Finite Group Databasebeta

← #18080321

Subgroups — #18080321

Order 4864.

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

normal subgroups only

This group has 912 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, complemented
2#14566991C211yesmaximal, characteristic
3#14563565C212yesmaximal, complemented
4#14561502C212yesmaximal, complemented
5C19×#1799C211yesmaximal, characteristic, complemented
6C23×D76C2211yescharacteristic
7C2×#10597376—21no—
8C2×#10597383—21no—
9#11926616—24no—
10#11926601—21no—
11C2×#10597266—24no—
12#11926508—21no—
13C2×C22⋊(C19⋊C8)C2212yes—
14#11926461C412yescomplemented
15#11926453C412yescomplemented
16#11926446—21no—
17#11926404C2211yescharacteristic
18#11926399—21no—
19C2×C4×D4×C19C2211yescharacteristic
20C2×C19×#99—21no—
21C19×#380C2212yes—
22C19×#342—21no—
23C24×D19—21no—
24C22×D4×C19D411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C22×C22⋊D19—22no—
28C22×D76—22no—
29C22×D76—21no—
30C22×D76—22no—
31C22×D76—44no—
32C22×D76C2×C412yes—
33C4×D4×C19—22no—
34C4×D4×C19—22no—
35C2×C4⋊C4×C19—22no—
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C22⋊C4×C19—22no—
38C2×C22⋊C4×C19C2×C411yescharacteristic
39C2×C22⋊C4×C19D411yescharacteristic
40C2×C42×C19D411yescharacteristic
41C2×C22⋊Dic19—21no—
42#10597383—44no—
43#10597376—44no—
44C2×(C2×D19)⋊C4—22no—
45C2×(C2×D19)⋊C4—22no—
46C2×(C2×D19)⋊C4—22no—
47C2×C4⋊Dic19—21no—
48C2×#64520—22no—
49C22×C19⋊C8D414yescomplemented
50C19×#99—42no—
51C19×#95—22no—
52C19⋊#95C2×C412yes—
53C22⋊(C19⋊C8)—22no—
54C22⋊(C19⋊C8)—22no—
55C22⋊(C19⋊C8)—22no—
56#10597266—48no—
57C4⋊(C19⋊C8)—22no—
58#10597260—22no—
59C24×C19C22⋊C411yescharacteristic
60C24×C19C2×D411yescharacteristic
61C23×D19—22no—
62C23×D19—44no—
63C23×D19—42no—
64C23×D19—42no—
65C23×D19—41no—
66C23×D19—41no—
67C23×D19—82no—
68C2×D4×C19—22no—
69C2×D4×C19—22no—
70C2×D4×C19—21no—
71C2×D4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—42no—
75C22×C4×C19—42no—
76C22×C4×C19—42no—
77C22×C4×C19C22⋊C411yescharacteristic
78C22×C4×C19C22⋊C411yescharacteristic
79C22×C4×C19C22⋊C411yescharacteristic
80C22×C4×C19C22×C411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19C2×D412yes—
83C22×C4×C19#4112yes—
84C2×C22⋊D19—44no—
85C2×C22⋊D19—44no—
86C2×C22⋊D19—82no—
87C22×Dic19—22no—
88C2×D76—28no—
89C2×D76—24no—
90C2×D76—24no—
91C2×D76—44no—
92C2×D76—48no—
93C2×D76—44no—
94C2×D76—42no—
95C2×D76—41no—
96C2×D76—41no—
97C4⋊C4×C19—22no—
98C4⋊C4×C19—44no—
99C22⋊C4×C19—22no—
100C22⋊C4×C19—22no—
101C22⋊C4×C19—42no—
102C22⋊C4×C19—42no—
103C42×C19—21no—
104C42×C19—21no—
105C22⋊Dic19—42no—
106(C2×D19)⋊C4—44no—
107(C2×D19)⋊C4—44no—
108(C2×D19)⋊C4—82no—
109C4⋊Dic19—42no—
110#64520—82no—
111C2×C19⋊C8—24no—
112C2×C19⋊C8—44no—
113#9472—191nomaximal, Sylow
114C23×C19—21no—
115C23×C19—21no—
116C23×C19—21no—
117C23×C19—41no—
118C23×C19—41no—
119C23×C19—41no—
120C23×C19—41no—
121C23×C19C2×C22⋊C411yescharacteristic
122C23×C19#12112yes—
123C23×C19AGL(1,ℤ/8)11yescharacteristic
124C23×C19AGL(1,ℤ/8)12yes—
