Finite Group Databasebeta

← #18075035

Subgroups — #18075035

Order 4864.

1040 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 1040 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
1C2×#11927122C211yesmaximal, characteristic
2#14563563C211yesmaximal, characteristic, complemented
3#14562167C212yesmaximal, complemented
4#14562163C212yesmaximal, complemented
5C19×#1782C211yesmaximal, characteristic, complemented
6C22×#64541C411yescharacteristic, complemented
7#11927122—24no—
8#11927122—24no—
9C2×#10597370C411yescharacteristic, complemented
10C2×#10597370C2211yescharacteristic
11C2×#10597392—21no—
12C2×#10597376C411yescharacteristic, complemented
13C2×#10597376C2211yescharacteristic
14C2×#10597385—21no—
15C2×#10597385—21no—
16C2×#10597384—21no—
17C22×C4⋊Dic19C411yescharacteristic, complemented
18C2×#10597293—21no—
19C2×#10597290—21no—
20#11926508C2212yes—
21#11926280—24no—
22#11926277—24no—
23C22×#41×C19C2211yescharacteristic
24C2×C19×#99—21no—
25C2×C19×#99—21no—
26C19×#381C2212yes—
27C2×#41×C19—22no—
28C2×#41×C19—22no—
29C2×#41×C19—42no—
30C2×#41×C19—42no—
31C22×Q8×C19D411yescharacteristic
32C22×D4×C19D411yescharacteristic
33C22×D4×C19D411yescharacteristic
34C22×D4×C19D411yescharacteristic
35C23×C4×C19C2×C411yescharacteristic
36C23×C4×C19C2×C411yescharacteristic
37C23×C4×C19C2311yescharacteristic
38C22×C22⋊D19—21no—
39C22×C22⋊D19—21no—
40C22×C22⋊D19—21no—
41C23×Dic19—21no—
42C2×#64541—22no—
43C2×#64541—22no—
44C2×#64541—42no—
45C2×#64541—42no—
46C22×D76C2×C411yescharacteristic
47C22×C4×D19—21no—
48C22×Dic38C2×C411yescharacteristic
49C2×C22⋊C4×C19—22no—
50C2×C22⋊Dic19—21no—
51C2×C22⋊Dic19—21no—
52#10597392—28no—
53#10597385—28no—
54#10597385—28no—
55#10597384—28no—
56#10597376—22no—
57#10597376—22no—
58#10597376—22no—
59#10597376D414yes—
60C2×(C2×D19)⋊C4—21no—
61C2×(C2×D19)⋊C4—21no—
62C2×C4⋊Dic19—21no—
63C2×C4⋊Dic19—22no—
64C2×C4⋊Dic19—22no—
65C2×C4⋊Dic19C2×C411yescharacteristic
66C2×C4⋊Dic19C2×C411yescharacteristic
67#10597370—22no—
68#10597370—22no—
69#10597370—22no—
70#10597370D414yes—
71C2×Dic19⋊C4—21no—
72C2×Dic19⋊C4—21no—
73C2×#64520—22no—
74C19×#99—42no—
75C19×#99—42no—
76C19×#95—22no—
77C19×#95—22no—
78#10597293—42no—
79#10597290—42no—
80C22⋊(C19⋊C8)—22no—
81C22⋊(C19⋊C8)—22no—
82C24×C19C22⋊C411yescharacteristic
83C24×C19C22⋊C411yescharacteristic
84C24×C19C2×D411yescharacteristic
85C23×D19—21no—
86#41×C19—48no—
87#41×C19—48no—
88C2×Q8×C19—22no—
89C2×Q8×C19—22no—
90C2×Q8×C19—41no—
91C2×D4×C19—22no—
92C2×D4×C19—22no—
93C2×D4×C19—22no—
94C2×D4×C19—22no—
95C2×D4×C19—22no—
96C2×D4×C19—22no—
97C2×D4×C19—41no—
98C2×D4×C19—41no—
99C2×D4×C19—41no—
100C22×C4×C19—22no—
101C22×C4×C19—22no—
