Finite Group Databasebeta

← #18075178

Subgroups — #18075178

Order 4864.

1166 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 123 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×#10597332C211yesmaximal, characteristic
2#14563713C212yesmaximal, complemented
3#14561962C211yesmaximal, characteristic, complemented
4#14561961C212yesmaximal, complemented
5C19×#1462C211yesmaximal, characteristic, complemented
6C23×C22⋊D19C411yescharacteristic
7C24×Dic19C411yescharacteristic
8C2×#10597332—24no—
9C2×#10597332—24no—
10C2×#10597332—22no—
11C2×#10597332—22no—
12C22×C4⋊Dic19C411yescharacteristic
13C22×C4⋊Dic19C2211yescharacteristic
14C22×(C2×D19)⋊C4C411yescharacteristic
15C22×(C2×D19)⋊C4C2211yescharacteristic
16#11926508C2212yes—
17#11926312—24no—
18#11926268—22no—
19#11926267—24no—
20C22×C22⋊C4×C19C2211yescharacteristic
21C19×#407C2212yes—
22C19×#323—22no—
23C25×C19C2×C411yescharacteristic
24C24×D19C2×C411yescharacteristic
25C23×C4×C19C2×C411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C22×C22⋊D19—22no—
28C22×C22⋊D19—22no—
29C22×C22⋊D19—22no—
30C22×C22⋊D19—44no—
31C23×Dic19—22no—
32C23×Dic19—22no—
33C23×Dic19—22no—
34C23×Dic19—44no—
35C23×Dic19C2×C411yescharacteristic
36C23×Dic19C2×C411yescharacteristic
37C23×Dic19C2×C411yescharacteristic
38C2×M16×C19—22no—
39C2×C22⋊C4×C19—22no—
40C2×C22⋊C4×C19—22no—
41C2×C22⋊C4×C19D412yes—
42C2×C22⋊C4×C19D412yes—
43C2×(C2×D19)⋊C4—22no—
44C2×(C2×D19)⋊C4—22no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—22no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—22no—
49C2×(C2×D19)⋊C4D414yes—
50C2×C4⋊Dic19—22no—
51C2×C4⋊Dic19—21no—
52C2×C4⋊Dic19—22no—
53C2×C4⋊Dic19—21no—
54C2×C4⋊Dic19—22no—
55C2×C4⋊Dic19—22no—
56C2×C4⋊Dic19D414yes—
57C2×#64520—22no—
58#10597332—216no—
59#10597332—216no—
60C19×C22⋊C8—22no—
61C19×C22⋊C8—22no—
62C22⋊(C19⋊C8)—22no—
63C22⋊(C19⋊C8)—22no—
64C24×C19—24no—
65C24×C19—21no—
66C24×C19—21no—
67C24×C19—42no—
68C24×C19—42no—
69C24×C19C22⋊C412yes—
70C24×C19C22×C411yescharacteristic
71C23×D19—21no—
72C23×D19—21no—
73C23×D19—42no—
74C23×D19—42no—
75C23×D19—42no—
76C23×D19C22⋊C412yes—
77C22×C4×C19—21no—
78C22×C4×C19—21no—
79C22×C4×C19—42no—
80C22×C4×C19—42no—
81C22×C4×C19C22⋊C412yes—
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19C2×D412yes—
84C22×C4×C19C2×D412yes—
85C22×C4×C19C2×D411yescharacteristic
86C2×C22⋊D19—28no—
87C2×C22⋊D19—48no—
88C2×C22⋊D19—44no—
89C2×C22⋊D19—48no—
90C2×C22⋊D19—44no—
91C22×Dic19—28no—
92C22×Dic19—21no—
93C22×Dic19—21no—
94C22×Dic19—21no—
95C22×Dic19—21no—
96C22×Dic19—21no—
97C22×Dic19—21no—
98C22×Dic19—48no—
99C22×Dic19—48no—
100C22×Dic19—44no—
101C22×Dic19—44no—
102C22×Dic19—42no—
103C22×Dic19—42no—
104C22×Dic19—42no—
105C22×Dic19C22⋊C412yes—
106C22×Dic19C22⋊C412yes—
107C22×Dic19C22⋊C412yes—
108M16×C19—44no—
109C2×C8×C19—42no—
110C22⋊C4×C19—24no—
111C22⋊C4×C19—24no—
112(C2×D19)⋊C4—28no—
113(C2×D19)⋊C4—24no—
114(C2×D19)⋊C4—24no—
115C4⋊Dic19—28no—
116C4⋊Dic19—24no—
117C4⋊Dic19—24no—
118#64520—44no—
119C2×C19⋊C8—42no—
