Finite Group Databasebeta

← #18079079

Subgroups — #18079079

Order 4864.

428 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572584C211yesmaximal, characteristic
2#14564480C211yesmaximal, characteristic
3#14562325C211yesmaximal, characteristic
4C2×#11926290C211yesmaximal, characteristic
5#14561531C211yesmaximal, characteristic
6#14561484C211yesmaximal, characteristic
7C19×#3229C211yesmaximal, characteristic
8#11926675—21no—
9#11926675—22no—
10Q8×C19⋊C8—21no—
11#11926571—21no—
12#11926568C2211yescharacteristic
13C2×C4⋊(C19⋊C8)C2211yescharacteristic
14C2×C4⋊(C19⋊C8)C2211yescharacteristic
15C2×#10597293—21no—
16C2×#10597293—21no—
17#11926500—21no—
18C4×#64520C2211yescharacteristic
19#11926293—21no—
20#11926290—21no—
21#11926290—21no—
22#11926290—21no—
23C19×#533C2211yescharacteristic
24C2×C19×C4⋊Q8C2211yescharacteristic
25C19×#498—21no—
26C19×#487—21no—
27C19×#483C414yes—
28C19×#475—22no—
29C19×#431C2211yescharacteristic
30C22×Q8×C19—21no—
31C19×C4⋊Q8—21no—
32C19×C4⋊Q8—21no—
33C19×C4⋊Q8—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8D411yescharacteristic
36C19×C4⋊Q8D411yescharacteristic
37C19×#125—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8C2×C412yes—
40C4×Q8×C19—21no—
41C4×Q8×C19D412yes—
42C19×#117—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19C2×C412yes—
45C2×C42×C19C2311yescharacteristic
46C2×#64520—21no—
47C2×#64520D411yescharacteristic
48C2×#64520D411yescharacteristic
49C22×C19⋊C8—21no—
50C22×C19⋊C8—21no—
51C19×#106—24no—
52C19×C4⋊C8—21no—
53C19×#103—24no—
54C19×C22⋊C8C2×C412yes—
55C4×C8×C19—21no—
56#10597293—42no—
57#10597293—42no—
58C4⋊(C19⋊C8)—22no—
59C4⋊(C19⋊C8)—22no—
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—22no—
68#10597260—21no—
69C4×C19⋊C8—22no—
70C4×C19⋊C8—21no—
71C2×Q8×C19—21no—
72C2×Q8×C19—41no—
73C2×Q8×C19—41no—
74C2×Q8×C19—41no—
75C2×Q8×C19—41no—
76C2×Q8×C19—41no—
77C2×Q8×C19—41no—
78C2×Q8×C19C22⋊C412yes—
79C22×C4×C19—22no—
80C22×C4×C19C22×C411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19#4111yescharacteristic
83C2×C8×C19—22no—
84C4⋊C4×C19—22no—
85C4⋊C4×C19—21no—
86C4⋊C4×C19—21no—
87C4⋊C4×C19—21no—
88C4⋊C4×C19—22no—
89C4⋊C4×C19—22no—
90C4⋊C4×C19—22no—
91C4⋊C4×C19—41no—
92C4⋊C4×C19—41no—
93C4⋊C4×C19C22⋊C412yes—
94C22⋊C4×C19—22no—
95C42×C19—22no—
96C42×C19C2×D411yescharacteristic
97C42×C19C2×D411yescharacteristic
98C42×C19C2×D411yescharacteristic
99C42×C19#4111yescharacteristic
100#64520—21no—
101#64520—21no—
102#64520—21no—
103#64520—41no—
104#64520—41no—
105#64520SD1612yes—
106C2×C19⋊C8—21no—
107C2×C19⋊C8—21no—
108C2×C19⋊C8—21no—
109C2×C19⋊C8—21no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8—41no—
112C2×C19⋊C8—41no—
113C2×C19⋊C8—41no—
114C2×C19⋊C8—81no—
115#9272—191nomaximal, Sylow
116C23×C19C4×D411yescharacteristic
117Q8×C19—42no—
118Q8×C19—41no—
119Q8×C19—41no—
120Q8×C19—81no—
121Q8×C19—81no—
122Q8×C19—81no—
123Q8×C19—81no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—22no—
127C2×C4×C19—22no—
128C2×C4×C19—41no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19—42no—
132C2×C4×C19C2×C22⋊C411yescharacteristic
133C2×C4×C19C4×D411yescharacteristic
134C2×C4×C19#12011yescharacteristic
135C2×C4×C19#12111yescharacteristic
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
142C8×C19—42no—
143C19⋊C8—22no—
144C19⋊C8—41no—
145C19⋊C8—41no—
146C19⋊C8—41no—
147C19⋊C8—81no—
148C19⋊C8—81no—
149#3229D1911yescharacteristic
150#2962—191no—
151#1966—191no—
152#1550—191no—
153C2×#332—191no—
154#1301—191no—
155#1283—191no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19#38611yescharacteristic
159C22×C19C4×SD1611yescharacteristic
160C22×C19#44011yescharacteristic
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—21no—
164C4×C19—42no—
165C4×C19—42no—
166C4×C19—82no—
167C4×C19#44811yescharacteristic
