Finite Group Databasebeta

← #18074213

Subgroups — #18074213

Order 4864.

1060 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 1060 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#11927203C211yesmaximal, characteristic
2#14563569C212yesmaximal, complemented
3#14562202C212yesmaximal, complemented
4#14561953C211yesmaximal, characteristic, complemented
5C19×#1799C211yesmaximal, characteristic, complemented
6C22×#64541C411yescharacteristic, complemented
7C23×Dic38C2211yescharacteristic
8#11927203—24no—
9#11927203—24no—
10C2×#10597321C411yescharacteristic, complemented
11C2×#10597331—21no—
12C2×#10597370C411yescharacteristic, complemented
13C2×#10597342—21no—
14C2×#10597376C2211yescharacteristic
15C2×#10597385—21no—
16C2×C4×Dic38C411yescharacteristic, complemented
17C2×(C22⋊D19)⋊C4—21no—
18C2×#10597267—24no—
19C2×C22⋊(C19⋊C8)C2212yes—
20#11926277—24no—
21#11926270—21no—
22#11926268—21no—
23C2×C4×D4×C19C2211yescharacteristic
24C2×C19×#99—21no—
25C19×#380C2212yes—
26C19×#342—21no—
27C22×D4×C19D411yescharacteristic
28C23×C4×C19C2×C411yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C22×C22⋊D19—21no—
31C22×C22⋊D19—21no—
32C23×Dic19—21no—
33C2×#64541—22no—
34C2×#64541—22no—
35C2×#64541—44no—
36C22×D76C2×C411yescharacteristic
37C22×C4×D19—21no—
38C22×Dic38—21no—
39C22×Dic38—22no—
40C22×Dic38—44no—
41C22×Dic38C2×C411yescharacteristic
42C22×Dic38C2×C411yescharacteristic
43C22×Dic38D414yes—
44C4×D4×C19—22no—
45C4×D4×C19—22no—
46C2×C4⋊C4×C19—22no—
47C2×C4⋊C4×C19D411yescharacteristic
48C2×C22⋊C4×C19—22no—
49C2×C22⋊C4×C19D411yescharacteristic
50C2×C22⋊C4×C19D411yescharacteristic
51C2×C42×C19C2×C411yescharacteristic
52C2×C22⋊Dic19—21no—
53#10597385—28no—
54#10597376—22no—
55#10597376D414yes—
56C2×(C2×D19)⋊C4—21no—
57C2×(C2×D19)⋊C4—21no—
58C2×(C2×D19)⋊C4—21no—
59C2×C4⋊Dic19C2×C411yescharacteristic
60#10597370—22no—
61#10597370—22no—
62C2×Dic19⋊C4—21no—
63C2×Dic19⋊C4—21no—
64C2×C4×Dic19—21no—
65C22×C19⋊C8—22no—
66#10597342—28no—
67#10597331—28no—
68(C22⋊D19)⋊C4—28no—
69#10597321—22no—
70#10597321—22no—
71C4×Dic38—22no—
72C4×Dic38—22no—
73C19×#99—42no—
74C19×#95—22no—
75C22⋊(C19⋊C8)—22no—
76C22⋊(C19⋊C8)—22no—
77#10597267—48no—
78C24×C19C22⋊C411yescharacteristic
79C24×C19C2×D411yescharacteristic
80C23×D19—21no—
81C2×D4×C19—22no—
82C2×D4×C19—22no—
83C2×D4×C19—21no—
84C2×D4×C19—21no—
85C22×C4×C19—21no—
86C22×C4×C19—21no—
87C22×C4×C19—42no—
88C22×C4×C19—42no—
89C22×C4×C19—42no—
90C22×C4×C19C22⋊C411yescharacteristic
91C22×C4×C19C22⋊C411yescharacteristic
92C22×C4×C19C22⋊C411yescharacteristic
93C22×C4×C19C22×C411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D412yes—
