Finite Group Databasebeta

← #18075148

Subgroups — #18075148

Order 4864.

1266 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 1266 conjugacy classes of subgroups — too many to draw. Only its 119 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×#10597329C211yesmaximal, characteristic
2#14563709C211yesmaximal, characteristic, complemented
3#14563707C212yesmaximal, complemented
4#14563549C212yesmaximal
5C19×#1819C211yesmaximal, characteristic, complemented
6C23×C22⋊D19C2211yescharacteristic
7C23×C4×D19C411yescharacteristic, complemented
8C2×#10597329—24no—
9C2×#10597329—22no—
10C2×#10597329—22no—
11C2×#10597329—24no—
12C22×C4⋊Dic19C411yescharacteristic, complemented
13C22×Dic19⋊C4C411yescharacteristic, complemented
14C22×C22⋊Dic19C2211yescharacteristic
15C22×(C2×D19)⋊C4C411yescharacteristic, complemented
16C2×#10597263—24no—
17#11926400C2212yes—
18#11926311—22no—
19#11926310—24no—
20C22×C22⋊C4×C19C2211yescharacteristic
21C19×#379C2212yes—
22C19×#342—22no—
23C25×C19C2311yescharacteristic
24C24×D19C2×C411yescharacteristic
25C23×C4×C19C2×C411yescharacteristic
26C23×C4×C19C2×C411yescharacteristic
27C22×C22⋊D19—21no—
28C22×C22⋊D19—22no—
29C22×C22⋊D19—21no—
30C22×C22⋊D19—44no—
31C22×C22⋊D19D414yes—
32C23×Dic19C2×C411yescharacteristic
33C23×Dic19C2×C411yescharacteristic
34C23×Dic19C2×C411yescharacteristic
35C22×C4×D19—22no—
36C22×C4×D19—22no—
37C22×C4×D19—22no—
38C22×C4×D19—44no—
39C2×C22⋊C4×C19—22no—
40C2×C22⋊C4×C19—22no—
41C2×C22⋊C4×C19—22no—
42C2×C22⋊C4×C19—22no—
43C2×C22⋊C4×C19—22no—
44C2×C22⋊C4×C19D412yes—
45C2×C22⋊C4×C19D412yes—
46C2×C22⋊Dic19—21no—
47C2×C22⋊Dic19—22no—
48C2×C22⋊Dic19—21no—
49C2×C22⋊Dic19—22no—
50C2×C22⋊Dic19—22no—
51C2×C22⋊Dic19—22no—
52C2×C22⋊Dic19D414yes—
53C2×(C2×D19)⋊C4—22no—
54C2×(C2×D19)⋊C4—22no—
55C2×(C2×D19)⋊C4—22no—
56C2×C4⋊Dic19—22no—
57C2×C4⋊Dic19—22no—
58C2×C4⋊Dic19—22no—
59C2×Dic19⋊C4—22no—
60C2×Dic19⋊C4—22no—
61C2×Dic19⋊C4—22no—
62#10597329—216no—
63#10597329—216no—
64#10597263—48no—
65C24×C19—42no—
66C24×C19—42no—
67C24×C19—42no—
68C24×C19C22×C411yescharacteristic
69C24×C19C2×D411yescharacteristic
70C24×C19C2×D412yes—
71C24×C19C2×D412yes—
72C24×C19C2×D411yescharacteristic
73C23×D19—21no—
74C23×D19—21no—
75C23×D19—24no—
76C23×D19—42no—
77C23×D19—42no—
78C23×D19C22⋊C412yes—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—42no—
84C22×C4×C19—42no—
85C22×C4×C19—42no—
86C22×C4×C19C22⋊C412yes—
87C22×C4×C19C22⋊C412yes—
88C2×C22⋊D19—24no—
89C2×C22⋊D19—24no—
90C2×C22⋊D19—28no—
91C2×C22⋊D19—44no—
92C2×C22⋊D19—44no—
93C2×C22⋊D19—48no—
94C2×C22⋊D19—44no—
95C22×Dic19—21no—
96C22×Dic19—21no—
97C22×Dic19—21no—
98C22×Dic19—21no—
99C22×Dic19—21no—
100C22×Dic19—21no—
101C22×Dic19—42no—
102C22×Dic19—42no—
103C22×Dic19—42no—
104C22×Dic19—42no—
105C22×Dic19C22⋊C412yes—
106C22×Dic19C22⋊C412yes—
107C22×Dic19C22⋊C412yes—
108C2×C4×D19—28no—
109C2×C4×D19—48no—
110C2×C4×D19—44no—
111C2×C4×D19—48no—
112C2×C4×D19—44no—
113C22⋊C4×C19—24no—
114C22⋊C4×C19—24no—
115C22⋊C4×C19—44no—
116C22⋊C4×C19—44no—
117C22⋊C4×C19—44no—
118C22⋊Dic19—24no—
119C22⋊Dic19—24no—
120C22⋊Dic19—44no—
121C22⋊Dic19—44no—
122C22⋊Dic19—44no—
123(C2×D19)⋊C4—28no—
124C4⋊Dic19—28no—
125Dic19⋊C4—28no—
