Finite Group Databasebeta

← #18080541

Subgroups — #18080541

Order 4864.

626 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 99 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#14572676C211yesmaximal, characteristic, complemented
2#14568521C211yesmaximal, characteristic
3#14561961C212yesmaximal, complemented
4#14561540C212yesmaximal, complemented
5C19×#1465C211yesmaximal, characteristic, complemented
6C2×#10597381C411yescharacteristic
7C2×#10597383C411yescharacteristic
8C22×(C2×D19)⋊C4C2211yescharacteristic
9#11926622—24no—
10#11926597—21no—
11#11926508—21no—
12#11926508C2212yes—
13#11926466—21no—
14#11926460—21no—
15#11926435—21no—
16#11926423—21no—
17#11926405C411yescharacteristic
18#11926404C2211yescharacteristic
19#11926399C411yescharacteristic
20#11926267—24no—
21C2×C4×D4×C19C2211yescharacteristic
22C19×#407C2212yes—
23C19×#324—21no—
24C19×#323—21no—
25C24×D19C2×C411yescharacteristic
26C22×D4×C19C2×C411yescharacteristic
27C23×C4×C19D411yescharacteristic
28C23×C4×C19C2311yescharacteristic
29C22×C22⋊D19—21no—
30C23×Dic19C2×C411yescharacteristic
31C2×M16×C19—22no—
32C4×D4×C19—22no—
33C4×D4×C19—22no—
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C22⋊C4×C19C2×C411yescharacteristic
36C2×C22⋊C4×C19D411yescharacteristic
37C2×C42×C19D411yescharacteristic
38C2×C22⋊Dic19—21no—
39C2×C22⋊Dic19C2×C411yescharacteristic
40C2×C22⋊Dic19C2×C411yescharacteristic
41#10597383—42no—
42#10597381—42no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—22no—
48C2×(C2×D19)⋊C4—22no—
49C2×(C2×D19)⋊C4—21no—
50C2×C4⋊Dic19—21no—
51C2×Dic19⋊C4—21no—
52C2×#64520—22no—
53C2×#64520—22no—
54C19×C22⋊C8—22no—
55C19×C22⋊C8—22no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C22⋊(C19⋊C8)—22no—
60C22⋊(C19⋊C8)—22no—
61C22⋊(C19⋊C8)D414yescomplemented
62C4⋊(C19⋊C8)—22no—
63C4×C19⋊C8—22no—
64C24×C19C22⋊C411yescharacteristic
65C24×C19C22×C411yescharacteristic
66C23×D19—21no—
67C23×D19—22no—
68C23×D19—42no—
69C23×D19—41no—
70C23×D19—41no—
71C23×D19—81no—
72C2×D4×C19—22no—
73C2×D4×C19—22no—
74C2×D4×C19—41no—
75C22×C4×C19—21no—
76C22×C4×C19—21no—
77C22×C4×C19—81no—
78C22×C4×C19—81no—
79C22×C4×C19C22⋊C411yescharacteristic
80C22×C4×C19C22⋊C411yescharacteristic
81C22×C4×C19C22⋊C411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19C2×D412yes—
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19#4112yes—
86C2×C22⋊D19—42no—
87C2×C22⋊D19—42no—
88C2×C22⋊D19—81no—
89C22×Dic19—21no—
90C22×Dic19—21no—
91C22×Dic19—21no—
92C22×Dic19—22no—
93C22×Dic19—41no—
94C22×Dic19—41no—
95M16×C19—82no—
96C2×C8×C19—42no—
97C4⋊C4×C19—22no—
98C22⋊C4×C19—22no—
99C22⋊C4×C19—22no—
100C42×C19—21no—
101C42×C19—21no—
102C22⋊Dic19—42no—
103C22⋊Dic19—41no—
104C22⋊Dic19—41no—
105(C2×D19)⋊C4—42no—
106(C2×D19)⋊C4—42no—
107(C2×D19)⋊C4—41no—
108(C2×D19)⋊C4—42no—
109(C2×D19)⋊C4—41no—
110(C2×D19)⋊C4—81no—
111C4⋊Dic19—81no—
112Dic19⋊C4—42no—
113#64520—82no—
114#64520—82no—
115C2×C19⋊C8—24no—
116#9516—191nomaximal, Sylow
117C23×C19—21no—
118C23×C19—21no—
