Finite Group Databasebeta

← #14577746

Subgroups — #14577746

Order 2432.

1030 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927279C213yesmaximal, complemented
2#11927270C211yesmaximal, characteristic, complemented
3#11927257C213yesmaximal, complemented
4#11927238C213yesmaximal, complemented
5#11927235C213yesmaximal, complemented
6#11927216C211yesmaximal, characteristic, complemented
7#11927205C211yesmaximal, characteristic, complemented
8#11927205C211yesmaximal, characteristic, complemented
9#11927166C213yesmaximal, complemented
10#11927149C213yesmaximal, complemented
11#11927081C213yesmaximal, complemented
12#11927072C213yesmaximal, complemented
13#11927026C211yesmaximal, characteristic, complemented
14C4×#64545C211yesmaximal, characteristic, complemented
15C19×#519C211yesmaximal, characteristic, complemented
16C22×Q8×C19C2211yescharacteristic
17C2×#64545C2211yescharacteristic
18C2×#64545C2211yescharacteristic
19C4×Q8×C19C2213yes—
20C4×Q8×C19C2211yescharacteristic
21C4×Q8×C19C2213yes—
22C4×Q8×C19C2211yescharacteristic
23C19×#117C2213yes—
24C19×#117C2213yes—
25#10597393C2213yes—
26#10597393C2213yes—
27#10597392C2213yes—
28#10597392C2213yes—
29Q8×Dic19C2211yescharacteristic
30Q8×Dic19C2211yescharacteristic
31#10597376C2213yes—
32#10597376C2213yes—
33C4×C22⋊D19C2213yes—
34C4×C22⋊D19C2213yes—
35#10597344C2213yes—
36#10597342C2213yes—
37#10597341C2213yes—
38#10597341C2213yes—
39#10597340C2213yes—
40#10597340C2216yes—
41#10597340C2216yes—
42#10597339C2213yes—
43#10597339C2213yes—
44#10597338C2213yes—
45C4⋊C4×D19C2213yes—
46#10597336C2213yes—
47#10597335C2213yes—
48#10597334C2213yes—
49#10597331C2213yes—
50#10597330C2213yes—
51#10597330C2216yes—
52#10597329C2213yes—
53#10597325C2211yescharacteristic
54#10597322C2216yes—
55#10597321C2216yes—
56#10597320C2213yes—
57C4×D76C2213yes—
58C4×D76C2213yes—
59C4×D76C2216yes—
60C4×D76C2213yes—
61#10597318C2213yes—
62#10597318C2216yes—
63C42×D19C2213yes—
64#10597316C2213yes—
65C4×Dic38C2213yes—
66C2×Q8×C19—24no—
67C2×Q8×C19C2313yes—
68C2×Q8×C19C2311yescharacteristic
69C22×C4×C19C2313yes—
70C2×C22⋊D19C2313yes—
71C2×C22⋊D19C2313yes—
72#64545—24no—
73#64545—24no—
74C2×D76C2313yes—
75C2×D76C2313yes—
76C2×D76C2313yes—
77C2×D76C2316yes—
78C2×C4×D19C2313yes—
79C2×C4×D19C2313yes—
80C2×C4×D19C2313yes—
81C2×C4×D19C2313yes—
82C2×C4×D19C2316yes—
83C2×Dic38C2313yes—
84C4⋊C4×C19C2313yes—
85C4⋊C4×C19C2313yes—
86C4⋊C4×C19C2313yes—
87C4⋊C4×C19C2313yes—
88C22⋊C4×C19C2311yescharacteristic
89C22⋊C4×C19C2313yes—
90C42×C19C2313yes—
91C42×C19C2313yes—
92C42×C19C2316yes—
93C22⋊Dic19C2311yescharacteristic
94C22⋊Dic19C2311yescharacteristic
95(C2×D19)⋊C4C2316yes—
96(C2×D19)⋊C4C2316yes—
97(C2×D19)⋊C4C2313yes—
98(C2×D19)⋊C4C2313yes—
99(C2×D19)⋊C4C2313yes—
100(C2×D19)⋊C4C2313yes—
101(C2×D19)⋊C4C2313yes—
102(C2×D19)⋊C4C2316yes—
