Finite Group Databasebeta

← #18082757

Subgroups — #18082757

Order 4864.

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

normal subgroups only

This group has 872 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
1C2×#11926683C211yesmaximal, characteristic
2#14569380C211yesmaximal, characteristic
3C2×#11926463C211yesmaximal, characteristic, complemented
4C2×#11926279C211yesmaximal, characteristic
5C2×#11926269C211yesmaximal, characteristic, complemented
6#14561513C211yesmaximal, characteristic, complemented
7C19×#1787C211yesmaximal, characteristic, complemented
8C22×#64527—21no—
9C2×#10597332—21no—
10C2×#10597376C2211yescharacteristic
11C22×Dic19⋊C4—21no—
12C22×Dic19⋊C4C2211yescharacteristic
13#11926683—22no—
14#11926683—22no—
15C2×#10597292—21no—
16C2×C22⋊(C19⋊C8)C2211yescharacteristic
17#11926476—21no—
18#11926466—22no—
19#11926463—22no—
20#11926463—22no—
21#11926462—21no—
22#11926421—21no—
23C2×C19⋊#95—21no—
24C2×C19⋊#95C2211yescharacteristic
25#11926279—22no—
26#11926269—22no—
27C23×Q8×C19C2211yescharacteristic
28C2×C19×#103—22no—
29C2×C19×C22⋊C8C2211yescharacteristic
30C19×#380C2211yescharacteristic
31C22×Q8×C19—21no—
32C22×Q8×C19—21no—
33C22×Q8×C19—21no—
34C22×Q8×C19—21no—
35C22×Q8×C19—21no—
36C22×Q8×C19—44no—
37C22×Q8×C19D412yes—
38C23×C4×C19—21no—
39C23×C4×C19C2311yescharacteristic
40C22×C22⋊D19—21no—
41C23×Dic19—21no—
42C23×Dic19D411yescharacteristic
43C23×Dic19D411yescharacteristic
44C22×D76D411yescharacteristic
45C22×C8×C19—21no—
46C2×C4⋊C4×C19D412yes—
47C2×C22⋊C4×C19—21no—
48C2×#64527—24no—
49C2×#64527—44no—
50#10597376—21no—
51#10597376—21no—
52#10597376—21no—
53#10597376—21no—
54C2×(C2×D19)⋊C4—22no—
55C2×(C2×D19)⋊C4—21no—
56C2×(C2×D19)⋊C4—22no—
57C2×C4⋊Dic19—22no—
58C2×C4⋊Dic19D411yescharacteristic
59C2×Dic19⋊C4—24no—
60C2×Dic19⋊C4—21no—
61C2×Dic19⋊C4—21no—
62C2×Dic19⋊C4—21no—
63C2×Dic19⋊C4—21no—
64C2×Dic19⋊C4—21no—
65C2×Dic19⋊C4—21no—
66C2×Dic19⋊C4—44no—
67C22×C19⋊C8—21no—
68#10597332—42no—
69#10597332—42no—
70C19×#103—44no—
71C19×C22⋊C8—21no—
72C19×C22⋊C8—21no—
73C19×#95—21no—
74#10597292—24no—
75C19⋊#95—24no—
76C19⋊#95—22no—
77C19⋊#95—21no—
78C19⋊#95D412yes—
79C22⋊(C19⋊C8)—21no—
80C22⋊(C19⋊C8)D412yes—
81C24×C19C2×D411yescharacteristic
82C23×D19—21no—
83C2×Q8×C19—24no—
84C2×Q8×C19—24no—
85C2×Q8×C19—22no—
86C2×Q8×C19—22no—
87C2×Q8×C19—44no—
88C2×Q8×C19—42no—
89C2×Q8×C19—42no—
90C2×Q8×C19—44no—
91C2×Q8×C19—44no—
92C2×Q8×C19—44no—
93C2×Q8×C19—41no—
94C2×Q8×C19—41no—
95C22×C4×C19—24no—
96C22×C4×C19—22no—
97C22×C4×C19—22no—
98C22×C4×C19—42no—
99C22×C4×C19—42no—
100C22×C4×C19—41no—
101C22×C4×C19—41no—
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19C2×D411yescharacteristic
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19C2×D411yescharacteristic
106C22×C4×C19C2×D411yescharacteristic
