Finite Group Databasebeta

← #18078579

Subgroups — #18078579

Order 4864.

684 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 113 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#14569442C211yesmaximal, characteristic
2#14566248C211yesmaximal, characteristic
3#14562207C211yesmaximal, characteristic, complemented
4C2×#11926267C211yesmaximal, characteristic
5#14561503C211yesmaximal, characteristic, complemented
6#14561502C211yesmaximal, characteristic, complemented
7C19×#1520C211yesmaximal, characteristic, complemented
8C22×(C2×D19)⋊C4C2211yescharacteristic
9C2×C22⋊C4×D19—21no—
10C2×C22⋊(C19⋊C8)C2211yescharacteristic
11#11926479C412yescomplemented
12#11926466—22no—
13#11926455C412yescomplemented
14#11926418—22no—
15#11926416—21no—
16#11926415—22no—
17#11926404C2211yescharacteristic
18#11926404C2211yescharacteristic
19#11926402—21no—
20#11926399—21no—
21#11926281—22no—
22#11926267—22no—
23C2×C19×C22⋊Q8C2211yescharacteristic
24C2×C19×C22⋊C8C2211yescharacteristic
25C19×#380C2211yescharacteristic
26C19×#328—22no—
27C24×D19D411yescharacteristic
28C22×Q8×C19C2×C411yescharacteristic, complemented
29C23×C4×C19C2311yescharacteristic
30C23×Dic19D411yescharacteristic
31C22×C4×D19—22no—
32C22×C8×C19—21no—
33C19×C22⋊Q8—21no—
34C19×C22⋊Q8—21no—
35C19×C22⋊Q8—21no—
36C19×C22⋊Q8—21no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19C2×C411yescharacteristic, complemented
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊Dic19—21no—
43C2×C22⋊Dic19—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—22no—
49C2×(C2×D19)⋊C4—22no—
50C2×(C2×D19)⋊C4—22no—
51C2×(C2×D19)⋊C4C2×C412yes—
52C2×(C2×D19)⋊C4D412yes—
53C2×C4⋊Dic19—21no—
54C2×C4⋊Dic19—21no—
55C2×Dic19⋊C4—22no—
56C2×Dic19⋊C4—22no—
57C22×C19⋊C8—21no—
58C22⋊C4×D19—42no—
59C22⋊C4×D19—42no—
60C19×C22⋊C8—21no—
61C19×C22⋊C8—21no—
62C19×#95D412yes—
63C19⋊#95—22no—
64C19⋊#95—22no—
65C19⋊#95C2×C412yescomplemented
66C19⋊#95D412yes—
67C22⋊(C19⋊C8)—21no—
68C22⋊(C19⋊C8)—21no—
69C24×C19C2×D411yescharacteristic
70C23×D19—21no—
71C23×D19—21no—
72C23×D19—21no—
73C23×D19—21no—
74C23×D19—81no—
75C23×D19—81no—
76C23×D19C22⋊C412yes—
77C23×D19SD1612yes—
78C23×D19Q1612yes—
79C2×Q8×C19—21no—
80C2×Q8×C19—21no—
81C2×Q8×C19—81no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—22no—
85C22×C4×C19—81no—
86C22×C4×C19C22×C411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19#4111yescharacteristic
91C22×C4×C19#4111yescharacteristic
92C22×Dic19—21no—
93C22×Dic19—21no—
94C22×Dic19—22no—
95C22×Dic19—22no—
96C22×Dic19—81no—
97C22×Dic19C22⋊C412yes—
98C2×C4×D19—44no—
99C2×C4×D19—82no—
100C2×C4×D19—82no—
101C2×C8×C19—41no—
102C2×C8×C19—81no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—81no—
108C22⋊C4×C19—41no—
109C22⋊C4×C19—41no—
110C22⋊C4×C19—41no—
111C22⋊C4×C19—41no—
112C22⋊Dic19—41no—
113C22⋊Dic19—41no—
114C22⋊Dic19—41no—
115C22⋊Dic19—41no—
116(C2×D19)⋊C4—22no—
117(C2×D19)⋊C4—22no—
118(C2×D19)⋊C4—22no—
119(C2×D19)⋊C4—22no—
120(C2×D19)⋊C4—44no—
121(C2×D19)⋊C4—82no—
122(C2×D19)⋊C4—82no—
123C4⋊Dic19—81no—
124C4⋊Dic19—81no—
125Dic19⋊C4—82no—
126Dic19⋊C4—82no—
127C2×C19⋊C8—41no—
128C2×C19⋊C8—81no—
129#9199—191nomaximal, Sylow
130C23×C19—41no—
131C23×C19—41no—
132C23×C19C2×C22⋊C411yescharacteristic
133C23×C19#12011yescharacteristic
134C23×C19#12311yescharacteristic
135C23×C19C2×SD1611yescharacteristic
136C23×C19C2×Q1611yescharacteristic
