Finite Group Databasebeta

← #18080279

Subgroups — #18080279

Order 4864.

1034 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 1034 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#14566213C211yesmaximal, characteristic, complemented
2#14563556C211yesmaximal, characteristic, complemented
3#14562164C212yesmaximal, complemented
4#14561488C212yesmaximal, complemented
5C19×#2433C211yesmaximal, characteristic
6C22×C22⋊Dic19—21no—
7C2×#10597290—22no—
8#11926508C2212yes—
9#11926424—24no—
10#11926407C2212yes—
11#11926400—21no—
12#11926278—24no—
13C23×D4×C19C2211yescharacteristic
14C2×C19×#127C412yescomplemented
15C2×C19×#121C2211yescharacteristic
16C2×C19×#120—21no—
17C2×C19×#120—21no—
18C19×#392—22no—
19C19×#390C412yescomplemented
20C4×C22⋊C4×C19C2211yescharacteristic
21C25×C19D411yescharacteristic
22C25×C19D411yescharacteristic
23C22×D4×C19—21no—
24C22×D4×C19—22no—
25C22×D4×C19—22no—
26C22×D4×C19—22no—
27C22×D4×C19—22no—
28C22×D4×C19—44no—
29C22×D4×C19C2×C412yes—
30C22×D4×C19C2×C411yescharacteristic, complemented
31C22×D4×C19D412yes—
32C23×C4×C19C2311yescharacteristic
33C23×Dic19—22no—
34C19×#127—44no—
35C19×#121—22no—
36C19×#121—22no—
37C19×#120—44no—
38C19×#120—44no—
39C2×C4⋊C4×C19C2×C411yescharacteristic, complemented
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—22no—
42C2×C22⋊C4×C19—22no—
43C2×C22⋊C4×C19—21no—
44C2×C42×C19C2×C412yescomplemented
45C2×C22⋊Dic19—22no—
46C2×C22⋊Dic19—22no—
47C2×C22⋊Dic19—22no—
48C2×C22⋊Dic19—22no—
49C2×C22⋊Dic19—44no—
50C2×#64520—22no—
51C19×#95—21no—
52#10597290—44no—
53C19⋊#95—22no—
54C19⋊#95D414yescomplemented
55C22⋊(C19⋊C8)—22no—
56C22⋊(C19⋊C8)—22no—
57C24×C19—21no—
58C24×C19—24no—
59C24×C19—21no—
60C24×C19—21no—
61C24×C19—21no—
62C24×C19—21no—
63C24×C19—42no—
64C24×C19—42no—
65C24×C19—42no—
66C24×C19—81no—
67C24×C19—81no—
68C24×C19C22⋊C412yes—
69C24×C19C22⋊C412yes—
70C24×C19C2×D411yescharacteristic
71C2×D4×C19—24no—
72C2×D4×C19—24no—
73C2×D4×C19—24no—
74C2×D4×C19—22no—
75C2×D4×C19—24no—
76C2×D4×C19—42no—
77C2×D4×C19—42no—
78C2×D4×C19—42no—
79C2×D4×C19—44no—
80C2×D4×C19—44no—
81C2×D4×C19—44no—
82C2×D4×C19—44no—
83C2×D4×C19—48no—
84C2×D4×C19—42no—
85C2×D4×C19—42no—
86C2×D4×C19—44no—
87C2×D4×C19—44no—
88C2×D4×C19—41no—
89C2×D4×C19—41no—
90C2×D4×C19—82no—
91C2×D4×C19—82no—
92C22×C4×C19—22no—
93C22×C4×C19—21no—
94C22×C4×C19—42no—
95C22×C4×C19C22×C411yescharacteristic
96C22×C4×C19C2×D412yes—
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19#4112yes—
99C22×Dic19—24no—
100C22×Dic19—44no—
101C22×Dic19—82no—
102C22×Dic19—82no—
103C4⋊C4×C19—22no—
104C22⋊C4×C19—24no—
105C22⋊C4×C19—44no—
106C22⋊C4×C19—44no—
107C22⋊C4×C19—42no—
108C42×C19—42no—
109C22⋊Dic19—44no—
110C22⋊Dic19—44no—
111C22⋊Dic19—82no—
112C22⋊Dic19—82no—
113#64520—44no—
114C2×C19⋊C8—42no—
115#9463—191nomaximal, Sylow
116C23×C19—22no—
117C23×C19—22no—
118C23×C19—24no—
119C23×C19—22no—
120C23×C19—22no—
121C23×C19—22no—
122C23×C19—22no—
123C23×C19—22no—
124C23×C19—22no—
125C23×C19—22no—
126C23×C19—41no—
127C23×C19—42no—
128C23×C19—42no—
129C23×C19—42no—
130C23×C19—42no—
131C23×C19—42no—
132C23×C19—42no—
133C23×C19—42no—
