Finite Group Databasebeta

← #18088172

Subgroups — #18088172

Order 4864.

1194 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926311C212yesmaximal
2C2×#11926311C212yesmaximal
3#14561858C212yesmaximal
4C2×C4×C22⋊C4×C19C211yesmaximal, characteristic
5C22×C22⋊Dic19C2214yes—
6C2×C19⋊#95—24no—
7#11926311—24no—
8#11926311C418yescomplemented
9C24×C4×C19C2211yescharacteristic
10C22×C22⋊C4×C19C2211yescharacteristic
11C22×C22⋊C4×C19C2211yescharacteristic
12C22×C42×C19C412yescomplemented
13C4×C22⋊C4×C19—24no—
14C2×C19×#95C412yescomplemented
15C25×C19C2311yescharacteristic
16C23×C4×C19—22no—
17C23×C4×C19—22no—
18C23×C4×C19—44no—
19C23×C4×C19C2×C411yescharacteristic
20C23×C4×C19C2×C412yes—
21C23×C4×C19C2×C411yescharacteristic
22C23×C4×C19C2×C412yes—
23C23×C4×C19D414yes—
24C23×Dic19—24no—
25C2×C22⋊C4×C19—22no—
26C2×C22⋊C4×C19—22no—
27C2×C22⋊C4×C19—22no—
28C2×C22⋊C4×C19—22no—
29C2×C22⋊C4×C19C2×C414yes—
30C2×C22⋊C4×C19D412yes—
31C2×C22⋊C4×C19Q812yes—
32C2×C42×C19—22no—
33C2×C42×C19—22no—
34C2×C42×C19—44no—
35C2×C22⋊Dic19—24no—
36C2×C22⋊Dic19—24no—
37C2×C22⋊Dic19—24no—
38C2×C22⋊Dic19—24no—
39C2×C22⋊Dic19—24no—
40C2×C22⋊Dic19C2×C418yes—
41C19×#95—24no—
42C19⋊#95—48no—
43C24×C19—42no—
44C24×C19—42no—
45C24×C19C22×C412yes—
46C24×C19C22×C411yescharacteristic
47C24×C19C2×D411yescharacteristic
48C24×C19C2×D412yes—
49C24×C19C2×Q811yescharacteristic
50C24×C19#4112yes—
51C24×C19#4112yes—
52C24×C19#4112yes—
53C24×C19#4112yes—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—24no—
57C22×C4×C19—22no—
58C22×C4×C19—22no—
59C22×C4×C19—22no—
60C22×C4×C19—22no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—28no—
64C22×C4×C19—28no—
65C22×C4×C19—42no—
66C22×C4×C19—44no—
67C22×C4×C19—48no—
68C22×C4×C19—48no—
69C22×C4×C19—42no—
70C22×C4×C19—42no—
71C22×C4×C19—42no—
72C22×C4×C19—42no—
73C22×C4×C19C4214yes—
74C22×C4×C19C22⋊C412yes—
75C22×C4×C19C22⋊C412yes—
76C22×C4×C19C4⋊C414yes—
77C22×Dic19—28no—
78C22×Dic19—48no—
79C22×Dic19—48no—
80C22×Dic19—44no—
81C22×Dic19—44no—
82C22⋊C4×C19—28no—
83C22⋊C4×C19—24no—
84C22⋊C4×C19—24no—
85C42×C19—44no—
86C42×C19—44no—
87C22⋊Dic19—28no—
88C22⋊Dic19—28no—
89C22⋊Dic19—44no—
90C22⋊Dic19—44no—
91#10801—191nomaximal, Sylow
92C23×C19—24no—
93C23×C19—22no—
94C23×C19—24no—
95C23×C19—22no—
96C23×C19—42no—
97C23×C19—42no—
98C23×C19—44no—
99C23×C19—42no—
100C23×C19—42no—
101C23×C19—44no—
102C23×C19—42no—
103C23×C19—42no—
104C23×C19—44no—
105C23×C19C2×C4211yescharacteristic
106C23×C19C2×C22⋊C411yescharacteristic
107C23×C19C2×C4⋊C411yescharacteristic
108C23×C19#11714yes—
109C23×C19#11711yescharacteristic
110C23×C19#11711yescharacteristic
111C23×C19#11711yescharacteristic
112C23×C19#11711yescharacteristic
113C23×C19C4×D412yes—
114C23×C19C4×D414yes—
115C23×C19C4×Q812yes—
116C23×C19#12112yes—
117C23×C19C22⋊Q812yes—
118C23×C19#12314yes—
119C23×C19#12412yes—
120C23×C19#12512yes—
