Finite Group Databasebeta

← #18072334

Subgroups — #18072334

Order 4864.

608 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572268C211yesmaximal, characteristic
2C2×#11926568C211yesmaximal, characteristic
3#14561493C214yesmaximal, complemented
4C19×#2283C211yesmaximal, characteristic
5C22×#64520—21no—
6#11926601—21no—
7#11926601—21no—
8#11926597C412yescomplemented
9#11926597C2212yes—
10#11926568—21no—
11#11926568—21no—
12#11926568—21no—
13#11926568C412yescomplemented
14#11926568C2212yes—
15C2×C4⋊(C19⋊C8)—21no—
16C2×C4⋊(C19⋊C8)C412yescomplemented
17#11926508—21no—
18C4×#64520C412yescomplemented
19C22×C42×C19C2211yescharacteristic
20C19×#383—21no—
21C19×#382C2212yes—
22C19×#381C412yes—
23C19×#380—21no—
24C4×C4⋊C4×C19—21no—
25C4×C22⋊C4×C19—21no—
26C19×#376C412yes—
27C23×C4×C19C2×C411yescharacteristic
28C23×C4×C19D411yescharacteristic
29C23×C4×C19D411yescharacteristic
30C2×C4⋊C4×C19—22no—
31C2×C22⋊C4×C19—22no—
32C2×C42×C19—22no—
33C2×C42×C19C2×C411yescharacteristic
34C2×C42×C19C2×C411yescharacteristic
35C2×C42×C19C2×C411yescharacteristic
36C2×C42×C19C2×C411yescharacteristic
37C2×C42×C19C2×C411yescharacteristic
38C2×C42×C19D411yescharacteristic
39C2×C42×C19D411yescharacteristic
40C2×C42×C19D411yescharacteristic
41C2×C42×C19D411yescharacteristic
42C2×C42×C19Q811yescharacteristic
43C2×C42×C19Q811yescharacteristic
44C2×C42×C19C2311yescharacteristic
45C2×#64520—22no—
46C2×#64520—22no—
47C2×#64520—22no—
48C2×#64520—44no—
49C22×C19⋊C8—22no—
50C19×#95—22no—
51C19×#95—22no—
52C19×#95—22no—
53C19×#95C2×C414yes—
54C22⋊(C19⋊C8)—22no—
55C22⋊(C19⋊C8)—22no—
56C4⋊(C19⋊C8)—22no—
57C4⋊(C19⋊C8)—22no—
58C4⋊(C19⋊C8)—22no—
59C4⋊(C19⋊C8)—22no—
60C4⋊(C19⋊C8)—22no—
61C4⋊(C19⋊C8)C2×C414yes—
62#10597260—22no—
63C4×C19⋊C8C2×C414yes—
64C24×C19C22⋊C411yescharacteristic
65C22×C4×C19—22no—
66C22×C4×C19—22no—
67C22×C4×C19—24no—
68C22×C4×C19—42no—
69C22×C4×C19—42no—
70C22×C4×C19C4211yescharacteristic
71C22×C4×C19C4211yescharacteristic
72C22×C4×C19C22⋊C411yescharacteristic
73C22×C4×C19C22⋊C411yescharacteristic
74C22×C4×C19C22⋊C411yescharacteristic
75C22×C4×C19C22⋊C411yescharacteristic
76C22×C4×C19C22⋊C411yescharacteristic
77C22×C4×C19C22⋊C411yescharacteristic
78C22×C4×C19C22⋊C411yescharacteristic
79C22×C4×C19C4⋊C411yescharacteristic
80C22×C4×C19C4⋊C411yescharacteristic
81C22×C4×C19C4⋊C411yescharacteristic
82C22×C4×C19C4⋊C411yescharacteristic
83C22×C4×C19C4⋊C411yescharacteristic
84C22×C4×C19C4⋊C411yescharacteristic
85C22×C4×C19C22×C411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C4⋊C4×C19—42no—
89C4⋊C4×C19—42no—
90C22⋊C4×C19—44no—
91C42×C19—44no—
92C42×C19C4211yescharacteristic
93C42×C19C4211yescharacteristic
94C42×C19C22⋊C411yescharacteristic
95C42×C19C22⋊C411yescharacteristic
96C42×C19C22⋊C411yescharacteristic
97C42×C19C22⋊C411yescharacteristic
98C42×C19C4⋊C411yescharacteristic
99C42×C19C4⋊C411yescharacteristic
100C42×C19C4⋊C411yescharacteristic
101C42×C19C4⋊C411yescharacteristic
102C42×C19C4⋊C411yescharacteristic
103C42×C19C4⋊C411yescharacteristic
104C42×C19C22×C411yescharacteristic
105C42×C19C22×C411yescharacteristic
106C42×C19C2×D411yescharacteristic
107C42×C19C2×Q811yescharacteristic
108#64520—44no—
