Finite Group Databasebeta

← #14569013

Subgroups — #14569013

Order 2432.

544 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597342C211yesmaximal, characteristic
2C2×C4⋊C4×D19C211yesmaximal, characteristic
3#11926478C211yesmaximal, characteristic, complemented
4#11926477C211yesmaximal, characteristic, complemented
5#11926465C211yesmaximal, characteristic, complemented
6#11926464C211yesmaximal, characteristic, complemented
7#11926442C211yesmaximal, characteristic, complemented
8#11926439C211yesmaximal, characteristic, complemented
9#11926439C211yesmaximal, characteristic, complemented
10#11926418C211yesmaximal, characteristic
11#11926418C211yesmaximal, characteristic
12#11926415C211yesmaximal, characteristic
13#11926415C211yesmaximal, characteristic
14C4×(C2×D19)⋊C4C211yesmaximal, characteristic
15C19×#389C211yesmaximal, characteristic, complemented
16C22×C4×D19C2211yescharacteristic
17C22×C4×D19C2211yescharacteristic
18C22×C4×D19C2211yescharacteristic
19C22×Dic38C2211yescharacteristic
20C2×C4⋊C4×C19C2211yescharacteristic
21C2×C4⋊C4×C19C2211yescharacteristic
22C2×C4⋊C4×C19C2211yescharacteristic
23C2×C4⋊C4×C19C2211yescharacteristic
24C2×C42×C19C2211yescharacteristic
25C2×(C2×D19)⋊C4C2211yescharacteristic
26C2×(C2×D19)⋊C4C2211yescharacteristic
27C2×(C2×D19)⋊C4C2211yescharacteristic
28C2×(C2×D19)⋊C4C2211yescharacteristic
29C2×C4⋊Dic19C2211yescharacteristic
30C2×C4⋊Dic19C2211yescharacteristic
31C2×C4⋊Dic19C2211yescharacteristic
32C2×Dic19⋊C4C2211yescharacteristic
33C2×Dic19⋊C4C2211yescharacteristic
34C2×Dic19⋊C4C2211yescharacteristic
35C2×Dic19⋊C4C2211yescharacteristic
36C2×Dic19⋊C4C2211yescharacteristic
37C2×Dic19⋊C4C2211yescharacteristic
38C2×Dic19⋊C4C2211yescharacteristic
39C2×Dic19⋊C4C2211yescharacteristic
40C2×C4×Dic19C2211yescharacteristic
41#10597342—24no—
42C4⋊C4×D19—24no—
43C19×#95C2211yescharacteristic
44C19×#95C2211yescharacteristic
45C19⋊#95C2211yescharacteristic
46C19⋊#95C2211yescharacteristic
47C19⋊#95C2211yescharacteristic
48C19⋊#95C2211yescharacteristic
49C19⋊#95C2211yescharacteristic
50C19⋊#95C2211yescharacteristic
51C19⋊#95C2211yescharacteristic
52C19⋊#95C2211yescharacteristic
53C23×D19C2311yescharacteristic
54C22×C4×C19C2311yescharacteristic
55C22×C4×C19C2311yescharacteristic
56C22×C4×C19C2311yescharacteristic
57C22×C4×C19C2311yescharacteristic
58C22×C4×C19C2311yescharacteristic
59C22×C4×C19C2311yescharacteristic
60C22×C4×C19C2311yescharacteristic
61C22×Dic19C2311yescharacteristic
62C22×Dic19C2311yescharacteristic
63C22×Dic19C2311yescharacteristic
64C22×Dic19C2311yescharacteristic
65C22×Dic19C2311yescharacteristic
66C22×Dic19C2311yescharacteristic
67C22×Dic19C2311yescharacteristic
68C2×C4×D19—22no—
69C2×C4×D19—22no—
70C2×C4×D19—22no—
71C2×C4×D19—22no—
72C2×C4×D19—41no—
73C2×C4×D19—41no—
74C2×C4×D19—41no—
75C2×C4×D19—41no—
76C2×C4×D19D414yes—
77C2×Dic38—22no—
78C2×Dic38—41no—
79C2×Dic38—41no—
80C4⋊C4×C19—22no—
81C4⋊C4×C19—22no—
82C4⋊C4×C19—22no—
83C4⋊C4×C19—41no—
84C42×C19—41no—
