Finite Group Databasebeta

← #18076666

Subgroups — #18076666

Order 4864.

360 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#14572774C211yesmaximal, characteristic
2#14563755C211yesmaximal, characteristic, complemented
3#14562420C211yesmaximal, characteristic, complemented
4#14562048C211yesmaximal, characteristic
5#14561528C211yesmaximal, characteristic, complemented
6#14561484C211yesmaximal, characteristic, complemented
7C19×#1500C211yesmaximal, characteristic
8#11926675—21no—
9#11926616—21no—
10#11926616—21no—
11D4×C19⋊C8—21no—
12#11926605—21no—
13#11926601C2211yescharacteristic
14#11926571—21no—
15C2×C4⋊(C19⋊C8)C2211yescharacteristic
16C2×C4⋊(C19⋊C8)C2211yescharacteristic
17C4×#64520C2211yescharacteristic
18#11926299—21no—
19#11926299—21no—
20#11926297—21no—
21#11926295—21no—
22Q8⋊(C19⋊C8)—21no—
23D4⋊(C19⋊C8)—21no—
24C19×#529C2211yescharacteristic
25C19×#431C2211yescharacteristic
26C19×#376C2211yescharacteristic
27C19×#328C411yescharacteristic
28C19×#328C411yescharacteristic
29C19×#327C411yescharacteristic
30C19×#327C411yescharacteristic
31C19×#126—21no—
32C19×#125Q811yescharacteristic
33C19×#124Q811yescharacteristic
34C19×#123—21no—
35C19×C22⋊Q8C2×C411yescharacteristic
36C19×#121C2×C411yescharacteristic
37C4×Q8×C19D411yescharacteristic
38C4×D4×C19—21no—
39C4×D4×C19D411yescharacteristic
40C19×#117—21no—
41C2×C42×C19—21no—
42C2×C42×C19C2311yescharacteristic
43C2×#64520—21no—
44C2×#64520—21no—
45C22×C19⋊C8—21no—
46C22×C19⋊C8—21no—
47C22×C19⋊C8D411yescharacteristic
48C22×C19⋊C8D411yescharacteristic
49C19×C4⋊C8—21no—
50C19×C22⋊C8C2×C411yescharacteristic
51C19×C22⋊C8C2×C411yescharacteristic
52C4×C8×C19—21no—
53C19×#95—21no—
54C19×#95C2×C411yescharacteristic
55C19×#95C2×C411yescharacteristic
56C22⋊(C19⋊C8)—21no—
57C22⋊(C19⋊C8)—21no—
58C22⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)—21no—
62C4⋊(C19⋊C8)—21no—
63C4⋊(C19⋊C8)—21no—
64C4⋊(C19⋊C8)—21no—
65C4⋊(C19⋊C8)D411yescharacteristic
66C4⋊(C19⋊C8)D411yescharacteristic
67#10597260—21no—
68#10597260—21no—
69#10597260—21no—
70C4×C19⋊C8—21no—
71C4×C19⋊C8—21no—
72C2×Q8×C19C4⋊C411yescharacteristic
73C2×D4×C19—21no—
74C2×D4×C19C4⋊C411yescharacteristic
75C22×C4×C19—21no—
76C22×C4×C19—21no—
77C22×C4×C19—21no—
78C22×C4×C19C22×C411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19#4111yescharacteristic
81C2×C8×C19—21no—
82C2×C8×C19—21no—
83C4⋊C4×C19—21no—
84C4⋊C4×C19—21no—
85C4⋊C4×C19—21no—
86C4⋊C4×C19—21no—
87C4⋊C4×C19C4⋊C411yescharacteristic
88C4⋊C4×C19C4⋊C411yescharacteristic
89C22⋊C4×C19—21no—
90C22⋊C4×C19—21no—
91C22⋊C4×C19—21no—
92C22⋊C4×C19—21no—
93C22⋊C4×C19—21no—
94C42×C19—21no—
95C42×C19—41no—
96C42×C19—41no—
97C42×C19C2×D411yescharacteristic
98C42×C19C2×D411yescharacteristic
99C42×C19C2×Q811yescharacteristic
100C42×C19#4111yescharacteristic
101#64520—22no—
102#64520—41no—
103#64520—81no—
104C2×C19⋊C8—21no—
105C2×C19⋊C8—21no—
106C2×C19⋊C8—21no—
107C2×C19⋊C8—21no—
108C2×C19⋊C8—41no—
109C2×C19⋊C8—41no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8—42no—
112C2×C19⋊C8—41no—
113C2×C19⋊C8—81no—
114#8877—191nomaximal, Sylow
115C23×C19—21no—
116C23×C19C4×D411yescharacteristic
117Q8×C19—41no—
118D4×C19—41no—
119D4×C19—41no—
120D4×C19—41no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19C2×C4⋊C411yescharacteristic
138C2×C4×C19C4×D411yescharacteristic
139C2×C4×C19#12011yescharacteristic
140C2×C4×C19C22⋊Q811yescharacteristic
141C2×C4×C19C22⋊Q811yescharacteristic
142C2×C4×C19#12311yescharacteristic
143C8×C19—41no—
144C8×C19—41no—
145C19⋊C8—42no—
146C19⋊C8—41no—
147C19⋊C8—41no—
148C19⋊C8—41no—
149C19⋊C8—41no—
150C19⋊C8—81no—
151#2992—191no—
152#1832—191no—
153#1573—191no—
154#1500D1911yescharacteristic
155#1483—191no—
156#1300—191no—
157#1283—191no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19—41no—
163C22×C19#38511yescharacteristic
164C22×C19#44311yescharacteristic
165C22×C19#44411yescharacteristic
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—21no—
