Finite Group Databasebeta

← #18078087

Subgroups — #18078087

Order 4864.

560 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 115 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#14572664C211yesmaximal, characteristic
2#14566300C211yesmaximal, characteristic
3C2×#11926269C212yesmaximal, complemented
4#14561482C212yesmaximal, complemented
5C19×#1459C211yesmaximal, characteristic
6C2×#10597381C411yescharacteristic
7C22×Dic19⋊C4C2211yescharacteristic
8#11926616—24no—
9#11926601—21no—
10#11926508—21no—
11C2×C22⋊(C19⋊C8)C2212yes—
12#11926439—21no—
13#11926438—21no—
14#11926428—21no—
15#11926424C411yescharacteristic
16#11926417—21no—
17#11926416C411yescharacteristic
18#11926405C411yescharacteristic
19C4×C22⋊Dic19C2211yescharacteristic
20#11926269—24no—
21C2×C4×D4×C19C2211yescharacteristic
22C2×C19×C22⋊C8C2212yes—
23C19×#324—21no—
24C19×#323—21no—
25C22×D4×C19C2×C411yescharacteristic
26C23×C4×C19D411yescharacteristic
27C23×C4×C19C2311yescharacteristic
28C23×Dic19C2×C411yescharacteristic
29C23×Dic19C2×C411yescharacteristic
30C22×C8×C19—22no—
31C4×D4×C19—22no—
32C4×D4×C19—22no—
33C2×C4⋊C4×C19D411yescharacteristic
34C2×C22⋊C4×C19C2×C411yescharacteristic
35C2×C22⋊C4×C19D411yescharacteristic
36C2×C42×C19D411yescharacteristic
37C2×C22⋊Dic19—21no—
38C2×C22⋊Dic19—21no—
39C2×C22⋊Dic19C2×C411yescharacteristic
40C2×C22⋊Dic19C2×C411yescharacteristic
41#10597381—22no—
42#10597381—22no—
43C2×Dic19⋊C4—21no—
44C2×Dic19⋊C4—21no—
45C2×Dic19⋊C4—21no—
46C2×Dic19⋊C4—22no—
47C2×Dic19⋊C4—22no—
48C2×Dic19⋊C4—21no—
49C2×C4×Dic19—21no—
50C2×#64520—22no—
51C22×C19⋊C8—22no—
52C19×C22⋊C8—22no—
53C19×C22⋊C8—22no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C22⋊(C19⋊C8)—22no—
60C22⋊(C19⋊C8)—22no—
61C22⋊(C19⋊C8)D414yes—
62C4⋊(C19⋊C8)—22no—
63#10597260—22no—
64C24×C19C22⋊C411yescharacteristic
65C24×C19C22×C411yescharacteristic
66C2×D4×C19—22no—
67C2×D4×C19—21no—
68C2×D4×C19—21no—
69C2×D4×C19—22no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—81no—
73C22×C4×C19—81no—
74C22×C4×C19C22⋊C411yescharacteristic
75C22×C4×C19C22⋊C411yescharacteristic
76C22×C4×C19C22⋊C411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D412yes—
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19#4112yes—
81C22×Dic19—21no—
82C22×Dic19—21no—
83C22×Dic19—22no—
84C22×Dic19—21no—
85C22×Dic19—22no—
86C22×Dic19—21no—
87C22×Dic19—21no—
88C22×Dic19—22no—
89C22×Dic19—81no—
90C22×Dic19M1612yescomplemented
91C2×C8×C19—42no—
92C2×C8×C19—82no—
93C4⋊C4×C19—22no—
94C22⋊C4×C19—22no—
95C22⋊C4×C19—22no—
96C42×C19—21no—
97C42×C19—21no—
98C22⋊Dic19—24no—
99C22⋊Dic19—21no—
100C22⋊Dic19—22no—
101C22⋊Dic19—81no—
102C22⋊Dic19M1612yescomplemented
103Dic19⋊C4—24no—
104Dic19⋊C4—41no—
105Dic19⋊C4—42no—
106Dic19⋊C4—41no—
107Dic19⋊C4—81no—
108C4×Dic19—81no—
109#64520—82no—
110C2×C19⋊C8—24no—
