Finite Group Databasebeta

← #14568583

Subgroups — #14568583

Order 2432.

676 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 171 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×#10597334C211yesmaximal, characteristic, complemented
2C2×#10597342C212yesmaximal, complemented
3C2×#10597324C212yesmaximal, complemented
4C2×(C22⋊D19)⋊C4C211yesmaximal, characteristic
5#11926481C211yesmaximal, characteristic, complemented
6#11926480C211yesmaximal, characteristic, complemented
7#11926479C211yesmaximal, characteristic, complemented
8#11926444C212yesmaximal
9#11926413C212yesmaximal, complemented
10#11926395C211yesmaximal, characteristic, complemented
11C19×#399C211yesmaximal, characteristic, complemented
12C22×C22⋊D19C2211yescharacteristic
13C23×Dic19C2211yescharacteristic
14C22×C4×D19C2211yescharacteristic
15C22×Dic38C2212yes—
16C2×C4⋊C4×C19C2212yes—
17C2×C4⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19C2212yes—
19C2×C22⋊C4×C19C2211yescharacteristic
20C2×C22⋊Dic19C2212yes—
21C2×(C2×D19)⋊C4C2212yes—
22C2×(C2×D19)⋊C4C2212yes—
23C2×(C2×D19)⋊C4C2211yescharacteristic
24C2×C4⋊Dic19C2212yes—
25C2×C4⋊Dic19C2211yescharacteristic
26C2×Dic19⋊C4C2212yes—
27C2×Dic19⋊C4C2212yes—
28C2×Dic19⋊C4C2212yes—
29C2×Dic19⋊C4C2211yescharacteristic
30C2×Dic19⋊C4C2212yes—
31C2×C4×Dic19C2212yes—
32C2×C4×Dic19C2211yescharacteristic
33#10597342—28no—
34#10597334—24no—
35(C22⋊D19)⋊C4—24no—
36#10597324—28no—
37C19×#95C2211yescharacteristic
38C19⋊#95C2211yescharacteristic
39C24×C19C2311yescharacteristic
40C23×D19C2311yescharacteristic
41C22×C4×C19C2312yes—
42C22×C4×C19C2311yescharacteristic
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2312yes—
45C2×C22⋊D19—22no—
46C2×C22⋊D19—22no—
47C2×C22⋊D19Q814yescomplemented
48C22×Dic19—24no—
49C22×Dic19—22no—
50C22×Dic19C2312yes—
51C22×Dic19C2311yescharacteristic
52C22×Dic19C2312yes—
53C22×Dic19C2311yescharacteristic
54C22×Dic19C2311yescharacteristic
55C2×C4×D19—22no—
56C2×C4×D19—24no—
57C2×Dic38—24no—
58C2×Dic38—24no—
59C2×Dic38—24no—
60C4⋊C4×C19—22no—
61C4⋊C4×C19—24no—
62C22⋊C4×C19—24no—
63C22⋊C4×C19—22no—
64C22⋊Dic19—24no—
65(C2×D19)⋊C4—22no—
66(C2×D19)⋊C4—24no—
67(C2×D19)⋊C4—24no—
68C4⋊Dic19—24no—
69C4⋊Dic19—22no—
70Dic19⋊C4—24no—
71Dic19⋊C4—22no—
72Dic19⋊C4—24no—
73Dic19⋊C4—24no—
74Dic19⋊C4D418yescomplemented
75C4×Dic19—24no—
76C4×Dic19D414yes—
77C23×C19—22no—
78C23×C19—21no—
79C23×C19—21no—
80C23×C19—22no—
81C23×C19C2×Q812yes—
82C23×C19C2411yescharacteristic
83C22×D19—22no—
84C22×D19—21no—
85C22×D19—21no—
86C22×D19—22no—
87C22×D19C2×Q812yes—
88C2×C4×C19—22no—
89C2×C4×C19—22no—
90C2×C4×C19—22no—
91C2×C4×C19—22no—
92C2×C4×C19—21no—
93C2×C4×C19—22no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19C2×D412yes—
97C2×C4×C19C2×D414yes—
98C22⋊D19—28no—
99C2×Dic19—22no—
100C2×Dic19—22no—
101C2×Dic19—22no—
102C2×Dic19—22no—
103C2×Dic19—22no—
104C2×Dic19—21no—
105C2×Dic19—22no—
106C2×Dic19—44no—
107C2×Dic19C2×D414yes—
108C2×Dic19C2×D412yes—
109C2×Dic19C2×D412yes—
110C2×Dic19C2×D414yes—
111C2×Dic19C2×Q812yes—
112C2×Dic19#4112yes—
113C4×D19—44no—
114Dic38—48no—
115#2542—191nomaximal, Sylow
116C22×C19—22no—
117C22×C19—24no—
118C22×C19—41no—
119C22×C19—41no—
120C22×C19—42no—
121C22×C19C22×D411yescharacteristic
122C22×C19C22×D412yes—
123C22×C19C22×Q811yescharacteristic
124C22×C19C2×#4111yescharacteristic
125C22×C192−1+412yes—
126C2×D19—22no—
127C2×D19—24no—
128C2×D19—41no—
129C2×D19—41no—
130C2×D19—42no—
131C4×C19—22no—
132C4×C19—24no—
133C4×C19—42no—
134C4×C19—41no—
135Dic19—24no—
136Dic19—42no—
137Dic19—41no—
138Dic19C22⋊Q814yescomplemented
