Finite Group Databasebeta

← #18073885

Subgroups — #18073885

Order 4864.

1238 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1238 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C22×#10597375C211yesmaximal, characteristic
2#14563545C211yesmaximal, characteristic, complemented
3C2×#11926269C212yesmaximal, complemented
4C2×#11926267C212yesmaximal, complemented
5C19×#1779C211yesmaximal, characteristic, complemented
6C23×C22⋊D19C411yescharacteristic
7C2×#10597375—24no—
8C2×#10597375—24no—
9C2×#10597375—22no—
10C2×#10597375—22no—
11C22×Dic19⋊C4C411yescharacteristic
12C22×Dic19⋊C4C2211yescharacteristic
13C22×C22⋊Dic19C411yescharacteristic
14C22×(C2×D19)⋊C4C411yescharacteristic
15C22×(C2×D19)⋊C4C2211yescharacteristic
16C2×C22⋊(C19⋊C8)—22no—
17C2×C22⋊(C19⋊C8)C2212yes—
18#11926269—24no—
19#11926267—24no—
20C24×C4×C19C2211yescharacteristic
21C2×C19×C22⋊C8—22no—
22C2×C19×C22⋊C8C2212yes—
23C25×C19C2×C411yescharacteristic
24C24×D19C2×C411yescharacteristic
25C23×C4×C19—22no—
26C23×C4×C19—22no—
27C23×C4×C19—44no—
28C23×C4×C19C2×C411yescharacteristic
29C23×C4×C19D412yes—
30C23×C4×C19D412yes—
31C23×C4×C19C2311yescharacteristic
32C22×C22⋊D19—22no—
33C22×C22⋊D19—22no—
34C22×C22⋊D19—22no—
35C22×C22⋊D19—44no—
36C23×Dic19C2×C411yescharacteristic
37C23×Dic19C2×C411yescharacteristic
38C23×Dic19C2×C411yescharacteristic
39C22×C8×C19—22no—
40C2×C22⋊Dic19—22no—
41C2×C22⋊Dic19—22no—
42C2×C22⋊Dic19—22no—
43#10597375—216no—
44#10597375—216no—
45C2×(C2×D19)⋊C4—22no—
46C2×(C2×D19)⋊C4—22no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—22no—
49C2×(C2×D19)⋊C4—21no—
50C2×(C2×D19)⋊C4—22no—
51C2×(C2×D19)⋊C4D414yes—
52C2×Dic19⋊C4—22no—
53C2×Dic19⋊C4—21no—
54C2×Dic19⋊C4—22no—
55C2×Dic19⋊C4—21no—
56C2×Dic19⋊C4—22no—
57C2×Dic19⋊C4—22no—
58C2×Dic19⋊C4D414yes—
59C22×C19⋊C8—22no—
60C19×C22⋊C8—22no—
61C19×C22⋊C8—22no—
62C19×C22⋊C8—44no—
63C22⋊(C19⋊C8)—22no—
64C22⋊(C19⋊C8)—22no—
65C22⋊(C19⋊C8)—44no—
66C24×C19—24no—
67C24×C19—21no—
68C24×C19—21no—
69C24×C19—22no—
70C24×C19—22no—
71C24×C19—42no—
72C24×C19C22⋊C412yes—
73C24×C19C22×C411yescharacteristic
74C23×D19—21no—
75C23×D19—21no—
76C23×D19—22no—
77C23×D19—22no—
78C23×D19—42no—
79C23×D19—42no—
80C23×D19C22⋊C412yes—
81C22×C4×C19—24no—
82C22×C4×C19—24no—
83C22×C4×C19—21no—
84C22×C4×C19—21no—
85C22×C4×C19—24no—
86C22×C4×C19—24no—
87C22×C4×C19—42no—
88C22×C4×C19—42no—
89C22×C4×C19—42no—
90C22×C4×C19—42no—
91C22×C4×C19—48no—
92C22×C4×C19—48no—
93C22×C4×C19C22⋊C412yes—
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D412yes—
96C22×C4×C19C2×D412yes—
97C22×C4×C19C2×D411yescharacteristic
98C2×C22⋊D19—28no—
99C2×C22⋊D19—48no—
100C2×C22⋊D19—44no—
101C2×C22⋊D19—48no—
102C2×C22⋊D19—44no—
103C22×Dic19—21no—
104C22×Dic19—21no—
105C22×Dic19—21no—
106C22×Dic19—21no—
107C22×Dic19—21no—
108C22×Dic19—21no—
109C22×Dic19—22no—
110C22×Dic19—22no—
111C22×Dic19—42no—
112C22×Dic19—42no—
113C22×Dic19C22⋊C412yes—
114C22×Dic19C22⋊C412yes—
115C22×Dic19C22⋊C412yes—
116C2×C8×C19—44no—
117C2×C8×C19—42no—
118C22⋊Dic19—28no—
119(C2×D19)⋊C4—28no—
120(C2×D19)⋊C4—24no—
121(C2×D19)⋊C4—24no—
122Dic19⋊C4—28no—
123Dic19⋊C4—24no—
124Dic19⋊C4—24no—
125C2×C19⋊C8—44no—
126C2×C19⋊C8—42no—
127#8304—191nomaximal, Sylow
128C23×C19—22no—
129C23×C19—22no—
130C23×C19—24no—
131C23×C19—24no—
132C23×C19—22no—
133C23×C19—22no—
