Finite Group Databasebeta

← #14563986

Subgroups — #14563986

Order 2432.

438 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 103 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×#64525C211yesmaximal, characteristic
2C2×C4×D76C211yesmaximal, characteristic, complemented
3C2×#10597289C211yesmaximal, characteristic, complemented
4C2×#10597266C211yesmaximal, characteristic, complemented
5#11926306C211yesmaximal, characteristic, complemented
6#11926299C211yesmaximal, characteristic, complemented
7C19×#390C211yesmaximal, characteristic, complemented
8C22×D4×C19C2211yescharacteristic
9C22×D76C2211yescharacteristic
10C22×C4×D19—21no—
11C2×C4⋊C4×C19C2211yescharacteristic
12C2×C22⋊C4×C19—21no—
13C2×C22⋊C4×C19—21no—
14C2×C42×C19C2211yescharacteristic
15C2×#64525—22no—
16C2×#64525—22no—
17C2×#64525C414yescomplemented
18C2×(C2×D19)⋊C4—21no—
19C2×C4⋊Dic19C2211yescharacteristic
20C22×C19⋊C8C2211yescharacteristic
21C22×C19⋊C8C2211yescharacteristic
22C4×D76—22no—
23C4×D76—22no—
24#10597289—22no—
25#10597266—22no—
26C24×C19—21no—
27C23×D19—21no—
28C2×D4×C19—21no—
29C2×D4×C19—21no—
30C2×D4×C19—21no—
31C2×D4×C19—21no—
32C2×D4×C19—21no—
33C2×D4×C19C2×C412yescomplemented
34C22×C4×C19—21no—
35C22×C4×C19D411yescharacteristic
36C22×C4×C19D411yescharacteristic
37C22×C4×C19C2311yescharacteristic
38C22×Dic19—21no—
39C2×D76—21no—
40C2×D76—21no—
41C2×D76—21no—
42C2×D76C2×C412yes—
43C2×D76D412yes—
44C2×D76D412yes—
45C2×C4×D19—24no—
46C2×C4×D19—42no—
47C2×C4×D19—42no—
48C4⋊C4×C19—21no—
49C4⋊C4×C19—21no—
50C22⋊C4×C19—42no—
51C22⋊C4×C19—42no—
52C42×C19—21no—
53C42×C19—21no—
54#64525—28no—
55(C2×D19)⋊C4—24no—
56C4⋊Dic19—21no—
57C4⋊Dic19D412yes—
58C2×C19⋊C8—21no—
59C2×C19⋊C8—21no—
60C2×C19⋊C8—21no—
61C2×C19⋊C8—21no—
62C2×C19⋊C8—21no—
63C2×C19⋊C8C2×C412yescomplemented
64C23×C19—22no—
65C23×C19—41no—
66C23×C19—41no—
67C23×C19—41no—
68C23×C19—41no—
69C23×C19—41no—
70C23×C19—41no—
71C23×C19C2×D411yescharacteristic
72C22×D19—22no—
73C22×D19—22no—
74C22×D19—22no—
75C22×D19—41no—
76C22×D19—41no—
77C22×D19—41no—
78C22×D19—41no—
79D4×C19—22no—
80D4×C19—22no—
81D4×C19—41no—
82D4×C19—41no—
83C2×C4×C19—21no—
84C2×C4×C19—21no—
85C2×C4×C19—21no—
86C2×C4×C19—21no—
87C2×C4×C19—21no—
88C2×C4×C19—41no—
89C2×C4×C19—41no—
90C2×C4×C19—41no—
91C2×C4×C19D812yescomplemented
92C2×C4×C19C22×C411yescharacteristic
93C2×C4×C19C2×D411yescharacteristic
94C2×C4×C19C2×D411yescharacteristic
95C2×C4×C19C2×D411yescharacteristic
96C2×C4×C19#4111yescharacteristic
97C2×C4×C19#4111yescharacteristic
98C2×Dic19—22no—
99C2×Dic19—41no—
100C2×Dic19—41no—
101D76—22no—
102D76—22no—
103D76—22no—
104D76C22⋊C414yescomplemented
105C4×D19—48no—
106C19⋊C8—22no—
107C19⋊C8—41no—
108#1879—191nomaximal, Sylow
109C22×C19—42no—
110C22×C19—42no—
111C22×C19—42no—
112C22×C19—81no—
113C22×C19—81no—
114C22×C19—81no—
115C22×C19—81no—
116C22×C19C4×D411yescharacteristic
117C22×C19#12011yescharacteristic
118C22×C19#12111yescharacteristic
119C22×C19C2×D811yescharacteristic
120C22×C19#13511yescharacteristic
121C22×C19AGL(1,ℤ/8)11yescharacteristic
122C22×C19AGL(1,ℤ/8)11yescharacteristic
123C2×D19—24no—
124C2×D19—42no—
125C2×D19—42no—
126C2×D19—42no—
127C2×D19—42no—
128C2×D19—42no—
129C2×D19—42no—
130C4×C19—22no—
131C4×C19—41no—
132C4×C19—81no—
133C4×C19C2×C22⋊C411yescharacteristic
134C4×C19C4×D411yescharacteristic
135C4×C19#12111yescharacteristic
136C4×C19#12311yescharacteristic
137Dic19—42no—
138C22×D8—191no—
139C2×C4×D4—191no—
140C2×#102—191no—
141C2×#102—191no—
142#390D1911yescharacteristic, complemented
143#340—191no—
144#336—191no—
145C2×C19—82no—
146C2×C19#38611yescharacteristic
147C2×C19C4×D811yescharacteristic
148C2×C19#44211yescharacteristic
