Finite Group Databasebeta

← #18080449

Subgroups — #18080449

Order 4864.

1184 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 1184 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#14566217C211yesmaximal, characteristic, complemented
2#14563550C211yesmaximal, characteristic, complemented
3#14563550C212yesmaximal, complemented
4C19⋊#1304C212yesmaximal, complemented
5C19×#2403C211yesmaximal, characteristic
6C2×#10597372—21no—
7C2×#10597291—22no—
8C2×#10597291—24no—
9#11926447—24no—
10#11926400—21no—
11#11926400C2212yes—
12#11926400C2212yes—
13C23×D4×C19C2211yescharacteristic
14C23×D4×C19C2211yescharacteristic
15C2×C19×#120—21no—
16C2×C19×#120C412yescomplemented
17C19×#392—22no—
18C19×#386—21no—
19C19×#386C412yescomplemented
20C19×#379C2211yescharacteristic
21C25×C19C2×C411yescharacteristic
22C25×C19D411yescharacteristic
23C25×C19C2311yescharacteristic
24C22×D4×C19—21no—
25C22×D4×C19—22no—
26C22×D4×C19—22no—
27C22×D4×C19—22no—
28C22×D4×C19—21no—
29C22×D4×C19—22no—
30C22×D4×C19—22no—
31C22×D4×C19—44no—
32C22×D4×C19—44no—
33C22×D4×C19C2×C412yes—
34C22×D4×C19D412yes—
35C23×C4×C19C2×C411yescharacteristic
36C23×C4×C19D411yescharacteristic
37C19×#120—44no—
38C19×#120—44no—
39C2×C22⋊C4×C19—22no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—22no—
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19C2×C412yes—
44C2×C22⋊Dic19—22no—
45C2×C22⋊Dic19—22no—
46C2×C22⋊Dic19—22no—
47C2×C22⋊Dic19—22no—
48C2×C22⋊Dic19—22no—
49C2×C22⋊Dic19—22no—
50C2×C22⋊Dic19—22no—
51C2×C22⋊Dic19D414yescomplemented
52#10597372—44no—
53C2×C4⋊Dic19—22no—
54C2×C4×Dic19—22no—
55C19×#95—22no—
56#10597291—48no—
57#10597291—44no—
58C24×C19—21no—
59C24×C19—21no—
60C24×C19—22no—
61C24×C19—21no—
62C24×C19—42no—
63C24×C19—42no—
64C24×C19—42no—
65C24×C19—42no—
66C24×C19—42no—
67C24×C19—42no—
68C24×C19—81no—
69C24×C19—81no—
70C24×C19—81no—
71C24×C19C22⋊C412yes—
72C24×C19C22×C411yescharacteristic
73C24×C19C2×D412yes—
74C24×C19C2×D411yescharacteristic
75C24×C19C2×D411yescharacteristic
76C24×C19#4112yes—
77C2×D4×C19—24no—
78C2×D4×C19—28no—
79C2×D4×C19—24no—
80C2×D4×C19—24no—
81C2×D4×C19—24no—
82C2×D4×C19—24no—
83C2×D4×C19—42no—
84C2×D4×C19—42no—
85C2×D4×C19—44no—
86C2×D4×C19—44no—
87C2×D4×C19—48no—
88C2×D4×C19—42no—
89C2×D4×C19—44no—
90C2×D4×C19—42no—
91C2×D4×C19—44no—
92C2×D4×C19—42no—
93C2×D4×C19—44no—
94C2×D4×C19—41no—
95C2×D4×C19—42no—
96C2×D4×C19—41no—
97C2×D4×C19—44no—
98C2×D4×C19—44no—
99C2×D4×C19—82no—
100C22×C4×C19—21no—
101C22×C4×C19—21no—
102C22×C4×C19—24no—
103C22×C4×C19—21no—
104C22×C4×C19—22no—
105C22×C4×C19—22no—
106C22×C4×C19—42no—
107C22×C4×C19C22⋊C412yes—
108C22×Dic19—24no—
109C22×Dic19—42no—
110C22⋊C4×C19—44no—
111C22⋊C4×C19—42no—
112C22⋊C4×C19—44no—
113C22⋊C4×C19—42no—
114C22⋊C4×C19—81no—
115C22⋊Dic19—44no—
116C22⋊Dic19—44no—
117C22⋊Dic19—44no—
118C22⋊Dic19—44no—
119C22⋊Dic19—82no—
120C22⋊Dic19—82no—
121C22⋊Dic19—82no—
122C22⋊Dic19—82no—
123C4⋊Dic19—44no—
124C4×Dic19—44no—
125#9497—191nomaximal, Sylow
126C23×C19—22no—
127C23×C19—22no—
128C23×C19—22no—
129C23×C19—22no—
130C23×C19—24no—
131C23×C19—22no—
132C23×C19—24no—
133C23×C19—22no—
134C23×C19—22no—
135C23×C19—22no—
136C23×C19—41no—
137C23×C19—41no—
138C23×C19—41no—
139C23×C19—42no—
140C23×C19—42no—
141C23×C19—41no—
142C23×C19—42no—
143C23×C19—41no—
144C23×C19—42no—