96C22×C4×C19C2×D412yes—
97C2×C22⋊D19—24no—
98C2×C22⋊D19—24no—
99C2×C22⋊D19—44no—
100C2×C22⋊D19—42no—
101C2×C22⋊D19—41no—
102C2×C22⋊D19—41no—
103C22×Dic19—21no—
104C22×Dic19—21no—
105C22×Dic19—21no—
106C22×Dic19—24no—
107C22×Dic19—44no—
108#64541—48no—
109#64541—44no—
110#64541—44no—
111C2×D76—21no—
112C2×D76—42no—
113C2×D76C22⋊C412yes—
114C2×C4×D19—24no—
115C2×C4×D19—44no—
116C2×Dic38—21no—
117C2×Dic38—24no—
118C2×Dic38—28no—
119C2×Dic38—21no—
120C2×Dic38—24no—
121C2×Dic38—42no—
122C2×Dic38—44no—
123C2×Dic38—48no—
124C2×Dic38—44no—
125C2×Dic38C22⋊C412yes—
126C2×Dic38C22⋊C412yes—
127C4⋊C4×C19—22no—
128C4⋊C4×C19—44no—
129C22⋊C4×C19—22no—
130C22⋊C4×C19—22no—
131C22⋊C4×C19—42no—
132C22⋊C4×C19—42no—
133C42×C19—21no—
134C42×C19—21no—
135C22⋊Dic19—24no—
136(C2×D19)⋊C4—24no—
137(C2×D19)⋊C4—24no—
138(C2×D19)⋊C4—24no—
139C4⋊Dic19—21no—
140C4⋊Dic19C22⋊C412yes—
141Dic19⋊C4—24no—
142Dic19⋊C4—24no—
143C4×Dic19—24no—
144C2×C19⋊C8—44no—
145C2×C19⋊C8—42no—
146#8377—191nomaximal, Sylow
147C23×C19—21no—
148C23×C19—21no—
149C23×C19—21no—
150C23×C19—41no—
151C23×C19—41no—
152C23×C19—41no—
153C23×C19—41no—
154C23×C19C2×C22⋊C411yescharacteristic
155C23×C19#12012yes—
156C23×C19#13512yes—
157C23×C19AGL(1,ℤ/8)11yescharacteristic
158C23×C19#13711yescharacteristic
159C22×D19—22no—
160C22×D19—42no—
161C22×D19—42no—
162C22×D19—41no—
163C22×D19—41no—
164D4×C19—42no—
165D4×C19—42no—
166C2×C4×C19—24no—
167C2×C4×C19—22no—
168C2×C4×C19—21no—
169C2×C4×C19—21no—
170C2×C4×C19—21no—
171C2×C4×C19—21no—
172C2×C4×C19—21no—
173C2×C4×C19—41no—
174C2×C4×C19—42no—
175C2×C4×C19—42no—
176C2×C4×C19—42no—
177C2×C4×C19—41no—
178C2×C4×C19—41no—
179C2×C4×C19—82no—
180C2×C4×C19—82no—
181C2×C4×C19—82no—
182C2×C4×C19C2×C22⋊C411yescharacteristic
183C2×C4×C19C2×C22⋊C411yescharacteristic
184C2×C4×C19#12012yes—
185C22⋊D19—48no—
186C22⋊D19—44no—
187C22⋊D19—44no—
188C2×Dic19—24no—
189C2×Dic19—22no—
190C2×Dic19—22no—
191C2×Dic19—22no—
192C2×Dic19—48no—
193C2×Dic19—42no—
194C2×Dic19—41no—
195C2×Dic19—41no—
196D76—42no—
197D76—42no—
198C4×D19—48no—
199Dic38—24no—
200Dic38—22no—
201Dic38—24no—
202Dic38—48no—
203Dic38—42no—
204Dic38#9914yescomplemented
205C19⋊C8—82no—
206C2×#548—191no—
207#1799D1911yescharacteristic, complemented
208#1787—192no—
209#1519—192no—
210#1459—191no—
211C22×C19—21no—
212C22×C19—22no—
213C22×C19—21no—
214C22×C19—22no—
215C22×C19—42no—
216C22×C19—41no—
217C22×C19—41no—
218C22×C19—41no—
219C22×C19—41no—
220C22×C19—41no—
221C22×C19—81no—
222C22×C19—81no—
223C22×C19#37911yescharacteristic
224C22×C19#41611yescharacteristic
225C22×C19#41711yescharacteristic
226C22×C19#44912yes—