134C23×C19—42no—
135C23×C19—41no—
136C23×C19—41no—
137C23×C19—42no—
138C23×C19—42no—
139C23×C19—42no—
140C23×C19—41no—
141C23×C19—42no—
142C23×C19—81no—
143C23×C19—81no—
144C23×C19—81no—
145C23×C19—81no—
146C23×C19—88no—
147C23×C19—88no—
148C23×C19#9914yes—
149C23×C19C2×C22⋊C411yescharacteristic
150C23×C19#12011yescharacteristic
151C23×C19#12311yescharacteristic
152D4×C19—48no—
153D4×C19—48no—
154D4×C19—82no—
155D4×C19—88no—
156D4×C19—88no—
157D4×C19—82no—
158D4×C19—82no—
159C2×C4×C19—22no—
160C2×C4×C19—22no—
161C2×C4×C19—24no—
162C2×C4×C19—42no—
163C2×C4×C19—42no—
164C2×C4×C19—42no—
165C2×C4×C19—42no—
166C2×C4×C19—41no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19C4×D412yes—
170C2×C4×C19#12112yes—
171C2×Dic19—44no—
172C2×Dic19—44no—
173C2×Dic19—44no—
174C2×Dic19—88no—
175C19⋊C8—82no—
176#2433D1911yescharacteristic
177#2308—191no—
178#1783—191no—
179#1510—192no—
180#1284—192no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—21no—
186C22×C19—21no—
187C22×C19—24no—
188C22×C19—21no—
189C22×C19—44no—
190C22×C19—44no—
191C22×C19—44no—
192C22×C19—44no—
193C22×C19—44no—
194C22×C19—42no—
195C22×C19—42no—
196C22×C19—42no—
197C22×C19—42no—
198C22×C19—42no—
199C22×C19—82no—
200C22×C19—82no—
201C22×C19—84no—
202C22×C19—82no—
203C22×C19—82no—
204C22×C19—84no—
205C22×C19—84no—
206C22×C19—81no—
207C22×C19—81no—
208C22×C19—81no—
209C22×C19#38611yescharacteristic
210C22×C19C2×#9912yes—
211C22×C19#45312yes—
212C4×C19—22no—
213C4×C19—22no—
214C4×C19—44no—
215C4×C19—81no—
216Dic19—84no—
217C23×D4C2×D1911yescharacteristic
218C2×#127Dic1912yescomplemented
219C2×#121C2×D1911yescharacteristic
220C2×#120—21no—
221C2×#120—21no—
222C22×C22⋊C4—381no—
223C2×#100—382no—
224#407—192no—
225#392—22no—
226#390Dic1912yescomplemented
227#386—384no—
228#381—192no—
229#379—381no—
230C4×C22⋊C4C2×D1911yescharacteristic
231#327—384no—
232C2×C19—22no—
233C2×C19—22no—
234C2×C19—41no—
235C2×C19—44no—
236C2×C19—82no—
237C2×C19—161no—
238C2×C19#188711yescharacteristic
239C2×C19#189811yescharacteristic
240C2×C19#191111yescharacteristic
241C25C22⋊D1911yescharacteristic
242C25C22⋊D1911yescharacteristic
243C22×D4—21no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—44no—
249C22×D4C2×Dic1912yes—
250C22×D4C2×Dic1911yescharacteristic, complemented
251C22×D4C22⋊D1912yes—
252C23×C4—382no—
253C23×C4C22×D1911yescharacteristic
254C2×M16—382no—
255#127—44no—
256#121—22no—
257#121—22no—
258#120—44no—
259#120—44no—
260C2×C4⋊C4C2×Dic1911yescharacteristic, complemented
261C2×C22⋊C4—21no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—382no—
266C2×C22⋊C4—382no—
267C2×C22⋊C4—382no—
268C2×C22⋊C4—382no—
269C2×C22⋊C4—764no—
270C2×C42C2×Dic1912yescomplemented
271#100—764no—
272C22⋊C8—382no—
273C22⋊C8—382no—
274#95—21no—
275#95—194no—
276#95—382no—
277C19#946311yescharacteristic, complemented, Sylow
278C24—21no—
279C24—21no—
280C24—24no—
281C24—21no—
282C24—21no—
283C24—21no—
284C24—42no—
285C24—42no—
286C24—42no—
287C24—81no—
288C24—81no—
289C24C22⋊Dic1912yes—
290C24C22⋊Dic1912yes—
291C24C2×C22⋊D1911yescharacteristic
292C2×D4—24no—
293C2×D4—24no—
294C2×D4—24no—
