Finite Group Databasebeta

← #14575018

Subgroups — #14575018

Order 2432.

386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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#11927094C211yesmaximal, characteristic
2#11926839C212yesmaximal, complemented
3#11926821C212yesmaximal, complemented
4#11926792C214yesmaximal, complemented
5#11926746C212yesmaximal, complemented
6#11926744C212yesmaximal, complemented
7#11926568C211yesmaximal, characteristic, complemented
8C19×#533C211yesmaximal, characteristic, complemented
9C2×#64541—21no—
10C19×C4⋊Q8C2211yescharacteristic
11C19×C4⋊Q8C2211yescharacteristic
12C19×#125—21no—
13C19×C22⋊Q8—21no—
14C19×C22⋊Q8C2212yes—
15C4×Q8×C19—21no—
16C4×Q8×C19C2212yes—
17C19×#117—21no—
18C2×C42×C19C2211yescharacteristic
19C2×#64527C2214yes—
20#10597376—21no—
21#10597376C2212yes—
22C2×#64520C2212yes—
23#10597321—21no—
24#10597320C2211yescharacteristic
25C4×D76—21no—
26C4×D76C2212yes—
27#10597315C2211yescharacteristic
28#10597292C2214yes—
29#10597266C2214yes—
30#10597264C2214yes—
31C4⋊(C19⋊C8)C2212yes—
32C4⋊(C19⋊C8)C2212yes—
33C2×Q8×C19—21no—
34C2×Q8×C19C2312yes—
35C22×C4×C19D411yescharacteristic
36C22×C4×C19D411yescharacteristic
37C22×C4×C19C2311yescharacteristic
38C2×C22⋊D19—22no—
39#64541—44no—
40C2×D76—21no—
41C2×D76—21no—
42C2×D76C2312yes—
43C2×C4×D19—22no—
44C2×Dic38—21no—
45C4⋊C4×C19—21no—
46C4⋊C4×C19—21no—
47C4⋊C4×C19—21no—
48C4⋊C4×C19—22no—
49C4⋊C4×C19—22no—
50C4⋊C4×C19C2312yes—
51C22⋊C4×C19—22no—
52C42×C19—22no—
53C42×C19D411yescharacteristic
54C42×C19D411yescharacteristic
55C42×C19C2311yescharacteristic
56C42×C19C2311yescharacteristic
57#64527—44no—
58(C2×D19)⋊C4—22no—
59(C2×D19)⋊C4—22no—
60C4⋊Dic19—21no—
61C4⋊Dic19C2312yes—
62#64520—42no—
63C2×C19⋊C8C2314yes—
64C23×C19C2×D411yescharacteristic
65C22×D19—22no—
66Q8×C19—22no—
67Q8×C19—22no—
68Q8×C19—42no—
69C2×C4×C19—22no—
70C2×C4×C19—22no—
71C2×C4×C19—21no—
72C2×C4×C19—21no—
73C2×C4×C19—22no—
74C2×C4×C19—22no—
75C2×C4×C19C2×D411yescharacteristic
76C2×C4×C19C2×D411yescharacteristic
77C2×C4×C19C2×D411yescharacteristic
78C2×C4×C19C2×D411yescharacteristic
79C2×C4×C19C2×D411yescharacteristic
80C2×C4×C19C2411yescharacteristic
81C22⋊D19—44no—
82C2×Dic19—22no—
83D76—22no—
84D76—22no—
85D76—42no—
86D76—42no—
87C4×D19—44no—
88Dic38—42no—
89C19⋊C8—24no—
90#3254—191nomaximal, Sylow
91C22×C19—21no—
92C22×C19—21no—
93C22×C19—21no—
94C22×C19C22×D411yescharacteristic
95C2×D19—42no—
96C2×D19—42no—
97C2×D19—42no—
98C4×C19—21no—
99C4×C19—21no—
100C4×C19—21no—
101C4×C19—42no—
102C4×C19—42no—
103C4×C19AGL(1,ℤ/8)12yes—
104C4×C19#13712yes—
105C4×C19H(5,𝔽2)11yescharacteristic
106C4×C192−1+411yescharacteristic
107Dic19—42no—
108#533D1911yescharacteristic, complemented
109#532—191no—
110#477—192no—
111#474—192no—
112#468—194no—
113#461—192no—
