Finite Group Databasebeta

← #18069501

Subgroups — #18069501

Order 4864.

462 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926270C211yesmaximal, characteristic
2#14561864C211yesmaximal, characteristic
3C2×C19×#324C211yesmaximal, characteristic
4C22×C4⋊Dic19C411yescharacteristic
5C22×C4×Dic19C411yescharacteristic
6C2×C22⋊(C19⋊C8)—21no—
7C2×C19⋊#95—21no—
8C2×C19⋊#95—21no—
9#11926270—21no—
10#11926270C412yescomplemented
11C22×C4⋊C4×C19C2211yescharacteristic
12C2×C19×C22⋊C8—21no—
13C19×#324—21no—
14C19×#324C412yescomplemented
15C23×C4×C19C2×C411yescharacteristic
16C23×C4×C19D411yescharacteristic
17C23×C4×C19D411yescharacteristic
18C23×Dic19—21no—
19C23×Dic19—21no—
20C22×C8×C19—41no—
21C2×C4⋊C4×C19—41no—
22C2×C4⋊C4×C19—41no—
23C2×C4⋊C4×C19C2×C411yescharacteristic
24C2×C4⋊C4×C19C2×C411yescharacteristic
25C2×C4⋊C4×C19D411yescharacteristic
26C2×C4⋊C4×C19Q811yescharacteristic
27C2×C4⋊Dic19—21no—
28C2×C4⋊Dic19—41no—
29C2×C4⋊Dic19—41no—
30C2×C4⋊Dic19C812yescomplemented
31C2×C4×Dic19—21no—
32C2×C4×Dic19—41no—
33C2×C4×Dic19—41no—
34C2×C4×Dic19C812yescomplemented
35C22×C19⋊C8—41no—
36C19×C22⋊C8—22no—
37C19×C22⋊C8—41no—
38C19⋊#95—42no—
39C19⋊#95—42no—
40C22⋊(C19⋊C8)—22no—
41C22⋊(C19⋊C8)—41no—
42C24×C19C22⋊C411yescharacteristic
43C22×C4×C19—21no—
44C22×C4×C19—21no—
45C22×C4×C19—21no—
46C22×C4×C19—21no—
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19—21no—
50C22×C4×C19—21no—
51C22×C4×C19—41no—
52C22×C4×C19—41no—
53C22×C4×C19—41no—
54C22×C4×C19—41no—
55C22×C4×C19C4211yescharacteristic
56C22×C4×C19C22⋊C411yescharacteristic
57C22×C4×C19C22⋊C411yescharacteristic
58C22×C4×C19C4⋊C411yescharacteristic
59C22×C4×C19C4⋊C411yescharacteristic
60C22×C4×C19C4⋊C411yescharacteristic
61C22×C4×C19C2×C811yescharacteristic
62C22×C4×C19C2×C811yescharacteristic
63C22×C4×C19M1611yescharacteristic
64C22×C4×C19M1611yescharacteristic
65C22×Dic19—22no—
66C22×Dic19—22no—
67C22×Dic19—22no—
68C22×Dic19—22no—
69C22×Dic19—41no—
70C22×Dic19—41no—
71C22×Dic19—41no—
72C22×Dic19—41no—
73C22×Dic19—41no—
74C22×Dic19—41no—
75C22×Dic19—41no—
76C22×Dic19—41no—
77C22×Dic19—41no—
78C22×Dic19—41no—
79C2×C8×C19—42no—
80C2×C8×C19—81no—
81C2×C8×C19—81no—
82C4⋊C4×C19—41no—
83C4⋊C4×C19—41no—
84C4⋊C4×C19—41no—
85C4⋊C4×C19—41no—
86C4⋊Dic19—42no—
87C4⋊Dic19—42no—
88C4×Dic19—42no—
89C4×Dic19—42no—
90C2×C19⋊C8—42no—
91C2×C19⋊C8—81no—
92C2×C19⋊C8—81no—
93#7189—191nomaximal, Sylow
94C23×C19—21no—
95C23×C19—21no—
96C23×C19—21no—
97C23×C19—21no—
98C23×C19#9511yescharacteristic
99C23×C19C22⋊C811yescharacteristic
100C23×C19C22⋊C811yescharacteristic
101C23×C19#9911yescharacteristic
102C23×C19#9911yescharacteristic
103C23×C19#10011yescharacteristic
104C23×C19#10111yescharacteristic
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—81no—
130C2×C4×C19—81no—
131C2×C4×C19C4×C811yescharacteristic
132C2×C4×C19#9711yescharacteristic
133C2×C4×C19C4⋊C811yescharacteristic
134C2×C4×C19C4⋊C811yescharacteristic
135C2×Dic19—24no—
136C2×Dic19—42no—
137C2×Dic19—42no—
138C2×Dic19—42no—
139C2×Dic19—42no—
140C2×Dic19—42no—
141C2×Dic19—42no—
142C2×Dic19—42no—
143C2×Dic19—42no—
144C2×Dic19—42no—
145C2×Dic19—81no—
146C2×Dic19—81no—
147C2×Dic19—81no—
148C2×Dic19—81no—
149C8×C19—82no—
150C19⋊C8—82no—
151C2×#324—191no—
152C2×#324D1911yescharacteristic
153C4⋊#95—191no—
154C22×C19—21no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19#32311yescharacteristic
167C22×C19#32311yescharacteristic
168C22×C19#32411yescharacteristic
169C22×C19#32411yescharacteristic
170C22×C19#33611yescharacteristic
171C22×C19#34211yescharacteristic
172C22×C19#34311yescharacteristic
173C22×C19#35311yescharacteristic
174C22×C19#35411yescharacteristic
175C22×C19#35511yescharacteristic
176C22×C19#35611yescharacteristic
177C4×C19—21no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—41no—
182C4×C19—41no—
183C4×C19—41no—
184C4×C19—41no—
185Dic19—44no—
186Dic19—82no—
187C22×C4⋊C4—191no—
188C22×C4⋊C4C2×D1911yescharacteristic
189C22×C42—191no—
190C2×C22⋊C8—21no—
191C2×C22⋊C8—381no—
192C2×#95—381no—
193C2×#95—381no—
194#324—21no—
