Finite Group Databasebeta

← #18085414

Subgroups — #18085414

Order 4864.

664 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 105 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#14574392C211yesmaximal, characteristic
2#14571974C211yesmaximal, characteristic, complemented
3#14563703C211yesmaximal, characteristic, complemented
4#14562206C211yesmaximal, characteristic, complemented
5#14562203C211yesmaximal, characteristic
6#14561502C211yesmaximal, characteristic, complemented
7C19×#2854C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9#11926874—21no—
10#11926860—21no—
11#11926771—22no—
12#11926695—21no—
13#11926682—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16#11926450—21no—
17#11926442—21no—
18#11926428—22no—
19#11926417—21no—
20#11926407—21no—
21#11926404C2211yescharacteristic
22#11926299—22no—
23#11926280—22no—
24#11926278—22no—
25C2×C19×#123—21no—
26C2×C19×#121C2211yescharacteristic
27C22×C42×C19C2211yescharacteristic
28C19×#390—21no—
29C19×#389—21no—
30C19×#388—22no—
31C19×#386—21no—
32C19×#380C2211yescharacteristic
33C22×D4×C19—21no—
34C22×D4×C19D411yescharacteristic
35C23×C4×C19D411yescharacteristic
36C23×C4×C19D411yescharacteristic
37C23×C4×C19C2311yescharacteristic
38C22×Dic38D411yescharacteristic
39C19×#123—42no—
40C19×#123—42no—
41C19×#121—21no—
42C19×#121—21no—
43C19×#121—21no—
44C19×#121—21no—
45C2×C4⋊C4×C19—22no—
46C2×C4⋊C4×C19—21no—
47C2×C4⋊C4×C19D411yescharacteristic
48C2×C22⋊C4×C19—22no—
49C2×C22⋊C4×C19—22no—
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19—21no—
52C2×C42×C19—21no—
53C2×C42×C19—21no—
54C2×C42×C19—21no—
55C2×C42×C19—21no—
56C2×C42×C19—21no—
57C2×C42×C19—21no—
58C2×C22⋊Dic19—21no—
59C2×C22⋊Dic19—21no—
60C2×#64526—22no—
61C2×C4⋊Dic19—21no—
62C2×C4⋊Dic19D411yescharacteristic
63#10597370—21no—
64#10597370—21no—
65#10597370—21no—
66#10597370—21no—
67C2×Dic19⋊C4—22no—
68C2×Dic19⋊C4—21no—
69C22×C19⋊C8—21no—
70C22×C19⋊C8D412yes—
71C19×#95—22no—
72C19×#95D412yes—
73#10597289—22no—
74C19⋊#95—22no—
75C19⋊#95—22no—
76C19⋊#95—22no—
77C19⋊#95D412yes—
78C22⋊(C19⋊C8)—21no—
79C22⋊(C19⋊C8)—21no—
80C22⋊(C19⋊C8)—21no—
81C22⋊(C19⋊C8)—21no—
82#10597267—22no—
83#10597265—22no—
84C24×C19—21no—
85C24×C19C2×D411yescharacteristic
86C2×D4×C19—21no—
87C2×D4×C19—21no—
88C2×D4×C19—42no—
89C2×D4×C19—41no—
90C2×D4×C19—41no—
91C2×D4×C19—41no—
92C2×D4×C19—41no—
93C2×D4×C19—41no—
94C2×D4×C19—41no—
95C22×C4×C19—21no—
96C22×C4×C19—21no—
97C22×C4×C19—21no—
98C22×C4×C19—21no—
99C22×C4×C19—21no—
100C22×C4×C19—21no—
101C22×C4×C19—21no—
102C22×C4×C19—21no—
103C22×C4×C19—21no—
104C22×C4×C19—22no—
105C22×C4×C19—21no—
106C22×C4×C19—42no—
107C22×C4×C19—42no—
108C22×C4×C19SD1612yescomplemented
109C22×C4×C19C2×D411yescharacteristic
110C22×C4×C19C2×D411yescharacteristic
111C22×C4×C19C2×D411yescharacteristic
112C22×C4×C19C2×D411yescharacteristic
113C22×C4×C19C2×D411yescharacteristic
114C22×C4×C19#4111yescharacteristic
115C22×Dic19—21no—
116C22×Dic19—22no—
117C22×Dic19—21no—
118C2×Dic38—21no—
119C2×Dic38—21no—
120C2×Dic38—42no—
121C4⋊C4×C19—21no—
122C4⋊C4×C19—21no—
123C4⋊C4×C19—42no—
124C4⋊C4×C19—44no—
125C22⋊C4×C19—44no—
126C22⋊C4×C19—44no—
127C22⋊C4×C19—41no—
128C22⋊C4×C19—41no—
129C22⋊C4×C19—41no—
130C22⋊C4×C19—41no—
131C42×C19—41no—
132C42×C19—41no—
133C42×C19—41no—
134C42×C19—41no—
135C22⋊Dic19—41no—
136C22⋊Dic19—41no—
137C22⋊Dic19—41no—
138C22⋊Dic19—41no—
139#64526—82no—
140C4⋊Dic19—21no—
141C4⋊Dic19—21no—
142C4⋊Dic19—42no—
143Dic19⋊C4—44no—
