Finite Group Databasebeta

← C2×#11927201 #14577099

Subgroups — C2×#11927201 #14577099

Order 2432.

1620 conjugacy classes of subgroups; only the 573 normal subgroups are shown.

normal subgroups only

This group has 1620 conjugacy classes of subgroups — too many to draw. Only its 573 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
1C22×Q8×D19C211yesmaximal, characteristic, complemented
2#11927201C2116yesmaximal, direct product factor
3C2×#10597382C213yesmaximal, complemented
4C2×#10597370C213yesmaximal, complemented
5C2×#10597384C213yesmaximal, complemented
6C2×Q8×Dic19C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊D19C213yesmaximal, complemented
8C22×#41×C19C211yesmaximal, characteristic, complemented
9C2×#41×C19—28no—
10C2×#41×C19C2218yescomplemented
11C22×Q8×C19C2211yescharacteristic
12C22×D4×C19C2213yes—
13C23×C4×C19C2213yes—
14C22×C22⋊D19C2213yes—
15C2×Q8×D19—28no—
16C2×Q8×D19C2218yescomplemented
17C22×C4×D19C2213yes—
18C22×Dic38C2213yes—
19C2×C22⋊Dic19C2216yes—
20C2×C22⋊Dic19C2213yes—
21Q8×Dic19C2218yescomplemented
22#10597384C22124yescomplemented
23#10597382C22124yescomplemented
24C4×C22⋊D19C22124yescomplemented
25C2×(C2×D19)⋊C4C2211yescharacteristic
26C2×C4⋊Dic19C2213yes—
27#10597370C22124yescomplemented
28C2×Dic19⋊C4C2213yes—
29C2×C4×Dic19C2213yes—
30C24×C19C2313yes—
31C23×D19C2311yescharacteristic
32#41×C19—232no—
33C2×Q8×C19D418yescomplemented
34C2×Q8×C19C2314yes—
35C2×D4×C19—212no—
36C2×D4×C19C23112yes—
37C22×C4×C19—212no—
38C22×C4×C19C2311yescharacteristic
39C22×C4×C19C23112yes—
40C22×C4×C19C2313yes—
41C2×C22⋊D19—212no—
42C2×C22⋊D19C23112yes—
43C22×Dic19C2313yes—
44C22×Dic19C2311yescharacteristic
45C22×Dic19C2313yes—
46Q8×D19—232no—
47C2×C4×D19—212no—
48C2×C4×D19C23112yes—
49C2×Dic38—212no—
50C2×Dic38C23112yes—
51C22⋊Dic19C23112yes—
52C22⋊Dic19C23124yes—
53(C2×D19)⋊C4C2314yes—
54C4⋊Dic19C23112yes—
55Dic19⋊C4C23112yes—
56C4×Dic19C23112yes—
57C23×C19—26no—
58C23×C19—26no—
59C23×C19—26no—
60C23×C19C2416yes—
61C23×C19C2411yescharacteristic
62C22×D19—22no—
63C22×D19—22no—
64C22×D19#4114yescomplemented
65C22×D19C2412yes—
66Q8×C19C2×D4116yescomplemented
67D4×C19—224no—
68C2×C4×C19—22no—
69C2×C4×C19—224no—
70C2×C4×C19C2×D4112yes—
71C2×C4×C19C2412yes—
72C2×C4×C19C2416yes—
73C22⋊D19—224no—
74C2×Dic19—26no—
75C2×Dic19—26no—
76C2×Dic19—22no—
77C2×Dic19C2412yes—
78C2×Dic19C2416yes—
79C2×Dic19C2416yes—
80C4×D19—224no—
81Dic38—224no—
82C2×#548—191nomaximal, Sylow
83C22×C19—26no—
84C22×C19—26no—
85C22×C19—26no—
86C22×C19—412no—
87C22×C19C22×D412yes—
88C22×C19C2×#4112yes—
89C22×C192−1+412yes—
90C22×C19C2511yescharacteristic
91C2×D19—28no—
92C2×D19—22no—
93C2×D19—22no—
94C2×D19C2×#4114yescomplemented
95C4×C19—22no—
96C4×C19C22×D4112yes—
97Dic19—26no—
98Dic19—26no—
99Dic19—22no—
100C22×#41D1911yescharacteristic, complemented
101C23×Q8—191no—
102#548—1916no—
103C2×#124—193no—
104C2×C22⋊Q8—193no—
105C2×#121—193no—
106C2×C4×Q8—191no—
107C2×C4×D4—193no—
108C2×C19—46no—
109C2×C19#54814yescomplemented
110C2×C19C23×D411yescharacteristic
