Finite Group Databasebeta

← #18076664

Subgroups — #18076664

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#14563754C211yesmaximal, characteristic, complemented
2#14562421C211yesmaximal, characteristic, complemented
3#14562121C211yesmaximal, characteristic
4#14562048C211yesmaximal, characteristic
5#14561527C211yesmaximal, characteristic, complemented
6#14561485C211yesmaximal, characteristic, complemented
7C19×#2992C211yesmaximal, characteristic
8#11926597C2211yescharacteristic
9C2×C4⋊(C19⋊C8)C2211yescharacteristic
10C4×#64520C2211yescharacteristic
11#11926390C2211yescharacteristic
12#11926298—21no—
13#11926298—21no—
14#11926296—21no—
15#11926294—21no—
16#11926281C411yescharacteristic
17#11926281C411yescharacteristic
18#11926278C411yescharacteristic
19#11926278C411yescharacteristic
20Q8⋊(C19⋊C8)—21no—
21D4⋊(C19⋊C8)—21no—
22C19×#529C2211yescharacteristic
23C19×#446—21no—
24C19×#435—21no—
25C19×#435—21no—
26C8×D4×C19—21no—
27C19×#433—21no—
28C19×#432C2211yescharacteristic
29C19×#424—21no—
30C2×C19×C4⋊C8C2211yescharacteristic
31C2×M16×C19—21no—
32C22×C8×C19—21no—
33C22×C8×C19D411yescharacteristic
34C22×C8×C19D411yescharacteristic
35C19×#126—21no—
36C19×#125Q811yescharacteristic
37C19×#124Q811yescharacteristic
38C19×#123—21no—
39C19×C22⋊Q8C2×C411yescharacteristic
40C19×#121C2×C411yescharacteristic
41C4×Q8×C19D411yescharacteristic
42C4×D4×C19—21no—
43C4×D4×C19D411yescharacteristic
44C19×#117—21no—
45C2×C42×C19C2311yescharacteristic
46C2×C4×Dic19—21no—
47C2×#64520—21no—
48C22×C19⋊C8—21no—
49C19×C4⋊C8—21no—
50C19×C4⋊C8—21no—
51C19×C4⋊C8—21no—
52C19×C4⋊C8—21no—
53C19×C4⋊C8D411yescharacteristic
54C19×C4⋊C8D411yescharacteristic
55C19×C22⋊C8—21no—
56C19×C22⋊C8—21no—
57C19×C22⋊C8—21no—
58C19×#97—21no—
59C19×#97—21no—
60C4×C8×C19—21no—
61C19⋊#95—21no—
62C19⋊#95C2×C411yescharacteristic
63C19⋊#95C2×C411yescharacteristic
64C22⋊(C19⋊C8)C2×C411yescharacteristic
65C22⋊(C19⋊C8)C2×C411yescharacteristic
66C4⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)—21no—
68C4⋊(C19⋊C8)—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×C19C22×C411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19#4111yescharacteristic
79C22×Dic19—21no—
80C22×Dic19—21no—
81M16×C19—81no—
82C2×C8×C19—21no—
83C2×C8×C19—21no—
84C2×C8×C19—21no—
85C2×C8×C19—21no—
86C2×C8×C19—41no—
87C2×C8×C19—41no—
88C2×C8×C19—81no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19—21no—
91C4⋊C4×C19—21no—
92C4⋊C4×C19—21no—
93C4⋊C4×C19C4⋊C411yescharacteristic
94C4⋊C4×C19C4⋊C411yescharacteristic
95C22⋊C4×C19—21no—
96C22⋊C4×C19—21no—
97C22⋊C4×C19—21no—
98C22⋊C4×C19—21no—
99C22⋊C4×C19—21no—
100C42×C19—21no—
101C42×C19C2×D411yescharacteristic
102C42×C19C2×D411yescharacteristic
103C42×C19C2×Q811yescharacteristic
104C42×C19#4111yescharacteristic
105C4×Dic19—41no—
106C4×Dic19—41no—
107#64520—22no—
108#64520—41no—
109C2×C19⋊C8—21no—
110C2×C19⋊C8—21no—
111C2×C19⋊C8—41no—
112C2×C19⋊C8—42no—
113C2×C19⋊C8—41no—
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×C19C2×C4⋊C411yescharacteristic
132C2×C4×C19C4×D411yescharacteristic
133C2×C4×C19#12011yescharacteristic
134C2×C4×C19C22⋊Q811yescharacteristic
135C2×C4×C19C22⋊Q811yescharacteristic
136C2×C4×C19#12311yescharacteristic
137C2×Dic19—41no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C8×C19—41no—
144C8×C19—41no—
145C8×C19—41no—
146C8×C19—41no—
147C19⋊C8—41no—
148C19⋊C8—41no—
149C19⋊C8—42no—
150C19⋊C8—81no—
151#2992D1911yescharacteristic
152#1832—191no—
153#1573—191no—
154#1500—191no—
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#45411yescharacteristic
175C4×C19#45511yescharacteristic
176Dic19—81no—
