Finite Group Databasebeta

← #18081779

Subgroups — #18081779

Order 4864.

518 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926923C211yesmaximal, characteristic
2#14564587C211yesmaximal, characteristic
3C4⋊C4×C19⋊C8C211yesmaximal, characteristic
4C2×#11926296C211yesmaximal, characteristic
5C2×#11926290C211yesmaximal, characteristic
6C2×#11926289C211yesmaximal, characteristic
7C19×#1988C211yesmaximal, characteristic
8C22×#64528—21no—
9C22×#64528—21no—
10C2×#10597315C2211yescharacteristic
11#11926923—22no—
12#11926923C414yescomplemented
13C2×C4⋊(C19⋊C8)C2211yescharacteristic
14C2×C4⋊(C19⋊C8)C2211yescharacteristic
15C2×C4×C19⋊C8—21no—
16C2×C4×C19⋊C8C2211yescharacteristic
17#11926306—22no—
18#11926299—21no—
19#11926296—22no—
20#11926290—22no—
21#11926289—22no—
22C2×C19×C4⋊Q8C2211yescharacteristic
23C2×C19×C4⋊C8C2211yescharacteristic
24C4×C4⋊C4×C19C2211yescharacteristic
25C19×#340—22no—
26C22×Q8×C19—21no—
27C22×Dic38—21no—
28C22×C8×C19—21no—
29C19×C4⋊Q8—21no—
30C19×C4⋊Q8—21no—
31C19×C4⋊Q8—21no—
32C19×C4⋊Q8C2×C412yes—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19D412yes—
36C2×C42×C19—21no—
37C2×C42×C19C2311yescharacteristic
38C2×#64528—24no—
39C2×#64528—24no—
40C2×#64528—42no—
41C2×#64528—42no—
42C2×#64528—42no—
43C2×#64528—42no—
44C2×C4⋊Dic19—21no—
45C2×C4⋊Dic19—21no—
46C22×C19⋊C8—21no—
47C22×C19⋊C8—21no—
48C22×C19⋊C8D411yescharacteristic
49C22×C19⋊C8D411yescharacteristic
50#10597315—21no—
51#10597315—21no—
52#10597315—21no—
53#10597315C2×C412yes—
54C19×C4⋊C8—21no—
55C19×C4⋊C8—21no—
56C19×#95—21no—
57C4⋊(C19⋊C8)—21no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)D412yes—
61C4×C19⋊C8—42no—
62C4×C19⋊C8C2×C412yes—
63C4×C19⋊C8D412yes—
64C2×Q8×C19—22no—
65C2×Q8×C19—41no—
66C2×Q8×C19—41no—
67C2×Q8×C19—41no—
68C2×Q8×C19—41no—
69C2×Q8×C19—41no—
70C22×C4×C19—22no—
71C22×C4×C19—41no—
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19#4111yescharacteristic
75C22×Dic19—41no—
76C2×Dic38—22no—
77C2×Dic38—41no—
78C2×Dic38—41no—
79C2×Dic38—41no—
80C2×Dic38—41no—
81C2×Dic38—41no—
82C2×C8×C19—41no—
83C2×C8×C19—42no—
84C4⋊C4×C19—22no—
85C4⋊C4×C19—22no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—41no—
88C4⋊C4×C19—41no—
89C4⋊C4×C19Q1614yescomplemented
90C42×C19—41no—
91C42×C19—41no—
92C42×C19C22×C411yescharacteristic
93C42×C19C2×D411yescharacteristic
94C42×C19C2×D411yescharacteristic
95C42×C19#4111yescharacteristic
96#64528—48no—
97#64528—48no—
98C4⋊Dic19—22no—
99C4⋊Dic19—22no—
100C4⋊Dic19—41no—
101C4⋊Dic19—41no—
102C2×C19⋊C8—21no—
103C2×C19⋊C8—21no—
104C2×C19⋊C8—22no—
105C2×C19⋊C8—41no—
106C2×C19⋊C8—41no—
107C2×C19⋊C8—41no—
108C2×C19⋊C8—42no—
109C2×C19⋊C8C22⋊C412yes—
110C2×C19⋊C8C22⋊C412yes—
111C2×C19⋊C8D812yes—
