Finite Group Databasebeta

← #18082917

Subgroups — #18082917

Order 4864.

768 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 85 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#14573575C211yesmaximal, characteristic, complemented
2#14568566C211yesmaximal, characteristic
3#14563734C211yesmaximal, characteristic, complemented
4#14562163C211yesmaximal, characteristic, complemented
5#14561962C211yesmaximal, characteristic, complemented
6#14561487C211yesmaximal, characteristic, complemented
7C19×#2482C211yesmaximal, characteristic, complemented
8C2×#10597375—21no—
9C2×#10597376C2211yescharacteristic
10C2×#10597399—21no—
11#11926868—22no—
12#11926862—21no—
13#11926857—21no—
14#11926587—21no—
15#11926548—21no—
16#11926508C2211yescharacteristic
17#11926508C2211yescharacteristic
18#11926480—21no—
19#11926453—21no—
20#11926444—22no—
21C4×C22⋊Dic19C2211yescharacteristic
22#11926303—22no—
23#11926277—22no—
24#11926268—22no—
25C2×C19×#117C2211yescharacteristic
26C22×C22⋊C4×C19C2211yescharacteristic
27C19×#399—21no—
28C19×#397—21no—
29C19×#388—22no—
30C19×#385—21no—
31C19×#381C2211yescharacteristic
32C19×#379—21no—
33C25×C19D411yescharacteristic
34C23×C4×C19D411yescharacteristic
35C23×C4×C19C2311yescharacteristic
36C22×C22⋊D19—21no—
37C22×C22⋊D19—22no—
38C22×D76D411yescharacteristic
39C19×#117—21no—
40C19×#117—21no—
41C19×#117—21no—
42C19×#117—21no—
43C2×C4⋊C4×C19—22no—
44C2×C4⋊C4×C19D411yescharacteristic, complemented
45C2×C4⋊C4×C19D411yescharacteristic, complemented
46C2×C22⋊C4×C19—22no—
47C2×C22⋊C4×C19—21no—
48C2×C22⋊C4×C19—21no—
49C2×C22⋊C4×C19—21no—
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19—21no—
52C2×C22⋊C4×C19—21no—
53C2×C22⋊C4×C19—21no—
54C2×C22⋊C4×C19—21no—
55C2×C22⋊C4×C19—22no—
56C2×C42×C19—21no—
57#10597399—44no—
58C2×C22⋊Dic19—21no—
59C2×C22⋊Dic19—22no—
60#10597376—21no—
61#10597376—21no—
62#10597376—21no—
63#10597376—21no—
64#10597375—44no—
65C2×(C2×D19)⋊C4—22no—
66C2×(C2×D19)⋊C4—21no—
67C2×C4⋊Dic19D411yescharacteristic
68C2×Dic19⋊C4—22no—
69C2×C4×Dic19D412yes—
70C2×#64520—21no—
71C2×#64520—21no—
72C19×#95—22no—
73C19×#95—21no—
74C19×#95D412yescomplemented
75C19⋊#95—21no—
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)—21no—
78C22⋊(C19⋊C8)—21no—
79C22⋊(C19⋊C8)D412yescomplemented
80#10597266—22no—
81#10597266—22no—
82#10597265—22no—
83#10597264—22no—
84C24×C19—21no—
85C24×C19—21no—
86C24×C19—21no—
87C24×C19—42no—
88C24×C19—42no—
89C24×C19—42no—
90C24×C19C2×D411yescharacteristic
91C23×D19—21no—
92C22×C4×C19—21no—
93C22×C4×C19—21no—
94C22×C4×C19—22no—
95C22×C4×C19—21no—
96C22×C4×C19—21no—
97C22×C4×C19—21no—
98C22×C4×C19—42no—
99C22×C4×C19—42no—
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19C2×D411yescharacteristic
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19#4111yescharacteristic
106C2×C22⋊D19—44no—
107C2×C22⋊D19—42no—
108C2×C22⋊D19—44no—
109C2×C22⋊D19—42no—
110C2×C22⋊D19—41no—
111C2×C22⋊D19—41no—
112C2×C22⋊D19—82no—
113C22×Dic19—22no—
114C22×Dic19—21no—
115C2×D76—21no—
116C2×D76—21no—
117C2×D76—42no—
118C4⋊C4×C19—21no—
119C4⋊C4×C19—21no—
120C4⋊C4×C19—21no—
121C4⋊C4×C19—21no—
122C4⋊C4×C19—82no—
123C22⋊C4×C19—42no—
124C22⋊C4×C19—44no—
125C22⋊C4×C19—41no—
126C22⋊C4×C19—41no—
127C22⋊C4×C19—41no—
128C22⋊C4×C19—41no—
129C22⋊C4×C19—41no—
130C22⋊C4×C19—41no—
131C22⋊C4×C19—82no—
132C42×C19—41no—
133C42×C19—41no—
134C22⋊Dic19—24no—
135C22⋊Dic19—44no—
136(C2×D19)⋊C4—44no—
