Finite Group Databasebeta

← #14577631

Subgroups — #14577631

Order 2432.

1012 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927267C213yesmaximal, complemented
2#11927255C213yesmaximal, complemented
3#11927247C213yesmaximal, complemented
4#11927232C213yesmaximal, complemented
5Q8×D76C211yesmaximal, characteristic, complemented
6#11927206C211yesmaximal, characteristic, complemented
7#11927206C211yesmaximal, characteristic, complemented
8#11927168C213yesmaximal, complemented
9#11927157C213yesmaximal, complemented
10#11927081C213yesmaximal, complemented
11#11927079C213yesmaximal, complemented
12#11927026C211yesmaximal, characteristic, complemented
13#11927020C211yesmaximal, characteristic, complemented
14C4×Q8×D19C211yesmaximal, characteristic, complemented
15C19×#557C211yesmaximal, characteristic, complemented
16C2×#64545C2211yescharacteristic
17C2×Q8×D19C2211yescharacteristic
18C2×Q8×D19C2211yescharacteristic
19C19×C4⋊Q8C2213yes—
20C19×#125C2213yes—
21C19×#125C2213yes—
22C4×Q8×C19C2213yes—
23C4×Q8×C19C2211yescharacteristic
24C4×Q8×C19C2211yescharacteristic
25C4×Q8×C19C2211yescharacteristic
26#10597393C2213yes—
27#10597392C2213yes—
28#10597392C2216yes—
29Q8×Dic19C2211yescharacteristic
30#10597344C2216yes—
31#10597344C2213yes—
32#10597344C2213yes—
33#10597344C2216yes—
34#10597343C2213yes—
35#10597343C2213yes—
36#10597343C2213yes—
37#10597343C2213yes—
38#10597341C2213yes—
39#10597341C2213yes—
40#10597341C2213yes—
41#10597340C2213yes—
42#10597340C2211yescharacteristic
43#10597340C2216yes—
44#10597339C2213yes—
45#10597339C2216yes—
46#10597338C2216yes—
47#10597338C2213yes—
48C4⋊C4×D19C2213yes—
49C4⋊C4×D19C2213yes—
50#10597336C2213yes—
51#10597336C2216yes—
52#10597333C2213yes—
53#10597333C2213yes—
54#10597321C2213yes—
55#10597321C2213yes—
56C4×D76C2213yes—
57C4×D76C2213yes—
58C4×D76C2213yes—
59C4×D76C2213yes—
60#10597318C2213yes—
61#10597318C2213yes—
62C42×D19C2213yes—
63#10597315C2213yes—
64C4×Dic38C2213yes—
65C4×Dic38C2213yes—
66C2×Q8×C19C2313yes—
67C2×Q8×C19C2311yescharacteristic
68#64545—24no—
69Q8×D19—24no—
70Q8×D19—24no—
71C2×D76C2313yes—
72C2×D76C2311yescharacteristic
73C2×D76C2313yes—
74C2×D76C2313yes—
75C2×C4×D19C2313yes—
76C2×C4×D19C2313yes—
77C2×C4×D19C2313yes—
78C2×C4×D19C2311yescharacteristic
79C2×C4×D19C2313yes—
80C2×C4×D19C2316yes—
81C2×Dic38C2313yes—
82C2×Dic38C2313yes—
83C4⋊C4×C19C2311yescharacteristic
84C4⋊C4×C19C2313yes—
85C4⋊C4×C19C2313yes—
86C4⋊C4×C19C2313yes—
87C4⋊C4×C19C2313yes—
88C4⋊C4×C19C2313yes—
89C4⋊C4×C19C2316yes—
90C42×C19C2313yes—
91C42×C19C2313yes—
92C42×C19C2313yes—
93(C2×D19)⋊C4C2311yescharacteristic
94(C2×D19)⋊C4C2313yes—
95(C2×D19)⋊C4C2313yes—
96(C2×D19)⋊C4C2316yes—
97(C2×D19)⋊C4C2311yescharacteristic
98(C2×D19)⋊C4C2313yes—
99(C2×D19)⋊C4C2313yes—
100(C2×D19)⋊C4C2313yes—
