Finite Group Databasebeta

← #18079885

Subgroups — #18079885

Order 4864.

496 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 103 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#14572273C211yesmaximal, characteristic, complemented
2#14562233C212yesmaximal, complemented
3#14561969C211yesmaximal, characteristic, complemented
4#14561528C212yesmaximal, complemented
5C19×#2610C211yesmaximal, characteristic
6#11926605—24no—
7#11926601C2212yes—
8#11926568—21no—
9#11926508—21no—
10C4×#64520C2212yes—
11#11926284—24no—
12#11926270—21no—
13#11926268—21no—
14C2×C19×#124C2211yescharacteristic
15C2×C19×#117C2211yescharacteristic
16C19×#395C411yescharacteristic
17C19×#394C411yescharacteristic
18C19×#393C411yescharacteristic
19C19×#392C411yescharacteristic
20C19×#390—21no—
21C19×#388—21no—
22C19×#388—21no—
23C19×#386—21no—
24C19×#376C2211yescharacteristic
25C22×Q8×C19C2×C411yescharacteristic
26C22×D4×C19—21no—
27C22×D4×C19C2×C411yescharacteristic
28C23×C4×C19D411yescharacteristic
29C19×#124—22no—
30C19×#124—22no—
31C19×#117—22no—
32C19×#117—22no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C22⋊C4×C19—21no—
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19C2×C411yescharacteristic
43C2×C22⋊C4×C19D411yescharacteristic
44C2×C42×C19—21no—
45C2×C42×C19D411yescharacteristic
46C2×C42×C19C2311yescharacteristic
47C2×#64520—22no—
48C19×#95—21no—
49C19×#95—21no—
50C19×#95—21no—
51C19×#95C2×C411yescharacteristic
52C19×#95C2×C411yescharacteristic
53C22⋊(C19⋊C8)—24no—
54C22⋊(C19⋊C8)—22no—
55C4⋊(C19⋊C8)—24no—
56C4⋊(C19⋊C8)—22no—
57#10597260—22no—
58#10597260D414yescomplemented
59C4×C19⋊C8—22no—
60C24×C19—21no—
61C24×C19C22⋊C411yescharacteristic
62C2×Q8×C19—22no—
63C2×Q8×C19—81no—
64C2×D4×C19—22no—
65C2×D4×C19—42no—
66C2×D4×C19—42no—
67C2×D4×C19—81no—
68C2×D4×C19—81no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—41no—
75C22×C4×C19—41no—
76C22×C4×C19C22⋊C411yescharacteristic
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—81no—
85C22⋊C4×C19—22no—
86C22⋊C4×C19—22no—
87C22⋊C4×C19—42no—
88C22⋊C4×C19—42no—
89C22⋊C4×C19—41no—
90C22⋊C4×C19—42no—
91C22⋊C4×C19—41no—
92C22⋊C4×C19—81no—
93C22⋊C4×C19—81no—
94C42×C19—21no—
95C42×C19—21no—
96C42×C19—42no—
97C42×C19C2×D412yes—
98C42×C19#4112yes—
99#64520—42no—
100#64520—42no—
101C2×C19⋊C8—24no—
102C2×C19⋊C8—42no—
103#9389—191nomaximal, Sylow
104C23×C19—21no—
105C23×C19—21no—
106C23×C19—21no—
107C23×C19—41no—
108C23×C19—41no—
109C23×C19—41no—
110C23×C19—41no—
111C23×C19—41no—
112C23×C19—41no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19—41no—
116C23×C19C2×C22⋊C411yescharacteristic
117Q8×C19—82no—
118D4×C19—82no—
119D4×C19—84no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—22no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—42no—
131C2×C4×C19—42no—
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—41no—
141C2×C4×C19—41no—
142C2×C4×C19C4×D412yes—
143C2×C4×C19#12011yescharacteristic
144C2×C4×C19#12112yes—
145C2×C4×C19#12311yescharacteristic
146C19⋊C8—44no—
147C19⋊C8—82no—
148#2921—191no—
149#2610D1911yescharacteristic
150#1527—192no—
151#1464—191no—
152#1300—192no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19—42no—
156C22×C19—41no—
157C22×C19—41no—
158C22×C19—41no—
159C22×C19—81no—
160C22×C19—81no—
161C22×C19—81no—
162C22×C19—81no—
163C22×C19—81no—
164C22×C19—81no—
165C22×C19—81no—
166C22×C19—81no—
167C22×C19#38611yescharacteristic
168C22×C19#42111yescharacteristic
169C22×C19#42111yescharacteristic
170C4×C19—22no—
171C4×C19—21no—
172C4×C19—21no—
173C4×C19—22no—
174C4×C19—42no—