171C4×C19—41no—
172C4×C19—41no—
173C4×C19—41no—
174C4×C19—81no—
175C4×C19—81no—
176C4×C19#45411yescharacteristic
177C4×C19#45511yescharacteristic
178#529C2×D1911yescharacteristic
179#446—381no—
180#435—381no—
181#435—381no—
182C8×D4—381no—
183#433—381no—
184#432—191no—
185#431C2×D1911yescharacteristic
186#424—381no—
187C2×C4⋊C8—191no—
188C2×C4⋊C8—191no—
189C4×M16—191no—
190#376C2×D1911yescharacteristic
191#336—381no—
192#336—381no—
193#335—381no—
194#334—381no—
195#328Dic1911yescharacteristic
196#328Dic1911yescharacteristic
197#327Dic1911yescharacteristic
198#327Dic1911yescharacteristic
199Q8⋊C8—381no—
200D4⋊C8—381no—
201C2×C19—21no—
202C2×C19—21no—
203C2×C19—81no—
204C2×C19#186011yescharacteristic
205C2×C19#186611yescharacteristic
206C2×C19#186811yescharacteristic
207C2×M16—381no—
208C2×M16—381no—
209C22×C8—191no—
210C22×C8—191no—
211C22×C8—381no—
212C22×C8—381no—
213#126—21no—
214#125Dic3811yescharacteristic
215#124Dic3811yescharacteristic
216#123—21no—
217C22⋊Q8C2×Dic1911yescharacteristic
218#121C2×Dic1911yescharacteristic
219C4×Q8D7611yescharacteristic
220C4×D4—21no—
221C4×D4D7611yescharacteristic
222#117—21no—
223C2×C42—21no—
224C2×C42C22×D1911yescharacteristic
225C4⋊C8—21no—
226C4⋊C8—191no—
227C4⋊C8—191no—
228C4⋊C8—381no—
229C4⋊C8—381no—
230C4⋊C8—381no—
231C4⋊C8—381no—
232C4⋊C8—381no—
233C4⋊C8—381no—
234C22⋊C8—381no—
235C22⋊C8—381no—
236C22⋊C8—381no—
237C22⋊C8C2×Dic1911yescharacteristic
238C22⋊C8C2×Dic1911yescharacteristic
239#97—381no—
240#97—381no—
241#97—381no—
242C4×C8—21no—
243C4×C8—381no—
244C4×C8—381no—
245#95—21no—
246#95C2×Dic1911yescharacteristic
247#95C2×Dic1911yescharacteristic
248C19#887711yescharacteristic, complemented, Sylow
249C2×Q8C4⋊Dic1911yescharacteristic
250C2×D4—21no—
251C2×D4C4⋊Dic1911yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4D4×D1911yescharacteristic
256C22×C4#6454311yescharacteristic
257C22×C4C22×Dic1911yescharacteristic
258M16—382no—
259M16—761no—
260M16—1521no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—381no—
264C2×C8—381no—
265C2×C8—381no—
266C2×C8—381no—
267C2×C8—761no—
268C2×C8—761no—
269C2×C8—761no—
270C2×C8—762no—
271C2×C8—761no—
272C2×C8—1521no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4C4⋊Dic1911yescharacteristic
278C4⋊C4C4⋊Dic1911yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C42—21no—
285C42—41no—
286C42—41no—
287C42C2×Dic3811yescharacteristic
288C42C2×D7611yescharacteristic
289C42D4×D1911yescharacteristic
290C42#6454311yescharacteristic
291C23—21no—
292C23D4×Dic1911yescharacteristic
293Q8—41no—
294D4—41no—
295D4—41no—
296D4—41no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4#1059732411yescharacteristic
314C2×C4#1059732411yescharacteristic
315C2×C4#1059732811yescharacteristic
316C2×C4#1059733211yescharacteristic
317C2×C4C2×C4⋊Dic1911yescharacteristic
318C2×C4D4×Dic1911yescharacteristic
319C8—41no—
320C8—41no—
321C8—762no—
322C8—761no—
323C8—761no—
324C8—761no—
325C8—761no—
326C8—1521no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22#1192641911yescharacteristic
333C22#1192666111yescharacteristic
334C22#1192666611yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4#1192671811yescharacteristic
346C4#1192672311yescharacteristic
347C2—21no—
348C2—21no—
349C2—81no—
350C2#1456387011yescharacteristic
351C2#1456391211yescharacteristic
352C2#1456392311yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1500C2
socleC22×C19#385
prime radicalC19×#121C2×C4
cosocleC2×C42×C19C23
hypercenter#1500D19
hypocenterC19#8877
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1500

Complements

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

NH ≅ G/Ntype
2. #14563755C2semidirect
3. #14562420C2semidirect
5. #14561528C2semidirect
6. #14561484C2semidirect
248. C19#8877semidirect

Maximal subgroups

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

subgroupindex
#145727742
#145637552
#145624202
#145620482
#145615282
#145614842
C19×#15002
#887719