111C2×C19⋊C8—82no—
112#9110—191nomaximal, Sylow
113C23×C19—21no—
114C23×C19—21no—
115C23×C19—21no—
116C23×C19—41no—
117C23×C19—41no—
118C23×C19—41no—
119C23×C19—41no—
120C23×C19C2×C22⋊C411yescharacteristic
121C23×C19C4×D412yes—
122C23×C19C2×M1611yescharacteristic
123C23×C19C2×M1611yescharacteristic
124C23×C19#13112yes—
125D4×C19—42no—
126D4×C19—42no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—42no—
133C2×C4×C19—41no—
134C2×C4×C19—42no—
135C2×C4×C19—41no—
136C2×C4×C19—42no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—81no—
140C2×C4×C19#12011yescharacteristic
141C2×C4×C19#12112yes—
142C2×C4×C19#12311yescharacteristic
143C2×Dic19—22no—
144C2×Dic19—22no—
145C2×Dic19—24no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150C2×Dic19—42no—
151C2×Dic19—41no—
152C2×Dic19—41no—
153C2×Dic19—41no—
154C2×Dic19—41no—
155C2×Dic19—41no—
156C2×Dic19—41no—
157C2×Dic19—82no—
158C8×C19—82no—
159C19⋊C8—44no—
160#2973—191no—
161#2322—191no—
162#1459D1911yescharacteristic
163C2×#324—192no—
164#1282—192no—
165C22×C19—21no—
166C22×C19—22no—
167C22×C19—21no—
168C22×C19—22no—
169C22×C19—41no—
170C22×C19—41no—
171C22×C19—42no—
172C22×C19—42no—
173C22×C19—41no—
174C22×C19—41no—
175C22×C19—41no—
176C22×C19—81no—
177C22×C19#38611yescharacteristic
178C22×C19#40711yescharacteristic
179C22×C19#40811yescharacteristic
180C22×C19#43512yes—
181C22×C19#43612yes—
182C4×C19—21no—
183C4×C19—22no—
184C4×C19—21no—
185C4×C19—41no—
186C4×C19—41no—
187C4×C19—41no—
188Dic19—42no—
189Dic19—42no—
190Dic19—81no—
191Dic19—81no—
192C2×#123—191no—
193C2×C4×D4C2×D1911yescharacteristic
194C22×C4⋊C4—191no—
195#435—384no—
196#432—381no—
197#407—381no—
198C2×C22⋊C8—192no—
199C2×C22⋊C8C2×D1912yes—
200#389—381no—
201#388—381no—
202#387—381no—
203#386—191no—
204#385—191no—
205#385—381no—
206#381—191no—
207C4×C22⋊C4—191no—
208#324—21no—
209#324—384no—
210#323—21no—
211C2×C19—21no—
212C2×C19—21no—
213C2×C19—22no—
214C2×C19—22no—
215C2×C19—81no—
216C2×C19#187011yescharacteristic
217C2×C19#191311yescharacteristic
218C2×C19#191511yescharacteristic
219C22×D4C4×D1911yescharacteristic
220C23×C4—191no—
221C23×C4—191no—
222C23×C4D7611yescharacteristic
223C23×C4C22×D1911yescharacteristic
224C2×M16—382no—
225C22×C8—22no—
226C22×C8—382no—
227#123—382no—
228#123—382no—
229C4×D4—22no—
230C4×D4—22no—
231C2×C4⋊C4—381no—
232C2×C4⋊C4—381no—
233C2×C4⋊C4—382no—
234C2×C4⋊C4—382no—
235C2×C4⋊C4—381no—
236C2×C4⋊C4—381no—
237C2×C4⋊C4C22⋊D1911yescharacteristic
238C2×C22⋊C4—191no—
239C2×C22⋊C4—191no—
240C2×C22⋊C4—381no—
241C2×C22⋊C4—381no—
242C2×C22⋊C4C4×D1911yescharacteristic
243C2×C22⋊C4C22⋊D1911yescharacteristic
244C2×C42—381no—
245C2×C42D7611yescharacteristic
246C4⋊C8—382no—
247C22⋊C8—22no—
248C22⋊C8—22no—
249C22⋊C8—194no—
250C22⋊C8—382no—
251C22⋊C8—382no—
252#97—382no—
253#95—381no—