134C23×C19—22no—
135C23×C19—22no—
136C23×C19—22no—
137C23×C19—22no—
138C23×C19—48no—
139C23×C19—48no—
140C23×C19—42no—
141C23×C19—42no—
142C23×C19—42no—
143C23×C19—42no—
144C23×C19#9914yes—
145C23×C19C2×C22⋊C411yescharacteristic
146C23×C19C2×C22⋊C411yescharacteristic
147C23×C19C2×C22⋊C411yescharacteristic
148C23×C19#13112yes—
149C23×C19#13112yes—
150C22×D19—22no—
151C22×D19—24no—
152C22×D19—42no—
153C22×D19—42no—
154C22×D19—42no—
155C22×D19—41no—
156C22×D19—41no—
157C22×D19—42no—
158C22×D19—42no—
159C22×D19—42no—
160C22×D19—42no—
161C22×D19—84no—
162C22×D19—84no—
163C2×C4×C19—22no—
164C2×C4×C19—22no—
165C2×C4×C19—22no—
166C2×C4×C19—22no—
167C2×C4×C19—22no—
168C2×C4×C19—42no—
169C2×C4×C19—42no—
170C2×C4×C19—48no—
171C2×C4×C19—48no—
172C2×C4×C19—42no—
173C2×C4×C19—42no—
174C2×C4×C19#12012yes—
175C2×C4×C19#12012yes—
176C22⋊D19—416no—
177C2×Dic19—22no—
178C2×Dic19—22no—
179C2×Dic19—22no—
180C2×Dic19—24no—
181C2×Dic19—42no—
182C2×Dic19—42no—
183C2×Dic19—42no—
184C2×Dic19—41no—
185C2×Dic19—41no—
186C2×Dic19—42no—
187C2×Dic19—42no—
188C2×Dic19—42no—
189C2×Dic19—42no—
190C8×C19—82no—
191C19⋊C8—82no—
192C22×#123—191no—
193#1779—191no—
194#1779D1911yescharacteristic, complemented
195C2×#324—192no—
196C2×#323—192no—
197C22×C19—24no—
198C22×C19—24no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—21no—
203C22×C19—24no—
204C22×C19—24no—
205C22×C19—24no—
206C22×C19—48no—
207C22×C19—48no—
208C22×C19—42no—
209C22×C19—42no—
210C22×C19—42no—
211C22×C19—42no—
212C22×C19#37911yescharacteristic
213C22×C19#40812yes—
214C22×C19#40812yes—
215C22×C19#40811yescharacteristic
216C22×C19#40811yescharacteristic
217C22×C19C2×#9912yes—
218C22×C19#41312yes—
219C2×D19—42no—
220C2×D19—42no—
221C2×D19—42no—
222C2×D19—84no—
223C2×D19—82no—
224C2×D19—82no—
225C2×D19—84no—
226C4×C19—22no—
227C4×C19—22no—
228C4×C19—42no—
229Dic19—42no—
230Dic19—42no—
231Dic19—42no—
232C23×D4—191no—
233C24×C4C2×D1911yescharacteristic
234C2×#123—384no—
235C2×#123—384no—
236C2×#123—382no—
237C2×#123—382no—
238C22×C4⋊C4—191no—
239C22×C4⋊C4—191no—
240C22×C22⋊C4—191no—
241C22×C22⋊C4—191no—
242C22×C22⋊C4—191no—
243C2×C22⋊C8—22no—
244C2×C22⋊C8—192no—
245C2×C22⋊C8—382no—
246C2×C22⋊C8C2×D1912yes—
247#324—384no—
248#323—384no—
249C2×C19—22no—
250C2×C19—22no—
251C2×C19—44no—
252C2×C19#146812yes—
253C2×C19#146812yes—
254C2×C19#178011yescharacteristic
255C2×C19#178111yescharacteristic
256C2×C19#178511yescharacteristic
257D19—82no—
258C25—191no—
259C25C4×D1911yescharacteristic
260C22×D4—382no—
261C22×D4—382no—
262C22×D4—382no—
263C22×D4—764no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—44no—
267C23×C4—191no—
268C23×C4—191no—
269C23×C4—191no—
270C23×C4C4×D1911yescharacteristic
271C23×C4D7612yes—
272C23×C4C22⋊D1912yes—
273C23×C4C22×D1911yescharacteristic
274C22×C8—22no—
275C22×C8—382no—
276#123—3816no—
277#123—3816no—
278C2×C4⋊C4—194no—
279C2×C4⋊C4—382no—
280C2×C4⋊C4—382no—
281C2×C4⋊C4—382no—
282C2×C4⋊C4—381no—
283C2×C4⋊C4—382no—
284C2×C4⋊C4—381no—
285C2×C22⋊C4—194no—
286C2×C22⋊C4—382no—
287C2×C22⋊C4—382no—
288C2×C22⋊C4—382no—
289C2×C22⋊C4—382no—
290C2×C22⋊C4—382no—
291C2×C22⋊C4—382no—
292C2×C22⋊C4—381no—
293C2×C22⋊C4—382no—
294C2×C22⋊C4—381no—
295C22⋊C8—22no—
296C22⋊C8—22no—
297C22⋊C8—44no—
298C22⋊C8—382no—
299C22⋊C8—382no—
300C22⋊C8—764no—
301C19#830411yescharacteristic, complemented, Sylow