114#460—192no—
115#423—191no—
116C2×C19—41no—
117C2×C19#53711yescharacteristic
118C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
119C2×C19C2×#13711yescharacteristic
120D19—82no—
121C2×#41—381no—
122C2×SD16—194no—
123C2×M16—192no—
124C4⋊Q8—191no—
125C4⋊Q8C2×D1911yescharacteristic
126C4⋊Q8C2×D1911yescharacteristic
127#127—191no—
128#125—21no—
129#124—381no—
130C22⋊Q8—21no—
131C22⋊Q8C2×D1912yes—
132#121—192no—
133#121—381no—
134C4×Q8—21no—
135C4×Q8C2×D1912yes—
136C4×D4—192no—
137C4×D4—381no—
138#117—21no—
139C2×C42C2×D1911yescharacteristic
140#107—194no—
141C4⋊C8—192no—
142C4⋊C8—192no—
143#103—194no—
144#102—194no—
145C19#325411yescharacteristic, complemented, Sylow
146#41—764no—
147C2×Q8—21no—
148C2×Q8—381no—
149C2×Q8C22×D1912yes—
150C2×D4—192no—
151C2×D4—382no—
152C2×D4—381no—
153C2×D4—381no—
154C22×C4—382no—
155C22×C4C22⋊D1911yescharacteristic
156C22×C4C22⋊D1911yescharacteristic
157C22×C4C22×D1911yescharacteristic
158SD16—764no—
159M16—762no—
160C2×C8—194no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—192no—
167C4⋊C4—381no—
168C4⋊C4C22×D1912yes—
169C22⋊C4—22no—
170C22⋊C4—382no—
171C22⋊C4—382no—
172C42—22no—
173C42C22⋊D1911yescharacteristic
174C42C22⋊D1911yescharacteristic
175C42C22×D1911yescharacteristic
176C42C22×D1911yescharacteristic
177C23—382no—
178C23C2×C22⋊D1911yescharacteristic
179Q8—22no—
180Q8—22no—
181Q8—42no—
182Q8—762no—
183D4—382no—
184D4—382no—
185D4—762no—
186D4—764no—
187D4—762no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—382no—
195C2×C4—764no—
196C2×C4C2×C22⋊D1911yescharacteristic
197C2×C4C2×C22⋊D1911yescharacteristic
198C2×C4C2×C22⋊D1911yescharacteristic
199C2×C4C2×C22⋊D1911yescharacteristic
200C2×C4C2×C22⋊D1911yescharacteristic
201C2×C4C23×D1911yescharacteristic
202C8—384no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—762no—
207C22—762no—
208C22—762no—
209C22C22×C22⋊D1911yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—42no—
214C4—42no—
215C4—762no—
216C4#1059738812yes—
217C4#1059739512yes—
218C4#1059743511yescharacteristic
219C4#1059743611yescharacteristic
220C2—41no—
221C2—1522no—
222C2#1192712211yescharacteristic
223C2C2×#1059739511yescharacteristic
224C2C2×#1059738811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#533C2
socleC22×C19C22×D4
prime radical#11927094C2
hypercenter#533D19
hypocenterC19#3254
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #11926839C2semidirect
3. #11926821C2semidirect
4. #11926792C2semidirect
5. #11926746C2semidirect
6. #11926744C2semidirect
7. #11926568C2semidirect
8. C19×#533C2semidirect
108. #533D19semidirect
145. C19#3254semidirect

Maximal subgroups

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

subgroupindex
#119270942
#119268392
#119268212
#119267922
#119267462
#119267442
#119265682
C19×#5332
#325419