Finite Group Databasebeta

← #14577646

Subgroups — #14577646

Order 2432.

1010 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
1Q8×Dic38C211yesmaximal, characteristic, complemented
2#11927267C213yesmaximal, complemented
3#11927266C213yesmaximal, complemented
4#11927262C213yesmaximal, complemented
5#11927257C213yesmaximal, complemented
6Q8×C22⋊D19C211yesmaximal, characteristic, complemented
7#11927206C211yesmaximal, characteristic, complemented
8#11927205C211yesmaximal, characteristic, complemented
9#11927166C213yesmaximal, complemented
10#11927165C213yesmaximal, complemented
11#11927098C213yesmaximal, complemented
12#11927072C213yesmaximal, complemented
13#11927020C211yesmaximal, characteristic, complemented
14C4×#64545C211yesmaximal, characteristic, complemented
15C19×#519C211yesmaximal, characteristic, complemented
16C22×Q8×C19C2211yescharacteristic
17C2×#64545C2211yescharacteristic
18C2×Q8×D19C2211yescharacteristic
19C4×Q8×C19C2213yes—
20C4×Q8×C19C2211yescharacteristic
21C4×Q8×C19C2213yes—
22C4×Q8×C19C2211yescharacteristic
23C19×#117C2213yes—
24C19×#117C2213yes—
25#10597393C2213yes—
26#10597392C2213yes—
27#10597392C2213yes—
28Q8×Dic19C2211yescharacteristic
29Q8×Dic19C2211yescharacteristic
30#10597390C2213yes—
31#10597376C2213yes—
32C4×C22⋊D19C2213yes—
33C4×C22⋊D19C2213yes—
34#10597370C2213yes—
35#10597344C2213yes—
36#10597344C2216yes—
37#10597343C2213yes—
38#10597342C2213yes—
39#10597342C2216yes—
40#10597341C2213yes—
41#10597340C2213yes—
42#10597339C2213yes—
43#10597338C2213yes—
44#10597338C2213yes—
45#10597335C2213yes—
46#10597334C2213yes—
47#10597334C2213yes—
48#10597333C2213yes—
49#10597331C2211yescharacteristic
50#10597331C2216yes—
51#10597330C2213yes—
52#10597329C2213yes—
53#10597325C2213yes—
54#10597322C2216yes—
55#10597321C2213yes—
56#10597321C2216yes—
57C4×D76C2213yes—
58C4×D76C2213yes—
59#10597318C2213yes—
60#10597318C2216yes—
61C42×D19C2213yes—
62#10597315C2213yes—
63C4×Dic38C2213yes—
64C4×Dic38C2213yes—
65C4×Dic38C2216yes—
66C2×Q8×C19—24no—
67C2×Q8×C19C2313yes—
68C2×Q8×C19C2311yescharacteristic
69C22×C4×C19C2313yes—
70C2×C22⋊D19C2311yescharacteristic
71C2×C22⋊D19C2313yes—
72#64545—24no—
73Q8×D19—24no—
74C2×D76C2313yes—
75C2×D76C2313yes—
76C2×C4×D19C2313yes—
77C2×C4×D19C2313yes—
78C2×C4×D19C2313yes—
79C2×C4×D19C2313yes—
80C2×Dic38C2313yes—
81C2×Dic38C2311yescharacteristic
82C2×Dic38C2316yes—
83C4⋊C4×C19C2313yes—
84C4⋊C4×C19C2313yes—
85C4⋊C4×C19C2313yes—
86C4⋊C4×C19C2313yes—
87C22⋊C4×C19C2313yes—
88C22⋊C4×C19C2311yescharacteristic
89C42×C19C2313yes—
90C42×C19C2313yes—
91C42×C19C2316yes—
92C22⋊Dic19C2311yescharacteristic
93C22⋊Dic19C2313yes—
94(C2×D19)⋊C4C2316yes—
95(C2×D19)⋊C4C2313yes—
96(C2×D19)⋊C4C2313yes—
97(C2×D19)⋊C4C2311yescharacteristic
98(C2×D19)⋊C4C2313yes—
99(C2×D19)⋊C4C2316yes—
