Finite Group Databasebeta

← #14577620

Subgroups — #14577620

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#11927270C211yesmaximal, characteristic, complemented
2#11927264C213yesmaximal, complemented
3#11927249C213yesmaximal, complemented
4#11927244C213yesmaximal, complemented
5#11927229C213yesmaximal, complemented
6Q8×D76C211yesmaximal, characteristic, complemented
7#11927201C211yesmaximal, characteristic, complemented
8#11927201C211yesmaximal, characteristic, complemented
9#11927159C213yesmaximal, complemented
10#11927156C213yesmaximal, complemented
11#11927076C213yesmaximal, complemented
12#11927072C213yesmaximal, complemented
13#11927020C211yesmaximal, characteristic, complemented
14C4×Q8×D19C211yesmaximal, characteristic, complemented
15C19×#520C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×Q8×D19C2211yescharacteristic
18C2×Q8×D19C2211yescharacteristic
19C4×Q8×C19C2211yescharacteristic
20C4×Q8×C19C2211yescharacteristic
21C4×D4×C19C2213yes—
22C4×D4×C19C2213yes—
23C19×#117C2213yes—
24C2×C4⋊C4×C19C2213yes—
25Q8×Dic19C2211yescharacteristic
26Q8×Dic19C2211yescharacteristic
27#10597384C2213yes—
28#10597384C2213yes—
29#10597382C2213yes—
30#10597382C2213yes—
31#10597375C2216yes—
32C4×C22⋊D19C2213yes—
33C4×C22⋊D19C2213yes—
34C4×C22⋊D19C2216yes—
35#10597372C2216yes—
36#10597370C2213yes—
37#10597370C2213yes—
38#10597370C2216yes—
39#10597344C2213yes—
40#10597343C2213yes—
41#10597343C2213yes—
42#10597342C2213yes—
43#10597340C2211yescharacteristic
44#10597338C2213yes—
45C4⋊C4×D19C2213yes—
46#10597336C2213yes—
47#10597335C2213yes—
48#10597335C2216yes—
49#10597334C2213yes—
50#10597333C2213yes—
51#10597333C2213yes—
52#10597331C2213yes—
53#10597330C2213yes—
54#10597329C2213yes—
55#10597325C2213yes—
56#10597325C2216yes—
57#10597325C2216yes—
58C4×D76C2213yes—
59#10597318C2213yes—
60C42×D19C2213yes—
61#10597316C2213yes—
62#10597315C2213yes—
63C4×Dic38C2213yes—
64C4×Dic38C2213yes—
65C4×Dic38C2213yes—
66#41×C19—24no—
67C2×Q8×C19C2311yescharacteristic
68C2×D4×C19C2313yes—
69C22×C4×C19C2313yes—
70C22×C4×C19C2316yes—
71C2×C22⋊D19C2313yes—
72C2×C22⋊D19C2313yes—
73Q8×D19—24no—
74Q8×D19—24no—
75C2×D76C2311yescharacteristic
76C2×C4×D19C2313yes—
77C2×C4×D19C2313yes—
78C2×C4×D19C2311yescharacteristic
79C2×C4×D19C2313yes—
80C2×Dic38C2313yes—
81C2×Dic38C2313yes—
82C2×Dic38C2313yes—
83C4⋊C4×C19C2313yes—
84C4⋊C4×C19C2313yes—
85C4⋊C4×C19C2313yes—
86C4⋊C4×C19C2311yescharacteristic
87C22⋊C4×C19C2313yes—
88C22⋊C4×C19C2313yes—
89C42×C19C2313yes—
90C42×C19C2313yes—
91C22⋊Dic19C2313yes—
92C22⋊Dic19C2313yes—
93C22⋊Dic19C2316yes—
94C22⋊Dic19C2316yes—
95(C2×D19)⋊C4C2311yescharacteristic
96(C2×D19)⋊C4C2313yes—
97(C2×D19)⋊C4C2313yes—
98(C2×D19)⋊C4C2313yes—
