Finite Group Databasebeta

← #18075189

Subgroups — #18075189

Order 4864.

842 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 842 conjugacy classes of subgroups — too many to draw. Only its 115 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×#10597344C211yesmaximal, characteristic
2#14563715C211yesmaximal, characteristic, complemented
3#14561964C212yesmaximal, complemented
4#14561961C212yesmaximal
5C19×#1821C211yesmaximal, characteristic, complemented
6C2×#10597344—24no—
7C2×#10597344—24no—
8C2×#10597344—22no—
9C2×#10597344—22no—
10C22×C4⋊Dic19C411yescharacteristic
11C22×Dic19⋊C4C2211yescharacteristic
12C22×(C2×D19)⋊C4C411yescharacteristic
13C22×(C2×D19)⋊C4C411yescharacteristic
14C22×(C2×D19)⋊C4C2211yescharacteristic
15C22×C4×Dic19C411yescharacteristic
16#11926508C2212yes—
17#11926313—22no—
18#11926269—24no—
19#11926267—24no—
20C22×C4⋊C4×C19C2211yescharacteristic
21C19×#407C2212yes—
22C19×#343—22no—
23C24×D19C2×C411yescharacteristic
24C23×C4×C19C2×C411yescharacteristic
25C23×C4×C19C2×C411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C23×Dic19C2×C411yescharacteristic
28C23×Dic19C2×C411yescharacteristic
29C23×Dic19C2×C411yescharacteristic
30C2×M16×C19—22no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19—22no—
33C2×C4⋊C4×C19D412yes—
34C2×C4⋊C4×C19D412yes—
35C2×(C2×D19)⋊C4—22no—
36C2×(C2×D19)⋊C4—22no—
37C2×(C2×D19)⋊C4—22no—
38C2×(C2×D19)⋊C4—22no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—22no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—22no—
43C2×(C2×D19)⋊C4—22no—
44C2×(C2×D19)⋊C4D414yes—
45C2×C4⋊Dic19—22no—
46C2×C4⋊Dic19—22no—
47C2×C4⋊Dic19—22no—
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—22no—
50C2×Dic19⋊C4—21no—
51C2×Dic19⋊C4D414yes—
52C2×C4×Dic19—22no—
53C2×C4×Dic19—22no—
54C2×C4×Dic19—22no—
55C2×#64520—22no—
56#10597344—216no—
57#10597344—216no—
58C19×C22⋊C8—22no—
59C19×C22⋊C8—22no—
60C22⋊(C19⋊C8)—22no—
61C22⋊(C19⋊C8)—22no—
62C24×C19C22×C411yescharacteristic
63C23×D19—21no—
64C23×D19—21no—
65C23×D19—42no—
66C23×D19—42no—
67C23×D19—42no—
68C23×D19C22⋊C412yes—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—42no—
74C22×C4×C19—42no—
75C22×C4×C19—42no—
76C22×C4×C19C22⋊C412yes—
77C22×C4×C19C22⋊C412yes—
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D412yes—
80C22×C4×C19C2×D412yes—
81C22×C4×C19C2×D411yescharacteristic
82C22×Dic19—21no—
83C22×Dic19—21no—
84C22×Dic19—21no—
85C22×Dic19—21no—
86C22×Dic19—21no—
87C22×Dic19—21no—
88C22×Dic19—42no—
89C22×Dic19—42no—
90C22×Dic19—42no—
91C22×Dic19C22⋊C412yes—
92C22×Dic19C22⋊C412yes—
93C22×Dic19C22⋊C412yes—
94M16×C19—44no—
95C2×C8×C19—42no—
96C4⋊C4×C19—24no—
97C4⋊C4×C19—24no—
98(C2×D19)⋊C4—28no—
99(C2×D19)⋊C4—28no—
100(C2×D19)⋊C4—24no—
101(C2×D19)⋊C4—24no—
102C4⋊Dic19—28no—
103Dic19⋊C4—24no—
104Dic19⋊C4—24no—
105C4×Dic19—28no—
106#64520—44no—
107C2×C19⋊C8—42no—
108#8556—191nomaximal, Sylow
109C23×C19—22no—
110C23×C19—22no—
111C23×C19—22no—
112C23×C19C2×C22⋊C411yescharacteristic
113C23×C19C2×C22⋊C411yescharacteristic
114C23×C19C2×C22⋊C411yescharacteristic
115C22×D19—22no—
116C22×D19—24no—
117C22×D19—42no—
118C22×D19—42no—
119C22×D19—42no—
120C22×D19—42no—
121C22×D19—42no—
122C22×D19—42no—
123C22×D19—42no—
124C22×D19—42no—
125C22×D19—88no—
126C2×C4×C19—22no—
127C2×C4×C19—22no—
128C2×C4×C19—22no—
129C2×C4×C19—22no—
130C2×C4×C19—42no—
131C2×C4×C19—42no—
132C2×C4×C19—42no—
133C2×C4×C19—42no—
134C2×C4×C19—42no—
135C2×C4×C19—42no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19#12012yes—
139C2×C4×C19#12012yes—
140C2×Dic19—22no—
141C2×Dic19—22no—
142C2×Dic19—22no—
143C2×Dic19—24no—
144C2×Dic19—42no—
145C2×Dic19—42no—
146C2×Dic19—42no—
147C2×Dic19—42no—
148C2×Dic19—42no—
149C2×Dic19—42no—
150C2×Dic19—42no—
151C2×Dic19—42no—
152C8×C19—82no—
153C19⋊C8—82no—
154C22×#126—191no—
155#1821—191no—
156#1821D1911yescharacteristic, complemented
157#1463—192no—
158#1462—192no—
159C22×C19—28no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19#37911yescharacteristic
