Finite Group Databasebeta

← #14567942

Subgroups — #14567942

Order 2432.

624 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#10597332C211yesmaximal, characteristic
2C2×#10597375C211yesmaximal, characteristic
3C2×(C22⋊D19)⋊C4C211yesmaximal, characteristic
4C22×Dic19⋊C4C211yesmaximal, characteristic, complemented
5#11926478C212yesmaximal, complemented
6#11926473C212yesmaximal, complemented
7#11926441C212yesmaximal, complemented
8#11926405C211yesmaximal, characteristic, complemented
9#11926403C212yesmaximal, complemented
10#11926402C211yesmaximal, characteristic, complemented
11C19×#381C211yesmaximal, characteristic, complemented
12C23×C4×C19C2211yescharacteristic
13C22×C22⋊D19C2211yescharacteristic
14C23×Dic19C2211yescharacteristic
15C23×Dic19C2211yescharacteristic
16C22×C4×D19C2211yescharacteristic
17C2×C22⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19C2211yescharacteristic
19C2×C22⋊Dic19C2211yescharacteristic
20#10597375—24no—
21C2×(C2×D19)⋊C4C2212yes—
22C2×(C2×D19)⋊C4C2212yes—
23C2×(C2×D19)⋊C4C2211yescharacteristic
24C2×C4⋊Dic19C2212yes—
25C2×Dic19⋊C4—24no—
26C2×Dic19⋊C4C2212yes—
27C2×Dic19⋊C4C2212yes—
28C2×Dic19⋊C4C2212yes—
29C2×Dic19⋊C4C2212yes—
30C2×Dic19⋊C4C2211yescharacteristic
31C2×C4×Dic19C2211yescharacteristic
32#10597332—24no—
33(C22⋊D19)⋊C4—24no—
34C19×#95C2212yes—
35C19×#95C2212yes—
36C19⋊#95C2212yes—
37C19⋊#95C2212yes—
38C19⋊#95C2212yes—
39C24×C19C2311yescharacteristic
40C23×D19C2311yescharacteristic
41C22×C4×C19—22no—
42C22×C4×C19—22no—
43C22×C4×C19—22no—
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2311yescharacteristic
46C22×C4×C19C2312yes—
47C22×C4×C19C2312yes—
48C2×C22⋊D19—22no—
49C2×C22⋊D19—22no—
50C2×C22⋊D19D414yes—
51C22×Dic19—24no—
52C22×Dic19—22no—
53C22×Dic19—22no—
54C22×Dic19—22no—
55C22×Dic19D414yes—
56C22×Dic19C2312yes—
57C22×Dic19C2312yes—
58C22×Dic19C2311yescharacteristic
59C22×Dic19C2311yescharacteristic
60C22×Dic19C2311yescharacteristic
61C2×C4×D19—22no—
62C2×C4×D19—24no—
63C22⋊C4×C19—22no—
64C22⋊C4×C19—22no—
65C22⋊Dic19—22no—
66(C2×D19)⋊C4—24no—
67(C2×D19)⋊C4—24no—
68(C2×D19)⋊C4—22no—
69C4⋊Dic19—24no—
70Dic19⋊C4—22no—
71Dic19⋊C4—24no—
72Dic19⋊C4—24no—
73Dic19⋊C4—24no—
74Dic19⋊C4—24no—
75C4×Dic19—22no—
76C23×C19—22no—
77C23×C19—22no—
78C23×C19C2×D412yes—
79C23×C19C2×D412yes—
80C23×C19#4112yes—
81C23×C19C2411yescharacteristic
82C22×D19—21no—
83C22×D19—22no—
84C22×D19—21no—
85C22×D19—22no—
86C22×D19C2×D412yes—
87C2×C4×C19—21no—
88C2×C4×C19—22no—
89C2×C4×C19—22no—
90C2×C4×C19—21no—
91C2×C4×C19—22no—
92C2×C4×C19—22no—
93C2×C4×C19—22no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—44no—
98C22⋊D19—28no—
99C2×Dic19—21no—
100C2×Dic19—22no—
101C2×Dic19—21no—
102C2×Dic19—28no—
103C2×Dic19—22no—
104C2×Dic19—22no—
105C2×Dic19—22no—
106C2×Dic19—22no—
107C2×Dic19—22no—
108C2×Dic19—22no—
109C2×Dic19—44no—
110C2×Dic19C2×D412yes—
111C2×Dic19C2×D412yes—
112C2×Dic19C2×D412yes—
113C2×Dic19#4114yes—
114C4×D19—44no—
115#2486—191nomaximal, Sylow
116C22×C19—22no—
117C22×C19—22no—
118C22×C19—24no—
119C22×C19—24no—
120C22×C19#12114yes—
121C22×C19C22×D411yescharacteristic
122C22×C19C22×D411yescharacteristic
123C22×C19C2×#4111yescharacteristic
124C22×C19C2×#4112yes—
125C22×C192−1+412yes—
126C2×D19—22no—
127C2×D19—24no—
128C2×D19—41no—
129C2×D19—41no—
130C2×D19—42no—
131C4×C19—42no—
132C4×C19—41no—
133C4×C19—41no—
134C4×C19—42no—
135Dic19—22no—
136Dic19—22no—
137Dic19—42no—
138Dic19—42no—
139Dic19#12314yescomplemented