99(C2×D19)⋊C4C2311yescharacteristic
100(C2×D19)⋊C4C2311yescharacteristic
101C4⋊Dic19C2313yes—
102C4⋊Dic19C2313yes—
103C4⋊Dic19C2313yes—
104C4⋊Dic19C2313yes—
105C4⋊Dic19C2316yes—
106Dic19⋊C4C2311yescharacteristic
107Dic19⋊C4C2313yes—
108Dic19⋊C4C2313yes—
109Dic19⋊C4C2316yes—
110Dic19⋊C4C2316yes—
111Dic19⋊C4C2313yes—
112Dic19⋊C4C2313yes—
113Dic19⋊C4C2313yes—
114C4×Dic19C2313yes—
115C4×Dic19C2313yes—
116C4×Dic19C2313yes—
117C4×Dic19C2316yes—
118C4×Dic19C2313yes—
119C23×C19C2413yes—
120C22×D19C2411yescharacteristic
121C22×D19C2411yescharacteristic
122Q8×C19#4114yes—
123D4×C19—26no—
124C2×C4×C19—26no—
125C2×C4×C19—46no—
126C2×C4×C19C2411yescharacteristic
127C2×C4×C19C2413yes—
128C2×C4×C19C2411yescharacteristic
129C2×C4×C19C2411yescharacteristic
130C2×C4×C19C2413yes—
131C2×C4×C19C2413yes—
132C22⋊D19—26no—
133C22⋊D19—43no—
134C2×Dic19C2411yescharacteristic
135C2×Dic19C2413yes—
136C2×Dic19C2411yescharacteristic
137C2×Dic19C2413yes—
138C2×Dic19C2413yes—
139C2×Dic19C2413yes—
140D76—22no—
141C4×D19—22no—
142C4×D19—26no—
143C4×D19—26no—
144C4×D19—43no—
145Dic38—26no—
146Dic38—26no—
147Dic38—43no—
148#3516—191nomaximal, Sylow
149C22×C19—23no—
150C22×C19—23no—
151C22×C19—23no—
152C22×C19C2511yescharacteristic
153C2×D19—21no—
154C2×D19—21no—
155C2×D19—21no—
156C2×D19—21no—
157C2×D19—21no—
158C2×D192−1+412yes—
159C4×C19—21no—
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—23no—
163C4×C19—23no—
164C4×C19C2×#4116yes—
165Dic19—23no—
166Dic19—23no—
167Dic19—21no—
168Dic19—23no—
169Dic19—21no—
170Dic19—23no—
171#557—191no—
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#520D1911yescharacteristic, complemented
184#519—191no—
185C2×C4×Q8—191no—
186C2×C19—43no—
187C2×C19C22×#4111yescharacteristic
188C2×C19C2×2−1+411yescharacteristic
189C2×C19#58511yescharacteristic
190D19—22no—
191D19—41no—
192C2×#41C2×D1911yescharacteristic
193C22×Q8—191no—
194C22×Q8—191no—
195C4⋊Q8—193no—
196C4⋊Q8—193no—
197#126—193no—
198#126—196no—
199#126—193no—
200#126—196no—
201#125—193no—
202#125—193no—
203#125—196no—
204#125—193no—
205#124—193no—
206#124—193no—
207#124—193no—
208#123—196no—
209#123—191no—
210#123—193no—
211C22⋊Q8—193no—
212C22⋊Q8—193no—
213C22⋊Q8—196no—
214C22⋊Q8—193no—
215C22⋊Q8—193no—
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—193no—
226C4×Q8—193no—
227C4×Q8C2×D1911yescharacteristic
228C4×Q8C2×D1911yescharacteristic
229C4×D4—193no—
230C4×D4—193no—
231C4×D4—196no—
232C4×D4—193no—
233C4×D4C2×D1913yes—
234C4×D4C2×D1913yes—
235#117—196no—
236#117—193no—
237#117—193no—
238#117C2×D1913yes—
239C2×C4⋊C4—193no—
240C2×C4⋊C4C2×D1913yes—
241C2×C42—193no—
242C19#351611yescharacteristic, complemented, Sylow
243#41—24no—
244C2×Q8—193no—
245C2×Q8—193no—