149C2×C19#44711yescharacteristic
150C2×C19#44911yescharacteristic
151C2×C19#45911yescharacteristic
152C2×C19#46311yescharacteristic
153D19—44no—
154C22×D4—191no—
155C22×D4C2×D1911yescharacteristic
156C23×C4—381no—
157C2×D8—194no—
158C2×D8—382no—
159C2×D8—382no—
160C22×C8—191no—
161C22×C8—191no—
162C4×D4—382no—
163C4×D4—382no—
164C2×C4⋊C4—191no—
165C2×C4⋊C4C2×D1911yescharacteristic
166C2×C22⋊C4—21no—
167C2×C22⋊C4—21no—
168C2×C22⋊C4—381no—
169C2×C42C2×D1911yescharacteristic
170#102—382no—
171#102—382no—
172C19#187911yescharacteristic, complemented, Sylow
173C24—21no—
174C24—381no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—192no—
181C2×D4—192no—
182C2×D4—192no—
183C2×D4—381no—
184C2×D4—381no—
185C2×D4—381no—
186C2×D4C4×D1912yescomplemented
187C22×C4—21no—
188C22×C4—384no—
189C22×C4—381no—
190C22×C4—762no—
191C22×C4—762no—
192C22×C4C22⋊D1911yescharacteristic
193C22×C4C22⋊D1911yescharacteristic
194C22×C4C22×D1911yescharacteristic
195D8—388no—
196C2×C8—192no—
197C2×C8—381no—
198C2×C8—381no—
199C2×C8—381no—
200C2×C8—381no—
201C2×C8—381no—
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—192no—
205C4⋊C4—381no—
206C22⋊C4—42no—
207C22⋊C4—42no—
208C22⋊C4—384no—
209C42—21no—
210C42—21no—
211C23—22no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23—41no—
217C23—41no—
218C23—382no—
219C23—382no—
220C23—382no—
221C23—761no—
222C23—761no—
223C23—761no—
224C23—761no—
225C23C2×C22⋊D1911yescharacteristic
226D4—22no—
227D4—22no—
228D4—41no—
229D4—41no—
230D4—194no—
231D4—382no—
232D4—382no—
233D4—382no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—382no—
243C2×C4—768no—
244C2×C4—761no—
245C2×C4—761no—
246C2×C4#6452512yescomplemented
247C2×C4C2×C4×D1911yescharacteristic
248C2×C4#6454111yescharacteristic
249C2×C4D4×D1911yescharacteristic
250C2×C4D4×D1911yescharacteristic
251C2×C4D4×D1911yescharacteristic
252C2×C4#6454311yescharacteristic
253C8—382no—
254C8—761no—
255C22—42no—
256C22—42no—
257C22—42no—
258C22—81no—
259C22—81no—
260C22—81no—
261C22—81no—
262C22—384no—
263C22—762no—
264C22—762no—
265C22—762no—
266C22—762no—
267C22—762no—
268C22—762no—
269C22C4×C22⋊D1911yescharacteristic
270C22C2×#6452511yescharacteristic
271C22#1059737811yescharacteristic
272C22#1059738311yescharacteristic
273C22#1059738411yescharacteristic
274C22#1059739511yescharacteristic
275C22#1059739611yescharacteristic
276C4—22no—
277C4—41no—
278C4—81no—
279C4—762no—
280C4C22⋊C4×D1911yescharacteristic
281C4(C22⋊D19)⋊C411yescharacteristic
282C4#1059732911yescharacteristic
283C4#1059733011yescharacteristic
284C2—82no—
285C2—764no—
286C2#1192642011yescharacteristic
287C2C4×#6452511yescharacteristic
288C2#1192665411yescharacteristic
289C2#1192667711yescharacteristic
290C2#1192668711yescharacteristic
291C2#1192673611yescharacteristic
292C2#1192675611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D19
commutatorC2×C4×C19C22×C4
FrattiniC22×C4C22×D19
FittingC19×#390C2
socleC23×C19C2×D4
prime radicalC22×#64525C2
cosocleC22×C4×C19C23
hypercenter#390D19
hypocenterC19#1879
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×C4×D76C2semidirect
3. C2×#10597289C2semidirect
4. C2×#10597266C2semidirect
5. #11926306C2semidirect
6. #11926299C2semidirect
7. C19×#390C2semidirect
17. C2×#64525C4semidirect
33. C2×D4×C19C2×C4semidirect
63. C2×C19⋊C8C2×C4semidirect
91. C2×C4×C19D8semidirect
104. D76C22⋊C4semidirect
142. #390D19semidirect
172. C19#1879semidirect
186. C2×D4C4×D19semidirect
246. C2×C4#64525semidirect

Maximal subgroups

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

subgroupindex
C22×#645252
C2×C4×D762
C2×#105972892
C2×#105972662
#119263062
#119262992
C19×#3902
#187919