Finite Group Databasebeta

← #18080201

Subgroups — #18080201

Order 4864.

486 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 99 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#14572720C211yesmaximal, characteristic, complemented
2#14568611C211yesmaximal, characteristic
3#14562258C212yesmaximal
4#14561492C212yesmaximal, complemented
5C19×#1467C211yesmaximal, characteristic, complemented
6C2×#10597390C411yescharacteristic
7C2×#10597393C411yescharacteristic
8C2×#10597321C2211yescharacteristic
9#11926675—24no—
10#11926601—21no—
11#11926601C2212yes—
12#11926597—21no—
13#11926466—21no—
14#11926466—21no—
15#11926449C411yescharacteristic
16#11926445C411yescharacteristic
17#11926435—21no—
18#11926435—21no—
19C4×C4⋊Dic19C2211yescharacteristic
20#11926283—24no—
21C2×C4×Q8×C19C2211yescharacteristic
22C19×#432C2212yes—
23C19×#324—21no—
24C19×#324—21no—
25C22×Q8×C19C2×C411yescharacteristic
26C22×D76C2×C411yescharacteristic
27C22×Dic38C2×C411yescharacteristic
28C4×Q8×C19—22no—
29C4×Q8×C19—22no—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C4⋊C4×C19D411yescharacteristic
32C2×C4⋊C4×C19D411yescharacteristic
33C2×C42×C19D411yescharacteristic
34C2×C42×C19D411yescharacteristic
35C2×C42×C19C2311yescharacteristic
36#10597393—42no—
37#10597390—42no—
38C2×(C2×D19)⋊C4—21no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—21no—
44C2×C4⋊Dic19—21no—
45C2×Dic19⋊C4—21no—
46C2×Dic19⋊C4—21no—
47C2×C4×Dic19C2×C411yescharacteristic
48C2×C4×Dic19C2×C411yescharacteristic
49#10597321—22no—
50#10597321—22no—
51C19×C4⋊C8—22no—
52C19×C22⋊C8—22no—
53C19×#97—22no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57C22⋊(C19⋊C8)—22no—
58C4⋊(C19⋊C8)—22no—
59C4⋊(C19⋊C8)—22no—
60C4⋊(C19⋊C8)—22no—
61#10597260—22no—
62#10597260D414yes—
63C4×C19⋊C8—22no—
64C23×D19—21no—
65C2×Q8×C19—22no—
66C2×Q8×C19—22no—
67C2×Q8×C19—41no—
68C22×C4×C19C22⋊C411yescharacteristic
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19C22⋊C411yescharacteristic
72C22×C4×C19C22×C411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×Dic19—21no—
76C22×Dic19—21no—
77C22×Dic19—21no—
78C2×D76—22no—
79C2×D76—41no—
80C2×D76—41no—
81C2×Dic38—22no—
82C2×Dic38—41no—
83C2×Dic38—41no—
84C2×C8×C19—42no—
85C4⋊C4×C19—22no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—22no—
88C42×C19—21no—
89C42×C19—21no—
90C42×C19—21no—
91C42×C19—21no—
92C42×C19C2×D412yes—
93C42×C19#4112yes—
94(C2×D19)⋊C4—42no—
95(C2×D19)⋊C4—42no—
96(C2×D19)⋊C4—42no—
97(C2×D19)⋊C4—42no—
98(C2×D19)⋊C4—41no—
99(C2×D19)⋊C4—42no—
100(C2×D19)⋊C4—41no—
101C4⋊Dic19—42no—
102Dic19⋊C4—42no—
103Dic19⋊C4—42no—
104C4×Dic19—41no—
105C4×Dic19—41no—
106C2×C19⋊C8—24no—
107#9448—191nomaximal, Sylow
108C23×C19C2×C22⋊C411yescharacteristic
109C22×D19—41no—
110C22×D19—41no—
111C22×D19—41no—
112C22×D19—41no—
113C22×D19—41no—
114C22×D19—41no—
115C22×D19—41no—
116Q8×C19—44no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19#10012yes—
131C2×C4×C19C4×D412yes—
132C2×C4×C19#12011yescharacteristic
133C2×C4×C19#12112yes—
134C2×C4×C19#12311yescharacteristic
135C2×Dic19—22no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144D76—82no—
145Dic38—82no—
146C8×C19—82no—
147C19⋊C8—44no—
148#2983—191no—
149#2545—191no—
150#1533—192no—
151#1467D1911yescharacteristic, complemented
152#1285—192no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19#38611yescharacteristic
156C22×C19C2×#10011yescharacteristic
157C22×C19#41311yescharacteristic
158C2×D19—81no—
159C2×D19—81no—
160C2×D19—81no—
161C2×D19—81no—
162C2×D19—81no—
163C2×D19—81no—
164C2×D19—81no—
165C4×C19—22no—
166C4×C19—22no—
167C4×C19—22no—
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—41no—
171C4×C19—41no—
172C4×C19—41no—
173Dic19—42no—
174Dic19—81no—
