Finite Group Databasebeta

← #14569109

Subgroups — #14569109

Order 2432.

596 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 139 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×#10597384C211yesmaximal, characteristic
2C2×C4⋊C4×D19C211yesmaximal, characteristic, complemented
3#11926484C211yesmaximal, characteristic, complemented
4#11926483C211yesmaximal, characteristic, complemented
5#11926458C211yesmaximal, characteristic, complemented
6#11926437C212yesmaximal, complemented
7#11926432C212yesmaximal, complemented
8#11926420C212yesmaximal, complemented
9#11926420C212yesmaximal, complemented
10#11926391C211yesmaximal, characteristic, complemented
11C19×#394C211yesmaximal, characteristic, complemented
12C22×D4×C19C2211yescharacteristic
13C22×C22⋊D19C2212yes—
14C22×C4×D19C2211yescharacteristic
15C22×C4×D19C2211yescharacteristic
16C22×C4×D19C2211yescharacteristic
17C2×C4⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19C2212yes—
19C2×C22⋊C4×C19C2212yes—
20C2×C22⋊Dic19C2212yes—
21C2×C22⋊Dic19C2212yes—
22C2×C22⋊Dic19C2212yes—
23#10597384—24no—
24C2×(C2×D19)⋊C4C2212yes—
25C2×C4⋊Dic19C2211yescharacteristic
26C2×C4⋊Dic19C2211yescharacteristic
27C2×Dic19⋊C4C2211yescharacteristic
28C2×Dic19⋊C4C2211yescharacteristic
29C2×C4×Dic19C2212yes—
30C4⋊C4×D19—24no—
31C19×#95C2211yescharacteristic
32C19⋊#95C2211yescharacteristic
33C19⋊#95C2212yes—
34C19⋊#95C2212yes—
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C24×C19C2312yes—
38C23×D19C2311yescharacteristic
39C2×D4×C19—22no—
40C2×D4×C19—42no—
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2312yes—
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2311yescharacteristic
45C2×C22⋊D19—24no—
46C2×C22⋊D19—24no—
47C2×C22⋊D19—24no—
48C22×Dic19C2311yescharacteristic
49C22×Dic19C2312yes—
50C22×Dic19C2312yes—
51C22×Dic19C2311yescharacteristic
52C22×Dic19C2311yescharacteristic
53C2×C4×D19—22no—
54C2×C4×D19—22no—
55C2×C4×D19—22no—
56C2×C4×D19—22no—
57C2×C4×D19—42no—
58C2×C4×D19—42no—
59C2×C4×D19D414yes—
60C4⋊C4×C19—22no—
61C22⋊C4×C19—24no—
62C22⋊C4×C19—42no—
63C22⋊Dic19—24no—
64C22⋊Dic19—24no—
65C22⋊Dic19—42no—
66(C2×D19)⋊C4—24no—
67C4⋊Dic19—22no—
68C4⋊Dic19—22no—
69Dic19⋊C4—22no—
70Dic19⋊C4—22no—
71C4×Dic19—42no—
72C23×C19—22no—
73C23×C19—22no—
74C23×C19—22no—
75C23×C19—22no—
76C23×C19—22no—
77C23×C19—22no—
78C23×C19—22no—
79C23×C19C2411yescharacteristic
80C22×D19—21no—
81C22×D19—21no—
82C22×D19—22no—
83C22×D19C2×D412yes—
84C22×D19#4114yes—
85D4×C19—44no—
86C2×C4×C19—21no—
87C2×C4×C19—21no—
88C2×C4×C19—22no—
89C2×C4×C19—21no—
90C2×C4×C19—22no—
91C2×C4×C19—22no—
92C2×C4×C19—22no—
93C2×C4×C19—22no—
94C2×C4×C19C2×D412yes—
95C2×C4×C19#4112yes—
96C22⋊D19—48no—
97C2×Dic19—21no—
98C2×Dic19—21no—
99C2×Dic19—22no—
100C2×Dic19—21no—
101C2×Dic19—22no—
102C2×Dic19—22no—
103C2×Dic19—22no—
104C2×Dic19—22no—
105C2×Dic19—22no—
106C2×Dic19—22no—
107C2×Dic19—22no—
108C2×Dic19C2×D412yes—
109C2×Dic19#4112yes—
110C4×D19—28no—
111C4×D19—44no—
112C4×D19—44no—
113#2591—191nomaximal, Sylow
114C22×C19—42no—
115C22×C19—42no—
116C22×C19—42no—
117C22×C19—42no—
118C22×C19—42no—
119C22×C19—42no—
120C22×C19—42no—
121C22×C19C22×D411yescharacteristic
122C22×C19C2×#4111yescharacteristic
123C22×C19C2×#4111yescharacteristic
124C22×C19C2×#4112yes—
125C22×C19H(5,𝔽2)12yes—
126C2×D19—22no—
127C2×D19—22no—
128C2×D19—24no—
129C2×D19—24no—
130C2×D19#12414yes—
131C4×C19—22no—
132C4×C19—22no—
133C4×C19—41no—
134C4×C19—42no—
135Dic19—22no—
