Finite Group Databasebeta

← #18072081

Subgroups — #18072081

Order 4864.

614 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926596C211yesmaximal, characteristic
2C2×#11926595C211yesmaximal, characteristic
3#14566031C211yesmaximal, characteristic
4#14561476C211yesmaximal, characteristic, complemented
5#14561475C211yesmaximal, characteristic, complemented
6#14561474C211yesmaximal, characteristic, complemented
7C19×#1279C211yesmaximal, characteristic, complemented
8C2×C42×D19C2211yescharacteristic
9#11926596—22no—
10#11926596C414yescomplemented
11#11926595—22no—
12#11926595C414yescomplemented
13C2×C4⋊(C19⋊C8)C2211yescharacteristic
14C2×Dic19⋊C8—21no—
15C2×(C2×D19)⋊C8—21no—
16C2×(C2×D19)⋊C8—21no—
17C2×C4×C19⋊C8C2211yescharacteristic
18C2×C8×Dic19—21no—
19#11926411—21no—
20#11926409C412yes—
21#11926406—21no—
22#11926401C412yes—
23C4×C4⋊Dic19C2211yescharacteristic
24C4×(C2×D19)⋊C4—21no—
25#11926390—21no—
26C2×C19×C4⋊C8C2211yescharacteristic
27C2×C4×C8×C19C2211yescharacteristic
28C4×C4⋊C4×C19C2211yescharacteristic
29C22×C4×D19C2×C411yescharacteristic
30C22×C4×D19D411yescharacteristic
31C22×C4×D19D411yescharacteristic
32C22×C8×C19—21no—
33C22×C8×C19—21no—
34C2×C4⋊C4×C19C2×C412yes—
35C2×C42×C19—21no—
36C2×C42×C19C2311yescharacteristic
37C2×(C2×D19)⋊C4—22no—
38C2×C4⋊Dic19C2×C412yes—
39C2×C4×Dic19—21no—
40C2×C4×Dic19C2×C411yescharacteristic
41C2×C4×Dic19D411yescharacteristic
42C2×C4×Dic19D411yescharacteristic
43C22×C19⋊C8—21no—
44C22×C19⋊C8—21no—
45C42×D19C2×C412yes—
46C42×D19C2×C412yes—
47C42×D19D412yes—
48C42×D19Q812yes—
49C19×C4⋊C8—21no—
50C19×C4⋊C8C2×C412yes—
51C4×C8×C19—21no—
52C4×C8×C19C2×C412yes—
53C19×#95—21no—
54C19⋊#95—21no—
55C19⋊#95—22no—
56C19⋊#95—22no—
57C19⋊#95—22no—
58(C2×D19)⋊C8—24no—
59(C2×D19)⋊C8—24no—
60Dic19⋊C8—24no—
61C8×Dic19—24no—
62C4⋊(C19⋊C8)—21no—
63C4⋊(C19⋊C8)C2×C412yes—
64C4×C19⋊C8—21no—
65C4×C19⋊C8C2×C412yes—
66C23×D19C22⋊C411yescharacteristic
67C22×C4×C19—22no—
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C22×Dic19—22no—
72C22×Dic19C22⋊C411yescharacteristic
73C22×Dic19C22⋊C411yescharacteristic
74C22×Dic19C22⋊C411yescharacteristic
75C2×C4×D19—22no—
76C2×C4×D19—22no—
77C2×C4×D19—21no—
78C2×C4×D19—21no—
79C2×C4×D19—21no—
80C2×C4×D19—21no—
81C2×C4×D19—42no—
82C2×C4×D19C4212yes—
83C2×C4×D19C22⋊C412yes—
84C2×C4×D19C22⋊C412yes—
85C2×C4×D19C4⋊C412yes—
86C2×C4×D19C4⋊C412yes—
87C2×C4×D19C4⋊C412yes—
88C2×C8×C19—22no—
89C2×C8×C19—22no—
90C2×C8×C19—42no—
91C2×C8×C19—41no—
92C2×C8×C19—41no—
93C4⋊C4×C19—22no—
94C4⋊C4×C19—22no—
95C42×C19—41no—
96C42×C19—41no—
97C42×C19C22×C411yescharacteristic
98C42×C19C22×C411yescharacteristic
99C42×C19C2×D411yescharacteristic
100C42×C19C2×Q811yescharacteristic
101(C2×D19)⋊C4—44no—
102C4⋊Dic19—22no—
103C4⋊Dic19—22no—
104C4×Dic19—41no—
105C4×Dic19—41no—
106C4×Dic19C4212yes—
107C4×Dic19C22⋊C412yes—
108C4×Dic19C22⋊C412yes—
109C4×Dic19C4⋊C412yes—
110C4×Dic19C4⋊C412yes—
111C4×Dic19C4⋊C412yes—
112C2×C19⋊C8—22no—
113C2×C19⋊C8—22no—
114C2×C19⋊C8—42no—
115C2×C19⋊C8—41no—
116C2×C19⋊C8—41no—
117#7894—191nomaximal, Sylow
118C23×C19C2×C22⋊C411yescharacteristic
119C22×D19—22no—
120C22×D19—21no—
