Finite Group Databasebeta

← #14562954

Subgroups — #14562954

Order 2432.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#11927292C211yesmaximal, characteristic
2#11926954C211yesmaximal, characteristic, complemented
3#11926938C211yesmaximal, characteristic, complemented
4#11926904C211yesmaximal, characteristic, complemented
5#11926283C211yesmaximal, characteristic, complemented
6#11926283C211yesmaximal, characteristic, complemented
7C19×#330C211yesmaximal, characteristic, complemented
8C19×#125C2211yescharacteristic
9C2×Dic76—21no—
10C2×#64516—21no—
11#10597342—21no—
12#10597342—21no—
13#10597341—21no—
14#10597341—21no—
15#10597340—21no—
16#10597340—21no—
17#10597321C2211yescharacteristic
18#10597321C2211yescharacteristic
19#10597315C2211yescharacteristic
20C19×#97C2211yescharacteristic
21C19×#97C2211yescharacteristic
22#10597278—21no—
23#10597273—21no—
24#10597265—21no—
25#10597264—21no—
26#10597260C2211yescharacteristic
27C2×D76—21no—
28C2×D76—21no—
29C2×D76D411yescharacteristic
30C2×D76D411yescharacteristic
31C2×C4×D19—21no—
32C2×C4×D19—21no—
33C2×Dic38—21no—
34C2×Dic38D411yescharacteristic
35C2×Dic38D411yescharacteristic
36C2×C8×C19—21no—
37C2×C8×C19—21no—
38C4⋊C4×C19—21no—
39C4⋊C4×C19—21no—
40C4⋊C4×C19D411yescharacteristic
41C4⋊C4×C19D411yescharacteristic
42C42×C19C2311yescharacteristic
43(C2×D19)⋊C4—21no—
44(C2×D19)⋊C4—21no—
45(C2×D19)⋊C4—21no—
46(C2×D19)⋊C4—21no—
47(C2×D19)⋊C4—21no—
48(C2×D19)⋊C4—21no—
49C4⋊Dic19—21no—
50C4⋊Dic19—21no—
51Dic19⋊C4—21no—
52Dic19⋊C4—21no—
53C2×C19⋊C8—21no—
54Dic76—42no—
55#64516—42no—
56C22×D19—21no—
57C22×D19—21no—
58C2×C4×C19—21no—
59C2×C4×C19—21no—
60C2×C4×C19C2×D411yescharacteristic
61C2×C4×C19C2×D411yescharacteristic
62C2×C4×C19C2×D411yescharacteristic
63C2×Dic19—21no—
64C2×Dic19—21no—
65C2×Dic19—41no—
66D76—41no—
67D76—41no—
68D76—81no—
69D76—81no—
70C4×D19—81no—
71C4×D19—81no—
72Dic38—41no—
73Dic38—41no—
74Dic38—41no—
75Dic38—41no—
76C8×C19—22no—
77C8×C19—41no—
78C19⋊C8—22no—
79#1661—191nomaximal, Sylow
80C22×C19#12011yescharacteristic
81C2×D19—41no—
82C2×D19—41no—
83C2×D19—41no—
84C2×D19—41no—
85C2×D19—41no—
86C2×D19—41no—
87C4×C19—21no—
88C4×C19—21no—
89C4×C19—21no—
90C4×C19—41no—
91C4×C19—41no—
92Dic19—41no—
93Dic19—41no—
94Dic19—81no—
95#562—191no—
96#501—191no—
97#497—191no—
98#489—191no—
99#330D1911yescharacteristic, complemented
100#329—191no—
101#329—191no—
102C2×C19#45311yescharacteristic
103C2×C19#45511yescharacteristic
104C2×C19#45611yescharacteristic
105D19—81no—
106D19—81no—
107C2×Q16—381no—
108C2×SD16—381no—
109C4⋊Q8—191no—
110#125C2×D1911yescharacteristic
111#124—191no—
112#124—191no—
113#123—381no—
114#123—381no—
115C22⋊Q8—381no—
116C22⋊Q8—381no—
117#121—381no—
118#121—381no—
119#107—381no—
120#106—381no—
121#103—381no—
122#102—381no—
123#97—191no—
124#97C2×D1911yescharacteristic
125#97C2×D1911yescharacteristic
126C19#166111yescharacteristic, complemented, Sylow
127C2×Q8—191no—
128C2×Q8—191no—
129C2×Q8—381no—
130C2×D4—191no—
131C2×D4—191no—
132C2×D4—381no—
133C2×D4—381no—
134C22×C4—381no—
135C22×C4—381no—
136Q16—762no—
137SD16—762no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—381no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—381no—
144C4⋊C4—381no—
145C4⋊C4—381no—
146C4⋊C4—381no—
147C4⋊C4D7611yescharacteristic
148C4⋊C4D7611yescharacteristic
149C22⋊C4—381no—
150C22⋊C4—381no—
151C22⋊C4—381no—
152C22⋊C4—381no—
153C22⋊C4—381no—
154C22⋊C4—381no—
155C42C22×D1911yescharacteristic
156C23—381no—
157C23—381no—
158Q8—761no—
159Q8—761no—
160Q8—761no—
161Q8—761no—
162D4—761no—
163D4—761no—
164D4—1521no—
165D4—1521no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—381no—
169C2×C4—381no—
170C2×C4—761no—
171C2×C4—1521no—
172C2×C4—1521no—
173C2×C4C2×D7611yescharacteristic
174C2×C4D4×D1911yescharacteristic
175C2×C4D4×D1911yescharacteristic
176C8—22no—
177C8—41no—
178C8—382no—
179C22—761no—
180C22—761no—
181C22—761no—
182C22—761no—
183C22—761no—
184C22—761no—
185C22#1059732811yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—761no—
192C4—761no—
193C4—1521no—
194C2—1521no—
195C2—1521no—
196C2#1192671311yescharacteristic
197C2#1192672311yescharacteristic
198C2#1192672911yescharacteristic
subgroupG/H
centerC22#10597328
commutator, cosocleC42×C19C23
FrattiniC42C22×D19
FittingC19×#330C2
socleC22×C19#120
prime radical#11927292C2
hypercenter#330D19
hypocenterC19#1661
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #11926954C2semidirect
3. #11926938C2semidirect
4. #11926904C2semidirect
5. #11926283C2semidirect
6. #11926283C2semidirect
7. C19×#330C2semidirect
99. #330D19semidirect
126. C19#1661semidirect

Maximal subgroups

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

subgroupindex
#119272922
#119269542
#119269382
#119269042
#119262832
C19×#3302
#166119