Finite Group Databasebeta

← #18086925

Subgroups — #18086925

Order 4864.

574 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 99 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#14574386C211yesmaximal, characteristic
2#14564471C212yesmaximal, complemented
3#14564063C212yesmaximal, complemented
4#14561503C211yesmaximal, characteristic, complemented
5C19×#1850C211yesmaximal, characteristic, complemented
6C2×#10597376C2212yes—
7#11926858—22no—
8#11926780—21no—
9#11926780—21no—
10#11926680—22no—
11C2×#10597278—22no—
12C2×#10597263—22no—
13C2×#10597263—22no—
14#11926404C2212yes—
15#11926307—22no—
16C23×C8×C19C2211yescharacteristic
17C2×C19×C4⋊C8—21no—
18C2×C19×C22⋊C8C2211yescharacteristic
19C4×C22⋊C4×C19C2211yescharacteristic
20C19×#336—21no—
21C23×C4×C19C2311yescharacteristic
22C22×C22⋊D19—22no—
23C22×D76D412yes—
24C22×C8×C19—22no—
25C22×C8×C19—21no—
26C22×C8×C19—42no—
27C22×C8×C19D411yescharacteristic
28C22×C8×C19D411yescharacteristic
29C2×C22⋊C4×C19D411yescharacteristic
30C2×C22⋊C4×C19D411yescharacteristic
31C2×C42×C19—21no—
32C2×C22⋊Dic19—22no—
33#10597376—22no—
34#10597376—22no—
35#10597376—22no—
36#10597376—22no—
37C2×(C2×D19)⋊C4—22no—
38C2×C4⋊Dic19—22no—
39C2×C4⋊Dic19D412yes—
40C2×D152—21no—
41C2×D152—21no—
42C19×C4⋊C8—42no—
43C19×C22⋊C8—22no—
44C19×#95—21no—
45C19⋊#95—22no—
46#10597278—22no—
47#10597278—22no—
48#10597278—44no—
49#10597275—21no—
50#10597275—21no—
51#10597263—44no—
52#10597263—44no—
53C24×C19C2×D411yescharacteristic
54C23×D19—22no—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—41no—
58C22×C4×C19—41no—
59C22×C4×C19C2×D412yes—
60C22×C4×C19C2×D411yescharacteristic
61C22×C4×C19#4111yescharacteristic
62C22×C4×C19#4112yes—
63C2×C22⋊D19—42no—
64C2×C22⋊D19—42no—
65C2×C22⋊D19—42no—
66C2×C22⋊D19—42no—
67C2×C22⋊D19—42no—
68C2×C22⋊D19—42no—
69C22×Dic19—22no—
70C22×Dic19—42no—
71C2×D76—22no—
72C2×D76—22no—
73C2×D76—42no—
74C2×D76—42no—
75C2×C8×C19—24no—
76C2×C8×C19—22no—
77C2×C8×C19—21no—
78C2×C8×C19—21no—
79C2×C8×C19—42no—
80C2×C8×C19—41no—
81C2×C8×C19—41no—
82C2×C8×C19—41no—
83C2×C8×C19—41no—
84C22⋊C4×C19—21no—
85C22⋊C4×C19—22no—
86C22⋊C4×C19D812yescomplemented
87C42×C19—41no—
88C42×C19—41no—
89C22⋊Dic19—42no—
90C22⋊Dic19—42no—
91(C2×D19)⋊C4—42no—
92(C2×D19)⋊C4—42no—
93C4⋊Dic19—22no—
94C4⋊Dic19—22no—
95C4⋊Dic19—42no—
96C4⋊Dic19—42no—
97D152—81no—
98D152—81no—
99#10564—191nomaximal, Sylow
100C23×C19—41no—
101C23×C19—41no—
102C23×C19#12111yescharacteristic
103C23×C19#12112yes—
104C23×C19C2×D811yescharacteristic
105C23×C19#13511yescharacteristic
106C23×C19AGL(1,ℤ/8)12yes—
107C22×D19—42no—
108C22×D19—42no—
109C22×D19—42no—
110C22×D19—82no—
111C22×D19—82no—
112C2×C4×C19—22no—
113C2×C4×C19—21no—
114C2×C4×C19—22no—
115C2×C4×C19—21no—
116C2×C4×C19—22no—
117C2×C4×C19—41no—
118C2×C4×C19—42no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19#12011yescharacteristic
125C2×C4×C19#12312yes—
126C2×C4×C19#12411yescharacteristic
127C22⋊D19—82no—
128C22⋊D19—82no—
129C22⋊D19—82no—
130C22⋊D19—82no—
131C2×Dic19—42no—
132C2×Dic19—42no—
133C2×Dic19—42no—
134C2×Dic19—82no—
135C2×Dic19—82no—
136C2×Dic19—82no—
137D76—44no—
138D76—42no—
139D76—42no—
140C8×C19—41no—
141C8×C19—42no—
142C8×C19—41no—
143#3186—191no—
144#1964—192no—
145#1893—192no—
146#1850D1911yescharacteristic, complemented
147#1289—191no—
148C22×C19—22no—
149C22×C19—21no—
150C22×C19—22no—
151C22×C19—21no—
152C22×C19—41no—
153C22×C19—41no—
154C22×C19—42no—
155C22×C19#39411yescharacteristic
156C22×C19#45912yes—
157C22×C19#46312yes—
158C22×C19#46611yescharacteristic
159C22×C19#46911yescharacteristic
160C2×D19—82no—
161C2×D19—82no—
162C2×D19—82no—
163C2×D19—162no—
164C2×D19—162no—
165C4×C19—22no—
166C4×C19—21no—
167C4×C19—42no—
168C4×C19—81no—
169C4×C19B(4,𝔽2)11yescharacteristic
170C4×C19#45811yescharacteristic
171Dic19—82no—
172Dic19—162no—