137C23×C19AGL(1,ℤ/8)11yescharacteristic
138C23×C19#13711yescharacteristic
139C22×D19—22no—
140C22×D19—22no—
141C22×D19—22no—
142C22×D19—22no—
143C22×D19—22no—
144C22×D19—22no—
145C22×D19—42no—
146C22×D19—42no—
147C22×D19—42no—
148C22×D19—42no—
149C22×D19—82no—
150C22×D19—82no—
151C22×D19—81no—
152C22×D19—81no—
153C22×D19—82no—
154C22×D19—82no—
155C22×D19#10314yes—
156Q8×C19—81no—
157Q8×C19—81no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—42no—
165C2×C4×C19—42no—
166C2×C4×C19—42no—
167C2×C4×C19—42no—
168C2×C4×C19—41no—
169C2×C4×C19—41no—
170C2×C4×C19—42no—
171C2×C4×C19C4×D411yescharacteristic
172C2×C4×C19C4×D411yescharacteristic
173C2×C4×C19#12111yescharacteristic
174C2×C4×C19#12111yescharacteristic
175C2×Dic19—22no—
176C2×Dic19—42no—
177C2×Dic19—42no—
178C2×Dic19—42no—
179C2×Dic19—42no—
180C2×Dic19—42no—
181C2×Dic19—42no—
182C2×Dic19—42no—
183C2×Dic19—42no—
184C2×Dic19—81no—
185C4×D19—88no—
186C8×C19—81no—
187C19⋊C8—81no—
188#2626—191no—
189#2315—191no—
190#1520—191no—
191#1520D1911yescharacteristic, complemented
192C2×#323—191no—
193#1289—191no—
194#1289—191no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—41no—
202C22×C19—41no—
203C22×C19—41no—
204C22×C19—41no—
205C22×C19#38611yescharacteristic
206C22×C19C2×#10311yescharacteristic
207C22×C19#41711yescharacteristic
208C22×C19#45011yescharacteristic
209C22×C19#45111yescharacteristic
210C22×C19#48311yescharacteristic
211C22×C19#48411yescharacteristic
212C2×D19—24no—
213C2×D19—44no—
214C2×D19—44no—
215C2×D19—42no—
216C2×D19—42no—
217C2×D19—44no—
218C2×D19—82no—
219C2×D19—82no—
220C2×D19—82no—
221C4×C19—21no—
222C4×C19—21no—
223C4×C19—21no—
224C4×C19—21no—
225C4×C19—82no—
226C4×C19—81no—
227C4×C19—81no—
228Dic19—42no—
229Dic19—82no—
230Dic19—82no—
231C2×C22⋊Q8C2×D1911yescharacteristic
232C22×C22⋊C4—191no—
233C22×C22⋊C4—381no—
234C2×C22⋊C8—191no—
235C2×C22⋊C8C2×D1911yescharacteristic
236#399—192no—
237#396—382no—
238#393—192no—
239#385—382no—
240#385—381no—
241#385—382no—
242#380—191no—
243#380—191no—
244#380—381no—
245#380C2×D1911yescharacteristic
246#379—381no—
247#328—22no—
248#328—382no—
249#323—382no—
250C2×C19—21no—
251C2×C19—21no—
252C2×C19—21no—
253C2×C19—21no—
254C2×C19—21no—
255C2×C19—21no—
256C2×C19#187211yescharacteristic
257C2×C19#191111yescharacteristic
258C2×C19#191311yescharacteristic
259D19—44no—
260C25—191no—
261C22×Q8C4×D1911yescharacteristic, complemented
262C23×C4—191no—
263C23×C4—382no—
264C23×C4C22×D1911yescharacteristic
265C22×C8—21no—
266C22×C8—381no—
267C22⋊Q8—21no—
268C22⋊Q8—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—382no—
274C2×C4⋊C4—382no—
275C2×C4⋊C4—381no—
276C2×C4⋊C4—381no—
277C2×C4⋊C4C4×D1911yescharacteristic, complemented
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—192no—
281C2×C22⋊C4—192no—
282C2×C22⋊C4—381no—
283C2×C22⋊C4—381no—
284C2×C22⋊C4—381no—
285C2×C22⋊C4—381no—
286C2×C22⋊C4—382no—
287C2×C22⋊C4—381no—
288C2×C22⋊C4—381no—
289C2×C22⋊C4—382no—
290C2×C22⋊C4—382no—
291C2×C22⋊C4—762no—
292C2×C22⋊C4—762no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—381no—
296C22⋊C8—381no—
297#95—192no—
298#95—192no—
299#95—382no—
300#95—382no—
301#95C22⋊D1912yes—
302C19#919911yescharacteristic, complemented, Sylow
303C24—192no—
304C24—192no—
305C24—192no—
306C24—381no—
307C24—381no—
308C24—381no—
309C24—381no—
310C24—1521no—
311C24—1521no—
