Finite Group Databasebeta

← #14574987

Subgroups — #14574987

Order 2432.

360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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#11927078C212yesmaximal, complemented
2#11926852C212yesmaximal, complemented
3#11926845C212yesmaximal, complemented
4#11926785C211yesmaximal, characteristic, complemented
5#11926780C211yesmaximal, characteristic
6#11926773C212yesmaximal, complemented
7#11926767C212yesmaximal, complemented
8#11926760C212yesmaximal, complemented
9C2×C19×C4⋊C8C211yesmaximal, characteristic, complemented
10C22×C8×C19C2211yescharacteristic
11C22×C8×C19C2211yescharacteristic
12C2×C42×C19C2211yescharacteristic
13#10597376C2212yes—
14#10597375—22no—
15C4×C22⋊D19—22no—
16#10597370C2212yes—
17C2×Dic76C2211yescharacteristic
18C2×D152C2211yescharacteristic
19C2×#64516C2212yes—
20#10597322—22no—
21#10597321C2212yes—
22C4×D76C2212yes—
23#10597318—22no—
24#10597316C2212yes—
25C4×Dic38C2212yes—
26C19×C4⋊C8C2212yes—
27C19×C4⋊C8C2212yes—
28#10597278C2212yes—
29#10597278C2212yes—
30#10597275C2211yescharacteristic
31#10597275C2211yescharacteristic
32#10597274C2212yes—
33#10597273C2212yes—
34#10597273C2212yes—
35C22×C4×C19D411yescharacteristic
36C22×C4×C19D411yescharacteristic
37C22×C4×C19C2311yescharacteristic
38C2×C22⋊D19—22no—
39C2×D76C2312yes—
40C2×C4×D19—22no—
41C2×Dic38C2312yes—
42C2×C8×C19—41no—
43C2×C8×C19—41no—
44C2×C8×C19C2311yescharacteristic
45C2×C8×C19C2312yes—
46C2×C8×C19C2311yescharacteristic
47C42×C19D412yes—
48C42×C19C2312yes—
49C22⋊Dic19—22no—
50(C2×D19)⋊C4—22no—
51(C2×D19)⋊C4—22no—
52(C2×D19)⋊C4—22no—
53(C2×D19)⋊C4—22no—
54C4⋊Dic19C2312yes—
55C4⋊Dic19C2312yes—
56Dic19⋊C4—22no—
57Dic19⋊C4—22no—
58Dic19⋊C4—22no—
59Dic19⋊C4—22no—
60C4×Dic19—22no—
61Dic76—41no—
62D152—41no—
63#64516—42no—
64C23×C19C2×D411yescharacteristic
65C22×D19—22no—
66C2×C4×C19—22no—
67C2×C4×C19—21no—
68C2×C4×C19—21no—
69C2×C4×C19—41no—
70C2×C4×C19C2×D412yes—
71C2×C4×C19C2×D411yescharacteristic
72C2×C4×C19C2×D412yes—
73C2×C4×C19C2411yescharacteristic
74C22⋊D19—44no—
75C2×Dic19—22no—
76C2×Dic19—22no—
77C2×Dic19—22no—
78D76—22no—
79D76—22no—
80C4×D19—44no—
81Dic38—22no—
82Dic38—22no—
83C8×C19—22no—
84C8×C19—21no—
85C8×C19—21no—
86#3250—191nomaximal, Sylow
87C22×C19—21no—
88C22×C19—21no—
89C22×C19#13512yes—
90C22×C19C22×D411yescharacteristic
91C2×D19—42no—
92C2×D19—42no—
93C2×D19—42no—
94C4×C19—21no—
95C4×C19—22no—
96C4×C19—22no—
97C4×C19H(5,𝔽2)11yescharacteristic
98C4×C192−1+411yescharacteristic
99Dic19—42no—
100Dic19—42no—
101Dic19—42no—
102#529—192no—
103#479—192no—
104#478—192no—
105#467—191no—
106#466—191no—
107#465—192no—
108#464—192no—
109#463—192no—
110C2×C4⋊C8D1911yescharacteristic, complemented
