Finite Group Databasebeta

← #18080521

Subgroups — #18080521

Order 4864.

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

normal subgroups only

This group has 558 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#14572273C211yesmaximal, characteristic, complemented
2#14567905C211yesmaximal, characteristic
3#14561961C212yesmaximal
4#14561544C212yesmaximal, complemented
5C19×#1822C211yesmaximal, characteristic, complemented
6C22×(C2×D19)⋊C4C2211yescharacteristic
7#11926605—24no—
8#11926568—21no—
9#11926508C2212yes—
10C4×#64520—21no—
11#11926479—21no—
12#11926470—21no—
13#11926435—21no—
14#11926435—21no—
15#11926416C411yescharacteristic
16#11926416C411yescharacteristic
17#11926407C2211yescharacteristic
18#11926399C411yescharacteristic
19#11926399C411yescharacteristic
20#11926267—24no—
21C2×C19×#117C2211yescharacteristic
22C19×#407C2212yes—
23C19×#343—21no—
24C19×#343—21no—
25C24×D19C2×C411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C23×Dic19C2×C411yescharacteristic
28C2×M16×C19—22no—
29C19×#117—22no—
30C19×#117—22no—
31C2×C4⋊C4×C19D411yescharacteristic
32C2×C4⋊C4×C19D411yescharacteristic
33C2×C22⋊C4×C19C2×C411yescharacteristic
34C2×C22⋊C4×C19C2×C411yescharacteristic
35C2×C42×C19D411yescharacteristic
36C2×C42×C19D411yescharacteristic
37C2×C22⋊Dic19C2×C411yescharacteristic
38C2×C22⋊Dic19C2×C411yescharacteristic
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—22no—
44C2×(C2×D19)⋊C4—22no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×Dic19⋊C4—21no—
48C2×Dic19⋊C4—21no—
49C2×#64520—22no—
50C19×C22⋊C8—22no—
51C19×C22⋊C8—22no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C22⋊(C19⋊C8)—22no—
57C22⋊(C19⋊C8)D414yes—
58C4⋊(C19⋊C8)—24no—
59#10597260—22no—
60C4×C19⋊C8—22no—
61C24×C19C22×C411yescharacteristic
62C23×D19—21no—
63C23×D19—22no—
64C23×D19—42no—
65C23×D19—41no—
66C23×D19—41no—
67C23×D19—81no—
68C22×C4×C19—41no—
69C22×C4×C19—41no—
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19C22⋊C411yescharacteristic
72C22×C4×C19C22⋊C411yescharacteristic
73C22×C4×C19C22⋊C411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D412yes—
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19#4112yes—
78C22×Dic19—21no—
79C22×Dic19—21no—
80C22×Dic19—21no—
81C22×Dic19—22no—
82C22×Dic19—81no—
83M16×C19—42no—
84M16×C19—42no—
85C2×C8×C19—42no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—22no—
88C22⋊C4×C19—22no—
89C22⋊C4×C19—22no—
90C42×C19—21no—
91C42×C19—21no—
92C42×C19—21no—
93C42×C19—21no—
94C22⋊Dic19—41no—
95C22⋊Dic19—41no—
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—
102(C2×D19)⋊C4—81no—
103Dic19⋊C4—81no—
104Dic19⋊C4—81no—
105#64520—42no—
106#64520—42no—
107C2×C19⋊C8—24no—
108#9512—191nomaximal, Sylow
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—41no—
112C23×C19—41no—
113C23×C19C2×C22⋊C411yescharacteristic
114C23×C19C4×D412yes—
115C22×D19—22no—
116C22×D19—24no—
117C22×D19—41no—
118C22×D19—41no—
119C22×D19—41no—
120C22×D19—42no—
121C22×D19—41no—
122C22×D19—41no—
123C22×D19—41no—
124C22×D19—84no—
125C22×D19—84no—
126C22×D19—82no—
127C22×D19—82no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19#12011yescharacteristic
143C2×C4×C19#12112yes—
144C2×C4×C19#12311yescharacteristic
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150C2×Dic19—41no—
151C2×Dic19—41no—
152C2×Dic19—41no—
153C2×Dic19—41no—
154C2×Dic19—82no—
155C8×C19—82no—
156C19⋊C8—44no—
157#2921—191no—
158#2482—191no—
159#1822D1911yescharacteristic, complemented
160#1462—192no—
161#1306—192no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—22no—
165C22×C19—22no—
166C22×C19—22no—
167C22×C19—42no—
168C22×C19—42no—
169C22×C19#38611yescharacteristic
170C22×C19#41011yescharacteristic
171C22×C19#41011yescharacteristic
172C2×D19—42no—
173C2×D19—42no—
174C2×D19—42no—
175C2×D19—81no—
176C2×D19—81no—
177C2×D19—84no—
178C2×D19—81no—
179C2×D19—81no—
180C2×D19—84no—
181C4×C19—21no—
182C4×C19—22no—
183C4×C19—21no—
184C4×C19—41no—
185C4×C19—41no—
186C4×C19—41no—
187C4×C19—41no—
188Dic19—81no—
189Dic19—81no—
190Dic19—81no—