312C24D4×D1911yescharacteristic
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—81no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—81no—
320C22×C4—192no—
321C22×C4—381no—
322C22×C4—381no—
323C22×C4—382no—
324C22×C4—382no—
325C22×C4—764no—
326C22×C4—1522no—
327C22×C4—1522no—
328C22×C4—1521no—
329C22×C4C2×C4×D1911yescharacteristic
330C22×C4#6454111yescharacteristic
331C22×C4D4×D1911yescharacteristic
332C22×C4D4×D1911yescharacteristic
333C22×C4#6454311yescharacteristic
334C22×C4C2×C22⋊D1911yescharacteristic
335C2×C8—41no—
336C2×C8—81no—
337C2×C8—761no—
338C2×C8—1521no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—81no—
344C4⋊C4—1522no—
345C4⋊C4—1522no—
346C4⋊C4—1521no—
347C4⋊C4—1521no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—382no—
353C22⋊C4—382no—
354C22⋊C4—382no—
355C22⋊C4—382no—
356C22⋊C4—764no—
357C22⋊C4—761no—
358C22⋊C4—761no—
359C22⋊C4—761no—
360C22⋊C4—761no—
361C22⋊C4—1522no—
362C22⋊C4—1522no—
363C23—41no—
364C23—41no—
365C23—194no—
366C23—382no—
367C23—382no—
368C23—382no—
369C23—382no—
370C23—382no—
371C23—382no—
372C23—762no—
373C23—762no—
374C23—762no—
375C23—762no—
376C23—1521no—
377C23—1521no—
378C23—1522no—
379C23—1522no—
380C23—1522no—
381C23—1522no—
382C23C22⋊C4×D1911yescharacteristic
383C23#1059732911yescharacteristic
384C23SD16×D1911yescharacteristic
385C23#1059736011yescharacteristic
386C23Q16×D1911yescharacteristic
387C23#1059736411yescharacteristic
388C23#1059738311yescharacteristic
389Q8—81no—
390Q8—81no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—382no—
405C2×C4—762no—
406C2×C4—762no—
407C2×C4—762no—
408C2×C4—762no—
409C2×C4—762no—
410C2×C4—762no—
411C2×C4—762no—
412C2×C4—762no—
413C2×C4—1528no—
414C2×C4—1521no—
415C2×C4(C22⋊D19)⋊C411yescharacteristic
416C2×C4#1059733011yescharacteristic
417C2×C4C4×C22⋊D1911yescharacteristic
418C2×C4#1059738411yescharacteristic
419C8—81no—
420C8—1521no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—384no—
432C22—764no—
433C22—764no—
434C22—764no—
435C22—762no—
436C22—762no—
437C22—1522no—
438C22—1522no—
439C22—1522no—
440C22#1192642011yescharacteristic
441C22#103×D1911yescharacteristic
442C22#1192654411yescharacteristic
443C22#1192669311yescharacteristic
444C22#1192669811yescharacteristic
445C22#1192687311yescharacteristic
446C22#1192687811yescharacteristic
447C4—21no—
448C4—21no—
449C4—21no—
450C4—21no—
451C4—82no—
452C4—81no—
453C4—81no—
454C4—762no—
455C4—1522no—
456C4—1522no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2—21no—
463C2—764no—
464C2#1456393911yescharacteristic
465C2#1456416411yescharacteristic
466C2#1456417411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1520C2
socleC22×C19#386
prime radicalC24×D19D4
cosocleC23×C4×C19C23
hypercenter#1520D19
hypocenterC19#9199
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
3. #14562207C2semidirect
5. #14561503C2semidirect
6. #14561502C2semidirect
7. C19×#1520C2semidirect
11. #11926479C4semidirect
13. #11926455C4semidirect
28. C22×Q8×C19C2×C4semidirect
39. C2×C4⋊C4×C19C2×C4semidirect
65. C19⋊#95C2×C4semidirect
191. #1520D19semidirect
261. C22×Q8C4×D19semidirect
277. C2×C4⋊C4C4×D19semidirect
302. C19#9199semidirect

Maximal subgroups

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

subgroupindex
#145694422
#145662482
#145622072
C2×#119262672
#145615032
#145615022
C19×#15202
#919919