125C23×C19#13711yescharacteristic
126C22×D19—24no—
127C22×D19—42no—
128C22×D19—48no—
129C22×D19—42no—
130C22×D19—42no—
131C22×D19—42no—
132C22×D19—42no—
133C22×D19—42no—
134C22×D19—88no—
135C22×D19—84no—
136C22×D19—84no—
137C22×D19—84no—
138C22×D19—82no—
139C22×D19—82no—
140D4×C19—42no—
141D4×C19—42no—
142C2×C4×C19—24no—
143C2×C4×C19—22no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—21no—
147C2×C4×C19—21no—
148C2×C4×C19—21no—
149C2×C4×C19—41no—
150C2×C4×C19—42no—
151C2×C4×C19—42no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—81no—
155C2×C4×C19—82no—
156C2×C4×C19—82no—
157C2×C4×C19—82no—
158C2×C4×C19C4×D412yes—
159C2×C4×C19#12011yescharacteristic
160C2×C4×C19#12311yescharacteristic
161C22⋊D19—88no—
162C2×Dic19—42no—
163C2×Dic19—42no—
164C2×Dic19—42no—
165D76—28no—
166D76—44no—
167D76—44no—
168D76—44no—
169C19⋊C8—44no—
170#2973—191no—
171#2408—191no—
172#1799D1911yescharacteristic, complemented
173#1786—192no—
174#1289—192no—
175C22×C19—21no—
176C22×C19—22no—
177C22×C19—21no—
178C22×C19—22no—
179C22×C19—41no—
180C22×C19—42no—
181C22×C19—41no—
182C22×C19—42no—
183C22×C19—41no—
184C22×C19—41no—
185C22×C19—41no—
186C22×C19—81no—
187C22×C19#38611yescharacteristic
188C22×C19#41711yescharacteristic
189C22×C19#41811yescharacteristic
190C22×C19#46812yes—
191C22×C19#46912yes—
192C2×D19—44no—
193C2×D19—44no—
194C2×D19—44no—
195C2×D19—82no—
196C2×D19—82no—
197C2×D19—88no—
198C2×D19—88no—
199C2×D19—82no—
200C2×D19—82no—
201C4×C19—22no—
202C4×C19—21no—
203C4×C19—41no—
204C4×C19—41no—
205C4×C19—41no—
206C4×C19—162no—
207C4×C19B(4,𝔽2)12yes—
208Dic19—82no—
209C23×D4—191no—
210C2×#121—381no—
211C2×#120—381no—
212C2×C4×D4C2×D1911yescharacteristic
213#435—384no—
214#432—381no—
215C2×#102—384no—
216C2×#99—21no—
217#407—381no—
218C2×C22⋊C8—192no—
219#394—192no—
220#392—192no—
221#390—381no—
222#380—191no—
223#380C2×D1912yes—
224#379—381no—
225#342—21no—
226C2×C19—21no—
227C2×C19—22no—
228C2×C19—21no—
229C2×C19—22no—
230C2×C19—81no—
231C2×C19#188911yescharacteristic
232C2×C19#189511yescharacteristic
233C2×C19#191011yescharacteristic
234D19—84no—
235C25—381no—
236C22×D4—192no—
237C22×D4—382no—
238C22×D4—381no—
239C22×D4—382no—
240C22×D4—382no—
241C22×D4—764no—
242C22×D4C22⋊D1911yescharacteristic
243C23×C4D7611yescharacteristic
244C23×C4C22×D1911yescharacteristic
245C2×M16—382no—
246C22×C8—194no—
247#121—764no—
248#120—764no—
249C4×D4—22no—
250C4×D4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—381no—
253C2×C4⋊C4C4×D1911yescharacteristic
254C2×C22⋊C4—22no—
255C2×C22⋊C4—381no—
256C2×C22⋊C4—382no—
257C2×C22⋊C4—382no—
258C2×C22⋊C4—382no—
259C2×C22⋊C4C4×D1911yescharacteristic
260C2×C22⋊C4C22⋊D1911yescharacteristic
261C2×C42D7611yescharacteristic
262C4⋊C8—382no—
263#102—768no—
264#99—42no—
265C22⋊C8—382no—
266C22⋊C8—382no—
267C22⋊C8—382no—
268#97—382no—
269#95—22no—
270#95—192no—
271C19#947211yescharacteristic, complemented, Sylow
272C24—382no—
273C24—764no—
274C24—762no—
275C24—761no—
276C24—761no—
277C24—762no—
278C24—1522no—
