Finite Group Databasebeta

← #18082914

Subgroups — #18082914

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#14568567C211yesmaximal, characteristic
2#14567905C211yesmaximal, characteristic, complemented
3#14563734C211yesmaximal, characteristic, complemented
4#14562164C211yesmaximal, characteristic, complemented
5#14561961C211yesmaximal, characteristic, complemented
6#14561489C211yesmaximal, characteristic, complemented
7C19×#3094C211yesmaximal, characteristic, complemented
8C2×#10597381—21no—
9C2×#10597383—21no—
10C22×(C2×D19)⋊C4C2211yescharacteristic
11#11926508C2211yescharacteristic
12#11926479—21no—
13#11926479—21no—
14#11926470—21no—
15#11926452—21no—
16#11926444—22no—
17#11926435—22no—
18#11926416—21no—
19#11926407C2211yescharacteristic
20#11926399—21no—
21C4×C22⋊Dic19C2211yescharacteristic
22#11926303—22no—
23#11926278—22no—
24#11926267—22no—
25C2×C19×#121C2211yescharacteristic
26C2×C19×#117C2211yescharacteristic
27C19×#482—22no—
28C19×#481—21no—
29C19×#480—21no—
30C19×#428—21no—
31C19×#418—21no—
32C19×#407C2211yescharacteristic
33C24×D19D411yescharacteristic
34C22×D4×C19—21no—
35C22×D4×C19D411yescharacteristic
36C23×C4×C19C2311yescharacteristic
37C22×C22⋊D19—22no—
38C23×Dic19D411yescharacteristic
39C2×M16×C19—21no—
40C19×#121—21no—
41C19×#121—21no—
42C19×#121—21no—
43C19×#121—21no—
44C19×#117—21no—
45C19×#117—21no—
46C19×#117—21no—
47C19×#117—21no—
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C4⋊C4×C19D411yescharacteristic, complemented
50C2×C4⋊C4×C19D411yescharacteristic, complemented
51C2×C22⋊C4×C19—21no—
52C2×C22⋊C4×C19—21no—
53C2×C42×C19—21no—
54C2×C22⋊Dic19—21no—
55C2×C22⋊Dic19—22no—
56C2×C22⋊Dic19—21no—
57#10597383—44no—
58#10597381—44no—
59C2×(C2×D19)⋊C4—22no—
60C2×(C2×D19)⋊C4—22no—
61C2×(C2×D19)⋊C4—21no—
62C2×(C2×D19)⋊C4—21no—
63C2×(C2×D19)⋊C4—21no—
64C2×(C2×D19)⋊C4—21no—
65C2×(C2×D19)⋊C4—21no—
66C2×(C2×D19)⋊C4—21no—
67C2×(C2×D19)⋊C4—22no—
68C2×Dic19⋊C4—22no—
69C2×Dic19⋊C4—22no—
70C2×C4×Dic19D412yes—
71C2×#64520—21no—
72C19×#107—22no—
73C19×#106—22no—
74C19×#102—22no—
75C19×#102—22no—
76C19×C22⋊C8—21no—
77C19×C22⋊C8D412yescomplemented
78C19⋊#95—22no—
79C19⋊#95—21no—
80C19⋊#95—21no—
81C19⋊#95D412yescomplemented
82C22⋊(C19⋊C8)—21no—
83C22⋊(C19⋊C8)—21no—
84C24×C19—21no—
85C24×C19C2×D411yescharacteristic
86C23×D19—21no—
87C23×D19—21no—
88C23×D19—21no—
89C23×D19—42no—
90C23×D19—42no—
91C23×D19—42no—
92C2×D4×C19—21no—
93C2×D4×C19—21no—
94C2×D4×C19—42no—
95C2×D4×C19—42no—
96C2×D4×C19—42no—
97C2×D4×C19—41no—
98C2×D4×C19—41no—
99C22×C4×C19—21no—
100C22×C4×C19—21no—
101C22×C4×C19—21no—
102C22×C4×C19—42no—
103C22×C4×C19C2×D411yescharacteristic
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19C2×D411yescharacteristic
106C22×C4×C19C2×D411yescharacteristic
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19#4111yescharacteristic
109C2×C22⋊D19—44no—
110C2×C22⋊D19—44no—
111C2×C22⋊D19—82no—
112C22×Dic19—22no—
113C22×Dic19—21no—
114C22×Dic19—22no—
115C22×Dic19—21no—
116C22×Dic19—21no—
117C22×Dic19—42no—
118M16×C19—42no—
119C2×C8×C19—22no—
120C4⋊C4×C19—21no—
121C4⋊C4×C19—21no—
122C4⋊C4×C19—21no—
123C4⋊C4×C19—21no—
124C4⋊C4×C19—21no—
125C4⋊C4×C19—21no—
126C22⋊C4×C19—41no—
127C22⋊C4×C19—41no—
128C22⋊C4×C19—41no—
129C22⋊C4×C19—41no—
130C42×C19—41no—
131C42×C19—41no—
132C22⋊Dic19—24no—
133C22⋊Dic19—44no—
134C22⋊Dic19—42no—
135(C2×D19)⋊C4—44no—
136(C2×D19)⋊C4—44no—
137(C2×D19)⋊C4—41no—
138(C2×D19)⋊C4—41no—
139(C2×D19)⋊C4—41no—
140(C2×D19)⋊C4—41no—
