Finite Group Databasebeta

← #14569363

Subgroups — #14569363

Order 2432.

816 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 153 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×#64543C211yesmaximal, characteristic
2C2×#10597342C211yesmaximal, characteristic, complemented
3C2×#10597324C212yesmaximal, complemented
4#11926465C211yesmaximal, characteristic, complemented
5#11926464C211yesmaximal, characteristic, complemented
6#11926460C212yesmaximal, complemented
7#11926459C212yesmaximal, complemented
8#11926458C211yesmaximal, characteristic, complemented
9#11926403C211yesmaximal, characteristic, complemented
10#11926402C212yesmaximal, complemented
11C19×#394C211yesmaximal, characteristic, complemented
12C22×D4×C19C2211yescharacteristic
13C22×C22⋊D19C2212yes—
14C23×Dic19C2212yes—
15C2×#64543—28no—
16C2×#64543—24no—
17C22×C4×D19C2211yescharacteristic
18C22×Dic38C2211yescharacteristic
19C22×Dic38C2211yescharacteristic
20C2×C4⋊C4×C19C2211yescharacteristic
21C2×C22⋊C4×C19C2212yes—
22C2×C22⋊C4×C19C2212yes—
23C2×C22⋊Dic19C2212yes—
24C2×C22⋊Dic19C2212yes—
25C2×(C2×D19)⋊C4C2211yescharacteristic
26C2×(C2×D19)⋊C4C2211yescharacteristic
27C2×(C2×D19)⋊C4C2212yes—
28C2×C4⋊Dic19C2212yes—
29C2×Dic19⋊C4C2212yes—
30C2×Dic19⋊C4C2212yes—
31C2×Dic19⋊C4C2211yescharacteristic
32C2×Dic19⋊C4C2211yescharacteristic
33#10597342—24no—
34#10597324—28no—
35C19×#95C2211yescharacteristic
36C19⋊#95C2212yes—
37C19⋊#95C2212yes—
38C19⋊#95C2211yescharacteristic
39C24×C19C2312yes—
40C23×D19C2311yescharacteristic
41C2×D4×C19—24no—
42C2×D4×C19—22no—
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2312yes—
46C22×C4×C19C2311yescharacteristic
47C2×C22⋊D19—24no—
48C2×C22⋊D19—24no—
49C2×C22⋊D19—24no—
50C22×Dic19—24no—
51C22×Dic19—24no—
52C22×Dic19D418yes—
53C22×Dic19C2311yescharacteristic
54C22×Dic19C2311yescharacteristic
55C22×Dic19C2312yes—
56C22×Dic19C2312yes—
57C22×Dic19C2311yescharacteristic
58#64543—232no—
59C2×C4×D19—24no—
60C2×C4×D19D414yes—
61C2×Dic38—22no—
62C2×Dic38—24no—
63C2×Dic38—24no—
64C2×Dic38—22no—
65C4⋊C4×C19—22no—
66C22⋊C4×C19—24no—
67C22⋊C4×C19—42no—
68C22⋊Dic19—24no—
69C22⋊Dic19—42no—
70(C2×D19)⋊C4—22no—
71(C2×D19)⋊C4—22no—
72(C2×D19)⋊C4—42no—
73C4⋊Dic19—24no—
74Dic19⋊C4—22no—
75Dic19⋊C4—24no—
76Dic19⋊C4—24no—
77Dic19⋊C4—22no—
78C23×C19—22no—
79C23×C19—22no—
80C23×C19—22no—
81C23×C19—22no—
82C23×C19—22no—
83C23×C19—22no—
84C23×C19C2×D414yes—
85C23×C19C2411yescharacteristic
86C22×D19—22no—
87C22×D19—21no—
88C22×D19—22no—
89C22×D19—21no—
90C22×D19C2×D412yes—
91D4×C19—28no—
92C2×C4×C19—22no—
93C2×C4×C19—22no—
94C2×C4×C19—21no—
95C2×C4×C19—22no—
96C2×C4×C19—21no—
97C2×C4×C19—22no—
98C2×C4×C19—21no—
99C2×C4×C19—21no—
100C2×C4×C19—22no—
101C2×C4×C19C2×D412yes—
102C22⋊D19—216no—
103C2×Dic19—22no—
104C2×Dic19—22no—
105C2×Dic19—216no—
106C2×Dic19—21no—
107C2×Dic19—22no—
108C2×Dic19—21no—
109C2×Dic19—22no—
110C2×Dic19—22no—
111C2×Dic19—21no—
112C2×Dic19—22no—
113C2×Dic19—21no—
114C2×Dic19C2×D414yes—
115C2×Dic19C2×D414yes—
116C2×Dic19C2×D412yes—
117C4×D19—28no—
118Dic38—28no—
119Dic38—44no—
120#2616—191nomaximal, Sylow
121C22×C19—24no—
122C22×C19—24no—
123C22×C19—24no—
124C22×C19—42no—
125C22×C19—42no—
126C22×C19—42no—
127C22×C19—42no—
128C22×C19C22×D411yescharacteristic
129C22×C19C22×D412yes—
130C22×C19H(5,𝔽2)11yescharacteristic
131C22×C192−1+412yes—
132C22×C192−1+411yescharacteristic
133C2×D19—22no—
134C2×D19—22no—
135C2×D19—22no—
136C2×D19—42no—
137C2×D19—42no—
138C4×C19—22no—
139C4×C19—41no—
140C4×C19—42no—
141C4×C19—41no—
142Dic19—24no—
143Dic19—41no—
144Dic19—42no—