102C22×C4×C19—21no—
103C22×C4×C19—21no—
104C22×C4×C19—21no—
105C22×C4×C19—21no—
106C22×C4×C19—41no—
107C22×C4×C19—41no—
108C22×C4×C19—41no—
109C22×C4×C19—41no—
110C22×C4×C19—42no—
111C22×C4×C19C22⋊C411yescharacteristic
112C22×C4×C19C22⋊C411yescharacteristic
113C22×C4×C19C22×C411yescharacteristic
114C22×C4×C19C2×D411yescharacteristic
115C22×C4×C19C2×D412yes—
116C22×C4×C19C2×D412yes—
117C2×C22⋊D19—24no—
118C2×C22⋊D19—24no—
119C2×C22⋊D19—24no—
120C2×C22⋊D19—42no—
121C2×C22⋊D19—42no—
122C2×C22⋊D19—82no—
123C2×C22⋊D19—82no—
124C22×Dic19—21no—
125C22×Dic19—21no—
126C22×Dic19—21no—
127C22×Dic19—24no—
128C22×Dic19—82no—
129#64541—48no—
130#64541—48no—
131C2×D76—21no—
132C2×D76—41no—
133C2×D76—41no—
134C2×D76C22⋊C412yes—
135C2×C4×D19—24no—
136C2×C4×D19—42no—
137C2×C4×D19—42no—
138C2×Dic38—21no—
139C2×Dic38—41no—
140C2×Dic38—41no—
141C2×Dic38C22⋊C412yes—
142C22⋊C4×C19—42no—
143C22⋊C4×C19—42no—
144C22⋊Dic19—24no—
145C22⋊Dic19—24no—
146(C2×D19)⋊C4—24no—
147(C2×D19)⋊C4—24no—
148C4⋊Dic19—24no—
149C4⋊Dic19—21no—
150C4⋊Dic19—21no—
151C4⋊Dic19C22⋊C412yes—
152C4⋊Dic19C22⋊C412yes—
153Dic19⋊C4—24no—
154Dic19⋊C4—24no—
155#64520—42no—
156#64520—42no—
157C2×C19⋊C8—42no—
158#8517—191nomaximal, Sylow
159C23×C19—21no—
160C23×C19—21no—
161C23×C19—21no—
162C23×C19—21no—
163C23×C19—21no—
164C23×C19—21no—
165C23×C19—21no—
166C23×C19—41no—
167C23×C19—41no—
168C23×C19—41no—
169C23×C19—41no—
170C23×C19—41no—
171C23×C19—41no—
172C23×C19#9912yes—
173C23×C19C2×C22⋊C411yescharacteristic
174C23×C19#12012yes—
175C22×D19—22no—
176C22×D19—42no—
177C22×D19—42no—
178C22×D19—41no—
179C22×D19—41no—
180Q8×C19—44no—
181D4×C19—44no—
182D4×C19—44no—
183D4×C19—44no—
184C2×C4×C19—24no—
185C2×C4×C19—24no—
186C2×C4×C19—21no—
187C2×C4×C19—21no—
188C2×C4×C19—21no—
189C2×C4×C19—21no—
190C2×C4×C19—21no—
191C2×C4×C19—21no—
192C2×C4×C19—21no—
193C2×C4×C19—21no—
194C2×C4×C19—21no—
195C2×C4×C19—42no—
196C2×C4×C19—42no—
197C2×C4×C19—42no—
198C2×C4×C19—42no—
199C2×C4×C19—82no—
200C2×C4×C19—82no—
201C2×C4×C19—82no—
202C2×C4×C19#9912yes—
203C2×C4×C19C2×C22⋊C411yescharacteristic
204C2×C4×C19C2×C22⋊C411yescharacteristic
205C2×C4×C19#12012yes—
206C22⋊D19—48no—
207C22⋊D19—84no—
208C22⋊D19—84no—
209C2×Dic19—22no—
210C2×Dic19—22no—
211C2×Dic19—22no—
212C2×Dic19—42no—
213C2×Dic19—42no—
214C2×Dic19—41no—
215C2×Dic19—41no—
216C2×Dic19—84no—
217D76—42no—
218D76—42no—
219C4×D19—48no—
220Dic38—42no—
221Dic38—42no—
222C19⋊C8—82no—
223C2×#537—191no—
224#1785—191no—
225#1782D1911yescharacteristic, complemented
226#1511—192no—
227#1510—192no—
228C22×C19—21no—
229C22×C19—21no—
230C22×C19—22no—
231C22×C19—22no—
232C22×C19—22no—
233C22×C19—22no—
234C22×C19—42no—
235C22×C19—42no—