85(C2×D19)⋊C4—22no—
86(C2×D19)⋊C4—22no—
87(C2×D19)⋊C4Q814yescomplemented
88(C2×D19)⋊C4Q814yescomplemented
89C4⋊Dic19—22no—
90C4⋊Dic19—22no—
91C4⋊Dic19—41no—
92Dic19⋊C4—22no—
93Dic19⋊C4—22no—
94Dic19⋊C4—22no—
95Dic19⋊C4—22no—
96Dic19⋊C4—22no—
97Dic19⋊C4—22no—
98Dic19⋊C4—41no—
99Dic19⋊C4—41no—
100C4×Dic19—41no—
101C23×C19C2411yescharacteristic
102C22×D19—21no—
103C22×D19—21no—
104C22×D19—21no—
105C22×D19—21no—
106C22×D19C2×D412yes—
107C22×D19C2×Q812yes—
108C22×D19C2×Q812yes—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
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×C19C2×D412yes—
127C2×C4×C19C2×Q812yes—
128C2×C4×C19C2×Q812yes—
129C2×C4×C19#4112yes—
130C2×Dic19—21no—
131C2×Dic19—21no—
132C2×Dic19—21no—
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×Dic19C2×D412yes—
148C2×Dic19C2×Q812yes—
149C2×Dic19C2×Q812yes—
150C2×Dic19#4112yes—
151C4×D19—28no—
152C4×D19—44no—
153C4×D19—44no—
154Dic38—44no—
155#2583—191nomaximal, Sylow
156C22×C19C22×D411yescharacteristic
157C22×C19C22×Q811yescharacteristic
158C22×C19C22×Q811yescharacteristic
159C22×C19C2×#4111yescharacteristic
160C22×C19C2×#4111yescharacteristic
161C22×C19H(5,𝔽2)11yescharacteristic
162C22×C19H(5,𝔽2)11yescharacteristic
163C2×D19—22no—
164C2×D19—22no—
165C2×D19—22no—
166C2×D19—22no—
167C2×D19—22no—
168C2×D19—22no—
169C2×D19C4⋊Q814yes—
170C4×C19—22no—
171C4×C19—22no—
172C4×C19—22no—
173C4×C19—22no—
174C4×C19—41no—
175C4×C19—41no—
176C4×C19—41no—
177Dic19—22no—
178Dic19—22no—
179Dic19—22no—
180Dic19—22no—
181Dic19—41no—
182Dic19—41no—
183Dic19—41no—
184C2×C22⋊Q8—191no—
185C22×C4⋊C4—191no—
186#398—191no—
187#398—191no—
188#395—191no—
189#395—191no—
190#389—191no—
191#389—191no—
192#389—191no—
193#389D1911yescharacteristic, complemented
194#385—191no—
195#385—191no—
196#385—191no—
197#385—191no—
198C4×C22⋊C4—191no—
199C2×C19#52511yescharacteristic
200C2×C19C2×C4⋊Q811yescharacteristic
201C2×C19#53411yescharacteristic
202C2×C19#55411yescharacteristic
203C2×C19#55411yescharacteristic
204C2×C19#55411yescharacteristic
205C2×C19#55411yescharacteristic
206D19—24no—
207C22×Q8—191no—
208C23×C4—191no—
209C23×C4—191no—
210C23×C4—191no—
211C22⋊Q8—384no—
212C2×C4⋊C4—191no—
213C2×C4⋊C4—191no—
214C2×C4⋊C4—191no—
215C2×C4⋊C4—191no—
216C2×C4⋊C4—191no—
217C2×C4⋊C4—191no—
218C2×C4⋊C4—191no—
219C2×C4⋊C4—191no—
220C2×C4⋊C4—191no—
221C2×C4⋊C4—191no—
222C2×C4⋊C4—191no—
223C2×C4⋊C4—384no—
224C2×C4⋊C4C2×D1911yescharacteristic
225C2×C4⋊C4C2×D1911yescharacteristic
226C2×C4⋊C4C2×D1911yescharacteristic
227C2×C4⋊C4C2×D1911yescharacteristic
228C2×C22⋊C4—191no—
229C2×C22⋊C4—191no—
230C2×C22⋊C4—191no—
231C2×C22⋊C4—191no—
232C2×C42—191no—
233C2×C42C2×D1911yescharacteristic
234#95—191no—
235#95—191no—
236#95—191no—
237#95—191no—
238#95—191no—
239#95—191no—
240#95—191no—
241#95—191no—
242#95C2×D1911yescharacteristic
243#95C2×D1911yescharacteristic
244C19#258311yescharacteristic, complemented, Sylow
245C24—191no—
246C2×Q8—382no—
247C2×Q8—761no—
248C2×Q8—761no—
249C22×C4—191no—