126#8543—191nomaximal, Sylow
127C23×C19—22no—
128C23×C19—22no—
129C23×C19—22no—
130C23×C19—24no—
131C23×C19—22no—
132C23×C19—24no—
133C23×C19—22no—
134C23×C19—41no—
135C23×C19—42no—
136C23×C19—41no—
137C23×C19—41no—
138C23×C19—42no—
139C23×C19—42no—
140C23×C19—42no—
141C23×C19—41no—
142C23×C19—88no—
143C23×C19C2×C22⋊C411yescharacteristic
144C23×C19C2×C22⋊C411yescharacteristic
145C23×C19C2×C22⋊C411yescharacteristic
146C23×C19#12012yes—
147C23×C19#12012yes—
148C22×D19—24no—
149C22×D19—24no—
150C22×D19—22no—
151C22×D19—22no—
152C22×D19—416no—
153C22×D19—42no—
154C22×D19—42no—
155C22×D19—42no—
156C22×D19—42no—
157C22×D19—42no—
158C22×D19—42no—
159C22×D19#9914yes—
160C2×C4×C19—22no—
161C2×C4×C19—22no—
162C2×C4×C19—42no—
163C2×C4×C19—42no—
164C2×C4×C19—42no—
165C2×C4×C19—42no—
166C2×C4×C19—42no—
167C2×C4×C19—42no—
168C2×C4×C19—82no—
169C2×C4×C19—82no—
170C2×C4×C19—82no—
171C22⋊D19—48no—
172C22⋊D19—48no—
173C2×Dic19—22no—
174C2×Dic19—22no—
175C2×Dic19—22no—
176C2×Dic19—24no—
177C2×Dic19—42no—
178C2×Dic19—42no—
179C2×Dic19—42no—
180C2×Dic19—42no—
181C2×Dic19—42no—
182C2×Dic19—42no—
183C2×Dic19—42no—
184C2×Dic19—42no—
185C2×Dic19—82no—
186C2×Dic19—82no—
187C2×Dic19—82no—
188C4×D19—416no—
189C22×#123—191no—
190#1819—192no—
191#1819—191no—
192#1819D1911yescharacteristic, complemented
193#1781—192no—
194C22×C19—28no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—22no—
202C22×C19—22no—
203C22×C19—22no—
204C22×C19—22no—
205C22×C19—22no—
206C22×C19—22no—
207C22×C19—84no—
208C22×C19—82no—
209C22×C19—84no—
210C22×C19—82no—
211C22×C19#37911yescharacteristic
212C22×C19C2×#9912yes—
213C22×C19#41012yes—
214C22×C19#41012yes—
215C2×D19—24no—
216C2×D19—44no—
217C2×D19—48no—
218C2×D19—48no—
219C2×D19—42no—
220C2×D19—42no—
221C2×D19—44no—
222C4×C19—42no—
223C4×C19—42no—
224C4×C19—162no—
225Dic19—42no—
226Dic19—42no—
227Dic19—42no—
228Dic19—162no—
229C23×D4—191no—
230C24×C4—191no—
231C2×#123—384no—
232C2×#123—384no—
233C2×#123—382no—
234C2×#123—382no—
235C22×C4⋊C4—191no—
236C22×C4⋊C4—191no—
237C22×C22⋊C4—191no—
238C22×C22⋊C4—191no—
239C22×C22⋊C4C2×D1911yescharacteristic
240C2×#99—384no—
241#379—192no—
242#379C2×D1912yes—
243#342—22no—
244#342—384no—
245#342—382no—
246C2×C19—22no—
247C2×C19—22no—
248C2×C19—22no—
249C2×C19—42no—
250C2×C19—42no—
251C2×C19#178111yescharacteristic
252C2×C19#178211yescharacteristic
253C2×C19#178211yescharacteristic
254D19—44no—
255C25—191no—
256C25C22×D1911yescharacteristic
257C22×D4—194no—
258C22×D4—381no—
259C22×D4—382no—
260C22×D4—381no—
261C22×D4—764no—
262C23×C4—191no—
263C23×C4—191no—
264C23×C4—191no—
265C23×C4—382no—
266C23×C4—382no—
267C23×C4—382no—
268C23×C4—764no—
269C23×C4C4×D1911yescharacteristic
270C23×C4C4×D1911yescharacteristic
271#123—3816no—
272#123—3816no—
273C2×C4⋊C4—382no—
274C2×C4⋊C4—382no—
275C2×C4⋊C4—382no—
276C2×C4⋊C4—382no—
277C2×C4⋊C4—382no—
278C2×C4⋊C4—382no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—194no—
285C2×C22⋊C4—382no—
286C2×C22⋊C4—382no—
287C2×C22⋊C4—381no—
288C2×C22⋊C4—382no—
289C2×C22⋊C4—381no—
290C2×C22⋊C4—382no—
291C2×C22⋊C4—382no—
292C2×C22⋊C4—382no—
293C2×C22⋊C4—382no—
294C2×C22⋊C4D7612yes—
295C2×C22⋊C4C22⋊D1912yes—