195#324—192no—
196#324—381no—
197#324Dic1912yescomplemented
198C2×C19—21no—
199C2×C19—21no—
200C2×C19—21no—
201C2×C19—21no—
202C2×C19#128011yescharacteristic
203C2×C19#131811yescharacteristic
204C2×C19#131911yescharacteristic
205C2×C19#132411yescharacteristic
206C2×C19#132511yescharacteristic
207C2×C19#139311yescharacteristic
208C2×C19#139411yescharacteristic
209C23×C4—381no—
210C23×C4—381no—
211C23×C4C4×D1911yescharacteristic
212C23×C4D7611yescharacteristic
213C23×C4C22⋊D1911yescharacteristic
214C22×C8—41no—
215C22×C8—761no—
216C2×C4⋊C4—41no—
217C2×C4⋊C4—41no—
218C2×C4⋊C4—192no—
219C2×C4⋊C4—381no—
220C2×C4⋊C4—761no—
221C2×C4⋊C4—761no—
222C2×C4⋊C4Dic3811yescharacteristic
223C2×C4⋊C4C4×D1911yescharacteristic
224C2×C4⋊C4C2×Dic1911yescharacteristic
225C2×C4⋊C4C22⋊D1911yescharacteristic
226C2×C42—192no—
227C2×C42—381no—
228C2×C42—761no—
229C2×C42—761no—
230C22⋊C8—22no—
231C22⋊C8—41no—
232C22⋊C8—382no—
233C22⋊C8—761no—
234#95—762no—
235#95—762no—
236C19#718911yescharacteristic, complemented, Sylow
237C24(C2×D19)⋊C411yescharacteristic
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—382no—
251C22×C4—382no—
252C22×C4—382no—
253C22×C4—382no—
254C22×C4—761no—
255C22×C4—761no—
256C22×C4—761no—
257C22×C4—761no—
258C22×C4—761no—
259C22×C4—761no—
260C22×C4—761no—
261C22×C4—761no—
262C22×C4—761no—
263C22×C4—761no—
264C22×C4C8×D1911yescharacteristic
265C22×C4C8×D1911yescharacteristic
266C22×C4#6451511yescharacteristic
267C22×C4#6451511yescharacteristic
268C22×C4C4×Dic1911yescharacteristic
269C22×C4Dic19⋊C411yescharacteristic
270C22×C4Dic19⋊C411yescharacteristic
271C22×C4C4⋊Dic1911yescharacteristic
272C22×C4(C2×D19)⋊C411yescharacteristic
273C22×C4C22⋊Dic1911yescharacteristic
274C2×C8—42no—
275C2×C8—81no—
276C2×C8—81no—
277C2×C8—762no—
278C2×C8—1521no—
279C2×C8—1521no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—762no—
285C4⋊C4—762no—
286C42—762no—
287C42—762no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23#1059726311yescharacteristic
293C23#1059726311yescharacteristic
294C23(C2×D19)⋊C811yescharacteristic
295C23(C2×D19)⋊C811yescharacteristic
296C23#1059728011yescharacteristic
297C23#1059728111yescharacteristic
298C23C19⋊#9511yescharacteristic
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—384no—
326C2×C4—762no—
327C2×C4—762no—
328C2×C4—762no—
329C2×C4—762no—
330C2×C4—762no—
331C2×C4—762no—
332C2×C4—762no—
333C2×C4—762no—
334C2×C4—762no—
335C2×C4—1521no—
336C2×C4—1521no—
337C2×C4—1521no—
338C2×C4—1521no—
339C2×C4C8×Dic1911yescharacteristic
340C2×C4Dic19⋊C811yescharacteristic
341C2×C4Dic19⋊C811yescharacteristic
342C2×C4#1059727211yescharacteristic
343C8—82no—
344C8—1522no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22#1192626711yescharacteristic
358C22#1192626711yescharacteristic
359C22#1192626911yescharacteristic
360C22#1192626911yescharacteristic
361C22#1192629811yescharacteristic
362C22#1192631011yescharacteristic
363C22#1192631211yescharacteristic
364C22#1192633611yescharacteristic
365C22#1192633811yescharacteristic
366C22#1192634011yescharacteristic
367C22#1192634211yescharacteristic
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—764no—
377C4—1522no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—21no—
382C2#1456147711yescharacteristic
383C2#1456156611yescharacteristic
384C2#1456156811yescharacteristic
385C2#1456157811yescharacteristic
386C2#1456158011yescharacteristic
387C2#1456175911yescharacteristic
388C2#1456176111yescharacteristic
subgroupG/H
centerC23#10597263
commutatorC2×C4×C19C4×C8
FrattiniC22×C4⋊C4C2×D19
FittingC2×C19×#324C2
socleC23×C19#99
prime radicalC24×C19C22⋊C4
cosocleC22×C4⋊C4×C19C22
hypercenterC2×#324D19
hypocenterC19#7189
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
10. #11926270C4semidirect
14. C19×#324C4semidirect
30. C2×C4⋊Dic19C8semidirect
34. C2×C4×Dic19C8semidirect
197. #324Dic19semidirect
236. C19#7189semidirect

Maximal subgroups

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

subgroupindex
C2×#119262702
#145618642
C2×C19×#3242
#718919