Finite Group Databasebeta

← #14569378

Subgroups — #14569378

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×#10597340C212yesmaximal, complemented
2C2×#10597341C211yesmaximal, characteristic
3C2×C4⋊C4×D19C211yesmaximal, characteristic, complemented
4#11926475C211yesmaximal, characteristic, complemented
5#11926468C212yesmaximal, complemented
6#11926466C212yesmaximal, complemented
7#11926462C211yesmaximal, characteristic, complemented
8#11926461C211yesmaximal, characteristic, complemented
9#11926422C212yesmaximal, complemented
10#11926403C211yesmaximal, characteristic, complemented
11C19×#398C211yesmaximal, characteristic, complemented
12C22×D76C2212yes—
13C22×D76C2211yescharacteristic
14C22×C4×D19C2211yescharacteristic
15C22×C4×D19C2211yescharacteristic
16C22×C4×D19C2211yescharacteristic
17C2×C4⋊C4×C19C2212yes—
18C2×C4⋊C4×C19C2211yescharacteristic
19C2×C4⋊C4×C19C2211yescharacteristic
20C2×(C2×D19)⋊C4C2212yes—
21C2×(C2×D19)⋊C4C2212yes—
22C2×(C2×D19)⋊C4C2212yes—
23C2×(C2×D19)⋊C4C2212yes—
24C2×(C2×D19)⋊C4C2212yes—
25C2×(C2×D19)⋊C4C2212yes—
26C2×C4⋊Dic19C2211yescharacteristic
27C2×Dic19⋊C4C2212yes—
28C2×Dic19⋊C4C2211yescharacteristic
29C2×Dic19⋊C4C2211yescharacteristic
30C2×Dic19⋊C4C2212yes—
31#10597341—24no—
32#10597340—28no—
33C4⋊C4×D19—24no—
34C19×#95C2211yescharacteristic
35C19×#95C2212yes—
36C19⋊#95C2211yescharacteristic
37C19⋊#95C2212yes—
38C23×D19C2312yes—
39C23×D19C2311yescharacteristic
40C22×C4×C19C2312yes—
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2312yes—
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2311yescharacteristic
45C22×Dic19C2311yescharacteristic
46C22×Dic19C2312yes—
47C22×Dic19C2311yescharacteristic
48C22×Dic19C2311yescharacteristic
49C2×D76—24no—
50C2×D76—24no—
51C2×D76—24no—
52C2×D76—22no—
53C2×D76—42no—
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—
62C4⋊C4×C19—24no—
63C4⋊C4×C19—22no—
64(C2×D19)⋊C4—24no—
65(C2×D19)⋊C4—24no—
66(C2×D19)⋊C4—24no—
67(C2×D19)⋊C4—24no—
68(C2×D19)⋊C4—42no—
69(C2×D19)⋊C4—42no—
70C4⋊Dic19—22no—
71Dic19⋊C4—22no—
72Dic19⋊C4—22no—
73Dic19⋊C4—24no—
74Dic19⋊C4—42no—
75C23×C19C2411yescharacteristic
76C22×D19—22no—
77C22×D19—22no—
78C22×D19—22no—
79C22×D19—22no—
80C22×D19—22no—
81C22×D19—22no—
82C22×D19—22no—
83C22×D19—22no—
84C22×D19—22no—
85C22×D19C2×D412yes—
86C22×D19C2×D412yes—
87C22×D19#4112yes—
88C2×C4×C19—21no—
89C2×C4×C19—21no—
90C2×C4×C19—22no—
91C2×C4×C19—21no—
92C2×C4×C19—22no—
93C2×C4×C19—22no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19C2×D412yes—
100C2×C4×C19C2×D412yes—
101C2×Dic19—21no—
102C2×Dic19—21no—
103C2×Dic19—22no—
104C2×Dic19—21no—
105C2×Dic19—22no—
106C2×Dic19—22no—
107C2×Dic19—22no—
108C2×Dic19—22no—
109C2×Dic19C2×D412yes—
110C2×Dic19C2×D412yes—
111D76—44no—
112D76—48no—
113C4×D19—28no—
114C4×D19—44no—
115C4×D19—44no—
116#2618—191nomaximal, Sylow
117C22×C19C22×D411yescharacteristic
118C22×C19C22×D411yescharacteristic
119C22×C19C2×#4111yescharacteristic
120C22×C19H(5,𝔽2)12yes—
121C22×C192−1+412yes—
122C2×D19—22no—
123C2×D19—22no—
124C2×D19—24no—
125C2×D19—24no—
126C2×D19—42no—
127C2×D19—42no—
128C2×D19—42no—
129C2×D19—42no—
130C2×D19—42no—
131C2×D19—42no—
132C2×D19—42no—
133C2×D19#12114yes—
134C4×C19—22no—
135C4×C19—22no—
136C4×C19—42no—
137C4×C19—41no—
138C4×C19—42no—
139Dic19—22no—
140Dic19—22no—
141Dic19—41no—
142Dic19—42no—
143C2×#123—192no—
144C2×#121—191no—
145C22×C4⋊C4—191no—
