Finite Group Databasebeta

← #14569775

Subgroups — #14569775

Order 2432.

534 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 137 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×#10597321C211yesmaximal, characteristic, complemented
2#11926466C212yesmaximal, complemented
3#11926464C211yesmaximal, characteristic, complemented
4#11926461C211yesmaximal, characteristic, complemented
5#11926460C212yesmaximal, complemented
6#11926456C211yesmaximal, characteristic, complemented
7#11926453C211yesmaximal, characteristic
8#11926444C212yesmaximal, complemented
9#11926434C212yesmaximal, complemented
10C4×C4⋊Dic19C211yesmaximal, characteristic, complemented
11C2×C19×#126C211yesmaximal, characteristic, complemented
12C22×C22⋊D19C2212yes—
13C22×D76C2211yescharacteristic
14C22×Dic38C2211yescharacteristic
15C19×#126—24no—
16C2×C4⋊C4×C19C2211yescharacteristic
17C2×C4⋊C4×C19C2211yescharacteristic
18C2×C4⋊C4×C19C2211yescharacteristic
19C2×C22⋊C4×C19C2211yescharacteristic
20C2×C22⋊C4×C19C2211yescharacteristic
21C2×C22⋊C4×C19C2211yescharacteristic
22C2×C42×C19C2211yescharacteristic
23C2×C22⋊Dic19C2212yes—
24C2×(C2×D19)⋊C4C2212yes—
25C2×(C2×D19)⋊C4C2212yes—
26C2×(C2×D19)⋊C4C2212yes—
27C2×(C2×D19)⋊C4C2212yes—
28C2×(C2×D19)⋊C4C2212yes—
29C2×C4⋊Dic19C2212yes—
30C2×Dic19⋊C4C2212yes—
31C2×C4×Dic19C2212yes—
32#10597321—24no—
33C19⋊#95C2211yescharacteristic
34C19⋊#95C2211yescharacteristic
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C24×C19C2311yescharacteristic
38C23×D19C2312yes—
39C22×C4×C19C2311yescharacteristic
40C22×C4×C19C2311yescharacteristic
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2311yescharacteristic
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2311yescharacteristic
45C2×C22⋊D19—24no—
46C2×C22⋊D19—42no—
47C2×C22⋊D19—42no—
48C22×Dic19C2312yes—
49C22×Dic19C2312yes—
50C22×Dic19C2312yes—
51C2×D76—22no—
52C2×D76—42no—
53C2×Dic38—22no—
54C2×Dic38—42no—
55C4⋊C4×C19—22no—
56C4⋊C4×C19—22no—
57C4⋊C4×C19—22no—
58C22⋊C4×C19—22no—
59C22⋊C4×C19—22no—
60C22⋊C4×C19—22no—
61C42×C19D414yescomplemented
62C22⋊Dic19—42no—
63(C2×D19)⋊C4—24no—
64(C2×D19)⋊C4—24no—
65(C2×D19)⋊C4—24no—
66(C2×D19)⋊C4—42no—
67(C2×D19)⋊C4—42no—
68C4⋊Dic19—24no—
69Dic19⋊C4—42no—
70C4×Dic19—42no—
71C23×C19—21no—
72C23×C19—22no—
73C23×C19—22no—
74C23×C19—21no—
75C23×C19—21no—
76C23×C19C2411yescharacteristic
77C22×D19—22no—
78C22×D19—22no—
79C22×D19—22no—
80C22×D19—22no—
81C22×D19—22no—
82C22×D19—22no—
83C22×D19—22no—
84C2×C4×C19—22no—
85C2×C4×C19—21no—
86C2×C4×C19—22no—
87C2×C4×C19—21no—
88C2×C4×C19—21no—
89C2×C4×C19—21no—
90C2×C4×C19—21no—
91C2×C4×C19—22no—
92C2×C4×C19—22no—
93C2×C4×C19—21no—
94C2×C4×C19—21no—
95C2×C4×C19C2×D412yes—
96C2×C4×C19C2×D412yes—
97C2×C4×C19C2×D412yes—
98C22⋊D19—48no—
99C2×Dic19—22no—
100C2×Dic19—22no—
101C2×Dic19—22no—
102C2×Dic19—22no—
103C2×Dic19—22no—
104C2×Dic19—22no—
105C2×Dic19—22no—
106C2×Dic19—22no—
107C2×Dic19#4114yes—
108D76—44no—
109Dic38—44no—
110#2662—191nomaximal, Sylow
111C22×C19—41no—
112C22×C19—41no—
113C22×C19—41no—
114C22×C19—42no—
115C22×C19—42no—
116C22×C19C22×D411yescharacteristic
117C22×C19C2×#4112yes—
118C22×C19H(5,𝔽2)12yes—
119C22×C19H(5,𝔽2)11yescharacteristic
120C22×C192−1+411yescharacteristic
121C2×D19—42no—
122C2×D19—42no—
123C2×D19—42no—
124C2×D19—42no—
125C2×D19—42no—
126C2×D19—42no—
127C2×D19—42no—
128C4×C19—22no—
129C4×C19—22no—
130C4×C19—22no—
131C4×C19—41no—
132C4×C19—41no—
133C4×C19—41no—
134Dic19—24no—
135Dic19—42no—
136Dic19—42no—