100(C2×D19)⋊C4C2311yescharacteristic
101(C2×D19)⋊C4C2313yes—
102(C2×D19)⋊C4C2316yes—
103C4⋊Dic19C2313yes—
104C4⋊Dic19C2313yes—
105C4⋊Dic19C2313yes—
106C4⋊Dic19C2313yes—
107Dic19⋊C4C2313yes—
108Dic19⋊C4C2316yes—
109Dic19⋊C4C2313yes—
110Dic19⋊C4C2313yes—
111Dic19⋊C4C2313yes—
112Dic19⋊C4C2313yes—
113Dic19⋊C4C2313yes—
114C4×Dic19C2313yes—
115C4×Dic19C2313yes—
116C4×Dic19C2313yes—
117C4×Dic19C2316yes—
118C4×Dic19C2311yescharacteristic
119C23×C19C2411yescharacteristic
120C22×D19C2411yescharacteristic
121C22×D19C2413yes—
122Q8×C19—26no—
123Q8×C19#4114yes—
124C2×C4×C19—26no—
125C2×C4×C19C2413yes—
126C2×C4×C19C2411yescharacteristic
127C2×C4×C19C2413yes—
128C2×C4×C19C2413yes—
129C2×C4×C19C2411yescharacteristic
130C2×C4×C19C2413yes—
131C22⋊D19—22no—
132C22⋊D19—43no—
133C2×Dic19C2411yescharacteristic
134C2×Dic19C2411yescharacteristic
135C2×Dic19C2413yes—
136C2×Dic19C2413yes—
137C2×Dic19C2413yes—
138C2×Dic19C2411yescharacteristic
139D76—26no—
140D76—43no—
141C4×D19—26no—
142C4×D19—26no—
143C4×D19—26no—
144C4×D19—43no—
145Dic38—26no—
146Dic38—22no—
147Dic38—46no—
148#3518—191nomaximal, Sylow
149C22×C19—21no—
150C22×C19—21no—
151C22×C19—21no—
152C22×C19C2511yescharacteristic
153C2×D19—21no—
154C2×D19—23no—
155C2×D19—23no—
156C2×D19—21no—
157C2×D19—23no—
158C2×D19—21no—
159C4×C19—23no—
160C4×C19—21no—
161C4×C19—23no—
162C4×C19—23no—
163C4×C19—21no—
164C4×C19C2×#4116yes—
165Dic19—23no—
166Dic19—21no—
167Dic19—21no—
168Dic19—23no—
169Dic19—23no—
170Dic192−1+412yes—
171Q82—191no—
172#556—193no—
173#556—193no—
174#556—193no—
175#555—193no—
176D4×Q8—191no—
177#548—191no—
178#548—191no—
179#542—193no—
180#542—193no—
181#533—193no—
182#529—193no—
183#519—191no—
184#519D1911yescharacteristic, complemented
185C4×#41—191no—
186C2×C19—41no—
187C2×C19C22×#4111yescharacteristic
188C2×C19C2×2−1+411yescharacteristic
189C2×C19#58511yescharacteristic
190D19—41no—
191D19—43no—
192C2×#41—191no—
193C22×Q8—191no—
194C22×Q8C2×D1911yescharacteristic
195C4⋊Q8—193no—
196C4⋊Q8—193no—
197C4⋊Q8—193no—
198C4⋊Q8—193no—
199#126—193no—
200#126—196no—
201#126—193no—
202#126—196no—
203#125—193no—
204#124—193no—
205#124—191no—
206#124—196no—
207#124—193no—
208#124—196no—
209#123—193no—
210#123—193no—
211C22⋊Q8—193no—
212C22⋊Q8—193no—
213C22⋊Q8—193no—
214C22⋊Q8—193no—
215C22⋊Q8—196no—
216C22⋊Q8—193no—
217#121—193no—
218#121—193no—
219#121—193no—
220C4×Q8—191no—
221C4×Q8—191no—
222C4×Q8—193no—
223C4×Q8—193no—
224C4×Q8—193no—
225C4×Q8—196no—
226C4×Q8C2×D1911yescharacteristic
227C4×Q8C2×D1913yes—
228C4×Q8C2×D1911yescharacteristic
229C4×Q8C2×D1913yes—
230C4×D4—193no—
231C4×D4—193no—
232C4×D4—193no—
233C4×D4—193no—
234C4×D4—193no—
235#117—193no—
236#117—193no—
237#117—193no—
238#117—196no—
239#117C2×D1913yes—
240#117C2×D1913yes—
241C2×C42—193no—
242C19#351811yescharacteristic, complemented, Sylow
