Finite Group Databasebeta

← #14566971

Subgroups — #14566971

Order 2432.

864 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 159 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×#64545C211yesmaximal, characteristic
2C2×#10597340C212yesmaximal, complemented
3C2×C4⋊C4×D19C211yesmaximal, characteristic, complemented
4#11926463C211yesmaximal, characteristic, complemented
5#11926462C211yesmaximal, characteristic, complemented
6#11926461C211yesmaximal, characteristic, complemented
7#11926422C212yesmaximal, complemented
8#11926418C212yesmaximal, complemented
9#11926415C212yesmaximal, complemented
10#11926406C211yesmaximal, characteristic, complemented
11C19×#395C211yesmaximal, characteristic, complemented
12C22×Q8×C19C2211yescharacteristic
13C2×#64545—28no—
14C2×#64545—24no—
15C22×D76C2211yescharacteristic
16C22×D76C2212yes—
17C22×C4×D19C2211yescharacteristic
18C22×C4×D19C2212yes—
19C22×C4×D19C2211yescharacteristic
20C22×C4×D19C2211yescharacteristic
21C2×C4⋊C4×C19C2212yes—
22C2×C4⋊C4×C19C2211yescharacteristic
23C2×(C2×D19)⋊C4C2212yes—
24C2×(C2×D19)⋊C4C2212yes—
25C2×(C2×D19)⋊C4C2212yes—
26C2×(C2×D19)⋊C4C2212yes—
27C2×(C2×D19)⋊C4C2212yes—
28C2×C4⋊Dic19C2211yescharacteristic
29C2×Dic19⋊C4C2212yes—
30C2×Dic19⋊C4C2211yescharacteristic
31C2×Dic19⋊C4C2211yescharacteristic
32#10597340—28no—
33C4⋊C4×D19—24no—
34C19×#95C2211yescharacteristic
35C19×#95C2212yes—
36C19⋊#95C2212yes—
37C19⋊#95C2211yescharacteristic
38C19⋊#95C2212yes—
39C23×D19C2312yes—
40C23×D19C2311yescharacteristic
41C2×Q8×C19—24no—
42C2×Q8×C19—22no—
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2312yes—
45C22×C4×C19C2312yes—
46C22×C4×C19C2311yescharacteristic
47C22×C4×C19C2311yescharacteristic
48C22×Dic19C2311yescharacteristic
49C22×Dic19C2312yes—
50C22×Dic19C2311yescharacteristic
51C22×Dic19C2311yescharacteristic
52#64545—232no—
53C2×D76—24no—
54C2×D76—24no—
55C2×D76—24no—
56C2×D76—22no—
57C2×D76D418yes—
58C2×C4×D19—24no—
59C2×C4×D19—24no—
60C2×C4×D19—22no—
61C2×C4×D19—24no—
62C2×C4×D19—22no—
63C2×C4×D19—24no—
64C2×C4×D19—22no—
65C2×C4×D19—22no—
66C2×C4×D19—24no—
67C2×C4×D19D414yes—
68C4⋊C4×C19—22no—
69C4⋊C4×C19—24no—
70(C2×D19)⋊C4—24no—
71(C2×D19)⋊C4—24no—
72(C2×D19)⋊C4—24no—
73(C2×D19)⋊C4—24no—
74(C2×D19)⋊C4—24no—
75C4⋊Dic19—22no—
76Dic19⋊C4—22no—
77Dic19⋊C4—24no—
78Dic19⋊C4—22no—
79C23×C19C2411yescharacteristic
80C22×D19—21no—
81C22×D19—21no—
82C22×D19—22no—
83C22×D19—22no—
84C22×D19—22no—
85C22×D19—22no—
86C22×D19—22no—
87C22×D19—22no—
88C22×D19—22no—
89C22×D19C2×D414yes—
90C22×D19C2×D414yes—
91C22×D19C2×D412yes—
92Q8×C19—28no—
93C2×C4×C19—21no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—21no—
98C2×C4×C19—21no—
99C2×C4×C19—22no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19—22no—
103C2×C4×C19C2×D414yes—
104C2×C4×C19C2×D412yes—
105C2×C4×C19#4112yescomplemented
106C2×Dic19—21no—
107C2×Dic19—22no—
108C2×Dic19—21no—
109C2×Dic19—21no—
110C2×Dic19—22no—
111C2×Dic19—22no—
112C2×Dic19—22no—
113C2×Dic19—22no—
114C2×Dic19C2×D412yes—
115C2×Dic19#4112yescomplemented
116D76—28no—
117D76—216no—
118C4×D19—28no—
119C4×D19—216no—
120C4×D19—28no—
121C4×D19—44no—
122#2406—191nomaximal, Sylow
123C22×C19C22×D411yescharacteristic
124C22×C19C22×D412yes—
125C22×C19C2×#4111yescharacteristic
126C22×C19C2×#4111yescharacteristic
127C22×C192−1+412yes—
128C2×D19—22no—
129C2×D19—22no—
130C2×D19—24no—
131C2×D19—24no—
132C2×D19—24no—
133C2×D19—24no—
134C2×D19—24no—
135C2×D19—42no—
136C2×D19—42no—
137C2×D19—42no—
138C2×D19—42no—
139C2×D19#12014yes—
140C4×C19—24no—
141C4×C19—22no—
142C4×C19—22no—
143C4×C19—41no—
144C4×C19—42no—
145Dic19—22no—
146Dic19—22no—
147Dic19—41no—
148Dic19—42no—
149C22×#41—191no—