177Dic19—81no—
178#529C2×D1911yescharacteristic
179#446—21no—
180#435—21no—
181#435—21no—
182C8×D4—21no—
183#433—21no—
184#432C2×D1911yescharacteristic
185#431—191no—
186#424—21no—
187C2×C4⋊C8—191no—
188C2×C4⋊C8C2×D1911yescharacteristic
189C4×M16—191no—
190#376—191no—
191#336—381no—
192#336—381no—
193#335—381no—
194#334—381no—
195#328—191no—
196#328—191no—
197#327—191no—
198#327—191no—
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—21no—
208C2×M16—381no—
209C22×C8—21no—
210C22×C8—381no—
211C22×C8C22⋊D1911yescharacteristic
212C22×C8C22⋊D1911yescharacteristic
213#126—21no—
214#125Dic3811yescharacteristic
215#124Dic3811yescharacteristic
216#123—21no—
217C22⋊Q8C4×D1911yescharacteristic
218#121C4×D1911yescharacteristic
219C4×Q8C22⋊D1911yescharacteristic
220C4×D4—21no—
221C4×D4C22⋊D1911yescharacteristic
222#117—21no—
223C2×C42—381no—
224C2×C42C22×D1911yescharacteristic
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—381no—
230C4⋊C8—381no—
231C4⋊C8—381no—
232C4⋊C8C22⋊D1911yescharacteristic
233C4⋊C8C22⋊D1911yescharacteristic
234C22⋊C8—21no—
235C22⋊C8—21no—
236C22⋊C8—21no—
237C22⋊C8—191no—
238C22⋊C8—191no—
239#97—21no—
240#97—21no—
241#97—381no—
242C4×C8—21no—
243C4×C8—381no—
244C4×C8—381no—
245#95—191no—
246#95—191no—
247#95—381no—
248C19#887711yescharacteristic, complemented, Sylow
249C2×Q8Dic19⋊C411yescharacteristic
250C2×D4—21no—
251C2×D4Dic19⋊C411yescharacteristic
252C22×C4—21no—
253C22×C4—381no—
254C22×C4—381no—
255C22×C4C2×C4×D1911yescharacteristic
256C22×C4#6454111yescharacteristic
257C22×C4C2×C22⋊D1911yescharacteristic
258M16—81no—
259M16—382no—
260M16—761no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—81no—
268C2×C8—381no—
269C2×C8—381no—
270C2×C8—761no—
271C2×C8—762no—
272C2×C8—761no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4Dic19⋊C411yescharacteristic
278C4⋊C4Dic19⋊C411yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C42—21no—
285C42—761no—
286C42—761no—
287C42C2×Dic3811yescharacteristic
288C42#6454111yescharacteristic
289C42C2×C22⋊D1911yescharacteristic
290C42C2×C22⋊D1911yescharacteristic
291C23—21no—
292C23C4×C22⋊D1911yescharacteristic
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—761no—
308C2×C4—761no—
309C2×C4—761no—
310C2×C4—761no—
311C2×C4—761no—
312C2×C4—761no—
313C2×C4C2×Dic19⋊C411yescharacteristic
314C2×C4#1059737011yescharacteristic
315C2×C4#1059737011yescharacteristic
316C2×C4C4×C22⋊D1911yescharacteristic
317C2×C4#1059737511yescharacteristic
318C2×C4#1059739911yescharacteristic
319C8—41no—
320C8—41no—
321C8—41no—
322C8—41no—
323C8—761no—
324C8—761no—
325C8—762no—
326C8—1521no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22#1192641711yescharacteristic
333C22#1192665911yescharacteristic
334C22#1192666411yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—1521no—
344C4—1521no—
345C4#1192671711yescharacteristic
346C4#1192672211yescharacteristic
347C2—21no—
348C2—21no—
349C2—81no—
350C2#1456386811yescharacteristic
351C2#1456391011yescharacteristic
352C2#1456392111yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2992C2
socleC22×C19#385
prime radicalC19×#121C2×C4
cosocleC2×C42×C19C23
hypercenter#2992D19
hypocenterC19#8877
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2992

Complements

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

NH ≅ G/Ntype
1. #14563754C2semidirect
2. #14562421C2semidirect
5. #14561527C2semidirect
6. #14561485C2semidirect
248. C19#8877semidirect

Maximal subgroups

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

subgroupindex
#145637542
#145624212
#145621212
#145620482
#145615272
#145614852
C19×#29922
#887719