Finite Group Databasebeta

← #14569376

Subgroups — #14569376

Order 2432.

632 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 143 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×#10597329C212yesmaximal, complemented
2C2×#10597384C211yesmaximal, characteristic
3C2×C4⋊C4×D19C211yesmaximal, characteristic, complemented
4#11926476C211yesmaximal, characteristic, complemented
5#11926474C211yesmaximal, characteristic, complemented
6#11926467C212yesmaximal, complemented
7#11926467C212yesmaximal, complemented
8#11926458C211yesmaximal, characteristic, complemented
9#11926420C212yesmaximal, complemented
10#11926403C211yesmaximal, 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⋊Dic19C2212yes—
26C2×C4⋊Dic19C2211yescharacteristic
27C2×C4⋊Dic19C2211yescharacteristic
28C2×Dic19⋊C4C2212yes—
29C2×Dic19⋊C4C2211yescharacteristic
30C2×Dic19⋊C4C2211yescharacteristic
31C2×Dic19⋊C4C2212yes—
32C4⋊C4×D19—24no—
33#10597329—28no—
34C19×#95C2211yescharacteristic
35C19⋊#95C2211yescharacteristic
36C19⋊#95C2212yes—
37C19⋊#95C2212yes—
38C24×C19C2312yes—
39C23×D19C2311yescharacteristic
40C2×D4×C19—22no—
41C2×D4×C19—42no—
42C22×C4×C19C2311yescharacteristic
43C22×C4×C19C2312yes—
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2311yescharacteristic
46C2×C22⋊D19—24no—
47C2×C22⋊D19—24no—
48C2×C22⋊D19—24no—
49C22×Dic19C2311yescharacteristic
50C22×Dic19C2312yes—
51C22×Dic19C2312yes—
52C22×Dic19C2311yescharacteristic
53C22×Dic19C2311yescharacteristic
54C2×C4×D19—22no—
55C2×C4×D19—22no—
56C2×C4×D19—22no—
57C2×C4×D19—42no—
58C2×C4×D19—42no—
59C2×C4×D19D414yes—
60C2×C4×D19D414yescomplemented
61C4⋊C4×C19—22no—
62C22⋊C4×C19—24no—
63C22⋊C4×C19—42no—
64C22⋊Dic19—24no—
65C22⋊Dic19—24no—
66C22⋊Dic19—42no—
67(C2×D19)⋊C4—24no—
68C4⋊Dic19—22no—
69C4⋊Dic19—24no—
70C4⋊Dic19—22no—
71Dic19⋊C4—24no—
72Dic19⋊C4—22no—
73Dic19⋊C4—22no—
74Dic19⋊C4—42no—
75C23×C19—22no—
76C23×C19—22no—
77C23×C19—22no—
78C23×C19—22no—
79C23×C19—22no—
80C23×C19—22no—
81C23×C19—22no—
82C23×C19C2411yescharacteristic
83C22×D19—22no—
84C22×D19—22no—
85C22×D19C2×D412yes—
86C22×D19C2×D412yes—
87C22×D19#4112yes—
88D4×C19—44no—
89C2×C4×C19—21no—
90C2×C4×C19—21no—
91C2×C4×C19—22no—
92C2×C4×C19—21no—
93C2×C4×C19—22no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19C2×D412yes—
98C2×C4×C19C2×D412yes—
99C22⋊D19—48no—
100C2×Dic19—21no—
101C2×Dic19—21no—
102C2×Dic19—22no—
103C2×Dic19—21no—
104C2×Dic19—22no—
105C2×Dic19—22no—
106C2×Dic19—22no—
107C2×Dic19—22no—
108C2×Dic19—22no—
109C2×Dic19—22no—
110C2×Dic19—22no—
111C2×Dic19C2×D412yes—
112C2×Dic19C2×D412yes—
113C4×D19—28no—
114C4×D19—44no—
115C4×D19—44no—
116#2618—191nomaximal, Sylow
117C22×C19—42no—
118C22×C19—42no—
119C22×C19—42no—
120C22×C19—42no—
121C22×C19—42no—
122C22×C19—42no—
123C22×C19—42no—
124C22×C19C22×D411yescharacteristic
125C22×C19C22×D411yescharacteristic
126C22×C19C2×#4111yescharacteristic
127C22×C19H(5,𝔽2)12yes—
128C22×C192−1+412yes—
129C2×D19—22no—
130C2×D19—22no—
131C2×D19—24no—
132C2×D19—24no—
133C2×D19#12114yes—
134C4×C19—22no—
135C4×C19—22no—
136C4×C19—41no—
137C4×C19—42no—
138Dic19—22no—
139Dic19—22no—
140Dic19—42no—
141Dic19—41no—
142Dic19—42no—
143C2×#123—192no—
144C2×#121—191no—
145C22×C4⋊C4—191no—
146#398—191no—
147#398—191no—
148#396—192no—
149#396—192no—
150#394—191no—
