Finite Group Databasebeta

← #14569322

Subgroups — #14569322

Order 2432.

576 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 145 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#11926464C211yesmaximal, characteristic, complemented
3#11926461C211yesmaximal, characteristic, complemented
4#11926456C211yesmaximal, characteristic, complemented
5#11926453C211yesmaximal, characteristic
6#11926444C212yesmaximal, complemented
7#11926435C212yesmaximal, complemented
8#11926434C212yesmaximal, complemented
9#11926423C212yesmaximal, complemented
10#11926390C211yesmaximal, characteristic, complemented
11C2×C19×#117C211yesmaximal, characteristic, complemented
12C23×C4×C19C2211yescharacteristic
13C22×C22⋊D19C2212yes—
14C22×D76C2211yescharacteristic
15C22×Dic38C2211yescharacteristic
16C19×#117—24no—
17C2×C4⋊C4×C19C2211yescharacteristic
18C2×C4⋊C4×C19C2211yescharacteristic
19C2×C22⋊C4×C19C2211yescharacteristic
20C2×C22⋊C4×C19C2211yescharacteristic
21C2×C42×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×Dic19⋊C4C2212yes—
30C2×C4×Dic19C2212yes—
31#10597321—24no—
32C19⋊#95C2212yes—
33C19⋊#95C2211yescharacteristic
34C19⋊#95C2211yescharacteristic
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C24×C19C2311yescharacteristic
38C23×D19C2312yes—
39C22×C4×C19—22no—
40C22×C4×C19—22no—
41C22×C4×C19—22no—
42C22×C4×C19C2311yescharacteristic
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2311yescharacteristic
46C22×C4×C19C2311yescharacteristic
47C22×C4×C19C2311yescharacteristic
48C2×C22⋊D19—24no—
49C2×C22⋊D19—24no—
50C2×C22⋊D19—42no—
51C22×Dic19C2312yes—
52C22×Dic19C2312yes—
53C22×Dic19C2312yes—
54C2×D76—22no—
55C2×D76—42no—
56C2×Dic38—22no—
57C2×Dic38—42no—
58C4⋊C4×C19—22no—
59C4⋊C4×C19—22no—
60C22⋊C4×C19—22no—
61C22⋊C4×C19—22no—
62C42×C19—22no—
63C42×C19D414yescomplemented
64C22⋊Dic19—42no—
65(C2×D19)⋊C4—24no—
66(C2×D19)⋊C4—24no—
67(C2×D19)⋊C4—24no—
68(C2×D19)⋊C4—24no—
69(C2×D19)⋊C4—42no—
70Dic19⋊C4—42no—
71C4×Dic19—24no—
72C23×C19—21no—
73C23×C19—22no—
74C23×C19—21no—
75C23×C19—22no—
76C23×C19#4112yes—
77C23×C19C2411yescharacteristic
78C22×D19—22no—
79C22×D19—22no—
80C22×D19—22no—
81C22×D19—22no—
82C22×D19—22no—
83C22×D19—22no—
84C22×D19—22no—
85C2×C4×C19—28no—
86C2×C4×C19—21no—
87C2×C4×C19—22no—
88C2×C4×C19—21no—
89C2×C4×C19—21no—
90C2×C4×C19—21no—
91C2×C4×C19—22no—
92C2×C4×C19—21no—
93C2×C4×C19—21no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19C2×D412yes—
97C2×C4×C19C2×D412yes—
98C2×C4×C19C2×D412yes—
99C2×C4×C19#4112yes—
100C22⋊D19—48no—
101C2×Dic19—22no—
102C2×Dic19—22no—
103C2×Dic19—22no—
104C2×Dic19—22no—
105C2×Dic19—22no—
106C2×Dic19—22no—
107C2×Dic19—22no—
108C2×Dic19—22no—
109C2×Dic19#4114yes—
110D76—44no—
111Dic38—44no—
112#2610—191nomaximal, Sylow
113C22×C19—22no—
114C22×C19—24no—
115C22×C19—41no—
116C22×C19—41no—
117C22×C19—42no—
118C22×C19C22×D411yescharacteristic
119C22×C19C2×#4111yescharacteristic
120C22×C19C2×#4111yescharacteristic
121C22×C19C2×#4112yes—
122C22×C19H(5,𝔽2)12yes—
123C2×D19—42no—
124C2×D19—42no—
125C2×D19—42no—
126C2×D19—42no—
127C2×D19—42no—
128C2×D19—42no—
129C2×D19—42no—
130C4×C19—22no—
131C4×C19—22no—
132C4×C19—22no—
133C4×C19—22no—
134C4×C19—41no—
135C4×C19—41no—
136Dic19—24no—
137Dic19—42no—
138Dic19—42no—
139C2×#124—191no—
140C2×#117D1911yescharacteristic, complemented
141#395—191no—
142#394—191no—
143#393—191no—
144#392—191no—
145#390—192no—
146#388—192no—