137(C2×D19)⋊C4—41no—
138(C2×D19)⋊C4—41no—
139C4⋊Dic19—21no—
140C4⋊Dic19—21no—
141Dic19⋊C4—44no—
142C4×Dic19—42no—
143#64520—42no—
144#64520—42no—
145C2×C19⋊C8—22no—
146C2×C19⋊C8—41no—
147#9940—191nomaximal, Sylow
148C23×C19—22no—
149C23×C19—22no—
150C23×C19—22no—
151C23×C19—22no—
152C23×C19—22no—
153C23×C19—41no—
154C23×C19—42no—
155C23×C19—41no—
156C23×C19—41no—
157C23×C19—42no—
158C23×C19—41no—
159C23×C19—41no—
160C23×C19—42no—
161C23×C19—42no—
162C23×C19—81no—
163C23×C19—81no—
164C23×C19—88no—
165C23×C19#12011yescharacteristic
166C23×C19#12011yescharacteristic
167C23×C19#12111yescharacteristic
168C22×D19—41no—
169C22×D19—41no—
170C22×D19—42no—
171C22×D19—41no—
172C22×D19—42no—
173C2×C4×C19—22no—
174C2×C4×C19—22no—
175C2×C4×C19—41no—
176C2×C4×C19—41no—
177C2×C4×C19—41no—
178C2×C4×C19—41no—
179C2×C4×C19—42no—
180C2×C4×C19—42no—
181C2×C4×C19—42no—
182C2×C4×C19—42no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—41no—
186C2×C4×C19—42no—
187C2×C4×C19—42no—
188C2×C4×C19—42no—
189C2×C4×C19—81no—
190C2×C4×C19#12011yescharacteristic
191C2×C4×C19#12111yescharacteristic
192C2×C4×C19#12111yescharacteristic
193C2×C4×C19#12711yescharacteristic
194C22⋊D19—88no—
195C22⋊D19—82no—
196C22⋊D19—82no—
197C2×Dic19—24no—
198C2×Dic19—42no—
199C2×Dic19—42no—
200C2×Dic19—41no—
201C2×Dic19—41no—
202C2×Dic19—41no—
203D76—42no—
204D76—81no—
205C19⋊C8—42no—
206C19⋊C8—81no—
207#3094—191no—
208#2539—191no—
209#2482D1911yescharacteristic, complemented
210#1826—191no—
211#1510—191no—
212#1462—191no—
213#1284—191no—
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—42no—
225C22×C19—82no—
226C22×C19—82no—
227C22×C19—82no—
228C22×C19—82no—
229C22×C19—81no—
230C22×C19—81no—
231C22×C19#39211yescharacteristic
232C22×C19#45312yes—
233C22×C19#45812yes—
234C2×D19—82no—
235C2×D19—82no—
236C2×D19—81no—
237C2×D19—81no—
238C2×D19—81no—
239C4×C19—21no—
240C4×C19—21no—
241C4×C19—21no—
242C4×C19—21no—
243C4×C19—82no—
244C4×C19—81no—
245C4×C19—81no—
246C4×C19—81no—
247Dic19—44no—
248Dic19—81no—
249C2×#123—381no—
250C2×#121—191no—
251C2×#120—381no—
252C2×#117C2×D1911yescharacteristic
253C22×C22⋊C4C2×D1911yescharacteristic
254#482—382no—
255#481—381no—
256#480—381no—
257#428—381no—
258#418—381no—
259#407—191no—
260#407—191no—
261#399—21no—
262#399—381no—
263#397—21no—
264#392—381no—
265#390—382no—
266#388—22no—
267#385—21no—
268#381C2×D1911yescharacteristic
269#379—21no—
270C4×C22⋊C4—191no—
271#339—382no—
272#327—382no—
273#323—382no—
274C2×C19—22no—
275C2×C19—22no—
276C2×C19—41no—
277C2×C19—82no—
278C2×C19#200211yescharacteristic
279C2×C19#201011yescharacteristic
280C2×C19#202211yescharacteristic
281D19—161no—
282C25C22⋊D1911yescharacteristic
283C22×D4—191no—
284C22×D4—381no—
285C22×D4—382no—
286C23×C4C22⋊D1911yescharacteristic
287C23×C4C22×D1911yescharacteristic
288C2×M16—381no—
289C2×M16—381no—
290#123—764no—
291#121—381no—
292#121—381no—
293#121—381no—
294#121—381no—
295#120—764no—
296#117—21no—
297#117—21no—
298#117—21no—
299#117—21no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—191no—
302C2×C4⋊C4—382no—
303C2×C4⋊C4C22⋊D1911yescharacteristic, complemented
304C2×C4⋊C4C22⋊D1911yescharacteristic, complemented
305C2×C22⋊C4—22no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—381no—
316C2×C22⋊C4—382no—
317C2×C22⋊C4—382no—
318C2×C22⋊C4—381no—
319C2×C42—21no—
320C2×C42—192no—
321#107—382no—
322#106—382no—
323#102—382no—
324#102—382no—
325C22⋊C8—192no—