112C2×C19⋊C8SD1612yes—
113#9733—191nomaximal, Sylow
114C23×C19#12111yescharacteristic
115Q8×C19—42no—
116Q8×C19—42no—
117Q8×C19—81no—
118Q8×C19—81no—
119C2×C4×C19—22no—
120C2×C4×C19—24no—
121C2×C4×C19—42no—
122C2×C4×C19—42no—
123C2×C4×C19—42no—
124C2×C4×C19—81no—
125C2×C4×C19—81no—
126C2×C4×C19C2×C22⋊C411yescharacteristic
127C2×C4×C19C4×D411yescharacteristic
128C2×C4×C19C4×D411yescharacteristic
129C2×C4×C19#12111yescharacteristic
130C2×C4×C19#12411yescharacteristic
131C2×C4×C19#12711yescharacteristic
132C2×C4×C19C2×D811yescharacteristic
133C2×C4×C19C2×SD1611yescharacteristic
134C2×C4×C19C2×Q1612yes—
135C2×C4×C19#13512yes—
136C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
138C2×Dic19—42no—
139C2×Dic19—81no—
140C2×Dic19—81no—
141Dic38—42no—
142Dic38—42no—
143Dic38—81no—
144Dic38—81no—
145C8×C19—81no—
146C19⋊C8—22no—
147C19⋊C8—42no—
148C19⋊C8—81no—
149C19⋊C8#10214yes—
150C2×#494—191no—
151#1988—191no—
152#1988D1911yescharacteristic
153C8×C4⋊C4—191no—
154C2×#335—191no—
155C2×#332—191no—
156C2×#332—191no—
157C22×C19#39011yescharacteristic
158C22×C19#45911yescharacteristic
159C22×C19#46011yescharacteristic
160C22×C19#46712yes—
161C22×C19#47312yes—
162C4×C19—21no—
163C4×C19—21no—
164C4×C19—44no—
165C4×C19—82no—
166C4×C19C2×#10211yescharacteristic
167C4×C19#41811yescharacteristic
168C4×C19C4×Q1612yes—
169C4×C19#45911yescharacteristic
170C4×C19#46011yescharacteristic
171C4×C19#49411yescharacteristic
172C4×C19#49511yescharacteristic
173Dic19—82no—
174C22×Q16—381no—
175C22×Q16—381no—
176C2×C4⋊Q8—191no—
177C2×C4⋊Q8C2×D1911yescharacteristic
178#494—194no—
179#494—382no—
180C2×C4⋊C8—191no—
181C2×C4⋊C8—191no—
182C2×C4⋊C8C2×D1911yescharacteristic
183C2×C4×C8—191no—
184C2×C4×C8—381no—
185C4×C4⋊C4C2×D1911yescharacteristic
186#340—22no—
187#340—382no—
188#336—381no—
189#335—382no—
190#332—382no—
191#332—382no—
192C2×C19#166912yes—
193C2×C19#167012yes—
194C2×C19#196911yescharacteristic
195C2×C19#197911yescharacteristic
196C2×C19#198211yescharacteristic
197C22×Q8—21no—
198C22×Q8—381no—
199C2×Q16—384no—
200C2×Q16—384no—
201C2×Q16—762no—
202C2×Q16—762no—
203C2×Q16—762no—
204C2×Q16—762no—
205C22×C8—21no—
206C22×C8—191no—
207C22×C8—191no—
208C22×C8—381no—
209C22×C8—381no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—192no—
214C4⋊Q8—381no—
215C4⋊Q8—381no—
216C4⋊Q8—381no—
217C4⋊Q8C4×D1912yes—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—381no—
221C2×C4⋊C4—381no—
222C2×C4⋊C4C22⋊D1912yes—
223C2×C42—21no—
224C2×C42C22×D1911yescharacteristic
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—192no—
228C4⋊C8—381no—
229C4⋊C8—381no—
230C4⋊C8—381no—
231C4×C8—192no—
232C4×C8—192no—
233C4×C8—762no—
234#95—21no—
235C19#973311yescharacteristic, complemented, Sylow
