Finite Group Databasebeta

← #18069838

Subgroups — #18069838

Order 4864.

620 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563556C211yesmaximal, characteristic
2#14563550C211yesmaximal, characteristic
3C19×#1781C211yesmaximal, characteristic
4C2×#10597290—21no—
5C2×#10597290—21no—
6C2×#10597291—21no—
7C2×#10597291—21no—
8#11926508C412yescomplemented
9#11926400C412yescomplemented
10C23×D4×C19C2211yescharacteristic
11C2×C19×#99—21no—
12C2×C19×#99—21no—
13C19×#379C412yescomplemented
14C25×C19C2×C411yescharacteristic
15C25×C19C2×C411yescharacteristic
16C22×D4×C19—42no—
17C22×D4×C19—42no—
18C22×D4×C19—42no—
19C22×D4×C19D411yescharacteristic
20C22×D4×C19D411yescharacteristic
21C22×D4×C19D411yescharacteristic
22C22×D4×C19Q811yescharacteristic
23C23×C4×C19C2×C411yescharacteristic
24C2×C22⋊C4×C19—22no—
25C2×C22⋊C4×C19—42no—
26C2×C22⋊Dic19—22no—
27C2×C22⋊Dic19—42no—
28C2×#64520—22no—
29C19×#99—42no—
30C19×#99—42no—
31#10597291—42no—
32#10597291—42no—
33#10597290—42no—
34#10597290—42no—
35C22⋊(C19⋊C8)—42no—
36C24×C19—22no—
37C24×C19—22no—
38C24×C19—41no—
39C24×C19—41no—
40C24×C19—41no—
41C24×C19—41no—
42C24×C19—82no—
43C24×C19—82no—
44C24×C19C4211yescharacteristic
45C24×C19C22⋊C411yescharacteristic
46C24×C19C22⋊C411yescharacteristic
47C24×C19C4⋊C411yescharacteristic
48C24×C19C4⋊C411yescharacteristic
49C2×D4×C19—22no—
50C2×D4×C19—22no—
51C2×D4×C19—22no—
52C2×D4×C19—22no—
53C2×D4×C19—22no—
54C2×D4×C19—22no—
55C2×D4×C19—41no—
56C2×D4×C19—41no—
57C2×D4×C19—41no—
58C2×D4×C19—41no—
59C2×D4×C19—41no—
60C2×D4×C19—41no—
61C2×D4×C19—416no—
62C22×C4×C19—22no—
63C22×C4×C19—41no—
64C22×C4×C19—41no—
65C22×C4×C19—42no—
66C22×C4×C19C22⋊C411yescharacteristic
67C22×C4×C19C4⋊C411yescharacteristic
68C22×Dic19—42no—
69C22⋊C4×C19—42no—
70C22⋊C4×C19—42no—
71C22⋊C4×C19—84no—
72C22⋊Dic19—42no—
73C22⋊Dic19—42no—
74C22⋊Dic19—84no—
75#64520—42no—
76#64520—42no—
77C2×C19⋊C8—42no—
78#7316—191nomaximal, Sylow
79C23×C19—21no—
80C23×C19—21no—
81C23×C19—21no—
82C23×C19—21no—
83C23×C19—21no—
84C23×C19—21no—
85C23×C19—21no—
86C23×C19—21no—
87C23×C19—21no—
88C23×C19—21no—
89C23×C19—21no—
90C23×C19—21no—
91C23×C19—21no—
92C23×C19—42no—
93C23×C19—44no—
94C23×C19—44no—
95C23×C19—44no—
96C23×C19—44no—
97C23×C19—82no—
98C23×C19—82no—
99C23×C19—82no—
100C23×C19—82no—
101C23×C19—81no—
102C23×C19—81no—
103C23×C19—81no—
104C23×C19—81no—
105C23×C19—82no—
106C23×C19—82no—
107C23×C19—82no—
108C23×C19—82no—
109C23×C19—82no—
110C23×C19—82no—
111C23×C19#9511yescharacteristic
112C23×C19#9912yes—
113C23×C19#9912yes—
114D4×C19—44no—
115D4×C19—44no—
116D4×C19—44no—
117D4×C19—44no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—44no—
124C2×C4×C19—82no—
125C2×C4×C19—84no—
126C2×C4×C19#9912yes—
127C2×Dic19—82no—
128C2×Dic19—84no—
129C19⋊C8—82no—
130#1783—191no—
131#1781—191no—
132#1781D1911yescharacteristic
133C22×C19—22no—
134C22×C19—22no—
135C22×C19—22no—
136C22×C19—22no—
137C22×C19—22no—
138C22×C19—41no—
139C22×C19—42no—
140C22×C19—42no—
141C22×C19—41no—
142C22×C19—41no—
143C22×C19—41no—
144C22×C19—42no—
145C22×C19—42no—
146C22×C19—41no—
147C22×C19—41no—
148C22×C19—41no—
149C22×C19—81no—
150C22×C19—81no—
151C22×C19—81no—
152C22×C19—81no—
153C22×C19—81no—
154C22×C19—81no—
155C22×C19—81no—
156C22×C19—81no—
157C22×C19—88no—
158C22×C19—88no—
159C22×C19#34211yescharacteristic
160C22×C19#34211yescharacteristic
161C22×C19#34211yescharacteristic
162C4×C19—22no—
163C4×C19—41no—
164C4×C19—162no—
165Dic19—162no—
