Finite Group Databasebeta

← #14575037

Subgroups — #14575037

Order 2432.

354 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 109 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#11927080C212yesmaximal, complemented
2#11926849C212yesmaximal, complemented
3#11926843C212yesmaximal, complemented
4#11926797C211yesmaximal, characteristic
5#11926792C212yesmaximal, complemented
6#11926768C212yesmaximal, complemented
7#11926762C212yesmaximal, complemented
8#11926567C211yesmaximal, characteristic, complemented
9C19×#470C211yesmaximal, characteristic, complemented
10C2×Q16×C19C2211yescharacteristic
11C2×M16×C19C2211yescharacteristic
12C19×C22⋊Q8C2212yes—
13#10597393C2212yes—
14Q8×Dic19C2212yes—
15C2×#64527C2212yes—
16#10597376C2212yes—
17C2×C4×Dic19C2211yescharacteristic
18C2×#64520C2211yescharacteristic
19C2×D152C2211yescharacteristic
20#10597344—22no—
21#10597339C2212yes—
22#10597338—22no—
23#10597336C2212yes—
24#10597332—22no—
25(C22⋊D19)⋊C4—22no—
26C19×#106C2211yescharacteristic
27C19×#103C2212yes—
28#10597292C2212yes—
29#10597278C2212yes—
30#10597274C2211yescharacteristic
31Dic19⋊C8C2212yes—
32Dic19⋊C8C2212yes—
33#10597266C2212yes—
34#10597264C2212yes—
35C2×Q8×C19C2312yes—
36C22×C4×C19C2311yescharacteristic
37C2×C22⋊D19—22no—
38C22×Dic19D412yes—
39C2×D76C2312yes—
40C2×C4×D19—22no—
41Q16×C19—41no—
42M16×C19—41no—
43C2×C8×C19C2311yescharacteristic
44C2×C8×C19C2311yescharacteristic
45C4⋊C4×C19—22no—
46C4⋊C4×C19C2312yes—
47C22⋊C4×C19—22no—
48#64527—42no—
49(C2×D19)⋊C4—22no—
50(C2×D19)⋊C4—22no—
51(C2×D19)⋊C4—22no—
52(C2×D19)⋊C4—22no—
53C4⋊Dic19—22no—
54C4⋊Dic19—22no—
55C4⋊Dic19C2312yes—
56Dic19⋊C4—22no—
57C4×Dic19—22no—
58C4×Dic19D411yescharacteristic
59C4×Dic19D411yescharacteristic
60C4×Dic19C2312yes—
61#64520—41no—
62C2×C19⋊C8C2312yes—
63D152—41no—
64C23×C19C2×D411yescharacteristic
65C22×D19—22no—
66Q8×C19—22no—
67Q8×C19—22no—
68C2×C4×C19—21no—
69C2×C4×C19—21no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19C2×D411yescharacteristic
73C2×C4×C19C2411yescharacteristic
74C22⋊D19—44no—
75C2×Dic19—22no—
76C2×Dic19—42no—
77C2×Dic19C2×D412yes—
78C2×Dic19C2×D412yes—
79D76—22no—
80D76—22no—
81C4×D19—44no—
82C8×C19—21no—
83C8×C19—21no—
84C19⋊C8—22no—
85#3256—191nomaximal, Sylow
86C22×C19—21no—
87C22×C19—22no—
88C22×C19C22×D411yescharacteristic
89C2×D19—42no—
90C2×D19—42no—
91C2×D19—42no—
92C4×C19—21no—
93C4×C19—42no—
94C4×C19—42no—
95C4×C19H(5,𝔽2)11yescharacteristic
96C4×C192−1+411yescharacteristic
97Dic19—22no—
98Dic19—22no—
99Dic19—42no—
100#529—192no—
101#479—192no—
102#478—192no—
103#470D1911yescharacteristic, complemented
104#469—191no—
105#468—192no—
106#464—192no—
107#463—192no—
108#423—191no—
109C2×C19—41no—
110C2×C19#53711yescharacteristic
111C2×C19#57512yes—
112D19—82no—
113C2×Q16C2×D1911yescharacteristic
114C2×SD16—192no—
115C2×D8—191no—
116C2×M16—191no—
117C2×M16C2×D1911yescharacteristic
118#126—382no—
119#125—192no—
120#124—192no—
121#123—382no—
122C22⋊Q8C2×D1912yes—
123#121—192no—
124C4×Q8—192no—
125C4×D4—192no—
126C4×D4—382no—
127#117—382no—
128C2×C42—191no—
129#107—192no—
130#106—191no—
131#106C2×D1911yescharacteristic
132C4⋊C8—192no—
133C4⋊C8—192no—
134#103—192no—
135#103C2×D1912yes—
136#102—192no—
137#102—192no—
138C19#325611yescharacteristic, complemented, Sylow
139C2×Q8C22×D1912yes—
140C2×D4—192no—
141C2×D4—382no—
142C22×C4—192no—
143C22×C4—382no—
144C22×C4C22×D1911yescharacteristic
145Q16—41no—
146SD16—762no—
147D8—761no—
148M16—41no—
149M16—761no—
150C2×C8—192no—
151C2×C8C22×D1911yescharacteristic
152C2×C8C22×D1911yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—192no—
155C4⋊C4—382no—
156C4⋊C4—382no—
157C4⋊C4—382no—
158C4⋊C4C22×D1912yes—
159C22⋊C4—22no—
160C22⋊C4—382no—
161C22⋊C4—382no—
162C22⋊C4—382no—
163C22⋊C4—382no—
164C42—191no—
165C42—191no—
166C42—192no—
167C42—382no—
168C23—382no—
169C23D4×D1911yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—382no—
173D4—382no—
174D4—764no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—192no—
180C2×C4—192no—
181C2×C4—382no—
182C2×C4—764no—
183C2×C4—762no—
184C2×C4D4×D1911yescharacteristic
185C2×C4C23×D1911yescharacteristic
186C8—21no—
187C8—21no—
188C8—382no—
189C22—22no—
190C22—21no—
191C22—762no—
192C22—762no—
193C22—762no—
194C22C2×D4×D1911yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—382no—
199C4—382no—
200C4—762no—
201C4#1059743011yescharacteristic
202C4#1059743611yescharacteristic
203C2—41no—
204C2—1522no—
205C2#1192712111yescharacteristic
206C2#1192734312yes—
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#470C2
socleC22×C19C22×D4
prime radical#11926797C2
hypercenter#470D19
hypocenterC19#3256
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #11927080C2semidirect
2. #11926849C2semidirect
3. #11926843C2semidirect
5. #11926792C2semidirect
6. #11926768C2semidirect
7. #11926762C2semidirect
8. #11926567C2semidirect
9. C19×#470C2semidirect
103. #470D19semidirect
138. C19#3256semidirect

Maximal subgroups

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

subgroupindex
#119270802
#119268492
#119268432
#119267972
#119267922
#119267682
#119267622
#119265672
C19×#4702
#325619