Finite Group Databasebeta

← #18079983

Subgroups — #18079983

Order 4864.

840 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 97 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#14568561C211yesmaximal, characteristic
2#14565987C211yesmaximal, characteristic, complemented
3#14562152C211yesmaximal, characteristic, complemented
4#14562150C211yesmaximal, characteristic, complemented
5#14561961C211yesmaximal, characteristic, complemented
6#14561521C211yesmaximal, characteristic, complemented
7C19×#1297C211yesmaximal, characteristic, complemented
8C2×#10597332—21no—
9C2×#10597376C2211yescharacteristic
10C2×#10597328—21no—
11C22×(C2×D19)⋊C4C2211yescharacteristic
12C2×C22⋊C4×D19—21no—
13#11926508C2211yescharacteristic
14#11926481C412yescomplemented
15#11926454C412yescomplemented
16#11926446—22no—
17C22⋊C4×Dic19—21no—
18C4×(C2×D19)⋊C4—22no—
19C4×C22⋊Dic19C2211yescharacteristic
20#11926391—22no—
21#11926279—22no—
22#11926277—22no—
23#11926267—22no—
24C19×#407C2211yescharacteristic
25C4×C22⋊C4×C19C2211yescharacteristic
26C4×C22⋊C4×C19C2211yescharacteristic
27C24×D19D411yescharacteristic
28C23×C4×C19C2311yescharacteristic
29C22×C22⋊D19—21no—
30C23×Dic19D411yescharacteristic
31C22×D76—22no—
32C22×D76C2×C411yescharacteristic, complemented
33C22×C4×D19—22no—
34C2×M16×C19—21no—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—21no—
37C2×C42×C19—21no—
38C2×C42×C19—21no—
39C2×C22⋊Dic19—21no—
40#10597376—21no—
41#10597376—21no—
42#10597376—21no—
43#10597376—21no—
44C2×(C2×D19)⋊C4—22no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—21no—
49C2×(C2×D19)⋊C4—22no—
50C2×(C2×D19)⋊C4—21no—
51C2×(C2×D19)⋊C4—22no—
52C2×(C2×D19)⋊C4C2×C412yes—
53C2×(C2×D19)⋊C4D412yes—
54C2×C4⋊Dic19—22no—
55C2×C4⋊Dic19C2×C411yescharacteristic, complemented
56C2×C4×Dic19—22no—
57C2×C4×Dic19—21no—
58C2×#64520—21no—
59#10597332—44no—
60#10597328—44no—
61C22⋊C4×D19—28no—
62C19×C22⋊C8—21no—
63C19×C22⋊C8—21no—
64C19×#95C2×C412yescomplemented
65C19×#95D412yescomplemented
66C19⋊#95—22no—
67C19⋊#95D412yescomplemented
68C22⋊(C19⋊C8)—21no—
69C22⋊(C19⋊C8)—21no—
70C24×C19C2×D411yescharacteristic
71C23×D19—21no—
72C23×D19—21no—
73C23×D19—24no—
74C23×D19—21no—
75C23×D19—42no—
76C23×D19—81no—
77C23×D19C22⋊C412yes—
78C22×C4×C19—22no—
79C22×C4×C19—22no—
80C22×C4×C19—81no—
81C22×C4×C19C22×C411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19#4111yescharacteristic
86C22×C4×C19#4111yescharacteristic
87C2×C22⋊D19—42no—
88C2×C22⋊D19—42no—
89C2×C22⋊D19—41no—
90C2×C22⋊D19—41no—
91C22×Dic19—22no—
92C22×Dic19—21no—
93C22×Dic19—21no—
94C22×Dic19—21no—
95C22×Dic19—42no—
96C22×Dic19C22⋊C412yes—
97C2×D76—21no—
98C2×D76—21no—
99C2×D76—44no—
100C2×D76—44no—
101C2×D76—82no—
102C2×D76—81no—
103C2×C4×D19—28no—
104C2×C4×D19—82no—
105C2×C4×D19—82no—
106M16×C19—81no—
107C2×C8×C19—41no—
108C22⋊C4×C19—24no—
109C22⋊C4×C19—24no—
110C42×C19—81no—
111C42×C19—81no—
112C22⋊Dic19—24no—
113(C2×D19)⋊C4—28no—
114(C2×D19)⋊C4—22no—
115(C2×D19)⋊C4—22no—
116(C2×D19)⋊C4—22no—
117(C2×D19)⋊C4—22no—
118(C2×D19)⋊C4—44no—
119(C2×D19)⋊C4—44no—
120(C2×D19)⋊C4—41no—
121(C2×D19)⋊C4—41no—
122C4⋊Dic19—21no—
123C4⋊Dic19—21no—
124C4⋊Dic19—44no—
125C4×Dic19—81no—
126C4×Dic19—82no—
127#64520—81no—
128C2×C19⋊C8—41no—
129#9409—191nomaximal, Sylow
130C23×C19—22no—
