Finite Group Databasebeta

← #18079245

Subgroups — #18079245

Order 4864.

470 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#14574779C211yesmaximal, characteristic
2#14564616C211yesmaximal, characteristic
3#14562307C211yesmaximal, characteristic
4#14562198C211yesmaximal, characteristic
5#14561493C211yesmaximal, characteristic
6#14561464C211yesmaximal, characteristic
7C19×#2327C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926940C412yescomplemented
10#11926896C412yescomplemented
11#11926874—22no—
12#11926826—22no—
13#11926597C2211yescharacteristic
14#11926597C2211yescharacteristic
15#11926568C2211yescharacteristic
16#11926304—21no—
17#11926304—21no—
18#11926290—22no—
19#11926280—22no—
20C2×C19×C4⋊Q8C2211yescharacteristic
21C2×C4×Q8×C19—21no—
22C19×#391—21no—
23C19×#387—22no—
24C19×#387—22no—
25C19×#382C2211yescharacteristic
26C19×#376C2211yescharacteristic
27C22×Q8×C19—21no—
28C19×C4⋊Q8—21no—
29C19×C4⋊Q8—21no—
30C19×C4⋊Q8C2×C412yes—
31C19×C4⋊Q8D412yes—
32C4×Q8×C19—42no—
33C4×Q8×C19—42no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—22no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19D412yes—
38C2×C42×C19—22no—
39C2×C42×C19D411yescharacteristic
40C2×C42×C19D411yescharacteristic
41C2×C42×C19C2311yescharacteristic
42#10597372—21no—
43#10597370—21no—
44#10597370—21no—
45C2×#64520—21no—
46#10597316—21no—
47#10597315C2×C411yescharacteristic
48#10597315C2×C411yescharacteristic
49C4×Dic38—21no—
50C4×Dic38—21no—
51C19×#95—24no—
52C19×#95—21no—
53C19×#95—21no—
54C19×#95—21no—
55C19×#95D412yes—
56C22⋊(C19⋊C8)—21no—
57C22⋊(C19⋊C8)—21no—
58#10597267—24no—
59#10597265—24no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)—21no—
62C4⋊(C19⋊C8)—21no—
63C4⋊(C19⋊C8)—21no—
64C4×C19⋊C8—21no—
65C4×C19⋊C8C2×C412yes—
66C2×Q8×C19—22no—
67C2×Q8×C19—22no—
68C2×Q8×C19—41no—
69C2×Q8×C19—41no—
70C2×Q8×C19—41no—
71C2×Q8×C19—41no—
72C22×C4×C19—21no—
73C22×C4×C19—22no—
74C22×C4×C19—22no—
75C22×C4×C19—21no—
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C2×Dic38—21no—
80C2×Dic38—21no—
81C4⋊C4×C19—22no—
82C4⋊C4×C19—22no—
83C4⋊C4×C19—22no—
84C4⋊C4×C19—44no—
85C4⋊C4×C19—41no—
86C4⋊C4×C19—41no—
87C4⋊C4×C19C22⋊C414yes—
88C42×C19—21no—
89C42×C19—21no—
90C42×C19—21no—
91C42×C19—44no—
92C42×C19SD1612yes—
93C42×C19C22×C411yescharacteristic
94C42×C19C2×D411yescharacteristic
95C42×C19#4111yescharacteristic
96C42×C19#4111yescharacteristic
97C22⋊Dic19—41no—
98C4⋊Dic19—21no—
99C4⋊Dic19—21no—
100C4⋊Dic19—21no—
101C4⋊Dic19—21no—
102Dic19⋊C4—41no—
103Dic19⋊C4—41no—
104C4×Dic19—41no—
105#64520—41no—
106#64520—41no—
107C2×C19⋊C8—22no—
108C2×C19⋊C8—41no—
109C2×C19⋊C8—41no—
110#9296—191nomaximal, Sylow
111C23×C19#12011yescharacteristic
112Q8×C19—42no—
113Q8×C19—42no—
114Q8×C19—42no—
115Q8×C19—42no—
116C2×C4×C19—24no—
117C2×C4×C19—22no—
118C2×C4×C19—41no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—42no—
123C2×C4×C19—42no—
124C2×C4×C19—42no—
125C2×C4×C19—41no—
126C2×C4×C19—42no—
127C2×C4×C19—41no—
128C2×C4×C19—42no—
129C2×C4×C19—41no—
130C2×C4×C19C2×C22⋊C411yescharacteristic
131C2×C4×C19C4×D411yescharacteristic
132C2×C4×C19C4×D411yescharacteristic
133C2×C4×C19#12111yescharacteristic
134C2×C4×C19#12111yescharacteristic
135C2×C4×C19#12311yescharacteristic
136C2×C4×C19C2×SD1611yescharacteristic
137C2×C4×C19#13511yescharacteristic
138C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C19#13711yescharacteristic
140C2×Dic19—41no—
141C2×Dic19—41no—
142Dic38—42no—
143Dic38—81no—
144C19⋊C8—42no—
145C19⋊C8—81no—
146C19⋊C8—81no—
147#3229—191no—
148#2327D1911yescharacteristic
149#1995—191no—
150#1546—191no—
151#1518—191no—
152#1286—191no—
153#1274—191no—
154C22×C19—21no—
155C22×C19—21no—
156C22×C19#38611yescharacteristic
157C22×C19#45011yescharacteristic
158C22×C19#45211yescharacteristic
159C4×C19—21no—
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—42no—
164C4×C19—44no—
165C4×C19—82no—