246C2×Q8—193no—
247C2×Q8—384no—
248C2×Q8—384no—
249C2×Q8C22×D1911yescharacteristic
250C2×D4—193no—
251C2×D4—193no—
252C2×D4—191no—
253C2×D4C22×D1913yes—
254C22×C4—191no—
255C22×C4—193no—
256C22×C4—193no—
257C22×C4—193no—
258C22×C4C22×D1913yes—
259C22×C4C22×D1916yes—
260C4⋊C4—196no—
261C4⋊C4—193no—
262C4⋊C4—193no—
263C4⋊C4—193no—
264C4⋊C4—193no—
265C4⋊C4—196no—
266C4⋊C4—191no—
267C4⋊C4—193no—
268C4⋊C4—193no—
269C4⋊C4—193no—
270C4⋊C4—193no—
271C4⋊C4—196no—
272C4⋊C4—193no—
273C4⋊C4C22×D1913yes—
274C4⋊C4C22×D1913yes—
275C4⋊C4C22×D1913yes—
276C4⋊C4C22×D1911yescharacteristic
277C22⋊C4—193no—
278C22⋊C4—196no—
279C22⋊C4—196no—
280C22⋊C4—193no—
281C22⋊C4—193no—
282C22⋊C4—191no—
283C22⋊C4—191no—
284C22⋊C4—193no—
285C22⋊C4—191no—
286C22⋊C4—193no—
287C22⋊C4C22×D1913yes—
288C22⋊C4C22×D1913yes—
289C42—193no—
290C42—193no—
291C42—193no—
292C42—196no—
293C42—193no—
294C42C22×D1913yes—
295C42C22×D1913yes—
296C23—191no—
297C23—191no—
298C23C23×D1913yes—
299Q8—386no—
300Q8—386no—
301Q8—763no—
302Q8#6454114yes—
303D4—26no—
304D4—382no—
305D4—386no—
306D4—763no—
307C2×C4—26no—
308C2×C4—46no—
309C2×C4—191no—
310C2×C4—191no—
311C2×C4—193no—
312C2×C4—193no—
313C2×C4—193no—
314C2×C4—193no—
315C2×C4—382no—
316C2×C4—386no—
317C2×C4—386no—
318C2×C4—763no—
319C2×C4C23×D1911yescharacteristic
320C2×C4C23×D1913yes—
321C2×C4C23×D1911yescharacteristic
322C2×C4C23×D1913yes—
323C2×C4C23×D1911yescharacteristic
324C2×C4C23×D1913yes—
325C22—23no—
326C22—23no—
327C22—23no—
328C22—192no—
329C22—381no—
330C22—381no—
331C22—381no—
332C22—381no—
333C22—381no—
334C22C24×D1911yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—23no—
339C4—23no—
340C4—383no—
341C4—383no—
342C4—381no—
343C4—383no—
344C4—383no—
345C4—381no—
346C4C2×#6454116yes—
347C2—43no—
348C2—382no—
349C2—761no—
350C2C22×#6454111yescharacteristic
351C22−1+4×D1911yescharacteristic
352C2#1192737911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#520C2
hypercenter#520D19
hypocenterC19#3516
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #11927270C2semidirect
2. #11927264C2semidirect
3. #11927249C2semidirect
4. #11927244C2semidirect
5. #11927229C2semidirect
6. Q8×D76C2semidirect
7. #11927201C2semidirect
8. #11927201C2semidirect
9. #11927159C2semidirect
10. #11927156C2semidirect
11. #11927076C2semidirect
12. #11927072C2semidirect
13. #11927020C2semidirect
14. C4×Q8×D19C2semidirect
15. C19×#520C2semidirect
183. #520D19semidirect
242. C19#3516semidirect

Maximal subgroups

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

subgroupindex
#119272702
#119272642
#119272492
#119272442
#119272292
Q8×D762
#119272012
#119271592
#119271562
#119270762
#119270722
#119270202
C4×Q8×D192
C19×#5202
#351619