103(C2×D19)⋊C4C2313yes—
104C4⋊Dic19C2313yes—
105C4⋊Dic19C2313yes—
106C4⋊Dic19C2313yes—
107C4⋊Dic19C2311yescharacteristic
108Dic19⋊C4C2313yes—
109Dic19⋊C4C2313yes—
110Dic19⋊C4C2311yescharacteristic
111Dic19⋊C4C2313yes—
112Dic19⋊C4C2316yes—
113Dic19⋊C4C2311yescharacteristic
114Dic19⋊C4C2313yes—
115C4×Dic19C2313yes—
116C4×Dic19C2313yes—
117C4×Dic19C2311yescharacteristic
118C4×Dic19C2313yes—
119C23×C19C2411yescharacteristic
120C22×D19C2413yes—
121C22×D19C2413yes—
122Q8×C19—26no—
123Q8×C19#4114yes—
124C2×C4×C19—26no—
125C2×C4×C19C2411yescharacteristic
126C2×C4×C19C2413yes—
127C2×C4×C19C2411yescharacteristic
128C2×C4×C19C2413yes—
129C2×C4×C19C2413yes—
130C2×C4×C19C2413yes—
131C22⋊D19—43no—
132C22⋊D19—43no—
133C2×Dic19C2411yescharacteristic
134C2×Dic19C2411yescharacteristic
135C2×Dic19C2411yescharacteristic
136C2×Dic19C2413yes—
137C2×Dic19C2413yes—
138C2×Dic19C2411yescharacteristic
139D76—26no—
140D76—26no—
141D76—46no—
142D76—43no—
143C4×D19—26no—
144C4×D19—26no—
145C4×D19—43no—
146C4×D19—43no—
147C4×D19—46no—
148Dic38—43no—
149#3524—191nomaximal, Sylow
150C22×C19—21no—
151C22×C19—21no—
152C22×C19—21no—
153C22×C19C2511yescharacteristic
154C2×D19—23no—
155C2×D19—23no—
156C2×D19—23no—
157C2×D19—23no—
158C2×D19—23no—
159C2×D19—23no—
160C4×C19—23no—
161C4×C19—23no—
162C4×C19—21no—
163C4×C19—23no—
164C4×C19—21no—
165C4×C19C2×#4116yes—
166Dic19—21no—
167Dic19—21no—
168Dic19—21no—
169Dic19—23no—
170Dic19—21no—
171Dic19—23no—
172#559—193no—
173#557—191no—
174#555—193no—
175#553—193no—
176#552—193no—
177#550—191no—
178#548—191no—
179#548—191no—
180#542—193no—
181#540—193no—
182#529—193no—
183#529—193no—
184#520—191no—
185#519D1911yescharacteristic, complemented
186C4×#41—191no—
187C2×C19—41no—
188C2×C19C22×#4111yescharacteristic
189C2×C19#58511yescharacteristic
190C2×C19#58511yescharacteristic
191D19—43no—
192D19—43no—
193C2×#41—191no—
194C2×#41—191no—
195C22×Q8C2×D1911yescharacteristic
196C4⋊Q8—193no—
197#127—193no—
198#126—193no—
199#126—191no—
200#126—196no—
201#125—193no—
202#125—193no—
203#125—193no—
204#124—193no—
205#124—193no—
206#124—193no—
207#124—196no—
208#123—196no—
209#123—193no—
210#123—196no—
211#123—193no—
212C22⋊Q8—193no—
213C22⋊Q8—193no—
214C22⋊Q8—193no—
215#121—193no—
216#121—193no—
217#121—193no—
218#121—193no—
219#121—193no—
220#121—196no—
221C4×Q8—191no—
222C4×Q8—191no—
223C4×Q8—193no—
224C4×Q8C2×D1911yescharacteristic
225C4×Q8C2×D1913yes—
226C4×Q8C2×D1911yescharacteristic
227C4×Q8C2×D1913yes—
228C4×D4—193no—
229C4×D4—193no—
230C4×D4—193no—
231C4×D4—193no—
232C4×D4—193no—
233C4×D4—193no—
234C4×D4—193no—
235C4×D4—196no—
236#117—193no—
237#117—193no—
238#117—196no—
239#117C2×D1913yes—
240#117C2×D1913yes—
241C2×C4⋊C4—193no—
242C2×C42—193no—
243C19#352411yescharacteristic, complemented, Sylow
244#41—384no—
245#41—384no—
246C2×Q8—24no—
