Finite Group Databasebeta

← #18085509

Subgroups — #18085509

Order 4864.

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

normal subgroups only

This group has 900 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
1#14569749C211yesmaximal, characteristic, complemented
2#14563566C212yesmaximal
3#14561514C212yesmaximal, complemented
4#14561478C211yesmaximal, characteristic, complemented
5C19×#1438C211yesmaximal, characteristic
6C2×#10597370—21no—
7C2×#10597289—22no—
8C2×#10597289—22no—
9C2×C22⋊(C19⋊C8)C2212yes—
10#11926476—22no—
11#11926465—22no—
12#11926404—21no—
13#11926404C2212yes—
14C23×D4×C19C2211yescharacteristic
15C22×C22⋊C4×C19—21no—
16C22×C22⋊C4×C19—21no—
17C2×C19×#95C2211yescharacteristic
18C2×C19×#95C2211yescharacteristic
19C25×C19—21no—
20C22×D4×C19—22no—
21C22×D4×C19—22no—
22C22×D4×C19—21no—
23C22×D4×C19—42no—
24C22×D4×C19—42no—
25C22×D4×C19Q812yescomplemented
26C23×C4×C19—21no—
27C23×C4×C19D411yescharacteristic
28C23×C4×C19D411yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C22×Dic38—21no—
31C2×C22⋊C4×C19—42no—
32C2×C22⋊C4×C19—42no—
33C2×C22⋊C4×C19—42no—
34C2×C22⋊C4×C19—42no—
35C2×C22⋊C4×C19—42no—
36C2×C22⋊C4×C19—42no—
37C2×C22⋊Dic19—22no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19D412yes—
42C2×C4⋊Dic19D412yes—
43#10597370—42no—
44#10597370—42no—
45C2×Dic19⋊C4—22no—
46C22×C19⋊C8—22no—
47C19×#95—22no—
48C19×#95—22no—
49#10597289—44no—
50#10597289—44no—
51C19⋊#95—22no—
52C19⋊#95—22no—
53C22⋊(C19⋊C8)—22no—
54C22⋊(C19⋊C8)—22no—
55C24×C19—22no—
56C24×C19—22no—
57C24×C19—22no—
58C24×C19—41no—
59C24×C19—41no—
60C24×C19—41no—
61C24×C19—41no—
62C24×C19—41no—
63C24×C19—41no—
64C24×C19—41no—
65C24×C19—41no—
66C24×C19—41no—
67C24×C19—41no—
68C24×C19—41no—
69C24×C19—41no—
70C24×C19C2×D411yescharacteristic
71C2×D4×C19—24no—
72C2×D4×C19—24no—
73C2×D4×C19—24no—
74C2×D4×C19—42no—
75C2×D4×C19—42no—
76C2×D4×C19—44no—
77C2×D4×C19—48no—
78C2×D4×C19—44no—
79C2×D4×C19—42no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—22no—
85C22×C4×C19—41no—
86C22×C4×C19—41no—
87C22×C4×C19—41no—
88C22×C4×C19—41no—
89C22×C4×C19—41no—
90C22×C4×C19—41no—
91C22×C4×C19—41no—
92C22×C4×C19—41no—
93C22×C4×C19—41no—
94C22×C4×C19—41no—
95C22×C4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19D812yes—
98C22×C4×C19SD1612yes—
99C22×C4×C19C2×D412yes—
100C22×C4×C19C2×Q811yescharacteristic
101C22×C4×C19#4111yescharacteristic
102C22×C4×C19#4112yes—
103C22×Dic19—22no—
104C22×Dic19—22no—
105C2×Dic38—42no—
106C2×Dic38—81no—
107C2×Dic38—81no—
108C22⋊C4×C19—48no—
109C22⋊C4×C19—48no—
110C22⋊Dic19—42no—
111C22⋊Dic19—42no—
112C4⋊Dic19—42no—
113C4⋊Dic19—42no—
114C4⋊Dic19—42no—
115C4⋊Dic19—81no—
116C4⋊Dic19—81no—
117Dic19⋊C4—44no—
118C2×C19⋊C8—42no—
119C2×C19⋊C8—42no—
120C2×C19⋊C8—42no—
121#10340—191nomaximal, Sylow
122C23×C19—21no—
123C23×C19—21no—
124C23×C19—21no—
125C23×C19—21no—
126C23×C19—24no—
127C23×C19—42no—
128C23×C19—42no—
129C23×C19—42no—
130C23×C19—42no—
131C23×C19—42no—
132C23×C19—42no—
133C23×C19—42no—
134C23×C19—42no—
135C23×C19—42no—
136C23×C19—42no—
137C23×C19—42no—
138C23×C19—42no—
139C23×C19—42no—
140C23×C19—42no—
141C23×C19—42no—
142C23×C19—42no—
143C23×C19—42no—
144C23×C19—42no—
145C23×C19—81no—
146C23×C19—81no—
147C23×C19—81no—
148C23×C19—81no—
149C23×C19—81no—
150C23×C19—81no—
151C23×C19—81no—
152C23×C19—81no—
153C23×C19—81no—
154C23×C19—81no—
155C23×C19—81no—
156C23×C19—81no—
157C23×C19—81no—
158C23×C19—81no—
