Finite Group Databasebeta

← #18077737

Subgroups — #18077737

Order 4864.

476 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573639C211yesmaximal, characteristic
2#14572576C211yesmaximal, characteristic, complemented
3#14564432C211yesmaximal, characteristic
4#14562061C211yesmaximal, characteristic
5#14561532C211yesmaximal, characteristic, complemented
6#14561479C211yesmaximal, characteristic, complemented
7C19×#1542C211yesmaximal, characteristic, complemented
8C2×C4×D76C2211yescharacteristic
9#11926872C412yes—
10#11926831—21no—
11#11926746—21no—
12#11926694C412yes—
13#11926675—22no—
14#11926675—22no—
15C4×#64527—22no—
16#11926597C2211yescharacteristic
17#11926571—21no—
18#11926568C2211yescharacteristic
19C2×(C2×D19)⋊C8—21no—
20C2×(C2×D19)⋊C8—21no—
21#11926500—21no—
22C2×#10597260C2211yescharacteristic
23#11926273—22no—
24C19×#533C2211yescharacteristic
25C19×#431C2211yescharacteristic
26C2×C19×C4⋊C8C2211yescharacteristic
27C19×#333—21no—
28C19×#332—21no—
29C22×D76C2×C411yescharacteristic
30C22×C4×D19—21no—
31C22×C8×C19—21no—
32C19×C4⋊Q8D411yescharacteristic
33C19×C4⋊Q8D411yescharacteristic
34C19×#125—21no—
35C19×C22⋊Q8—21no—
36C19×C22⋊Q8C2×C412yes—
37C4×Q8×C19—21no—
38C4×Q8×C19D412yes—
39C19×#117—21no—
40C2×C42×C19C2311yescharacteristic
41C2×#64527—22no—
42C2×(C2×D19)⋊C4—21no—
43C2×C4⋊Dic19C2×C411yescharacteristic
44C2×#64520—21no—
45C22×C19⋊C8D411yescharacteristic
46C22×C19⋊C8D411yescharacteristic
47C4×D76—21no—
48C4×D76—21no—
49C4×D76—21no—
50C4×D76—21no—
51C19×C4⋊C8—21no—
52C19×C4⋊C8—21no—
53C19×C4⋊C8—21no—
54C19×C22⋊C8—21no—
55C4×C8×C19—21no—
56#10597292—22no—
57C22⋊(C19⋊C8)C2×C412yes—
58(C2×D19)⋊C8—42no—
59(C2×D19)⋊C8—42no—
60#10597266—22no—
61#10597265—22no—
62C4⋊(C19⋊C8)—24no—
63C4⋊(C19⋊C8)—21no—
64C4⋊(C19⋊C8)—21no—
65C4⋊(C19⋊C8)D412yes—
66#10597260—22no—
67#10597260—21no—
68#10597260—21no—
69C4×C19⋊C8—22no—
70C4×C19⋊C8—21no—
71C23×D19—21no—
72C2×Q8×C19—21no—
73C2×Q8×C19C22⋊C412yes—
74C22×C4×C19C22×C411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19#4111yescharacteristic
77C22×Dic19—21no—
78C2×D76—21no—
79C2×D76—21no—
80C2×D76—42no—
81C2×C4×D19—41no—
82C2×C4×D19—41no—
83C2×C4×D19—41no—
84C2×C4×D19—41no—
85C2×C4×D19—41no—
86C2×C4×D19—41no—
87C2×C8×C19—41no—
88C2×C8×C19—41no—
89C2×C8×C19—41no—
90C2×C8×C19—41no—
91C4⋊C4×C19—22no—
92C4⋊C4×C19—21no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—22no—
96C4⋊C4×C19C22⋊C412yes—
97C22⋊C4×C19—22no—
98C42×C19—22no—
99C42×C19C2×D411yescharacteristic
100C42×C19C2×D411yescharacteristic
101C42×C19C2×D411yescharacteristic
102C42×C19#4111yescharacteristic
103#64527—44no—
104(C2×D19)⋊C4—41no—
105(C2×D19)⋊C4—41no—
106C4⋊Dic19—21no—
107C4⋊Dic19—21no—
108#64520—41no—
109#64520—41no—
110C2×C19⋊C8—21no—
111C2×C19⋊C8—21no—
112C2×C19⋊C8—22no—
113C2×C19⋊C8—22no—
114C2×C19⋊C8—21no—
115C2×C19⋊C8—21no—
116C2×C19⋊C8—21no—
117C2×C19⋊C8SD1612yescomplemented