166C4×C19—81no—
167C4×C19C4×SD1611yescharacteristic
168C4×C19#44011yescharacteristic
169C4×C19#46111yescharacteristic
170C4×C19#46311yescharacteristic
171Dic19—81no—
172Dic19—81no—
173#533—191no—
174C2×C4⋊Q8C2×D1911yescharacteristic
175C2×C4×Q8—21no—
176#498—192no—
177#487—192no—
178#483—382no—
179#475—382no—
180#431—191no—
181#431—191no—
182#423—191no—
183#391—21no—
184#387—22no—
185#387—22no—
186#382C2×D1911yescharacteristic
187#376C2×D1911yescharacteristic
188#339—381no—
189#339—381no—
190#332—382no—
191#328—382no—
192C2×C19—21no—
193C2×C19—21no—
194C2×C19#187711yescharacteristic
195C2×C19#190511yescharacteristic
196C2×C19#191211yescharacteristic
197C22×Q8—21no—
198C2×M16—381no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—191no—
202C4⋊Q8—191no—
203C4⋊Q8C4×D1912yes—
204C4⋊Q8D7612yes—
205#125—381no—
206C22⋊Q8—381no—
207C22⋊Q8—381no—
208C4×Q8—42no—
209C4×Q8—42no—
210C4×Q8—381no—
211C4×Q8—381no—
212#117—381no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4C22⋊D1912yes—
217C2×C42—22no—
218C2×C42C22⋊D1911yescharacteristic
219C2×C42C22⋊D1911yescharacteristic
220C2×C42C22×D1911yescharacteristic
221#106—384no—
222C4⋊C8—381no—
223C4⋊C8—381no—
224C4⋊C8—381no—
225C4⋊C8—381no—
226#103—384no—
227C22⋊C8—381no—
228C22⋊C8—381no—
229C4×C8—192no—
230C4×C8—381no—
231#95—24no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95C22⋊D1912yes—
236C19#929611yescharacteristic, complemented, Sylow
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—381no—
244C2×Q8—381no—
245C22×C4—21no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4C2×C22⋊D1911yescharacteristic
250C22×C4C2×C22⋊D1911yescharacteristic
251C22×C4C2×C22⋊D1911yescharacteristic
252M16—761no—
253M16—761no—
254C2×C8—382no—
255C2×C8—761no—
256C2×C8—761no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—44no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—381no—
264C4⋊C4—381no—
265C4⋊C4—381no—
266C4⋊C4—381no—
267C4⋊C4—761no—
268C4⋊C4—761no—
269C4⋊C4(C2×D19)⋊C414yes—
270C22⋊C4—761no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—44no—
275C42—761no—
276C42#6452612yes—
277C42C2×C4×D1911yescharacteristic
278C42C2×D7611yescharacteristic
279C42#6454111yescharacteristic
280C42#6454111yescharacteristic
281C23#1059739911yescharacteristic
282Q8—42no—
283Q8—42no—
284Q8—42no—
285Q8—42no—
286Q8—762no—
287Q8—1521no—
288C2×C4—24no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—761no—
303C2×C4—761no—
304C2×C4C2×(C2×D19)⋊C411yescharacteristic
305C2×C4C4×C22⋊D1911yescharacteristic
306C2×C4C4×C22⋊D1911yescharacteristic
307C2×C4#1059737511yescharacteristic
308C2×C4#1059737611yescharacteristic
309C2×C4#1059737611yescharacteristic
310C2×C4#1059737811yescharacteristic
311C2×C4C2×#6452611yescharacteristic
312C2×C4#1059739611yescharacteristic
313C2×C4#1059739711yescharacteristic
314C8—762no—
315C8—1521no—
316C8—1521no—
317C22—21no—
318C22—21no—
319C22#1192642311yescharacteristic
320C22#1192669511yescharacteristic
321C22#1192670611yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—44no—
328C4—82no—
329C4—81no—
330C4—1521no—
331C4—1521no—
332C4C4×#6452611yescharacteristic
333C4#1192664411yescharacteristic
334C4#1192674911yescharacteristic
335C4#1192675911yescharacteristic
336C2—21no—
337C2—21no—
338C2#1456396911yescharacteristic
339C2#1456412911yescharacteristic
340C2#1456417211yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2327C2
socleC22×C19#386
prime radicalC23×C19#120
cosocleC2×C42×C19C23
hypercenter#2327D19
hypocenterC19#9296
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2327

Complements

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

NH ≅ G/Ntype
9. #11926940C4semidirect
10. #11926896C4semidirect
236. C19#9296semidirect

Maximal subgroups

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

subgroupindex
#145747792
#145646162
#145623072
#145621982
#145614932
#145614642
C19×#23272
#929619