159C23×C19—81no—
160C23×C19—81no—
161C23×C19#12011yescharacteristic
162C23×C19C22⋊Q811yescharacteristic
163C23×C19#12411yescharacteristic
164C23×C19C2×D811yescharacteristic
165C23×C19C2×SD1611yescharacteristic
166C23×C19AGL(1,ℤ/8)11yescharacteristic
167C23×C19#13711yescharacteristic
168D4×C19—28no—
169D4×C19—44no—
170D4×C19—44no—
171D4×C19—44no—
172C2×C4×C19—22no—
173C2×C4×C19—22no—
174C2×C4×C19—22no—
175C2×C4×C19—22no—
176C2×C4×C19—41no—
177C2×C4×C19—41no—
178C2×C4×C19—42no—
179C2×C4×C19—41no—
180C2×C4×C19—41no—
181C2×C4×C19—41no—
182C2×C4×C19—41no—
183C2×C4×C19—42no—
184C2×C4×C19—42no—
185C2×C4×C19—42no—
186C2×C4×C19—42no—
187C2×C4×C19—42no—
188C2×C4×C19—81no—
189C2×C4×C19—81no—
190C2×C4×C19—81no—
191C2×C4×C19—81no—
192C2×C4×C19—81no—
193C2×C4×C19—81no—
194C2×C4×C19C22⋊Q812yes—
195C2×C4×C19#12412yes—
196C2×Dic19—42no—
197C2×Dic19—42no—
198C2×Dic19—42no—
199C2×Dic19—42no—
200C2×Dic19—42no—
201C2×Dic19—42no—
202Dic38—84no—
203C19⋊C8—82no—
204#2659—191no—
205#1786—192no—
206#1438D1911yescharacteristic
207#1294—192no—
208#1280—191no—
209C22×C19—21no—
210C22×C19—21no—
211C22×C19—21no—
212C22×C19—21no—
213C22×C19—21no—
214C22×C19—21no—
215C22×C19—21no—
216C22×C19—21no—
217C22×C19—21no—
218C22×C19—21no—
219C22×C19—21no—
220C22×C19—21no—
221C22×C19—44no—
222C22×C19—44no—
223C22×C19—44no—
224C22×C19—82no—
225C22×C19—82no—
226C22×C19—82no—
227C22×C19—82no—
228C22×C19—82no—
229C22×C19—82no—
230C22×C19—82no—
231C22×C19—82no—
232C22×C19—82no—
233C22×C19—82no—
234C22×C19—82no—
235C22×C19—82no—
236C22×C19#39311yescharacteristic
237C22×C19#44711yescharacteristic
238C22×C19#44811yescharacteristic
239C22×C19#45311yescharacteristic
240C22×C19#45411yescharacteristic
241C22×C19B(4,𝔽2)11yescharacteristic
242C22×C19B(4,𝔽2)11yescharacteristic
243C22×C19#47411yescharacteristic
244C22×C19#47611yescharacteristic
245C22×C19#48611yescharacteristic
246C22×C19#48911yescharacteristic
247C4×C19—22no—
248C4×C19—22no—
249C4×C19—42no—
250C4×C19—42no—
251C4×C19—82no—
252Dic19—82no—
253Dic19—82no—
254C23×D4C2×D1911yescharacteristic
255C2×C22⋊Q8—381no—
256C22×C22⋊C4—21no—
257C22×C22⋊C4—21no—
258C2×#102—382no—
259C2×#102—382no—
260C2×C22⋊C8—192no—
261#398—382no—
262#395—382no—
263#380—192no—
264#380—381no—
265C2×#95C2×D1911yescharacteristic
266C2×#95C2×D1911yescharacteristic
267C2×C19—21no—
268C2×C19—21no—
269C2×C19—21no—
270C2×C19—21no—
271C2×C19—84no—
272C2×C19#159511yescharacteristic
273C2×C19#159611yescharacteristic
274C2×C19#159811yescharacteristic
275C2×C19#159911yescharacteristic
276C2×C19#202311yescharacteristic
277C2×C19#202711yescharacteristic
278C2×C19#202911yescharacteristic
279C25—21no—
280C22×Q8—381no—
281C22×D4—21no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—42no—
285C22×D4—42no—
286C22×D4Dic3812yescomplemented
287C23×C4—21no—
288C23×C4C22⋊D1911yescharacteristic
289C23×C4C22⋊D1911yescharacteristic
290C23×C4C22×D1911yescharacteristic
291C22×C8—382no—
292C22⋊Q8—762no—
293C22⋊Q8—762no—
294C2×C4⋊C4—192no—
295C2×C4⋊C4—192no—
296C2×C4⋊C4—382no—
297C2×C4⋊C4—381no—
298C2×C4⋊C4—381no—
299C2×C4⋊C4—381no—
300C2×C22⋊C4—42no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4—42no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4—42no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—382no—
307#102—764no—
308#102—764no—
309C22⋊C8—382no—
310C22⋊C8—382no—
311#95—22no—
312#95—22no—
313#95—382no—
314#95—382no—
315C19#1034011yescharacteristic, complemented, Sylow
