Finite Group Databasebeta

← #18072299

Subgroups — #18072299

Order 4864.

564 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572268C211yesmaximal, characteristic
2C2×#11926601C211yesmaximal, characteristic
3#14561491C214yesmaximal, complemented
4C19×#2283C211yesmaximal, characteristic
5#11926601—21no—
6#11926601—21no—
7#11926601—21no—
8#11926601C412yescomplemented
9#11926601C2212yes—
10#11926601C2212yes—
11#11926597—21no—
12#11926597C412yescomplemented
13#11926568C412yescomplemented
14C2×C4⋊(C19⋊C8)—21no—
15#11926508—21no—
16C2×C22⋊(C19⋊C8)—21no—
17C4×#64520—21no—
18C2×#10597260C412yescomplemented
19C22×C42×C19C2211yescharacteristic
20C19×#383—21no—
21C19×#382—21no—
22C19×#381—21no—
23C19×#380—21no—
24C4×C4⋊C4×C19C2212yes—
25C4×C22⋊C4×C19C412yes—
26C19×#376C412yes—
27C23×C4×C19C2×C411yescharacteristic
28C23×C4×C19D411yescharacteristic
29C23×C4×C19D411yescharacteristic
30C2×C4⋊C4×C19—22no—
31C2×C22⋊C4×C19—22no—
32C2×C42×C19C2×C414yes—
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—
46C22×C19⋊C8—22no—
47C19×#95—22no—
48C19×#95—22no—
49C19×#95—22no—
50C19×#95—22no—
51C22⋊(C19⋊C8)—22no—
52C22⋊(C19⋊C8)—22no—
53C22⋊(C19⋊C8)—22no—
54C22⋊(C19⋊C8)—22no—
55C4⋊(C19⋊C8)—22no—
56C4⋊(C19⋊C8)—22no—
57C4⋊(C19⋊C8)—22no—
58C4⋊(C19⋊C8)C2×C414yes—
59#10597260—22no—
60#10597260—22no—
61#10597260C2×C414yes—
62C4×C19⋊C8—22no—
63C24×C19C22⋊C411yescharacteristic
64C22×C4×C19—24no—
65C22×C4×C19—42no—
66C22×C4×C19—42no—
67C22×C4×C19—42no—
68C22×C4×C19C4211yescharacteristic
69C22×C4×C19C4211yescharacteristic
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19C22⋊C411yescharacteristic
72C22×C4×C19C22⋊C411yescharacteristic
73C22×C4×C19C22⋊C411yescharacteristic
74C22×C4×C19C22⋊C411yescharacteristic
75C22×C4×C19C22⋊C411yescharacteristic
76C22×C4×C19C22⋊C411yescharacteristic
77C22×C4×C19C4⋊C411yescharacteristic
78C22×C4×C19C4⋊C411yescharacteristic
79C22×C4×C19C4⋊C411yescharacteristic
80C22×C4×C19C4⋊C411yescharacteristic
81C22×C4×C19C4⋊C411yescharacteristic
82C22×C4×C19C4⋊C411yescharacteristic
83C22×C4×C19C22×C411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C4⋊C4×C19—44no—
87C22⋊C4×C19—44no—
88C42×C19—44no—
89C42×C19C4211yescharacteristic
90C42×C19C4211yescharacteristic
91C42×C19C22⋊C411yescharacteristic
92C42×C19C22⋊C411yescharacteristic
93C42×C19C22⋊C411yescharacteristic
94C42×C19C22⋊C411yescharacteristic
95C42×C19C4⋊C411yescharacteristic
96C42×C19C4⋊C411yescharacteristic
97C42×C19C4⋊C411yescharacteristic
98C42×C19C4⋊C411yescharacteristic
99C42×C19C4⋊C411yescharacteristic
100C42×C19C4⋊C411yescharacteristic
101C42×C19C22×C411yescharacteristic
102C42×C19C22×C411yescharacteristic
103C42×C19C2×D411yescharacteristic
104C42×C19C2×Q811yescharacteristic
105#64520—44no—
106C2×C19⋊C8—24no—
107C2×C19⋊C8—24no—
108C2×C19⋊C8—44no—
109#7951—191nomaximal, Sylow
110C23×C19—22no—
