Finite Group Databasebeta

← #14567278

Subgroups — #14567278

Order 2432.

800 conjugacy classes of subgroups; only the 193 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 193 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
2C2×#10597315C211yesmaximal, characteristic, complemented
3C2×#10597390C211yesmaximal, characteristic, complemented
4C2×#10597343C211yesmaximal, characteristic
5#11926465C214yesmaximal, complemented
6#11926449C211yesmaximal, characteristic, complemented
7#11926418C214yesmaximal
8C4×(C2×D19)⋊C4C211yesmaximal, characteristic
9C19×#391C211yesmaximal, characteristic, complemented
10C22×Q8×C19C2211yescharacteristic
11C2×Q8×D19—24no—
12C2×Q8×D19—24no—
13C2×Q8×D19—24no—
14C22×C4×D19C2212yes—
15C22×C4×D19C2211yescharacteristic
16C22×Dic38C2211yescharacteristic
17C22×Dic38C2212yes—
18C22×Dic38C2211yescharacteristic
19C2×C4⋊C4×C19C2211yescharacteristic
20C2×C42×C19C2211yescharacteristic
21#10597390—24no—
22C2×(C2×D19)⋊C4C2212yes—
23C2×(C2×D19)⋊C4C2212yes—
24C2×C4⋊Dic19C2212yes—
25C2×C4⋊Dic19C2214yes—
26C2×Dic19⋊C4C2214yes—
27C2×C4×Dic19C2211yescharacteristic
28#10597343—24no—
29#10597315—24no—
30C19×#95C2214yes—
31C19⋊#95C2212yes—
32C19⋊#95C2214yes—
33C23×D19C2311yescharacteristic
34C2×Q8×C19—22no—
35C2×Q8×C19—22no—
36C2×Q8×C19D414yes—
37C22×C4×C19C2312yes—
38C22×C4×C19C2312yes—
39C22×C4×C19C2312yes—
40C22×C4×C19C2311yescharacteristic
41C22×Dic19C2312yes—
42C22×Dic19C2311yescharacteristic
43C22×Dic19C2312yes—
44C22×Dic19C2312yes—
45Q8×D19—232no—
46C2×C4×D19—24no—
47C2×C4×D19—24no—
48C2×C4×D19—22no—
49C2×C4×D19—22no—
50C2×C4×D19—24no—
51C2×C4×D19D414yes—
52C2×Dic38—24no—
53C2×Dic38—22no—
54C2×Dic38—22no—
55C2×Dic38—24no—
56C2×Dic38—24no—
57C2×Dic38—22no—
58C2×Dic38—22no—
59C2×Dic38—22no—
60C2×Dic38D414yes—
61C4⋊C4×C19—22no—
62C42×C19—22no—
63(C2×D19)⋊C4—24no—
64(C2×D19)⋊C4Q818yescomplemented
65C4⋊Dic19—28no—
66C4⋊Dic19—24no—
67Dic19⋊C4—28no—
68C4×Dic19—22no—
69C23×C19C2411yescharacteristic
70C22×D19—21no—
71C22×D19—21no—
72C22×D19—22no—
73C22×D19C2×D412yes—
74C22×D19C2×Q814yes—
75Q8×C19—28no—
76C2×C4×C19—22no—
77C2×C4×C19—22no—
78C2×C4×C19—22no—
79C2×C4×C19—22no—
80C2×C4×C19—22no—
81C2×C4×C19—24no—
82C2×C4×C19C2×D414yes—
83C2×C4×C19C2×D412yes—
84C2×C4×C19C2×D412yes—
85C2×C4×C19C2×D412yes—
86C2×C4×C19C2×Q814yescomplemented
87C2×Dic19—22no—
88C2×Dic19—21no—
89C2×Dic19—22no—
90C2×Dic19—22no—
91C2×Dic19—21no—
92C2×Dic19—22no—
93C2×Dic19—22no—
94C2×Dic19—22no—
95C2×Dic19—22no—
96C2×Dic19C2×D412yes—
97C2×Dic19C2×D414yes—
98C2×Dic19C2×Q814yescomplemented
99C4×D19—216no—
100C4×D19—28no—
101Dic38—216no—
102Dic38—28no—
103Dic38—44no—
104#2434—191nomaximal, Sylow
105C22×C19C22×D411yescharacteristic
106C22×C19C22×D411yescharacteristic
107C22×C19C22×D411yescharacteristic
108C22×C19C22×Q812yes—
109C22×C192−1+412yes—
110C2×D19—22no—
111C2×D19—22no—
112C2×D19—24no—
113C2×D19—24no—
114C2×D19C4⋊Q814yescomplemented
115C4×C19—24no—
116C4×C19—24no—
117C4×C19—42no—
118C4×C19#12014yes—
119Dic19—22no—
120Dic19—24no—
121Dic19—24no—
122Dic19—42no—
123C23×Q8—191no—
124C2×C4⋊Q8—191no—
125C2×C4⋊Q8—191no—
126C2×C22⋊Q8—191no—
