Finite Group Databasebeta

← #18088205

Subgroups — #18088205

Order 4864.

850 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
1C2×#11926303C212yesmaximal
2C2×#11926303C212yesmaximal
3#14563329C211yesmaximal, characteristic
4C4×C19⋊#95C211yesmaximal, characteristic
5C4×C19×#117C211yesmaximal, characteristic
6C22×#64520C2212yes—
7C22×C4×Dic19C2212yes—
8C2×C19⋊#95—22no—
9#11926303—24no—
10#11926303C418yescomplemented
11#11926299—21no—
12#11926299—21no—
13C2×C19×#117C2211yescharacteristic
14C2×C19×#117C2211yescharacteristic
15C22×C42×C19C2211yescharacteristic
16C4×C4⋊C4×C19C412yescomplemented
17C4×C4⋊C4×C19C412yescomplemented
18C4×C22⋊C4×C19—22no—
19C19×#376—21no—
20C43×C19—21no—
21C23×C4×C19D412yes—
22C23×C4×C19C2311yescharacteristic
23C23×Dic19—22no—
24C19×#117—22no—
25C19×#117—21no—
26C19×#117—21no—
27C19×#117C2×C414yes—
28C19×#117D412yes—
29C19×#117Q812yes—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C4⋊C4×C19C2×C411yescharacteristic
32C2×C4⋊C4×C19C2×C412yes—
33C2×C22⋊C4×C19—21no—
34C2×C22⋊C4×C19—21no—
35C2×C42×C19—21no—
36C2×C42×C19—21no—
37C2×C42×C19—22no—
38C2×C42×C19—22no—
39C2×C42×C19—22no—
40C2×C42×C19—22no—
41C2×C42×C19C2×C412yes—
42C2×C42×C19D411yescharacteristic
43C2×C42×C19D411yescharacteristic
44C2×C4×Dic19—22no—
45C2×C4×Dic19—22no—
46C2×C4×Dic19—22no—
47C2×C4×Dic19—22no—
48C2×C4×Dic19—22no—
49C2×C4×Dic19C2×C414yes—
50C2×#64520—22no—
51C2×#64520—22no—
52C2×#64520—22no—
53C2×#64520—22no—
54C2×#64520—22no—
55C2×#64520C2×C414yes—
56C22×C19⋊C8—22no—
57C19×#95—22no—
58C19×#95—22no—
59C19⋊#95—28no—
60C24×C19C2×D411yescharacteristic
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—22no—
64C22×C4×C19—24no—
65C22×C4×C19—24no—
66C22×C4×C19—42no—
67C22×C4×C19C22⋊C412yes—
68C22×C4×C19C22⋊C412yes—
69C22×C4×C19C22×C412yes—
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×Q811yescharacteristic
74C22×C4×C19#4111yescharacteristic
75C22×C4×C19#4111yescharacteristic
76C22×C4×C19#4112yes—
77C22×C4×C19#4112yes—
78C22×C4×C19#4112yes—
79C22×Dic19—28no—
80C22×Dic19—24no—
81C22×Dic19—44no—
82C22×Dic19—42no—
83C22×Dic19—42no—
84C4⋊C4×C19—21no—
85C4⋊C4×C19—21no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19C4212yes—
88C4⋊C4×C19C4212yes—
89C4⋊C4×C19C4⋊C414yes—
90C22⋊C4×C19—24no—
91C22⋊C4×C19—22no—
92C22⋊C4×C19—22no—
93C42×C19—22no—
94C42×C19—22no—
95C42×C19—24no—
96C42×C19—22no—
97C42×C19—22no—
98C42×C19—22no—
99C42×C19—22no—
100C42×C19—44no—
101C42×C19—44no—
102C4×Dic19—24no—
103C4×Dic19—24no—
104C4×Dic19—42no—
105C4×Dic19—42no—
106#64520—24no—
107#64520—24no—
108#64520—42no—
109#64520—42no—
110C2×C19⋊C8—24no—
111C2×C19⋊C8—42no—
112C2×C19⋊C8—42no—
113#10808—191nomaximal, Sylow
114C23×C19—22no—
115C23×C19—22no—
116C23×C19C2×C22⋊C411yescharacteristic
117C23×C19C4×D412yes—
118C23×C19#12111yescharacteristic
119C23×C19C22⋊Q811yescharacteristic
120C23×C19#12312yes—
121C2×C4×C19—22no—
122C2×C4×C19—22no—
123C2×C4×C19—22no—
124C2×C4×C19—22no—
125C2×C4×C19—24no—
126C2×C4×C19—22no—
127C2×C4×C19—22no—
128C2×C4×C19—22no—
129C2×C4×C19—48no—
