Finite Group Databasebeta

← #14575097

Subgroups — #14575097

Order 2432.

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

normal subgroups only

This group has 346 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#11927167C212yesmaximal, complemented
2#11926837C212yesmaximal, complemented
3#11926823C212yesmaximal, complemented
4#11926792C212yesmaximal, complemented
5#11926780C211yesmaximal, characteristic
6#11926768C212yesmaximal, complemented
7#11926762C212yesmaximal, complemented
8#11926570C211yesmaximal, characteristic, complemented
9C19×#467C211yesmaximal, characteristic, complemented
10C2×Q16×C19C2211yescharacteristic
11C22×C8×C19C2211yescharacteristic
12C19×C22⋊Q8C2212yes—
13#10597393C2212yes—
14Q8×Dic19C2212yes—
15C2×#64527C2212yes—
16#10597376C2212yes—
17#10597372C2211yescharacteristic
18C2×#64520C2211yescharacteristic
19C2×D152C2211yescharacteristic
20#10597344—22no—
21#10597343—22no—
22#10597339C2212yes—
23#10597334C2212yes—
24#10597331—22no—
25#10597329—22no—
26C19×#107C2211yescharacteristic
27C19×#103C2212yes—
28#10597292C2212yes—
29#10597278C2212yes—
30#10597275C2211yescharacteristic
31Dic19⋊C8C2212yes—
32Dic19⋊C8C2212yes—
33#10597266C2212yes—
34#10597264C2212yes—
35C2×Q8×C19C2312yes—
36C22×C4×C19C2311yescharacteristic
37C2×C22⋊D19—22no—
38C2×D76C2312yes—
39C2×C4×D19—22no—
40C2×Dic38—22no—
41Q16×C19—41no—
42C2×C8×C19—41no—
43C2×C8×C19C2311yescharacteristic
44C2×C8×C19C2311yescharacteristic
45C4⋊C4×C19—22no—
46C4⋊C4×C19C2312yes—
47C22⋊C4×C19—22no—
48C22⋊Dic19D412yes—
49#64527—42no—
50(C2×D19)⋊C4—22no—
51(C2×D19)⋊C4—22no—
52(C2×D19)⋊C4—22no—
53(C2×D19)⋊C4—22no—
54C4⋊Dic19—22no—
55C4⋊Dic19D411yescharacteristic
56C4⋊Dic19D411yescharacteristic
57C4⋊Dic19C2312yes—
58Dic19⋊C4—22no—
59C4×Dic19—22no—
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—82no—
75C2×Dic19—22no—
76C2×Dic19C2×D412yes—
77C2×Dic19C2×D412yes—
78D76—22no—
79D76—22no—
80C4×D19—82no—
81Dic38—82no—
82C8×C19—21no—
83C8×C19—21no—
84C19⋊C8—22no—
85#3262—191nomaximal, Sylow
86C22×C19—21no—
87C22×C19—21no—
88C22×C19—21no—
89C22×C19C22×D411yescharacteristic
90C2×D19—42no—
91C2×D19—42no—
92C2×D19—42no—
93C4×C19—21no—
94C4×C19—42no—
95C4×C19—42no—
96C4×C19H(5,𝔽2)11yescharacteristic
97C4×C192−1+411yescharacteristic
98Dic19—22no—
99Dic19—22no—
100Dic19—42no—
101#542—192no—
102#477—192no—
103#474—192no—
104#468—192no—
105#467D1911yescharacteristic, complemented
106#466—191no—
107#464—192no—
108#463—192no—
109#424—191no—
110C2×C19—41no—
111C2×C19#53711yescharacteristic
112C2×C19#57611yescharacteristic
113C2×C19#57811yescharacteristic
114D19—82no—
115C2×Q16C2×D1911yescharacteristic
116C2×SD16—192no—
117C2×D8—191no—
118C2×M16—191no—
119C22×C8C2×D1911yescharacteristic
120C4⋊Q8—192no—
121#126—382no—
122#124—192no—
123#124—382no—
124#123—382no—
125C22⋊Q8—382no—
126C22⋊Q8C2×D1912yes—
127#121—192no—
128C4×Q8—192no—
129C4×D4—192no—
130#117—191no—
131#107—191no—
132#107—192no—
133#107C2×D1911yescharacteristic
134C4⋊C8—192no—
135C4⋊C8—192no—
136#103—192no—
137#103C2×D1912yes—
138#102—192no—
139#102—192no—
140C19#326211yescharacteristic, complemented, Sylow
141C2×Q8—382no—
142C2×Q8C22×D1912yes—
143C2×D4—192no—
144C2×D4—382no—
145C22×C4—382no—
146C22×C4C22×D1911yescharacteristic
147Q16—41no—
148SD16—762no—
149D8—761no—
150M16—761no—
151C2×C8—41no—
152C2×C8—192no—
153C2×C8C22×D1911yescharacteristic
154C2×C8C22×D1911yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—191no—
157C4⋊C4—191no—
158C4⋊C4—192no—
159C4⋊C4—382no—
160C4⋊C4—382no—
161C4⋊C4C22×D1912yes—
162C22⋊C4—22no—
163C22⋊C4—192no—
164C22⋊C4—382no—
165C22⋊C4—382no—
166C22⋊C4—382no—
167C22⋊C4—382no—
168C42—192no—
169C42—382no—
170C23—382no—
171C23D4×D1911yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—1522no—
175D4—382no—
176D4—382no—
177D4—1522no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—192no—
183C2×C4—192no—
184C2×C4—382no—
185C2×C4—1522no—
186C2×C4D4×D1911yescharacteristic
187C2×C4C23×D1911yescharacteristic
188C8—21no—
189C8—21no—
190C8—382no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—762no—
195C22—762no—
196C22—762no—
197C22C2×D4×D1911yescharacteristic
198C4—21no—
199C4—42no—
200C4—42no—
201C4—382no—
202C4—382no—
203C4—762no—
204C4#1059743011yescharacteristic
205C4#1059743611yescharacteristic
206C2—41no—
207C2—1522no—
208C2#1192712111yescharacteristic
209C2#1192734611yescharacteristic
210C2#1192735711yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#467C2
socleC22×C19C22×D4
prime radical#11926780C2
hypercenter#467D19
hypocenterC19#3262
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #11927167C2semidirect
2. #11926837C2semidirect
3. #11926823C2semidirect
4. #11926792C2semidirect
6. #11926768C2semidirect
7. #11926762C2semidirect
8. #11926570C2semidirect
9. C19×#467C2semidirect
105. #467D19semidirect
140. C19#3262semidirect

Maximal subgroups

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

subgroupindex
#119271672
#119268372
#119268232
#119267922
#119267802
#119267682
#119267622
#119265702
C19×#4672
#326219