Finite Group Databasebeta

← #18078601

Subgroups — #18078601

Order 4864.

762 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 113 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#14569372C211yesmaximal, characteristic
2#14566248C211yesmaximal, characteristic, complemented
3#14562204C211yesmaximal, characteristic, complemented
4#14562202C211yesmaximal, characteristic, complemented
5C2×#11926267C211yesmaximal, characteristic, complemented
6#14561502C211yesmaximal, characteristic, complemented
7C19×#1289C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C2×#10597328—21no—
10C22×(C2×D19)⋊C4C2211yescharacteristic
11C2×C22⋊C4×D19—21no—
12C2×C22⋊(C19⋊C8)C2211yescharacteristic
13#11926471C412yescomplemented
14#11926461—22no—
15#11926454C412yescomplemented
16#11926421—21no—
17#11926418—22no—
18#11926415—22no—
19#11926404C2211yescharacteristic
20#11926402—21no—
21#11926279—22no—
22#11926277—22no—
23#11926267—22no—
24C2×C19×C22⋊C8C2211yescharacteristic
25C19×#380C2211yescharacteristic
26C19×#380C2211yescharacteristic
27C24×D19D411yescharacteristic
28C23×C4×C19C2311yescharacteristic
29C22×C22⋊D19—21no—
30C23×Dic19D411yescharacteristic
31C22×D76—22no—
32C22×D76C2×C411yescharacteristic, complemented
33C22×C4×D19—22no—
34C22×C8×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C22⋊Dic19—21no—
40#10597376—21no—
41#10597376—21no—
42#10597376—21no—
43#10597376—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—22no—
49C2×(C2×D19)⋊C4—22no—
50C2×(C2×D19)⋊C4—21no—
51C2×(C2×D19)⋊C4—22no—
52C2×(C2×D19)⋊C4C2×C412yes—
53C2×(C2×D19)⋊C4D412yes—
54C2×C4⋊Dic19—21no—
55C2×C4⋊Dic19C2×C411yescharacteristic, complemented
56C2×Dic19⋊C4—22no—
57C22×C19⋊C8—21no—
58#10597328—42no—
59#10597328—42no—
60C22⋊C4×D19—42no—
61C22⋊C4×D19—42no—
62C19×C22⋊C8—21no—
63C19×C22⋊C8—21no—
64C19×#95C2×C412yescomplemented
65C19×#95D412yescomplemented
66C19⋊#95—22no—
67C19⋊#95—22no—
68C19⋊#95D412yescomplemented
69C22⋊(C19⋊C8)—21no—
70C22⋊(C19⋊C8)—21no—
71C24×C19C2×D411yescharacteristic
72C23×D19—21no—
73C23×D19—21no—
74C23×D19—21no—
75C23×D19—21no—
76C23×D19—21no—
77C23×D19—81no—
78C23×D19—81no—
79C23×D19C22⋊C412yes—
80C23×D19D812yes—
81C23×D19SD1612yes—
82C22×C4×C19—22no—
83C22×C4×C19—22no—
84C22×C4×C19—81no—
85C22×C4×C19C22×C411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19#4111yescharacteristic
90C22×C4×C19#4111yescharacteristic
91C2×C22⋊D19—41no—
92C2×C22⋊D19—41no—
93C2×C22⋊D19—41no—
94C2×C22⋊D19—41no—
95C2×C22⋊D19—41no—
96C2×C22⋊D19—41no—
97C22×Dic19—21no—
98C22×Dic19—21no—
99C22×Dic19—21no—
100C22×Dic19—22no—
101C22×Dic19—81no—
102C22×Dic19C22⋊C412yes—
103C2×D76—21no—
104C2×D76—21no—
105C2×D76—44no—
106C2×D76—82no—
107C2×D76—82no—
108C2×D76—81no—
109C2×C4×D19—44no—
110C2×C4×D19—82no—
