Finite Group Databasebeta

← #18075862

Subgroups — #18075862

Order 4864.

1158 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563545C212yesmaximal
2#14561478C214yesmaximal, complemented
3C22×C19×#95C211yesmaximal, characteristic
4C2×C22⋊(C19⋊C8)—22no—
5C2×C22⋊(C19⋊C8)—22no—
6C2×C22⋊(C19⋊C8)C2214yes—
7C24×C4×C19C411yescharacteristic
8C24×C4×C19C411yescharacteristic
9C24×C4×C19C2211yescharacteristic
10C2×C19×#95—22no—
11C2×C19×#95—22no—
12C2×C19×#95C412yes—
13C2×C19×#95C2212yes—
14C25×C19C2×C411yescharacteristic
15C23×C4×C19—21no—
16C23×C4×C19—21no—
17C23×C4×C19—21no—
18C23×C4×C19—21no—
19C23×C4×C19—22no—
20C23×C4×C19—24no—
21C23×C4×C19—24no—
22C23×C4×C19—42no—
23C23×C4×C19—42no—
24C23×C4×C19—42no—
25C23×C4×C19—42no—
26C23×C4×C19—42no—
27C23×C4×C19—42no—
28C23×C4×C19C814yescomplemented
29C23×C4×C19C2×C411yescharacteristic
30C23×C4×C19C2×C412yes—
31C23×C4×C19C2×C412yes—
32C23×C4×C19D412yes—
33C23×C4×C19D412yes—
34C23×C4×C19C2311yescharacteristic
35C22×C19⋊C8—24no—
36C19×#95—24no—
37C19×#95—24no—
38C22⋊(C19⋊C8)—28no—
39C22⋊(C19⋊C8)—44no—
40C22⋊(C19⋊C8)—44no—
41C24×C19—22no—
42C24×C19—22no—
43C24×C19—22no—
44C24×C19—22no—
45C24×C19—22no—
46C24×C19—22no—
47C24×C19C22⋊C411yescharacteristic
48C24×C19C22⋊C411yescharacteristic
49C24×C19C2×C812yes—
50C24×C19M1612yes—
51C24×C19C22×C411yescharacteristic
52C22×C4×C19—24no—
53C22×C4×C19—24no—
54C22×C4×C19—24no—
55C22×C4×C19—24no—
56C22×C4×C19—24no—
57C22×C4×C19—24no—
58C22×C4×C19—22no—
59C22×C4×C19—22no—
60C22×C4×C19—22no—
61C22×C4×C19—22no—
62C22×C4×C19—22no—
63C22×C4×C19—24no—
64C22×C4×C19—24no—
65C22×C4×C19—41no—
66C22×C4×C19—41no—
67C22×C4×C19—42no—
68C22×C4×C19—42no—
69C22×C4×C19—41no—
70C22×C4×C19—41no—
71C22×C4×C19—416no—
72C22×C4×C19—416no—
73C22×C4×C19—48no—
74C22×C4×C19—42no—
75C22×C4×C19—42no—
76C22×C4×C19—42no—
77C22×C4×C19—42no—
78C22×C4×C19—42no—
79C22×C4×C19—42no—
80C22×C4×C19—42no—
81C22×C4×C19—42no—
82C22×C4×C19—48no—
83C22×C4×C19—42no—
84C22×C4×C19—42no—
85C22×C4×C19—42no—
86C22×C4×C19—42no—
87C22×C4×C19C22⋊C412yes—
88C22×C4×C19C2×C814yes—
89C22×C4×C19M1614yes—
90C22×C4×C19C2×D412yes—
91C22×C4×C19#4114yes—
92C2×C19⋊C8—44no—
93C2×C19⋊C8—44no—
94C2×C19⋊C8—44no—
95#8698—191nomaximal, Sylow
96C23×C19—28no—
97C23×C19—28no—
98C23×C19—28no—
99C23×C19—28no—
100C23×C19—24no—
101C23×C19—24no—
102C23×C19—24no—
103C23×C19—24no—
104C23×C19—21no—
105C23×C19—21no—
106C23×C19—21no—
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—21no—
112C23×C19—21no—
113C23×C19—21no—
114C23×C19—21no—
115C23×C19—21no—
116C23×C19—24no—
117C23×C19—24no—
118C23×C19C22⋊C812yes—
119C23×C19C22⋊C812yes—
120C23×C19#9912yes—
121C23×C19#9912yes—
122C23×C19#10012yes—
123C23×C19#10112yes—
124C23×C19C2×C22⋊C411yescharacteristic
125C23×C19#11712yes—
126C23×C19C22×C811yescharacteristic
127C23×C19C2×M1611yescharacteristic
128C23×C19C2×M1612yes—
129C2×C4×C19—22no—
130C2×C4×C19—22no—
131C2×C4×C19—22no—
132C2×C4×C19—24no—
133C2×C4×C19—24no—
134C2×C4×C19—22no—
135C2×C4×C19—22no—
136C2×C4×C19—44no—
137C2×C4×C19—48no—
138C2×C4×C19—48no—
139C2×C4×C19—44no—
140C2×C4×C19—48no—
141C2×C4×C19—44no—
142C2×C4×C19—48no—
143C2×C4×C19—48no—
144C2×C4×C19—44no—
145C2×C4×C19—48no—
146C2×C4×C19—42no—
147C2×C4×C19—42no—
148C2×C4×C19—42no—
149C2×C4×C19—42no—
150C2×C4×C19—44no—
151C2×C4×C19—44no—
152C2×C4×C19#12314yes—
153C19⋊C8—84no—
154C22×#95D1911yescharacteristic
155#1779—192no—
156#1280—194no—
157C22×C19—216no—
158C22×C19—216no—
159C22×C19—22no—
160C22×C19—22no—
161C22×C19—22no—
162C22×C19—22no—
163C22×C19—22no—
164C22×C19—22no—
165C22×C19—22no—
166C22×C19—22no—
167C22×C19—22no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—22no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—22no—
174C22×C19—22no—
175C22×C19—22no—
176C22×C19—22no—
177C22×C19—22no—
178C22×C19—22no—
179C22×C19#32314yes—
180C22×C19#32414yes—
181C22×C19#38111yescharacteristic
182C22×C19C2×C22⋊C811yescharacteristic
183C22×C19#40711yescharacteristic
184C22×C19C2×#9911yescharacteristic
185C22×C19C2×#9911yescharacteristic
