Finite Group Databasebeta

← #14567925

Subgroups — #14567925

Order 2432.

540 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic19C211yesmaximal, characteristic
2C2×#10597323C211yesmaximal, characteristic, complemented
3#11926472C211yesmaximal, characteristic, complemented
4#11926469C211yesmaximal, characteristic, complemented
5#11926458C211yesmaximal, characteristic
6#11926441C211yesmaximal, characteristic, complemented
7#11926439C211yesmaximal, characteristic, complemented
8#11926438C211yesmaximal, characteristic, complemented
9#11926437C211yesmaximal, characteristic, complemented
10#11926431C211yesmaximal, characteristic, complemented
11#11926430C211yesmaximal, characteristic, complemented
12#11926402C211yesmaximal, characteristic, complemented
13#11926402C211yesmaximal, characteristic, complemented
14#11926402C211yesmaximal, characteristic, complemented
15C19×#394C211yesmaximal, characteristic
16C22×D4×C19C2211yescharacteristic
17C23×Dic19C2211yescharacteristic
18C23×Dic19C2211yescharacteristic
19C2×C4⋊C4×C19C2211yescharacteristic
20C2×C22⋊C4×C19C2211yescharacteristic
21C2×C22⋊C4×C19C2211yescharacteristic
22C2×C22⋊C4×C19C2211yescharacteristic
23C2×C22⋊C4×C19C2211yescharacteristic
24C2×C22⋊Dic19C2211yescharacteristic
25C2×C22⋊Dic19C2211yescharacteristic
26C2×C22⋊Dic19C2211yescharacteristic
27C2×C22⋊Dic19C2211yescharacteristic
28C2×C22⋊Dic19C2211yescharacteristic
29C2×C22⋊Dic19C2211yescharacteristic
30D4×Dic19—24no—
31C2×C4⋊Dic19C2211yescharacteristic
32C2×C4⋊Dic19C2211yescharacteristic
33C2×Dic19⋊C4C2211yescharacteristic
34C2×Dic19⋊C4C2211yescharacteristic
35C2×Dic19⋊C4C2211yescharacteristic
36C2×Dic19⋊C4C2211yescharacteristic
37C2×Dic19⋊C4C2211yescharacteristic
38C2×Dic19⋊C4C2211yescharacteristic
39C2×C4×Dic19C2211yescharacteristic
40C2×C4×Dic19C2211yescharacteristic
41C2×C4×Dic19C2211yescharacteristic
42#10597323—24no—
43C19×#95C2211yescharacteristic
44C19⋊#95C2211yescharacteristic
45C19⋊#95C2211yescharacteristic
46C19⋊#95C2211yescharacteristic
47C19⋊#95C2211yescharacteristic
48C19⋊#95C2211yescharacteristic
49C19⋊#95C2211yescharacteristic
50C19⋊#95C2211yescharacteristic
51C19⋊#95C2211yescharacteristic
52C19⋊#95C2211yescharacteristic
53C24×C19C2311yescharacteristic
54C24×C19C2311yescharacteristic
55C2×D4×C19—22no—
56C2×D4×C19—22no—
57C2×D4×C19—22no—
58C22×C4×C19C2311yescharacteristic
59C22×C4×C19C2311yescharacteristic
60C22×C4×C19C2311yescharacteristic
61C22×C4×C19C2311yescharacteristic
62C22×C4×C19C2311yescharacteristic
63C22×Dic19—22no—
64C22×Dic19—22no—
65C22×Dic19—22no—
66C22×Dic19—22no—
67C22×Dic19—22no—
68C22×Dic19D414yes—
69C22×Dic19C2311yescharacteristic
70C22×Dic19C2311yescharacteristic
71C22×Dic19C2311yescharacteristic
72C22×Dic19C2311yescharacteristic
73C22×Dic19C2311yescharacteristic
74C22×Dic19C2311yescharacteristic
75C22×Dic19C2311yescharacteristic
76C22×Dic19C2311yescharacteristic
77C4⋊C4×C19—22no—
78C22⋊C4×C19—22no—
79C22⋊C4×C19—22no—
80C22⋊C4×C19—41no—
81C22⋊C4×C19—41no—
82C22⋊Dic19—22no—
83C22⋊Dic19—22no—
84C22⋊Dic19—22no—