145Dic19—41no—
146Dic19#12014yes—
147C22×#41—191no—
148C2×C22⋊Q8—191no—
149C2×C22⋊Q8—192no—
150#395—191no—
151#395—191no—
152#394—191no—
153#394—192no—
154#394—192no—
155#394D1911yescharacteristic, complemented
156#380—192no—
157#380—191no—
158C2×C19—44no—
159C2×C19C2×#12011yescharacteristic
160C2×C19#53611yescharacteristic
161C2×C19#53612yes—
162C2×C19#53712yes—
163C2×C19#53711yescharacteristic
164D19—42no—
165C2×#41—388no—
166C2×#41—384no—
167C22×Q8—191no—
168C22×Q8—191no—
169C22×D4—192no—
170C22×D4C2×D1911yescharacteristic
171C23×C4—192no—
172C23×C4—191no—
173C22⋊Q8—388no—
174C22⋊Q8—384no—
175C2×C4⋊C4—191no—
176C2×C4⋊C4—192no—
177C2×C4⋊C4—192no—
178C2×C4⋊C4—191no—
179C2×C4⋊C4—192no—
180C2×C4⋊C4C2×D1911yescharacteristic
181C2×C22⋊C4—192no—
182C2×C22⋊C4—191no—
183C2×C22⋊C4—191no—
184C2×C22⋊C4—192no—
185C2×C22⋊C4—192no—
186C2×C22⋊C4C2×D1912yes—
187C2×C22⋊C4C2×D1912yes—
188#95—192no—
189#95—192no—
190#95—191no—
191#95C2×D1911yescharacteristic
192C19#261611yescharacteristic, complemented, Sylow
193C24—191no—
194C24C22×D1912yes—
195#41—3832no—
196C2×Q8—384no—
197C2×Q8—384no—
198C2×Q8—382no—
199C2×Q8—382no—
200C2×D4—24no—
201C2×D4—22no—
202C2×D4—384no—
203C2×D4—384no—
204C2×D4—384no—
205C22×C4—191no—
206C22×C4—198no—
207C22×C4—192no—
208C22×C4—194no—
209C22×C4—192no—
210C22×C4—191no—
211C22×C4—191no—
212C22×C4—384no—
213C22×C4—384no—
214C22×C4—384no—
215C22×C4C22×D1911yescharacteristic
216C22×C4C22×D1912yes—
217C22×C4C22×D1911yescharacteristic
218C22×C4C22×D1911yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—384no—
221C4⋊C4—384no—
222C4⋊C4—382no—
223C4⋊C4—384no—
224C4⋊C4—382no—
225C22⋊C4—24no—
226C22⋊C4—42no—
227C22⋊C4—382no—
228C22⋊C4—382no—
229C22⋊C4—384no—
230C22⋊C4—762no—
231C22⋊C4—762no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—192no—
239C23—382no—
240C23—381no—
241C23—382no—
242C23—381no—
243C23D4×D1914yes—
244C23C23×D1911yescharacteristic
245Q8—388no—
246Q8—764no—
247D4—28no—
248D4—3816no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—192no—
259C2×C4—194no—
260C2×C4—194no—
261C2×C4—388no—
262C2×C4—3816no—
263C2×C4—382no—
264C2×C4—382no—
265C2×C4—382no—
266C2×C4—381no—
267C2×C4—381no—
268C2×C4—382no—
269C2×C4—382no—
270C2×C4—381no—
271C2×C4—382no—
272C2×C4—381no—
273C2×C4D4×D1912yes—
274C22—24no—
275C22—24no—
276C22—24no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—382no—
282C22—382no—
283C22—382no—
284C22—762no—
285C22—762no—
286C22C2×D4×D1911yescharacteristic
287C22C2×D4×D1912yes—
288C22#1059743011yescharacteristic
289C22#1059743612yes—
290C22#1059743611yescharacteristic
291C4—22no—
292C4—42no—
293C4—41no—
294C4—41no—
295C4—194no—
296C4—384no—
297C4—762no—
298C4—761no—
299C4—761no—
300C2—44no—
301C2—762no—
302C2#120×D1911yescharacteristic
303C2#1192711411yescharacteristic
304C2#1192711612yes—
305C2#1192712112yes—
306C2#1192712311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#394C2
prime radicalC22×#64543C2
hypercenter#394D19
hypocenterC19#2616
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#10597342C2semidirect
3. C2×#10597324C2semidirect
4. #11926465C2semidirect
5. #11926464C2semidirect
6. #11926460C2semidirect
7. #11926459C2semidirect
8. #11926458C2semidirect
9. #11926403C2semidirect
10. #11926402C2semidirect
11. C19×#394C2semidirect
155. #394D19semidirect
192. C19#2616semidirect

Maximal subgroups

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

subgroupindex
C22×#645432
C2×#105973422
C2×#105973242
#119264652
#119264642
#119264602
#119264592
#119264582
#119264032
#119264022
C19×#3942
#261619