Finite Group Databasebeta

← #18079872

Subgroups — #18079872

Order 4864.

582 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 103 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#14572054C211yesmaximal, characteristic, complemented
2#14569322C211yesmaximal, characteristic
3#14562234C212yesmaximal, complemented
4#14561527C212yesmaximal, complemented
5C19×#1464C211yesmaximal, characteristic, complemented
6C22×#64520—21no—
7C2×#10597321C2211yescharacteristic
8#11926500—24no—
9C4×#64520—21no—
10C4×#64520C2212yes—
11#11926464C411yescharacteristic
12#11926461C411yescharacteristic
13#11926456C411yescharacteristic
14#11926453C411yescharacteristic
15#11926444—21no—
16#11926435—21no—
17#11926434—21no—
18#11926423—21no—
19#11926390C2211yescharacteristic
20#11926283—24no—
21C2×C19×#117C2211yescharacteristic
22C19×#432C2212yes—
23C19×#324—21no—
24C19×#323—21no—
25C23×C4×C19D411yescharacteristic
26C22×C22⋊D19—21no—
27C22×D76C2×C411yescharacteristic
28C22×Dic38C2×C411yescharacteristic
29C19×#117—22no—
30C19×#117—22no—
31C2×C4⋊C4×C19C2×C411yescharacteristic
32C2×C4⋊C4×C19D411yescharacteristic
33C2×C22⋊C4×C19C2×C411yescharacteristic
34C2×C22⋊C4×C19D411yescharacteristic
35C2×C42×C19D411yescharacteristic
36C2×C42×C19C2311yescharacteristic
37C2×C22⋊Dic19—21no—
38C2×(C2×D19)⋊C4—21no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×Dic19⋊C4—21no—
44C2×C4×Dic19—21no—
45C2×#64520—24no—
46C2×#64520—24no—
47C2×#64520—22no—
48C2×#64520—22no—
49C22×C19⋊C8—22no—
50#10597321—22no—
51#10597321—22no—
52C19×C4⋊C8—22no—
53C19×C22⋊C8—22no—
54C19×#97—22no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C19⋊#95C2×C411yescharacteristic
59C19⋊#95C2×C411yescharacteristic
60#10597260—22no—
61#10597260D414yescomplemented
62C4×C19⋊C8—22no—
63C4×C19⋊C8—22no—
64C24×C19C22⋊C411yescharacteristic
65C23×D19—21no—
66C22×C4×C19—22no—
67C22×C4×C19—22no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19C22⋊C411yescharacteristic
72C22×C4×C19C22⋊C411yescharacteristic
73C22×C4×C19C22×C411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C2×C22⋊D19—42no—
77C2×C22⋊D19—42no—
78C2×C22⋊D19—81no—
79C22×Dic19—21no—
80C22×Dic19—21no—
81C22×Dic19—21no—
82C2×D76—22no—
83C2×D76—81no—
84C2×Dic38—22no—
85C2×Dic38—81no—
86C2×C8×C19—42no—
87C4⋊C4×C19—22no—
88C4⋊C4×C19—22no—
89C22⋊C4×C19—22no—
90C22⋊C4×C19—22no—
91C42×C19—21no—
92C42×C19—21no—
93C42×C19C2×D412yes—
94C42×C19#4112yes—
95C22⋊Dic19—81no—
96(C2×D19)⋊C4—42no—
97(C2×D19)⋊C4—42no—
98(C2×D19)⋊C4—41no—
99(C2×D19)⋊C4—42no—
100(C2×D19)⋊C4—41no—
101(C2×D19)⋊C4—81no—
102Dic19⋊C4—81no—
103C4×Dic19—42no—
104#64520—28no—
105#64520—24no—
106#64520—24no—
107C2×C19⋊C8—28no—
108C2×C19⋊C8—24no—
109#9387—191nomaximal, Sylow
110C23×C19—21no—
111C23×C19—21no—
112C23×C19—41no—
113C23×C19—41no—
114C23×C19#10412yes—
115C23×C19C2×C22⋊C411yescharacteristic
116C22×D19—41no—
117C22×D19—41no—
118C22×D19—41no—
119C22×D19—41no—
120C22×D19—41no—
121C22×D19—41no—
122C22×D19—41no—
123C2×C4×C19—22no—
124C2×C4×C19—22no—
125C2×C4×C19—24no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19#10412yes—
137C2×C4×C19C4×D412yes—
138C2×C4×C19#12011yescharacteristic
139C2×C4×C19#12112yes—
140C2×C4×C19#12311yescharacteristic
141C22⋊D19—84no—
142C2×Dic19—22no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150C2×Dic19—41no—
151D76—82no—
152Dic38—82no—
153C8×C19—82no—
154C19⋊C8—28no—
155#2873—191no—
156#2610—191no—
157#1527—192no—
158#1464D1911yescharacteristic, complemented
159#1300—192no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—22no—
163C22×C19—42no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—81no—
167C22×C19#38611yescharacteristic
168C22×C19C2×#10411yescharacteristic
169C22×C19C2×#10411yescharacteristic
170C2×D19—81no—
171C2×D19—81no—
172C2×D19—81no—
173C2×D19—81no—
174C2×D19—81no—
175C2×D19—81no—
176C2×D19—81no—
177C4×C19—22no—
178C4×C19—21no—
179C4×C19—22no—
180C4×C19—21no—
181C4×C19—22no—
182C4×C19—41no—
183C4×C19—41no—
184Dic19—42no—
