Finite Group Databasebeta

← #18079233

Subgroups — #18079233

Order 4864.

490 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#14572576C211yesmaximal, characteristic, complemented
2#14564460C211yesmaximal, characteristic
3#14562303C211yesmaximal, characteristic
4#14562199C211yesmaximal, characteristic, complemented
5#14561494C211yesmaximal, characteristic, complemented
6#14561465C211yesmaximal, characteristic, complemented
7C19×#3208C211yesmaximal, characteristic
8#11926675—22no—
9#11926675—22no—
10#11926597C2211yescharacteristic
11#11926571—21no—
12#11926568C2211yescharacteristic
13C2×#10597289—21no—
14C2×#10597289—21no—
15#11926500—21no—
16C2×#10597260C2211yescharacteristic
17#11926410C2211yescharacteristic
18#11926288—22no—
19#11926281—22no—
20C19×#533C2211yescharacteristic
21C2×C19×#127C2211yescharacteristic
22C19×#492C412yescomplemented
23C19×#486C412yescomplemented
24C19×#460—22no—
25C19×#450—22no—
26C19×#431C2211yescharacteristic
27C22×D4×C19—21no—
28C22×D4×C19—21no—
29C22×D4×C19—21no—
30C2×SD16×C19—24no—
31C19×C4⋊Q8C2×C411yescharacteristic
32C19×C4⋊Q8C2×C411yescharacteristic
33C19×#127—21no—
34C19×#127—21no—
35C19×#127—21no—
36C19×#127C2×C412yes—
37C19×#125—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8D412yes—
40C4×Q8×C19—21no—
41C4×Q8×C19D412yes—
42C19×#117—21no—
43C2×C42×C19C2311yescharacteristic
44C2×C4⋊Dic19—21no—
45C2×#64520—21no—
46C22×C19⋊C8D411yescharacteristic
47C22×C19⋊C8D411yescharacteristic
48C19×C4⋊C8—21no—
49C19×#102—24no—
50C19×C22⋊C8—21no—
51C4×C8×C19C2×C412yes—
52#10597289—42no—
53#10597289—42no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C22⋊(C19⋊C8)—21no—
57C4⋊(C19⋊C8)—24no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)D412yes—
61#10597260—22no—
62#10597260—21no—
63#10597260—21no—
64C4×C19⋊C8—22no—
65C4×C19⋊C8—21no—
66C24×C19—41no—
67C2×Q8×C19—21no—
68C2×Q8×C19C22⋊C412yes—
69C2×D4×C19—22no—
70C2×D4×C19—22no—
71C2×D4×C19—22no—
72C2×D4×C19—41no—
73C2×D4×C19—41no—
74C2×D4×C19—41no—
75C2×D4×C19—41no—
76C2×D4×C19—41no—
77C2×D4×C19—41no—
78C2×D4×C19—41no—
79C2×D4×C19—82no—
80C2×D4×C19—82no—
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19#4111yescharacteristic
84C22×Dic19—41no—
85SD16×C19—84no—
86C2×C8×C19—22no—
87C4⋊C4×C19—21no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19—22no—
91C4⋊C4×C19—22no—
92C4⋊C4×C19C22⋊C412yes—
93C22⋊C4×C19—22no—
94C42×C19—22no—
95C42×C19C22×C411yescharacteristic
96C42×C19C2×D411yescharacteristic
97C42×C19C2×D411yescharacteristic
98C42×C19#4111yescharacteristic
99C4⋊Dic19—41no—
100C4⋊Dic19—41no—
101#64520—41no—
102#64520—41no—
103C2×C19⋊C8—21no—
104C2×C19⋊C8—21no—
105C2×C19⋊C8—22no—
106C2×C19⋊C8—21no—
107C2×C19⋊C8—21no—
108C2×C19⋊C8—21no—
109C2×C19⋊C8—41no—
110C2×C19⋊C8SD1612yescomplemented
111#9294—191nomaximal, Sylow
112C23×C19—42no—
113C23×C19—82no—
114C23×C19—82no—
115C23×C19—81no—
116C23×C19—81no—
117C23×C19#12111yescharacteristic
118Q8×C19—42no—
119Q8×C19—81no—
120D4×C19—44no—
121D4×C19—42no—
122D4×C19—42no—
123D4×C19—82no—
124D4×C19—82no—
125D4×C19—82no—
126D4×C19—81no—
127D4×C19—81no—
128C2×C4×C19—22no—
129C2×C4×C19—22no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19C2×C22⋊C411yescharacteristic
133C2×C4×C19C4×D411yescharacteristic
134C2×C4×C19C4×D411yescharacteristic
135C2×C4×C19#12011yescharacteristic
136C2×C4×C19#12111yescharacteristic
137C2×C4×C19#12311yescharacteristic
138C2×C4×C19C2×SD1611yescharacteristic
139C2×C4×C19#13511yescharacteristic
140C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C19#13711yescharacteristic
142C2×Dic19—81no—
143C2×Dic19—81no—
144C2×Dic19—81no—
145C8×C19—42no—
146C19⋊C8—22no—
147C19⋊C8—41no—
148C19⋊C8—42no—
149C19⋊C8—81no—
150#3208D1911yescharacteristic
151#2961—191no—
152#1961—191no—
153#1545—191no—
154#1518—191no—
155#1286—191no—
156#1275—191no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—82no—
160C22×C19—82no—
161C22×C19—82no—
162C22×C19—162no—
163C22×C19—162no—
164C22×C19#38611yescharacteristic
165C22×C19#46011yescharacteristic
166C22×C19#46411yescharacteristic
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—21no—
171C4×C19—42no—
172C4×C19—42no—
173C4×C19C4×SD1611yescharacteristic