118#9050—191nomaximal, Sylow
119C23×C19C4×D411yescharacteristic
120C22×D19—22no—
121C22×D19—41no—
122C22×D19—41no—
123C22×D19—41no—
124C22×D19—41no—
125C22×D19—41no—
126C22×D19—41no—
127Q8×C19—42no—
128Q8×C19—81no—
129C2×C4×C19—22no—
130C2×C4×C19—22no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19C2×C22⋊C411yescharacteristic
134C2×C4×C19C4×D411yescharacteristic
135C2×C4×C19#12011yescharacteristic
136C2×C4×C19#12111yescharacteristic
137C2×C4×C19#12111yescharacteristic
138C2×C4×C19#12311yescharacteristic
139C2×C4×C19C2×SD1611yescharacteristic
140C2×C4×C19#13511yescharacteristic
141C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C19#13711yescharacteristic
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146D76—22no—
147D76—22no—
148D76—41no—
149D76—41no—
150C4×D19—81no—
151C4×D19—81no—
152C4×D19—81no—
153C4×D19—81no—
154C8×C19—81no—
155C8×C19—81no—
156C19⋊C8—22no—
157C19⋊C8—42no—
158C19⋊C8—41no—
159C19⋊C8—42no—
160#3101—191no—
161#2961—191no—
162#1955—191no—
163#1542D1911yescharacteristic, complemented
164#1486—191no—
165#1301—191no—
166#1281—191no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19#38611yescharacteristic
170C22×C19C4×SD1611yescharacteristic
171C22×C19#44011yescharacteristic
172C2×D19—42no—
173C2×D19—42no—
174C2×D19—42no—
175C2×D19—81no—
176C2×D19—81no—
177C2×D19—81no—
178C2×D19—81no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—42no—
184C4×C19—42no—
185C4×C19#44811yescharacteristic
186C4×C19#44911yescharacteristic
187C4×C19#46011yescharacteristic
188C4×C19#46411yescharacteristic
189Dic19—81no—
190#533C2×D1911yescharacteristic
191C2×C4×D4—191no—
192#483—192no—
193#476—381no—
194#461—381no—
195#450—192no—
196#446—382no—
197#446—382no—
198C4×SD16—382no—
199#431—191no—
200#431C2×D1911yescharacteristic
201#424—381no—
202#423—191no—
203C2×C4⋊C8C2×D1911yescharacteristic
204C2×C22⋊C8—381no—
205C2×C22⋊C8—381no—
206#405—381no—
207C2×#97—191no—
208#333—21no—
209#332—21no—
210D4⋊C8—382no—
211C2×C19—21no—
212C2×C19—21no—
213C2×C19#188011yescharacteristic
214C2×C19#188111yescharacteristic
215C2×C19#189111yescharacteristic
216D19—82no—
217C22×D4—191no—
218C23×C4—381no—
219C2×SD16—382no—
220C2×M16—381no—
221C22×C8—21no—
222C22×C8—191no—
223C22×C8—191no—
224C4⋊Q8C22⋊D1911yescharacteristic
225C4⋊Q8C22⋊D1911yescharacteristic
226#125—21no—
227C22⋊Q8—21no—
228C22⋊Q8C4×D1912yes—
229C4×Q8—21no—
230C4×Q8D7612yes—
231C4×D4—381no—
232C4×D4—381no—
233C4×D4—381no—
234C4×D4—381no—
235#117—21no—
236C2×C4⋊C4—191no—
237C2×C22⋊C4—381no—
238C2×C42C22×D1911yescharacteristic
239#106—382no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—192no—
244C4⋊C8—384no—
245C4⋊C8—381no—
246C4⋊C8—381no—
247#103—382no—
248#102—382no—
249C22⋊C8—21no—
250C22⋊C8—192no—
251C22⋊C8—762no—
252C22⋊C8—762no—
253#97—382no—
254#97—381no—
255#97—381no—
256C4×C8—21no—
257C4×C8—382no—
