Finite Group Databasebeta

← #18083295

Subgroups — #18083295

Order 4864.

632 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 101 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#14573639C211yesmaximal, characteristic, complemented
2#14568532C211yesmaximal, characteristic
3#14562199C211yesmaximal, characteristic, complemented
4#14562059C211yesmaximal, characteristic, complemented
5#14562026C211yesmaximal, characteristic, complemented
6#14561495C211yesmaximal, characteristic, complemented
7C19×#3077C211yesmaximal, characteristic, complemented
8C2×#10597384—21no—
9C2×C4×D76C2211yescharacteristic
10#11926872—21no—
11#11926831—21no—
12#11926746—21no—
13#11926694—21no—
14C4×#64527—22no—
15#11926597C2211yescharacteristic
16#11926597C2211yescharacteristic
17#11926469—21no—
18#11926453—21no—
19#11926423—22no—
20#11926410C2211yescharacteristic
21#11926401—21no—
22#11926281—22no—
23D4⋊(C19⋊C8)—22no—
24#11926271—22no—
25C19×#533C2211yescharacteristic
26C2×C4×D4×C19C2211yescharacteristic
27C19×#478—22no—
28C19×#476—21no—
29C19×#474—21no—
30C19×#428—21no—
31C19×#423C2211yescharacteristic
32C19×#418—21no—
33C22×D4×C19D411yescharacteristic
34C23×C4×C19—21no—
35C22×C22⋊D19—22no—
36C22×D76D411yescharacteristic
37C22×C4×D19—21no—
38C2×M16×C19—21no—
39C19×C4⋊Q8D411yescharacteristic, complemented
40C19×C4⋊Q8D411yescharacteristic, complemented
41C19×#125—21no—
42C19×C22⋊Q8—21no—
43C19×C22⋊Q8—21no—
44C4×Q8×C19—21no—
45C4×Q8×C19—21no—
46C4×D4×C19—21no—
47C4×D4×C19—21no—
48C4×D4×C19—21no—
49C4×D4×C19—21no—
50C19×#117—21no—
51C2×C4⋊C4×C19D411yescharacteristic
52C2×C22⋊C4×C19—21no—
53C2×C42×C19C2311yescharacteristic
54C2×C22⋊Dic19—22no—
55C2×#64527—22no—
56#10597384—42no—
57#10597384—42no—
58C2×(C2×D19)⋊C4—21no—
59C2×(C2×D19)⋊C4—22no—
60C2×C4⋊Dic19—21no—
61C2×C4⋊Dic19D411yescharacteristic
62C4×D76—21no—
63C4×D76—21no—
64C4×D76—21no—
65C4×D76—21no—
66C19×#107—22no—
67C19×#106—22no—
68C19×C4⋊C8—21no—
69C19×C4⋊C8D412yescomplemented
70C19×#102—22no—
71C19×#102—22no—
72#10597292—22no—
73C19⋊#95—22no—
74C19⋊#95—21no—
75C19⋊#95D412yes—
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)—21no—
78#10597266—22no—
79#10597265—22no—
80C4⋊(C19⋊C8)—21no—
81C4⋊(C19⋊C8)—21no—
82C4×C19⋊C8—21no—
83C4×C19⋊C8D412yescomplemented
84C24×C19—21no—
85C23×D19—21no—
86C2×Q8×C19—21no—
87C2×Q8×C19—21no—
88C2×D4×C19—21no—
89C2×D4×C19—21no—
90C2×D4×C19—21no—
91C2×D4×C19—21no—
92C2×D4×C19—21no—
93C2×D4×C19SD1612yescomplemented
94C22×C4×C19—21no—
95C22×C4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19—82no—
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19C2×D411yescharacteristic
101C2×C22⋊D19—44no—
102C2×C22⋊D19—44no—
103C2×C22⋊D19—82no—
104C22×Dic19—21no—
105C22×Dic19—22no—
106C2×D76—21no—
107C2×D76—21no—
108C2×D76—42no—
109C2×C4×D19—41no—
110C2×C4×D19—41no—
111C2×C4×D19—41no—
112C2×C4×D19—41no—
113C2×C4×D19—41no—
114C2×C4×D19—41no—
115M16×C19—41no—
116M16×C19—41no—
117C2×C8×C19—22no—
118C4⋊C4×C19—21no—
119C4⋊C4×C19—21no—
120C4⋊C4×C19—21no—
121C4⋊C4×C19—21no—
122C4⋊C4×C19—21no—
123C4⋊C4×C19—21no—
124C4⋊C4×C19—41no—
125C4⋊C4×C19—41no—
126C22⋊C4×C19—41no—
127C22⋊C4×C19—41no—
128C22⋊C4×C19—41no—
129C42×C19—41no—
130C42×C19C2×D411yescharacteristic
131C42×C19C2×D411yescharacteristic
132C42×C19C2×D411yescharacteristic
133C42×C19#4111yescharacteristic
134C22⋊Dic19—44no—
135#64527—44no—
136(C2×D19)⋊C4—41no—
137(C2×D19)⋊C4—41no—
138(C2×D19)⋊C4—82no—
139C4⋊Dic19—21no—
140C4⋊Dic19—21no—
141C4⋊Dic19—41no—
142C4⋊Dic19—41no—
143C2×C19⋊C8—22no—