121C23×C19#12614yes—
122C2×C4×C19—24no—
123C2×C4×C19—24no—
124C2×C4×C19—22no—
125C2×C4×C19—22no—
126C2×C4×C19—24no—
127C2×C4×C19—24no—
128C2×C4×C19—22no—
129C2×C4×C19—24no—
130C2×C4×C19—416no—
131C2×C4×C19—44no—
132C2×C4×C19—44no—
133C2×C4×C19—42no—
134C2×C4×C19—42no—
135C2×C4×C19—42no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19—42no—
139C2×C4×C19—44no—
140C2×C4×C19—44no—
141C2×C4×C19#9914yes—
142C2×Dic19—416no—
143C2×Dic19—48no—
144C2×Dic19—88no—
145C2×Dic19—84no—
146C2×Dic19—84no—
147C2×C4×C22⋊C4D1911yescharacteristic
148C2×#342—192no—
149C2×#342—192no—
150C22⋊#95—192no—
151C22×C19—24no—
152C22×C19—22no—
153C22×C19—22no—
154C22×C19—24no—
155C22×C19—24no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—24no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—28no—
162C22×C19—22no—
163C22×C19—22no—
164C22×C19—44no—
165C22×C19—42no—
166C22×C19—42no—
167C22×C19—42no—
168C22×C19—42no—
169C22×C19—44no—
170C22×C19#37611yescharacteristic
171C22×C19C4×C22⋊C411yescharacteristic
172C22×C19C4×C4⋊C411yescharacteristic
173C22×C19#38011yescharacteristic
174C22×C19#38111yescharacteristic
175C22×C19#38211yescharacteristic
176C22×C19#38311yescharacteristic
177C22×C19#38714yes—
178C22×C19#38814yes—
179C22×C19C2×#9912yes—
180C22×C19#41012yes—
181C4×C19—24no—
182C4×C19—44no—
183C4×C19—42no—
184C4×C19—44no—
185Dic19—88no—
186C24×C4C2×D1911yescharacteristic
187C22×C22⋊C4—194no—
188C22×C22⋊C4C2×D1911yescharacteristic
189C22×C22⋊C4C2×D1911yescharacteristic
190C22×C42Dic1912yescomplemented
191C4×C22⋊C4—24no—
192C2×#95—384no—
193C2×#95Dic1912yescomplemented
194#342—198no—
195#342—384no—
196C2×C19—24no—
197C2×C19—21no—
198C2×C19—21no—
199C2×C19—21no—
200C2×C19—21no—
201C2×C19—24no—
202C2×C19#143411yescharacteristic
203C2×C19C4×#9912yes—
204C2×C19#179912yes—
205C2×C19#181911yescharacteristic
206C2×C19#182011yescharacteristic
207C25C22×D1911yescharacteristic
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—44no—
211C23×C4—384no—
212C23×C4C2×Dic1911yescharacteristic
213C23×C4C2×Dic1912yes—
214C23×C4C2×Dic1912yes—
215C23×C4C2×Dic1911yescharacteristic
216C23×C4C22⋊D1914yes—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—198no—
222C2×C22⋊C4—384no—
223C2×C22⋊C4—384no—
224C2×C22⋊C4—384no—
225C2×C22⋊C4—384no—
226C2×C22⋊C4—384no—
227C2×C22⋊C4Dic3812yes—
228C2×C22⋊C4C4×D1914yes—
229C2×C22⋊C4D7612yes—
230C2×C42—22no—
231C2×C42—22no—
232C2×C42—44no—
233#95—24no—
234#95—768no—
235C19#1080111yescharacteristic, complemented, Sylow
236C24—42no—
237C24—42no—
238C24C2×Dic3811yescharacteristic
239C24C2×C4×D1912yes—
240C24C2×D7611yescharacteristic
241C24#6454112yes—
242C24#6454112yes—
243C24#6454112yes—
244C24#6454112yes—
245C24C22×Dic1911yescharacteristic
246C24C2×C22⋊D1912yes—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—24no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—28no—