121C22×D19—21no—
122C22×D19—22no—
123C22×D19#9512yes—
124C2×C4×C19—22no—
125C2×C4×C19—42no—
126C2×C4×C19—42no—
127C2×C4×C19—42no—
128C2×C4×C19C2×C4211yescharacteristic
129C2×C4×C19C2×C22⋊C411yescharacteristic
130C2×C4×C19C2×C22⋊C411yescharacteristic
131C2×C4×C19C2×C4⋊C411yescharacteristic
132C2×C4×C19C2×C4⋊C411yescharacteristic
133C2×C4×C19C2×C4⋊C411yescharacteristic
134C2×C4×C19#13112yes—
135C2×C4×C19#13112yes—
136C2×C4×C19#13511yescharacteristic
137C2×C4×C19#13511yescharacteristic
138C2×C4×C19#13511yescharacteristic
139C2×C4×C19#13511yescharacteristic
140C2×Dic19—22no—
141C2×Dic19—21no—
142C2×Dic19—21no—
143C2×Dic19—22no—
144C2×Dic19—42no—
145C2×Dic19—42no—
146C2×Dic19—42no—
147C2×Dic19#9512yes—
148C2×Dic19#9512yes—
149C2×Dic19#9512yes—
150C4×D19—22no—
151C4×D19—22no—
152C4×D19—22no—
153C4×D19—22no—
154C4×D19—24no—
155C4×D19—22no—
156C4×D19—22no—
157C4×D19—42no—
158C4×D19—42no—
159C8×C19—42no—
160C8×C19—42no—
161C19⋊C8—42no—
162C19⋊C8—42no—
163C2×#431—191no—
164C2×#431—191no—
165#2283—191no—
166#1279—191no—
167#1279—191no—
168#1279—191no—
169#1279D1911yescharacteristic, complemented
170C22×C19C2×#9511yescharacteristic
171C22×C19#40812yes—
172C22×C19#41611yescharacteristic
173C22×C19#41611yescharacteristic
174C22×C19#42112yes—
175C2×D19—22no—
176C2×D19—22no—
177C2×D19—22no—
178C2×D19—42no—
179C2×D19—42no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—82no—
183C4×C19#40511yescharacteristic
184C4×C19#40511yescharacteristic
185C4×C19#41611yescharacteristic
186C4×C19#41611yescharacteristic
187C4×C19#42412yes—
188C4×C19#42711yescharacteristic
189C4×C19#42711yescharacteristic
190Dic19—22no—
191Dic19—22no—
192Dic19—22no—
193Dic19—82no—
194C22×C42—191no—
195#431—194no—
196#431—194no—
197#431—382no—
198#431—382no—
199C2×C4⋊C8—191no—
200C2×C4⋊C8—381no—
201C2×C4⋊C8C2×D1911yescharacteristic
202C2×C22⋊C8—381no—
203C2×C22⋊C8—381no—
204C2×C4×C8—191no—
205C2×C4×C8—381no—
206C2×C4×C8C2×D1911yescharacteristic
207#383—381no—
208#382—192no—
209#381—381no—
210#380—192no—
211C4×C4⋊C4—191no—
212C4×C4⋊C4C2×D1911yescharacteristic
213C4×C22⋊C4—381no—
214#376—381no—
215C2×C19#148212yes—
216C2×C19#148212yes—
217C2×C19#172911yescharacteristic
218C2×C19#173311yescharacteristic
219C2×C19#173511yescharacteristic
220D19—42no—
221C23×C4—191no—
222C23×C4—191no—
223C23×C4—191no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—381no—
227C22×C8—381no—
228C2×C4⋊C4—192no—
229C2×C4⋊C4C4×D1912yes—
230C2×C22⋊C4—382no—
231C2×C42—21no—
232C2×C42—191no—
233C2×C42—191no—
234C2×C42—191no—
235C2×C42—192no—
236C2×C42—192no—
237C2×C42—192no—
238C2×C42—192no—
239C2×C42—381no—
240C2×C42C22×D1911yescharacteristic
241C4⋊C8—21no—
242C4⋊C8—192no—
243C4⋊C8—384no—
244C4⋊C8—381no—
245C4⋊C8C4×D1912yes—
246C22⋊C8—384no—
247C22⋊C8—384no—
248C4×C8—21no—
249C4×C8—192no—
250C4×C8—384no—
251C4×C8—381no—
252C4×C8C4×D1912yes—
253#95—21no—
254#95—382no—
255#95—382no—
256#95—382no—
257#95—381no—
258C19#789411yescharacteristic, complemented, Sylow
259C24—191no—
260C22×C4—22no—
261C22×C4—191no—
262C22×C4—191no—
263C22×C4—191no—
264C22×C4—192no—
265C22×C4—192no—
266C22×C4—192no—
267C22×C4—192no—