101(C2×D19)⋊C4C2313yes—
102(C2×D19)⋊C4C2311yescharacteristic
103(C2×D19)⋊C4C2313yes—
104(C2×D19)⋊C4C2316yes—
105C4⋊Dic19C2313yes—
106C4⋊Dic19C2316yes—
107C4⋊Dic19C2313yes—
108C4⋊Dic19C2313yes—
109C4⋊Dic19C2313yes—
110Dic19⋊C4C2313yes—
111Dic19⋊C4C2316yes—
112Dic19⋊C4C2313yes—
113Dic19⋊C4C2311yescharacteristic
114Dic19⋊C4C2313yes—
115C4×Dic19C2313yes—
116C4×Dic19C2313yes—
117C4×Dic19C2313yes—
118C4×Dic19C2316yes—
119C22×D19C2411yescharacteristic
120C22×D19C2413yes—
121C22×D19C2411yescharacteristic
122Q8×C19—43no—
123Q8×C19#4114yes—
124C2×C4×C19C2411yescharacteristic
125C2×C4×C19C2413yes—
126C2×C4×C19C2413yes—
127C2×C4×C19C2411yescharacteristic
128C2×C4×C19C2411yescharacteristic
129C2×C4×C19C2413yes—
130C2×C4×C19C2413yes—
131C2×Dic19C2411yescharacteristic
132C2×Dic19C2413yes—
133C2×Dic19C2413yes—
134C2×Dic19C2413yes—
135C2×Dic19C2411yescharacteristic
136D76—22no—
137D76—26no—
138D76—26no—
139D76—43no—
140C4×D19—22no—
141C4×D19—26no—
142C4×D19—26no—
143C4×D19—26no—
144C4×D19—46no—
145C4×D19—43no—
146Dic38—26no—
147Dic38—26no—
148#3516—191nomaximal, Sylow
149C22×C19C2511yescharacteristic
150C2×D19—21no—
151C2×D19—21no—
152C2×D19—21no—
153C2×D19—23no—
154C2×D19—21no—
155C2×D19—23no—
156C2×D19—23no—
157C2×D19—21no—
158C2×D192−1+412yes—
159C4×C19—21no—
160C4×C19—23no—
161C4×C19—21no—
162C4×C19—23no—
163C4×C19—23no—
164C4×C19—21no—
165C4×C19C2×#4116yes—
166Dic19—23no—
167Dic19—23no—
168Dic19—21no—
169Dic19—21no—
170Dic19—23no—
171#557D1911yescharacteristic, complemented
172#556—193no—
173#554—193no—
174#553—193no—
175#552—193no—
176D4×Q8—191no—
177#548—191no—
178#548—191no—
179#542—193no—
180#541—193no—
181#529—193no—
182#529—193no—
183#520—191no—
184#519—191no—
185C2×C4×Q8—191no—
186C2×C19C22×#4111yescharacteristic
187C2×C19C2×2−1+411yescharacteristic
188C2×C19#58511yescharacteristic
189D19—22no—
190D19—41no—
191D19—43no—
192C2×#41—191no—
193C22×Q8—191no—
194C22×Q8—191no—
195C4⋊Q8—193no—
196C4⋊Q8C2×D1913yes—
197#126—196no—
198#126—193no—
199#126—193no—
200#126—196no—
201#125—193no—
202#125—196no—
203#125C2×D1913yes—
204#125C2×D1913yes—
205#124—193no—
206#124—193no—
207#124—193no—
208#123—191no—
209#123—193no—
210#123—196no—
211C22⋊Q8—193no—
212C22⋊Q8—196no—
213C22⋊Q8—193no—
214C22⋊Q8—193no—
215C22⋊Q8—193no—
216C22⋊Q8—193no—
217#121—193no—
218#121—193no—
219#121—193no—
220C4×Q8—191no—
221C4×Q8—193no—
222C4×Q8—193no—
223C4×Q8—193no—
224C4×Q8—193no—
225C4×Q8C2×D1911yescharacteristic
226C4×Q8C2×D1911yescharacteristic
227C4×Q8C2×D1911yescharacteristic
228C4×Q8C2×D1913yes—
229C4×D4—193no—
230C4×D4—196no—
231C4×D4—193no—
232C4×D4—193no—
233C4×D4—193no—
234C4×D4—193no—
235#117—193no—
236#117—196no—
237#117—193no—
238#117—193no—
239C2×C4⋊C4—193no—
240C2×C4⋊C4—193no—
241C2×C42—193no—
242C19#351611yescharacteristic, complemented, Sylow