145C23×C19—42no—
146C23×C19—42no—
147C23×C19—42no—
148C23×C19—42no—
149C23×C19—41no—
150C23×C19—42no—
151C23×C19—42no—
152C23×C19—42no—
153C23×C19—42no—
154C23×C19—41no—
155C23×C19—42no—
156C23×C19—42no—
157C23×C19—81no—
158C23×C19—81no—
159C23×C19—82no—
160C23×C19—82no—
161C23×C19—88no—
162C23×C19—88no—
163C23×C19—88no—
164C23×C19C2×C22⋊C411yescharacteristic
165C23×C19C4×D412yes—
166C23×C19#12011yescharacteristic
167C23×C19#12112yes—
168C23×C19#12311yescharacteristic
169D4×C19—48no—
170D4×C19—48no—
171D4×C19—48no—
172D4×C19—44no—
173D4×C19—44no—
174D4×C19—88no—
175C2×C4×C19—22no—
176C2×C4×C19—22no—
177C2×C4×C19—24no—
178C2×C4×C19—22no—
179C2×C4×C19—22no—
180C2×C4×C19—22no—
181C2×C4×C19—24no—
182C2×C4×C19—41no—
183C2×C4×C19—42no—
184C2×C4×C19—41no—
185C2×C4×C19—42no—
186C2×C4×C19—42no—
187C2×C4×C19—42no—
188C2×C4×C19#9914yescomplemented
189C2×Dic19—44no—
190C2×Dic19—44no—
191C2×Dic19—44no—
192C2×Dic19—82no—
193C2×Dic19—82no—
194C2×Dic19—82no—
195#2403D1911yescharacteristic
196#2309—191no—
197#1781—192no—
198#1781—191no—
199#1304—192no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—21no—
203C22×C19—21no—
204C22×C19—22no—
205C22×C19—22no—
206C22×C19—21no—
207C22×C19—22no—
208C22×C19—21no—
209C22×C19—22no—
210C22×C19—22no—
211C22×C19—22no—
212C22×C19—21no—
213C22×C19—44no—
214C22×C19—44no—
215C22×C19—44no—
216C22×C19—44no—
217C22×C19—42no—
218C22×C19—42no—
219C22×C19—42no—
220C22×C19—42no—
221C22×C19—84no—
222C22×C19—82no—
223C22×C19—82no—
224C22×C19—84no—
225C22×C19—82no—
226C22×C19—84no—
227C22×C19—84no—
228C22×C19—84no—
229C22×C19—84no—
230C22×C19—81no—
231C22×C19—81no—
232C22×C19#38611yescharacteristic
233C22×C19C2×#9912yes—
234C22×C19B(4,𝔽2)12yes—
235C4×C19—24no—
236C4×C19—42no—
237C4×C19—82no—
238Dic19—84no—
239Dic19—162no—
240C23×D4C2×D1911yescharacteristic
241C23×D4C2×D1911yescharacteristic
242C2×#120—21no—
243C2×#120Dic1912yescomplemented
244C2×#117—381no—
245C2×#99—384no—
246C2×#99—382no—
247#392—22no—
248#390—384no—
249#386—21no—
250#386Dic1912yescomplemented
251#379—192no—
252#379—192no—
253#379—381no—
254#379C2×D1911yescharacteristic
255C2×C19—22no—
256C2×C19—22no—
257C2×C19—42no—
258C2×C19—42no—
259C2×C19—41no—
260C2×C19—82no—
261C2×C19—82no—
262C2×C19#188911yescharacteristic
263C2×C19#189811yescharacteristic
264C2×C19#191311yescharacteristic
265C25C2×Dic1911yescharacteristic
266C25C22⋊D1911yescharacteristic
267C25C22×D1911yescharacteristic
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—21no—
272C22×D4—22no—
273C22×D4—21no—
274C22×D4—22no—
275C22×D4—44no—
276C22×D4—44no—
277C22×D4C2×Dic1912yes—
278C22×D4C22⋊D1912yes—
279C23×C4C2×Dic1911yescharacteristic
280C23×C4C22⋊D1911yescharacteristic
281#120—44no—
282#120—44no—
283#117—764no—
284C2×C4⋊C4—382no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—194no—
290C2×C22⋊C4—382no—
291C2×C22⋊C4—382no—
292C2×C22⋊C4—382no—
293C2×C22⋊C4—382no—
294C2×C22⋊C4—382no—
295C2×C22⋊C4—382no—
296C2×C22⋊C4—382no—
297C2×C22⋊C4C2×Dic1912yes—
298C2×C42—382no—
299#99—768no—
300#99—764no—
301#95—22no—
302C19#949711yescharacteristic, complemented, Sylow
303C24—21no—
304C24—21no—
305C24—22no—
306C24—21no—
307C24—42no—
308C24—42no—
309C24—42no—
310C24—42no—
311C24—42no—
312C24—42no—
313C24—81no—
314C24—81no—
315C24—81no—
316C24C22⋊Dic1912yes—