175Dic19—81no—
176C2×C4⋊Q8—191no—
177C2×#124—191no—
178C2×#124—191no—
179C2×C4×Q8C2×D1911yescharacteristic
180#446—384no—
181#432—192no—
182#432—381no—
183#432C2×D1912yes—
184#431—381no—
185#396—381no—
186#396—381no—
187#391—191no—
188#390—191no—
189#388—381no—
190#388—381no—
191C4×C4⋊C4—191no—
192#329—384no—
193#324—21no—
194#324—21no—
195C2×C19—21no—
196C2×C19—21no—
197C2×C19#188411yescharacteristic
198C2×C19#190011yescharacteristic
199C2×C19#191211yescharacteristic
200D19—161no—
201C22×Q8—191no—
202C22×Q8C4×D1911yescharacteristic
203C22×D4—191no—
204C4⋊Q8—762no—
205#124—382no—
206#124—382no—
207#124—762no—
208C4×Q8—22no—
209C4×Q8—22no—
210C2×C4⋊C4—381no—
211C2×C4⋊C4—381no—
212C2×C4⋊C4—381no—
213C2×C4⋊C4C4×D1911yescharacteristic
214C2×C4⋊C4C22⋊D1911yescharacteristic
215C2×C4⋊C4C22⋊D1911yescharacteristic
216C2×C22⋊C4—381no—
217C2×C22⋊C4—381no—
218C2×C22⋊C4—381no—
219C2×C22⋊C4—381no—
220C2×C22⋊C4—381no—
221C2×C22⋊C4—381no—
222C2×C42—191no—
223C2×C42—191no—
224C2×C42D7611yescharacteristic
225C2×C42D7611yescharacteristic
226C2×C42C22×D1911yescharacteristic
227C4⋊C8—22no—
228C4⋊C8—382no—
229C4⋊C8—382no—
230C4⋊C8—382no—
231C22⋊C8—22no—
232C22⋊C8—382no—
233#97—22no—
234#97—194no—
235#97—382no—
236C4×C8—382no—
237#95—381no—
238#95—381no—
239#95—381no—
240C19#944811yescharacteristic, complemented, Sylow
241C24—381no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—382no—
246C2×Q8—761no—
247C2×Q8—761no—
248C2×D4—382no—
249C2×D4—761no—
250C2×D4—761no—
251C22×C4—381no—
252C22×C4—381no—
253C22×C4—381no—
254C22×C4(C2×D19)⋊C411yescharacteristic
255C22×C4(C2×D19)⋊C411yescharacteristic
256C22×C4(C2×D19)⋊C411yescharacteristic
257C22×C4(C2×D19)⋊C411yescharacteristic
258C22×C4C2×C4×D1911yescharacteristic
259C22×C4C2×D7611yescharacteristic
260C22×C4C2×C22⋊D1911yescharacteristic
261C2×C8—42no—
262C2×C8—384no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—762no—
267C4⋊C4—762no—
268C4⋊C4—762no—
269C22⋊C4—762no—
270C22⋊C4—762no—
271C22⋊C4—762no—
272C22⋊C4—762no—
273C22⋊C4—762no—
274C22⋊C4—761no—
275C22⋊C4—761no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—21no—
280C42—761no—
281C42—761no—
282C42D4×D1912yes—
283C42#6454312yes—
284C23—761no—
285C23—761no—
286C23—761no—
287C23—761no—
288C23—761no—
289C23—761no—
290C23—761no—
291C23C2×(C2×D19)⋊C411yescharacteristic
292Q8—44no—
293Q8—1522no—
294D4—1522no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—382no—
309C2×C4—761no—
310C2×C4—761no—
311C2×C4—761no—
312C2×C4—761no—
313C2×C4—761no—
314C2×C4—761no—
315C2×C4—761no—
316C2×C4—761no—
317C2×C4#1059728012yes—
318C2×C4(C22⋊D19)⋊C412yes—
319C2×C4#1059732811yescharacteristic
320C2×C4#1059733211yescharacteristic
321C2×C4#1059738512yes—
322C8—82no—
323C8—764no—
324C22—21no—
325C22—21no—
326C22—1521no—
327C22—1521no—
328C22—1521no—
329C22—1521no—
330C22—1521no—
331C22—1521no—
332C22—1521no—
333C22#1192642111yescharacteristic
334C22C2×#1059728011yescharacteristic
335C22#1192652611yescharacteristic
336C4—22no—
337C4—22no—
338C4—21no—
339C4—21no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—762no—
345C4—1521no—
346C4—1521no—
347C2—21no—
348C2—21no—
349C2—3041no—
350C2#1456401611yescharacteristic
351C2#1456409611yescharacteristic
352C2#1456417011yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1467C2
socleC22×C19#386
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1467D19
hypocenterC19#9448
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
1. #14572720C2semidirect
4. #14561492C2semidirect
5. C19×#1467C2semidirect
151. #1467D19semidirect
240. C19#9448semidirect

Maximal subgroups

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

subgroupindex
#145727202
#145686112
#145622582
#145614922
C19×#14672
#944819