Finite Group Databasebeta

← #18080209

Subgroups — #18080209

Order 4864.

490 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 107 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#14572664C211yesmaximal, characteristic
2#14562262C212yesmaximal, complemented
3#14561976C211yesmaximal, characteristic
4#14561491C212yesmaximal, complemented
5C19×#2566C211yesmaximal, characteristic
6#11926616—24no—
7#11926601C2212yes—
8#11926601C2212yes—
9#11926508—21no—
10C2×C22⋊(C19⋊C8)—21no—
11#11926286—24no—
12#11926268—21no—
13#11926268—21no—
14C2×C19×#125C2211yescharacteristic
15C2×C4×D4×C19C2211yescharacteristic
16C19×#396—21no—
17C19×#396—21no—
18C19×#390C411yescharacteristic
19C19×#390C411yescharacteristic
20C19×#385—21no—
21C19×#385—21no—
22C19×#384C411yescharacteristic
23C19×#382C411yescharacteristic
24C4×C4⋊C4×C19C2211yescharacteristic
25C22×D4×C19C2×C411yescharacteristic
26C23×C4×C19D411yescharacteristic
27C23×C4×C19D411yescharacteristic
28C19×#125—22no—
29C19×#125—22no—
30C4×D4×C19—22no—
31C4×D4×C19—22no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19C2×C411yescharacteristic
38C2×C4⋊C4×C19C2×C411yescharacteristic
39C2×C4⋊C4×C19C2×C411yescharacteristic
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19D411yescharacteristic
45C2×C22⋊C4×C19D411yescharacteristic
46C2×C42×C19C2×C411yescharacteristic
47C2×C42×C19C2×C411yescharacteristic
48C2×C42×C19C2311yescharacteristic
49C2×#64520—22no—
50C22×C19⋊C8—22no—
51C19×#95—21no—
52C19×#95—21no—
53C19×#95—21no—
54C22⋊(C19⋊C8)—22no—
55C22⋊(C19⋊C8)—22no—
56C22⋊(C19⋊C8)—22no—
57C22⋊(C19⋊C8)—22no—
58C4⋊(C19⋊C8)—22no—
59C4⋊(C19⋊C8)—22no—
60#10597260—22no—
61#10597260D414yes—
62C24×C19C22⋊C411yescharacteristic
63C24×C19C22⋊C411yescharacteristic
64C2×D4×C19—22no—
65C2×D4×C19—22no—
66C2×D4×C19—41no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19—81no—
76C22×C4×C19—81no—
77C22×C4×C19C22⋊C411yescharacteristic
78C22×C4×C19C22⋊C411yescharacteristic
79C22×C4×C19C22×C411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C4⋊C4×C19—22no—
83C4⋊C4×C19—22no—
84C4⋊C4×C19—22no—
85C4⋊C4×C19—42no—
86C4⋊C4×C19—41no—
87C4⋊C4×C19—42no—
88C4⋊C4×C19—41no—
89C4⋊C4×C19—81no—
90C4⋊C4×C19—81no—
91C22⋊C4×C19—22no—
92C22⋊C4×C19—22no—
93C22⋊C4×C19—42no—
94C22⋊C4×C19—42no—
95C22⋊C4×C19—81no—
96C22⋊C4×C19—81no—
97C42×C19—41no—
98C42×C19—41no—
99C42×C19C2×D412yes—
100C42×C19#4112yes—
101#64520—82no—
102C2×C19⋊C8—24no—
103C2×C19⋊C8—42no—
104C2×C19⋊C8—82no—
105#9449—191nomaximal, Sylow
106C23×C19—21no—
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—41no—
112C23×C19—41no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19#10112yes—
116C23×C19C2×C22⋊C411yescharacteristic
117D4×C19—44no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—22no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—42no—
126C2×C4×C19—42no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—81no—
141C2×C4×C19—81no—
142C2×C4×C19C4×D412yes—
143C2×C4×C19#12011yescharacteristic
144C2×C4×C19#12112yes—
145C2×C4×C19#12311yescharacteristic
146C19⋊C8—44no—
147C19⋊C8—82no—
148#2973—191no—
149#2566D1911yescharacteristic
150#1534—192no—
151#1466—191no—
152#1285—192no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19—22no—
156C22×C19—42no—
157C22×C19—42no—
158C22×C19—41no—
159C22×C19—41no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—81no—
164C22×C19—81no—
165C22×C19#38611yescharacteristic
166C22×C19C2×#10111yescharacteristic
167C22×C19#41311yescharacteristic
168C4×C19—22no—
169C4×C19—22no—