144Dic19⋊C4—41no—
145Dic19⋊C4—41no—
146C2×C19⋊C8—22no—
147C2×C19⋊C8—42no—
148C2×C19⋊C8—42no—
149C2×C19⋊C8—41no—
150#10323—191nomaximal, Sylow
151C23×C19—41no—
152C23×C19—41no—
153C23×C19—42no—
154C23×C19—42no—
155C23×C19—41no—
156C23×C19—41no—
157C23×C19—41no—
158C23×C19#12011yescharacteristic
159C23×C19#12011yescharacteristic
160C23×C19#12111yescharacteristic
161C23×C19C2×SD1611yescharacteristic
162C23×C19#13511yescharacteristic
163C23×C19AGL(1,ℤ/8)11yescharacteristic
164C23×C19#13711yescharacteristic
165D4×C19—42no—
166D4×C19—81no—
167D4×C19—81no—
168D4×C19—81no—
169D4×C19—81no—
170D4×C19—81no—
171C2×C4×C19—22no—
172C2×C4×C19—22no—
173C2×C4×C19—22no—
174C2×C4×C19—22no—
175C2×C4×C19—22no—
176C2×C4×C19—22no—
177C2×C4×C19—22no—
178C2×C4×C19—22no—
179C2×C4×C19—22no—
180C2×C4×C19—41no—
181C2×C4×C19—41no—
182C2×C4×C19—41no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—41no—
186C2×C4×C19—41no—
187C2×C4×C19—41no—
188C2×C4×C19—41no—
189C2×C4×C19—41no—
190C2×C4×C19—41no—
191C2×C4×C19—42no—
192C2×C4×C19—42no—
193C2×C4×C19—41no—
194C2×C4×C19—42no—
195C2×C4×C19—41no—
196C2×C4×C19—41no—
197C2×C4×C19#12011yescharacteristic
198C2×C4×C19#12111yescharacteristic
199C2×C4×C19#12111yescharacteristic
200C2×C4×C19#12711yescharacteristic
201C2×Dic19—42no—
202C2×Dic19—42no—
203C2×Dic19—42no—
204C2×Dic19—42no—
205C2×Dic19—41no—
206C2×Dic19—41no—
207C2×Dic19—42no—
208Dic38—42no—
209Dic38—81no—
210C19⋊C8—42no—
211C19⋊C8—81no—
212#3187—191no—
213#2855—191no—
214#2854D1911yescharacteristic
215#1817—191no—
216#1520—191no—
217#1519—191no—
218#1289—191no—
219C22×C19—21no—
220C22×C19—21no—
221C22×C19—21no—
222C22×C19—21no—
223C22×C19—21no—
224C22×C19—21no—
225C22×C19—41no—
226C22×C19—41no—
227C22×C19—41no—
228C22×C19—41no—
229C22×C19—82no—
230C22×C19—82no—
231C22×C19—81no—
232C22×C19—81no—
233C22×C19—81no—
234C22×C19#39211yescharacteristic
235C22×C19#44811yescharacteristic
236C22×C19#44911yescharacteristic
237C22×C19#45011yescharacteristic
238C22×C19#45211yescharacteristic
239C22×C19#46511yescharacteristic
240C22×C19#46811yescharacteristic
241C4×C19—21no—
242C4×C19—21no—
243C4×C19—21no—
244C4×C19—42no—
245C4×C19—42no—
246C4×C19—82no—
247C4×C19—81no—
248C4×C19#45812yes—
249Dic19—82no—
250Dic19—81no—
251Dic19—81no—
252C2×#123—21no—
253C2×C22⋊Q8—191no—
254C2×#121C2×D1911yescharacteristic
255C22×C42C2×D1911yescharacteristic
256#483—381no—
257#481—381no—
258#465—382no—
259#450—381no—
260#448—381no—
261C2×C22⋊C8—191no—
262C2×C22⋊C8—191no—
263#391—381no—
264#390—21no—
265#389—21no—
266#389—381no—
267#388—22no—
268#387—382no—
269#386—21no—
270#385—381no—
271#381—381no—
272#380—191no—
273#380C2×D1911yescharacteristic
274#336—382no—
275#328—382no—
276#327—382no—
277C2×C19—21no—
278C2×C19—21no—
279C2×C19—21no—
280C2×C19—21no—
281C2×C19—21no—
282C2×C19—21no—
283C2×C19—161no—
284C2×C19#200011yescharacteristic
285C2×C19#201011yescharacteristic
286C2×C19#202211yescharacteristic
287C22×Q8—191no—
288C22×D4—21no—
289C22×D4C22⋊D1911yescharacteristic
290C23×C4C22⋊D1911yescharacteristic
291C23×C4C22⋊D1911yescharacteristic
292C23×C4C22×D1911yescharacteristic
293C2×SD16—382no—
294C22×C8—192no—
295C22×C8—381no—
296#123—42no—
297#123—42no—
298C22⋊Q8—381no—
299C22⋊Q8—381no—
300C22⋊Q8—381no—
301C22⋊Q8—381no—
302#121—21no—
303#121—21no—
304#121—21no—
305#121—21no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—191no—
309C2×C4⋊C4—382no—
310C2×C4⋊C4—381no—
311C2×C4⋊C4—381no—
312C2×C4⋊C4C22⋊D1911yescharacteristic