144C2×C19⋊C8—41no—
145#10000—191nomaximal, Sylow
146C23×C19—22no—
147C23×C19—42no—
148C23×C19—42no—
149C23×C19—41no—
150C23×C19—41no—
151C23×C19#12011yescharacteristic
152C22×D19—22no—
153C22×D19—41no—
154C22×D19—41no—
155C22×D19—41no—
156C22×D19—41no—
157C22×D19—41no—
158C22×D19—41no—
159Q8×C19—42no—
160Q8×C19—81no—
161D4×C19—22no—
162D4×C19—22no—
163D4×C19—41no—
164D4×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19—42no—
168C2×C4×C19—41no—
169C2×C4×C19—41no—
170C2×C4×C19—41no—
171C2×C4×C19—82no—
172C2×C4×C19—82no—
173C2×C4×C19#12011yescharacteristic
174C2×C4×C19#12011yescharacteristic
175C2×C4×C19#12111yescharacteristic
176C2×C4×C19#12111yescharacteristic
177C2×C4×C19#12111yescharacteristic
178C2×C4×C19#12711yescharacteristic
179C2×C4×C19C2×SD1611yescharacteristic
180C2×C4×C19#13511yescharacteristic
181C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C19#13711yescharacteristic
183C22⋊D19—88no—
184C2×Dic19—42no—
185C2×Dic19—42no—
186C2×Dic19—41no—
187C2×Dic19—42no—
188C2×Dic19—41no—
189C2×Dic19—41no—
190D76—22no—
191D76—22no—
192D76—41no—
193D76—41no—
194C4×D19—81no—
195C4×D19—81no—
196C4×D19—81no—
197C4×D19—81no—
198C8×C19—42no—
199C19⋊C8—42no—
200C19⋊C8—81no—
201#3101—191no—
202#3077D1911yescharacteristic, complemented
203#2535—191no—
204#1518—191no—
205#1486—191no—
206#1478—191no—
207#1286—191no—
208C22×C19—21no—
209C22×C19—21no—
210C22×C19—44no—
211C22×C19—42no—
212C22×C19—82no—
213C22×C19—81no—
214C22×C19—81no—
215C22×C19#39211yescharacteristic
216C22×C19#45011yescharacteristic
217C22×C19#45211yescharacteristic
218C2×D19—42no—
219C2×D19—42no—
220C2×D19—42no—
221C2×D19—81no—
222C2×D19—81no—
223C2×D19—81no—
224C2×D19—81no—
225C4×C19—21no—
226C4×C19—21no—
227C4×C19—21no—
228C4×C19—21no—
229C4×C19—81no—
230C4×C19—81no—
231C4×C19—81no—
232C4×C19#44811yescharacteristic
233C4×C19#44911yescharacteristic
234C4×C19#46511yescharacteristic
235C4×C19#46811yescharacteristic
236Dic19—82no—
237Dic19—81no—
238#533C2×D1911yescharacteristic
239C2×#121—381no—
240C2×C4×D4—191no—
241C2×C4×D4C2×D1911yescharacteristic
242#483—381no—
243#478—22no—
244#476—21no—
245#476—381no—
246#474—21no—
247#461—381no—
248#450—381no—
249C4×SD16—382no—
250#431—191no—
251#431—191no—
252#428—21no—
253#423C2×D1911yescharacteristic
254#418—21no—
255#397—381no—
256#392—381no—
257#386—382no—
258#382—191no—
259#380—381no—
260#328—382no—
261D4⋊C8—382no—
262D4⋊C8—382no—
263C2×C19—21no—
264C2×C19—21no—
265C2×C19—82no—
266C2×C19#200011yescharacteristic
267C2×C19#200811yescharacteristic
268C2×C19#201011yescharacteristic
269D19—82no—
270C22×D4—191no—
271C22×D4—382no—
272C22×D4C22⋊D1911yescharacteristic
273C23×C4—21no—
274C23×C4—381no—
275C2×SD16—382no—
276C2×M16—21no—
277C4⋊Q8C22⋊D1911yescharacteristic, complemented
278C4⋊Q8C22⋊D1911yescharacteristic, complemented
279#125—21no—
280C22⋊Q8—21no—
281C22⋊Q8—21no—
282#121—762no—
283#121—762no—
284C4×Q8—21no—
285C4×Q8—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—381no—
291C4×D4—381no—
292C4×D4—381no—
293C4×D4—381no—
294#117—21no—
295C2×C4⋊C4—191no—
296C2×C4⋊C4—381no—
297C2×C4⋊C4C22⋊D1911yescharacteristic
298C2×C22⋊C4—21no—
299C2×C22⋊C4—382no—
300C2×C22⋊C4—381no—
301C2×C22⋊C4—382no—
302C2×C42C22×D1911yescharacteristic
303#107—22no—
304#106—22no—
305#106—382no—
306C4⋊C8—21no—
307C4⋊C8—381no—
308C4⋊C8—381no—
309C4⋊C8C22⋊D1912yescomplemented
310#103—382no—
311#102—22no—
312#102—22no—
313#102—382no—
314C22⋊C8—381no—
315C22⋊C8—381no—
316C4×C8—192no—
317C4×C8—381no—
318#95—192no—