317C24D4×D1912yes—
318C24#6454312yes—
319C24C22×Dic1911yescharacteristic
320C24C2×C22⋊D1911yescharacteristic
321C24C2×C22⋊D1911yescharacteristic
322C2×D4—28no—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—24no—
327C2×D4—24no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—44no—
331C2×D4—44no—
332C2×D4—48no—
333C2×D4—42no—
334C2×D4—44no—
335C2×D4—42no—
336C2×D4—44no—
337C2×D4—42no—
338C2×D4—44no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—42no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—82no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—42no—
352C22×C4—384no—
353C22×C4—762no—
354C22×C4C22⋊Dic1912yes—
355C4⋊C4—764no—
356C22⋊C4—44no—
357C22⋊C4—42no—
358C22⋊C4—44no—
359C22⋊C4—42no—
360C22⋊C4—81no—
361C22⋊C4—764no—
362C22⋊C4—764no—
363C22⋊C4—764no—
364C22⋊C4—764no—
365C22⋊C4—1522no—
366C22⋊C4—1522no—
367C22⋊C4—1522no—
368C22⋊C4—1522no—
369C42—764no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—24no—
374C23—22no—
375C23—22no—
376C23—24no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—41no—
384C23—42no—
385C23—42no—
386C23—42no—
387C23—42no—
388C23—42no—
389C23—41no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—41no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—41no—
399C23—42no—
400C23—42no—
401C23—81no—
402C23—81no—
403C23—82no—
404C23—82no—
405C23—88no—
406C23—88no—
407C23—88no—
408C23D4×Dic1912yes—
409C23#1059738111yescharacteristic
410C23#1059738311yescharacteristic
411C23#1059738512yes—
412C23C2×C22⋊Dic1911yescharacteristic
413D4—48no—
414D4—48no—
415D4—48no—
416D4—44no—
417D4—44no—
418D4—88no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—764no—
433C2×C4—764no—
434C2×C4—764no—
435C2×C4—1522no—
436C2×C4—1522no—
437C2×C4—1522no—
438C2×C4#1059729114yescomplemented
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—22no—
444C22—22no—
445C22—21no—
446C22—22no—
447C22—22no—
448C22—21no—
449C22—21no—
450C22—22no—
451C22—22no—
452C22—44no—
453C22—44no—
454C22—44no—
455C22—44no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—82no—
461C22—84no—
462C22—82no—
463C22—82no—
464C22—84no—
465C22—84no—
466C22—84no—
467C22—84no—
468C22—84no—
469C22—81no—
470C22—81no—
471C22#1192642411yescharacteristic
472C22C2×#1059729112yes—
473C22#1192673012yes—
474C4—24no—
475C4—42no—
476C4—82no—
477C4—3042no—
478C4—1524no—
479C2—22no—
480C2—22no—
481C2—42no—
482C2—42no—
483C2—41no—
484C2—82no—
485C2—82no—
486C2#1456404411yescharacteristic
487C2#1456408911yescharacteristic
488C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC24×C19C22×C4
FrattiniC25C22×D19
Fitting, prime radicalC19×#2403C2
socleC22×C19#386
cosocleC25×C19C23
hypercenter#2403D19
hypocenterC19#9497
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C25 ◁ #2403

Complements

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

NH ≅ G/Ntype
1. #14566217C2semidirect
2. #14563550C2semidirect
3. #14563550C2semidirect
4. C19⋊#1304C2semidirect
16. C2×C19×#120C4semidirect
19. C19×#386C4semidirect
51. C2×C22⋊Dic19D4semidirect
188. C2×C4×C19#99semidirect
243. C2×#120Dic19semidirect
250. #386Dic19semidirect
302. C19#9497semidirect
438. C2×C4#10597291semidirect

Maximal subgroups

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

subgroupindex
#145662172
#145635502
C19⋊#13042
C19×#24032
#949719