127#395—194no—
128#391—191no—
129#391D1911yescharacteristic, complemented
130#385—194no—
131C4×C22⋊C4—191no—
132C2×C19C2×#12011yescharacteristic
133C2×C19C2×C4⋊Q811yescharacteristic
134C2×C19#53611yescharacteristic
135C2×C19D4×Q812yes—
136C2×C19D4×Q812yes—
137D19—24no—
138C22×Q8—191no—
139C22×Q8—191no—
140C22×Q8—192no—
141C22×Q8—384no—
142C22×Q8—384no—
143C22×Q8—384no—
144C22×Q8C2×D1911yescharacteristic
145C23×C4—191no—
146C23×C4—192no—
147C4⋊Q8—384no—
148C4⋊Q8—384no—
149C22⋊Q8—384no—
150C2×C4⋊C4—192no—
151C2×C4⋊C4—194no—
152C2×C4⋊C4—194no—
153C2×C4⋊C4C2×D1911yescharacteristic
154C2×C22⋊C4—192no—
155C2×C22⋊C4—192no—
156C2×C42—191no—
157C2×C42C2×D1911yescharacteristic
158#95—192no—
159#95—194no—
160#95C2×D1914yes—
161C19#243411yescharacteristic, complemented, Sylow
162C24—191no—
163C2×Q8—22no—
164C2×Q8—22no—
165C2×Q8—194no—
166C2×Q8—384no—
167C2×Q8—384no—
168C2×Q8—3832no—
169C2×Q8—384no—
170C2×Q8—382no—
171C2×Q8—382no—
172C2×Q8—382no—
173C2×Q8—382no—
174C2×Q8—382no—
175C2×Q8D7614yes—
176C22×C4—192no—
177C22×C4—191no—
178C22×C4—192no—
179C22×C4—194no—
180C22×C4—192no—
181C22×C4—384no—
182C22×C4—384no—
183C22×C4—384no—
184C22×C4—382no—
185C22×C4—382no—
186C22×C4C22×D1912yes—
187C22×C4C22×D1912yes—
188C22×C4C22×D1912yes—
189C22×C4C22×D1911yescharacteristic
190C4⋊C4—22no—
191C4⋊C4—384no—
192C4⋊C4—388no—
193C4⋊C4—388no—
194C22⋊C4—198no—
195C22⋊C4—384no—
196C42—22no—
197C42—382no—
198C23—192no—
199C23—194no—
200C23—381no—
201C23—381no—
202C23—382no—
203C23C23×D1911yescharacteristic
204Q8—28no—
205Q8—3816no—
206Q8—388no—
207Q8—764no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—24no—
214C2×C4—192no—
215C2×C4—194no—
216C2×C4—194no—
217C2×C4—3816no—
218C2×C4—382no—
219C2×C4—381no—
220C2×C4—382no—
221C2×C4—382no—
222C2×C4—381no—
223C2×C4—382no—
224C2×C4—388no—
225C2×C4—382no—
226C2×C4—382no—
227C2×C4—382no—
228C2×C4C2×D7614yes—
229C2×C4C2×D7612yes—
230C2×C4D4×D1912yes—
231C2×C4D4×D1912yes—
232C2×C4Q8×D1914yescomplemented
233C22—194no—
234C22—382no—
235C22—384no—
236C22—384no—
237C22—382no—
238C22C22×D7611yescharacteristic
239C22C2×D4×D1911yescharacteristic
240C22C2×D4×D1911yescharacteristic
241C22C2×Q8×D1912yes—
242C22#1059743612yes—
243C4—24no—
244C4—24no—
245C4—42no—
246C4—384no—
247C4—382no—
248C4—384no—
249C4—762no—
250C4#1059732814yes—
251C2—384no—
252C2C2×#1059732811yescharacteristic
253C2C4⋊Q8×D1911yescharacteristic
254C2#1192711411yescharacteristic
255C2#1192720712yes—
256C2Q8×D7612yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#391C2
prime radicalC23×D19C23
hypercenter#391D19
hypocenterC19#2434
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#10597315C2semidirect
3. C2×#10597390C2semidirect
5. #11926465C2semidirect
6. #11926449C2semidirect
9. C19×#391C2semidirect
64. (C2×D19)⋊C4Q8semidirect
86. C2×C4×C19C2×Q8semidirect
98. C2×Dic19C2×Q8semidirect
114. C2×D19C4⋊Q8semidirect
129. #391D19semidirect
161. C19#2434semidirect
232. C2×C4Q8×D19semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D192
C2×#105973152
C2×#105973902
C2×#105973432
#119264652
#119264492
#119264182
C4×(C2×D19)⋊C42
C19×#3912
#243419