147#388—192no—
148#386—192no—
149#376—191no—
150C2×C19—42no—
151C2×C19#52511yescharacteristic
152C2×C19#53211yescharacteristic
153C2×C19#53511yescharacteristic
154C2×C19#55112yes—
155C2×C19#55512yes—
156D19—82no—
157C22×Q8—191no—
158C22×D4—192no—
159C22×D4—191no—
160C23×C4C2×D1911yescharacteristic
161#124—384no—
162#117—24no—
163C2×C4⋊C4—192no—
164C2×C4⋊C4C2×D1911yescharacteristic
165C2×C4⋊C4C2×D1911yescharacteristic
166C2×C22⋊C4—192no—
167C2×C22⋊C4—192no—
168C2×C22⋊C4—192no—
169C2×C22⋊C4—192no—
170C2×C22⋊C4—192no—
171C2×C22⋊C4—192no—
172C2×C22⋊C4C2×D1911yescharacteristic
173C2×C22⋊C4C2×D1911yescharacteristic
174C2×C42—192no—
175C2×C42C2×D1911yescharacteristic
176C2×C42C2×D1911yescharacteristic
177#95—192no—
178#95—191no—
179#95—191no—
180#95—192no—
181#95—192no—
182C19#261011yescharacteristic, complemented, Sylow
183C24—192no—
184C24C22×D1911yescharacteristic
185C2×Q8—382no—
186C2×Q8—762no—
187C2×D4—384no—
188C2×D4—384no—
189C2×D4—382no—
190C2×D4—762no—
191C2×D4—762no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—192no—
196C22×C4—192no—
197C22×C4—192no—
198C22×C4C22×D1911yescharacteristic
199C22×C4C22×D1911yescharacteristic
200C22×C4C22×D1911yescharacteristic
201C22×C4C22×D1911yescharacteristic
202C22×C4C22×D1911yescharacteristic
203C22×C4C22×D1911yescharacteristic
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4—762no—
207C22⋊C4—22no—
208C22⋊C4—22no—
209C22⋊C4—384no—
210C22⋊C4—384no—
211C22⋊C4—384no—
212C22⋊C4—384no—
213C22⋊C4—762no—
214C22⋊C4—762no—
215C42—22no—
216C42—384no—
217C42C22⋊D1914yescomplemented
218C23—21no—
219C23—22no—
220C23—22no—
221C23—21no—
222C23—382no—
223C23—382no—
224C23—382no—
225C23—382no—
226C23—382no—
227C23—382no—
228C23—382no—
229C23#6454112yes—
230C23C23×D1911yescharacteristic
231Q8—764no—
232D4—764no—
233D4—768no—
234C2×C4—28no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—194no—
246C2×C4—382no—
247C2×C4—382no—
248C2×C4—382no—
249C2×C4—382no—
250C2×C4—382no—
251C2×C4—382no—
252C2×C4—382no—
253C2×C4—382no—
254C2×C4#6454112yes—
255C2×C4C2×C22⋊D1912yes—
256C2×C4C2×C22⋊D1912yes—
257C2×C4C2×C22⋊D1912yes—
258C22—22no—
259C22—24no—
260C22—41no—
261C22—41no—
262C22—42no—
263C22—762no—
264C22—762no—
265C22—762no—
266C22—762no—
267C22—762no—
268C22—762no—
269C22—762no—
270C22C2×#6454111yescharacteristic
271C22C2×#6454111yescharacteristic
272C22#41×D1912yes—
273C22#1059743512yes—
274C22C22×C22⋊D1911yescharacteristic
275C4—22no—
276C4—22no—
277C4—22no—
278C4—22no—
279C4—41no—
280C4—41no—
281C4—384no—
282C4—762no—
283C4—762no—
284C2—42no—
285C2—1522no—
286C2#1192705511yescharacteristic
287C2#1192709011yescharacteristic
288C2#1192710811yescharacteristic
289C2#1192721812yes—
290C2#1192725712yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#117C2
prime radical#11926453C2
hypercenterC2×#117D19
hypocenterC19#2610
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×#10597321C2semidirect
2. #11926464C2semidirect
3. #11926461C2semidirect
4. #11926456C2semidirect
6. #11926444C2semidirect
7. #11926435C2semidirect
8. #11926434C2semidirect
9. #11926423C2semidirect
10. #11926390C2semidirect
11. C2×C19×#117C2semidirect
63. C42×C19D4semidirect
140. C2×#117D19semidirect
182. C19#2610semidirect
217. C42C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973212
#119264642
#119264612
#119264562
#119264532
#119264442
#119264352
#119264342
#119264232
#119263902
C2×C19×#1172
#261019