227C22×C19#45212yes—
228C2×D19—42no—
229C2×D19—42no—
230C2×D19—42no—
231C2×D19—82no—
232C2×D19—82no—
233C4×C19—22no—
234C4×C19—21no—
235C4×C19—41no—
236C4×C19—41no—
237C4×C19—41no—
238C4×C19—162no—
239C4×C19C2×#9912yes—
240Dic19—24no—
241Dic19—42no—
242Dic19—42no—
243C22×#41—191no—
244C23×Q8—191no—
245#548—384no—
246#548—384no—
247C2×#124—191no—
248C2×#124—381no—
249C2×C22⋊Q8—191no—
250C2×C22⋊Q8—381no—
251C2×#121—191no—
252C2×#121—381no—
253C2×C4×Q8—191no—
254C2×C4×D4—381no—
255C2×C4×D4C2×D1911yescharacteristic
256C2×#103—384no—
257C2×#99—21no—
258C2×C22⋊C8—192no—
259#380C2×D1912yes—
260#342—21no—
261#327—384no—
262#324—381no—
263#323—381no—
264C2×C19—22no—
265C2×C19—21no—
266C2×C19—21no—
267C2×C19—22no—
268C2×C19—81no—
269C2×C19#178111yescharacteristic
270C2×C19#178811yescharacteristic
271C2×C19#179611yescharacteristic
272D19—82no—
273C2×#41—382no—
274C2×#41—382no—
275C2×#41—764no—
276C22×Q8—191no—
277C22×Q8—191no—
278C22×Q8—194no—
279C22×Q8—381no—
280C22×Q8—382no—
281C22×Q8—764no—
282C22×D4—191no—
283C22×D4—381no—
284C22×D4—381no—
285C22×D4C22⋊D1911yescharacteristic
286C23×C4—381no—
287C23×C4—381no—
288C23×C4C4×D1911yescharacteristic
289C23×C4C22×D1911yescharacteristic
290C22×C8—382no—
291#124—382no—
292#124—382no—
293#124—388no—
294C22⋊Q8—388no—
295C22⋊Q8—382no—
296C22⋊Q8—382no—
297#121—194no—
298#121—388no—
299#121—382no—
300C4×Q8—382no—
301C4×Q8—382no—
302C4×D4—22no—
303C4×D4—22no—
304C4×D4—388no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—191no—
307C2×C4⋊C4—381no—
308C2×C4⋊C4—381no—
309C2×C4⋊C4D7611yescharacteristic
310C2×C22⋊C4—22no—
311C2×C22⋊C4—381no—
312C2×C22⋊C4—381no—
313C2×C22⋊C4—381no—
314C2×C22⋊C4—381no—
315C2×C22⋊C4D7611yescharacteristic
316C2×C22⋊C4C22⋊D1911yescharacteristic
317C2×C42—381no—
318C2×C42C4×D1911yescharacteristic
319#103—768no—
320#99—42no—
321C22⋊C8—382no—
322C22⋊C8—382no—
323#95—22no—
324C19#837711yescharacteristic, complemented, Sylow
325C24—381no—
326C24(C2×D19)⋊C411yescharacteristic
327C24C2×C22⋊D1911yescharacteristic
328#41—764no—
329#41—768no—
330#41—764no—
331C2×Q8—192no—
332C2×Q8—192no—
333C2×Q8—384no—
334C2×Q8—388no—
335C2×Q8—381no—
336C2×Q8—381no—
337C2×Q8—384no—
338C2×Q8—764no—
339C2×Q8—762no—
340C2×Q8—764no—
341C2×Q8—768no—
342C2×D4—21no—
343C2×D4—22no—
344C2×D4—21no—
345C2×D4—22no—
346C2×D4—192no—
347C2×D4—384no—
348C2×D4—384no—
349C2×D4—381no—
350C2×D4—762no—
351C2×D4—764no—
352C2×D4—761no—
353C2×D4—761no—
354C2×D4—762no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—384no—
361C22×C4—381no—
362C22×C4—384no—
363C22×C4—381no—
364C22×C4—381no—
365C22×C4—764no—
366C22×C4—764no—
367C22×C4(C2×D19)⋊C411yescharacteristic