107C22×C4×C19#4111yescharacteristic
108C2×C22⋊D19—41no—
109C2×C22⋊D19—41no—
110C2×C22⋊D19—41no—
111C2×C22⋊D19—41no—
112C2×C22⋊D19—41no—
113C2×C22⋊D19—41no—
114C22×Dic19—24no—
115C22×Dic19—22no—
116C22×Dic19—21no—
117C22×Dic19—21no—
118C22×Dic19—21no—
119C22×Dic19—21no—
120C22×Dic19—21no—
121C22×Dic19—21no—
122C22×Dic19—21no—
123C22×Dic19—21no—
124C22×Dic19—21no—
125C22×Dic19—21no—
126C22×Dic19—42no—
127C22×Dic19—41no—
128C22×Dic19—41no—
129C22×Dic19—42no—
130C22×Dic19SD1612yescomplemented
131C2×D76—21no—
132C2×D76—21no—
133C2×D76—42no—
134C2×C8×C19—42no—
135C2×C8×C19—41no—
136C4⋊C4×C19—42no—
137C22⋊C4×C19—41no—
138C22⋊C4×C19—41no—
139#64527—48no—
140(C2×D19)⋊C4—44no—
141(C2×D19)⋊C4—41no—
142(C2×D19)⋊C4—41no—
143(C2×D19)⋊C4—82no—
144C4⋊Dic19—21no—
145C4⋊Dic19—21no—
146C4⋊Dic19—44no—
147Dic19⋊C4—48no—
148Dic19⋊C4—41no—
149Dic19⋊C4—41no—
150Dic19⋊C4—41no—
151Dic19⋊C4—41no—
152C2×C19⋊C8—22no—
153C2×C19⋊C8—42no—
154#9917—191nomaximal, Sylow
155C23×C19—22no—
156C23×C19—22no—
157C23×C19#12011yescharacteristic
158C23×C19#12011yescharacteristic
159C23×C19#12111yescharacteristic
160C23×C19C2×SD1611yescharacteristic
161C23×C19#13511yescharacteristic
162C23×C19AGL(1,ℤ/8)11yescharacteristic
163C23×C19#13711yescharacteristic
164C22×D19—41no—
165C22×D19—41no—
166C22×D19—41no—
167C22×D19—42no—
168C22×D19—42no—
169Q8×C19—24no—
170Q8×C19—24no—
171Q8×C19—42no—
172Q8×C19—44no—
173Q8×C19—44no—
174Q8×C19—42no—
175C2×C4×C19—22no—
176C2×C4×C19—22no—
177C2×C4×C19—24no—
178C2×C4×C19—41no—
179C2×C4×C19—41no—
180C2×C4×C19—41no—
181C2×C4×C19—41no—
182C2×C4×C19—42no—
183C2×C4×C19—44no—
184C2×C4×C19—42no—
185C2×C4×C19—44no—
186C2×C4×C19—42no—
187C2×C4×C19—42no—
188C2×C4×C19—42no—
189C2×C4×C19#12011yescharacteristic
190C2×C4×C19#12111yescharacteristic
191C2×C4×C19#12111yescharacteristic
192C2×C4×C19#12711yescharacteristic
193C22⋊D19—81no—
194C22⋊D19—81no—
195C22⋊D19—81no—
196C22⋊D19—81no—
197C2×Dic19—24no—
198C2×Dic19—22no—
199C2×Dic19—22no—
200C2×Dic19—22no—
201C2×Dic19—42no—
202C2×Dic19—44no—
203C2×Dic19—44no—
204C2×Dic19—41no—
205C2×Dic19—41no—
206C2×Dic19—42no—
207C2×Dic19—41no—
208C2×Dic19—41no—
209C2×Dic19—42no—
210C2×Dic19—41no—
211C2×Dic19—41no—
212C2×Dic19—41no—
213C2×Dic19—41no—
214C2×Dic19—42no—
215C2×Dic19—81no—
216D76—42no—
217D76—81no—
218C8×C19—81no—
219C19⋊C8—42no—
220C2×#448—191no—
221#2618—191no—
222C2×#395—191no—
223#1787D1911yescharacteristic, complemented
224C2×#327—191no—
225C2×#324—191no—
226#1294—191no—
227C22×C19—22no—
228C22×C19—22no—
229C22×C19—22no—
230C22×C19—22no—
231C22×C19—21no—
232C22×C19—21no—
233C22×C19—21no—
234C22×C19—21no—
235C22×C19#39211yescharacteristic
236C22×C19#44811yescharacteristic
237C22×C19#44911yescharacteristic
238C22×C19#45011yescharacteristic
239C22×C19#45211yescharacteristic
240C22×C19#45612yes—
241C22×C19B(4,𝔽2)12yes—