141(C2×D19)⋊C4—82no—
142Dic19⋊C4—44no—
143Dic19⋊C4—82no—
144C4×Dic19—42no—
145#64520—42no—
146C2×C19⋊C8—41no—
147#9940—191nomaximal, Sylow
148C23×C19—22no—
149C23×C19—22no—
150C23×C19—41no—
151C23×C19—41no—
152C23×C19—41no—
153C23×C19—42no—
154C23×C19—41no—
155C23×C19—42no—
156C23×C19#12011yescharacteristic
157C23×C19#12011yescharacteristic
158C23×C19#12111yescharacteristic
159C22×D19—22no—
160C22×D19—22no—
161C22×D19—22no—
162C22×D19—42no—
163C22×D19—42no—
164C22×D19—41no—
165C22×D19—41no—
166C22×D19—41no—
167C22×D19—41no—
168C22×D19—42no—
169C22×D19—42no—
170C22×D19—88no—
171C22×D19—81no—
172C22×D19—81no—
173D4×C19—42no—
174D4×C19—81no—
175D4×C19—82no—
176D4×C19—82no—
177C2×C4×C19—22no—
178C2×C4×C19—22no—
179C2×C4×C19—41no—
180C2×C4×C19—41no—
181C2×C4×C19—41no—
182C2×C4×C19—41no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—42no—
186C2×C4×C19—41no—
187C2×C4×C19—41no—
188C2×C4×C19—41no—
189C2×C4×C19—42no—
190C2×C4×C19#12011yescharacteristic
191C2×C4×C19#12111yescharacteristic
192C2×C4×C19#12111yescharacteristic
193C2×C4×C19#12711yescharacteristic
194C22⋊D19—88no—
195C2×Dic19—24no—
196C2×Dic19—42no—
197C2×Dic19—42no—
198C2×Dic19—42no—
199C2×Dic19—42no—
200C2×Dic19—42no—
201C2×Dic19—41no—
202C2×Dic19—42no—
203C2×Dic19—42no—
204C2×Dic19—81no—
205C8×C19—42no—
206C19⋊C8—81no—
207#3094D1911yescharacteristic, complemented
208#2539—191no—
209#2482—191no—
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—82no—
223C22×C19—82no—
224C22×C19—81no—
225C22×C19—81no—
226C22×C19—81no—
227C22×C19#39211yescharacteristic
228C22×C19#45312yes—
229C22×C19#45812yes—
230C2×D19—44no—
231C2×D19—44no—
232C2×D19—42no—
233C2×D19—82no—
234C2×D19—82no—
235C2×D19—82no—
236C2×D19—81no—
237C2×D19—81no—
238C2×D19—82no—
239C4×C19—21no—
240C4×C19—21no—
241C4×C19—21no—
242C4×C19—21no—
243C4×C19—81no—
244C4×C19—81no—
245C4×C19—81no—
246Dic19—44no—
247Dic19—82no—
248Dic19—81no—
249C2×#123—381no—
250C2×#121C2×D1911yescharacteristic
251C2×#120—381no—
252C2×#117C2×D1911yescharacteristic
253C22×C22⋊C4—191no—
254#482—22no—
255#481—21no—
256#480—21no—
257#428—21no—
258#418—21no—
259#407—191no—
260#407C2×D1911yescharacteristic
261#399—381no—
262#399—381no—
263#397—381no—
264#392—381no—
265#390—382no—
266#388—382no—
267#385—381no—
268#381—191no—
269#379—381no—
270C4×C22⋊C4—191no—
271#339—382no—
272#327—382no—
273#323—382no—
274C2×C19—22no—
275C2×C19—22no—
276C2×C19—41no—
277C2×C19—161no—
278C2×C19#200211yescharacteristic
279C2×C19#201011yescharacteristic
280C2×C19#202211yescharacteristic
281D19—82no—
282C25—191no—
283C22×D4—21no—
284C22×D4—382no—
285C22×D4C22⋊D1911yescharacteristic
286C23×C4—191no—
287C23×C4C22×D1911yescharacteristic
288C2×M16—21no—
289C2×M16—381no—
290#123—764no—
291#121—21no—
292#121—21no—
293#121—21no—
294#121—21no—
295#120—764no—
296#117—21no—
297#117—21no—
298#117—21no—
299#117—21no—
300C2×C4⋊C4—382no—
301C2×C4⋊C4—382no—
302C2×C4⋊C4C22⋊D1911yescharacteristic
303C2×C4⋊C4C22⋊D1911yescharacteristic, complemented
304C2×C4⋊C4C22⋊D1911yescharacteristic, complemented
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—381no—
308C2×C22⋊C4—382no—
309C2×C22⋊C4—382no—
310C2×C22⋊C4—382no—
311C2×C22⋊C4—381no—
312C2×C22⋊C4—381no—
313C2×C22⋊C4—381no—
314C2×C22⋊C4—381no—
315C2×C22⋊C4—381no—
316C2×C22⋊C4—381no—
317C2×C22⋊C4—381no—
318C2×C22⋊C4—382no—
319C2×C42—21no—
320C2×C42—192no—
321#107—22no—
322#106—22no—
323#102—22no—
324#102—22no—
325C22⋊C8—21no—
326C22⋊C8—381no—
327C22⋊C8—381no—
328C22⋊C8C22⋊D1912yescomplemented
