Finite Group Databasebeta

← #18080524

Subgroups — #18080524

Order 4864.

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

normal subgroups only

This group has 558 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#14572273C211yesmaximal, characteristic, complemented
2#14563718C211yesmaximal, characteristic, complemented
3#14561962C212yesmaximal
4#14561543C212yesmaximal, complemented
5C19×#2482C211yesmaximal, characteristic
6#11926605—24no—
7#11926568—21no—
8#11926508C2212yes—
9#11926508C2212yes—
10C4×#64520—21no—
11#11926313—21no—
12#11926313—21no—
13#11926268—24no—
14C2×C19×#117C2211yescharacteristic
15C22×C22⋊C4×C19C2211yescharacteristic
16C19×#399—21no—
17C19×#397—21no—
18C19×#388—21no—
19C19×#388—21no—
20C19×#385C411yescharacteristic
21C19×#385C411yescharacteristic
22C19×#381C2211yescharacteristic
23C19×#379C411yescharacteristic
24C19×#379C411yescharacteristic
25C25×C19C2×C411yescharacteristic
26C23×C4×C19C2×C411yescharacteristic
27C23×C4×C19C2311yescharacteristic
28C19×#117—22no—
29C19×#117—22no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19D411yescharacteristic
33C2×C4⋊C4×C19D411yescharacteristic
34C2×C22⋊C4×C19—21no—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—21no—
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—22no—
39C2×C22⋊C4×C19—22no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19C2×C411yescharacteristic
43C2×C22⋊C4×C19C2×C411yescharacteristic
44C2×C22⋊C4×C19C2×C411yescharacteristic
45C2×C22⋊C4×C19C2×C411yescharacteristic
46C2×C42×C19D411yescharacteristic
47C2×C42×C19D411yescharacteristic
48C2×#64520—22no—
49C2×#64520—22no—
50C19×#95—21no—
51C19×#95—21no—
52C19×#95—21no—
53C19×#95—21no—
54C22⋊(C19⋊C8)—22no—
55C22⋊(C19⋊C8)—22no—
56C22⋊(C19⋊C8)—22no—
57C22⋊(C19⋊C8)D414yes—
58C4⋊(C19⋊C8)—24no—
59#10597260—22no—
60C4×C19⋊C8—22no—
61C24×C19—21no—
62C24×C19—22no—
63C24×C19—42no—
64C24×C19—41no—
65C24×C19—41no—
66C24×C19—81no—
67C24×C19C22×C411yescharacteristic
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—22no—
72C22×C4×C19—41no—
73C22×C4×C19—41no—
74C22×C4×C19—81no—
75C22×C4×C19C22⋊C411yescharacteristic
76C22×C4×C19C22⋊C411yescharacteristic
77C22×C4×C19C22⋊C411yescharacteristic
78C22×C4×C19C22⋊C411yescharacteristic
79C22×C4×C19C2×D412yes—
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19#4112yes—
83C4⋊C4×C19—22no—
84C4⋊C4×C19—22no—
85C4⋊C4×C19—81no—
86C4⋊C4×C19—81no—
87C22⋊C4×C19—22no—
88C22⋊C4×C19—22no—
89C22⋊C4×C19—42no—
90C22⋊C4×C19—42no—
91C22⋊C4×C19—41no—
92C22⋊C4×C19—42no—
93C22⋊C4×C19—41no—
94C22⋊C4×C19—41no—
95C22⋊C4×C19—41no—
96C22⋊C4×C19—81no—
97C22⋊C4×C19—81no—
98C42×C19—21no—
99C42×C19—21no—
100C42×C19—21no—
101C42×C19—21no—
102#64520—42no—
103#64520—42no—
104#64520—42no—
105#64520—42no—
106C2×C19⋊C8—24no—
107C2×C19⋊C8—42no—
108#9512—191nomaximal, Sylow
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—22no—
112C23×C19—24no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19—41no—
116C23×C19—41no—
117C23×C19—41no—
118C23×C19—42no—
119C23×C19—41no—
120C23×C19—41no—
121C23×C19—41no—
122C23×C19—82no—
123C23×C19—82no—
124C23×C19—84no—
125C23×C19—84no—
126C23×C19C2×C22⋊C411yescharacteristic
127C23×C19C4×D412yes—
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—41no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—82no—
152C2×C4×C19#12011yescharacteristic
153C2×C4×C19#12112yes—
154C2×C4×C19#12311yescharacteristic
155C19⋊C8—44no—
156C19⋊C8—82no—
157#2921—191no—
158#2482D1911yescharacteristic
159#1822—191no—
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—42no—
170C22×C19—42no—
171C22×C19—42no—
172C22×C19—81no—
173C22×C19—81no—
174C22×C19—84no—
175C22×C19—84no—
176C22×C19—81no—
177C22×C19—81no—
178C22×C19#38611yescharacteristic
179C22×C19#41011yescharacteristic
180C22×C19#41011yescharacteristic
181C4×C19—21no—
182C4×C19—22no—
183C4×C19—21no—
184C4×C19—41no—
185C4×C19—41no—