150C2×#123—192no—
151C22×C4⋊C4—191no—
152#395—191no—
153#395D1911yescharacteristic, complemented
154#394—191no—
155#394—191no—
156#386—192no—
157#385—192no—
158#385—192no—
159#381—191no—
160C2×C19C2×#12011yescharacteristic
161C2×C19#52511yescharacteristic
162C2×C19#53611yescharacteristic
163C2×C19#54712yes—
164C2×C19#54712yes—
165D19—24no—
166D19—44no—
167C2×#41—384no—
168C2×#41—388no—
169C22×Q8C2×D1911yescharacteristic
170C22×D4—192no—
171C22×D4—191no—
172C23×C4—191no—
173C23×C4—191no—
174C23×C4—191no—
175C23×C4—192no—
176#123—388no—
177C2×C4⋊C4—191no—
178C2×C4⋊C4—191no—
179C2×C4⋊C4—191no—
180C2×C4⋊C4—192no—
181C2×C4⋊C4—384no—
182C2×C4⋊C4C2×D1911yescharacteristic
183C2×C4⋊C4C2×D1912yes—
184C2×C22⋊C4—192no—
185C2×C22⋊C4—192no—
186C2×C22⋊C4—192no—
187C2×C22⋊C4—192no—
188C2×C22⋊C4—192no—
189#95—192no—
190#95—191no—
191#95—192no—
192#95C2×D1911yescharacteristic
193#95C2×D1912yes—
194C19#240611yescharacteristic, complemented, Sylow
195C24—191no—
196C24—192no—
197#41—3832no—
198C2×Q8—22no—
199C2×Q8—24no—
200C2×D4—198no—
201C2×D4—384no—
202C2×D4—384no—
203C2×D4—384no—
204C2×D4—382no—
205C22×C4—191no—
206C22×C4—191no—
207C22×C4—194no—
208C22×C4—192no—
209C22×C4—191no—
210C22×C4—382no—
211C22×C4—384no—
212C22×C4—382no—
213C22×C4—384no—
214C22×C4—384no—
215C22×C4—382no—
216C22×C4—384no—
217C22×C4—384no—
218C22×C4—382no—
219C22×C4C22×D1912yes—
220C22×C4C22×D1911yescharacteristic
221C22×C4C22×D1911yescharacteristic
222C22×C4C22×D1912yes—
223C22×C4C22×D1911yescharacteristic
224C4⋊C4—22no—
225C4⋊C4—24no—
226C4⋊C4—382no—
227C4⋊C4—382no—
228C4⋊C4—382no—
229C4⋊C4—384no—
230C22⋊C4—384no—
231C22⋊C4—384no—
232C22⋊C4—384no—
233C22⋊C4—384no—
234C22⋊C4—384no—
235C23—194no—
236C23—192no—
237C23—194no—
238C23—381no—
239C23—382no—
240C23—381no—
241C23—382no—
242C23—382no—
243C23—382no—
244C23—382no—
245C23—382no—
246C23—382no—
247C23C23×D1911yescharacteristic
248Q8—28no—
249D4—3816no—
250D4—388no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—192no—
262C2×C4—192no—
263C2×C4—388no—
264C2×C4—3816no—
265C2×C4—388no—
266C2×C4—381no—
267C2×C4—382no—
268C2×C4—381no—
269C2×C4—382no—
270C2×C4—382no—
271C2×C4—381no—
272C2×C4—382no—
273C2×C4—382no—
274C2×C4—764no—
275C2×C4D4×D1912yes—
276C2×C4D4×D1914yes—
277C2×C4#6454512yescomplemented
278C22—194no—
279C22—382no—
280C22—382no—
281C22—384no—
282C22—384no—
283C22—384no—
284C22—384no—
285C22—384no—
286C22—762no—
287C22—762no—
288C22—762no—
289C22—762no—
290C22C2×D4×D1911yescharacteristic
291C22C2×D4×D1912yes—
292C22C2×#6454511yescharacteristic
293C22#1059743312yes—
294C22#41×D1911yescharacteristic
295C4—22no—
296C4—22no—
297C4—24no—
298C4—42no—
299C4—41no—
300C4—382no—
301C4—382no—
302C4—762no—
303C4—761no—
304C2—384no—
305C2—764no—
306C2#120×D1911yescharacteristic
307C2#1192705711yescharacteristic
308C2#1192711911yescharacteristic
309C2#1192719612yes—
310C2#1192719712yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#395C2
prime radicalC22×#64545C2
hypercenter#395D19
hypocenterC19#2406
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#10597340C2semidirect
3. C2×C4⋊C4×D19C2semidirect
4. #11926463C2semidirect
5. #11926462C2semidirect
6. #11926461C2semidirect
7. #11926422C2semidirect
8. #11926418C2semidirect
9. #11926415C2semidirect
10. #11926406C2semidirect
11. C19×#395C2semidirect
105. C2×C4×C19#41semidirect
115. C2×Dic19#41semidirect
153. #395D19semidirect
194. C19#2406semidirect
277. C2×C4#64545semidirect

Maximal subgroups

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

subgroupindex
C22×#645452
C2×#105973402
C2×C4⋊C4×D192
#119264632
#119264622
#119264612
#119264222
#119264182
#119264152
#119264062
C19×#3952
#240619