Finite Group Databasebeta

← #14568703

Subgroups — #14568703

Order 2432.

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

normal subgroups only

This group has 696 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×#10597331C212yesmaximal, complemented
2C2×#10597385C212yesmaximal, complemented
3#11926464C211yesmaximal, characteristic, complemented
4#11926453C212yesmaximal, complemented
5#11926445C211yesmaximal, characteristic, complemented
6#11926433C212yesmaximal, complemented
7#11926421C212yesmaximal, complemented
8C22⋊C4×Dic19C212yesmaximal, complemented
9C19×#394C211yesmaximal, characteristic, complemented
10C22×D4×C19C2211yescharacteristic
11C22×C22⋊D19C2212yes—
12C22×C22⋊D19C2212yes—
13C23×Dic19C2212yes—
14C22×D76C2211yescharacteristic
15C22×Dic38C2211yescharacteristic
16C2×C4⋊C4×C19C2211yescharacteristic
17C2×C22⋊C4×C19C2212yes—
18C2×C22⋊C4×C19C2212yes—
19C2×C22⋊Dic19C2212yes—
20#10597385—28no—
21C2×(C2×D19)⋊C4C2212yes—
22C2×(C2×D19)⋊C4C2212yes—
23C2×(C2×D19)⋊C4C2212yes—
24C2×(C2×D19)⋊C4C2212yes—
25C2×Dic19⋊C4C2212yes—
26C2×C4×Dic19C2212yes—
27C2×C4×Dic19C2211yescharacteristic
28#10597331—28no—
29C19×#95C2211yescharacteristic
30C19⋊#95C2212yes—
31C19⋊#95C2212yes—
32C19⋊#95C2211yescharacteristic
33C24×C19C2312yes—
34C23×D19C2312yes—
35C2×D4×C19—24no—
36C2×D4×C19—41no—
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2312yes—
39C22×C4×C19C2311yescharacteristic
40C22×C4×C19C2311yescharacteristic
41C2×C22⋊D19—24no—
42C2×C22⋊D19—24no—
43C2×C22⋊D19—24no—
44C2×C22⋊D19—24no—
45C2×C22⋊D19—42no—
46C2×C22⋊D19—42no—
47C22×Dic19—24no—
48C22×Dic19—24no—
49C22×Dic19—42no—
50C22×Dic19C2312yes—
51C22×Dic19C2312yes—
52C22×Dic19C2312yes—
53C2×D76—22no—
54C2×D76—41no—
55C2×D76—41no—
56C2×Dic38—24no—
57C2×Dic38—41no—
58C4⋊C4×C19—41no—
59C22⋊C4×C19—24no—
60C22⋊C4×C19—24no—
61C22⋊Dic19D418yescomplemented
62(C2×D19)⋊C4—24no—
63(C2×D19)⋊C4—24no—
64(C2×D19)⋊C4—24no—
65(C2×D19)⋊C4—24no—
66Dic19⋊C4—24no—
67C4×Dic19—24no—
68C4×Dic19—41no—
69C23×C19—22no—
70C23×C19—22no—
71C23×C19—22no—
72C23×C19—22no—
73C23×C19—22no—
74C23×C19—22no—
75C23×C19C2×D414yes—
76C23×C19C2411yescharacteristic
77C22×D19—22no—
78C22×D19—22no—
79C22×D19—22no—
80C22×D19—22no—
81C22×D19—22no—
82C22×D19—22no—
83C22×D19—22no—
84D4×C19—44no—
85C2×C4×C19—21no—
86C2×C4×C19—21no—
87C2×C4×C19—22no—
88C2×C4×C19—22no—
89C2×C4×C19—22no—
90C2×C4×C19—22no—
91C2×C4×C19—22no—
92C2×C4×C19—21no—
93C2×C4×C19—21no—
94C2×C4×C19#4112yes—
95C22⋊D19—48no—
96C22⋊D19—48no—
97C2×Dic19—22no—
98C2×Dic19—22no—
99C2×Dic19—22no—
100C2×Dic19—22no—
101C2×Dic19—22no—
102C2×Dic19—22no—
103C2×Dic19—48no—
104C2×Dic19C2×D414yes—
105C2×Dic19C2×D414yes—
106C2×Dic19#4114yes—
107D76—44no—
108Dic38—44no—
109#2555—191nomaximal, Sylow
110C22×C19—24no—
111C22×C19—24no—
112C22×C19—24no—
113C22×C19—42no—
114C22×C19—42no—
115C22×C19—42no—
116C22×C19—42no—
117C22×C19C22×D412yes—
118C22×C19C2×#4111yescharacteristic
119C22×C19C2×#4112yes—
120C22×C19H(5,𝔽2)11yescharacteristic
121C22×C19H(5,𝔽2)11yescharacteristic
122C2×D19—42no—
123C2×D19—42no—
124C2×D19—42no—
125C2×D19—42no—
126C2×D19—42no—
127C2×D19—42no—
128C2×D19—42no—
129C4×C19—22no—
130C4×C19—42no—
131C4×C19—41no—
132C4×C19—41no—
133Dic19—24no—
134Dic19—24no—
135Dic19—24no—
136C2×#124—192no—
137C2×#121—192no—