111C2×C4×D19—82no—
112C2×C8×C19—41no—
113C2×C8×C19—81no—
114C4⋊C4×C19—81no—
115C4⋊C4×C19—81no—
116C22⋊C4×C19—41no—
117C22⋊C4×C19—41no—
118C22⋊C4×C19—41no—
119C22⋊C4×C19—41no—
120C22⋊Dic19—41no—
121C22⋊Dic19—41no—
122(C2×D19)⋊C4—22no—
123(C2×D19)⋊C4—22no—
124(C2×D19)⋊C4—22no—
125(C2×D19)⋊C4—22no—
126(C2×D19)⋊C4—44no—
127(C2×D19)⋊C4—44no—
128(C2×D19)⋊C4—41no—
129(C2×D19)⋊C4—41no—
130(C2×D19)⋊C4—82no—
131C4⋊Dic19—21no—
132C4⋊Dic19—21no—
133C4⋊Dic19—81no—
134Dic19⋊C4—82no—
135C2×C19⋊C8—41no—
136C2×C19⋊C8—81no—
137#9203—191nomaximal, Sylow
138C23×C19—41no—
139C23×C19—41no—
140C23×C19C2×C22⋊C411yescharacteristic
141C23×C19#12011yescharacteristic
142C23×C19#12311yescharacteristic
143C23×C19C2×D811yescharacteristic
144C23×C19C2×SD1611yescharacteristic
145C23×C19AGL(1,ℤ/8)11yescharacteristic
146C23×C19#13711yescharacteristic
147C22×D19—22no—
148C22×D19—22no—
149C22×D19—22no—
150C22×D19—22no—
151C22×D19—22no—
152C22×D19—22no—
153C22×D19—42no—
154C22×D19—42no—
155C22×D19—42no—
156C22×D19—42no—
157C22×D19—42no—
158C22×D19—42no—
159C22×D19—41no—
160C22×D19—41no—
161C22×D19—41no—
162C22×D19—82no—
163C22×D19—82no—
164C22×D19—81no—
165C22×D19—81no—
166C22×D19—82no—
167C22×D19—82no—
168C22×D19#10214yes—
169C2×C4×C19—41no—
170C2×C4×C19—41no—
171C2×C4×C19—41no—
172C2×C4×C19—41no—
173C2×C4×C19—41no—
174C2×C4×C19—41no—
175C2×C4×C19—42no—
176C2×C4×C19—42no—
177C2×C4×C19—42no—
178C2×C4×C19—42no—
179C2×C4×C19—42no—
180C2×C4×C19—42no—
181C2×C4×C19C4×D411yescharacteristic
182C2×C4×C19C4×D411yescharacteristic
183C2×C4×C19#12111yescharacteristic
184C2×C4×C19#12111yescharacteristic
185C22⋊D19—81no—
186C22⋊D19—81no—
187C22⋊D19—81no—
188C22⋊D19—81no—
189C2×Dic19—22no—
190C2×Dic19—42no—
191C2×Dic19—42no—
192C2×Dic19—42no—
193C2×Dic19—42no—
194C2×Dic19—41no—
195C2×Dic19—41no—
196C2×Dic19—41no—
197C2×Dic19—42no—
198C2×Dic19—81no—
199D76—81no—
200D76—81no—
201D76—88no—
202C4×D19—88no—
203C8×C19—81no—
204C19⋊C8—81no—
205#2617—191no—
206#2315—191no—
207#1519—191no—
208#1519—191no—
209C2×#323—191no—
210#1289—191no—
211#1289D1911yescharacteristic, complemented
212C22×C19—21no—
213C22×C19—21no—
214C22×C19—21no—
215C22×C19—21no—
216C22×C19—21no—
217C22×C19—21no—
218C22×C19—41no—
219C22×C19—41no—
220C22×C19—41no—
221C22×C19—41no—
222C22×C19#38611yescharacteristic
223C22×C19C2×#10211yescharacteristic
224C22×C19#41711yescharacteristic
225C22×C19#44711yescharacteristic
226C22×C19#44811yescharacteristic
227C22×C19#48011yescharacteristic
228C22×C19#48111yescharacteristic
229C2×D19—24no—
230C2×D19—44no—
231C2×D19—44no—
232C2×D19—42no—
233C2×D19—42no—
234C2×D19—44no—
235C2×D19—82no—
236C2×D19—82no—
237C2×D19—82no—
238C2×D19—82no—
239C2×D19—82no—
240C2×D19—81no—
241C2×D19—81no—
242C2×D19—81no—
243C4×C19—21no—
244C4×C19—21no—
