Finite Group Databasebeta

← #18086926

Subgroups — #18086926

Order 4864.

574 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 95 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#14564470C212yesmaximal, complemented
3#14564061C212yesmaximal, complemented
4#14563812C211yesmaximal, characteristic, complemented
5C19×#1289C211yesmaximal, characteristic, complemented
6C23×C19⋊C8C2211yescharacteristic
7C2×#10597376C2212yes—
8#11926858—22no—
9#11926780—21no—
10#11926780—21no—
11#11926680—22no—
12C2×Dic19⋊C8—21no—
13C2×#10597266—22no—
14C2×#10597263—22no—
15C2×#10597263—22no—
16C4×C22⋊Dic19C2211yescharacteristic
17#11926306—22no—
18#11926298—21no—
19C2×C19×C22⋊C8C2211yescharacteristic
20C19×#380C2212yes—
21C23×C4×C19C2311yescharacteristic
22C22×C22⋊D19—22no—
23C22×D76D412yes—
24C22×C8×C19D411yescharacteristic
25C22×C8×C19D411yescharacteristic
26C2×C4⋊C4×C19—22no—
27C2×C22⋊C4×C19—22no—
28C2×C22⋊Dic19D411yescharacteristic
29C2×C22⋊Dic19D411yescharacteristic
30#10597376—22no—
31#10597376—22no—
32#10597376—22no—
33#10597376—22no—
34C2×(C2×D19)⋊C4—22no—
35C2×C4⋊Dic19D412yes—
36C2×C4×Dic19—21no—
37C22×C19⋊C8—22no—
38C22×C19⋊C8—21no—
39C22×C19⋊C8—42no—
40C2×D152—21no—
41C2×D152—21no—
42C19×C22⋊C8—22no—
43C19×#95—22no—
44C19⋊#95—21no—
45#10597278—22no—
46#10597278—22no—
47#10597275—21no—
48#10597275—21no—
49Dic19⋊C8—42no—
50#10597266—44no—
51#10597263—44no—
52#10597263—44no—
53C24×C19C2×D411yescharacteristic
54C23×D19—22no—
55C22×C4×C19—41no—
56C22×C4×C19—41no—
57C22×C4×C19—42no—
58C22×C4×C19C2×D411yescharacteristic
59C22×C4×C19C2×D412yes—
60C22×C4×C19#4112yes—
61C22×C4×C19#4111yescharacteristic
62C2×C22⋊D19—42no—
63C2×C22⋊D19—42no—
64C2×C22⋊D19—42no—
65C2×C22⋊D19—42no—
66C2×C22⋊D19—42no—
67C2×C22⋊D19—42no—
68C22×Dic19—21no—
69C22×Dic19—21no—
70C22×Dic19—22no—
71C2×D76—22no—
72C2×D76—22no—
73C2×D76—42no—
74C2×D76—42no—
75C2×C8×C19—21no—
76C2×C8×C19—21no—
77C2×C8×C19—41no—
78C2×C8×C19—41no—
79C4⋊C4×C19—42no—
80C4⋊C4×C19—42no—
81C22⋊C4×C19—42no—
82C22⋊C4×C19—42no—
83C22⋊Dic19—21no—
84C22⋊Dic19—22no—
85C22⋊Dic19D812yescomplemented
86(C2×D19)⋊C4—42no—
87(C2×D19)⋊C4—42no—
88C4⋊Dic19—22no—
89C4⋊Dic19—22no—
90C4×Dic19—41no—
91C4×Dic19—41no—
92C2×C19⋊C8—24no—
93C2×C19⋊C8—22no—
94C2×C19⋊C8—41no—
95C2×C19⋊C8—42no—
96C2×C19⋊C8—41no—
97D152—81no—
98D152—81no—
99#10564—191nomaximal, Sylow
100C23×C19—41no—
101C23×C19—41no—
102C23×C19#12112yes—
103C23×C19#12111yescharacteristic
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—21no—
113C2×C4×C19—22no—
114C2×C4×C19—21no—
115C2×C4×C19—22no—
116C2×C4×C19—42no—
117C2×C4×C19—41no—
118C2×C4×C19—82no—
119C2×C4×C19—82no—
120C2×C4×C19—82no—
121C2×C4×C19#12011yescharacteristic
122C2×C4×C19#12312yes—
123C2×C4×C19#12411yescharacteristic
124C22⋊D19—82no—
125C22⋊D19—82no—
126C22⋊D19—82no—
127C22⋊D19—82no—
128C2×Dic19—22no—
129C2×Dic19—41no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—42no—
134C2×Dic19—42no—
135C2×Dic19—42no—
136C2×Dic19—41no—
137D76—44no—
138D76—42no—
139D76—42no—
140C8×C19—41no—
141C8×C19—41no—
142C19⋊C8—42no—
143#3186—191no—
144#1964—192no—
145#1893—192no—
146#1850—191no—
147#1289D1911yescharacteristic, complemented
148C22×C19—21no—
149C22×C19—22no—
150C22×C19—21no—
151C22×C19—22no—
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—162no—
168C4×C19B(4,𝔽2)11yescharacteristic
169C4×C19#45811yescharacteristic
170Dic19—42no—
171Dic19—81no—
172Dic19—82no—
173C23×C8—191no—
174C2×#121—192no—