254#95—381no—
255#95—381no—
256#95—381no—
257#95—381no—
258C19#911011yescharacteristic, complemented, Sylow
259C24(C2×D19)⋊C411yescharacteristic
260C24C2×C4×D1911yescharacteristic
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—21no—
264C2×D4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—81no—
268C22×C4—81no—
269C22×C4—192no—
270C22×C4—382no—
271C22×C4—382no—
272C22×C4—381no—
273C22×C4—381no—
274C22×C4—381no—
275C22×C4—381no—
276C22×C4—381no—
277C22×C4—382no—
278C22×C4—1521no—
279C22×C4(C2×D19)⋊C411yescharacteristic
280C22×C4(C2×D19)⋊C411yescharacteristic
281C22×C4(C2×D19)⋊C411yescharacteristic
282C22×C4C2×D7611yescharacteristic
283C22×C4D4×D1912yes—
284C22×C4#6454312yes—
285C22×C4C2×C22⋊D1911yescharacteristic
286M16—1522no—
287C2×C8—42no—
288C2×C8—82no—
289C2×C8—384no—
290C2×C8—1522no—
291C4⋊C4—22no—
292C4⋊C4—384no—
293C4⋊C4—762no—
294C4⋊C4—761no—
295C4⋊C4—761no—
296C4⋊C4—1521no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—192no—
300C22⋊C4—384no—
301C22⋊C4—381no—
302C22⋊C4—382no—
303C22⋊C4—1521no—
304C42—21no—
305C42—21no—
306C42—1521no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23(C22⋊D19)⋊C412yes—
315C23#1059734712yes—
316C23M16×D1911yescharacteristic
317C23M16×D1911yescharacteristic
318C23C2×(C2×D19)⋊C411yescharacteristic
319D4—42no—
320D4—42no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—384no—
335C2×C4—382no—
336C2×C4—382no—
337C2×C4—761no—
338C2×C4—761no—
339C2×C4—762no—
340C2×C4—761no—
341C2×C4—761no—
342C2×C4—761no—
343C2×C4—761no—
344C2×C4—761no—
345C2×C4—761no—
346C2×C4—761no—
347C2×C4—761no—
348C2×C4—1522no—
349C2×C4#1059732811yescharacteristic
350C2×C4#1059733211yescharacteristic
351C2×C4#1059738512yes—
352C8—82no—
353C8—764no—
354C22—21no—
355C22—22no—
356C22—21no—
357C22—22no—
358C22—42no—
359C22—41no—
360C22—41no—
361C22—42no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—81no—
366C22#1192642111yescharacteristic
367C22#1192650711yescharacteristic
368C22#1192651011yescharacteristic
369C22#1192661812yes—
370C22#1192661912yes—
371C4—22no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—762no—
378C4—762no—
379C4—1521no—
380C4—1521no—
381C2—21no—
382C2—21no—
383C2—22no—
384C2—22no—
385C2—81no—
386C2#1456393011yescharacteristic
387C2#1456417511yescharacteristic
388C2#1456418511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1459C2
socleC22×C19#386
prime radicalC22×D4×C19C2×C4
cosocleC23×C4×C19C23
hypercenter#1459D19
hypocenterC19#9110
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. C2×#11926269C2semidirect
4. #14561482C2semidirect
90. C22×Dic19M16semidirect
102. C22⋊Dic19M16semidirect
258. C19#9110semidirect

Maximal subgroups

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

subgroupindex
#145726642
#145663002
C2×#119262692
#145614822
C19×#14592
#911019