242C22×C19#46511yescharacteristic
243C22×C19#46811yescharacteristic
244C2×D19—82no—
245C2×D19—82no—
246C2×D19—81no—
247C2×D19—81no—
248C2×D19—81no—
249C4×C19—21no—
250C4×C19—21no—
251C4×C19—21no—
252C4×C19—21no—
253C4×C19—44no—
254C4×C19—82no—
255Dic19—44no—
256Dic19—42no—
257Dic19—81no—
258Dic19—81no—
259C23×Q8C2×D1911yescharacteristic
260C22×SD16—381no—
261C2×#123—381no—
262C2×#121—191no—
263C22×C4⋊C4—191no—
264C22×C4⋊C4—381no—
265#448—382no—
266#448—382no—
267C2×#103—22no—
268C2×#103—381no—
269C2×C22⋊C8—191no—
270C2×C22⋊C8C2×D1911yescharacteristic
271#398—381no—
272#396—382no—
273#395—382no—
274#395—382no—
275#394—381no—
276#386—381no—
277#380C2×D1911yescharacteristic
278C2×#95—191no—
279C2×#95—381no—
280#327—382no—
281#324—382no—
282C2×C19—21no—
283C2×C19—21no—
284C2×C19—21no—
285C2×C19—21no—
286C2×C19#160312yes—
287C2×C19#160412yes—
288C2×C19#200011yescharacteristic
289C2×C19#200511yescharacteristic
290C2×C19#202111yescharacteristic
291D19—161no—
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—44no—
298C22×Q8D7612yes—
299C22×D4—191no—
300C22×D4—381no—
301C23×C4—21no—
302C23×C4—191no—
303C23×C4—191no—
304C23×C4—381no—
305C23×C4C22×D1911yescharacteristic
306C2×SD16—384no—
307C2×SD16—764no—
308C22×C8—21no—
309C22×C8—381no—
310#123—762no—
311#123—762no—
312#121—381no—
313#121—381no—
314#121—381no—
315#121—381no—
316C2×C4⋊C4—191no—
317C2×C4⋊C4—384no—
318C2×C4⋊C4—382no—
319C2×C4⋊C4—381no—
320C2×C4⋊C4—381no—
321C2×C4⋊C4—381no—
322C2×C4⋊C4—381no—
323C2×C4⋊C4—381no—
324C2×C4⋊C4—381no—
325C2×C4⋊C4—764no—
326C2×C4⋊C4C22⋊D1912yes—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—382no—
329C2×C22⋊C4—381no—
330C2×C22⋊C4—382no—
331#103—44no—
332#103—384no—
333C22⋊C8—21no—
334C22⋊C8—21no—
335C22⋊C8—192no—
336C22⋊C8—381no—
337#95—21no—
338#95—192no—
339#95—384no—
340#95—382no—
341#95—381no—
342C19#991711yescharacteristic, complemented, Sylow
343C24—381no—
344C24D4×D1911yescharacteristic
345C2×Q8—24no—
346C2×Q8—24no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—44no—
350C2×Q8—42no—
351C2×Q8—42no—
352C2×Q8—44no—
353C2×Q8—44no—
354C2×Q8—44no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×D4—381no—
358C2×D4—381no—
359C2×D4—762no—
360C2×D4—761no—
361C2×D4—761no—
362C2×D4—761no—
363C2×D4—761no—
364C2×D4—761no—
365C2×D4—761no—
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—192no—
374C22×C4—384no—
375C22×C4—381no—
376C22×C4—382no—
377C22×C4—381no—
378C22×C4—381no—
379C22×C4—381no—
380C22×C4—381no—
381C22×C4—381no—
382C22×C4—381no—
383C22×C4—381no—
384C22×C4—381no—
385C22×C4—381no—
386C22×C4—762no—
387C22×C4—761no—
388C22×C4—761no—
389C22×C4—762no—
390C22×C4C2×D7611yescharacteristic
391C22×C4#6454111yescharacteristic
392C22×C4D4×D1911yescharacteristic
393C22×C4D4×D1911yescharacteristic
394C22×C4D4×D1911yescharacteristic