167C22×C19#41012yes—
168C22×C19#41312yes—
169C22×C19#41312yes—
170C2×D19—42no—
171C2×D19—42no—
172C2×D19—42no—
173C2×D19—84no—
174C2×D19—84no—
175C2×D19—84no—
176C4×C19—22no—
177C4×C19—22no—
178C4×C19—42no—
179C4×C19—42no—
180Dic19—42no—
181Dic19—42no—
182Dic19—42no—
183C2×#126—384no—
184C2×#126—384no—
185C2×#126—382no—
186C2×#126—382no—
187C22×C4⋊C4—191no—
188C22×C4⋊C4—191no—
189C22×C4⋊C4C2×D1911yescharacteristic
190C22×C22⋊C4—191no—
191C22×C22⋊C4—191no—
192C22×C22⋊C4—191no—
193C22×C42—191no—
194#407—192no—
195#407C2×D1912yes—
196#343—22no—
197#343—382no—
198#324—384no—
199#323—384no—
200C2×C19—22no—
201C2×C19—22no—
202C2×C19—22no—
203C2×C19#178211yescharacteristic
204C2×C19#178511yescharacteristic
205C2×C19#178511yescharacteristic
206D19—82no—
207C25—191no—
208C23×C4—191no—
209C23×C4—191no—
210C23×C4—191no—
211C23×C4C4×D1911yescharacteristic
212C23×C4C4×D1911yescharacteristic
213C23×C4C22×D1911yescharacteristic
214C2×M16—22no—
215C2×M16—382no—
216#126—3816no—
217#126—3816no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—194no—
221C2×C4⋊C4—382no—
222C2×C4⋊C4—382no—
223C2×C4⋊C4—382no—
224C2×C4⋊C4—381no—
225C2×C4⋊C4—382no—
226C2×C4⋊C4—381no—
227C2×C4⋊C4D7612yes—
228C2×C4⋊C4C22⋊D1912yes—
229C2×C22⋊C4—194no—
230C2×C22⋊C4—382no—
231C2×C22⋊C4—382no—
232C2×C22⋊C4—382no—
233C2×C22⋊C4—382no—
234C2×C22⋊C4—382no—
235C2×C22⋊C4—382no—
236C2×C22⋊C4—381no—
237C2×C22⋊C4—382no—
238C2×C22⋊C4—381no—
239C2×C42—382no—
240C2×C42—382no—
241C2×C42—382no—
242C22⋊C8—22no—
243C22⋊C8—22no—
244C22⋊C8—382no—
245C22⋊C8—382no—
246C19#855611yescharacteristic, complemented, Sylow
247C24—192no—
248C24—381no—
249C24—381no—
250C24—762no—
251C24—762no—
252C24—762no—
253C24C2×C4×D1911yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—192no—
262C22×C4—192no—
263C22×C4—192no—
264C22×C4—381no—
265C22×C4—381no—
266C22×C4—381no—
267C22×C4—381no—
268C22×C4—381no—
269C22×C4—381no—
270C22×C4—762no—
271C22×C4—762no—
272C22×C4—762no—
273C22×C4(C2×D19)⋊C412yes—
274C22×C4(C2×D19)⋊C412yes—
275C22×C4C2×D7611yescharacteristic
276C22×C4D4×D1912yes—
277C22×C4D4×D1912yes—
278C22×C4C2×C22⋊D1911yescharacteristic
279M16—44no—
280M16—764no—
281C2×C8—42no—
282C2×C8—762no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—388no—
286C4⋊C4—384no—
287C4⋊C4—384no—
288C22⋊C4—388no—
289C22⋊C4—388no—
290C22⋊C4—384no—
291C22⋊C4—384no—
292C42—388no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—382no—
297C23—384no—
298C23—762no—
299C23—762no—
300C23—762no—
301C23—762no—
302C23—762no—
303C23—762no—
304C23—762no—
305C23—762no—
306C23—1528no—
307C23C22⋊C4×D1911yescharacteristic
308C23C22⋊C4×D1911yescharacteristic
309C23C2×(C2×D19)⋊C411yescharacteristic
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—382no—
323C2×C4—382no—
324C2×C4—382no—
325C2×C4—384no—
326C2×C4—762no—
327C2×C4—762no—
328C2×C4—762no—
329C2×C4—762no—
330C2×C4—762no—
331C2×C4—762no—
332C2×C4—762no—
333C2×C4—762no—
334C2×C4#1059732812yes—
335C2×C4#1059738312yes—
336C8—82no—
337C8—1522no—
338C22—28no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—762no—
346C22—762no—
347C22—762no—
348C22—1524no—
349C22—1524no—
350C22—1524no—
351C22#1192639911yescharacteristic
352C22#1192651712yes—
353C22#1192652512yes—
354C22#1192652712yes—
355C4—22no—
356C4—22no—
357C4—42no—
358C4—42no—
359C4—762no—
360C4—762no—
361C4—762no—
362C2—22no—
363C2—22no—
364C2—22no—
365C2—1522no—
366C2#1456355211yescharacteristic
367C2#1456356011yescharacteristic
368C2#1456356211yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1821C2
socleC22×C19#379
prime radicalC24×D19C2×C4
cosocleC23×C4×C19C23
hypercenter#1821D19
hypocenterC19#8556
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
2. #14563715C2semidirect
3. #14561964C2semidirect
5. C19×#1821C2semidirect
156. #1821D19semidirect
246. C19#8556semidirect

Maximal subgroups

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

subgroupindex
C22×#105973442
#145637152
#145619642
#145619612
C19×#18212
#855619