316C24—22no—
317C24—22no—
318C24—22no—
319C24—41no—
320C24—41no—
321C24—41no—
322C24—41no—
323C24—41no—
324C24—41no—
325C24—41no—
326C24—41no—
327C24—41no—
328C24—41no—
329C24—41no—
330C24—41no—
331C24C2×C22⋊D1911yescharacteristic
332C2×Q8—762no—
333C2×Q8—1521no—
334C2×Q8—1521no—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—24no—
338C2×D4—42no—
339C2×D4—42no—
340C2×D4—44no—
341C2×D4—48no—
342C2×D4—44no—
343C2×D4—42no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—382no—
362C22×C4—382no—
363C22×C4#6452512yes—
364C22×C4#6452612yes—
365C22×C4C2×Dic3811yescharacteristic
366C22×C4#6454111yescharacteristic
367C22×C4D4×D1912yes—
368C22×C4#6454312yes—
369C2×C8—762no—
370C2×C8—762no—
371C2×C8—762no—
372C4⋊C4—762no—
373C4⋊C4—762no—
374C4⋊C4—764no—
375C4⋊C4—762no—
376C4⋊C4—1521no—
377C4⋊C4—1521no—
378C22⋊C4—48no—
379C22⋊C4—48no—
380C22⋊C4—762no—
381C22⋊C4—762no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—24no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—42no—
399C23—42no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23—42no—
404C23—42no—
405C23—81no—
406C23—81no—
407C23—81no—
408C23—81no—
409C23—81no—
410C23—81no—
411C23—81no—
412C23—81no—
413C23—81no—
414C23—81no—
415C23—81no—
416C23—81no—
417C23—81no—
418C23—81no—
419C23—81no—
420C23—81no—
421C23#1059737011yescharacteristic
422C23C2×#6452511yescharacteristic
423C23C2×#6452611yescharacteristic
424C23#1059738211yescharacteristic
425C23#1059738311yescharacteristic
426C23#1059739511yescharacteristic
427C23#1059739711yescharacteristic
428Q8—1524no—
429D4—28no—
430D4—44no—
431D4—44no—
432D4—44no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—81no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—81no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4—762no—
456C2×C4—762no—
457C2×C4—762no—
458C2×C4—762no—
459C2×C4—762no—
460C2×C4—762no—
461C2×C4#1059732412yes—
462C2×C4#1059733112yes—
463C8—1522no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—44no—
477C22—44no—
478C22—44no—
479C22—82no—
480C22—82no—
481C22—82no—
482C22—82no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—82no—
491C22#1192645611yescharacteristic
492C22#1192667711yescharacteristic
493C22#1192668211yescharacteristic
494C22#1192671111yescharacteristic
495C22#1192671611yescharacteristic
496C22#1192673011yescharacteristic
497C22#1192673011yescharacteristic
498C22#1192682411yescharacteristic
499C22#1192683411yescharacteristic
500C22#1192689011yescharacteristic
501C22#1192690311yescharacteristic
502C4—22no—
503C4—22no—
504C4—42no—
505C4—42no—
506C4—82no—
507C4—1522no—
508C4—1522no—
509C2—21no—
510C2—21no—
511C2—21no—
512C2—21no—
513C2—84no—
514C2#1456255211yescharacteristic
515C2#1456255711yescharacteristic
516C2#1456256911yescharacteristic
517C2#1456257411yescharacteristic
518C2#1456477111yescharacteristic
519C2#1456479111yescharacteristic
520C2#1456479911yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1438C2
socleC23×C19#120
prime radicalC23×D4×C19C22
hypercenter#1438D19
hypocenterC19#10340
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. #14569749C2semidirect
3. #14561514C2semidirect
4. #14561478C2semidirect
25. C22×D4×C19Q8semidirect
286. C22×D4Dic38semidirect
315. C19#10340semidirect

Maximal subgroups

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

subgroupindex
#145697492
#145635662
#145615142
#145614782
C19×#14382
#1034019