329#95—192no—
330#95—382no—
331#95—381no—
332#95—381no—
333C19#994011yescharacteristic, complemented, Sylow
334C24—21no—
335C24—381no—
336C24—381no—
337C24—381no—
338C24—762no—
339C24—762no—
340C24—762no—
341C24D4×D1911yescharacteristic
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—42no—
345C2×D4—42no—
346C2×D4—42no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—764no—
350C2×D4—764no—
351C2×D4—1522no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—42no—
356C22×C4—382no—
357C22×C4—382no—
358C22×C4—381no—
359C22×C4—381no—
360C22×C4—381no—
361C22×C4—762no—
362C22×C4D4×D1911yescharacteristic
363C22×C4D4×D1911yescharacteristic
364C22×C4#6454311yescharacteristic
365C22×C4C2×C22⋊D1911yescharacteristic
366C22×C4C2×C22⋊D1911yescharacteristic
367C22×C4C2×C22⋊D1911yescharacteristic
368M16—42no—
369M16—762no—
370C2×C8—22no—
371C2×C8—761no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—764no—
379C4⋊C4—1522no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—384no—
385C22⋊C4—764no—
386C22⋊C4—764no—
387C22⋊C4—764no—
388C22⋊C4—762no—
389C22⋊C4—761no—
390C22⋊C4—761no—
391C22⋊C4—761no—
392C22⋊C4—761no—
393C22⋊C4—1522no—
394C42—41no—
395C42—41no—
396C42—762no—
397C23—22no—
398C23—22no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—42no—
403C23—41no—
404C23—42no—
405C23—382no—
406C23—382no—
407C23—382no—
408C23—762no—
409C23—761no—
410C23—761no—
411C23—762no—
412C23—761no—
413C23—761no—
414C23—762no—
415C23—762no—
416C23—1521no—
417C23—1521no—
418C23—1528no—
419C23#1059738311yescharacteristic
420C23#1059738311yescharacteristic
421C23#1059738411yescharacteristic
422D4—42no—
423D4—81no—
424D4—82no—
425D4—82no—
426D4—1528no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—384no—
441C2×C4—762no—
442C2×C4—762no—
443C2×C4—762no—
444C2×C4—762no—
445C2×C4—762no—
446C2×C4—761no—
447C2×C4—762no—
448C2×C4—762no—
449C2×C4—1521no—
450C2×C4#1059738511yescharacteristic
451C2×C4#1059738511yescharacteristic
452C2×C4#1059738611yescharacteristic
453C2×C4#1059739911yescharacteristic
454C8—42no—
455C8—1521no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—44no—
464C22—82no—
465C22—82no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—764no—
470C22—764no—
471C22—762no—
472C22—1522no—
473C22—1522no—
474C22—1522no—
475C22—1522no—
476C22—1521no—
477C22—1521no—
478C22#1192645211yescharacteristic
479C22#1192671012yes—
480C22#1192673312yes—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—81no—
486C4—81no—
487C4—81no—
488C4—764no—
489C4—1522no—
490C4—1521no—
491C2—22no—
492C2—22no—
493C2—41no—
494C2—161no—
495C2—1522no—
496C2#1456464711yescharacteristic
497C2#1456469911yescharacteristic
498C2#1456476311yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#3094C2
socleC22×C19#392
prime radical#14568567C2
hypercenter#3094D19
hypocenterC19#9940
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
2. #14567905C2semidirect
3. #14563734C2semidirect
4. #14562164C2semidirect
5. #14561961C2semidirect
6. #14561489C2semidirect
7. C19×#3094C2semidirect
49. C2×C4⋊C4×C19D4semidirect
50. C2×C4⋊C4×C19D4semidirect
77. C19×C22⋊C8D4semidirect
81. C19⋊#95D4semidirect
207. #3094D19semidirect
303. C2×C4⋊C4C22⋊D19semidirect
304. C2×C4⋊C4C22⋊D19semidirect
328. C22⋊C8C22⋊D19semidirect
333. C19#9940semidirect

Maximal subgroups

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

subgroupindex
#145685672
#145679052
#145637342
#145621642
#145619612
#145614892
C19×#30942
#994019