245C4×C19—21no—
246C4×C19—21no—
247C4×C19—82no—
248C4×C19—82no—
249Dic19—42no—
250Dic19—82no—
251Dic19—81no—
252C2×#121—191no—
253C2×#120—381no—
254C22×C22⋊C4—191no—
255C22×C22⋊C4—381no—
256C2×C22⋊C8—191no—
257C2×C22⋊C8C2×D1911yescharacteristic
258#397—192no—
259#394—382no—
260#392—192no—
261#386—381no—
262#385—382no—
263#385—382no—
264#380—191no—
265#380—381no—
266#380C2×D1911yescharacteristic
267#380C2×D1911yescharacteristic
268#327—382no—
269#327—382no—
270#323—382no—
271C2×C19—21no—
272C2×C19—21no—
273C2×C19—21no—
274C2×C19—21no—
275C2×C19—21no—
276C2×C19—21no—
277C2×C19#187411yescharacteristic
278C2×C19#191111yescharacteristic
279C2×C19#191311yescharacteristic
280D19—44no—
281D19—161no—
282C25—191no—
283C22×D4—191no—
284C22×D4—382no—
285C22×D4—381no—
286C23×C4—191no—
287C23×C4—382no—
288C23×C4C22×D1911yescharacteristic
289C22×C8—21no—
290C22×C8—381no—
291#121—381no—
292#121—381no—
293#121—381no—
294#121—381no—
295#120—762no—
296#120—762no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—191no—
300C2×C4⋊C4—382no—
301C2×C4⋊C4—381no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—192no—
305C2×C22⋊C4—192no—
306C2×C22⋊C4—381no—
307C2×C22⋊C4—381no—
308C2×C22⋊C4—381no—
309C2×C22⋊C4—381no—
310C2×C22⋊C4—382no—
311C2×C22⋊C4—382no—
312C2×C22⋊C4—381no—
313C2×C22⋊C4—381no—
314C2×C22⋊C4—382no—
315C2×C22⋊C4—762no—
316C2×C22⋊C4—762no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8—381no—
320C22⋊C8—381no—
321#95—192no—
322#95—382no—
323#95—382no—
324#95C4×D1912yescomplemented
325#95D7612yescomplemented
326C19#920311yescharacteristic, complemented, Sylow
327C24—192no—
328C24—192no—
329C24—192no—
330C24—381no—
331C24—381no—
332C24—381no—
333C24—381no—
334C24—381no—
335C24—1521no—
336C24—1521no—
337C24D4×D1911yescharacteristic
338C2×D4—381no—
339C2×D4—381no—
340C2×D4—764no—
341C2×D4—761no—
342C2×D4—761no—
343C2×D4—761no—
344C2×D4—761no—
345C2×D4—761no—
346C2×D4—761no—
347C2×D4—1522no—
348C2×D4—1522no—
349C2×D4—1521no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—81no—
353C22×C4—192no—
354C22×C4—381no—
355C22×C4—381no—
356C22×C4—381no—
357C22×C4—382no—
358C22×C4—764no—
359C22×C4—1522no—
360C22×C4—1522no—
361C22×C4—1521no—
362C22×C4C2×C4×D1911yescharacteristic
363C22×C4C2×D7611yescharacteristic
364C22×C4#6454111yescharacteristic
365C22×C4D4×D1911yescharacteristic
366C22×C4D4×D1911yescharacteristic
367C22×C4#6454511yescharacteristic
368C2×C8—41no—
369C2×C8—81no—
370C2×C8—761no—
371C2×C8—1521no—
372C4⋊C4—81no—
373C4⋊C4—81no—
374C4⋊C4—381no—
375C4⋊C4—381no—
376C4⋊C4—1522no—
377C4⋊C4—1521no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—382no—
383C22⋊C4—382no—
384C22⋊C4—382no—
385C22⋊C4—382no—
386C22⋊C4—764no—
387C22⋊C4—764no—
388C22⋊C4—761no—
389C22⋊C4—761no—