295C2×D4—22no—
296C2×D4—24no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—44no—
301C2×D4—44no—
302C2×D4—44no—
303C2×D4—44no—
304C2×D4—48no—
305C2×D4—42no—
306C2×D4—42no—
307C2×D4—44no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—44no—
311C2×D4—82no—
312C2×D4—82no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—42no—
316C22×C4—384no—
317C22×C4—764no—
318C22×C4—1522no—
319C22×C4—1522no—
320C22×C4D4×D1912yes—
321C22×C4#6454312yes—
322C22×C4C22×Dic1911yescharacteristic
323C22×C4C2×C22⋊D1911yescharacteristic
324M16—764no—
325C2×C8—762no—
326C4⋊C4—22no—
327C22⋊C4—24no—
328C22⋊C4—44no—
329C22⋊C4—44no—
330C22⋊C4—42no—
331C22⋊C4—764no—
332C22⋊C4—764no—
333C22⋊C4—1522no—
334C22⋊C4—1522no—
335C42—42no—
336C23—22no—
337C23—22no—
338C23—24no—
339C23—22no—
340C23—22no—
341C23—22no—
342C23—22no—
343C23—22no—
344C23—22no—
345C23—22no—
346C23—41no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—42no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—41no—
356C23—41no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23—41no—
361C23—42no—
362C23—81no—
363C23—81no—
364C23—81no—
365C23—81no—
366C23—88no—
367C23—88no—
368C23#1059729114yes—
369C23#1059738111yescharacteristic
370C23#1059738311yescharacteristic
371C23C2×C22⋊Dic1911yescharacteristic
372D4—48no—
373D4—48no—
374D4—82no—
375D4—88no—
376D4—88no—
377D4—82no—
378D4—82no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—24no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—764no—
390C2×C4—764no—
391C2×C4—764no—
392C2×C4—1528no—
393C2×C4D4×Dic1912yes—
394C2×C4#1059738512yes—
395C8—1522no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—24no—
404C22—44no—
405C22—44no—
406C22—44no—
407C22—44no—
408C22—44no—
409C22—42no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—82no—
415C22—82no—
416C22—84no—
417C22—82no—
418C22—82no—
419C22—84no—
420C22—84no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22#1192642411yescharacteristic
425C22C2×#1059729112yes—
426C22#1192671112yes—
427C4—22no—
428C4—22no—
429C4—44no—
430C4—81no—
431C4—1524no—
432C2—22no—
433C2—22no—
434C2—41no—
435C2—44no—
436C2—82no—
437C2—161no—
438C2#1456403411yescharacteristic
439C2#1456408911yescharacteristic
440C2#1456416811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#2433C2
socleC22×C19#386
cosocleC23×C4×C19C23
hypercenter#2433D19
hypocenterC19#9463
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2433

Complements

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

NH ≅ G/Ntype
1. #14566213C2semidirect
2. #14563556C2semidirect
3. #14562164C2semidirect
4. #14561488C2semidirect
14. C2×C19×#127C4semidirect
19. C19×#390C4semidirect
30. C22×D4×C19C2×C4semidirect
39. C2×C4⋊C4×C19C2×C4semidirect
44. C2×C42×C19C2×C4semidirect
54. C19⋊#95D4semidirect
218. C2×#127Dic19semidirect
226. #390Dic19semidirect
250. C22×D4C2×Dic19semidirect
260. C2×C4⋊C4C2×Dic19semidirect
270. C2×C42C2×Dic19semidirect
277. C19#9463semidirect

Maximal subgroups

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

subgroupindex
#145662132
#145635562
#145621642
#145614882
C19×#24332
#946319