Finite Group Databasebeta

← #14569520

Subgroups — #14569520

Order 2432.

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

normal subgroups only

This group has 620 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×C4×C22⋊D19C211yesmaximal, characteristic, complemented
2#11926482C211yesmaximal, characteristic, complemented
3#11926479C211yesmaximal, characteristic, complemented
4#11926458C211yesmaximal, characteristic, complemented
5#11926458C212yesmaximal, complemented
6#11926452C212yesmaximal, complemented
7#11926452C211yesmaximal, characteristic, complemented
8#11926432C212yesmaximal, complemented
9#11926420C212yesmaximal, complemented
10#11926407C211yesmaximal, characteristic, complemented
11C2×C19×#121C211yesmaximal, characteristic, complemented
12C22×D4×C19C2212yes—
13C22×D4×C19C2211yescharacteristic
14C23×C4×C19C2211yescharacteristic
15C22×C22⋊D19C2211yescharacteristic
16C22×C22⋊D19C2212yes—
17C22×C4×D19C2211yescharacteristic
18C19×#121—24no—
19C2×C4⋊C4×C19C2211yescharacteristic
20C2×C22⋊C4×C19C2212yes—
21C2×C22⋊Dic19C2212yes—
22C2×C22⋊Dic19C2211yescharacteristic
23C2×C22⋊Dic19C2212yes—
24C2×C22⋊Dic19C2212yes—
25C2×C22⋊Dic19C2212yes—
26C4×C22⋊D19—24no—
27C2×(C2×D19)⋊C4C2211yescharacteristic
28C2×(C2×D19)⋊C4C2212yes—
29C2×Dic19⋊C4C2211yescharacteristic
30C2×Dic19⋊C4C2212yes—
31C2×C4×Dic19C2211yescharacteristic
32C19⋊#95C2212yes—
33C19⋊#95C2211yescharacteristic
34C19⋊#95C2211yescharacteristic
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C24×C19C2312yes—
38C24×C19C2311yescharacteristic
39C23×D19C2311yescharacteristic
40C2×D4×C19—24no—
41C2×D4×C19—22no—
42C2×D4×C19—42no—
43C2×D4×C19—42no—
44C2×D4×C19—42no—
45C22×C4×C19—42no—
46C22×C4×C19D414yescomplemented
47C22×C4×C19C2312yes—
48C22×C4×C19C2311yescharacteristic
49C22×C4×C19C2311yescharacteristic
50C2×C22⋊D19—22no—
51C2×C22⋊D19—22no—
52C2×C22⋊D19—24no—
53C2×C22⋊D19—22no—
54C2×C22⋊D19—42no—
55C2×C22⋊D19—42no—
56C22×Dic19C2311yescharacteristic
57C22×Dic19C2312yes—
58C22×Dic19C2311yescharacteristic
59C22×Dic19C2312yes—
60C22×Dic19C2311yescharacteristic
61C2×C4×D19—22no—
62C2×C4×D19—42no—
63C4⋊C4×C19—22no—
64C22⋊C4×C19—24no—
65C22⋊Dic19—22no—
66C22⋊Dic19—24no—
67C22⋊Dic19—42no—
68C22⋊Dic19—42no—
69C22⋊Dic19—42no—
70(C2×D19)⋊C4—22no—
71(C2×D19)⋊C4—42no—
72Dic19⋊C4—22no—
73Dic19⋊C4—42no—
74C4×Dic19—22no—
75C23×C19—21no—
76C23×C19—21no—
77C23×C19—22no—
78C23×C19—22no—
79C23×C19—22no—
80C23×C19—22no—
81C23×C19—22no—
82C23×C19—22no—
83C23×C19—22no—
84C23×C19—22no—
85C23×C19—22no—
86C23×C19C2×D412yes—
87C23×C19C2411yescharacteristic
88C22×D19—21no—
89C22×D19—21no—
90C22×D19—22no—
91C22×D19—22no—
92C22×D19#4112yes—
93D4×C19—44no—
94D4×C19—48no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×C4×C19—44no—
101C2×C4×C19C2×D412yes—
102C2×C4×C19C2×D412yes—
103C22⋊D19—28no—
104C22⋊D19—48no—
105C2×Dic19—21no—
106C2×Dic19—21no—
107C2×Dic19—21no—
108C2×Dic19—21no—
109C2×Dic19—22no—
110C2×Dic19—22no—
111C2×Dic19—22no—
112C2×Dic19—22no—
113C2×Dic19—22no—
114C2×Dic19—22no—
115C2×Dic19—22no—
116C2×Dic19—22no—
117C2×Dic19#4112yes—
118C4×D19—44no—
119#2635—191nomaximal, Sylow
120C22×C19—22no—
121C22×C19—22no—
122C22×C19—22no—
123C22×C19—42no—
124C22×C19—42no—
125C22×C19—42no—
126C22×C19—42no—
127C22×C19—42no—
128C22×C19—42no—
129C22×C19—42no—
130C22×C19—42no—
131C22×C19—42no—
132C22×C19C22×D411yescharacteristic
133C22×C19C2×#4111yescharacteristic
134C22×C19C2×#4111yescharacteristic
135C22×C19H(5,𝔽2)12yes—
136C22×C19H(5,𝔽2)12yes—
137C2×D19—22no—
138C2×D19—24no—
139C2×D19—41no—
140C2×D19—41no—
141C2×D19—42no—
142C4×C19—22no—
143C4×C19—22no—
144C4×C19—42no—
145Dic19—22no—
