Finite Group Databasebeta

← #18070669

Subgroups — #18070669

Order 4864.

892 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926446C211yesmaximal, characteristic
2#14563703C211yesmaximal, characteristic, complemented
3#14561455C214yesmaximal, complemented
4C19×#1728C211yesmaximal, characteristic, complemented
5C23×D76C411yescharacteristic
6C22×C4⋊Dic19C411yescharacteristic
7C22×(C2×D19)⋊C4—21no—
8C22×(C2×D19)⋊C4—21no—
9C2×C22⋊(C19⋊C8)—21no—
10#11926446—21no—
11#11926446—21no—
12#11926446C412yes—
13#11926446C2212yes—
14#11926299—21no—
15#11926299C2212yescomplemented
16C22×M16×C19—21no—
17C22×C42×C19C2211yescharacteristic
18C19×#336—21no—
19C19×#336C2212yescomplemented
20C24×D19—21no—
21C23×C4×C19C2×C411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×Dic19—21no—
25C22×D76—21no—
26C22×D76—24no—
27C22×D76—42no—
28C22×D76—42no—
29C22×D76C2×C412yes—
30C2×M16×C19—24no—
31C2×M16×C19—42no—
32C2×M16×C19—42no—
33C22×C8×C19—22no—
34C2×C42×C19—42no—
35C2×C42×C19C2×C411yescharacteristic
36C2×C42×C19D411yescharacteristic
37C2×C42×C19D411yescharacteristic
38C2×C42×C19C2311yescharacteristic
39C2×(C2×D19)⋊C4—22no—
40C2×(C2×D19)⋊C4—22no—
41C2×(C2×D19)⋊C4—22no—
42C2×(C2×D19)⋊C4—22no—
43C2×(C2×D19)⋊C4—44no—
44C2×(C2×D19)⋊C4—42no—
45C2×(C2×D19)⋊C4—42no—
46C2×C4⋊Dic19—21no—
47C2×C4⋊Dic19—42no—
48C2×C4⋊Dic19C2×C412yes—
49C22×C19⋊C8—22no—
50C22⋊(C19⋊C8)—42no—
51C24×C19C22⋊C411yescharacteristic
52C23×D19—24no—
53C23×D19—22no—
54C23×D19—42no—
55C23×D19—42no—
56C23×D19—42no—
57C23×D19—42no—
58C23×D19—42no—
59C23×D19—42no—
60C22×C4×C19—22no—
61C22×C4×C19—22no—
62C22×C4×C19—22no—
63C22×C4×C19—22no—
64C22×C4×C19—22no—
65C22×C4×C19—22no—
66C22×C4×C19—22no—
67C22×C4×C19—41no—
68C22×C4×C19C22⋊C411yescharacteristic
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19D812yes—
72C22×C4×C19SD1612yes—
73C22×C4×C19C22×C411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×Dic19—22no—
77C22×Dic19—42no—
78C22×Dic19—42no—
79C22×Dic19—42no—
80C2×D76—24no—
81C2×D76—22no—
82C2×D76—42no—
83C2×D76—42no—
84C2×D76—416no—
85C2×D76—42no—
86C2×D76—42no—
87C2×D76M1614yescomplemented
88M16×C19—48no—
89C2×C8×C19—24no—
90C2×C8×C19—42no—
91C2×C8×C19—42no—
92C42×C19—41no—
93C42×C19—41no—
94C42×C19—41no—
95C42×C19—41no—
96(C2×D19)⋊C4—44no—
97(C2×D19)⋊C4—44no—
98(C2×D19)⋊C4—42no—
99(C2×D19)⋊C4—42no—
100(C2×D19)⋊C4—44no—
101C4⋊Dic19—42no—
102C4⋊Dic19—42no—
103C2×C19⋊C8—42no—
104C2×C19⋊C8—42no—
105C2×C19⋊C8—42no—
106#7606—191nomaximal, Sylow
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—21no—
111C23×C19#9912yes—
112C23×C19#10212yes—
113C23×C19#10412yes—
114C23×C19C2×C22⋊C411yescharacteristic
115C22×D19—24no—
116C22×D19—48no—
117C22×D19—48no—
118C22×D19—48no—
119C22×D19—42no—
120C22×D19—42no—
121C22×D19—42no—
122C22×D19—42no—
123C22×D19—42no—
124C22×D19—42no—
125C22×D19—84no—
126C22×D19—84no—