85C22⋊Dic19—22no—
86C22⋊Dic19—41no—
87C22⋊Dic19—41no—
88C4⋊Dic19—22no—
89C4⋊Dic19—41no—
90Dic19⋊C4—22no—
91Dic19⋊C4—22no—
92Dic19⋊C4—22no—
93Dic19⋊C4—22no—
94Dic19⋊C4—22no—
95Dic19⋊C4—41no—
96C4×Dic19—22no—
97C4×Dic19—22no—
98C4×Dic19—22no—
99C23×C19—21no—
100C23×C19—21no—
101C23×C19—21no—
102C23×C19—21no—
103C23×C19—21no—
104C23×C19—21no—
105C23×C19—21no—
106C23×C19—21no—
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—21no—
111C23×C19C2×D412yes—
112C23×C19#4112yes—
113C23×C19C2411yescharacteristic
114D4×C19—28no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19#4112yes—
130C2×Dic19—21no—
131C2×Dic19—21no—
132C2×Dic19—28no—
133C2×Dic19—21no—
134C2×Dic19—21no—
135C2×Dic19—21no—
136C2×Dic19—21no—
137C2×Dic19—21no—
138C2×Dic19—21no—
139C2×Dic19—21no—
140C2×Dic19—21no—
141C2×Dic19—21no—
142C2×Dic19—21no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145C2×Dic19—21no—
146C2×Dic19—21no—
147C2×Dic19—21no—
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—21no—
151C2×Dic19—44no—
152C2×Dic19C2×D412yes—
153C2×Dic19C2×D412yes—
154C2×Dic19#4112yes—
155C2×Dic19#4112yes—
156#2485—191nomaximal, Sylow
157C22×C19—22no—
158C22×C19—22no—
159C22×C19—22no—
160C22×C19—22no—
161C22×C19—22no—
162C22×C19—22no—
163C22×C19—41no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19—41no—
168C22×C19—41no—
169C22×C19—41no—
170C22×C19—41no—
171C22×C19C22×D411yescharacteristic
172C22×C19C2×#4111yescharacteristic
173C22×C19C2×#4111yescharacteristic
174C22×C19C2×#4111yescharacteristic
175C22×C19C2×#4111yescharacteristic
176C22×C19H(5,𝔽2)11yescharacteristic
177C22×C192−1+411yescharacteristic
178C4×C19—22no—
179C4×C19—41no—
180C4×C19—41no—
181C4×C19—41no—
182C4×C19—41no—
183Dic19—22no—
184Dic19—41no—
185Dic19—41no—
186Dic19—41no—
187Dic19—41no—
188Dic19—41no—
189Dic19—41no—
190Dic19#12314yes—
191C2×C4×D4—191no—
192C2×#117—191no—
193#397—191no—
194#397—191no—
195#394—191no—
196#394D1911yescharacteristic
197#389—191no—
198#389—191no—
199#388—191no—
200#388—191no—
201#387—191no—
202#387—191no—
203#380—191no—
204#380—191no—
205#380—191no—
206C2×C19—42no—
207C2×C19—42no—
208C2×C19C2×#12311yescharacteristic
209C2×C19#52511yescharacteristic
210C2×C19#53711yescharacteristic
211C2×C19#55211yescharacteristic
212C2×C19#55311yescharacteristic
213C2×C19#55511yescharacteristic
214C2×C19#55611yescharacteristic
215C22×D4C2×D1911yescharacteristic
216C23×C4—191no—
217C23×C4—191no—
218C4×D4—384no—
219#117—384no—
220C2×C4⋊C4—191no—
221C2×C4⋊C4—191no—
222C2×C4⋊C4—191no—
223C2×C4⋊C4—191no—
224C2×C4⋊C4—191no—
225C2×C4⋊C4—191no—
226C2×C4⋊C4—191no—
227C2×C4⋊C4—191no—
228C2×C4⋊C4C2×D1911yescharacteristic
229C2×C22⋊C4—191no—
230C2×C22⋊C4—191no—
231C2×C22⋊C4—191no—
232C2×C22⋊C4—191no—
233C2×C22⋊C4—191no—
234C2×C22⋊C4—191no—
235C2×C22⋊C4C2×D1911yescharacteristic
236C2×C22⋊C4C2×D1911yescharacteristic
237C2×C22⋊C4C2×D1911yescharacteristic
238C2×C22⋊C4C2×D1911yescharacteristic
239C2×C42—191no—
240C2×C42—191no—
241C2×C42—191no—
242#95—191no—
243#95—191no—
244#95—191no—
245#95—191no—
246#95—191no—