243#41—384no—
244C2×Q8—24no—
245C2×Q8—191no—
246C2×Q8—193no—
247C2×Q8—196no—
248C2×Q8—384no—
249C2×Q8C22×D1913yes—
250C2×Q8C22×D1911yescharacteristic
251C2×D4—191no—
252C2×D4—193no—
253C2×D4—193no—
254C2×D4—193no—
255C22×C4—193no—
256C22×C4—193no—
257C22×C4—193no—
258C22×C4—193no—
259C22×C4C22×D1913yes—
260C4⋊C4—193no—
261C4⋊C4—193no—
262C4⋊C4—193no—
263C4⋊C4—193no—
264C4⋊C4—193no—
265C4⋊C4—196no—
266C4⋊C4—193no—
267C4⋊C4—193no—
268C4⋊C4—193no—
269C4⋊C4—193no—
270C4⋊C4—193no—
271C4⋊C4C22×D1913yes—
272C4⋊C4C22×D1913yes—
273C4⋊C4C22×D1913yes—
274C4⋊C4C22×D1913yes—
275C22⋊C4—191no—
276C22⋊C4—193no—
277C22⋊C4—193no—
278C22⋊C4—191no—
279C22⋊C4—196no—
280C22⋊C4—196no—
281C22⋊C4—196no—
282C22⋊C4—191no—
283C22⋊C4—193no—
284C22⋊C4—193no—
285C22⋊C4—193no—
286C22⋊C4C22×D1913yes—
287C22⋊C4C22×D1911yescharacteristic
288C42—191no—
289C42—193no—
290C42—193no—
291C42—196no—
292C42—193no—
293C42C22×D1913yes—
294C42C22×D1916yes—
295C42C22×D1913yes—
296C23—191no—
297C23—193no—
298C23C23×D1911yescharacteristic
299Q8—26no—
300Q8—382no—
301Q8—386no—
302Q8—766no—
303Q8#6454114yes—
304D4—382no—
305D4—386no—
306D4—763no—
307D4—763no—
308C2×C4—26no—
309C2×C4—191no—
310C2×C4—191no—
311C2×C4—191no—
312C2×C4—193no—
313C2×C4—193no—
314C2×C4—193no—
315C2×C4—386no—
316C2×C4—386no—
317C2×C4—386no—
318C2×C4—763no—
319C2×C4C23×D1913yes—
320C2×C4C23×D1911yescharacteristic
321C2×C4C23×D1911yescharacteristic
322C2×C4C23×D1913yes—
323C2×C4C23×D1913yes—
324C2×C4C23×D1913yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—381no—
329C22—383no—
330C22—383no—
331C22—381no—
332C22—383no—
333C22—381no—
334C22C24×D1911yescharacteristic
335C4—23no—
336C4—23no—
337C4—21no—
338C4—21no—
339C4—23no—
340C4—192no—
341C4—381no—
342C4—383no—
343C4—381no—
344C4—383no—
345C4—383no—
346C4C2×#6454116yes—
347C2—41no—
348C2—761no—
349C2—763no—
350C2C22×#6454111yescharacteristic
351C22−1+4×D1911yescharacteristic
352C2#1192738111yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#519C2
hypercenter#519D19
hypocenterC19#3518
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #519

Complements

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

NH ≅ G/Ntype
1. Q8×Dic38C2semidirect
2. #11927267C2semidirect
3. #11927266C2semidirect
4. #11927262C2semidirect
5. #11927257C2semidirect
6. Q8×C22⋊D19C2semidirect
7. #11927206C2semidirect
8. #11927205C2semidirect
9. #11927166C2semidirect
10. #11927165C2semidirect
11. #11927098C2semidirect
12. #11927072C2semidirect
13. #11927020C2semidirect
14. C4×#64545C2semidirect
15. C19×#519C2semidirect
184. #519D19semidirect
242. C19#3518semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic382
#119272672
#119272662
#119272622
#119272572
Q8×C22⋊D192
#119272062
#119272052
#119271662
#119271652
#119270982
#119270722
#119270202
C4×#645452
C19×#5192
#351819