Finite Group Databasebeta

← #18078613

Subgroups — #18078613

Order 4864.

690 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 119 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#14566233C211yesmaximal, characteristic, complemented
2#14562203C212yesmaximal, complemented
3C2×#11926268C211yesmaximal, characteristic, complemented
4#14561502C212yesmaximal, complemented
5C19×#2617C211yesmaximal, characteristic
6C2×C22⋊(C19⋊C8)C2212yes—
7#11926437—24no—
8#11926404C2212yes—
9#11926400—21no—
10C4×C22⋊Dic19—21no—
11#11926278—24no—
12#11926268—22no—
13C2×C19×#121C2211yescharacteristic
14C2×C19×#120—21no—
15C22×C22⋊C4×C19C2211yescharacteristic
16C19×#397C412yescomplemented
17C19×#394—22no—
18C19×#392C412yescomplemented
19C19×#386—21no—
20C19×#380C2211yescharacteristic
21C25×C19D411yescharacteristic
22C22×D4×C19—21no—
23C22×D4×C19—22no—
24C22×D4×C19C2×C411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C19×#121—22no—
28C19×#121—22no—
29C19×#120—44no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19C2×C411yescharacteristic
32C2×C22⋊C4×C19—22no—
33C2×C22⋊C4×C19—22no—
34C2×C22⋊C4×C19—22no—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—21no—
37C2×C22⋊C4×C19—22no—
38C2×C22⋊C4×C19C2×C412yes—
39C2×C22⋊C4×C19D412yes—
40C2×C22⋊Dic19—22no—
41C2×C22⋊Dic19—22no—
42C2×C22⋊Dic19—22no—
43C2×C4⋊Dic19—22no—
44C2×C4×Dic19—22no—
45C22×C19⋊C8—22no—
46C19×#95—22no—
47C19×#95C2×C412yes—
48C19⋊#95—22no—
49C19⋊#95D414yescomplemented
50C22⋊(C19⋊C8)—22no—
51C22⋊(C19⋊C8)—22no—
52C24×C19—21no—
53C24×C19—21no—
54C24×C19—22no—
55C24×C19—22no—
56C24×C19—21no—
57C24×C19—81no—
58C24×C19—81no—
59C24×C19C22⋊C412yes—
60C24×C19C2×D411yescharacteristic
61C2×D4×C19—22no—
62C2×D4×C19—44no—
63C2×D4×C19—41no—
64C2×D4×C19—41no—
65C2×D4×C19—42no—
66C2×D4×C19—42no—
67C2×D4×C19—82no—
68C2×D4×C19—82no—
69C2×D4×C19—81no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—22no—
73C22×C4×C19—21no—
74C22×C4×C19—81no—
75C22×C4×C19—81no—
76C22×C4×C19C22⋊C412yes—
77C22×C4×C19C22×C411yescharacteristic
78C22×C4×C19C2×D412yes—
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19#4112yes—
81C22×Dic19—24no—
82C4⋊C4×C19—22no—
83C4⋊C4×C19—81no—
84C22⋊C4×C19—24no—
85C22⋊C4×C19—24no—
86C22⋊C4×C19—44no—
87C22⋊C4×C19—42no—
88C22⋊C4×C19—42no—
89C22⋊C4×C19—82no—
90C22⋊Dic19—42no—
91C22⋊Dic19—42no—
92C22⋊Dic19—82no—
93C22⋊Dic19—82no—
94C4⋊Dic19—82no—
95C4×Dic19—82no—
96C2×C19⋊C8—42no—
97C2×C19⋊C8—82no—
98#9205—191nomaximal, Sylow
99C23×C19—22no—
100C23×C19—22no—
101C23×C19—22no—
102C23×C19—41no—
103C23×C19—41no—
104C23×C19—42no—
105C23×C19—42no—
106C23×C19—42no—
107C23×C19—42no—
108C23×C19—42no—
109C23×C19—42no—
110C23×C19—42no—
111C23×C19—42no—
112C23×C19—41no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19—81no—
116C23×C19—81no—
117C23×C19—84no—
118C23×C19—84no—
119C23×C19C2×C22⋊C411yescharacteristic
120C23×C19#12011yescharacteristic
121C23×C19#12311yescharacteristic
122C23×C19#13512yes—
123C23×C19AGL(1,ℤ/8)12yes—
124D4×C19—82no—
125D4×C19—88no—
126D4×C19—82no—
127D4×C19—82no—
128C2×C4×C19—22no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—42no—
134C2×C4×C19—42no—
135C2×C4×C19—42no—
136C2×C4×C19—42no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—42no—
140C2×C4×C19—41no—
141C2×C4×C19—81no—
142C2×C4×C19C4×D412yes—
143C2×C4×C19#12112yes—
144C2×Dic19—44no—
145C2×Dic19—44no—
146C2×Dic19—44no—
147C19⋊C8—82no—
148#2617D1911yescharacteristic
149#2312—191no—
150#1519—192no—
151C2×#323—191no—
152#1289—192no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—42no—
160C22×C19—42no—
161C22×C19—44no—
162C22×C19—42no—
163C22×C19—42no—
164C22×C19—42no—
165C22×C19—82no—
166C22×C19—84no—
167C22×C19—84no—
168C22×C19—82no—
169C22×C19—82no—
170C22×C19—81no—
171C22×C19—81no—
172C22×C19—81no—
173C22×C19#38611yescharacteristic
174C22×C19#41611yescharacteristic
175C22×C19#41811yescharacteristic
176C22×C19#44912yes—
177C22×C19#48212yes—
178C4×C19—22no—
179C4×C19—22no—
180C4×C19—42no—
181C4×C19—82no—