131C23×C19—22no—
132C23×C19—41no—
133C23×C19C2×C22⋊C411yescharacteristic
134C23×C19#12011yescharacteristic
135C23×C19#12311yescharacteristic
136C22×D19—22no—
137C22×D19—22no—
138C22×D19—22no—
139C22×D19—24no—
140C22×D19—22no—
141C22×D19—42no—
142C22×D19—42no—
143C22×D19—42no—
144C22×D19—42no—
145C22×D19—41no—
146C22×D19—41no—
147C22×D19—42no—
148C22×D19—41no—
149C22×D19—42no—
150C22×D19—88no—
151C22×D19—81no—
152C22×D19—81no—
153C22×D19#10414yes—
154C2×C4×C19—24no—
155C2×C4×C19—24no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—42no—
163C2×C4×C19—42no—
164C2×C4×C19—42no—
165C2×C4×C19—42no—
166C2×C4×C19C4×D411yescharacteristic
167C2×C4×C19C4×D411yescharacteristic
168C2×C4×C19#12111yescharacteristic
169C2×C4×C19#12111yescharacteristic
170C22⋊D19—82no—
171C22⋊D19—82no—
172C2×Dic19—24no—
173C2×Dic19—22no—
174C2×Dic19—42no—
175C2×Dic19—42no—
176C2×Dic19—42no—
177C2×Dic19—42no—
178C2×Dic19—41no—
179C2×Dic19—41no—
180C2×Dic19—41no—
181C2×Dic19—81no—
182D76—81no—
183D76—81no—
184D76—88no—
185C4×D19—88no—
186C8×C19—81no—
187C19⋊C8—81no—
188#2539—191no—
189#2273—191no—
190#1507—191no—
191#1507—191no—
192#1462—191no—
193#1297—191no—
194#1297D1911yescharacteristic, complemented
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—44no—
203C22×C19#38611yescharacteristic
204C22×C19C2×#10412yes—
205C22×C19#45312yes—
206C2×D19—24no—
207C2×D19—44no—
208C2×D19—44no—
209C2×D19—42no—
210C2×D19—42no—
211C2×D19—44no—
212C2×D19—82no—
213C2×D19—84no—
214C2×D19—82no—
215C2×D19—82no—
216C2×D19—81no—
217C2×D19—81no—
218C2×D19—81no—
219C4×C19—21no—
220C4×C19—21no—
221C4×C19—21no—
222C4×C19—21no—
223C4×C19—44no—
224C4×C19—44no—
225Dic19—44no—
226Dic19—42no—
227Dic19—81no—
228C2×#123—381no—
229C2×#121—191no—
230C2×#120—381no—
231C22×C22⋊C4—191no—
232C22×C22⋊C4—381no—
233#407—191no—
234#407C2×D1911yescharacteristic
235#399—192no—
236#392—192no—
237#390—382no—
238C4×C22⋊C4—191no—
239C4×C22⋊C4—382no—
240C4×C22⋊C4—381no—
241C4×C22⋊C4—382no—
242C4×C22⋊C4C2×D1911yescharacteristic
243C4×C22⋊C4C2×D1911yescharacteristic
244#327—382no—
245#327—382no—
246#323—382no—
247C2×C19—22no—
248C2×C19—22no—
249C2×C19—41no—
250C2×C19#188711yescharacteristic
251C2×C19#189611yescharacteristic
252C2×C19#191311yescharacteristic
253D19—44no—
254D19—161no—
255C25—191no—
256C22×D4—191no—
257C22×D4—382no—
258C22×D4—381no—
259C23×C4—191no—
260C23×C4—382no—
261C23×C4C22×D1911yescharacteristic
262C2×M16—21no—
263C2×M16—381no—
264#123—764no—
265#121—381no—
266#121—381no—
267#121—381no—
268#121—381no—
269#120—764no—
270C2×C4⋊C4—191no—
271C2×C4⋊C4—382no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—192no—
275C2×C22⋊C4—192no—
276C2×C22⋊C4—388no—
277C2×C22⋊C4—382no—
278C2×C22⋊C4—381no—
279C2×C22⋊C4—381no—
280C2×C22⋊C4—381no—
281C2×C22⋊C4—381no—
282C2×C22⋊C4—381no—
283C2×C22⋊C4—382no—
284C2×C22⋊C4—382no—
285C2×C22⋊C4—381no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—382no—
289C2×C42—381no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8—381no—
293C22⋊C8—381no—
294#95—192no—
295#95—382no—
296#95C4×D1912yescomplemented
297#95D7612yescomplemented
298C19#940911yescharacteristic, complemented, Sylow
299C24—192no—
300C24—384no—
301C24—381no—
302C24—381no—
303C24—381no—
304C24—762no—
305C24—1521no—
306C24D4×D1911yescharacteristic