174C4×C19#44011yescharacteristic
175C4×C19#44811yescharacteristic
176C4×C19#44911yescharacteristic
177Dic19—161no—
178#533C2×D1911yescharacteristic
179C2×#127C2×D1911yescharacteristic
180#492Dic1912yescomplemented
181#486Dic1912yescomplemented
182#460—22no—
183#450—22no—
184#446—382no—
185#446—382no—
186#431—191no—
187#431C2×D1911yescharacteristic
188#424—381no—
189#423—191no—
190C2×#102—381no—
191C2×#102—381no—
192#405—381no—
193C2×#97—191no—
194#382—191no—
195#331—382no—
196#328—382no—
197C2×C19—21no—
198C2×C19—21no—
199C2×C19—162no—
200C2×C19#188011yescharacteristic
201C2×C19#190311yescharacteristic
202C2×C19#191011yescharacteristic
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C2×SD16—24no—
207C2×M16—381no—
208C22×C8—191no—
209C22×C8—191no—
210C4⋊Q8C2×Dic1911yescharacteristic
211C4⋊Q8C2×Dic1911yescharacteristic
212#127—21no—
213#127—21no—
214#127—21no—
215#127C2×Dic1912yes—
216#125—21no—
217C22⋊Q8—21no—
218C22⋊Q8C22⋊D1912yes—
219C4×Q8—21no—
220C4×Q8C22⋊D1912yes—
221#117—21no—
222C2×C4⋊C4—381no—
223C2×C42C22×D1911yescharacteristic
224C4⋊C8—21no—
225C4⋊C8—192no—
226C4⋊C8—384no—
227C4⋊C8—381no—
228C4⋊C8—381no—
229#102—24no—
230#102—762no—
231#102—762no—
232C22⋊C8—21no—
233C22⋊C8—381no—
234#97—382no—
235#97—381no—
236#97—381no—
237C4×C8—382no—
238C4×C8—381no—
239C4×C8C2×Dic1912yes—
240#95—381no—
241#95—381no—
242C19#929411yescharacteristic, complemented, Sylow
243C24—41no—
244C2×Q8—21no—
245C2×Q8C22⋊Dic1912yes—
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—22no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—82no—
257C2×D4—82no—
258C22×C4—761no—
259C22×C4D4×D1911yescharacteristic
260C22×C4#6454311yescharacteristic
261C22×C4C2×C22⋊D1911yescharacteristic
262SD16—84no—
263M16—761no—
264M16—761no—
265C2×C8—22no—
266C2×C8—192no—
267C2×C8—381no—
268C2×C8—381no—
269C2×C8—382no—
270C2×C8—381no—
271C2×C8—381no—
272C2×C8—381no—
273C2×C8—761no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—761no—
280C4⋊C4—761no—
281C4⋊C4C22⋊Dic1912yes—
282C22⋊C4—22no—
283C42—22no—
284C42D4×D1911yescharacteristic
285C42#6454311yescharacteristic
286C42C22×Dic1911yescharacteristic
287C42C2×C22⋊D1911yescharacteristic
288C23—42no—
289C23—82no—
290C23—82no—
291C23—81no—
292C23—81no—
293C23#1059738511yescharacteristic
294Q8—42no—
295Q8—81no—
296D4—44no—
297D4—42no—
298D4—42no—
299D4—82no—
300D4—82no—
301D4—82no—
302D4—81no—
303D4—81no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—1521no—
309C2×C4—1521no—
310C2×C4—1521no—
311C2×C4SD16×D1911yescharacteristic
312C2×C4#1059736011yescharacteristic
313C2×C4#1059736111yescharacteristic
314C2×C4#1059736211yescharacteristic
315C2×C4D4×Dic1911yescharacteristic
316C2×C4D4×Dic1911yescharacteristic
317C2×C4#1059738111yescharacteristic
318C2×C4#1059738311yescharacteristic
319C2×C4#1059738511yescharacteristic
320C2×C4C2×C22⋊Dic1911yescharacteristic
321C8—42no—
322C8—382no—
323C8—761no—
324C8—762no—
325C8—1521no—
326C22—21no—
327C22—21no—
328C22—82no—
329C22—82no—
330C22—82no—
331C22—162no—
332C22—162no—
333C22#1192642411yescharacteristic
334C22#1192674211yescharacteristic
335C22#1192676411yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—42no—
342C4—3041no—
343C4SD16×Dic1911yescharacteristic
344C4#1192664511yescharacteristic
345C4#1192668111yescharacteristic
346C4#1192668811yescharacteristic
347C2—21no—
348C2—21no—
349C2—162no—
350C2#1456399211yescharacteristic
351C2#1456411711yescharacteristic
352C2#1456416311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3208C2
socleC22×C19#386
prime radicalC2×C19×#127C22
cosocleC2×C42×C19C23
hypercenter#3208D19
hypocenterC19#9294
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3208

Complements

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

NH ≅ G/Ntype
1. #14572576C2semidirect
4. #14562199C2semidirect
5. #14561494C2semidirect
6. #14561465C2semidirect
22. C19×#492C4semidirect
23. C19×#486C4semidirect
110. C2×C19⋊C8SD16semidirect
180. #492Dic19semidirect
181. #486Dic19semidirect
242. C19#9294semidirect

Maximal subgroups

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

subgroupindex
#145725762
#145644602
#145623032
#145621992
#145614942
#145614652
C19×#32082
#929419