139Dic19#12714yes—
140C2×C4⋊Q8—191no—
141C2×C22⋊Q8—192no—
142C2×C22⋊Q8—192no—
143C2×C4×D4—191no—
144#399—191no—
145#399—191no—
146#399—191no—
147#399D1911yescharacteristic, complemented
148#390—192no—
149#384—192no—
150C4×C4⋊C4—191no—
151C2×C19—42no—
152C2×C19C2×C22⋊Q811yescharacteristic
153C2×C19C2×#12711yescharacteristic
154C2×C19#53611yescharacteristic
155C2×C19#54712yes—
156C2×C19D4×Q812yes—
157D19—42no—
158C22×Q8—192no—
159C22×D4—191no—
160C23×C4—191no—
161C23×C4—191no—
162C4⋊Q8—384no—
163C22⋊Q8—388no—
164C22⋊Q8—388no—
165C4×D4—384no—
166C2×C4⋊C4—192no—
167C2×C4⋊C4—191no—
168C2×C4⋊C4—192no—
169C2×C4⋊C4—192no—
170C2×C4⋊C4—192no—
171C2×C4⋊C4—192no—
172C2×C4⋊C4—191no—
173C2×C4⋊C4C2×D1912yes—
174C2×C4⋊C4C2×D1911yescharacteristic
175C2×C22⋊C4—192no—
176C2×C22⋊C4—191no—
177C2×C22⋊C4—192no—
178C2×C22⋊C4—192no—
179C2×C22⋊C4C2×D1911yescharacteristic
180C2×C22⋊C4C2×D1912yes—
181C2×C42—191no—
182C2×C42—192no—
183#95—191no—
184#95C2×D1911yescharacteristic
185C19#254211yescharacteristic, complemented, Sylow
186C24—191no—
187C24C22×D1911yescharacteristic
188C2×Q8—384no—
189C2×Q8—384no—
190C2×Q8—384no—
191C2×D4—194no—
192C2×D4—382no—
193C2×D4—382no—
194C22×C4—191no—
195C22×C4—191no—
196C22×C4—192no—
197C22×C4—192no—
198C22×C4—191no—
199C22×C4—382no—
200C22×C4—384no—
201C22×C4—382no—
202C22×C4—384no—
203C22×C4C22×D1912yes—
204C22×C4C22×D1911yescharacteristic
205C22×C4C22×D1911yescharacteristic
206C22×C4C22×D1912yes—
207C4⋊C4—24no—
208C4⋊C4—22no—
209C4⋊C4—198no—
210C4⋊C4—382no—
211C4⋊C4—384no—
212C4⋊C4—384no—
213C4⋊C4—384no—
214C4⋊C4—384no—
215C4⋊C4—382no—
216C22⋊C4—22no—
217C22⋊C4—24no—
218C22⋊C4—384no—
219C22⋊C4—384no—
220C22⋊C4—382no—
221C22⋊C4—384no—
222C42—194no—
223C42—384no—
224C23—22no—
225C23—21no—
226C23—21no—
227C23—22no—
228C23—192no—
229C23—382no—
230C23—381no—
231C23—381no—
232C23—382no—
233C23Q8×D1912yes—
234C23C23×D1911yescharacteristic
235Q8—768no—
236D4—388no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—192no—
246C2×C4—192no—
247C2×C4—194no—
248C2×C4—192no—
249C2×C4—192no—
250C2×C4—194no—
251C2×C4—382no—
252C2×C4—382no—
253C2×C4—381no—
254C2×C4—382no—
255C2×C4—382no—
256C2×C4—382no—
257C2×C4—382no—
258C2×C4—764no—
259C2×C4—764no—
260C2×C4D4×D1912yes—
261C2×C4D4×D1914yes—
262C22—24no—
263C22—22no—
264C22—41no—
265C22—41no—
266C22—42no—
267C22—384no—
268C22—382no—
269C22—761no—
270C22—761no—
271C22—762no—
272C22C2×D4×D1911yescharacteristic
273C22C2×D4×D1912yes—
274C22C2×Q8×D1911yescharacteristic
275C22#41×D1911yescharacteristic
276C22#1059743612yes—
277C4—22no—
278C4—24no—
279C4—41no—
280C4—42no—
281C4—194no—
282C4—194no—
283C4—384no—
284C4—761no—
285C4—762no—
286C2—42no—
287C2—762no—
288C2C22⋊Q8×D1911yescharacteristic
289C2#127×D1911yescharacteristic
290C2#1192711611yescharacteristic
291C2#1192719212yes—
292C2#1192720712yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#399C2
prime radicalC22×C22⋊D19C22
hypercenter#399D19
hypocenterC19#2542
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#10597334C2semidirect
2. C2×#10597342C2semidirect
3. C2×#10597324C2semidirect
5. #11926481C2semidirect
6. #11926480C2semidirect
7. #11926479C2semidirect
9. #11926413C2semidirect
10. #11926395C2semidirect
11. C19×#399C2semidirect
47. C2×C22⋊D19Q8semidirect
74. Dic19⋊C4D4semidirect
138. Dic19C22⋊Q8semidirect
147. #399D19semidirect
185. C19#2542semidirect

Maximal subgroups

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

subgroupindex
C2×#105973342
C2×#105973422
C2×#105973242
C2×(C22⋊D19)⋊C42
#119264812
#119264802
#119264792
#119264442
#119264132
#119263952
C19×#3992
#254219