120#8553—191nomaximal, Sylow
121C23×C19—22no—
122C23×C19—22no—
123C23×C19—22no—
124C23×C19—24no—
125C23×C19—24no—
126C23×C19—22no—
127C23×C19—22no—
128C23×C19—42no—
129C23×C19—42no—
130C23×C19—416no—
131C23×C19—42no—
132C23×C19—42no—
133C23×C19—42no—
134C23×C19—42no—
135C23×C19#10014yes—
136C23×C19C2×C22⋊C411yescharacteristic
137C23×C19C2×C22⋊C411yescharacteristic
138C23×C19C2×C22⋊C411yescharacteristic
139C22×D19—22no—
140C22×D19—24no—
141C22×D19—42no—
142C22×D19—42no—
143C22×D19—42no—
144C22×D19—42no—
145C22×D19—42no—
146C22×D19—42no—
147C22×D19—42no—
148C22×D19—42no—
149C22×D19—88no—
150C2×C4×C19—24no—
151C2×C4×C19—22no—
152C2×C4×C19—41no—
153C2×C4×C19—42no—
154C2×C4×C19—41no—
155C2×C4×C19—42no—
156C2×C4×C19—42no—
157C2×C4×C19—42no—
158C2×C4×C19#12012yes—
159C2×C4×C19#12012yes—
160C22⋊D19—416no—
161C2×Dic19—22no—
162C2×Dic19—22no—
163C2×Dic19—22no—
164C2×Dic19—42no—
165C2×Dic19—42no—
166C2×Dic19—416no—
167C2×Dic19—42no—
168C2×Dic19—42no—
169C2×Dic19—42no—
170C2×Dic19—42no—
171C2×Dic19—42no—
172C2×Dic19—42no—
173C2×Dic19—42no—
174C8×C19—82no—
175C19⋊C8—82no—
176C22×#123—191no—
177#1821—192no—
178#1462—192no—
179#1462—191no—
180#1462D1911yescharacteristic, complemented
181C22×C19—28no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—21no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19—24no—
189C22×C19—44no—
190C22×C19—48no—
191C22×C19—44no—
192C22×C19—48no—
193C22×C19—42no—
194C22×C19—42no—
195C22×C19#37911yescharacteristic
196C22×C19#41012yes—
197C22×C19C2×#10012yes—
198C22×C19#41312yes—
199C2×D19—42no—
200C2×D19—42no—
201C2×D19—42no—
202C2×D19—84no—
203C2×D19—84no—
204C2×D19—84no—
205C4×C19—22no—
206C4×C19—22no—
207C4×C19—42no—
208Dic19—42no—
209Dic19—42no—
210Dic19—42no—
211C23×D4—191no—
212C24×C4—191no—
213C2×#123—384no—
214C2×#123—384no—
215C2×#123—382no—
216C2×#123—382no—
217C22×C4⋊C4—191no—
218C22×C4⋊C4—191no—
219C22×C22⋊C4—191no—
220C22×C22⋊C4—191no—
221C22×C22⋊C4C2×D1911yescharacteristic
222#407—192no—
223#407C2×D1912yes—
224#343—384no—
225#323—22no—
226#323—384no—
227#323—382no—
228C2×C19—22no—
229C2×C19—22no—
230C2×C19—22no—
231C2×C19—44no—
232C2×C19#178211yescharacteristic
233C2×C19#178311yescharacteristic
234C2×C19#178511yescharacteristic
235D19—82no—
236C25—191no—
237C25C4×D1911yescharacteristic
238C22×D4—382no—
239C22×D4—382no—
240C22×D4—382no—
241C22×D4—764no—
242C23×C4—191no—
243C23×C4—191no—
244C23×C4—191no—
245C23×C4—382no—
246C23×C4—382no—
247C23×C4—382no—
248C23×C4—764no—
249C23×C4C4×D1911yescharacteristic
250C23×C4C22×D1911yescharacteristic
251C2×M16—22no—
252C2×M16—382no—
253#123—3816no—
254#123—3816no—
255C2×C4⋊C4—194no—
256C2×C4⋊C4—382no—
257C2×C4⋊C4—382no—
258C2×C4⋊C4—382no—
259C2×C4⋊C4—381no—
260C2×C4⋊C4—382no—
261C2×C4⋊C4—381no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—194no—
265C2×C22⋊C4—382no—
266C2×C22⋊C4—382no—
267C2×C22⋊C4—382no—
268C2×C22⋊C4—381no—
269C2×C22⋊C4—382no—
270C2×C22⋊C4—381no—
271C2×C22⋊C4D7612yes—
272C2×C22⋊C4C22⋊D1912yes—
273C22⋊C8—22no—