127C22×D19—84no—
128C22×D19—84no—
129C2×C4×C19—28no—
130C2×C4×C19—24no—
131C2×C4×C19—24no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—44no—
146C2×C4×C19#10012yes—
147C2×C4×C19#10212yes—
148C2×C4×C19C2×M1612yes—
149C2×C4×C19C2×D811yescharacteristic
150C2×C4×C19C2×SD1611yescharacteristic
151C2×C4×C19AGL(1,ℤ/8)12yes—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—42no—
155C2×Dic19—84no—
156D76—44no—
157D76—48no—
158D76—44no—
159C8×C19—44no—
160C19⋊C8—82no—
161C2×#390—191no—
162#1817—191no—
163#1728D1911yescharacteristic, complemented
164#1270—194no—
165C22×C19—22no—
166C22×C19—22no—
167C22×C19—22no—
168C22×C19—22no—
169C22×C19—22no—
170C22×C19—22no—
171C22×C19#32714yes—
172C22×C19#40711yescharacteristic
173C22×C19C2×#9911yescharacteristic
174C22×C19C2×#10011yescharacteristic
175C22×C19C2×#10211yescharacteristic
176C22×C19#41811yescharacteristic
177C22×C19C2×#10411yescharacteristic
178C22×C19#42111yescharacteristic
179C2×D19—44no—
180C2×D19—44no—
181C2×D19—44no—
182C2×D19—816no—
183C2×D19—82no—
184C2×D19—82no—
185C2×D19—82no—
186C2×D19—82no—
187C4×C19—22no—
188C4×C19—22no—
189C4×C19—21no—
190C4×C19—22no—
191C4×C19—21no—
192C4×C19—22no—
193C4×C19—41no—
194Dic19—82no—
195C23×D4—191no—
196C22×M16—21no—
197C22×C4⋊C4—191no—
198C22×C22⋊C4—381no—
199C22×C22⋊C4—381no—
200C22×C42C2×D1911yescharacteristic
201C2×C22⋊C8—381no—
202#390—192no—
203#390—192no—
204#390—381no—
205#390—381no—
206#336—21no—
207#336—192no—
208#336—381no—
209#336C2×D1912yescomplemented
210C2×C19—24no—
211C2×C19#146211yescharacteristic
212C2×C19#148611yescharacteristic
213C2×C19#149011yescharacteristic
214C2×C19C2×#32711yescharacteristic
215C2×C19#151011yescharacteristic
216C2×C19#152711yescharacteristic
217C2×C19#154511yescharacteristic
218D19—84no—
219C25—381no—
220C22×D4—192no—
221C22×D4—384no—
222C22×D4—381no—
223C22×D4—762no—
224C22×D4—762no—
225C23×C4—381no—
226C23×C4C4×D1911yescharacteristic
227C23×C4D7611yescharacteristic
228C23×C4C22⋊D1911yescharacteristic
229C2×M16—24no—
230C2×M16—42no—
231C2×M16—42no—
232C22×C8—22no—
233C22×C8—382no—
234C2×C4⋊C4—192no—
235C2×C4⋊C4—381no—
236C2×C4⋊C4—762no—
237C2×C22⋊C4—382no—
238C2×C22⋊C4—382no—
239C2×C22⋊C4—382no—
240C2×C22⋊C4—382no—
241C2×C22⋊C4—764no—
242C2×C22⋊C4—762no—
243C2×C22⋊C4—762no—
244C2×C42—42no—
245C2×C42C4×D1911yescharacteristic
246C2×C42D7611yescharacteristic
247C2×C42C22⋊D1911yescharacteristic
248C2×C42C22×D1911yescharacteristic
249C22⋊C8—762no—
250C19#760611yescharacteristic, complemented, Sylow
251C24—384no—
252C24—382no—
253C24—762no—
254C24—762no—
255C24—762no—
256C24—762no—
257C24—762no—
258C24—762no—
259C24(C2×D19)⋊C411yescharacteristic
260C2×D4—194no—
261C2×D4—384no—
262C2×D4—382no—
263C2×D4—762no—
264C2×D4—762no—
265C2×D4—7616no—
266C2×D4—762no—
267C2×D4—762no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—41no—