247C2×Q8—193no—
248C2×Q8C22×D1913yes—
249C2×Q8C22×D1911yescharacteristic
250C2×D4—193no—
251C2×D4—193no—
252C2×D4—193no—
253C2×D4—193no—
254C2×D4—196no—
255C2×D4—193no—
256C22×C4—193no—
257C22×C4—193no—
258C22×C4—193no—
259C22×C4—193no—
260C22×C4—196no—
261C22×C4C22×D1913yes—
262C4⋊C4—193no—
263C4⋊C4—191no—
264C4⋊C4—193no—
265C4⋊C4—196no—
266C4⋊C4—193no—
267C4⋊C4—191no—
268C4⋊C4—193no—
269C4⋊C4—193no—
270C4⋊C4—193no—
271C4⋊C4—191no—
272C4⋊C4—193no—
273C4⋊C4C22×D1913yes—
274C4⋊C4C22×D1913yes—
275C4⋊C4C22×D1913yes—
276C4⋊C4C22×D1913yes—
277C22⋊C4—191no—
278C22⋊C4—191no—
279C22⋊C4—193no—
280C22⋊C4—193no—
281C22⋊C4—196no—
282C22⋊C4—193no—
283C22⋊C4—196no—
284C22⋊C4—193no—
285C22⋊C4—193no—
286C22⋊C4—196no—
287C22⋊C4—193no—
288C22⋊C4C22×D1911yescharacteristic
289C22⋊C4C22×D1913yes—
290C42—191no—
291C42—193no—
292C42—193no—
293C42—193no—
294C42C22×D1913yes—
295C42C22×D1916yes—
296C42C22×D1913yes—
297C23—193no—
298C23—193no—
299C23C23×D1911yescharacteristic
300Q8—26no—
301Q8—763no—
302Q8#6454114yes—
303D4—386no—
304D4—386no—
305D4—763no—
306D4—766no—
307D4—763no—
308D4—763no—
309C2×C4—26no—
310C2×C4—191no—
311C2×C4—191no—
312C2×C4—191no—
313C2×C4—193no—
314C2×C4—193no—
315C2×C4—191no—
316C2×C4—386no—
317C2×C4—386no—
318C2×C4—763no—
319C2×C4—766no—
320C2×C4—763no—
321C2×C4C23×D1911yescharacteristic
322C2×C4C23×D1913yes—
323C2×C4C23×D1913yes—
324C2×C4C23×D1911yescharacteristic
325C2×C4C23×D1913yes—
326C2×C4C23×D1913yes—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—383no—
331C22—383no—
332C22—383no—
333C22—383no—
334C22—383no—
335C22—383no—
336C22C24×D1911yescharacteristic
337C4—23no—
338C4—23no—
339C4—21no—
340C4—21no—
341C4—23no—
342C4—381no—
343C4—381no—
344C4—381no—
345C4—383no—
346C4—383no—
347C4—381no—
348C4C2×#6454116yes—
349C2—41no—
350C2—763no—
351C2—763no—
352C2C22×#6454111yescharacteristic
353C2#1192738111yescharacteristic
354C2#1192738111yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#519C2
hypercenter#519D19
hypocenterC19#3524
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #519

Complements

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

NH ≅ G/Ntype
1. #11927279C2semidirect
2. #11927270C2semidirect
3. #11927257C2semidirect
4. #11927238C2semidirect
5. #11927235C2semidirect
6. #11927216C2semidirect
7. #11927205C2semidirect
8. #11927205C2semidirect
9. #11927166C2semidirect
10. #11927149C2semidirect
11. #11927081C2semidirect
12. #11927072C2semidirect
13. #11927026C2semidirect
14. C4×#64545C2semidirect
15. C19×#519C2semidirect
185. #519D19semidirect
243. C19#3524semidirect

Maximal subgroups

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

subgroupindex
#119272792
#119272702
#119272572
#119272382
#119272352
#119272162
#119272052
#119271662
#119271492
#119270812
#119270722
#119270262
C4×#645452
C19×#5192
#352419