137C2×#126D1911yescharacteristic, complemented
138C2×#124—191no—
139#396—192no—
140#395—191no—
141#394—191no—
142#394—192no—
143#393—191no—
144#392—191no—
145#390—192no—
146#388—192no—
147C4×C4⋊C4—191no—
148C2×C19—81no—
149C2×C19#53211yescharacteristic
150C2×C19#53511yescharacteristic
151C2×C19#53711yescharacteristic
152C2×C19#53812yes—
153C2×C19#54212yes—
154D19—82no—
155C22×Q8—191no—
156C22×D4—192no—
157C22×D4—191no—
158#126—24no—
159#124—384no—
160C2×C4⋊C4—192no—
161C2×C4⋊C4—192no—
162C2×C4⋊C4C2×D1911yescharacteristic
163C2×C4⋊C4C2×D1911yescharacteristic
164C2×C4⋊C4C2×D1911yescharacteristic
165C2×C22⋊C4—192no—
166C2×C22⋊C4—192no—
167C2×C22⋊C4—192no—
168C2×C22⋊C4—192no—
169C2×C22⋊C4—192no—
170C2×C22⋊C4—192no—
171C2×C22⋊C4C2×D1911yescharacteristic
172C2×C22⋊C4C2×D1911yescharacteristic
173C2×C22⋊C4C2×D1911yescharacteristic
174C2×C42—192no—
175C2×C42C2×D1911yescharacteristic
176#95—191no—
177#95—191no—
178#95—192no—
179#95—192no—
180C19#266211yescharacteristic, complemented, Sylow
181C24—192no—
182C24C22×D1911yescharacteristic
183C2×Q8—382no—
184C2×Q8—762no—
185C2×D4—384no—
186C2×D4—382no—
187C2×D4—762no—
188C2×D4—762no—
189C2×D4—762no—
190C22×C4—192no—
191C22×C4—192no—
192C22×C4—192no—
193C22×C4C22×D1911yescharacteristic
194C22×C4C22×D1911yescharacteristic
195C22×C4C22×D1911yescharacteristic
196C22×C4C22×D1911yescharacteristic
197C22×C4C22×D1911yescharacteristic
198C22×C4C22×D1911yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—384no—
203C4⋊C4—762no—
204C22⋊C4—22no—
205C22⋊C4—22no—
206C22⋊C4—22no—
207C22⋊C4—384no—
208C22⋊C4—384no—
209C22⋊C4—384no—
210C22⋊C4—762no—
211C22⋊C4—762no—
212C22⋊C4—762no—
213C42—762no—
214C42C22⋊D1914yescomplemented
215C23—22no—
216C23—22no—
217C23—21no—
218C23—21no—
219C23—21no—
220C23—382no—
221C23—382no—
222C23—382no—
223C23—382no—
224C23—382no—
225C23—382no—
226C23—382no—
227C23C23×D1911yescharacteristic
228Q8—764no—
229D4—764no—
230D4—768no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—194no—
243C2×C4—382no—
244C2×C4—382no—
245C2×C4—382no—
246C2×C4—382no—
247C2×C4—382no—
248C2×C4—382no—
249C2×C4—382no—
250C2×C4—382no—
251C2×C4C2×C22⋊D1912yes—
252C2×C4C2×C22⋊D1912yes—
253C2×C4C2×C22⋊D1912yes—
254C22—41no—
255C22—41no—
256C22—41no—
257C22—42no—
258C22—42no—
259C22—762no—
260C22—762no—
261C22—762no—
262C22—762no—
263C22—762no—
264C22—762no—
265C22—762no—
266C22#41×D1912yes—
267C22#1059743512yes—
268C22#1059743511yescharacteristic
269C22#1059743611yescharacteristic
270C22C22×C22⋊D1911yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—384no—
278C4—762no—
279C4—762no—
280C2—81no—
281C2—1522no—
282C2#1192709011yescharacteristic
283C2#1192710811yescharacteristic
284C2#1192712211yescharacteristic
285C2#1192713312yes—
286C2#1192716012yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#126C2
prime radical#11926453C2
hypercenterC2×#126D19
hypocenterC19#2662
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×#10597321C2semidirect
2. #11926466C2semidirect
3. #11926464C2semidirect
4. #11926461C2semidirect
5. #11926460C2semidirect
6. #11926456C2semidirect
8. #11926444C2semidirect
9. #11926434C2semidirect
10. C4×C4⋊Dic19C2semidirect
11. C2×C19×#126C2semidirect
61. C42×C19D4semidirect
137. C2×#126D19semidirect
180. C19#2662semidirect
214. C42C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973212
#119264662
#119264642
#119264612
#119264602
#119264562
#119264532
#119264442
#119264342
C4×C4⋊Dic192
C2×C19×#1262
#266219