175#480—382no—
176#466—381no—
177#466—381no—
178#447—382no—
179C2×C4⋊C8—381no—
180C2×#102—382no—
181C2×#99—382no—
182C2×#99—382no—
183C2×C22⋊C8C2×D1911yescharacteristic
184#380C2×D1912yes—
185C4×C22⋊C4—191no—
186#340—382no—
187#336—381no—
188C2×C19—21no—
189C2×C19—21no—
190C2×C19—22no—
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—381no—
202C22×C8—382no—
203C22×C8—762no—
204C22×C8D7611yescharacteristic
205C22×C8D7611yescharacteristic
206#121—382no—
207#121—382no—
208#121—382no—
209#121—382no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—192no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—191no—
214C2×C22⋊C4—191no—
215C2×C22⋊C4—382no—
216C2×C42—381no—
217#107—381no—
218#107—381no—
219C4⋊C8—762no—
220#102—382no—
221#102—382no—
222#102—764no—
223#99—764no—
224#99—764no—
225C22⋊C8—22no—
226#95—22no—
227#95—381no—
228C19#1056411yescharacteristic, complemented, Sylow
229C24—382no—
230C24D4×D1911yescharacteristic
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—41no—
242C22×C4—41no—
243C22×C4—42no—
244C22×C4—381no—
245C22×C4—382no—
246C22×C4—381no—
247C22×C4C2×D7611yescharacteristic
248C22×C4#6454112yes—
249C22×C4D4×D1912yes—
250C22×C4#6454511yescharacteristic
251D8—1521no—
252D8—1521no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—384no—
258C2×C8—382no—
259C2×C8—761no—
260C2×C8—762no—
261C2×C8—761no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—382no—
265C4⋊C4—382no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—192no—
269C22⋊C4—381no—
270C22⋊C4—382no—
271C22⋊C4—762no—
272C22⋊C4—762no—
273C42—761no—
274C42—761no—
275C23—41no—
276C23—41no—
277C23—762no—
278C23—762no—
279C23—762no—
280C23—1522no—
281C23—1522no—
282C23#1059733012yes—
283C23#1059734111yescharacteristic
284C23D8×D1911yescharacteristic
285C23#1059736012yes—
286C23#1059736511yescharacteristic
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—42no—
299C2×C4—41no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—382no—
304C2×C4—761no—
305C2×C4—761no—
306C2×C4—761no—
307C2×C4—761no—
308C2×C4—761no—
309C2×C4—762no—
310C2×C4—762no—
311C2×C4—762no—
312C2×C4#1059732111yescharacteristic
313C2×C4#1059732811yescharacteristic
314C2×C4#1059734012yes—
315C8—41no—
316C8—41no—
317C8—762no—
318C22—22no—
319C22—21no—
320C22—22no—
321C22—21no—
322C22—41no—
323C22—42no—
324C22—41no—
325C22—3042no—
326C22—3042no—
327C22—1522no—
328C22—1522no—
329C22—1522no—
330C22#1192646211yescharacteristic
331C22#1192673812yes—
332C22#1192676212yes—
333C22#1192678111yescharacteristic
334C22#1192679811yescharacteristic
335C4—21no—
336C4—22no—
337C4—162no—
338C4—762no—
339C4—1521no—
340C4—1522no—
341C4#1192673211yescharacteristic
342C4#1192673511yescharacteristic
343C2—22no—
344C2—21no—
345C2—21no—
346C2—22no—
347C2—3042no—
348C2#1456488711yescharacteristic
349C2#1456494211yescharacteristic
350C2#1456494711yescharacteristic
subgroupG/H
centerC22#11926462
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1289C2
socleC22×C19#394
prime radical#14574386C2
hypercenter#1289D19
hypocenterC19#10564
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
2. #14564470C2semidirect
3. #14564061C2semidirect
4. #14563812C2semidirect
5. C19×#1289C2semidirect
85. C22⋊Dic19D8semidirect
147. #1289D19semidirect
228. C19#10564semidirect

Maximal subgroups

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

subgroupindex
#145743862
#145644702
#145640612
#145638122
C19×#12892
#1056419