111C2×C19—22no—
112C2×C19#53711yescharacteristic
113C2×C19C2×#13511yescharacteristic
114C2×C19#57511yescharacteristic
115D19—82no—
116C2×Q16—191no—
117C2×SD16—192no—
118C2×D8—191no—
119C22×C8C2×D1911yescharacteristic
120C22×C8C2×D1911yescharacteristic
121#126—382no—
122#125—192no—
123#124—192no—
124#123—382no—
125C22⋊Q8—192no—
126#121—192no—
127C4×Q8—192no—
128C4×D4—192no—
129C4×D4—382no—
130#117—382no—
131C2×C42C2×D1911yescharacteristic
132#107—191no—
133#107—191no—
134#106—192no—
135C4⋊C8C2×D1912yes—
136C4⋊C8C2×D1912yes—
137#103—192no—
138#103—192no—
139#102—192no—
140#102—192no—
141C19#325011yescharacteristic, complemented, Sylow
142C2×Q8—192no—
143C2×D4—192no—
144C2×D4—382no—
145C22×C4—382no—
146C22×C4D7611yescharacteristic
147C22×C4D7611yescharacteristic
148C22×C4C22×D1911yescharacteristic
149Q16—761no—
150SD16—762no—
151D8—761no—
152C2×C8—41no—
153C2×C8—41no—
154C2×C8C22×D1911yescharacteristic
155C2×C8C22×D1912yes—
156C2×C8C22×D1911yescharacteristic
157C4⋊C4—192no—
158C4⋊C4—192no—
159C4⋊C4—382no—
160C4⋊C4—382no—
161C4⋊C4—382no—
162C4⋊C4—382no—
163C22⋊C4—382no—
164C22⋊C4—382no—
165C22⋊C4—382no—
166C22⋊C4—382no—
167C22⋊C4—382no—
168C42—382no—
169C42D7612yes—
170C42C22×D1912yes—
171C23—382no—
172C23C2×D7611yescharacteristic
173Q8—382no—
174Q8—382no—
175D4—382no—
176D4—382no—
177D4—764no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—382no—
183C2×C4—382no—
184C2×C4—382no—
185C2×C4—764no—
186C2×C4C2×D7612yes—
187C2×C4C2×D7611yescharacteristic
188C2×C4C2×D7612yes—
189C2×C4C23×D1911yescharacteristic
190C8—21no—
191C8—22no—
192C8—21no—
193C22—21no—
194C22—21no—
195C22—762no—
196C22—762no—
197C22—762no—
198C22#1059735012yes—
199C22C22×D7611yescharacteristic
200C4—22no—
201C4—22no—
202C4—21no—
203C4—762no—
204C4—762no—
205C4—762no—
206C4#1059743011yescharacteristic
207C4#1059743311yescharacteristic
208C2—22no—
209C2—1522no—
210C2#1192712511yescharacteristic
211C2C2×#1059735011yescharacteristic
212C2#1192734411yescharacteristic
subgroupG/H
centerC22C22×D76
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×C4⋊C8C2
socleC22×C19C22×D4
prime radical#11926780C2
hypercenterC2×C4⋊C8D19
hypocenterC19#3250
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #11927078C2semidirect
2. #11926852C2semidirect
3. #11926845C2semidirect
4. #11926785C2semidirect
6. #11926773C2semidirect
7. #11926767C2semidirect
8. #11926760C2semidirect
9. C2×C19×C4⋊C8C2semidirect
110. C2×C4⋊C8D19semidirect
141. C19#3250semidirect

Maximal subgroups

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

subgroupindex
#119270782
#119268522
#119268452
#119267852
#119267802
#119267732
#119267672
#119267602
C2×C19×C4⋊C82
#325019