130C2×C4×C19—42no—
131C2×C4×C19—42no—
132C2×C4×C19—42no—
133C2×C4×C19—42no—
134C2×C4×C19#10414yes—
135C2×C4×C19C2×C4211yescharacteristic
136C2×C4×C19C2×C4⋊C411yescharacteristic
137C2×C4×C19#11712yes—
138C2×C4×C19#11712yes—
139C2×C4×C19#11711yescharacteristic
140C2×C4×C19#11711yescharacteristic
141C2×C4×C19#11711yescharacteristic
142C2×C4×C19#11711yescharacteristic
143C2×C4×C19C4×D412yes—
144C2×C4×C19C4×D412yes—
145C2×C4×C19C4×Q812yes—
146C2×C4×C19#12111yescharacteristic
147C2×C4×C19C22⋊Q811yescharacteristic
148C2×C4×C19#12312yes—
149C2×C4×C19#12412yes—
150C2×C4×C19#12512yes—
151C2×C4×C19#12612yes—
152C2×C4×C19#12612yes—
153C2×Dic19—28no—
154C2×Dic19—48no—
155C2×Dic19—48no—
156C2×Dic19—44no—
157C2×Dic19—44no—
158C19⋊C8—44no—
159C4×#117D1911yescharacteristic
160C2×#339—192no—
161C2×#339—192no—
162#1728—191no—
163C4×#95—191no—
164C22×C19—22no—
165C22×C19—22no—
166C22×C19—24no—
167C22×C19—22no—
168C22×C19—22no—
169C22×C19C4×C22⋊C411yescharacteristic
170C22×C19#38011yescharacteristic
171C22×C19#38111yescharacteristic
172C22×C19#38712yes—
173C22×C19#38812yes—
174C22×C19C2×#10412yes—
175C22×C19#42112yes—
176C4×C19—24no—
177C4×C19—44no—
178C4×C19—42no—
179C4×C19—42no—
180C4×C19—42no—
181C4×C19#37611yescharacteristic
182C4×C19C4×C4⋊C411yescharacteristic
183C4×C19#38211yescharacteristic
184C4×C19#38311yescharacteristic
185C4×C19#38712yes—
186C4×C19#38812yes—
187Dic19—48no—
188C22×M16—192no—
189C2×#117C2×D1911yescharacteristic
190C2×#117C2×D1911yescharacteristic
191C22×C42—192no—
192C22×C42C2×D1911yescharacteristic
193C4×C4⋊C4Dic1912yescomplemented
194C4×C4⋊C4Dic1912yescomplemented
195C4×C22⋊C4—22no—
196#376—21no—
197C2×#95—382no—
198C43—21no—
199#339—198no—
200#339—384no—
201#336—381no—
202#336—381no—
203C2×C19—22no—
204C2×C19—22no—
205C2×C19#143411yescharacteristic
206C2×C19C4×#10411yescharacteristic
207C2×C19#175911yescharacteristic
208C2×C19#180612yes—
209C2×C19#182612yes—
210C23×C4—382no—
211C23×C4C22⋊D1912yes—
212C23×C4C22×D1911yescharacteristic
213C2×M16—194no—
214C2×M16—382no—
215C2×M16—382no—
216C2×M16—382no—
217C2×M16—382no—
218C2×M16—382no—
219C22×C8—382no—
220#117—21no—
221#117—21no—
222#117—22no—
223#117Dic3812yes—
224#117C4×D1914yes—
225#117D7612yes—
226C2×C4⋊C4C2×Dic1911yescharacteristic
227C2×C4⋊C4C2×Dic1911yescharacteristic
228C2×C4⋊C4C2×Dic1912yes—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C42—22no—
232C2×C42—22no—
233C2×C42—21no—
234C2×C42—21no—
235C2×C42—22no—
236C2×C42—22no—
237C2×C42—194no—
238C2×C42—382no—
239C2×C42—382no—
240C2×C42—382no—
241C2×C42—382no—
242C2×C42—382no—
243C2×C42C2×Dic1912yes—
244C2×C42C22⋊D1911yescharacteristic
245C2×C42C22⋊D1911yescharacteristic
246#95—22no—
247#95—22no—
248#95—388no—
249C19#1080811yescharacteristic, complemented, Sylow
250C24C2×C22⋊D1911yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—22no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—42no—
257C22×C4—388no—
258C22×C4—384no—
259C22×C4—764no—
260C22×C4—762no—
261C22×C4—762no—
262C22×C4C22⋊Dic1912yes—
