Finite Group Databasebeta

← #18079875

Subgroups — #18079875

Order 4864.

582 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 111 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#14572054C211yesmaximal, characteristic, complemented
2#14562233C212yesmaximal, complemented
3#14561969C211yesmaximal, characteristic, complemented
4#14561528C212yesmaximal, complemented
5C19×#2610C211yesmaximal, characteristic
6C22×#64520—21no—
7#11926601C2212yes—
8#11926500—24no—
9C4×#64520—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—24no—
48C2×#64520—24no—
49C2×#64520—22no—
50C2×#64520—22no—
51C22×C19⋊C8—22no—
52C19×#95—21no—
53C19×#95—21no—
54C19×#95—21no—
55C19×#95C2×C411yescharacteristic
56C19×#95C2×C411yescharacteristic
57C22⋊(C19⋊C8)—22no—
58C4⋊(C19⋊C8)—22no—
59#10597260—22no—
60#10597260—22no—
61#10597260D414yescomplemented
62C4×C19⋊C8—22no—
63C4×C19⋊C8—22no—
64C24×C19—21no—
65C24×C19C22⋊C411yescharacteristic
66C2×Q8×C19—22no—
67C2×Q8×C19—81no—
68C2×D4×C19—22no—
69C2×D4×C19—42no—
70C2×D4×C19—42no—
71C2×D4×C19—81no—
72C2×D4×C19—81no—
73C22×C4×C19—22no—
74C22×C4×C19—22no—
75C22×C4×C19—21no—
76C22×C4×C19—21no—
77C22×C4×C19—21no—
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19C22⋊C411yescharacteristic
81C22×C4×C19C22⋊C411yescharacteristic
82C22×C4×C19C22⋊C411yescharacteristic
83C22×C4×C19C22×C411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C4⋊C4×C19—22no—
87C4⋊C4×C19—22no—
88C4⋊C4×C19—81no—
89C22⋊C4×C19—22no—
90C22⋊C4×C19—22no—
91C22⋊C4×C19—42no—
92C22⋊C4×C19—42no—
93C22⋊C4×C19—41no—
94C22⋊C4×C19—42no—
95C22⋊C4×C19—41no—
96C22⋊C4×C19—81no—
97C22⋊C4×C19—81no—
98C42×C19—21no—
99C42×C19—21no—
100C42×C19—42no—
101C42×C19C2×D412yes—
102C42×C19#4112yes—
103#64520—28no—
104#64520—24no—
105#64520—24no—
106C2×C19⋊C8—28no—
107C2×C19⋊C8—24no—
108C2×C19⋊C8—42no—
109#9387—191nomaximal, Sylow
110C23×C19—21no—
111C23×C19—21no—
112C23×C19—41no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19—41no—
116C23×C19—41no—
117C23×C19—41no—
118C23×C19—41no—
119C23×C19—41no—
120C23×C19—41no—
121C23×C19#10412yes—
122C23×C19C2×C22⋊C411yescharacteristic
123Q8×C19—82no—
124D4×C19—82no—
125D4×C19—84no—
126C2×C4×C19—22no—
127C2×C4×C19—22no—
128C2×C4×C19—24no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—22no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
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×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19#10412yes—
149C2×C4×C19C4×D412yes—
150C2×C4×C19#12011yescharacteristic
151C2×C4×C19#12112yes—
152C2×C4×C19#12311yescharacteristic
153C19⋊C8—28no—
154C19⋊C8—82no—
155#2873—191no—
156#2610D1911yescharacteristic
157#1527—192no—
158#1464—191no—
159#1300—192no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—22no—
163C22×C19—42no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—81no—
167C22×C19—81no—
168C22×C19—81no—
169C22×C19—81no—
170C22×C19—81no—
171C22×C19—81no—
172C22×C19—81no—
173C22×C19—81no—
174C22×C19#38611yescharacteristic
175C22×C19C2×#10411yescharacteristic
176C22×C19C2×#10411yescharacteristic
177C4×C19—22no—
178C4×C19—21no—
179C4×C19—22no—
180C4×C19—21no—
181C4×C19—22no—
182C4×C19—42no—
183C4×C19—41no—
184C4×C19—41no—
185C4×C19—81no—
186C4×C19—81no—
187C22×M16—381no—
188C2×#124C2×D1911yescharacteristic
189C2×#117C2×D1911yescharacteristic
190#432—192no—
191#405—384no—