296#99—768no—
297C19#854311yescharacteristic, complemented, Sylow
298C24—42no—
299C24—42no—
300C24—42no—
301C24—192no—
302C24—384no—
303C24—381no—
304C24—381no—
305C24—762no—
306C24—762no—
307C24C2×C4×D1911yescharacteristic
308C24C2×D7611yescharacteristic
309C24D4×D1912yes—
310C24D4×D1912yes—
311C24C2×C22⋊D1911yescharacteristic
312C2×D4—388no—
313C2×D4—384no—
314C2×D4—384no—
315C2×D4—764no—
316C2×D4—764no—
317C2×D4—768no—
318C2×D4—764no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—192no—
327C22×C4—192no—
328C22×C4—192no—
329C22×C4—388no—
330C22×C4—381no—
331C22×C4—381no—
332C22×C4—381no—
333C22×C4—381no—
334C22×C4—381no—
335C22×C4—381no—
336C22×C4—764no—
337C22×C4—768no—
338C22×C4—764no—
339C22×C4—768no—
340C22×C4—762no—
341C22×C4—762no—
342C22×C4—762no—
343C22×C4—762no—
344C22×C4(C2×D19)⋊C412yes—
345C22×C4(C2×D19)⋊C412yes—
346C4⋊C4—388no—
347C4⋊C4—388no—
348C22⋊C4—24no—
349C22⋊C4—24no—
350C22⋊C4—44no—
351C22⋊C4—44no—
352C22⋊C4—44no—
353C22⋊C4—388no—
354C22⋊C4—384no—
355C22⋊C4—384no—
356C22⋊C4—764no—
357C22⋊C4—764no—
358C22⋊C4—764no—
359C23—22no—
360C23—22no—
361C23—22no—
362C23—24no—
363C23—24no—
364C23—22no—
365C23—22no—
366C23—41no—
367C23—42no—
368C23—41no—
369C23—41no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23—41no—
374C23—88no—
375C23—194no—
376C23—384no—
377C23—384no—
378C23—382no—
379C23—382no—
380C23—762no—
381C23—762no—
382C23—7616no—
383C23—762no—
384C23—762no—
385C23—762no—
386C23—762no—
387C23C22⋊C4×D1911yescharacteristic
388C23C22⋊C4×D1911yescharacteristic
389C23#1059732812yes—
390C23C2×(C2×D19)⋊C411yescharacteristic
391C23#1059738312yes—
392D4—768no—
393D4—768no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—382no—
406C2×C4—382no—
407C2×C4—382no—
408C2×C4—384no—
409C2×C4—7616no—
410C2×C4—762no—
411C2×C4—762no—
412C2×C4—762no—
413C2×C4—762no—
414C2×C4—762no—
415C2×C4—762no—
416C2×C4—762no—
417C2×C4—762no—
418C2×C4—1522no—
419C2×C4—1522no—
420C2×C4—1522no—
421C22—28no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—84no—
435C22—84no—
436C22—82no—
437C22—82no—
438C22—384no—
439C22—764no—
440C22—764no—
441C22—768no—
442C22—768no—
443C22—762no—
444C22—762no—
445C22#1192639911yescharacteristic
446C22#99×D1912yes—
447C22#1192651612yes—
448C22#1192651712yes—
449C4—42no—
450C4—42no—
451C4—162no—
452C4—3042no—
453C4—762no—
454C4—762no—
455C4—762no—
456C2—22no—
457C2—22no—
458C2—22no—
459C2—42no—
460C2—42no—
461C2—764no—
462C2#1456354811yescharacteristic
463C2#1456355111yescharacteristic
464C2#1456355211yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC24×C19C22×C4
FrattiniC25C22×D19
FittingC19×#1819C2
socleC22×C19#379
prime radicalC23×C22⋊D19C22
cosocleC25×C19C23
hypercenter#1819D19
hypocenterC19#8543
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
2. #14563709C2semidirect
3. #14563707C2semidirect
5. C19×#1819C2semidirect
7. C23×C4×D19C4semidirect
12. C22×C4⋊Dic19C4semidirect
13. C22×Dic19⋊C4C4semidirect
15. C22×(C2×D19)⋊C4C4semidirect
192. #1819D19semidirect
297. C19#8543semidirect

Maximal subgroups

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

subgroupindex
C22×#105973292
#145637092
#145637072
#145635492
C19×#18192
#854319