307C2×D4—381no—
308C2×D4—381no—
309C2×D4—764no—
310C2×D4—764no—
311C2×D4—762no—
312C2×D4—762no—
313C2×D4—761no—
314C2×D4—761no—
315C2×D4—1522no—
316C2×D4—1521no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—81no—
320C22×C4—192no—
321C22×C4—388no—
322C22×C4—382no—
323C22×C4—381no—
324C22×C4—381no—
325C22×C4—381no—
326C22×C4—762no—
327C22×C4—1522no—
328C22×C4—1522no—
329C22×C4C2×C4×D1911yescharacteristic
330C22×C4C2×D7611yescharacteristic
331C22×C4#6454111yescharacteristic
332C22×C4D4×D1911yescharacteristic
333C22×C4D4×D1911yescharacteristic
334C22×C4#6454511yescharacteristic
335M16—81no—
336M16—1521no—
337C2×C8—41no—
338C2×C8—761no—
339C4⋊C4—381no—
340C4⋊C4—381no—
341C4⋊C4—764no—
342C22⋊C4—24no—
343C22⋊C4—24no—
344C22⋊C4—388no—
345C22⋊C4—384no—
346C22⋊C4—382no—
347C22⋊C4—382no—
348C22⋊C4—382no—
349C22⋊C4—382no—
350C22⋊C4—764no—
351C22⋊C4—764no—
352C22⋊C4—761no—
353C22⋊C4—761no—
354C42—81no—
355C42—81no—
356C42—1521no—
357C42—1522no—
358C23—22no—
359C23—22no—
360C23—41no—
361C23—194no—
362C23—382no—
363C23—382no—
364C23—384no—
365C23—382no—
366C23—382no—
367C23—762no—
368C23—762no—
369C23—762no—
370C23—761no—
371C23—761no—
372C23—762no—
373C23—762no—
374C23—762no—
375C23—761no—
376C23—1521no—
377C23—1521no—
378C23—1528no—
379C23C22⋊C4×D1911yescharacteristic
380C23#1059732811yescharacteristic
381C23#1059734011yescharacteristic
382D4—1521no—
383D4—1521no—
384D4—1528no—
385D4—1522no—
386D4—1522no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—384no—
400C2×C4—382no—
401C2×C4—762no—
402C2×C4—762no—
403C2×C4—762no—
404C2×C4—762no—
405C2×C4—761no—
406C2×C4—761no—
407C2×C4—761no—
408C2×C4—1528no—
409C2×C4—1521no—
410C2×C4C4×D7611yescharacteristic
411C2×C4#1059733011yescharacteristic
412C2×C4#1059733911yescharacteristic
413C2×C4#1059734111yescharacteristic
414C8—81no—
415C8—1521no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—44no—
424C22—384no—
425C22—764no—
426C22—764no—
427C22—764no—
428C22—762no—
429C22—762no—
430C22—1522no—
431C22—1522no—
432C22—1522no—
433C22—1524no—
434C22—1521no—
435C22—1521no—
436C22—1521no—
437C22#1192642211yescharacteristic
438C22#104×D1912yes—
439C22#1192671312yes—
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—44no—
445C4—44no—
446C4—764no—
447C4—762no—
448C4—1521no—
449C2—22no—
450C2—22no—
451C2—41no—
452C2—3041no—
453C2—764no—
454C2#1456403211yescharacteristic
455C2#1456407711yescharacteristic
456C2#1456417611yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1297C2
socleC22×C19#386
prime radical#14568561C2
cosocleC23×C4×C19C23
hypercenter#1297D19
hypocenterC19#9409
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
2. #14565987C2semidirect
3. #14562152C2semidirect
4. #14562150C2semidirect
5. #14561961C2semidirect
6. #14561521C2semidirect
7. C19×#1297C2semidirect
14. #11926481C4semidirect
15. #11926454C4semidirect
32. C22×D76C2×C4semidirect
55. C2×C4⋊Dic19C2×C4semidirect
64. C19×#95C2×C4semidirect
65. C19×#95D4semidirect
67. C19⋊#95D4semidirect
194. #1297D19semidirect
296. #95C4×D19semidirect
297. #95D76semidirect
298. C19#9409semidirect

Maximal subgroups

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

subgroupindex
#145685612
#145659872
#145621522
#145621502
#145619612
#145615212
C19×#12972
#940919