111C23×C19—22no—
112C23×C19—41no—
113C23×C19#9511yescharacteristic
114C23×C19#9511yescharacteristic
115C23×C19C2×C22⋊C411yescharacteristic
116C2×C4×C19—22no—
117C2×C4×C19—22no—
118C2×C4×C19—22no—
119C2×C4×C19—22no—
120C2×C4×C19—22no—
121C2×C4×C19—22no—
122C2×C4×C19—22no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—44no—
135C2×C4×C19—44no—
136C2×C4×C19—44no—
137C2×C4×C19#9511yescharacteristic
138C2×C4×C19#9511yescharacteristic
139C2×C4×C19#9511yescharacteristic
140C2×C4×C19#9511yescharacteristic
141C2×C4×C19#9511yescharacteristic
142C2×C4×C19#9511yescharacteristic
143C2×C4×C19C2×C4211yescharacteristic
144C2×C4×C19C2×C22⋊C411yescharacteristic
145C2×C4×C19C2×C22⋊C411yescharacteristic
146C2×C4×C19C2×C4⋊C411yescharacteristic
147C2×C4×C19C2×C4⋊C411yescharacteristic
148C2×C4×C19C2×C4⋊C411yescharacteristic
149C19⋊C8—44no—
150C19⋊C8—44no—
151#2920—191no—
152C2×#432—191no—
153#2283D1911yescharacteristic
154#1285—194no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—44no—
163C22×C19H(3,ℤ/4)12yes—
164C22×C19C2×#9511yescharacteristic
165C22×C19#41312yes—
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—21no—
171C4×C19—21no—
172C4×C19—21no—
173C4×C19—21no—
174C4×C19—21no—
175C4×C19—21no—
176C4×C19—21no—
177C4×C19—84no—
178C4×C19#42112yes—
179C22×C42C2×D1911yescharacteristic
180#432—192no—
181#432—192no—
182#432—192no—
183#432—381no—
184#432—381no—
185#432—381no—
186#431—192no—
187#431—381no—
188#423—192no—
189C2×C4⋊C8—381no—
190#407—381no—
191C2×C22⋊C8—381no—
192C4×M16—381no—
193C2×#97—192no—
194#383—21no—
195#382—21no—
196#381—21no—
197#380—21no—
198C4×C4⋊C4C2×D1912yes—
199C4×C22⋊C4Dic1912yes—
200#376Dic1912yes—
201C2×C19—22no—
202C2×C19—22no—
203C2×C19—41no—
204C2×C19C2×H(3,ℤ/4)11yescharacteristic
205C2×C19#173311yescharacteristic
206C2×C19#174211yescharacteristic
207C23×C4C2×Dic1911yescharacteristic
208C23×C4C22⋊D1911yescharacteristic
209C23×C4C22⋊D1911yescharacteristic
210C2×M16—382no—
211C22×C8—382no—
212C2×C4⋊C4—22no—
213C2×C22⋊C4—22no—
214C2×C42Dic3811yescharacteristic
215C2×C42Dic3811yescharacteristic
216C2×C42C4×D1911yescharacteristic
217C2×C42C4×D1911yescharacteristic
218C2×C42C4×D1911yescharacteristic
219C2×C42C4×D1911yescharacteristic
220C2×C42D7611yescharacteristic
221C2×C42D7611yescharacteristic
222C2×C42C2×Dic1914yes—
223C2×C42C2×Dic1911yescharacteristic
224C2×C42C22⋊D1911yescharacteristic
225C2×C42C22⋊D1911yescharacteristic
226C2×C42C22×D1911yescharacteristic
227C4⋊C8—194no—
228C4⋊C8—382no—
229C4⋊C8—382no—
230C4⋊C8—382no—
231C22⋊C8—382no—
232C22⋊C8—382no—
233C22⋊C8—382no—
234C22⋊C8—382no—
235#97—194no—
236#97—382no—
237#97—382no—
238C4×C8—382no—
239#95—22no—
240#95—22no—
241#95—22no—
242#95—22no—
243C19#795111yescharacteristic, complemented, Sylow
244C24C22⋊Dic1911yescharacteristic