185Dic19—81no—
186Dic19—81no—
187C22×M16—381no—
188C2×#124—191no—
189C2×#117C2×D1911yescharacteristic
190#432C2×D1912yes—
191#405—384no—
192C4×M16—192no—
193C4×M16—381no—
194#395—191no—
195#394—191no—
196#393—191no—
197#392—191no—
198#390—381no—
199#388—381no—
200#388—381no—
201#386—381no—
202#376—191no—
203#329—384no—
204#324—21no—
205#323—21no—
206C2×C19—21no—
207C2×C19—21no—
208C2×C19—42no—
209C2×C19#188411yescharacteristic
210C2×C19#189611yescharacteristic
211C2×C19#191411yescharacteristic
212D19—161no—
213C22×Q8—191no—
214C22×D4—191no—
215C22×D4—381no—
216C23×C4D7611yescharacteristic
217C2×M16—382no—
218C2×M16—384no—
219C2×M16—384no—
220C2×M16—382no—
221C22×C8—382no—
222#124—382no—
223#124—382no—
224#117—22no—
225#117—22no—
226C2×C4⋊C4—381no—
227C2×C4⋊C4C4×D1911yescharacteristic
228C2×C4⋊C4C22⋊D1911yescharacteristic
229C2×C22⋊C4—381no—
230C2×C22⋊C4—381no—
231C2×C22⋊C4—381no—
232C2×C22⋊C4—381no—
233C2×C22⋊C4—381no—
234C2×C22⋊C4—381no—
235C2×C22⋊C4C4×D1911yescharacteristic
236C2×C22⋊C4C22⋊D1911yescharacteristic
237C2×C42—381no—
238C2×C42D7611yescharacteristic
239C2×C42C22×D1911yescharacteristic
240C4⋊C8—22no—
241C22⋊C8—22no—
242#97—22no—
243#97—194no—
244#97—382no—
245C4×C8—382no—
246C4×C8—382no—
247#95—191no—
248#95—191no—
249#95—381no—
250#95—381no—
251#95—381no—
252C19#938711yescharacteristic, complemented, Sylow
253C24—381no—
254C24(C2×D19)⋊C411yescharacteristic
255C2×Q8—382no—
256C2×Q8—1521no—
257C2×D4—382no—
258C2×D4—762no—
259C2×D4—762no—
260C2×D4—1521no—
261C2×D4—1521no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—381no—
267C22×C4—381no—
268C22×C4—381no—
269C22×C4(C2×D19)⋊C411yescharacteristic
270C22×C4(C2×D19)⋊C411yescharacteristic
271C22×C4(C2×D19)⋊C411yescharacteristic
272C22×C4C2×C4×D1911yescharacteristic
273C22×C4C2×D7611yescharacteristic
274C22×C4C2×C22⋊D1911yescharacteristic
275M16—388no—
276M16—384no—
277M16—384no—
278C2×C8—42no—
279C2×C8—388no—
280C2×C8—384no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—1521no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—762no—
287C22⋊C4—762no—
288C22⋊C4—762no—
289C22⋊C4—761no—
290C22⋊C4—761no—
291C22⋊C4—1521no—
292C22⋊C4—1521no—
293C42—21no—
294C42—21no—
295C42—762no—
296C42D4×D1912yes—
297C42#6454312yes—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—761no—
303C23—761no—
304C23—761no—
305C23—761no—
306C23—761no—
307C23—761no—
308C23—761no—
309C23#1059728212yes—
310C23C2×(C2×D19)⋊C411yescharacteristic
311Q8—1522no—
312D4—1522no—
313D4—1524no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—382no—
328C2×C4—761no—
329C2×C4—761no—
330C2×C4—761no—
331C2×C4—761no—
332C2×C4—761no—
333C2×C4—761no—
334C2×C4—761no—
335C2×C4—761no—
336C2×C4#1059728212yes—
337C2×C4(C22⋊D19)⋊C412yes—
338C2×C4#1059732811yescharacteristic
339C2×C4#1059733211yescharacteristic
340C2×C4#1059738512yes—
341C8—82no—
342C8—388no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—1521no—
351C22—1521no—
352C22—1521no—
353C22—1521no—
354C22—1521no—
355C22—1521no—
356C22—1521no—
357C22#1192642111yescharacteristic
358C22C2×#1059728211yescharacteristic
359C22C2×#1059728211yescharacteristic
360C4—22no—
361C4—22no—
362C4—21no—
363C4—22no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—762no—
368C4—1521no—
369C4—1521no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—3041no—
374C2#1456401611yescharacteristic
375C2#1456407611yescharacteristic
376C2#1456418011yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1464C2
socleC22×C19#386
prime radical#11926453C4
cosocleC2×C42×C19C23
hypercenter#1464D19
hypocenterC19#9387
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
1. #14572054C2semidirect
3. #14562234C2semidirect
4. #14561527C2semidirect
5. C19×#1464C2semidirect
61. #10597260D4semidirect
158. #1464D19semidirect
252. C19#9387semidirect

Maximal subgroups

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

subgroupindex
#145720542
#145693222
#145622342
#145615272
C19×#14642
#938719