186C22×C19C2×#10011yescharacteristic
187C22×C19C2×#10111yescharacteristic
188C22×C19#43112yes—
189C22×C19#43212yes—
190C4×C19—24no—
191C4×C19—42no—
192C4×C19—44no—
193C4×C19—44no—
194C24×C4Dic1911yescharacteristic
195C24×C4Dic1911yescharacteristic
196C24×C4C2×D1911yescharacteristic
197C2×C22⋊C8—194no—
198C2×C22⋊C8—382no—
199C2×C22⋊C8—382no—
200C2×#95—22no—
201C2×#95—22no—
202C2×#95Dic1912yes—
203C2×#95C2×D1912yes—
204C2×C19—24no—
205C2×C19—24no—
206C2×C19—22no—
207C2×C19—22no—
208C2×C19C2×#32311yescharacteristic
209C2×C19C2×#32411yescharacteristic
210C2×C19#146211yescharacteristic
211C2×C19#146311yescharacteristic
212C2×C19#181711yescharacteristic
213C2×C19#181911yescharacteristic
214C2×C19#182111yescharacteristic
215C25C2×Dic1911yescharacteristic
216C23×C4—22no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—42no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4C19⋊C814yescomplemented
230C23×C4C2×Dic1912yes—
231C23×C4C2×Dic1912yes—
232C23×C4C2×Dic1911yescharacteristic
233C23×C4C22⋊D1912yes—
234C23×C4C22⋊D1912yes—
235C23×C4C22×D1911yescharacteristic
236C22×C8—384no—
237C22⋊C8—388no—
238C22⋊C8—764no—
239C22⋊C8—764no—
240#95—24no—
241#95—24no—
242C19#869811yescharacteristic, complemented, Sylow
243C24—22no—
244C24—22no—
245C24—22no—
246C24—22no—
247C24—22no—
248C24—22no—
249C24C2×C19⋊C812yes—
250C24#6452012yes—
251C24C22⋊Dic1911yescharacteristic
252C24C22⋊Dic1911yescharacteristic
253C24C22×Dic1911yescharacteristic
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—416no—
274C22×C4—416no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—48no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—48no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4C2×C19⋊C814yes—
290C22×C4#6452014yes—
291C22×C4C22⋊Dic1912yes—
292C22×C4#6454114yes—
293C22×C4C2×C22⋊D1912yes—
294C2×C8—764no—
295C2×C8—764no—
296C2×C8—764no—
297C23—28no—
298C23—28no—
299C23—28no—
300C23—28no—
301C23—24no—
302C23—24no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—24no—
314C23—24no—
315C23—21no—
316C23—21no—
317C23—24no—
318C23—24no—
319C23C22⋊(C19⋊C8)12yes—
320C23C22⋊(C19⋊C8)12yes—
321C23#1059729012yes—
322C23#1059729112yes—
323C23#1059729112yes—
324C23#1059729312yes—
325C23C22×C19⋊C811yescharacteristic
326C23C2×#6452012yes—
327C23C2×#6452011yescharacteristic
328C23#1059737212yes—
329C23C2×C22⋊Dic1911yescharacteristic
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—44no—
338C2×C4—48no—
339C2×C4—48no—
340C2×C4—44no—
341C2×C4—48no—
342C2×C4—44no—
343C2×C4—48no—
344C2×C4—48no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—48no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4#1059737514yes—
354C8—1524no—
355C22—216no—
356C22—216no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—21no—
367C22—21no—
368C22—22no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22#1192626814yes—
378C22#1192627014yes—
379C22#1192640711yescharacteristic
380C22C2×C22⋊(C19⋊C8)11yescharacteristic
381C22#1192650811yescharacteristic
382C22C2×#1059729111yescharacteristic
383C22C2×#1059729111yescharacteristic
384C22C2×#1059729011yescharacteristic
385C22C2×#1059729311yescharacteristic
386C22#1192659712yes—
387C22#1192660112yes—
388C4—24no—
389C4—42no—
390C4—44no—
391C4—44no—
392C2—22no—
393C2—22no—
394C2—24no—
395C2—24no—
396C2C2×#1192626811yescharacteristic
397C2C2×#1192627011yescharacteristic
398C2#1456196211yescharacteristic
399C2#1456196511yescharacteristic
400C2#1456370311yescharacteristic
401C2#1456370911yescharacteristic
402C2#1456371511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC23×C19C22×C8
FrattiniC23×C4C22×D19
FittingC22×C19×#95C2
socleC23×C19C2×C22⋊C4
prime radicalC25×C19C2×C4
cosocleC23×C4×C19C23
hypercenterC22×#95D19
hypocenterC19#8698
LCSG ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
2. #14561478C2semidirect
28. C23×C4×C19C8semidirect
229. C23×C4C19⋊C8semidirect
242. C19#8698semidirect

Maximal subgroups

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

subgroupindex
#145635452
#145614782
C22×C19×#952
#869819