319#95—382no—
320#95—381no—
321C19#1000011yescharacteristic, complemented, Sylow
322C24—21no—
323C24—381no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—381no—
332C2×D4—381no—
333C2×D4—762no—
334C2×D4—764no—
335C2×D4—764no—
336C2×D4—1522no—
337C2×D4#6452712yescomplemented
338C22×C4—21no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—82no—
342C22×C4—382no—
343C22×C4—381no—
344C22×C4—761no—
345C22×C4—761no—
346C22×C4—761no—
347C22×C4—761no—
348C22×C4—761no—
349C22×C4—761no—
350C22×C4D4×D1911yescharacteristic
351C22×C4D4×D1911yescharacteristic
352C22×C4C2×C22⋊D1911yescharacteristic
353SD16—764no—
354M16—41no—
355M16—41no—
356C2×C8—22no—
357C2×C8—382no—
358C2×C8—761no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—381no—
368C4⋊C4—381no—
369C4⋊C4—761no—
370C4⋊C4—761no—
371C22⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—764no—
375C22⋊C4—761no—
376C22⋊C4—761no—
377C22⋊C4—1522no—
378C42—41no—
379C42D4×D1911yescharacteristic
380C42#6454311yescharacteristic
381C42C2×C22⋊D1911yescharacteristic
382C42C2×C22⋊D1911yescharacteristic
383C23—22no—
384C23—42no—
385C23—42no—
386C23—41no—
387C23—41no—
388C23—382no—
389C23—761no—
390C23—761no—
391C23—761no—
392C23—761no—
393C23—761no—
394C23—761no—
395C23#1059738311yescharacteristic
396Q8—42no—
397Q8—81no—
398D4—22no—
399D4—22no—
400D4—41no—
401D4—41no—
402D4—382no—
403D4—382no—
404D4—761no—
405D4—761no—
406D4—1528no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—762no—
416C2×C4—762no—
417C2×C4—761no—
418C2×C4—762no—
419C2×C4—761no—
420C2×C4—761no—
421C2×C4—1521no—
422C2×C4—1521no—
423C2×C4—1521no—
424C2×C4—1521no—
425C2×C4#1059738311yescharacteristic
426C2×C4#1059738411yescharacteristic
427C2×C4#1059738511yescharacteristic
428C2×C4#1059738511yescharacteristic
429C2×C4#1059738611yescharacteristic
430C2×C4C2×#6452711yescharacteristic
431C2×C4#1059738811yescharacteristic
432C2×C4#1059739511yescharacteristic
433C2×C4#1059739611yescharacteristic
434C2×C4#1059739911yescharacteristic
435C8—42no—
436C8—762no—
437C8—1521no—
438C22—21no—
439C22—21no—
440C22—44no—
441C22—42no—
442C22—82no—
443C22—81no—
444C22—81no—
445C22—762no—
446C22—762no—
447C22—762no—
448C22—1521no—
449C22—1521no—
450C22—1521no—
451C22—1521no—
452C22#1192645211yescharacteristic
453C22#1192669411yescharacteristic
454C22#1192670411yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4—1522no—
463C4—1521no—
464C4#1192668311yescharacteristic
465C4#1192668911yescharacteristic
466C4#1192677511yescharacteristic
467C4#1192679211yescharacteristic
468C2—21no—
469C2—21no—
470C2—82no—
471C2—1522no—
472C2#1456463611yescharacteristic
473C2#1456468611yescharacteristic
474C2#1456469911yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#3077C2
socleC22×C19#392
prime radical#14568532C2
hypercenter#3077D19
hypocenterC19#10000
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #14573639C2semidirect
3. #14562199C2semidirect
4. #14562059C2semidirect
5. #14562026C2semidirect
6. #14561495C2semidirect
7. C19×#3077C2semidirect
39. C19×C4⋊Q8D4semidirect
40. C19×C4⋊Q8D4semidirect
69. C19×C4⋊C8D4semidirect
83. C4×C19⋊C8D4semidirect
93. C2×D4×C19SD16semidirect
202. #3077D19semidirect
277. C4⋊Q8C22⋊D19semidirect
278. C4⋊Q8C22⋊D19semidirect
309. C4⋊C8C22⋊D19semidirect
321. C19#10000semidirect
337. C2×D4#64527semidirect

Maximal subgroups

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

subgroupindex
#145736392
#145685322
#145621992
#145620592
#145620262
#145614952
C19×#30772
#1000019