Finite Group Databasebeta

← #37574520

Subgroups — #37574520

Order 24448.

270 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 41 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#27133405C211yesmaximal, characteristic, complemented
2#27132850C212yesmaximal, complemented
3#27132458C211yesmaximal, characteristic, complemented
4#27132451C212yesmaximal, complemented
5#455×C191C211yesmaximal, characteristic, complemented
6#20259311—21no—
7#20259310—21no—
8#20259308—22no—
9#20259292—22no—
10#20259290—22no—
11#20259290C2212yes—
12#20259237—22no—
13#20259237C2212yes—
14H(5,𝔽2)×C191C2211yescharacteristic
15#137×C191—21no—
16#124×C191C2211yescharacteristic
17#104×C191—21no—
18#100×C191C2211yescharacteristic
19C23×D191D412yescomplemented
20C2×Dic382—21no—
21C2×D764—21no—
22C2×D764—21no—
23C2×C22⋊D191—22no—
24C2×C22⋊D191—42no—
25C22⋊Dic191—22no—
26C22⋊Dic191D412yescomplemented
27(C2×D191)⋊C4—22no—
28(C2×D191)⋊C4—22no—
29(C2×D191)⋊C4—22no—
30(C2×D191)⋊C4—42no—
31C4×Dic191—21no—
32#41×C191—21no—
33#41×C191—41no—
34C2×Q8×C191D411yescharacteristic, complemented
35C2×D4×C191—22no—
36C2×D4×C191—41no—
37C2×D4×C191C2311yescharacteristic
38Q16×C191—41no—
39SD16×C191—41no—
40M16×C191—21no—
41C22⋊C4×C191—22no—
42C42×C191D411yescharacteristic, complemented
43C22×D191—22no—
44C22×D191—42no—
45C22×D191—82no—
46Dic382—81no—
47D764—81no—
48D764—81no—
49C22⋊D191—82no—
50C22⋊D191—84no—
51C2×Dic191—22no—
52C2×Dic191—42no—
53C23×C191—22no—
54C23×C191C2×D412yes—
55Q8×C191—21no—
56Q8×C191—41no—
57D4×C191—21no—
58D4×C191—41no—
59D4×C191—42no—
60D4×C191—41no—
61C2×C4×C191—22no—
62C2×C4×C191—21no—
63C2×C4×C191—21no—
64C2×C4×C191—41no—
65C2×C4×C191C2×D411yescharacteristic
66C8×C191—41no—
67C22×C191—22no—
68C22×C191—42no—
69C22×C191—41no—
70C22×C191—82no—
71C22×C191#12011yescharacteristic
72C2×D191—42no—
73C2×D191—42no—
74C2×D191—44no—
75C2×D191—42no—
76C2×D191—82no—
77C4×C191—21no—
78C4×C191—41no—
79C4×C191—41no—
80C4×C191—41no—
81Dic191—42no—
82Dic191—82no—
83C2×C191—21no—
84C2×C191—42no—
85C2×C191—81no—
86C2×C191B(4,𝔽2)11yescharacteristic
87D191—82no—
88C191#219911yescharacteristic, complemented, Sylow
89#2199—1911nomaximal, Sylow
90H(3,𝔽4)—1911no—
91B(4,𝔽2)—1912no—
92#455D19111yescharacteristic, complemented
93#354—1911no—
94AΣL(1,𝔽16)—1912no—
95H(5,𝔽2)C2×D19111yescharacteristic
96#137—21no—
97#124—3822no—
98#124—3821no—
99#124—3821no—
100#124C2×D19111yescharacteristic
101#120—3822no—
102#120—3822no—
103#120—1912no—
104#104—21no—
105#100C2×D19111yescharacteristic
106#99—3822no—
107#99—1912no—
108C24—1912no—
109#41—21no—
110#41—41no—
111C2×Q8—3821no—
112C2×Q8C22⋊D19111yescharacteristic, complemented
113C2×D4—22no—
114C2×D4—41no—
115C2×D4—3821no—
116C2×D4—3821no—
117C2×D4—3822no—
118C2×D4—7642no—
119C2×D4C22×D19111yescharacteristic
120Q16—41no—
121SD16—41no—
122M16—21no—
123C22⋊C4—22no—
124C22⋊C4—3822no—
125C22⋊C4—3822no—
126C22⋊C4—3822no—
127C22⋊C4—3822no—
128C22⋊C4—1912no—
129C22⋊C4—7642no—
130C42—3821no—
131C42C22⋊D19111yescharacteristic, complemented
132C23—22no—
133C23—3822no—
134C23—15282no—
135C23—7642no—
136C23D4×D19112yes—
137Q8—21no—
138Q8—41no—
139Q8—15281no—
140D4—21no—
141D4—41no—
142D4—42no—
143D4—41no—
144D4—15281no—
145D4—15281no—
146D4—15284no—
147D4—15282no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—3822no—
153C2×C4—7642no—
154C2×C4C2×C22⋊D19111yescharacteristic
155C8—41no—
156C22—22no—
157C22—42no—
158C22—41no—
159C22—82no—
160C22—15282no—
161C22—7642no—
162C22—7642no—
163C22—7644no—
164C22—7642no—
165C22#2025929011yescharacteristic
166C4—21no—
167C4—41no—
168C4—41no—
169C4—41no—
170C4—15282no—
171C4—7642no—
172C2—21no—
173C2—42no—
174C2—81no—
175C2—15282no—
176C2#2713284911yescharacteristic
subgroupG/H
centerC2#27132849
commutator, cosocleC2×D4×C191C23
FrattiniC2×D4C22×D191
Fitting#455×C191C2
socleC2×C191B(4,𝔽2)
hypercenter#455D191
hypocenterC191#2199
LCSG ▷ C2×D4×C191 ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #27133405C2semidirect
2. #27132850C2semidirect
3. #27132458C2semidirect
4. #27132451C2semidirect
5. #455×C191C2semidirect
19. C23×D191D4semidirect
26. C22⋊Dic191D4semidirect
34. C2×Q8×C191D4semidirect
42. C42×C191D4semidirect
88. C191#2199semidirect
92. #455D191semidirect
112. C2×Q8C22⋊D191semidirect
131. C42C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
#271334052
#271328502
#271324582
#271324512
#455×C1912
#2199191