119C23×C19—21no—
120C23×C19—21no—
121C23×C19—21no—
122C23×C19—41no—
123C23×C19—41no—
124C23×C19—41no—
125C23×C19—41no—
126C23×C19C2×C22⋊C411yescharacteristic
127C23×C19C4×D412yes—
128C22×D19—22no—
129C22×D19—24no—
130C22×D19—41no—
131C22×D19—41no—
132C22×D19—41no—
133C22×D19—42no—
134C22×D19—41no—
135C22×D19—41no—
136C22×D19—41no—
137C22×D19—84no—
138C22×D19—84no—
139C22×D19—82no—
140C22×D19—82no—
141D4×C19—44no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—42no—
147C2×C4×C19—41no—
148C2×C4×C19—42no—
149C2×C4×C19—41no—
150C2×C4×C19—42no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—81no—
154C2×C4×C19#10012yes—
155C2×C4×C19#12011yescharacteristic
156C2×C4×C19#12112yes—
157C2×C4×C19#12311yescharacteristic
158C22⋊D19—84no—
159C2×Dic19—41no—
160C2×Dic19—41no—
161C2×Dic19—41no—
162C2×Dic19—41no—
163C2×Dic19—41no—
164C2×Dic19—41no—
165C2×Dic19—41no—
166C2×Dic19—41no—
167C2×Dic19—41no—
168C2×Dic19—82no—
169C8×C19—82no—
170C19⋊C8—44no—
171#2975—191no—
172#2534—191no—
173#1465D1911yescharacteristic, complemented
174#1462—192no—
175#1305—192no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—22no—
179C22×C19—22no—
180C22×C19—22no—
181C22×C19—42no—
182C22×C19—42no—
183C22×C19—42no—
184C22×C19—41no—
185C22×C19—41no—
186C22×C19—41no—
187C22×C19—81no—
188C22×C19#38611yescharacteristic
189C22×C19C2×#10011yescharacteristic
190C22×C19#41311yescharacteristic
191C2×D19—42no—
192C2×D19—42no—
193C2×D19—42no—
194C2×D19—81no—
195C2×D19—81no—
196C2×D19—84no—
197C2×D19—81no—
198C2×D19—81no—
199C2×D19—84no—
200C4×C19—22no—
201C4×C19—21no—
202C4×C19—22no—
203C4×C19—21no—
204C4×C19—41no—
205C4×C19—41no—
206Dic19—81no—
207Dic19—81no—
208Dic19—81no—
209C2×#123—191no—
210C2×#120—191no—
211C2×C4×D4C2×D1911yescharacteristic
212C22×C22⋊C4—191no—
213#436—384no—
214#431—381no—
215#407—192no—
216#407—381no—
217#407C2×D1912yes—
218#396—381no—
219#394—381no—
220#388—381no—
221#386—381no—
222#381—191no—
223#380—191no—
224#379—191no—
225#324—21no—
226#323—21no—
227#323—384no—
228C2×C19—21no—
229C2×C19—21no—
230C2×C19—42no—
231C2×C19—81no—
232C2×C19#189111yescharacteristic
233C2×C19#190011yescharacteristic
234C2×C19#191311yescharacteristic
235D19—82no—
236C25—191no—
237C22×D4—381no—
238C22×D4C4×D1911yescharacteristic
239C23×C4—191no—
240C23×C4D7611yescharacteristic
241C23×C4C22×D1911yescharacteristic
242C2×M16—22no—
243C2×M16—382no—
244C2×M16—382no—
245#123—762no—
246#120—762no—
247C4×D4—22no—
248C4×D4—22no—
249C2×C4⋊C4—381no—
250C2×C4⋊C4—381no—
251C2×C4⋊C4C22⋊D1911yescharacteristic
252C2×C22⋊C4—191no—
253C2×C22⋊C4—191no—
254C2×C22⋊C4—381no—
255C2×C22⋊C4—381no—
256C2×C22⋊C4—381no—
257C2×C22⋊C4—381no—
258C2×C22⋊C4—382no—
259C2×C22⋊C4—382no—
260C2×C22⋊C4—381no—
261C2×C22⋊C4—381no—
262C2×C22⋊C4C4×D1911yescharacteristic
263C2×C22⋊C4C22⋊D1911yescharacteristic
264C2×C42D7611yescharacteristic
265C4⋊C8—382no—
266C22⋊C8—22no—
267C22⋊C8—22no—
268C22⋊C8—194no—
269C22⋊C8—382no—
270C22⋊C8—382no—
271C4×C8—382no—
272#95—381no—
273#95—381no—