274C22⋊C8—22no—
275C22⋊C8—382no—
276C22⋊C8—382no—
277C19#855311yescharacteristic, complemented, Sylow
278C24—24no—
279C24—21no—
280C24—21no—
281C24—42no—
282C24—42no—
283C24—192no—
284C24—381no—
285C24—381no—
286C24—762no—
287C24—762no—
288C24—762no—
289C24(C2×D19)⋊C412yes—
290C24C2×C4×D1911yescharacteristic
291C2×D4—388no—
292C2×D4—768no—
293C2×D4—764no—
294C2×D4—768no—
295C2×D4—764no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—192no—
301C22×C4—192no—
302C22×C4—192no—
303C22×C4—388no—
304C22×C4—381no—
305C22×C4—381no—
306C22×C4—381no—
307C22×C4—381no—
308C22×C4—381no—
309C22×C4—381no—
310C22×C4—768no—
311C22×C4—768no—
312C22×C4—764no—
313C22×C4—764no—
314C22×C4—762no—
315C22×C4—762no—
316C22×C4—762no—
317C22×C4(C2×D19)⋊C412yes—
318C22×C4C2×D7611yescharacteristic
319C22×C4D4×D1912yes—
320C22×C4D4×D1912yes—
321C22×C4C2×C22⋊D1911yescharacteristic
322M16—44no—
323M16—764no—
324C2×C8—42no—
325C2×C8—762no—
326C4⋊C4—388no—
327C4⋊C4—384no—
328C4⋊C4—384no—
329C22⋊C4—24no—
330C22⋊C4—24no—
331C22⋊C4—388no—
332C22⋊C4—384no—
333C22⋊C4—384no—
334C23—22no—
335C23—22no—
336C23—22no—
337C23—24no—
338C23—24no—
339C23—22no—
340C23—22no—
341C23—42no—
342C23—42no—
343C23—416no—
344C23—42no—
345C23—42no—
346C23—42no—
347C23—42no—
348C23—382no—
349C23—384no—
350C23—762no—
351C23—762no—
352C23—762no—
353C23—762no—
354C23—762no—
355C23—762no—
356C23—762no—
357C23—762no—
358C23—1528no—
359C23#1059728014yes—
360C23C22⋊C4×D1911yescharacteristic
361C23C22⋊C4×D1911yescharacteristic
362C23C2×(C2×D19)⋊C411yescharacteristic
363D4—7616no—
364C2×C4—24no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—382no—
373C2×C4—382no—
374C2×C4—382no—
375C2×C4—762no—
376C2×C4—762no—
377C2×C4—7616no—
378C2×C4—762no—
379C2×C4—762no—
380C2×C4—762no—
381C2×C4—762no—
382C2×C4—762no—
383C2×C4—762no—
384C2×C4—762no—
385C2×C4#1059732812yes—
386C2×C4#1059738312yes—
387C8—82no—
388C8—1522no—
389C22—28no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—24no—
397C22—44no—
398C22—48no—
399C22—44no—
400C22—48no—
401C22—42no—
402C22—42no—
403C22—762no—
404C22—762no—
405C22—762no—
406C22—1524no—
407C22—1524no—
408C22—1524no—
409C22#1192639911yescharacteristic
410C22#1192651612yes—
411C22C2×#1059728012yes—
412C22#1192652512yes—
413C4—22no—
414C4—22no—
415C4—42no—
416C4—762no—
417C4—762no—
418C4—762no—
419C2—22no—
420C2—22no—
421C2—22no—
422C2—44no—
423C2—1522no—
424C2#1456355111yescharacteristic
425C2#1456355511yescharacteristic
426C2#1456356011yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1462C2
socleC22×C19#379
prime radicalC23×C22⋊D19C4
cosocleC23×C4×C19C23
hypercenter#1462D19
hypocenterC19#8553
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
2. #14563713C2semidirect
3. #14561962C2semidirect
4. #14561961C2semidirect
5. C19×#1462C2semidirect
180. #1462D19semidirect
277. C19#8553semidirect

Maximal subgroups

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

subgroupindex
C22×#105973322
#145637132
#145619622
#145619612
C19×#14622
#855319