243#41—384no—
244C2×Q8—193no—
245C2×Q8—193no—
246C2×Q8—384no—
247C2×Q8—384no—
248C2×Q8C22×D1913yes—
249C2×Q8C22×D1911yescharacteristic
250C2×D4—193no—
251C2×D4—191no—
252C2×D4—193no—
253C2×D4—193no—
254C22×C4—191no—
255C22×C4—193no—
256C22×C4—193no—
257C22×C4—193no—
258C22×C4—193no—
259C22×C4—196no—
260C4⋊C4—193no—
261C4⋊C4—196no—
262C4⋊C4—191no—
263C4⋊C4—193no—
264C4⋊C4—193no—
265C4⋊C4—193no—
266C4⋊C4—196no—
267C4⋊C4—193no—
268C4⋊C4—193no—
269C4⋊C4—193no—
270C4⋊C4C22×D1913yes—
271C4⋊C4C22×D1913yes—
272C4⋊C4C22×D1913yes—
273C4⋊C4C22×D1913yes—
274C4⋊C4C22×D1916yes—
275C4⋊C4C22×D1911yescharacteristic
276C4⋊C4C22×D1913yes—
277C22⋊C4—193no—
278C22⋊C4—191no—
279C22⋊C4—193no—
280C22⋊C4—193no—
281C22⋊C4—193no—
282C22⋊C4—196no—
283C22⋊C4—193no—
284C22⋊C4—191no—
285C22⋊C4—191no—
286C22⋊C4—196no—
287C22⋊C4—193no—
288C22⋊C4—193no—
289C42—193no—
290C42—193no—
291C42—193no—
292C42—196no—
293C42C22×D1913yes—
294C42C22×D1913yes—
295C42C22×D1913yes—
296C23—191no—
297C23—191no—
298C23—193no—
299Q8—43no—
300Q8—386no—
301Q8—386no—
302Q8#6454514yes—
303D4—386no—
304D4—382no—
305D4—386no—
306D4—763no—
307C2×C4—191no—
308C2×C4—193no—
309C2×C4—193no—
310C2×C4—193no—
311C2×C4—191no—
312C2×C4—382no—
313C2×C4—386no—
314C2×C4—386no—
315C2×C4—386no—
316C2×C4—766no—
317C2×C4—763no—
318C2×C4C23×D1911yescharacteristic
319C2×C4C23×D1913yes—
320C2×C4C23×D1913yes—
321C2×C4C23×D1911yescharacteristic
322C2×C4C23×D1911yescharacteristic
323C2×C4C23×D1913yes—
324C2×C4C23×D1913yes—
325C22—192no—
326C22—381no—
327C22—381no—
328C22—381no—
329C22—383no—
330C22—381no—
331C22—383no—
332C22—383no—
333C22—381no—
334C22C24×D1911yescharacteristic
335C4—21no—
336C4—23no—
337C4—21no—
338C4—23no—
339C4—23no—
340C4—21no—
341C4—381no—
342C4—383no—
343C4—383no—
344C4—381no—
345C4—383no—
346C4C2×#6454516yes—
347C2—382no—
348C2—761no—
349C2—763no—
350C2C22×#6454511yescharacteristic
351C22−1+4×D1911yescharacteristic
352C2#1192738011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#557C2
hypercenter#557D19
hypocenterC19#3516
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. #11927267C2semidirect
2. #11927255C2semidirect
3. #11927247C2semidirect
4. #11927232C2semidirect
5. Q8×D76C2semidirect
6. #11927206C2semidirect
7. #11927206C2semidirect
8. #11927168C2semidirect
9. #11927157C2semidirect
10. #11927081C2semidirect
11. #11927079C2semidirect
12. #11927026C2semidirect
13. #11927020C2semidirect
14. C4×Q8×D19C2semidirect
15. C19×#557C2semidirect
171. #557D19semidirect
242. C19#3516semidirect

Maximal subgroups

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

subgroupindex
#119272672
#119272552
#119272472
#119272322
Q8×D762
#119272062
#119271682
#119271572
#119270812
#119270792
#119270262
#119270202
C4×Q8×D192
C19×#5572
#351619