173C23×C8C2×D1911yescharacteristic
174C2×#121—192no—
175#480—382no—
176#466—381no—
177#466—381no—
178#447—382no—
179C2×C4⋊C8—21no—
180C2×#102—382no—
181C2×#99—382no—
182C2×#99—382no—
183C2×C22⋊C8C2×D1911yescharacteristic
184#380—192no—
185C4×C22⋊C4C2×D1911yescharacteristic
186#340—382no—
187#336—21no—
188C2×C19—22no—
189C2×C19—21no—
190C2×C19—21no—
191C2×C19—22no—
192C2×C19#204411yescharacteristic
193C2×C19#205311yescharacteristic
194C2×C19#205411yescharacteristic
195D19—162no—
196C22×D4—192no—
197C22×D4—382no—
198C23×C4C22×D1911yescharacteristic
199C2×D8—381no—
200C2×D8—381no—
201C22×C8—22no—
202C22×C8—21no—
203C22×C8—42no—
204C22×C8C22⋊D1911yescharacteristic
205C22×C8C22⋊D1911yescharacteristic
206#121—382no—
207#121—382no—
208#121—382no—
209#121—382no—
210C2×C4⋊C4—192no—
211C2×C4⋊C4—382no—
212C2×C22⋊C4—382no—
213C2×C22⋊C4—382no—
214C2×C22⋊C4D7611yescharacteristic
215C2×C22⋊C4D7611yescharacteristic
216C2×C42—21no—
217#107—381no—
218#107—381no—
219C4⋊C8—42no—
220#102—382no—
221#102—382no—
222#102—764no—
223#99—764no—
224#99—764no—
225C22⋊C8—22no—
226#95—21no—
227#95—382no—
228C19#1056411yescharacteristic, complemented, Sylow
229C24—382no—
230C24C2×D7611yescharacteristic
231C2×D4—382no—
232C2×D4—382no—
233C2×D4—762no—
234C2×D4—762no—
235C2×D4—762no—
236C2×D4—762no—
237C2×D4—762no—
238C2×D4—762no—
239C2×D4—762no—
240C2×D4—762no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—382no—
246C22×C4—762no—
247C22×C4#6454111yescharacteristic
248C22×C4D4×D1912yes—
249C22×C4#6454512yes—
250C22×C4C2×C22⋊D1911yescharacteristic
251D8—1521no—
252D8—1521no—
253C2×C8—24no—
254C2×C8—22no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—41no—
258C2×C8—42no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C4⋊C4—382no—
263C4⋊C4—382no—
264C4⋊C4—762no—
265C4⋊C4—762no—
266C22⋊C4—21no—
267C22⋊C4—22no—
268C22⋊C4—762no—
269C22⋊C4—762no—
270C22⋊C4—762no—
271C22⋊C4—762no—
272C22⋊C4D15212yescomplemented
273C42—41no—
274C42—41no—
275C23—41no—
276C23—41no—
277C23—762no—
278C23—762no—
279C23—762no—
280C23—1522no—
281C23—1522no—
282C23#1059734112yes—
283C23C2×D15211yescharacteristic
284C23#1059735011yescharacteristic
285C23#1059735412yes—
286C23#1059737611yescharacteristic
287D4—764no—
288D4—762no—
289D4—762no—
290D4—1522no—
291D4—1522no—
292D4—1522no—
293D4—1522no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—762no—
307C2×C4—762no—
308C2×C4—762no—
309C2×C4—1522no—
310C2×C4—1522no—
311C2×C4—1522no—
312C2×C4#1059734012yes—
313C2×C4#1059738311yescharacteristic
314C2×C4#1059739311yescharacteristic
315C8—42no—
316C8—41no—
317C8—41no—
318C22—21no—
319C22—22no—
320C22—21no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—42no—
325C22—3042no—
326C22—3042no—
327C22—1522no—
328C22—1522no—
329C22—1522no—
330C22#1192646111yescharacteristic
331C22#1192674012yes—
332C22#1192676012yes—
333C22#1192678011yescharacteristic
334C22#1192679711yescharacteristic
335C4—21no—
336C4—22no—
337C4—42no—
338C4—81no—
339C4—3042no—
340C4—1522no—
341C4#1192673011yescharacteristic
342C4#1192673311yescharacteristic
343C2—21no—
344C2—21no—
345C2—22no—
346C2—22no—
347C2—3042no—
348C2#1456488611yescharacteristic
349C2#1456494111yescharacteristic
350C2#1456494611yescharacteristic
subgroupG/H
centerC22#11926461
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1850C2
socleC22×C19#394
prime radical#14574386C2
hypercenter#1850D19
hypocenterC19#10564
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
2. #14564471C2semidirect
3. #14564063C2semidirect
4. #14561503C2semidirect
5. C19×#1850C2semidirect
86. C22⋊C4×C19D8semidirect
146. #1850D19semidirect
228. C19#10564semidirect
272. C22⋊C4D152semidirect

Maximal subgroups

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

subgroupindex
#145743862
#145644712
#145640632
#145615032
C19×#18502
#1056419