109#64520—44no—
110#64520—44no—
111C2×C19⋊C8—24no—
112C2×C19⋊C8—24no—
113C2×C19⋊C8—44no—
114#7960—191nomaximal, Sylow
115C23×C19—22no—
116C23×C19—22no—
117C23×C19—41no—
118C23×C19#9511yescharacteristic
119C23×C19#9511yescharacteristic
120C23×C19C2×C22⋊C411yescharacteristic
121C2×C4×C19—22no—
122C2×C4×C19—22no—
123C2×C4×C19—22no—
124C2×C4×C19—22no—
125C2×C4×C19—22no—
126C2×C4×C19—22no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—22no—
132C2×C4×C19—22no—
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—44no—
141C2×C4×C19—44no—
142C2×C4×C19—44no—
143C2×C4×C19#9511yescharacteristic
144C2×C4×C19#9511yescharacteristic
145C2×C4×C19#9511yescharacteristic
146C2×C4×C19#9511yescharacteristic
147C2×C4×C19#9511yescharacteristic
148C2×C4×C19#9511yescharacteristic
149C2×C4×C19C2×C4211yescharacteristic
150C2×C4×C19C2×C22⋊C411yescharacteristic
151C2×C4×C19C2×C22⋊C411yescharacteristic
152C2×C4×C19C2×C4⋊C411yescharacteristic
153C2×C4×C19C2×C4⋊C411yescharacteristic
154C2×C4×C19C2×C4⋊C411yescharacteristic
155C2×C4×C19AGL(1,ℤ/8)12yes—
156C2×C4×C19#13712yes—
157C19⋊C8—44no—
158C19⋊C8—44no—
159#2920—191no—
160C2×#423—191no—
161#2283D1911yescharacteristic
162#1286—194no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—44no—
171C22×C19#34412yes—
172C22×C19C2×#9511yescharacteristic
173C22×C19#41712yes—
174C4×C19—21no—
175C4×C19—21no—
176C4×C19—21no—
177C4×C19—21no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—84no—
184C4×C19H(3,ℤ/4)12yes—
185C4×C19#41811yescharacteristic
186C4×C19#41911yescharacteristic
187C4×C19#42812yes—
188C22×M16—381no—
189C22×C42C2×D1911yescharacteristic
190#432—381no—
191#432—381no—
192#431—192no—
193#431—192no—
194#423—192no—
195#423—192no—
196#423—381no—
197#423—381no—
198#423—381no—
199C2×C4⋊C8—192no—
200C2×C4⋊C8—381no—
201#407—381no—
202C4×M16—192no—
203#383—21no—
204#382C2×D1912yes—
205#381Dic1912yes—
206#380—21no—
207C4×C4⋊C4—21no—
208C4×C22⋊C4—21no—
209#376Dic1912yes—
210C2×C19—22no—
211C2×C19—22no—
212C2×C19—41no—
213C2×C19C2×H(3,ℤ/4)11yescharacteristic
214C2×C19#173611yescharacteristic
215C2×C19C2×#34411yescharacteristic
216C23×C4C2×Dic1911yescharacteristic
217C23×C4C22⋊D1911yescharacteristic
218C23×C4C22⋊D1911yescharacteristic
219C2×M16—382no—
220C2×M16—382no—
221C2×M16—382no—
222C2×M16—764no—
223C22×C8—382no—
224C2×C4⋊C4—22no—
225C2×C22⋊C4—22no—
226C2×C42—22no—
227C2×C42Dic3811yescharacteristic
228C2×C42Dic3811yescharacteristic
229C2×C42C4×D1911yescharacteristic
230C2×C42C4×D1911yescharacteristic
231C2×C42C4×D1911yescharacteristic
232C2×C42C4×D1911yescharacteristic
233C2×C42D7611yescharacteristic
234C2×C42D7611yescharacteristic
235C2×C42C2×Dic1911yescharacteristic
236C2×C42C22⋊D1911yescharacteristic
237C2×C42C22⋊D1911yescharacteristic
238C2×C42C22×D1911yescharacteristic
239C4⋊C8—194no—
240C4⋊C8—382no—
241C4⋊C8—382no—
242C4⋊C8—382no—
243C4⋊C8—382no—
244C4⋊C8—382no—
245C22⋊C8—382no—
246C22⋊C8—382no—
247#97—382no—
248C4×C8—194no—
249#95—22no—
250#95—22no—
251#95—22no—
252#95C2×Dic1914yes—
253C19#796011yescharacteristic, complemented, Sylow
254C24C22⋊Dic1911yescharacteristic
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4C4×Dic1911yescharacteristic