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—381no—
318C2×C22⋊C4—381no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325#106—382no—
326#103—382no—
327#102—382no—
328C22⋊C8—381no—
329C22⋊C8—381no—
330C22⋊C8—381no—
331C22⋊C8—381no—
332#95—22no—
333#95—192no—
334#95—382no—
335#95—382no—
336#95—382no—
337#95C22⋊D1912yes—
338C19#1032311yescharacteristic, complemented, Sylow
339C24—21no—
340C24C2×C22⋊D1911yescharacteristic
341C2×Q8—381no—
342C2×Q8—381no—
343C2×Q8—762no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—42no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—382no—
367C22×C4—381no—
368C22×C4—381no—
369C22×C4#6452612yescomplemented
370C22×C4D4×D1911yescharacteristic
371C22×C4D4×D1911yescharacteristic
372C22×C4D4×D1911yescharacteristic
373C22×C4#6454311yescharacteristic
374C22×C4C2×C22⋊D1911yescharacteristic
375C22×C4C2×C22⋊D1911yescharacteristic
376SD16—1522no—
377C2×C8—382no—
378C2×C8—762no—
379C2×C8—762no—
380C2×C8—761no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—42no—
384C4⋊C4—44no—
385C4⋊C4—381no—
386C4⋊C4—381no—
387C4⋊C4—764no—
388C4⋊C4—762no—
389C4⋊C4—761no—
390C4⋊C4—761no—
391C22⋊C4—44no—
392C22⋊C4—44no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—761no—
398C22⋊C4—761no—
399C22⋊C4—761no—
400C22⋊C4—761no—
401C42—41no—
402C42—41no—
403C42—41no—
404C42—41no—
405C23—41no—
406C23—41no—
407C23—42no—
408C23—42no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23#1059737811yescharacteristic
413C23C2×#6452611yescharacteristic
414C23#1059738311yescharacteristic
415C23#1059738511yescharacteristic
416C23#1059739611yescharacteristic
417C23#1059739711yescharacteristic
418C23#1059739911yescharacteristic
419Q8—762no—
420Q8—1521no—
421D4—42no—
422D4—81no—
423D4—81no—
424D4—81no—
425D4—81no—
426D4—81no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—762no—
454C2×C4—762no—
455C2×C4—762no—
456C2×C4—762no—
457C2×C4—762no—
458C2×C4—761no—
459C2×C4—761no—
460C2×C4#1059738311yescharacteristic
461C2×C4#1059738411yescharacteristic
462C2×C4#1059738511yescharacteristic
463C2×C4#1059738611yescharacteristic
464C8—762no—
465C8—1521no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—82no—
477C22—82no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22#1192645211yescharacteristic
482C22#1192668211yescharacteristic
483C22#1192668711yescharacteristic
484C22#1192669511yescharacteristic
485C22#1192670611yescharacteristic
486C22#1192677111yescharacteristic
487C22#1192678811yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—42no—
492C4—42no—
493C4—82no—
494C4—81no—
495C4—1522no—
496C4—1521no—
497C4—1521no—
498C4#1192673312yes—
499C2—21no—
500C2—21no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—161no—
506C2#1456463811yescharacteristic
507C2#1456470011yescharacteristic
508C2#1456476311yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2854C2
socleC22×C19#392
prime radicalC2×C19×#121C22
hypercenter#2854D19
hypocenterC19#10323
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2854

Complements

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

NH ≅ G/Ntype
2. #14571974C2semidirect
3. #14563703C2semidirect
4. #14562206C2semidirect
6. #14561502C2semidirect
108. C22×C4×C19SD16semidirect
338. C19#10323semidirect
369. C22×C4#64526semidirect

Maximal subgroups

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

subgroupindex
#145743922
#145719742
#145637032
#145622062
#145622032
#145615022
C19×#28542
#1032319