191C2×#117C2×D1911yescharacteristic
192C22×C22⋊C4—191no—
193#433—384no—
194#423—381no—
195#407—192no—
196#407C2×D1912yes—
197C4×M16—381no—
198#399—381no—
199#397—381no—
200#388—381no—
201#388—381no—
202#385—191no—
203#385—191no—
204#381—191no—
205#379—191no—
206#379—191no—
207#343—21no—
208#343—21no—
209#323—384no—
210C2×C19—21no—
211C2×C19—21no—
212C2×C19—42no—
213C2×C19#189111yescharacteristic
214C2×C19#189911yescharacteristic
215C2×C19#191411yescharacteristic
216D19—82no—
217C25—191no—
218C23×C4—191no—
219C23×C4C22×D1911yescharacteristic
220C2×M16—22no—
221C2×M16—382no—
222#117—22no—
223#117—22no—
224C2×C4⋊C4—381no—
225C2×C4⋊C4—381no—
226C2×C4⋊C4C22⋊D1911yescharacteristic
227C2×C4⋊C4C22⋊D1911yescharacteristic
228C2×C22⋊C4—191no—
229C2×C22⋊C4—191no—
230C2×C22⋊C4—381no—
231C2×C22⋊C4—381no—
232C2×C22⋊C4—381no—
233C2×C22⋊C4—382no—
234C2×C22⋊C4—382no—
235C2×C22⋊C4—381no—
236C2×C22⋊C4—381no—
237C2×C22⋊C4—381no—
238C2×C22⋊C4C4×D1911yescharacteristic
239C2×C22⋊C4C4×D1911yescharacteristic
240C2×C42D7611yescharacteristic
241C2×C42D7611yescharacteristic
242C4⋊C8—384no—
243C22⋊C8—22no—
244C22⋊C8—22no—
245C22⋊C8—194no—
246C22⋊C8—382no—
247#97—382no—
248C4×C8—382no—
249#95—381no—
250#95—381no—
251#95—381no—
252#95—381no—
253C19#951211yescharacteristic, complemented, Sylow
254C24—381no—
255C24—382no—
256C24—761no—
257C24—761no—
258C24—762no—
259C24—1521no—
260C24C2×C4×D1911yescharacteristic
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—381no—
264C22×C4—381no—
265C22×C4—381no—
266C22×C4—382no—
267C22×C4—1521no—
268C22×C4(C2×D19)⋊C411yescharacteristic
269C22×C4(C2×D19)⋊C411yescharacteristic
270C22×C4(C2×D19)⋊C411yescharacteristic
271C22×C4(C2×D19)⋊C411yescharacteristic
272C22×C4C2×D7611yescharacteristic
273C22×C4D4×D1912yes—
274C22×C4#6454312yes—
275C22×C4C2×C22⋊D1911yescharacteristic
276M16—42no—
277M16—42no—
278M16—762no—
279M16—762no—
280C2×C8—42no—
281C2×C8—384no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—1521no—
285C4⋊C4—1521no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—762no—
289C22⋊C4—762no—
290C22⋊C4—762no—
291C22⋊C4—761no—
292C22⋊C4—761no—
293C22⋊C4—761no—
294C22⋊C4—761no—
295C22⋊C4—1521no—
296C22⋊C4—1521no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42—21no—
301C23—21no—
302C23—21no—
303C23—41no—
304C23—41no—
305C23—382no—
306C23—384no—
307C23—761no—
308C23—761no—
309C23—761no—
310C23—762no—
311C23—761no—
312C23—761no—
313C23—761no—
314C23—1522no—
315C23—1522no—
316C23—1524no—
317C23—1524no—
318C23(C22⋊D19)⋊C412yes—
319C23C2×(C2×D19)⋊C411yescharacteristic
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—761no—
335C2×C4—761no—
336C2×C4—761no—
337C2×C4—761no—
338C2×C4—761no—
339C2×C4—761no—
340C2×C4—761no—
341C2×C4—761no—
342C2×C4—761no—
343C2×C4—1522no—
344C2×C4#1059732811yescharacteristic
345C2×C4#1059733211yescharacteristic
346C2×C4#1059738512yes—
347C8—82no—
348C8—764no—
349C22—21no—
350C22—21no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—42no—
355C22—42no—
356C22—762no—
357C22—762no—
358C22—762no—
359C22—1521no—
360C22—1521no—
361C22—1524no—
362C22—1524no—
363C22—1521no—
364C22—1521no—
365C22#1192642111yescharacteristic
366C22#1192651711yescharacteristic
367C22#1192651711yescharacteristic
368C4—22no—
369C4—21no—
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—1521no—
376C4—1521no—
377C4—1521no—
378C2—21no—
379C2—21no—
380C2—42no—
381C2—1522no—
382C2#1456405111yescharacteristic
383C2#1456409111yescharacteristic
384C2#1456418011yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1822C2
socleC22×C19#386
prime radicalC24×D19C2×C4
cosocleC23×C4×C19C23
hypercenter#1822D19
hypocenterC19#9512
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1822

Complements

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

NH ≅ G/Ntype
1. #14572273C2semidirect
4. #14561544C2semidirect
5. C19×#1822C2semidirect
159. #1822D19semidirect
253. C19#9512semidirect

Maximal subgroups

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

subgroupindex
#145722732
#145679052
#145619612
#145615442
C19×#18222
#951219