no—
101C22⋊C4—1492no—
102C22⋊C4—1492no—
103C22⋊C4—1492no—
104C22⋊C4—1492no—
105C42—1491no—
106C42—1491no—
107C42—1491no—
108C42C2×D14911yescharacteristic
109C42C2×D14912yes—
110C23—1492no—
111C23—1491no—
112Q8—22no—
113D4—2984no—
114D4—2982no—
115C2×C4—2982no—
116C2×C4—2982no—
117C2×C4—2982no—
118C2×C4—2984no—
119C2×C4—1491no—
120C2×C4—1491no—
121C2×C4—1491no—
122C2×C4—1492no—
123C2×C4C22×D14911yescharacteristic
124C2×C4C22×D14912yes—
125C2×C4C22×D14912yes—
126C2×C4C22×D14911yescharacteristic
127C2×C4C22×D14911yescharacteristic
128C22—2981no—
129C22—2981no—
130C22—2982no—
131C22—2982no—
132C22—2982no—
133C22—1492no—
134C22C23×D14911yescharacteristic
135C4—21no—
136C4—22no—
137C4—22no—
138C4—2981no—
139C4—2981no—
140C4—2981no—
141C4—2982no—
142C4#1455873612yes—
143C4#1455873712yes—
144C2—2982no—
145C2—5962no—
146C2#41×D14911yescharacteristic
147C2C2×#1455873611yescharacteristic
148C2C2×#1455873711yescharacteristic
subgroupG/H
centerC2×C4C22×D149
commutator, socle, cosocleC22×C149C24
FrattiniC22C23×D149
FittingC4×Q8×C149C2
prime radical#18011886C2
hypercenterC4×Q8D149
hypocenterC149#529
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #18011906C2semidirect
2. #18011902C2semidirect
3. #18011900C2semidirect
4. #18011896C2semidirect
5. #18011887C2semidirect
7. C4×D596C2semidirect
8. C4×D596C2semidirect
9. #18011868C2semidirect
10. C42×D149C2semidirect
11. C4×Q8×C149C2semidirect
74. C149#529semidirect
82. C4×Q8D149semidirect