268C22×C4—192no—
269C22×C4—192no—
270C22×C4—382no—
271C22×C4—382no—
272C22×C4—381no—
273C22×C4—381no—
274C22×C4—381no—
275C22×C4—381no—
276C22×C4—382no—
277C22×C4—762no—
278C22×C4C2×C4×D1911yescharacteristic
279C22×C4D4×D1911yescharacteristic
280C22×C4D4×D1911yescharacteristic
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—42no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—382no—
287C2×C8—382no—
288C2×C8—762no—
289C2×C8—761no—
290C2×C8—761no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—382no—
294C4⋊C4—382no—
295C22⋊C4—764no—
296C42—41no—
297C42—41no—
298C42—192no—
299C42—192no—
300C42—192no—
301C42—192no—
302C42—192no—
303C42—192no—
304C42—761no—
305C42—761no—
306C42C2×C4×D1911yescharacteristic
307C42C2×C4×D1911yescharacteristic
308C42D4×D1911yescharacteristic
309C42Q8×D1911yescharacteristic
310C23—192no—
311C23—381no—
312C23—381no—
313C23—382no—
314C23—382no—
315C23C22⋊C4×D1911yescharacteristic
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—192no—
321C2×C4—192no—
322C2×C4—192no—
323C2×C4—381no—
324C2×C4—381no—
325C2×C4—382no—
326C2×C4—382no—
327C2×C4—382no—
328C2×C4—382no—
329C2×C4—384no—
330C2×C4—382no—
331C2×C4—382no—
332C2×C4—382no—
333C2×C4—382no—
334C2×C4—762no—
335C2×C4—762no—
336C2×C4—762no—
337C2×C4—762no—
338C2×C4—762no—
339C2×C4C42×D1911yescharacteristic
340C2×C4C22⋊C4×D1911yescharacteristic
341C2×C4C22⋊C4×D1911yescharacteristic
342C2×C4C4⋊C4×D1911yescharacteristic
343C2×C4C4⋊C4×D1911yescharacteristic
344C2×C4C4⋊C4×D1911yescharacteristic
345C2×C4#1059734712yes—
346C2×C4#1059735312yes—
347C2×C4#1059735811yescharacteristic
348C2×C4#1059736211yescharacteristic
349C2×C4#1059736211yescharacteristic
350C2×C4#1059736511yescharacteristic
351C8—42no—
352C8—42no—
353C8—762no—
354C8—762no—
355C22—382no—
356C22—382no—
357C22—382no—
358C22—762no—
359C22—762no—
360C22#95×D1911yescharacteristic
361C22#1192650912yes—
362C22#1192653711yescharacteristic
363C22#1192653911yescharacteristic
364C22#1192655912yes—
365C4—21no—
366C4—21no—
367C4—82no—
368C4—382no—
369C4—382no—
370C4—382no—
371C4—1522no—
372C4#1192649811yescharacteristic
373C4#1192650111yescharacteristic
374C4#1192653711yescharacteristic
375C4#1192653911yescharacteristic
376C4#1192656912yes—
377C4#1192657911yescharacteristic
378C4#1192658111yescharacteristic
379C2—762no—
380C2#1456204012yes—
381C2#1456204212yes—
382C2#1456333011yescharacteristic
383C2#1456334311yescharacteristic
384C2#1456335011yescharacteristic
subgroupG/H
centerC22×C4D4×D19
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC19×#1279C2
socleC23×C19C2×C22⋊C4
prime radicalC23×D19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1279D19
hypocenterC19#7894
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #14561476C2semidirect
5. #14561475C2semidirect
6. #14561474C2semidirect
7. C19×#1279C2semidirect
10. #11926596C4semidirect
12. #11926595C4semidirect
169. #1279D19semidirect
258. C19#7894semidirect

Maximal subgroups

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

subgroupindex
C2×#119265962
C2×#119265952
#145660312
#145614762
#145614752
#145614742
C19×#12792
#789419