276C22×C4—382no—
277C22×C4—762no—
278C22×C4—762no—
279C22×C4—762no—
280C22×C4(C2×D19)⋊C411yescharacteristic
281C22×C4(C2×D19)⋊C411yescharacteristic
282C22×C4(C2×D19)⋊C411yescharacteristic
283C22×C4#6452512yes—
284C22×C4#6452712yes—
285C22×C4C2×C4×D1911yescharacteristic
286C22×C4C2×D7611yescharacteristic
287C22×C4C2×C22⋊D1911yescharacteristic
288M16—48no—
289C2×C8—24no—
290C2×C8—42no—
291C2×C8—42no—
292C2×C8—762no—
293C2×C8—762no—
294C2×C8—762no—
295C4⋊C4—762no—
296C4⋊C4—762no—
297C22⋊C4—764no—
298C22⋊C4—762no—
299C22⋊C4—762no—
300C22⋊C4—764no—
301C22⋊C4—764no—
302C42—41no—
303C42—41no—
304C42—41no—
305C42—41no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—384no—
311C23—768no—
312C23—768no—
313C23—768no—
314C23—762no—
315C23—762no—
316C23—762no—
317C23—762no—
318C23—762no—
319C23—762no—
320C23—1524no—
321C23—1524no—
322C23—1524no—
323C23—1524no—
324C23#1059726212yes—
325C23#1059726312yes—
326C23#1059726612yes—
327C23C2×(C2×D19)⋊C411yescharacteristic
328D4—764no—
329D4—768no—
330D4—764no—
331C2×C4—28no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—44no—
348C2×C4—762no—
349C2×C4—762no—
350C2×C4—762no—
351C2×C4—1524no—
352C2×C4#1059726612yes—
353C2×C4#1059728012yes—
354C2×C4M16×D1912yes—
355C2×C4#1059735412yes—
356C2×C4C2×#6452511yescharacteristic
357C2×C4C2×#6452711yescharacteristic
358C8—44no—
359C8—1522no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—764no—
367C22—764no—
368C22—764no—
369C22—15216no—
370C22—1522no—
371C22—1522no—
372C22—1522no—
373C22—1522no—
374C22#1192627714yes—
375C22#1192650711yescharacteristic
376C22C2×#1059726311yescharacteristic
377C22C2×#1059728011yescharacteristic
378C22C2×#1059726611yescharacteristic
379C22#1192655011yescharacteristic
380C22C2×#1059726211yescharacteristic
381C22#1192656011yescharacteristic
382C4—21no—
383C4—21no—
384C4—22no—
385C4—22no—
386C4—22no—
387C4—22no—
388C4—41no—
389C4—1522no—
390C2—24no—
391C2—1524no—
392C2#1456196111yescharacteristic
393C2#1456205911yescharacteristic
394C2#1456207911yescharacteristic
395C2C2×#1192627711yescharacteristic
396C2#1456216511yescharacteristic
397C2#1456223211yescharacteristic
398C2#1456230411yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1728C2
socleC23×C19C2×C22⋊C4
prime radicalC23×D76C4
cosocleC2×C42×C19C23
hypercenter#1728D19
hypocenterC19#7606
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1728

Complements

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

NH ≅ G/Ntype
2. #14563703C2semidirect
3. #14561455C2semidirect
4. C19×#1728C2semidirect
15. #11926299C22semidirect
19. C19×#336C22semidirect
87. C2×D76M16semidirect
163. #1728D19semidirect
209. #336C2×D19semidirect
250. C19#7606semidirect

Maximal subgroups

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

subgroupindex
C2×#119264462
#145637032
#145614552
C19×#17282
#760619