236C22×C19—41no—
237C22×C19—41no—
238C22×C19—41no—
239C22×C19—41no—
240C22×C19—41no—
241C22×C19—81no—
242C22×C19—81no—
243C22×C19—81no—
244C22×C19—81no—
245C22×C19#37911yescharacteristic
246C22×C19C2×#9911yescharacteristic
247C22×C19C2×#9911yescharacteristic
248C2×D19—42no—
249C2×D19—42no—
250C2×D19—42no—
251C2×D19—82no—
252C2×D19—82no—
253C4×C19—22no—
254C4×C19—21no—
255C4×C19—21no—
256C4×C19—22no—
257C4×C19—41no—
258C4×C19—162no—
259Dic19—42no—
260Dic19—42no—
261Dic19—42no—
262C22×#41—191no—
263C22×#41C2×D1911yescharacteristic
264#537—384no—
265#537—384no—
266C2×C22⋊Q8—191no—
267C2×C22⋊Q8—191no—
268C2×C22⋊Q8—381no—
269C2×#121—191no—
270C2×#121—191no—
271C2×#121—381no—
272C2×#121—381no—
273C2×#121—381no—
274C22×C4⋊C4—191no—
275C2×#101—381no—
276C2×#100—381no—
277C2×#99—21no—
278C2×#99—21no—
279#407—192no—
280#381C2×D1912yes—
281#328—384no—
282#327—384no—
283C2×C19—21no—
284C2×C19—21no—
285C2×C19—42no—
286C2×C19—42no—
287C2×C19—81no—
288C2×C19#178111yescharacteristic
289C2×C19#179511yescharacteristic
290C2×C19#179611yescharacteristic
291D19—82no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—42no—
295C2×#41—42no—
296C2×#41—382no—
297C2×#41—382no—
298C2×#41—762no—
299C2×#41—762no—
300C22×Q8—191no—
301C22×Q8D7611yescharacteristic
302C22×D4—191no—
303C22×D4—381no—
304C22×D4—381no—
305C22×D4—381no—
306C22×D4D7611yescharacteristic
307C22×D4C22⋊D1911yescharacteristic
308C22×D4C22⋊D1911yescharacteristic
309C23×C4—381no—
310C23×C4—381no—
311C23×C4C4×D1911yescharacteristic
312C23×C4C4×D1911yescharacteristic
313C23×C4C22×D1911yescharacteristic
314C2×M16—382no—
315C22⋊Q8—194no—
316C22⋊Q8—382no—
317C22⋊Q8—382no—
318C22⋊Q8—388no—
319C22⋊Q8—382no—
320#121—194no—
321#121—382no—
322#121—382no—
323#121—388no—
324#121—388no—
325#121—388no—
326#121—382no—
327C2×C4⋊C4—191no—
328C2×C4⋊C4—191no—
329C2×C4⋊C4—382no—
330C2×C4⋊C4—382no—
331C2×C4⋊C4—381no—
332C2×C4⋊C4—381no—
333C2×C4⋊C4—381no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—381no—
336C2×C22⋊C4—381no—
337C2×C22⋊C4—381no—
338C2×C22⋊C4—381no—
339#101—762no—
340#100—762no—
341#99—42no—
342#99—42no—
343C22⋊C8—382no—
344C22⋊C8—382no—
345#95—22no—
346#95—22no—
347C19#851711yescharacteristic, complemented, Sylow
348C24—381no—
349C24(C2×D19)⋊C411yescharacteristic
350C24(C2×D19)⋊C411yescharacteristic
351C24C2×C22⋊D1911yescharacteristic
352#41—48no—
353#41—48no—
354#41—768no—
355#41—768no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—41no—
359C2×Q8—192no—
360C2×Q8—381no—
361C2×Q8—761no—
362C2×Q8—761no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—192no—
373C2×D4—384no—
374C2×D4—384no—
375C2×D4—384no—
376C2×D4—381no—
377C2×D4—761no—
378C2×D4—761no—