146Dic19—41no—
147Dic19—41no—
148Dic19—42no—
149Dic19—42no—
150C2×#121D1911yescharacteristic, complemented
151C2×C4×D4—191no—
152#400—191no—
153#399—191no—
154#394—191no—
155#394—192no—
156#392—191no—
157#392—192no—
158#388—192no—
159#386—192no—
160#381—191no—
161C2×C19—42no—
162C2×C19—82no—
163C2×C19#52511yescharacteristic
164C2×C19#53411yescharacteristic
165C2×C19#53511yescharacteristic
166C2×C19#53812yes—
167C2×C19#54012yes—
168D19—42no—
169C22×D4—191no—
170C22×D4—192no—
171C22×D4C2×D1912yes—
172C22×D4C2×D1911yescharacteristic
173C23×C4—191no—
174C23×C4C2×D1911yescharacteristic
175#121—24no—
176C4×D4—384no—
177C2×C4⋊C4—191no—
178C2×C4⋊C4—192no—
179C2×C4⋊C4C2×D1911yescharacteristic
180C2×C22⋊C4—191no—
181C2×C22⋊C4—192no—
182C2×C22⋊C4—191no—
183C2×C22⋊C4—192no—
184C2×C22⋊C4—192no—
185C2×C22⋊C4—192no—
186C2×C22⋊C4—192no—
187C2×C22⋊C4C2×D1912yes—
188C2×C42—191no—
189#95—192no—
190#95—191no—
191#95—191no—
192#95—192no—
193#95—192no—
194C19#263511yescharacteristic, complemented, Sylow
195C24—191no—
196C24C22×D1912yes—
197C24C22×D1911yescharacteristic
198C2×D4—24no—
199C2×D4—22no—
200C2×D4—42no—
201C2×D4—42no—
202C2×D4—42no—
203C2×D4—382no—
204C2×D4—382no—
205C2×D4—382no—
206C2×D4—384no—
207C2×D4—762no—
208C2×D4—762no—
209C22×C4—42no—
210C22×C4—191no—
211C22×C4—192no—
212C22×C4—192no—
213C22×C4—191no—
214C22×C4—191no—
215C22×C4—382no—
216C22×C4—762no—
217C22×C4C22⋊D1914yescomplemented
218C22×C4C22×D1912yes—
219C22×C4C22×D1911yescharacteristic
220C22×C4C22×D1911yescharacteristic
221C4⋊C4—22no—
222C4⋊C4—382no—
223C4⋊C4—762no—
224C22⋊C4—24no—
225C22⋊C4—384no—
226C22⋊C4—382no—
227C22⋊C4—382no—
228C22⋊C4—762no—
229C22⋊C4—762no—
230C22⋊C4—762no—
231C22⋊C4—762no—
232C42—382no—
233C23—22no—
234C23—22no—
235C23—21no—
236C23—21no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—22no—
243C23—22no—
244C23—192no—
245C23—382no—
246C23—382no—
247C23—381no—
248C23—381no—
249C23C2×C22⋊D1912yes—
250C23C23×D1911yescharacteristic
251D4—44no—
252D4—48no—
253D4—388no—
254D4—768no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—44no—
261C2×C4—192no—
262C2×C4—381no—
263C2×C4—381no—
264C2×C4—382no—
265C2×C4—382no—
266C2×C4—382no—
267C2×C4—382no—
268C2×C4—382no—
269C2×C4—382no—
270C2×C4—382no—
271C2×C4—382no—
272C2×C4—381no—
273C2×C4—381no—
274C2×C4—764no—
275C2×C4C2×C22⋊D1912yes—
276C2×C4C2×C22⋊D1912yes—
277C22—22no—
278C22—22no—
279C22—22no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—382no—
290C22—384no—
291C22—761no—
292C22—761no—
293C22—762no—
294C22#1059743012yes—
295C22#1059743012yes—
296C22#41×D1911yescharacteristic
297C22#41×D1911yescharacteristic
298C22C22×C22⋊D1911yescharacteristic
299C4—22no—
300C4—22no—
301C4—42no—
302C4—382no—
303C4—761no—
304C4—761no—
305C4—762no—
306C4—762no—
307C2—42no—
308C2—82no—
309C2—762no—
310C2#1192705111yescharacteristic
311C2#1192710311yescharacteristic
312C2#1192711111yescharacteristic
313C2#1192712612yes—
314C2#1192714412yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#121C2
hypercenterC2×#121D19
hypocenterC19#2635
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊D19C2semidirect
2. #11926482C2semidirect
3. #11926479C2semidirect
4. #11926458C2semidirect
5. #11926458C2semidirect
6. #11926452C2semidirect
7. #11926452C2semidirect
8. #11926432C2semidirect
9. #11926420C2semidirect
10. #11926407C2semidirect
11. C2×C19×#121C2semidirect
46. C22×C4×C19D4semidirect
150. C2×#121D19semidirect
194. C19#2635semidirect
217. C22×C4C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D192
#119264822
#119264792
#119264582
#119264522
#119264322
#119264202
#119264072
C2×C19×#1212
#263519