Finite Group Databasebeta

← #37573687

Subgroups — #37573687

Order 24448.

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

normal subgroups only

This group has 290 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#27133289C211yesmaximal, characteristic
2#27132526C212yesmaximal
3#27132430C211yesmaximal, characteristic
4#27132429C212yesmaximal
5#381×C191C211yesmaximal, characteristic
6#20259301—22no—
7#20259299—24no—
8C2×C22⋊Dic191C2212yes—
9C2×C22⋊Dic191C2212yes—
10C191⋊#95—24no—
11C23×C4×C191C2211yescharacteristic
12C2×C22⋊C4×C191C2211yescharacteristic
13C2×C22⋊C4×C191C2211yescharacteristic
14#95×C191—22no—
15C2×Dic382—22no—
16C22×Dic191—22no—
17C22×Dic191D414yes—
18C4⋊Dic191—22no—
19Dic191⋊C4—24no—
20C22⋊Dic191—22no—
21C22⋊Dic191—22no—
22C22⋊Dic191—22no—
23C22⋊Dic191—22no—
24C24×C191C2311yescharacteristic
25C22×C4×C191—21no—
26C22×C4×C191—22no—
27C22×C4×C191—22no—
28C22×C4×C191—21no—
29C22×C4×C191—21no—
30C22×C4×C191D412yes—
31C22×C4×C191Q812yescomplemented
32C22⋊C4×C191—22no—
33C22⋊C4×C191—22no—
34Dic382—82no—
35C2×Dic191—24no—
36C2×Dic191—44no—
37C2×Dic191—44no—
38C2×Dic191—42no—
39C23×C191—42no—
40C23×C191C2×D412yes—
41C23×C191C2×D411yescharacteristic
42C23×C191C2×Q811yescharacteristic
43C23×C191#4112yes—
44C23×C191#4111yescharacteristic
45C2×C4×C191—22no—
46C2×C4×C191—24no—
47C2×C4×C191—22no—
48C2×C4×C191—41no—
49C2×C4×C191—42no—
50C2×C4×C191—41no—
51C2×C4×C191—42no—
52C2×C4×C191—42no—
53C2×C4×C191—41no—
54C22×C191—22no—
55C22×C191—24no—
56C22×C191—41no—
57C22×C191—42no—
58C22×C191—41no—
59C22×C191#12011yescharacteristic
60C22×C191C22⋊Q812yes—
61C22×C191C22⋊Q811yescharacteristic
62C22×C191#12412yes—
63C22×C191#12411yescharacteristic
64C4×C191—42no—
65C4×C191—42no—
66C4×C191—81no—
67Dic191—44no—
68Dic191—82no—
69C2×C191—22no—
70C2×C191—21no—
71C2×C191—22no—
72C2×C191—21no—
73C2×C191#39311yescharacteristic
74C2×C191#45812yes—
75C191#203011yescharacteristic, complemented, Sylow
76#2030—1911nomaximal, Sylow
77#543—1911no—
78#381—1912no—
79#381D19111yescharacteristic
80#342—1912no—
81#342—1911no—
82C23×C4C2×D19111yescharacteristic
83C22⋊Q8—3824no—
84C22⋊Q8—3822no—
85C2×C22⋊C4—1912no—
86C2×C22⋊C4—1912no—
87C2×C22⋊C4C2×D19111yescharacteristic
88C2×C22⋊C4C2×D19111yescharacteristic
89#95—22no—
90#95—3824no—
91C24C22×D19111yescharacteristic
92C2×Q8—3822no—
93C22×C4—22no—
94C22×C4—21no—
95C22×C4—22no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—3822no—
99C22×C4—1914no—
100C22×C4C22⋊D19112yes—
101C22×C4Dic38212yescomplemented
102C4⋊C4—3824no—
103C4⋊C4—3822no—
104C22⋊C4—22no—
105C22⋊C4—22no—
106C22⋊C4—3822no—
107C22⋊C4—3822no—
108C22⋊C4—3822no—
109C22⋊C4—3822no—
110C23—42no—
111C23D4×D19112yes—
112C23C2×C22⋊D19111yescharacteristic
113C23C2×Dic38211yescharacteristic
114C23#1569028612yes—
115C23#1569028711yescharacteristic
116Q8—15282no—
117C2×C4—22no—
118C2×C4—24no—
119C2×C4—22no—
120C2×C4—41no—
121C2×C4—42no—
122C2×C4—41no—
123C2×C4—42no—
124C2×C4—42no—
125C2×C4—41no—
126C2×C4—3824no—
127C2×C4—7644no—
128C2×C4—7642no—
129C2×C4—7644no—
130C22—22no—
131C22—24no—
132C22—41no—
133C22—42no—
134C22—41no—
135C22#2025929011yescharacteristic
136C22#2025929912yes—
137C22#2025930111yescharacteristic
138C22#2025930812yes—
139C22#2025930911yescharacteristic
140C4—42no—
141C4—42no—
142C4—81no—
143C4—15282no—
144C4—7644no—
145C2—21no—
146C2—22no—
147C2—22no—
148C2—21no—
149C2#2713257511yescharacteristic
150C2#2713285212yes—
subgroupG/H
centerC22#20259290
commutator, prime radical, cosocleC24×C191C23
FrattiniC24C22×D191
Fitting#381×C191C2
socleC22×C191#120
hypercenter#381D191
hypocenterC191#2030
LCSG ▷ C24×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
31. C22×C4×C191Q8semidirect
75. C191#2030semidirect
101. C22×C4Dic382semidirect

Maximal subgroups

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

subgroupindex
#271332892
#271325262
#271324302
#271324292
#381×C1912
#2030191