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—382no—
243C2×Q8—761no—
244C2×Q8—761no—
245C2×Q8—761no—
246C2×Q8—761no—
247C2×Q8—761no—
248C22×C4—22no—
249C22×C4—41no—
250C22×C4—761no—
251C22×C4D4×D1911yescharacteristic
252C22×C4#6454311yescharacteristic
253C22×C4C2×C22⋊D1911yescharacteristic
254Q16—768no—
255Q16—768no—
256C2×C8—41no—
257C2×C8—42no—
258C2×C8—192no—
259C2×C8—192no—
260C2×C8—192no—
261C2×C8—192no—
262C2×C8—381no—
263C2×C8—381no—
264C2×C8—382no—
265C2×C8—761no—
266C2×C8—761no—
267C2×C8—761no—
268C2×C8—762no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—382no—
275C4⋊C4—382no—
276C4⋊C4—761no—
277C4⋊C4—761no—
278C4⋊C4#6452814yescomplemented
279C42—41no—
280C42—41no—
281C42C2×C4×D1911yescharacteristic
282C42#6454111yescharacteristic
283C42D4×D1911yescharacteristic
284C42D4×D1911yescharacteristic
285C23#1059738511yescharacteristic
286Q8—42no—
287Q8—42no—
288Q8—81no—
289Q8—81no—
290Q8—762no—
291Q8—762no—
292Q8—1521no—
293Q8—1521no—
294C2×C4—22no—
295C2×C4—24no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—762no—
302C2×C4—1521no—
303C2×C4—1521no—
304C2×C4C22⋊C4×D1911yescharacteristic
305C2×C4(C22⋊D19)⋊C411yescharacteristic
306C2×C4#1059733011yescharacteristic
307C2×C4#1059733111yescharacteristic
308C2×C4D8×D1911yescharacteristic
309C2×C4#1059735711yescharacteristic
310C2×C4SD16×D1911yescharacteristic
311C2×C4#1059736011yescharacteristic
312C2×C4C4×C22⋊D1911yescharacteristic
313C2×C4#1059738611yescharacteristic
314C2×C4C2×#6452812yes—
315C2×C4#1059739612yes—
316C8—81no—
317C8—194no—
318C8—382no—
319C8—762no—
320C8—1521no—
321C22#1192644411yescharacteristic
322C22#1192673711yescharacteristic
323C22#1192674211yescharacteristic
324C22#1192678312yes—
325C22#1192681712yes—
326C4—21no—
327C4—21no—
328C4—44no—
329C4—82no—
330C4—1522no—
331C4#102×D1911yescharacteristic
332C4#1192654711yescharacteristic
333C4C4×#6452812yes—
334C4#1192673811yescharacteristic
335C4#1192674311yescharacteristic
336C4#1192692311yescharacteristic
337C4#1192692611yescharacteristic
338C2#1456299812yes—
339C2#1456300312yes—
340C2#1456449511yescharacteristic
341C2#1456454911yescharacteristic
342C2#1456456011yescharacteristic
subgroupG/H
centerC23#10597385
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1988C2
socle, prime radicalC23×C19#121
cosocleC2×C42×C19C23
hypercenter#1988D19
hypocenterC19#9733
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
12. #11926923C4semidirect
89. C4⋊C4×C19Q16semidirect
235. C19#9733semidirect
278. C4⋊C4#64528semidirect

Maximal subgroups

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

subgroupindex
C2×#119269232
#145645872
C4⋊C4×C19⋊C82
C2×#119262962
C2×#119262902
C2×#119262892
C19×#19882
#973319