258C4×C8—381no—
259C19#905011yescharacteristic, complemented, Sylow
260C24—381no—
261C2×Q8—21no—
262C2×Q8(C2×D19)⋊C412yes—
263C2×D4—381no—
264C2×D4—381no—
265C2×D4—762no—
266C22×C4—381no—
267C22×C4—761no—
268C22×C4—761no—
269C22×C4—761no—
270C22×C4—761no—
271C22×C4—761no—
272C22×C4—761no—
273C22×C4C2×C4×D1911yescharacteristic
274C22×C4D4×D1911yescharacteristic
275C22×C4#6454311yescharacteristic
276SD16—764no—
277M16—761no—
278M16—761no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—192no—
284C2×C8—381no—
285C2×C8—381no—
286C2×C8—382no—
287C2×C8—381no—
288C2×C8—381no—
289C2×C8—381no—
290C2×C8—382no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—381no—
297C4⋊C4—381no—
298C4⋊C4(C2×D19)⋊C412yes—
299C22⋊C4—22no—
300C22⋊C4—761no—
301C22⋊C4—761no—
302C42—22no—
303C42C2×D7611yescharacteristic
304C42D4×D1911yescharacteristic
305C42#6454311yescharacteristic
306C42C2×C22⋊D1911yescharacteristic
307C23—382no—
308C23—761no—
309C23—761no—
310C23—761no—
311C23—761no—
312C23—761no—
313C23—761no—
314C23(C22⋊D19)⋊C411yescharacteristic
315Q8—42no—
316Q8—81no—
317D4—382no—
318D4—382no—
319D4—761no—
320D4—761no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—761no—
326C2×C4—761no—
327C2×C4—761no—
328C2×C4—1521no—
329C2×C4—1521no—
330C2×C4—1521no—
331C2×C4—1521no—
332C2×C4(C22⋊D19)⋊C411yescharacteristic
333C2×C4#1059732811yescharacteristic
334C2×C4#1059733211yescharacteristic
335C2×C4SD16×D1911yescharacteristic
336C2×C4#1059736011yescharacteristic
337C2×C4#1059736411yescharacteristic
338C2×C4#1059736511yescharacteristic
339C2×C4C2×(C2×D19)⋊C411yescharacteristic
340C2×C4#1059738511yescharacteristic
341C2×C4#1059738511yescharacteristic
342C8—81no—
343C8—81no—
344C8—382no—
345C8—762no—
346C8—761no—
347C8—762no—
348C22—21no—
349C22—21no—
350C22—762no—
351C22—762no—
352C22—762no—
353C22—1521no—
354C22—1521no—
355C22—1521no—
356C22—1521no—
357C22#1192642111yescharacteristic
358C22#1192662911yescharacteristic
359C22#1192664711yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—42no—
366C4—1521no—
367C4#1192668411yescharacteristic
368C4#1192669211yescharacteristic
369C4#1192674211yescharacteristic
370C4#1192676811yescharacteristic
371C2—21no—
372C2—21no—
373C2—1522no—
374C2#1456398811yescharacteristic
375C2#1456399511yescharacteristic
376C2#1456405111yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1542C2
socleC22×C19#386
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1542D19
hypocenterC19#9050
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
2. #14572576C2semidirect
5. #14561532C2semidirect
6. #14561479C2semidirect
7. C19×#1542C2semidirect
117. C2×C19⋊C8SD16semidirect
163. #1542D19semidirect
259. C19#9050semidirect

Maximal subgroups

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

subgroupindex
#145736392
#145725762
#145644322
#145620612
#145615322
#145614792
C19×#15422
#905019