326C22⋊C8—381no—
327C22⋊C8—381no—
328C22⋊C8—381no—
329#95—22no—
330#95—21no—
331#95—381no—
332#95C22⋊D1912yescomplemented
333C19#994011yescharacteristic, complemented, Sylow
334C24—21no—
335C24—21no—
336C24—21no—
337C24—42no—
338C24—42no—
339C24—42no—
340C24—381no—
341C24C2×C22⋊D1911yescharacteristic
342C2×D4—381no—
343C2×D4—381no—
344C2×D4—762no—
345C2×D4—764no—
346C2×D4—762no—
347C2×D4—762no—
348C2×D4—764no—
349C2×D4—761no—
350C2×D4—761no—
351C2×D4—1522no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—382no—
361C22×C4—381no—
362C22×C4D4×D1911yescharacteristic
363C22×C4D4×D1911yescharacteristic
364C22×C4D4×D1911yescharacteristic
365C22×C4#6454311yescharacteristic
366C22×C4C2×C22⋊D1911yescharacteristic
367C22×C4C2×C22⋊D1911yescharacteristic
368M16—762no—
369M16—762no—
370C2×C8—382no—
371C2×C8—761no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—82no—
377C4⋊C4—381no—
378C4⋊C4—381no—
379C4⋊C4—764no—
380C22⋊C4—42no—
381C22⋊C4—44no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—82no—
389C22⋊C4—384no—
390C22⋊C4—764no—
391C22⋊C4—764no—
392C22⋊C4—761no—
393C22⋊C4—761no—
394C42—41no—
395C42—41no—
396C42—762no—
397C23—22no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—41no—
403C23—42no—
404C23—41no—
405C23—41no—
406C23—42no—
407C23—41no—
408C23—41no—
409C23—42no—
410C23—42no—
411C23—81no—
412C23—81no—
413C23—88no—
414C23—761no—
415C23—761no—
416C23—762no—
417C23—761no—
418C23—762no—
419C23#1059738311yescharacteristic
420C23#1059738511yescharacteristic
421C23#1059739911yescharacteristic
422D4—762no—
423D4—1521no—
424D4—1528no—
425D4—1522no—
426D4—1522no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—81no—
444C2×C4—384no—
445C2×C4—762no—
446C2×C4—762no—
447C2×C4—761no—
448C2×C4—761no—
449C2×C4—761no—
450C2×C4#1059738311yescharacteristic
451C2×C4#1059738411yescharacteristic
452C2×C4#1059738511yescharacteristic
453C2×C4#1059738611yescharacteristic
454C8—762no—
455C8—1521no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—44no—
464C22—44no—
465C22—44no—
466C22—42no—
467C22—82no—
468C22—82no—
469C22—82no—
470C22—82no—
471C22—81no—
472C22—81no—
473C22—1522no—
474C22—1522no—
475C22—1521no—
476C22—1521no—
477C22—1521no—
478C22#1192645211yescharacteristic
479C22#1192671212yes—
480C22#1192673312yes—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—82no—
486C4—81no—
487C4—81no—
488C4—81no—
489C4—764no—
490C4—1521no—
491C2—22no—
492C2—22no—
493C2—41no—
494C2—82no—
495C2—3041no—
496C2#1456464811yescharacteristic
497C2#1456470011yescharacteristic
498C2#1456476311yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2482C2
socleC22×C19#392
prime radical#14568566C2
hypercenter#2482D19
hypocenterC19#9940
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2482

Complements

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

NH ≅ G/Ntype
1. #14573575C2semidirect
3. #14563734C2semidirect
4. #14562163C2semidirect
5. #14561962C2semidirect
6. #14561487C2semidirect
7. C19×#2482C2semidirect
44. C2×C4⋊C4×C19D4semidirect
45. C2×C4⋊C4×C19D4semidirect
74. C19×#95D4semidirect
79. C22⋊(C19⋊C8)D4semidirect
209. #2482D19semidirect
303. C2×C4⋊C4C22⋊D19semidirect
304. C2×C4⋊C4C22⋊D19semidirect
332. #95C22⋊D19semidirect
333. C19#9940semidirect

Maximal subgroups

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

subgroupindex
#145735752
#145685662
#145637342
#145621632
#145619622
#145614872
C19×#24822
#994019