140C2×#123—191no—
141C2×#123—191no—
142C2×C4×D4—191no—
143C22×C4⋊C4—191no—
144#398—192no—
145#397—192no—
146#389—192no—
147#381—191no—
148#381D1911yescharacteristic, complemented
149#380—191no—
150#380—192no—
151C2×C19—24no—
152C2×C19C2×#12111yescharacteristic
153C2×C19C2×#12311yescharacteristic
154C2×C19#53611yescharacteristic
155C2×C19#54712yes—
156C2×C19#55212yes—
157D19—42no—
158C22×D4—191no—
159C23×C4—191no—
160C23×C4—191no—
161C23×C4—191no—
162C23×C4C2×D1911yescharacteristic
163#123—384no—
164#123—384no—
165C4×D4—384no—
166C2×C4⋊C4—192no—
167C2×C4⋊C4—192no—
168C2×C4⋊C4—191no—
169C2×C4⋊C4—192no—
170C2×C4⋊C4—192no—
171C2×C4⋊C4—192no—
172C2×C4⋊C4—384no—
173C2×C22⋊C4—191no—
174C2×C22⋊C4—191no—
175C2×C22⋊C4—192no—
176C2×C22⋊C4—192no—
177C2×C22⋊C4C2×D1911yescharacteristic
178C2×C22⋊C4C2×D1911yescharacteristic
179C2×C42—191no—
180#95—192no—
181#95—192no—
182#95—192no—
183#95C2×D1912yes—
184#95C2×D1912yes—
185C19#248611yescharacteristic, complemented, Sylow
186C24—191no—
187C24C22×D1911yescharacteristic
188C2×D4—194no—
189C2×D4—382no—
190C2×D4—382no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—191no—
195C22×C4—194no—
196C22×C4—191no—
197C22×C4—191no—
198C22×C4—192no—
199C22×C4—192no—
200C22×C4—382no—
201C22×C4—384no—
202C22×C4—384no—
203C22×C4—382no—
204C22×C4—382no—
205C22×C4—382no—
206C22×C4C22×D1911yescharacteristic
207C22×C4C22×D1911yescharacteristic
208C22×C4C22×D1912yes—
209C22×C4C22×D1912yes—
210C4⋊C4—384no—
211C4⋊C4—384no—
212C4⋊C4—384no—
213C4⋊C4—382no—
214C4⋊C4—384no—
215C4⋊C4—384no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—382no—
219C22⋊C4—384no—
220C22⋊C4—384no—
221C22⋊C4—382no—
222C42—382no—
223C23—22no—
224C23—22no—
225C23—192no—
226C23—381no—
227C23—381no—
228C23—382no—
229C23—382no—
230C23#6454112yes—
231C23D4×D1912yes—
232C23D4×D1912yes—
233C23C23×D1911yescharacteristic
234D4—388no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—44no—
246C2×C4—192no—
247C2×C4—194no—
248C2×C4—192no—
249C2×C4—192no—
250C2×C4—388no—
251C2×C4—381no—
252C2×C4—381no—
253C2×C4—382no—
254C2×C4—382no—
255C2×C4—382no—
256C2×C4—382no—
257C2×C4—382no—
258C2×C4—382no—
259C2×C4—382no—
260C2×C4—764no—
261C2×C4—764no—
262C22—22no—
263C22—22no—
264C22—24no—
265C22—24no—
266C22—384no—
267C22—382no—
268C22—761no—
269C22—761no—
270C22—762no—
271C22#1059733014yes—
272C22C2×#6454111yescharacteristic
273C22C2×D4×D1911yescharacteristic
274C22C2×D4×D1911yescharacteristic
275C22#41×D1912yes—
276C22#1059743612yes—
277C4—41no—
278C4—41no—
279C4—42no—
280C4—42no—
281C4—194no—
282C4—382no—
283C4—382no—
284C4—762no—
285C4—762no—
286C2—24no—
287C2—762no—
288C2C2×#1059733011yescharacteristic
289C2#123×D1911yescharacteristic
290C2#1192711611yescharacteristic
291C2#1192719212yes—
292C2#1192722712yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#381C2
prime radicalC22×C22⋊D19C22
hypercenter#381D19
hypocenterC19#2486
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
4. C22×Dic19⋊C4C2semidirect
5. #11926478C2semidirect
6. #11926473C2semidirect
7. #11926441C2semidirect
8. #11926405C2semidirect
9. #11926403C2semidirect
10. #11926402C2semidirect
11. C19×#381C2semidirect
139. Dic19#123semidirect
148. #381D19semidirect
185. C19#2486semidirect

Maximal subgroups

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

subgroupindex
C2×#105973322
C2×#105973752
C2×(C22⋊D19)⋊C42
C22×Dic19⋊C42
#119264782
#119264732
#119264412
#119264052
#119264032
#119264022
C19×#3812
#248619