257C22×C4—28no—
258C22×C4—42no—
259C22×C4—44no—
260C22×C4—48no—
261C22×C4—48no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—388no—
267C22×C4—768no—
268C22×C4—768no—
269C22×C4—764no—
270C22×C4—764no—
271C22×C4C4×Dic1914yes—
272C22×C4C4⋊Dic1914yes—
273C22×C4C22⋊Dic1912yes—
274C22×C4C22⋊Dic1912yes—
275C22⋊C4—24no—
276C22⋊C4—24no—
277C22⋊C4—28no—
278C22⋊C4—388no—
279C22⋊C4—388no—
280C22⋊C4—764no—
281C22⋊C4—764no—
282C42—44no—
283C42—44no—
284C23—22no—
285C23—24no—
286C23—22no—
287C23—24no—
288C23—42no—
289C23—42no—
290C23—42no—
291C23—44no—
292C23—42no—
293C23—44no—
294C23—44no—
295C23—42no—
296C23—42no—
297C23C4×Dic3812yes—
298C23#1059731612yes—
299C23#1059731814yes—
300C23C4×D7612yes—
301C23#1059732112yes—
302C23#1059732214yes—
303C23C2×C4×Dic1911yescharacteristic
304C23#1059737012yes—
305C23C2×C4⋊Dic1911yescharacteristic
306C23#1059737211yescharacteristic
307C23#1059737211yescharacteristic
308C23#1059737211yescharacteristic
309C23#1059737211yescharacteristic
310C23C4×C22⋊D1914yes—
311C23#1059737514yes—
312C23#1059737612yes—
313C23C2×C22⋊Dic1911yescharacteristic
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—24no—
322C2×C4—416no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—44no—
326C2×C4—44no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—7616no—
334C2×C4—768no—
335C2×C4—1528no—
336C2×C4—1524no—
337C2×C4—1524no—
338C2×C4#1059729114yes—
339C22—22no—
340C22—22no—
341C22—24no—
342C22—24no—
343C22—22no—
344C22—22no—
345C22—28no—
346C22—21no—
347C22—21no—
348C22—24no—
349C22—24no—
350C22—21no—
351C22—21no—
352C22—42no—
353C22—42no—
354C22—44no—
355C22—42no—
356C22—42no—
357C22—44no—
358C22#1192639011yescharacteristic
359C22C4×C22⋊Dic1911yescharacteristic
360C22C4×C4⋊Dic1911yescharacteristic
361C22#1192640411yescharacteristic
362C22#1192640711yescharacteristic
363C22#1192641011yescharacteristic
364C22#1192641211yescharacteristic
365C22#1192642814yes—
366C22#1192643514yes—
367C22C2×#1059729112yes—
368C22#1192651812yes—
369C4—24no—
370C4—44no—
371C4—44no—
372C4—42no—
373C4—1528no—
374C2—24no—
375C2—21no—
376C2—21no—
377C2—21no—
378C2—21no—
379C2—24no—
380C2#1456186211yescharacteristic
381C2C4×#1059729112yes—
382C2#1456362312yes—
383C2#1456370911yescharacteristic
384C2#1456371211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC23×C19C2×C42
FrattiniC25C22×D19
FittingC2×C4×C22⋊C4×C19C2
socleC23×C19C2×C22⋊C4
prime radical, cosocleC25×C19C23
hypercenterC2×C4×C22⋊C4D19
hypocenterC19#10801
LCSG ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #11926311C4semidirect
12. C22×C42×C19C4semidirect
14. C2×C19×#95C4semidirect
190. C22×C42Dic19semidirect
193. C2×#95Dic19semidirect
235. C19#10801semidirect

Maximal subgroups

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

subgroupindex
C2×#119263112
#145618582
C2×C4×C22⋊C4×C192
#1080119