170C4×C19—21no—
171C4×C19—21no—
172C4×C19—42no—
173C4×C19—41no—
174C4×C19—41no—
175C4×C19—81no—
176C4×C19—81no—
177C4×C19—81no—
178C2×#125C2×D1911yescharacteristic
179C2×C4×D4C2×D1911yescharacteristic
180#435—384no—
181#432—192no—
182#432—192no—
183#407—381no—
184C2×C22⋊C8—381no—
185#396—21no—
186#396—21no—
187#390Dic1911yescharacteristic
188#390Dic1911yescharacteristic
189#385—21no—
190#385—21no—
191#384Dic1911yescharacteristic
192#382Dic1911yescharacteristic
193C4×C4⋊C4C2×D1911yescharacteristic
194#330—384no—
195#323—381no—
196#323—381no—
197C2×C19—21no—
198C2×C19—21no—
199C2×C19—42no—
200C2×C19—81no—
201C2×C19#188411yescharacteristic
202C2×C19#190111yescharacteristic
203C2×C19#191111yescharacteristic
204C22×D4C2×Dic1911yescharacteristic
205C23×C4C22⋊D1911yescharacteristic
206C23×C4C22⋊D1911yescharacteristic
207C2×M16—382no—
208C22×C8—382no—
209#125—22no—
210#125—22no—
211C4×D4—22no—
212C4×D4—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C2×Dic1911yescharacteristic
219C2×C4⋊C4C2×Dic1911yescharacteristic
220C2×C4⋊C4C2×Dic1911yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4C22⋊D1911yescharacteristic
226C2×C22⋊C4C22⋊D1911yescharacteristic
227C2×C42C2×Dic1911yescharacteristic
228C2×C42C2×Dic1911yescharacteristic
229C2×C42C22×D1911yescharacteristic
230C4⋊C8—382no—
231C4⋊C8—382no—
232C22⋊C8—382no—
233C22⋊C8—382no—
234C22⋊C8—382no—
235C22⋊C8—382no—
236#97—194no—
237#97—382no—
238#95—21no—
239#95—21no—
240#95—21no—
241C19#944911yescharacteristic, complemented, Sylow
242C24C22⋊Dic1911yescharacteristic
243C24C22⋊Dic1911yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—41no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4C22⋊Dic1911yescharacteristic
258C22×C4C22⋊Dic1911yescharacteristic
259C22×C4C22×Dic1911yescharacteristic
260C22×C4C2×C22⋊D1911yescharacteristic
261C22×C4C2×C22⋊D1911yescharacteristic
262M16—1522no—
263C2×C8—384no—
264C2×C8—762no—
265C2×C8—1522no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—42no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—42no—
273C4⋊C4—81no—
274C4⋊C4—81no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—81no—
280C22⋊C4—81no—
281C42—41no—
282C42—41no—
283C42D4×D1912yes—
284C42#6454312yes—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23#1059729312yes—
295C23C2×C22⋊Dic1911yescharacteristic
296D4—44no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4D4×Dic1912yes—
322C2×C4#1059738111yescharacteristic
323C2×C4#1059738311yescharacteristic
324C2×C4#1059738512yes—
325C8—764no—
326C8—1522no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22#1192642411yescharacteristic
340C22C2×#1059729311yescharacteristic
341C22#1192652811yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—22no—
346C4—42no—
347C4—41no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—81no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—81no—
356C2#1456401911yescharacteristic
357C2#1456410411yescharacteristic
358C2#1456416811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2566C2
socleC22×C19#386
prime radicalC22×D4×C19C2×C4
cosocleC2×C42×C19C23
hypercenter#2566D19
hypocenterC19#9449
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2566

Complements

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

NH ≅ G/Ntype
2. #14562262C2semidirect
4. #14561491C2semidirect
241. C19#9449semidirect

Maximal subgroups

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

subgroupindex
#145726642
#145622622
#145619762
#145614912
C19×#25662
#944919