186C4×C19—41no—
187C4×C19—41no—
188C4×C19—81no—
189C4×C19—81no—
190C4×C19—81no—
191C2×#117C2×D1911yescharacteristic
192C22×C22⋊C4C2×D1911yescharacteristic
193#433—384no—
194#423—381no—
195#407—192no—
196#407—192no—
197C4×M16—381no—
198#399—21no—
199#397—21no—
200#388—21no—
201#388—21no—
202#385Dic1911yescharacteristic
203#385Dic1911yescharacteristic
204#381C2×D1911yescharacteristic
205#379Dic1911yescharacteristic
206#379Dic1911yescharacteristic
207#343—381no—
208#343—381no—
209#323—384no—
210C2×C19—21no—
211C2×C19—21no—
212C2×C19—42no—
213C2×C19—82no—
214C2×C19#189111yescharacteristic
215C2×C19#189911yescharacteristic
216C2×C19#191411yescharacteristic
217C25C2×Dic1911yescharacteristic
218C23×C4C2×Dic1911yescharacteristic
219C23×C4C22×D1911yescharacteristic
220C2×M16—382no—
221C2×M16—382no—
222#117—22no—
223#117—22no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4C22⋊D1911yescharacteristic
227C2×C4⋊C4C22⋊D1911yescharacteristic
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4C2×Dic1911yescharacteristic
237C2×C22⋊C4C2×Dic1911yescharacteristic
238C2×C22⋊C4C2×Dic1911yescharacteristic
239C2×C22⋊C4C2×Dic1911yescharacteristic
240C2×C42C22⋊D1911yescharacteristic
241C2×C42C22⋊D1911yescharacteristic
242C4⋊C8—384no—
243C22⋊C8—194no—
244C22⋊C8—382no—
245C22⋊C8—382no—
246C22⋊C8—382no—
247#97—382no—
248C4×C8—382no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253C19#951211yescharacteristic, complemented, Sylow
254C24—21no—
255C24—22no—
256C24—42no—
257C24—41no—
258C24—41no—
259C24—81no—
260C24C22×Dic1911yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—81no—
268C22×C4C22⋊Dic1911yescharacteristic
269C22×C4C22⋊Dic1911yescharacteristic
270C22×C4C22⋊Dic1911yescharacteristic
271C22×C4C22⋊Dic1911yescharacteristic
272C22×C4D4×D1912yes—
273C22×C4#6454312yes—
274C22×C4C2×C22⋊D1911yescharacteristic
275C22×C4C2×C22⋊D1911yescharacteristic
276M16—762no—
277M16—762no—
278M16—762no—
279M16—762no—
280C2×C8—384no—
281C2×C8—762no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—81no—
285C4⋊C4—81no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—42no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—81no—
296C22⋊C4—81no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42—21no—
301C23—21no—
302C23—21no—
303C23—22no—
304C23—24no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—42no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—82no—
315C23—82no—
316C23—84no—
317C23—84no—
318C23D4×Dic1912yes—
319C23C2×C22⋊Dic1911yescharacteristic
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—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—82no—
344C2×C4#1059738111yescharacteristic
345C2×C4#1059738311yescharacteristic
346C2×C4#1059738512yes—
347C8—764no—
348C8—1522no—
349C22—21no—
350C22—21no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—42no—
355C22—42no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—81no—
360C22—81no—
361C22—84no—
362C22—84no—
363C22—81no—
364C22—81no—
365C22#1192642411yescharacteristic
366C22#1192651811yescharacteristic
367C22#1192651811yescharacteristic
368C4—21no—
369C4—22no—
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—81no—
376C4—81no—
377C4—81no—
378C2—21no—
379C2—21no—
380C2—42no—
381C2—82no—
382C2#1456405411yescharacteristic
383C2#1456409411yescharacteristic
384C2#1456418311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2482C2
socleC22×C19#386
prime radicalC25×C19C2×C4
cosocleC23×C4×C19C23
hypercenter#2482D19
hypocenterC19#9512
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2482

Complements

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

NH ≅ G/Ntype
1. #14572273C2semidirect
2. #14563718C2semidirect
4. #14561543C2semidirect
253. C19#9512semidirect

Maximal subgroups

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

subgroupindex
#145722732
#145637182
#145619622
#145615432
C19×#24822
#951219