166C23×D4C2×D1911yescharacteristic
167C2×#100—381no—
168C2×#100—381no—
169C2×#99—21no—
170C2×#99—21no—
171C2×#99—381no—
172C2×#99—381no—
173#407—192no—
174#379—192no—
175#379Dic1912yescomplemented
176C2×C19—21no—
177C2×C19—21no—
178C2×C19—21no—
179C2×C19—42no—
180C2×C19—42no—
181C2×C19—42no—
182C2×C19—81no—
183C2×C19—81no—
184C2×C19#130411yescharacteristic
185C25C4×D1911yescharacteristic
186C25C2×Dic1911yescharacteristic
187C22×D4—42no—
188C22×D4—42no—
189C22×D4—42no—
190C22×D4Dic3811yescharacteristic
191C22×D4D7611yescharacteristic
192C22×D4C22⋊D1911yescharacteristic
193C22×D4C22⋊D1911yescharacteristic
194C23×C4C4×D1911yescharacteristic
195C2×M16—382no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—42no—
198C2×C22⋊C4—382no—
199C2×C22⋊C4—762no—
200#100—762no—
201#100—762no—
202#99—42no—
203#99—42no—
204#99—762no—
205#99—762no—
206C22⋊C8—762no—
207C19#731611yescharacteristic, complemented, Sylow
208C24—22no—
209C24—22no—
210C24—41no—
211C24—41no—
212C24—41no—
213C24—41no—
214C24—82no—
215C24—82no—
216C24C4×Dic1911yescharacteristic
217C24Dic19⋊C411yescharacteristic
218C24C4⋊Dic1911yescharacteristic
219C24(C2×D19)⋊C411yescharacteristic
220C24C22⋊Dic1911yescharacteristic
221C2×D4—22no—
222C2×D4—22no—
223C2×D4—22no—
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—41no—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4—41no—
233C2×D4—416no—
234C22×C4—22no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—42no—
238C22×C4—762no—
239C22×C4Dic19⋊C411yescharacteristic
240C22×C4(C2×D19)⋊C411yescharacteristic
241M16—762no—
242M16—762no—
243C2×C8—762no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C22⋊C4—84no—
247C22⋊C4—762no—
248C22⋊C4—762no—
249C22⋊C4—1524no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—42no—
264C23—44no—
265C23—44no—
266C23—44no—
267C23—44no—
268C23—82no—
269C23—82no—
270C23—82no—
271C23—82no—
272C23—81no—
273C23—81no—
274C23—81no—
275C23—81no—
276C23—82no—
277C23—82no—
278C23—82no—
279C23—82no—
280C23—82no—
281C23—82no—
282C23#1059726312yes—
283C23C19⋊#9511yescharacteristic
284C23#1059729112yes—
285D4—44no—
286D4—44no—
287D4—44no—
288D4—44no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—44no—
295C2×C4—82no—
296C2×C4—84no—
297C2×C4—1522no—
298C2×C4—1524no—
299C2×C4#1059726312yes—
300C8—1522no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—41no—
307C22—42no—
308C22—42no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—42no—
313C22—42no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22—88no—
326C22—88no—
327C22#1192631011yescharacteristic
328C22#1192631011yescharacteristic
329C22#1192631111yescharacteristic
330C4—22no—
331C4—41no—
332C4—162no—
333C4—3042no—
334C2—21no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2—42no—
339C2—42no—
340C2—81no—
341C2—81no—
342C2C19⋊#130411yescharacteristic
subgroupG/H
centerC2C19⋊#1304
commutatorC24×C19C42
FrattiniC23×D4C2×D19
FittingC19×#1781C2
socleC2×C19#1304
prime radical, cosocleC23×D4×C19C22
hypercenter#1781D19
hypocenterC19#7316
LCSG ▷ C24×C19 ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C23 ◁ C23×D4 ◁ #1781

Complements

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

NH ≅ G/Ntype
8. #11926508C4semidirect
9. #11926400C4semidirect
13. C19×#379C4semidirect
175. #379Dic19semidirect
207. C19#7316semidirect

Maximal subgroups

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

subgroupindex
#145635562
#145635502
C19×#17812
#731619