245C22×C4—24no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4C4×Dic1911yescharacteristic
250C22×C4C4×Dic1911yescharacteristic
251C22×C4Dic19⋊C411yescharacteristic
252C22×C4Dic19⋊C411yescharacteristic
253C22×C4Dic19⋊C411yescharacteristic
254C22×C4Dic19⋊C411yescharacteristic
255C22×C4C4⋊Dic1911yescharacteristic
256C22×C4C4⋊Dic1911yescharacteristic
257C22×C4(C2×D19)⋊C411yescharacteristic
258C22×C4(C2×D19)⋊C411yescharacteristic
259C22×C4(C2×D19)⋊C411yescharacteristic
260C22×C4(C2×D19)⋊C411yescharacteristic
261C22×C4C22⋊Dic1911yescharacteristic
262C22×C4C22⋊Dic1911yescharacteristic
263C22×C4C22⋊Dic1911yescharacteristic
264C22×C4C22×Dic1911yescharacteristic
265C22×C4C2×C22⋊D1911yescharacteristic
266C22×C4C2×C22⋊D1911yescharacteristic
267M16—764no—
268C2×C8—384no—
269C2×C8—384no—
270C2×C8—764no—
271C4⋊C4—44no—
272C22⋊C4—44no—
273C42—44no—
274C42C4×Dic1911yescharacteristic
275C42C4×Dic1911yescharacteristic
276C42Dic19⋊C411yescharacteristic
277C42Dic19⋊C411yescharacteristic
278C42Dic19⋊C411yescharacteristic
279C42Dic19⋊C411yescharacteristic
280C42C4⋊Dic1911yescharacteristic
281C42C4⋊Dic1911yescharacteristic
282C42(C2×D19)⋊C411yescharacteristic
283C42(C2×D19)⋊C411yescharacteristic
284C42(C2×D19)⋊C411yescharacteristic
285C42(C2×D19)⋊C411yescharacteristic
286C42C2×Dic3811yescharacteristic
287C42C2×C4×D1911yescharacteristic
288C42C2×C4×D1911yescharacteristic
289C42C2×D7611yescharacteristic
290C23—22no—
291C23—22no—
292C23—41no—
293C23C19⋊#9511yescharacteristic
294C23C19⋊#9511yescharacteristic
295C23C2×C22⋊Dic1911yescharacteristic
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4C19⋊#9511yescharacteristic
318C2×C4C19⋊#9511yescharacteristic
319C2×C4C19⋊#9511yescharacteristic
320C2×C4C19⋊#9511yescharacteristic
321C2×C4C19⋊#9511yescharacteristic
322C2×C4C19⋊#9511yescharacteristic
323C2×C4C2×C4×Dic1911yescharacteristic
324C2×C4C2×Dic19⋊C411yescharacteristic
325C2×C4C2×Dic19⋊C411yescharacteristic
326C2×C4C2×C4⋊Dic1911yescharacteristic
327C2×C4C2×(C2×D19)⋊C411yescharacteristic
328C2×C4C2×(C2×D19)⋊C411yescharacteristic
329C8—764no—
330C8—764no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—44no—
339C22#1192630012yes—
340C22C2×C19⋊#9511yescharacteristic
341C22#1192652812yes—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—84no—
354C4#1192656212yes—
355C2—22no—
356C2—22no—
357C2—41no—
358C2C2×#1192630011yescharacteristic
359C2#1456334511yescharacteristic
360C2#1456337411yescharacteristic
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#7951
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. #14561491C2semidirect
8. #11926601C4semidirect
12. #11926597C4semidirect
13. #11926568C4semidirect
18. C2×#10597260C4semidirect
243. C19#7951semidirect

Maximal subgroups

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

subgroupindex
#145722682
C2×#119266012
#145614912
C19×#22832
#795119