261C22×C4C4×Dic1911yescharacteristic
262C22×C4Dic19⋊C411yescharacteristic
263C22×C4Dic19⋊C411yescharacteristic
264C22×C4Dic19⋊C411yescharacteristic
265C22×C4Dic19⋊C411yescharacteristic
266C22×C4C4⋊Dic1911yescharacteristic
267C22×C4C4⋊Dic1911yescharacteristic
268C22×C4(C2×D19)⋊C411yescharacteristic
269C22×C4(C2×D19)⋊C411yescharacteristic
270C22×C4(C2×D19)⋊C411yescharacteristic
271C22×C4(C2×D19)⋊C411yescharacteristic
272C22×C4C22⋊Dic1911yescharacteristic
273C22×C4C22⋊Dic1911yescharacteristic
274C22×C4C22⋊Dic1911yescharacteristic
275C22×C4C22×Dic1911yescharacteristic
276C22×C4C2×C22⋊D1911yescharacteristic
277C22×C4C2×C22⋊D1911yescharacteristic
278M16—764no—
279M16—764no—
280M16—764no—
281C2×C8—384no—
282C2×C8—384no—
283C2×C8—764no—
284C4⋊C4—42no—
285C4⋊C4—42no—
286C22⋊C4—44no—
287C42—44no—
288C42C4×Dic1911yescharacteristic
289C42C4×Dic1911yescharacteristic
290C42Dic19⋊C411yescharacteristic
291C42Dic19⋊C411yescharacteristic
292C42Dic19⋊C411yescharacteristic
293C42Dic19⋊C411yescharacteristic
294C42C4⋊Dic1911yescharacteristic
295C42C4⋊Dic1911yescharacteristic
296C42(C2×D19)⋊C411yescharacteristic
297C42(C2×D19)⋊C411yescharacteristic
298C42(C2×D19)⋊C411yescharacteristic
299C42(C2×D19)⋊C411yescharacteristic
300C42C2×Dic3811yescharacteristic
301C42C2×C4×D1911yescharacteristic
302C42C2×C4×D1911yescharacteristic
303C42C2×D7611yescharacteristic
304C23—22no—
305C23—22no—
306C23—41no—
307C23C19⋊#9511yescharacteristic
308C23C19⋊#9511yescharacteristic
309C23C2×C22⋊Dic1911yescharacteristic
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4C19⋊#9511yescharacteristic
333C2×C4C19⋊#9511yescharacteristic
334C2×C4C19⋊#9511yescharacteristic
335C2×C4C19⋊#9511yescharacteristic
336C2×C4C19⋊#9511yescharacteristic
337C2×C4C19⋊#9511yescharacteristic
338C2×C4C2×C4×Dic1911yescharacteristic
339C2×C4C2×Dic19⋊C411yescharacteristic
340C2×C4C2×Dic19⋊C411yescharacteristic
341C2×C4C2×C4⋊Dic1911yescharacteristic
342C2×C4C2×(C2×D19)⋊C411yescharacteristic
343C2×C4C2×(C2×D19)⋊C411yescharacteristic
344C2×C4#1059739512yes—
345C2×C4#1059739712yes—
346C8—764no—
347C8—764no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—44no—
356C22#1192631412yes—
357C22C2×C19⋊#9511yescharacteristic
358C22#1192654512yes—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—84no—
369C4#1192630012yes—
370C4#1192654811yescharacteristic
371C4#1192655211yescharacteristic
372C4#1192658712yes—
373C2—22no—
374C2—22no—
375C2—41no—
376C2C2×#1192630011yescharacteristic
377C2#1456335611yescharacteristic
378C2C2×#1192631411yescharacteristic
subgroupG/H
centerC22C2×C19⋊#95
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC19×#2283C2
socleC22×C19C2×#95
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2283D19
hypocenterC19#7960
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2283

Complements

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

NH ≅ G/Ntype
3. #14561493C2semidirect
8. #11926597C4semidirect
13. #11926568C4semidirect
16. C2×C4⋊(C19⋊C8)C4semidirect
18. C4×#64520C4semidirect
253. C19#7960semidirect

Maximal subgroups

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

subgroupindex
#145722682
C2×#119265682
#145614932
C19×#22832
#796019