182C4×C19—81no—
183Dic19—84no—
184C2×#121C2×D1911yescharacteristic
185C2×#120—21no—
186C22×C22⋊C4C2×D1911yescharacteristic
187C2×C22⋊C8—192no—
188#397Dic1912yescomplemented
189#394—22no—
190#392Dic1912yescomplemented
191#388—384no—
192#386—21no—
193#380—192no—
194#380C2×D1911yescharacteristic
195#379—381no—
196C4×C22⋊C4—381no—
197#327—384no—
198#323—382no—
199C2×C19—22no—
200C2×C19—21no—
201C2×C19—21no—
202C2×C19—22no—
203C2×C19—82no—
204C2×C19—161no—
205C2×C19#187511yescharacteristic
206C2×C19#191111yescharacteristic
207C2×C19#191311yescharacteristic
208C25C22⋊D1911yescharacteristic
209C22×D4—21no—
210C22×D4—22no—
211C22×D4C2×Dic1911yescharacteristic
212C23×C4C22⋊D1911yescharacteristic
213C23×C4C22×D1911yescharacteristic
214C22×C8—382no—
215#121—22no—
216#121—22no—
217#120—44no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—382no—
220C2×C4⋊C4C2×Dic1911yescharacteristic
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—382no—
228C2×C22⋊C4—382no—
229C2×C22⋊C4—382no—
230C2×C22⋊C4C2×Dic1912yes—
231C2×C22⋊C4C22⋊D1912yes—
232C2×C42—382no—
233C22⋊C8—382no—
234C22⋊C8—382no—
235#95—22no—
236#95—194no—
237#95—382no—
238#95C2×Dic1912yes—
239C19#920511yescharacteristic, complemented, Sylow
240C24—21no—
241C24—22no—
242C24—21no—
243C24—22no—
244C24—21no—
245C24—81no—
246C24—81no—
247C24C22⋊Dic1912yes—
248C24C2×C22⋊D1911yescharacteristic
249C2×D4—22no—
250C2×D4—44no—
251C2×D4—42no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—42no—
255C2×D4—82no—
256C2×D4—82no—
257C2×D4—81no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—81no—
263C22×C4—81no—
264C22×C4—384no—
265C22×C4C22⋊Dic1912yes—
266C22×C4D4×D1912yes—
267C22×C4#6454312yes—
268C22×C4C22×Dic1911yescharacteristic
269C22×C4C2×C22⋊D1911yescharacteristic
270C2×C8—762no—
271C2×C8—1522no—
272C4⋊C4—22no—
273C4⋊C4—81no—
274C4⋊C4—1522no—
275C22⋊C4—24no—
276C22⋊C4—24no—
277C22⋊C4—44no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—82no—
281C22⋊C4—762no—
282C22⋊C4—762no—
283C22⋊C4—1522no—
284C22⋊C4—1522no—
285C42—1522no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—41no—
290C23—41no—
291C23—42no—
292C23—42no—
293C23—42no—
294C23—42no—
295C23—42no—
296C23—42no—
297C23—42no—
298C23—42no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—81no—
303C23—81no—
304C23—84no—
305C23—84no—
306C23#1059737812yes—
307C23#1059738111yescharacteristic
308C23#1059738311yescharacteristic
309C23#1059739612yes—
310C23C2×C22⋊Dic1911yescharacteristic
311D4—82no—
312D4—88no—
313D4—82no—
314D4—82no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—764no—
330C2×C4—764no—
331C2×C4—764no—
332C2×C4D4×Dic1912yes—
333C2×C4#1059738512yes—
334C8—1522no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—42no—
342C22—42no—
343C22—44no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—82no—
348C22—84no—
349C22—84no—
350C22—82no—
351C22—82no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22#1192642411yescharacteristic
356C22#1192654011yescharacteristic
357C22#1192654911yescharacteristic
358C22#1192668712yes—
359C22#1192686512yes—
360C4—22no—
361C4—22no—
362C4—42no—
363C4—82no—
364C4—81no—
365C4—1524no—
366C2—21no—
367C2—22no—
368C2—21no—
369C2—22no—
370C2—82no—
371C2—161no—
372C2#1456395811yescharacteristic
373C2#1456416811yescharacteristic
374C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#2617C2
socleC22×C19#386
cosocleC23×C4×C19C23
hypercenter#2617D19
hypocenterC19#9205
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2617

Complements

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

NH ≅ G/Ntype
1. #14566233C2semidirect
2. #14562203C2semidirect
3. C2×#11926268C2semidirect
4. #14561502C2semidirect
16. C19×#397C4semidirect
18. C19×#392C4semidirect
49. C19⋊#95D4semidirect
188. #397Dic19semidirect
190. #392Dic19semidirect
239. C19#9205semidirect

Maximal subgroups

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

subgroupindex
#145662332
#145622032
C2×#119262682
#145615022
C19×#26172
#920519