138#395—191no—
139#394D1911yescharacteristic, complemented
140#392—192no—
141#390—191no—
142#388—192no—
143#386—192no—
144C4×C22⋊C4—192no—
145C2×C19—44no—
146C2×C19#53212yes—
147C2×C19#53811yescharacteristic
148C2×C19D4211yescharacteristic
149C2×C19#54612yes—
150C2×C19#55511yescharacteristic
151D19—82no—
152C22×Q8—191no—
153C22×D4—192no—
154C22×D4—192no—
155C22×D4—191no—
156C22×D4C2×D1911yescharacteristic
157C23×C4—192no—
158#124—388no—
159#121—388no—
160C2×C4⋊C4—192no—
161C2×C4⋊C4C2×D1911yescharacteristic
162C2×C22⋊C4—192no—
163C2×C22⋊C4—192no—
164C2×C22⋊C4—192no—
165C2×C22⋊C4—192no—
166C2×C22⋊C4—192no—
167C2×C22⋊C4C2×D1912yes—
168C2×C22⋊C4C2×D1912yes—
169C2×C42—192no—
170C2×C42—191no—
171#95—192no—
172#95—192no—
173#95—191no—
174#95C2×D1911yescharacteristic
175C19#255511yescharacteristic, complemented, Sylow
176C24—192no—
177C24C22×D1912yes—
178C2×Q8—384no—
179C2×Q8—761no—
180C2×D4—24no—
181C2×D4—41no—
182C2×D4—384no—
183C2×D4—384no—
184C2×D4—384no—
185C2×D4—384no—
186C2×D4—382no—
187C2×D4—761no—
188C2×D4—761no—
189C2×D4—762no—
190C2×D4—762no—
191C22×C4—192no—
192C22×C4—192no—
193C22×C4—192no—
194C22×C4—384no—
195C22×C4—384no—
196C22×C4—762no—
197C22×C4C22×D1912yes—
198C22×C4C22×D1911yescharacteristic
199C22×C4C22×D1911yescharacteristic
200C22×C4C22×D1911yescharacteristic
201C4⋊C4—41no—
202C4⋊C4—384no—
203C22⋊C4—24no—
204C22⋊C4—24no—
205C22⋊C4—198no—
206C22⋊C4—384no—
207C22⋊C4—384no—
208C22⋊C4—384no—
209C22⋊C4—384no—
210C42—384no—
211C42—761no—
212C23—22no—
213C23—22no—
214C23—22no—
215C23—22no—
216C23—22no—
217C23—22no—
218C23—382no—
219C23—382no—
220C23—382no—
221C23—382no—
222C23—382no—
223C23—382no—
224C23—382no—
225C23D4×D1914yes—
226C23C23×D1911yescharacteristic
227Q8—764no—
228D4—44no—
229D4—764no—
230D4—768no—
231D4—768no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—194no—
242C2×C4—194no—
243C2×C4—194no—
244C2×C4—382no—
245C2×C4—382no—
246C2×C4—382no—
247C2×C4—382no—
248C2×C4—382no—
249C2×C4—382no—
250C2×C4—768no—
251C2×C4#6454312yes—
252C22—24no—
253C22—24no—
254C22—24no—
255C22—42no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—762no—
260C22—762no—
261C22—762no—
262C22—762no—
263C22—762no—
264C22—762no—
265C22—762no—
266C22C2×D4×D1912yes—
267C22C2×#6454311yescharacteristic
268C22#1059743011yescharacteristic
269C22#41×D1912yes—
270C22#1059743511yescharacteristic
271C4—22no—
272C4—42no—
273C4—41no—
274C4—41no—
275C4—384no—
276C4—384no—
277C4—384no—
278C2—44no—
279C2—1522no—
280C2#1192708912yes—
281C2#1192713111yescharacteristic
282C2#1192717611yescharacteristic
283C2#1192718612yes—
284C2#1192725611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#394C2
hypercenter#394D19
hypocenterC19#2555
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#10597331C2semidirect
2. C2×#10597385C2semidirect
3. #11926464C2semidirect
4. #11926453C2semidirect
5. #11926445C2semidirect
6. #11926433C2semidirect
7. #11926421C2semidirect
8. C22⋊C4×Dic19C2semidirect
9. C19×#394C2semidirect
61. C22⋊Dic19D4semidirect
139. #394D19semidirect
175. C19#2555semidirect

Maximal subgroups

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

subgroupindex
C2×#105973312
C2×#105973852
#119264642
#119264532
#119264452
#119264332
#119264212
C22⋊C4×Dic192
C19×#3942
#255519