111C2×C19C22×#4111yescharacteristic
112C2×C19C2×2−1+411yescharacteristic
113D19—24no—
114C2×#41—28no—
115C2×#41C2×D1918yescomplemented
116C22×Q8—198no—
117C22×Q8—193no—
118C22×Q8—388no—
119C22×Q8C2×D1911yescharacteristic
120C22×D4—193no—
121C22×D4C2×D1913yes—
122C23×C4—193no—
123C23×C4C2×D1913yes—
124#124—1924no—
125C22⋊Q8—1924no—
126#121—1924no—
127C4×Q8—198no—
128C4×D4—1924no—
129C2×C4⋊C4—193no—
130C2×C4⋊C4—193no—
131C2×C22⋊C4—193no—
132C2×C22⋊C4—196no—
133C2×C22⋊C4—191no—
134C2×C42—193no—
135C19C2×#54811yescharacteristic, complemented, Sylow
136C24—191no—
137C24C22×D1913yes—
138#41—232no—
139C2×Q8—1912no—
140C2×Q8—3832no—
141C2×Q8—3812no—
142C2×Q8C22⋊D1918yescomplemented
143C2×Q8C22×D1914yes—
144C2×D4—212no—
145C2×D4—1912no—
146C2×D4—3812no—
147C2×D4C22×D19112yes—
148C22×C4—212no—
149C22×C4—191no—
150C22×C4—193no—
151C22×C4—193no—
152C22×C4—1912no—
153C22×C4—3812no—
154C22×C4C22×D19112yes—
155C22×C4C22×D1911yescharacteristic
156C22×C4C22×D1913yes—
157C4⋊C4—1912no—
158C4⋊C4—1912no—
159C22⋊C4—1912no—
160C22⋊C4—1924no—
161C22⋊C4—194no—
162C42—1912no—
163C23—26no—
164C23—26no—
165C23—26no—
166C23—194no—
167C23—192no—
168C23—382no—
169C23—382no—
170C23C23×D1916yes—
171C23C23×D1911yescharacteristic
172Q8—3824no—
173Q8C2×C22⋊D19116yescomplemented
174D4—224no—
175D4—3824no—
176C2×C4—22no—
177C2×C4—224no—
178C2×C4—192no—
179C2×C4—196no—
180C2×C4—196no—
181C2×C4—386no—
182C2×C4—382no—
183C2×C4—386no—
184C2×C4—3824no—
185C2×C4C2×C22⋊D19112yes—
186C2×C4C23×D1912yes—
187C2×C4C23×D1916yes—
188C22—26no—
189C22—26no—
190C22—26no—
191C22—412no—
192C22—194no—
193C22—382no—
194C22—382no—
195C22—388no—
196C22#41×D1912yes—
197C22#1059743612yes—
198C22C22×C22⋊D1912yes—
199C22C24×D1911yescharacteristic
200C4—22no—
201C4—386no—
202C4—386no—
203C4—382no—
204C4C22×C22⋊D19112yes—
205C2—46no—
206C2—384no—
207C2#1192720114yesdirect product factor
208C2C23×C22⋊D1911yescharacteristic
209C2C2×#41×D1911yescharacteristic
210C2C2×#1059743611yescharacteristic
subgroupG/H
centerC23C23×D19
commutator, cosocleC22×C19C25
FrattiniC22C24×D19
FittingC22×#41×C19C2
socleC23×C19C24
hypercenterC22×#41D19
hypocenterC19C2×#548
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D19C2semidirect
2. #11927201C2direct (N × H)
3. C2×#10597382C2semidirect
4. C2×#10597370C2semidirect
5. C2×#10597384C2semidirect
6. C2×Q8×Dic19C2semidirect
7. C2×C4×C22⋊D19C2semidirect
8. C22×#41×C19C2semidirect
10. C2×#41×C19C22semidirect
16. C2×Q8×D19C22semidirect
21. Q8×Dic19C22semidirect
22. #10597384C22semidirect
23. #10597382C22semidirect
24. C4×C22⋊D19C22semidirect
27. #10597370C22semidirect
33. C2×Q8×C19D4semidirect
64. C22×D19#41semidirect
66. Q8×C19C2×D4semidirect
94. C2×D19C2×#41semidirect
100. C22×#41D19semidirect
109. C2×C19#548semidirect
115. C2×#41C2×D19semidirect
135. C19C2×#548semidirect
142. C2×Q8C22⋊D19semidirect
173. Q8C2×C22⋊D19semidirect
207. C2#11927201direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D192
#119272012
C2×#105973822
C2×#105973702
C2×#105973842
C2×Q8×Dic192
C2×C4×C22⋊D192
C22×#41×C192
C2×#54819