274#95—381no—
275C19#951611yescharacteristic, complemented, Sylow
276C24—381no—
277C24—382no—
278C24—761no—
279C24—761no—
280C24—762no—
281C24—1521no—
282C24(C2×D19)⋊C411yescharacteristic
283C24C2×C4×D1911yescharacteristic
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—41no—
287C2×D4—762no—
288C2×D4—762no—
289C2×D4—1521no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—81no—
293C22×C4—81no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4—381no—
297C22×C4—382no—
298C22×C4—761no—
299C22×C4—761no—
300C22×C4(C2×D19)⋊C411yescharacteristic
301C22×C4(C2×D19)⋊C411yescharacteristic
302C22×C4(C2×D19)⋊C411yescharacteristic
303C22×C4C2×D7611yescharacteristic
304C22×C4D4×D1912yes—
305C22×C4#6454312yes—
306C22×C4C2×C22⋊D1911yescharacteristic
307M16—82no—
308M16—1522no—
309M16—1522no—
310C2×C8—42no—
311C2×C8—384no—
312C4⋊C4—22no—
313C4⋊C4—762no—
314C4⋊C4—1521no—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—762no—
318C22⋊C4—762no—
319C22⋊C4—762no—
320C22⋊C4—762no—
321C22⋊C4—761no—
322C22⋊C4—761no—
323C22⋊C4—761no—
324C22⋊C4—761no—
325C22⋊C4—1521no—
326C42—21no—
327C42—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—382no—
338C23—384no—
339C23—761no—
340C23—761no—
341C23—761no—
342C23—762no—
343C23—761no—
344C23—761no—
345C23—761no—
346C23—1522no—
347C23—1522no—
348C23—1524no—
349C23—1524no—
350C23(C22⋊D19)⋊C412yes—
351C23C2×(C2×D19)⋊C411yescharacteristic
352D4—44no—
353D4—1524no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—761no—
367C2×C4—761no—
368C2×C4—761no—
369C2×C4—761no—
370C2×C4—761no—
371C2×C4—761no—
372C2×C4—761no—
373C2×C4—761no—
374C2×C4—761no—
375C2×C4—1522no—
376C2×C4#1059728012yes—
377C2×C4#1059732811yescharacteristic
378C2×C4#1059733211yescharacteristic
379C2×C4#1059738512yes—
380C8—82no—
381C8—764no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—42no—
388C22—42no—
389C22—42no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—81no—
394C22—762no—
395C22—762no—
396C22—762no—
397C22—1521no—
398C22—1521no—
399C22—1524no—
400C22—1524no—
401C22—1521no—
402C22—1521no—
403C22#1192642111yescharacteristic
404C22C2×#1059728011yescharacteristic
405C22#1192652611yescharacteristic
406C4—22no—
407C4—22no—
408C4—21no—
409C4—21no—
410C4—41no—
411C4—41no—
412C4—1521no—
413C4—1521no—
414C4—1521no—
415C2—21no—
416C2—21no—
417C2—42no—
418C2—81no—
419C2—1522no—
420C2#1456405111yescharacteristic
421C2#1456409611yescharacteristic
422C2#1456417511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1465C2
socleC22×C19#386
prime radicalC2×#10597383C4
cosocleC23×C4×C19C23
hypercenter#1465D19
hypocenterC19#9516
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
1. #14572676C2semidirect
3. #14561961C2semidirect
4. #14561540C2semidirect
5. C19×#1465C2semidirect
61. C22⋊(C19⋊C8)D4semidirect
173. #1465D19semidirect
275. C19#9516semidirect

Maximal subgroups

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

subgroupindex
#145726762
#145685212
#145619612
#145615402
C19×#14652
#951619