192C4×M16—192no—
193C4×M16—381no—
194#395Dic1911yescharacteristic
195#394Dic1911yescharacteristic
196#393Dic1911yescharacteristic
197#392Dic1911yescharacteristic
198#390—21no—
199#388—21no—
200#388—21no—
201#386—21no—
202#376C2×D1911yescharacteristic
203#329—384no—
204#324—381no—
205#323—381no—
206C2×C19—21no—
207C2×C19—21no—
208C2×C19—42no—
209C2×C19—161no—
210C2×C19#188411yescharacteristic
211C2×C19#189611yescharacteristic
212C2×C19#191411yescharacteristic
213C22×Q8C2×Dic1911yescharacteristic
214C22×D4—21no—
215C22×D4C2×Dic1911yescharacteristic
216C23×C4C22⋊D1911yescharacteristic
217C2×M16—382no—
218C2×M16—384no—
219C2×M16—384no—
220C2×M16—382no—
221C22×C8—382no—
222#124—22no—
223#124—22no—
224#117—22no—
225#117—22no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4C2×Dic1911yescharacteristic
228C2×C4⋊C4C22⋊D1911yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4C2×Dic1911yescharacteristic
236C2×C22⋊C4C22⋊D1911yescharacteristic
237C2×C42—21no—
238C2×C42C22⋊D1911yescharacteristic
239C2×C42C22×D1911yescharacteristic
240C4⋊C8—382no—
241C22⋊C8—382no—
242#97—194no—
243#97—382no—
244#97—382no—
245C4×C8—382no—
246C4×C8—382no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95C2×Dic1911yescharacteristic
251#95C2×Dic1911yescharacteristic
252C19#938711yescharacteristic, complemented, Sylow
253C24—21no—
254C24C22⋊Dic1911yescharacteristic
255C2×Q8—22no—
256C2×Q8—81no—
257C2×D4—22no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—81no—
261C2×D4—81no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4C22⋊Dic1911yescharacteristic
270C22×C4C22⋊Dic1911yescharacteristic
271C22×C4C22⋊Dic1911yescharacteristic
272C22×C4C22×Dic1911yescharacteristic
273C22×C4C2×C22⋊D1911yescharacteristic
274C22×C4C2×C22⋊D1911yescharacteristic
275M16—388no—
276M16—384no—
277M16—384no—
278C2×C8—388no—
279C2×C8—384no—
280C2×C8—762no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—81no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—42no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—81no—
292C22⋊C4—81no—
293C42—21no—
294C42—21no—
295C42—42no—
296C42D4×D1912yes—
297C42#6454312yes—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23#1059729412yes—
310C23C2×C22⋊Dic1911yescharacteristic
311Q8—82no—
312D4—82no—
313D4—84no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4#1059729412yes—
337C2×C4D4×Dic1912yes—
338C2×C4#1059738111yescharacteristic
339C2×C4#1059738311yescharacteristic
340C2×C4#1059738512yes—
341C8—388no—
342C8—1522no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22#1192642411yescharacteristic
358C22C2×#1059729411yescharacteristic
359C22C2×#1059729411yescharacteristic
360C4—22no—
361C4—22no—
362C4—21no—
363C4—21no—
364C4—22no—
365C4—42no—
366C4—41no—
367C4—41no—
368C4—81no—
369C4—81no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—161no—
374C2#1456401911yescharacteristic
375C2#1456407911yescharacteristic
376C2#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#9387
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. #14572054C2semidirect
2. #14562233C2semidirect
3. #14561969C2semidirect
4. #14561528C2semidirect
61. #10597260D4semidirect
252. C19#9387semidirect

Maximal subgroups

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

subgroupindex
#145720542
#145622332
#145619692
#145615282
C19×#26102
#938719