368C22×C4(C2×D19)⋊C411yescharacteristic
369C22×C4(C2×D19)⋊C411yescharacteristic
370C22×C4C2×C4×D1911yescharacteristic
371C22×C4C2×D7611yescharacteristic
372C22×C4D4×D1912yes—
373C22×C4D4×D1912yes—
374C2×C8—764no—
375C2×C8—762no—
376C4⋊C4—22no—
377C4⋊C4—44no—
378C4⋊C4—192no—
379C4⋊C4—384no—
380C4⋊C4—384no—
381C4⋊C4—381no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—42no—
385C22⋊C4—42no—
386C22⋊C4—384no—
387C22⋊C4—384no—
388C22⋊C4—384no—
389C22⋊C4—384no—
390C42—21no—
391C42—21no—
392C42—384no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—382no—
401C23—762no—
402C23—762no—
403C23—761no—
404C23—761no—
405C23C2×(C2×D19)⋊C411yescharacteristic
406C23#1059737811yescharacteristic
407C23#1059738312yes—
408C23#1059738811yescharacteristic
409C23#1059739612yes—
410Q8—194no—
411Q8—384no—
412Q8—382no—
413Q8—384no—
414Q8—768no—
415Q8—762no—
416D4—42no—
417D4—42no—
418D4—762no—
419D4—768no—
420D4—764no—
421D4—764no—
422D4—762no—
423C2×C4—24no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—384no—
440C2×C4—382no—
441C2×C4—382no—
442C2×C4—382no—
443C2×C4—768no—
444C2×C4—768no—
445C2×C4—762no—
446C2×C4—761no—
447C2×C4—761no—
448C2×C4C22⋊C4×D1911yescharacteristic
449C2×C4C22⋊C4×D1911yescharacteristic
450C2×C4#1059732812yes—
451C8—1522no—
452C22—21no—
453C22—22no—
454C22—21no—
455C22—22no—
456C22—41no—
457C22—41no—
458C22—42no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—81no—
463C22—81no—
464C22—762no—
465C22—762no—
466C22—762no—
467C22—1522no—
468C22—1522no—
469C22#1192639911yescharacteristic
470C22#1192653811yescharacteristic
471C22#1192654311yescharacteristic
472C22#1192668712yes—
473C22#1192670412yes—
474C4—22no—
475C4—21no—
476C4—41no—
477C4—41no—
478C4—41no—
479C4—162no—
480C4—384no—
481C4—762no—
482C4—762no—
483C4#99×D1912yes—
484C2—22no—
485C2—21no—
486C2—21no—
487C2—22no—
488C2—81no—
489C2—1522no—
490C2#1456354811yescharacteristic
491C2#1456357311yescharacteristic
492C2#1456360811yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1799C2
socleC22×C19#379
prime radicalC2×#11927203C2
cosocleC23×C4×C19C23
hypercenter#1799D19
hypocenterC19#8377
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
2. #14563569C2semidirect
3. #14562202C2semidirect
4. #14561953C2semidirect
5. C19×#1799C2semidirect
6. C22×#64541C4semidirect
10. C2×#10597321C4semidirect
12. C2×#10597370C4semidirect
16. C2×C4×Dic38C4semidirect
204. Dic38#99semidirect
207. #1799D19semidirect
324. C19#8377semidirect

Maximal subgroups

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

subgroupindex
C2×#119272032
#145635692
#145622022
#145619532
C19×#17992
#837719