151#394D1911yescharacteristic, complemented
152#386—192no—
153#380—191no—
154C2×C19—82no—
155C2×C19C2×#12111yescharacteristic
156C2×C19#53411yescharacteristic
157C2×C19#53611yescharacteristic
158C2×C19#53712yes—
159C2×C19#53912yes—
160D19—24no—
161C22×D4—192no—
162C22×D4C2×D1911yescharacteristic
163C23×C4—191no—
164C23×C4—191no—
165C23×C4—191no—
166#123—388no—
167#121—384no—
168C2×C4⋊C4—191no—
169C2×C4⋊C4—191no—
170C2×C4⋊C4—191no—
171C2×C4⋊C4—191no—
172C2×C4⋊C4—192no—
173C2×C4⋊C4—192no—
174C2×C4⋊C4—192no—
175C2×C4⋊C4—384no—
176C2×C4⋊C4C2×D1911yescharacteristic
177C2×C22⋊C4—192no—
178C2×C22⋊C4—192no—
179C2×C22⋊C4—192no—
180C2×C22⋊C4—192no—
181C2×C22⋊C4C2×D1912yes—
182C2×C22⋊C4C2×D1912yes—
183#95—191no—
184#95—192no—
185#95—192no—
186#95C2×D1911yescharacteristic
187C19#261811yescharacteristic, complemented, Sylow
188C24—191no—
189C24C22×D1912yes—
190C2×D4—22no—
191C2×D4—42no—
192C2×D4—384no—
193C2×D4—384no—
194C2×D4—384no—
195C22×C4—191no—
196C22×C4—191no—
197C22×C4—194no—
198C22×C4—194no—
199C22×C4—192no—
200C22×C4—191no—
201C22×C4—192no—
202C22×C4—382no—
203C22×C4—382no—
204C22×C4—382no—
205C22×C4—762no—
206C22×C4—762no—
207C22×C4C22×D1911yescharacteristic
208C22×C4C22×D1912yes—
209C22×C4C22×D1911yescharacteristic
210C22×C4C22×D1911yescharacteristic
211C4⋊C4—22no—
212C4⋊C4—382no—
213C4⋊C4—382no—
214C4⋊C4—384no—
215C4⋊C4—382no—
216C4⋊C4—384no—
217C4⋊C4—382no—
218C4⋊C4—762no—
219C22⋊C4—24no—
220C22⋊C4—42no—
221C22⋊C4—384no—
222C22⋊C4—384no—
223C22⋊C4—384no—
224C22⋊C4—762no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—192no—
233C23—192no—
234C23—192no—
235C23—382no—
236C23—382no—
237C23C23×D1911yescharacteristic
238D4—44no—
239D4—768no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—192no—
249C2×C4—192no—
250C2×C4—388no—
251C2×C4—381no—
252C2×C4—382no—
253C2×C4—381no—
254C2×C4—382no—
255C2×C4—382no—
256C2×C4—381no—
257C2×C4—382no—
258C2×C4—382no—
259C2×C4—382no—
260C2×C4—382no—
261C2×C4—382no—
262C2×C4—764no—
263C2×C4—764no—
264C2×C4D4×D1912yes—
265C2×C4D4×D1912yes—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—194no—
274C22—382no—
275C22—382no—
276C22—384no—
277C22—384no—
278C22C2×D4×D1911yescharacteristic
279C22C2×D4×D1911yescharacteristic
280C22#1059743012yes—
281C22#41×D1911yescharacteristic
282C22#1059743612yes—
283C4—22no—
284C4—22no—
285C4—41no—
286C4—42no—
287C4—382no—
288C4—382no—
289C4—761no—
290C4—762no—
291C4—762no—
292C2—82no—
293C2—384no—
294C2#121×D1911yescharacteristic
295C2#1192710411yescharacteristic
296C2#1192711411yescharacteristic
297C2#1192712312yes—
298C2#1192713712yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#394C2
prime radicalC2×#10597384C2
hypercenter#394D19
hypocenterC19#2618
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#10597329C2semidirect
3. C2×C4⋊C4×D19C2semidirect
4. #11926476C2semidirect
5. #11926474C2semidirect
6. #11926467C2semidirect
7. #11926467C2semidirect
8. #11926458C2semidirect
9. #11926420C2semidirect
10. #11926403C2semidirect
11. C19×#394C2semidirect
60. C2×C4×D19D4semidirect
151. #394D19semidirect
187. C19#2618semidirect

Maximal subgroups

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

subgroupindex
C2×#105973292
C2×#105973842
C2×C4⋊C4×D192
#119264762
#119264742
#119264672
#119264582
#119264202
#119264032
C19×#3942
#261819