168C4×C19#44911yescharacteristic
169C4×C19#46011yescharacteristic
170C4×C19#46411yescharacteristic
171C4×C19#47111yescharacteristic
172C4×C19#47311yescharacteristic
173#533C2×D1911yescharacteristic
174C2×C4⋊Q8C2×D1911yescharacteristic
175#498—21no—
176#487—21no—
177#483Dic1914yes—
178#475—22no—
179#446—381no—
180#446—382no—
181C8×Q8—381no—
182#431C2×D1911yescharacteristic
183#424—381no—
184#423—191no—
185C2×C4⋊C8—191no—
186C2×C4⋊C8—191no—
187C2×#101—381no—
188C2×#101—381no—
189#405—381no—
190C4×M16—191no—
191#333—381no—
192#332—381no—
193#332—381no—
194#332—381no—
195C2×C19—21no—
196C2×C19—21no—
197C2×C19#188011yescharacteristic
198C2×C19#190811yescharacteristic
199C2×C19#191511yescharacteristic
200C22×Q8—21no—
201C2×M16—191no—
202C2×M16—191no—
203C2×M16—381no—
204C22×C8—381no—
205C22×C8—381no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8C22⋊D1911yescharacteristic
211C4⋊Q8C22⋊D1911yescharacteristic
212#125—21no—
213C22⋊Q8—21no—
214C22⋊Q8C2×Dic1912yes—
215C4×Q8—21no—
216C4×Q8C22⋊D1912yes—
217#117—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4C2×Dic1912yes—
220C2×C42C22×D1911yescharacteristic
221#106—24no—
222C4⋊C8—21no—
223C4⋊C8—191no—
224C4⋊C8—191no—
225C4⋊C8—382no—
226C4⋊C8—382no—
227C4⋊C8—381no—
228C4⋊C8—381no—
229C4⋊C8—381no—
230C4⋊C8—381no—
231C4⋊C8—381no—
232#103—24no—
233#101—762no—
234#101—762no—
235C22⋊C8C2×Dic1912yes—
236#97—382no—
237#97—381no—
238C4×C8—21no—
239C4×C8—382no—
240C4×C8—381no—
241C19#927211yescharacteristic, complemented, Sylow
242C2×Q8—21no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8C22⋊Dic1912yes—
250C22×C4—22no—
251C22×C4D4×D1911yescharacteristic
252C22×C4#6454311yescharacteristic
253C22×C4C22×Dic1911yescharacteristic
254M16—192no—
255M16—381no—
256M16—381no—
257M16—381no—
258M16—761no—
259M16—761no—
260C2×C8—22no—
261C2×C8—381no—
262C2×C8—381no—
263C2×C8—381no—
264C2×C8—381no—
265C2×C8—761no—
266C2×C8—761no—
267C2×C8—761no—
268C2×C8—761no—
269C2×C8—1521no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4C22⋊Dic1912yes—
280C22⋊C4—22no—
281C42—22no—
282C42D4×D1911yescharacteristic
283C42#6454311yescharacteristic
284C42C2×C22⋊D1911yescharacteristic
285C42C2×C22⋊D1911yescharacteristic
286C23D4×Dic1911yescharacteristic
287Q8—42no—
288Q8—41no—
289Q8—41no—
290Q8—81no—
291Q8—81no—
292Q8—81no—
293Q8—81no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4SD16×D1911yescharacteristic
303C2×C4#1059736011yescharacteristic
304C2×C4#1059736111yescharacteristic
305C2×C4#1059736211yescharacteristic
306C2×C4D4×Dic1911yescharacteristic
307C2×C4#1059738111yescharacteristic
308C2×C4#1059738311yescharacteristic
309C2×C4#1059738511yescharacteristic
310C2×C4#1059738511yescharacteristic
311C2×C4C2×C22⋊Dic1911yescharacteristic
312C8—42no—
313C8—382no—
314C8—761no—
315C8—761no—
316C8—761no—
317C8—1521no—
318C8—1521no—
319C22—21no—
320C22—21no—
321C22#1192642411yescharacteristic
322C22SD16×Dic1911yescharacteristic
323C22#1192664511yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—42no—
328C4—42no—
329C4—82no—
330C4#1192668111yescharacteristic
331C4#1192668811yescharacteristic
332C4#1192674211yescharacteristic
333C4#1192676411yescharacteristic
334C4#1192680911yescharacteristic
335C4#1192681711yescharacteristic
336C2—21no—
337C2—21no—
338C2#1456399211yescharacteristic
339C2#1456415211yescharacteristic
340C2#1456418811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3229C2
socleC22×C19#386
prime radicalC23×C19C4×D4
cosocleC2×C42×C19C23
hypercenter#3229D19
hypocenterC19#9272
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
241. C19#9272semidirect

Maximal subgroups

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

subgroupindex
#145725842
#145644802
#145623252
C2×#119262902
#145615312
#145614842
C19×#32292
#927219