390C22⋊C4—761no—
391C22⋊C4—761no—
392C22⋊C4—1522no—
393C23—41no—
394C23—41no—
395C23—194no—
396C23—382no—
397C23—382no—
398C23—382no—
399C23—382no—
400C23—382no—
401C23—382no—
402C23—762no—
403C23—762no—
404C23—762no—
405C23—762no—
406C23—762no—
407C23—762no—
408C23—761no—
409C23—761no—
410C23—761no—
411C23—1521no—
412C23—1521no—
413C23—1522no—
414C23—1522no—
415C23—1522no—
416C23—1522no—
417C23C22⋊C4×D1911yescharacteristic
418C23#1059732811yescharacteristic
419C23#1059734011yescharacteristic
420C23D8×D1911yescharacteristic
421C23SD16×D1911yescharacteristic
422C23#1059736011yescharacteristic
423C23#1059736411yescharacteristic
424D4—1521no—
425D4—1521no—
426D4—1528no—
427D4—1521no—
428D4—1521no—
429D4—1521no—
430D4—1521no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—382no—
444C2×C4—762no—
445C2×C4—762no—
446C2×C4—762no—
447C2×C4—762no—
448C2×C4—761no—
449C2×C4—761no—
450C2×C4—761no—
451C2×C4—762no—
452C2×C4—1528no—
453C2×C4—1521no—
454C2×C4C4×D7611yescharacteristic
455C2×C4#1059733011yescharacteristic
456C2×C4#1059733911yescharacteristic
457C2×C4#1059734111yescharacteristic
458C8—81no—
459C8—1521no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—384no—
471C22—764no—
472C22—764no—
473C22—764no—
474C22—762no—
475C22—762no—
476C22—1522no—
477C22—1522no—
478C22—1522no—
479C22—1522no—
480C22—1522no—
481C22—1521no—
482C22—1521no—
483C22—1521no—
484C22#1192642211yescharacteristic
485C22#102×D1911yescharacteristic
486C22#1192654411yescharacteristic
487C22#1192667911yescharacteristic
488C22#1192668411yescharacteristic
489C22#1192685911yescharacteristic
490C22#1192686411yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—82no—
496C4—82no—
497C4—762no—
498C4—1522no—
499C4—1521no—
500C2—21no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—21no—
506C2—3041no—
507C2—764no—
508C2#1456395111yescharacteristic
509C2#1456416611yescharacteristic
510C2#1456417611yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1289C2
socleC22×C19#386
prime radical#14569372C2
cosocleC23×C4×C19C23
hypercenter#1289D19
hypocenterC19#9203
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
2. #14566248C2semidirect
3. #14562204C2semidirect
4. #14562202C2semidirect
5. C2×#11926267C2semidirect
6. #14561502C2semidirect
7. C19×#1289C2semidirect
13. #11926471C4semidirect
15. #11926454C4semidirect
32. C22×D76C2×C4semidirect
55. C2×C4⋊Dic19C2×C4semidirect
64. C19×#95C2×C4semidirect
65. C19×#95D4semidirect
68. C19⋊#95D4semidirect
211. #1289D19semidirect
324. #95C4×D19semidirect
325. #95D76semidirect
326. C19#9203semidirect

Maximal subgroups

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

subgroupindex
#145693722
#145662482
#145622042
#145622022
C2×#119262672
#145615022
C19×#12892
#920319