247#95—191no—
248#95—191no—
249#95—191no—
250#95—191no—
251#95C2×D1911yescharacteristic
252C19#248511yescharacteristic, complemented, Sylow
253C24C22×D1911yescharacteristic
254C24C22×D1911yescharacteristic
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—22no—
258C22×C4—191no—
259C22×C4—194no—
260C22×C4—191no—
261C22×C4—191no—
262C22×C4—191no—
263C22×C4—191no—
264C22×C4—191no—
265C22×C4—191no—
266C22×C4—191no—
267C22×C4—382no—
268C22×C4—382no—
269C22×C4—382no—
270C22×C4—382no—
271C22×C4—382no—
272C22×C4C22×D1911yescharacteristic
273C22×C4C22×D1911yescharacteristic
274C22×C4C22×D1911yescharacteristic
275C22×C4C22×D1911yescharacteristic
276C22×C4C22×D1911yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—382no—
279C4⋊C4—382no—
280C4⋊C4—382no—
281C4⋊C4—382no—
282C4⋊C4—382no—
283C4⋊C4—382no—
284C4⋊C4—761no—
285C4⋊C4—761no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—382no—
291C22⋊C4—382no—
292C22⋊C4—382no—
293C22⋊C4—382no—
294C22⋊C4—761no—
295C22⋊C4—761no—
296C42—382no—
297C42—382no—
298C42—382no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23D4×D1912yes—
312C23#6454312yes—
313C23C23×D1911yescharacteristic
314D4—28no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—192no—
330C2×C4—192no—
331C2×C4—192no—
332C2×C4—192no—
333C2×C4—388no—
334C2×C4—381no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4—381no—
339C2×C4—381no—
340C2×C4—381no—
341C2×C4—381no—
342C2×C4—381no—
343C2×C4—381no—
344C2×C4—381no—
345C2×C4—381no—
346C2×C4—381no—
347C2×C4—381no—
348C2×C4—381no—
349C2×C4—381no—
350C2×C4—381no—
351C2×C4—381no—
352C2×C4—381no—
353C2×C4—381no—
354C2×C4—764no—
355C2×C4#6454312yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22C2×D4×D1911yescharacteristic
371C22C2×#6454311yescharacteristic
372C22C2×#6454311yescharacteristic
373C22#1059743011yescharacteristic
374C22#41×D1911yescharacteristic
375C22#41×D1911yescharacteristic
376C22#1059743611yescharacteristic
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—194no—
383C4—382no—
384C4—761no—
385C4—761no—
386C4—761no—
387C4—761no—
388C4—761no—
389C4—761no—
390C2—42no—
391C2—42no—
392C2#123×D1911yescharacteristic
393C2#1192705011yescharacteristic
394C2#1192712111yescharacteristic
395C2#1192723111yescharacteristic
396C2#1192723711yescharacteristic
397C2#1192725811yescharacteristic
398C2#1192726311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#394C2
prime radicalC22×D4×C19C22
hypercenter#394D19
hypocenterC19#2485
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#10597323C2semidirect
3. #11926472C2semidirect
4. #11926469C2semidirect
6. #11926441C2semidirect
7. #11926439C2semidirect
8. #11926438C2semidirect
9. #11926437C2semidirect
10. #11926431C2semidirect
11. #11926430C2semidirect
12. #11926402C2semidirect
13. #11926402C2semidirect
14. #11926402C2semidirect
252. C19#2485semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic192
C2×#105973232
#119264722
#119264692
#119264582
#119264412
#119264392
#119264382
#119264372
#119264312
#119264302
#119264022
C19×#3942
#248519