146#398—191no—
147#398D1911yescharacteristic, complemented
148#396—192no—
149#396—192no—
150#394—191no—
151#394—191no—
152#386—192no—
153#380—191no—
154C2×C19C2×#12111yescharacteristic
155C2×C19#53411yescharacteristic
156C2×C19#53611yescharacteristic
157C2×C19#53712yes—
158C2×C19#53912yes—
159D19—24no—
160D19—82no—
161C22×D4—192no—
162C22×D4—191no—
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—192no—
172C2×C4⋊C4—192no—
173C2×C4⋊C4—384no—
174C2×C4⋊C4C2×D1911yescharacteristic
175C2×C4⋊C4C2×D1911yescharacteristic
176C2×C4⋊C4C2×D1912yes—
177C2×C22⋊C4—192no—
178C2×C22⋊C4—192no—
179C2×C22⋊C4—192no—
180C2×C22⋊C4—192no—
181C2×C22⋊C4—192no—
182C2×C22⋊C4—192no—
183#95—191no—
184#95—192no—
185#95C2×D1911yescharacteristic
186#95C2×D1912yes—
187C19#261811yescharacteristic, complemented, Sylow
188C24—191no—
189C24—192no—
190C2×D4—384no—
191C2×D4—384no—
192C2×D4—384no—
193C2×D4—382no—
194C2×D4—762no—
195C22×C4—191no—
196C22×C4—191no—
197C22×C4—194no—
198C22×C4—194no—
199C22×C4—192no—
200C22×C4—191no—
201C22×C4—382no—
202C22×C4—382no—
203C22×C4—382no—
204C22×C4—762no—
205C22×C4—762no—
206C22×C4C22×D1912yes—
207C22×C4C22×D1912yes—
208C22×C4C22×D1911yescharacteristic
209C22×C4C22×D1911yescharacteristic
210C22×C4C22×D1911yescharacteristic
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—24no—
214C4⋊C4—382no—
215C4⋊C4—384no—
216C4⋊C4—382no—
217C4⋊C4—382no—
218C4⋊C4—762no—
219C22⋊C4—384no—
220C22⋊C4—384no—
221C22⋊C4—384no—
222C22⋊C4—384no—
223C22⋊C4—762no—
224C22⋊C4—762no—
225C23—192no—
226C23—192no—
227C23—192no—
228C23—382no—
229C23—382no—
230C23—382no—
231C23—382no—
232C23—382no—
233C23—382no—
234C23—382no—
235C23—382no—
236C23—382no—
237C23C23×D1911yescharacteristic
238D4—764no—
239D4—768no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—192no—
252C2×C4—192no—
253C2×C4—388no—
254C2×C4—381no—
255C2×C4—381no—
256C2×C4—382no—
257C2×C4—382no—
258C2×C4—381no—
259C2×C4—382no—
260C2×C4—382no—
261C2×C4—382no—
262C2×C4—764no—
263C2×C4—764no—
264C2×C4D4×D1912yes—
265C2×C4D4×D1912yes—
266C22—194no—
267C22—382no—
268C22—382no—
269C22—384no—
270C22—384no—
271C22—762no—
272C22—762no—
273C22—762no—
274C22—762no—
275C22—762no—
276C22—762no—
277C22—762no—
278C22C2×D4×D1911yescharacteristic
279C22C2×D4×D1911yescharacteristic
280C22#1059743312yes—
281C22#41×D1911yescharacteristic
282C22#1059743512yes—
283C4—22no—
284C4—22no—
285C4—41no—
286C4—42no—
287C4—42no—
288C4—382no—
289C4—382no—
290C4—761no—
291C4—762no—
292C2—384no—
293C2—1522no—
294C2#121×D1911yescharacteristic
295C2#1192710511yescharacteristic
296C2#1192711911yescharacteristic
297C2#1192712412yes—
298C2#1192714212yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#398C2
prime radicalC2×#10597341C2
hypercenter#398D19
hypocenterC19#2618
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#10597340C2semidirect
3. C2×C4⋊C4×D19C2semidirect
4. #11926475C2semidirect
5. #11926468C2semidirect
6. #11926466C2semidirect
7. #11926462C2semidirect
8. #11926461C2semidirect
9. #11926422C2semidirect
10. #11926403C2semidirect
11. C19×#398C2semidirect
60. C2×C4×D19D4semidirect
147. #398D19semidirect
187. C19#2618semidirect

Maximal subgroups

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

subgroupindex
C2×#105973402
C2×#105973412
C2×C4⋊C4×D192
#119264752
#119264682
#119264662
#119264622
#119264612
#119264222
#119264032
C19×#3982
#261819