302C24—24no—
303C24—21no—
304C24—21no—
305C24—22no—
306C24—22no—
307C24—42no—
308C24—192no—
309C24—381no—
310C24—381no—
311C24—382no—
312C24—382no—
313C24—762no—
314C24—762no—
315C24(C2×D19)⋊C412yes—
316C24C2×C4×D1911yescharacteristic
317C2×D4—388no—
318C2×D4—768no—
319C2×D4—764no—
320C2×D4—768no—
321C2×D4—764no—
322C22×C4—24no—
323C22×C4—24no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—48no—
333C22×C4—48no—
334C22×C4—192no—
335C22×C4—192no—
336C22×C4—192no—
337C22×C4—381no—
338C22×C4—381no—
339C22×C4—381no—
340C22×C4—382no—
341C22×C4—382no—
342C22×C4—381no—
343C22×C4—381no—
344C22×C4—381no—
345C22×C4—762no—
346C22×C4—762no—
347C22×C4(C2×D19)⋊C412yes—
348C22×C4C2×D7611yescharacteristic
349C22×C4D4×D1912yes—
350C22×C4D4×D1912yes—
351C22×C4C2×C22⋊D1911yescharacteristic
352C2×C8—44no—
353C2×C8—42no—
354C2×C8—764no—
355C2×C8—762no—
356C4⋊C4—388no—
357C4⋊C4—384no—
358C4⋊C4—384no—
359C22⋊C4—388no—
360C22⋊C4—388no—
361C22⋊C4—384no—
362C22⋊C4—384no—
363C23—22no—
364C23—22no—
365C23—24no—
366C23—24no—
367C23—22no—
368C23—22no—
369C23—22no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—48no—
374C23—48no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23—42no—
379C23—382no—
380C23—384no—
381C23—762no—
382C23—762no—
383C23—762no—
384C23—762no—
385C23—762no—
386C23—761no—
387C23—761no—
388C23—762no—
389C23—762no—
390C23—1524no—
391C23—1524no—
392C23#1059726314yes—
393C23C22⋊C4×D1911yescharacteristic
394C23C22⋊C4×D1911yescharacteristic
395C23#1059734712yes—
396C23#1059735312yes—
397C23C2×(C2×D19)⋊C411yescharacteristic
398D4—7616no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—48no—
407C2×C4—48no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—382no—
411C2×C4—382no—
412C2×C4—382no—
413C2×C4—384no—
414C2×C4—762no—
415C2×C4—762no—
416C2×C4—762no—
417C2×C4—761no—
418C2×C4—761no—
419C2×C4—762no—
420C2×C4—762no—
421C2×C4—762no—
422C2×C4—762no—
423C2×C4#1059732812yes—
424C2×C4#1059738312yes—
425C8—82no—
426C8—1522no—
427C22—24no—
428C22—24no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—24no—
434C22—24no—
435C22—24no—
436C22—48no—
437C22—48no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—42no—
442C22—762no—
443C22—762no—
444C22—762no—
445C22—1524no—
446C22—1524no—
447C22—1522no—
448C22—1522no—
449C22#1192639911yescharacteristic
450C22#1192650912yes—
451C22#1192650912yes—
452C22#1192651011yescharacteristic
453C22#1192651211yescharacteristic
454C22C2×#1059726312yes—
455C22#1192652612yes—
456C4—22no—
457C4—22no—
458C4—42no—
459C4—762no—
460C4—762no—
461C4—762no—
462C2—22no—
463C2—22no—
464C2—44no—
465C2—1522no—
466C2#1456198112yes—
467C2#1456198412yes—
468C2#1456354611yescharacteristic
469C2#1456354911yescharacteristic
470C2#1456356111yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1779C2
socleC23×C19C2×C22⋊C4
prime radicalC23×C22⋊D19C4
cosocleC23×C4×C19C23
hypercenter#1779D19
hypocenterC19#8304
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. #14563545C2semidirect
3. C2×#11926269C2semidirect
4. C2×#11926267C2semidirect
5. C19×#1779C2semidirect
194. #1779D19semidirect
301. C19#8304semidirect

Maximal subgroups

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

subgroupindex
C22×#105973752
#145635452
C2×#119262692
C2×#119262672
C19×#17792
#830419