263C22×C4C22⋊Dic1912yes—
264C22×C4C2×Dic3811yescharacteristic
265C22×C4C2×C4×D1912yes—
266C22×C4C2×D7611yescharacteristic
267C22×C4#6454111yescharacteristic
268C22×C4#6454112yes—
269C22×C4#6454112yes—
270C22×C4#6454112yes—
271C22×C4#6454111yescharacteristic
272C22×C4C22×Dic1911yescharacteristic
273C22×C4C2×C22⋊D1911yescharacteristic
274M16—384no—
275M16—384no—
276M16—762no—
277M16—762no—
278C2×C8—384no—
279C2×C8—762no—
280C2×C8—762no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—22no—
284C4⋊C4C4×Dic1912yes—
285C4⋊C4C4×Dic1912yes—
286C4⋊C4C4⋊Dic1914yes—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—24no—
290C42—22no—
291C42—22no—
292C42—22no—
293C42—22no—
294C42—24no—
295C42—22no—
296C42—22no—
297C42—44no—
298C42—44no—
299C42—384no—
300C42—384no—
301C42—762no—
302C42—762no—
303C23—22no—
304C23—22no—
305C23#1059737011yescharacteristic
306C23C4×C22⋊D1912yes—
307C23#1059737512yes—
308C23#1059737611yescharacteristic
309C23C2×C22⋊Dic1911yescharacteristic
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—22no—
318C2×C4—48no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—388no—
324C2×C4—768no—
325C2×C4—764no—
326C2×C4—768no—
327C2×C4—764no—
328C2×C4#1059729414yes—
329C2×C4C4×Dic3812yes—
330C2×C4#1059731612yes—
331C2×C4#1059731812yes—
332C2×C4#1059731812yes—
333C2×C4C4×D7612yes—
334C2×C4#1059732112yes—
335C2×C4#1059732212yes—
336C2×C4#1059732212yes—
337C2×C4C2×C4×Dic1911yescharacteristic
338C2×C4#1059737011yescharacteristic
339C2×C4C2×C4⋊Dic1911yescharacteristic
340C2×C4#1059737211yescharacteristic
341C2×C4#1059737211yescharacteristic
342C2×C4#1059737211yescharacteristic
343C2×C4#1059737211yescharacteristic
344C2×C4C4×C22⋊D1912yes—
345C2×C4#1059737512yes—
346C2×C4#1059737611yescharacteristic
347C8—764no—
348C22—22no—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—24no—
353C22C4×C22⋊Dic1911yescharacteristic
354C22#1192640411yescharacteristic
355C22#1192640711yescharacteristic
356C22#1192642812yes—
357C22#1192643512yes—
358C22C2×#1059729412yes—
359C22#1192656112yes—
360C4—24no—
361C4—44no—
362C4—42no—
363C4—42no—
364C4—42no—
365C4—768no—
366C4#1192639011yescharacteristic
367C4C4×C4⋊Dic1911yescharacteristic
368C4#1192641011yescharacteristic
369C4#1192641211yescharacteristic
370C4#1192642812yes—
371C4#1192643512yes—
372C2—22no—
373C2—22no—
374C2#1456186211yescharacteristic
375C2C4×#1059729411yescharacteristic
376C2#1456344511yescharacteristic
377C2#1456365512yes—
378C2#1456373412yes—
subgroupG/H
centerC22×C4C2×C22⋊D19
commutatorC2×C4×C19C2×C42
FrattiniC23×C4C22×D19
FittingC4×C19×#117C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenterC4×#117D19
hypocenterC19#10808
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
10. #11926303C4semidirect
16. C4×C4⋊C4×C19C4semidirect
17. C4×C4⋊C4×C19C4semidirect
193. C4×C4⋊C4Dic19semidirect
194. C4×C4⋊C4Dic19semidirect
249. C19#10808semidirect

Maximal subgroups

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

subgroupindex
C2×#119263032
#145633292
C4×C19⋊#952
C4×C19×#1172
#1080819