379C2×D4—762no—
380C2×D4—762no—
381C2×D4—1522no—
382C2×D4—1522no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—42no—
394C22×C4—384no—
395C22×C4—381no—
396C22×C4—381no—
397C22×C4—381no—
398C22×C4—384no—
399C22×C4—762no—
400C22×C4—762no—
401C22×C4—1522no—
402C22×C4(C2×D19)⋊C411yescharacteristic
403C22×C4(C2×D19)⋊C411yescharacteristic
404C22×C4C2×C4×D1911yescharacteristic
405C22×C4C2×D7611yescharacteristic
406C22×C4D4×D1912yes—
407C22×C4D4×D1912yes—
408M16—762no—
409M16—762no—
410C2×C8—762no—
411C4⋊C4—192no—
412C4⋊C4—192no—
413C4⋊C4—384no—
414C4⋊C4—384no—
415C4⋊C4—381no—
416C4⋊C4—381no—
417C4⋊C4—384no—
418C22⋊C4—42no—
419C22⋊C4—42no—
420C22⋊C4—384no—
421C22⋊C4—384no—
422C22⋊C4—384no—
423C22⋊C4—384no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—382no—
438C23—762no—
439C23—762no—
440C23—761no—
441C23—761no—
442C23#1059726312yes—
443C23C2×(C2×D19)⋊C411yescharacteristic
444C23#1059738312yes—
445Q8—44no—
446Q8—762no—
447Q8—762no—
448D4—44no—
449D4—44no—
450D4—44no—
451D4—762no—
452D4—762no—
453D4—768no—
454D4—1524no—
455D4—1524no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—82no—
472C2×C4—82no—
473C2×C4—82no—
474C2×C4—382no—
475C2×C4—382no—
476C2×C4—382no—
477C2×C4—768no—
478C2×C4—762no—
479C2×C4—762no—
480C2×C4—761no—
481C2×C4—761no—
482C2×C4—1524no—
483C2×C4#1059726312yes—
484C2×C4C22⋊C4×D1911yescharacteristic
485C2×C4C22⋊C4×D1911yescharacteristic
486C2×C4#1059732812yes—
487C8—1522no—
488C22—21no—
489C22—21no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—42no—
495C22—42no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—762no—
506C22—762no—
507C22—762no—
508C22—1522no—
509C22—1522no—
510C22#1192639911yescharacteristic
511C22C2×#1059726311yescharacteristic
512C22C2×#1059726311yescharacteristic
513C4—22no—
514C4—21no—
515C4—21no—
516C4—22no—
517C4—41no—
518C4—162no—
519C4—762no—
520C4—762no—
521C4—762no—
522C2—21no—
523C2—21no—
524C2—42no—
525C2—42no—
526C2—81no—
527C2—1522no—
528C2#1456354911yescharacteristic
529C2#1456360311yescharacteristic
530C2#1456360811yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1782C2
socleC22×C19#379
prime radicalC2×#11927122C2
cosocleC23×C4×C19C23
hypercenter#1782D19
hypocenterC19#8517
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
2. #14563563C2semidirect
3. #14562167C2semidirect
4. #14562163C2semidirect
5. C19×#1782C2semidirect
6. C22×#64541C4semidirect
9. C2×#10597370C4semidirect
12. C2×#10597376C4semidirect
17. C22×C4⋊Dic19C4semidirect
225. #1782D19semidirect
347. C19#8517semidirect

Maximal subgroups

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

subgroupindex
C2×#119271222
#145635632
#145621672
#145621632
C19×#17822
#851719