136Dic19—22no—
137Dic19—42no—
138Dic19—41no—
139Dic19—42no—
140C2×#121—191no—
141C22×C4⋊C4—191no—
142#400—191no—
143#400—191no—
144#394—191no—
145#394D1911yescharacteristic, complemented
146#388—192no—
147#388—192no—
148#386—192no—
149#386—192no—
150C4×C22⋊C4—191no—
151C2×C19—82no—
152C2×C19#52511yescharacteristic
153C2×C19C2×#12411yescharacteristic
154C2×C19#53411yescharacteristic
155C2×C19#55312yes—
156C2×C19#55312yes—
157D19—24no—
158C22×D4—192no—
159C22×D4C2×D1911yescharacteristic
160C23×C4—191no—
161C23×C4—191no—
162C23×C4—191no—
163#121—384no—
164C2×C4⋊C4—191no—
165C2×C4⋊C4—191no—
166C2×C4⋊C4—191no—
167C2×C4⋊C4—191no—
168C2×C4⋊C4—384no—
169C2×C4⋊C4C2×D1911yescharacteristic
170C2×C22⋊C4—192no—
171C2×C22⋊C4—192no—
172C2×C22⋊C4—192no—
173C2×C22⋊C4—192no—
174C2×C22⋊C4C2×D1912yes—
175C2×C22⋊C4C2×D1912yes—
176C2×C42—192no—
177#95—191no—
178#95—192no—
179#95—192no—
180#95—192no—
181#95—192no—
182#95C2×D1911yescharacteristic
183C19#259111yescharacteristic, complemented, Sylow
184C24—191no—
185C24C22×D1912yes—
186C2×D4—22no—
187C2×D4—42no—
188C2×D4—384no—
189C2×D4—384no—
190C2×D4—384no—
191C22×C4—191no—
192C22×C4—191no—
193C22×C4—194no—
194C22×C4—192no—
195C22×C4—192no—
196C22×C4—191no—
197C22×C4—382no—
198C22×C4—382no—
199C22×C4—382no—
200C22×C4—382no—
201C22×C4—762no—
202C22×C4—762no—
203C22×C4C22×D1912yes—
204C22×C4C22×D1911yescharacteristic
205C22×C4C22×D1911yescharacteristic
206C22×C4C22×D1911yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—382no—
209C4⋊C4—382no—
210C4⋊C4—382no—
211C4⋊C4—382no—
212C22⋊C4—24no—
213C22⋊C4—42no—
214C22⋊C4—384no—
215C22⋊C4—384no—
216C22⋊C4—384no—
217C22⋊C4—762no—
218C42—762no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—22no—
226C23—192no—
227C23—194no—
228C23—381no—
229C23—382no—
230C23—381no—
231C23C23×D1911yescharacteristic
232D4—44no—
233D4—768no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—192no—
243C2×C4—192no—
244C2×C4—388no—
245C2×C4—381no—
246C2×C4—381no—
247C2×C4—382no—
248C2×C4—382no—
249C2×C4—381no—
250C2×C4—382no—
251C2×C4—382no—
252C2×C4—382no—
253C2×C4—382no—
254C2×C4—382no—
255C2×C4—382no—
256C2×C4—764no—
257C2×C4—764no—
258C2×C4D4×D1912yes—
259C2×C4#6454312yes—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—42no—
267C22—194no—
268C22—382no—
269C22—382no—
270C22—384no—
271C22—384no—
272C22C2×D4×D1911yescharacteristic
273C22C2×#6454311yescharacteristic
274C22#1059743012yes—
275C22#41×D1911yescharacteristic
276C22#41×D1912yes—
277C4—22no—
278C4—22no—
279C4—41no—
280C4—42no—
281C4—382no—
282C4—382no—
283C4—762no—
284C4—761no—
285C4—762no—
286C2—82no—
287C2—384no—
288C2#1192705411yescharacteristic
289C2#124×D1911yescharacteristic
290C2#1192710411yescharacteristic
291C2#1192723912yes—
292C2#1192724112yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#394C2
prime radicalC2×#10597384C2
hypercenter#394D19
hypocenterC19#2591
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D19C2semidirect
3. #11926484C2semidirect
4. #11926483C2semidirect
5. #11926458C2semidirect
6. #11926437C2semidirect
7. #11926432C2semidirect
8. #11926420C2semidirect
9. #11926420C2semidirect
10. #11926391C2semidirect
11. C19×#394C2semidirect
145. #394D19semidirect
183. C19#2591semidirect

Maximal subgroups

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

subgroupindex
C2×#105973842
C2×C4⋊C4×D192
#119264842
#119264832
#119264582
#119264372
#119264322
#119264202
#119263912
C19×#3942
#259119