250C22×C4—191no—
251C22×C4—191no—
252C22×C4—191no—
253C22×C4—194no—
254C22×C4—191no—
255C22×C4—191no—
256C22×C4—191no—
257C22×C4—382no—
258C22×C4—382no—
259C22×C4—382no—
260C22×C4—382no—
261C22×C4—761no—
262C22×C4—761no—
263C22×C4—761no—
264C22×C4—761no—
265C22×C4C22×D1911yescharacteristic
266C22×C4C22×D1911yescharacteristic
267C22×C4C22×D1911yescharacteristic
268C22×C4C22×D1911yescharacteristic
269C22×C4C22×D1911yescharacteristic
270C22×C4C22×D1911yescharacteristic
271C22×C4C22×D1911yescharacteristic
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—382no—
277C4⋊C4—382no—
278C4⋊C4—382no—
279C4⋊C4—382no—
280C4⋊C4—382no—
281C4⋊C4—382no—
282C4⋊C4—382no—
283C4⋊C4—382no—
284C4⋊C4—761no—
285C4⋊C4—761no—
286C4⋊C4—761no—
287C22⋊C4—194no—
288C22⋊C4—194no—
289C22⋊C4—382no—
290C22⋊C4—382no—
291C42—41no—
292C42—761no—
293C23—192no—
294C23—192no—
295C23—192no—
296C23—381no—
297C23—381no—
298C23—381no—
299C23—381no—
300C23C23×D1911yescharacteristic
301Q8—764no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—192no—
320C2×C4—192no—
321C2×C4—192no—
322C2×C4—192no—
323C2×C4—388no—
324C2×C4—381no—
325C2×C4—381no—
326C2×C4—381no—
327C2×C4—381no—
328C2×C4—381no—
329C2×C4—381no—
330C2×C4—381no—
331C2×C4—381no—
332C2×C4—381no—
333C2×C4—381no—
334C2×C4—381no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4—381no—
339C2×C4—381no—
340C2×C4—381no—
341C2×C4—764no—
342C2×C4—764no—
343C2×C4#6454112yes—
344C2×C4D4×D1912yes—
345C2×C4Q8×D1912yes—
346C2×C4Q8×D1912yes—
347C22—194no—
348C22—382no—
349C22—382no—
350C22—382no—
351C22—382no—
352C22—382no—
353C22—382no—
354C22C2×#6454111yescharacteristic
355C22C2×D4×D1911yescharacteristic
356C22#1059743011yescharacteristic
357C22C2×Q8×D1911yescharacteristic
358C22C2×Q8×D1911yescharacteristic
359C22#41×D1911yescharacteristic
360C22#1059743511yescharacteristic
361C4—22no—
362C4—22no—
363C4—22no—
364C4—22no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—382no—
369C4—382no—
370C4—382no—
371C4—382no—
372C4—761no—
373C4—761no—
374C4—761no—
375C2—384no—
376C2#1192705311yescharacteristic
377C2C4⋊Q8×D1911yescharacteristic
378C2#1192710211yescharacteristic
379C2#1192724811yescharacteristic
380C2#1192724911yescharacteristic
381C2#1192725011yescharacteristic
382C2#1192725411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#389C2
prime radicalC23×D19C23
hypercenter#389D19
hypocenterC19#2583
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
3. #11926478C2semidirect
4. #11926477C2semidirect
5. #11926465C2semidirect
6. #11926464C2semidirect
7. #11926442C2semidirect
8. #11926439C2semidirect
9. #11926439C2semidirect
15. C19×#389C2semidirect
87. (C2×D19)⋊C4Q8semidirect
88. (C2×D19)⋊C4Q8semidirect
193. #389D19semidirect
244. C19#2583semidirect

Maximal subgroups

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

subgroupindex
C2×#105973422
C2×C4⋊C4×D192
#119264782
#119264772
#119264652
#119264642
#119264422
#119264392
#119264182
#119264152
C4×(C2×D19)⋊C42
C19×#3892
#258319