279C24(C2×D19)⋊C411yescharacteristic
280C24C2×C22⋊D1911yescharacteristic
281C2×D4—21no—
282C2×D4—22no—
283C2×D4—21no—
284C2×D4—22no—
285C2×D4—388no—
286C2×D4—384no—
287C2×D4—384no—
288C2×D4—764no—
289C2×D4—762no—
290C2×D4—764no—
291C2×D4—768no—
292C2×D4—764no—
293C2×D4—764no—
294C2×D4—761no—
295C2×D4—761no—
296C2×D4—1522no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—382no—
303C22×C4(C2×D19)⋊C411yescharacteristic
304C22×C4(C2×D19)⋊C411yescharacteristic
305C22×C4(C2×D19)⋊C411yescharacteristic
306C22×C4C2×C4×D1911yescharacteristic
307C22×C4C2×D7611yescharacteristic
308C22×C4D4×D1912yes—
309C22×C4#6454312yes—
310M16—1522no—
311C2×C8—384no—
312C2×C8—764no—
313C4⋊C4—22no—
314C4⋊C4—44no—
315C4⋊C4—762no—
316C22⋊C4—22no—
317C22⋊C4—22no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—764no—
321C22⋊C4—764no—
322C22⋊C4—762no—
323C22⋊C4—1522no—
324C42—21no—
325C42—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—384no—
334C23—762no—
335C23—768no—
336C23—762no—
337C23—762no—
338C23—762no—
339C23—762no—
340C23—762no—
341C23—1524no—
342C23—1524no—
343C23—1524no—
344C23—1528no—
345C23—1522no—
346C23—1522no—
347C23C2×(C2×D19)⋊C411yescharacteristic
348C23#1059737811yescharacteristic
349C23#1059738512yes—
350C23#1059738811yescharacteristic
351C23#1059739512yes—
352D4—42no—
353D4—42no—
354D4—388no—
355D4—764no—
356D4—764no—
357D4—764no—
358D4—1528no—
359C2×C4—24no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—81no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—762no—
376C2×C4—762no—
377C2×C4—762no—
378C2×C4(C22⋊D19)⋊C412yes—
379C2×C4#1059732811yescharacteristic
380C2×C4#1059733211yescharacteristic
381C8—764no—
382C22—21no—
383C22—22no—
384C22—21no—
385C22—22no—
386C22—41no—
387C22—41no—
388C22—42no—
389C22—42no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—81no—
394C22—764no—
395C22—764no—
396C22—764no—
397C22—1522no—
398C22—1522no—
399C22—1528no—
400C22—1528no—
401C22—1522no—
402C22—1522no—
403C22#1192642111yescharacteristic
404C22#1192654311yescharacteristic
405C22#1192654811yescharacteristic
406C22#1192679212yes—
407C22#1192679512yes—
408C4—21no—
409C4—22no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—162no—
414C4—1522no—
415C4#1192673212yes—
416C2—22no—
417C2—21no—
418C2—21no—
419C2—22no—
420C2—81no—
421C2—1524no—
422C2#1456404111yescharacteristic
423C2#1456407111yescharacteristic
424C2#1456416011yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1799C2
socleC22×C19#386
prime radical#14566991C2
cosocleC23×C4×C19C23
hypercenter#1799D19
hypocenterC19#9472
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
1. #14572664C2semidirect
3. #14563565C2semidirect
4. #14561502C2semidirect
5. C19×#1799C2semidirect
14. #11926461C4semidirect
15. #11926453C4semidirect
49. C22×C19⋊C8D4semidirect
172. #1799D19semidirect
271. C19#9472semidirect

Maximal subgroups

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

subgroupindex
#145726642
#145669912
#145635652
#145615022
C19×#17992
#947219