175C4×C19—41no—
176C4×C19—41no—
177C4×C19—41no—
178C4×C19—81no—
179C4×C19—81no—
180C2×#124C2×D1911yescharacteristic
181C2×#117C2×D1911yescharacteristic
182#433—384no—
183#432—192no—
184#423—381no—
185#407—381no—
186C4×M16—192no—
187#395Dic1911yescharacteristic
188#394Dic1911yescharacteristic
189#393Dic1911yescharacteristic
190#392Dic1911yescharacteristic
191#390—21no—
192#388—21no—
193#388—21no—
194#386—21no—
195#376C2×D1911yescharacteristic
196#329—384no—
197#324—381no—
198#323—381no—
199C2×C19—21no—
200C2×C19—21no—
201C2×C19—81no—
202C2×C19—161no—
203C2×C19#188411yescharacteristic
204C2×C19#189711yescharacteristic
205C2×C19#191411yescharacteristic
206C22×Q8C2×Dic1911yescharacteristic
207C22×D4—21no—
208C22×D4C2×Dic1911yescharacteristic
209C23×C4C22⋊D1911yescharacteristic
210C2×M16—382no—
211#124—22no—
212#124—22no—
213#117—22no—
214#117—22no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4C2×Dic1911yescharacteristic
217C2×C4⋊C4C22⋊D1911yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4C2×Dic1911yescharacteristic
225C2×C22⋊C4C22⋊D1911yescharacteristic
226C2×C42—21no—
227C2×C42C22⋊D1911yescharacteristic
228C2×C42C22×D1911yescharacteristic
229C4⋊C8—384no—
230C4⋊C8—382no—
231C22⋊C8—384no—
232C22⋊C8—382no—
233#97—194no—
234#97—382no—
235C4×C8—382no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95C2×Dic1911yescharacteristic
240#95C2×Dic1911yescharacteristic
241C19#938911yescharacteristic, complemented, Sylow
242C24—21no—
243C24C22⋊Dic1911yescharacteristic
244C2×Q8—22no—
245C2×Q8—81no—
246C2×D4—22no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—81no—
250C2×D4—81no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4C22⋊Dic1911yescharacteristic
259C22×C4C22⋊Dic1911yescharacteristic
260C22×C4C22⋊Dic1911yescharacteristic
261C22×C4C22×Dic1911yescharacteristic
262C22×C4C2×C22⋊D1911yescharacteristic
263C22×C4C2×C22⋊D1911yescharacteristic
264M16—762no—
265M16—762no—
266C2×C8—384no—
267C2×C8—762no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—81no—
271C22⋊C4—22no—
272C22⋊C4—22no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—42no—
278C22⋊C4—81no—
279C22⋊C4—81no—
280C42—21no—
281C42—21no—
282C42—42no—
283C42D4×D1912yes—
284C42#6454312yes—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23C2×C22⋊Dic1911yescharacteristic
298Q8—82no—
299D4—82no—
300D4—84no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4D4×Dic1912yes—
324C2×C4#1059738111yescharacteristic
325C2×C4#1059738311yescharacteristic
326C2×C4#1059738512yes—
327C8—764no—
328C8—1522no—
329C22—21no—
330C22—21no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22#1192642411yescharacteristic
344C22#1192656111yescharacteristic
345C22#1192656111yescharacteristic
346C4—22no—
347C4—22no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—81no—
355C4—81no—
356C2—21no—
357C2—21no—
358C2—81no—
359C2—161no—
360C2#1456401911yescharacteristic
361C2#1456408411yescharacteristic
362C2#1456418311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2610C2
socleC22×C19#386
prime radicalC19×#392C4
cosocleC2×C42×C19C23
hypercenter#2610D19
hypocenterC19#9389
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2610

Complements

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

NH ≅ G/Ntype
1. #14572273C2semidirect
2. #14562233C2semidirect
3. #14561969C2semidirect
4. #14561528C2semidirect
58. #10597260D4semidirect
241. C19#9389semidirect

Maximal subgroups

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

subgroupindex
#145722732
#145622332
#145619692
#145615282
C19×#26102
#938919