395C22×C4C2×C22⋊D1911yescharacteristic
396SD16—768no—
397C2×C8—42no—
398C2×C8—41no—
399C2×C8—382no—
400C2×C8—762no—
401C4⋊C4—42no—
402C4⋊C4—381no—
403C4⋊C4—381no—
404C4⋊C4—768no—
405C4⋊C4—764no—
406C4⋊C4—761no—
407C4⋊C4—761no—
408C4⋊C4—761no—
409C4⋊C4—761no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—764no—
413C22⋊C4—761no—
414C22⋊C4—761no—
415C22⋊C4—1522no—
416C23—22no—
417C23—22no—
418C23—761no—
419C23—761no—
420C23—761no—
421C23—762no—
422C23—762no—
423C23#1059732811yescharacteristic
424C23#1059733011yescharacteristic
425C23SD16×D1911yescharacteristic
426C23#1059736011yescharacteristic
427C23#1059736411yescharacteristic
428C23#1059736511yescharacteristic
429C23#1059738311yescharacteristic
430Q8—24no—
431Q8—24no—
432Q8—44no—
433Q8—42no—
434Q8—42no—
435Q8—44no—
436D4—762no—
437D4—1521no—
438D4—1521no—
439D4—1521no—
440D4—1521no—
441D4—1521no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—44no—
451C2×C4—42no—
452C2×C4—44no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—384no—
457C2×C4—382no—
458C2×C4—382no—
459C2×C4—382no—
460C2×C4—762no—
461C2×C4—764no—
462C2×C4—764no—
463C2×C4—761no—
464C2×C4—761no—
465C2×C4—762no—
466C2×C4—761no—
467C2×C4—761no—
468C2×C4—762no—
469C2×C4—761no—
470C2×C4—761no—
471C2×C4—761no—
472C2×C4—761no—
473C2×C4—762no—
474C2×C4—1521no—
475C2×C4#1059732811yescharacteristic
476C2×C4#1059733011yescharacteristic
477C2×C4#1059737611yescharacteristic
478C2×C4#1059738611yescharacteristic
479C8—81no—
480C8—762no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—1521no—
490C22—1522no—
491C22—1522no—
492C22—1521no—
493C22—1521no—
494C22#1192645311yescharacteristic
495C22#1192668411yescharacteristic
496C22#1192669211yescharacteristic
497C22#1192669311yescharacteristic
498C22#1192670511yescharacteristic
499C22#1192672512yes—
500C22#1192673012yes—
501C22#1192677611yescharacteristic
502C22#1192679311yescharacteristic
503C4—21no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—44no—
508C4—82no—
509C4—764no—
510C4—762no—
511C4—1521no—
512C4—1521no—
513C2—21no—
514C2—21no—
515C2—21no—
516C2—21no—
517C2—3041no—
518C2#1456259712yes—
519C2#1456260212yes—
520C2#1456463711yescharacteristic
521C2#1456467211yescharacteristic
522C2#1456476111yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1787C2
socleC23×C19#120
prime radicalC2×#10597376C22
hypercenter#1787D19
hypocenterC19#9917
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
3. C2×#11926463C2semidirect
5. C2×#11926269C2semidirect
6. #14561513C2semidirect
7. C19×#1787C2semidirect
130. C22×Dic19SD16semidirect
223. #1787D19semidirect
342. C19#9917semidirect

Maximal subgroups

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

subgroupindex
C2×#119266832
#145693802
C2×#119264632
C2×#119262792
C2×#119262692
#145615132
C19×#17872
#991719