Finite Group Databasebeta

← #18085567

Subgroups — #18085567

Order 4864.

500 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14568874C211yesmaximal, characteristic, complemented
2#14564562C211yesmaximal, characteristic
3#14564561C211yesmaximal, characteristic
4#14564441C211yesmaximal, characteristic
5#14561519C211yesmaximal, characteristic, complemented
6#14561475C211yesmaximal, characteristic, complemented
7C19×#1279C211yesmaximal, characteristic, complemented
8C2×#10597320C2211yescharacteristic
9C2×C4⋊(C19⋊C8)C2211yescharacteristic
10C2×#10597278—22no—
11C2×#10597278—21no—
12C2×#10597278—21no—
13C2×#10597266—21no—
14C2×#10597266—21no—
15#11926486—22no—
16#11926442—21no—
17#11926440—21no—
18#11926414C2211yescharacteristic
19#11926410—21no—
20#11926409—21no—
21C4×C4⋊Dic19C2211yescharacteristic
22C2×C19×C4⋊C8C2211yescharacteristic
23C2×C4×C8×C19C2211yescharacteristic
24C4×C4⋊C4×C19C2211yescharacteristic
25C22×D76—21no—
26C22×D76—21no—
27C22×D76—21no—
28C22×C8×C19—21no—
29C22×C8×C19—21no—
30C2×C4⋊C4×C19D411yescharacteristic
31C2×C4⋊C4×C19D411yescharacteristic
32C2×C42×C19—21no—
33C2×C42×C19C2311yescharacteristic
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19D411yescharacteristic
37C2×C4⋊Dic19D411yescharacteristic
38C2×C4⋊Dic19D412yes—
39C2×Dic19⋊C4—22no—
40C2×C4×Dic19—21no—
41C22×C19⋊C8—21no—
42#10597320—21no—
43#10597320—21no—
44#10597320—21no—
45#10597320Q812yes—
46C19×C4⋊C8—21no—
47C19×C4⋊C8—21no—
48C4×C8×C19—21no—
49C4×C8×C19—21no—
50C19×#95—21no—
51C19⋊#95—22no—
52C19⋊#95—22no—
53C19⋊#95—22no—
54C19⋊#95—21no—
55#10597278—42no—
56#10597278—42no—
57#10597278—44no—
58#10597266—42no—
59#10597266—42no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)—21no—
62C23×D19—41no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19C2×D411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C22×Dic19—21no—
69C22×Dic19—21no—
70C22×Dic19—22no—
71C2×D76—22no—
72C2×D76—22no—
73C2×D76—22no—
74C2×D76—42no—
75C2×D76—42no—
76C2×D76—41no—
77C2×D76—41no—
78C2×D76—41no—
79C2×D76—41no—
80C2×D76—41no—
81C2×D76—41no—
82C2×D76—41no—
83C2×D76—41no—
84C2×D76—41no—
85C2×D76—41no—
86C2×D76—41no—
87C2×C8×C19—22no—
88C2×C8×C19—41no—
89C2×C8×C19—41no—
90C2×C8×C19—41no—
91C2×C8×C19—41no—
92C2×C8×C19—41no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—21no—
96C4⋊C4×C19—21no—
97C42×C19—41no—
98C42×C19—41no—
99C42×C19C2×Q811yescharacteristic
100C42×C19#4111yescharacteristic
101C42×C19#4111yescharacteristic
102C42×C19#4111yescharacteristic
103C4⋊Dic19—21no—
104C4⋊Dic19—21no—
105C4⋊Dic19—21no—
106C4⋊Dic19—21no—
107C4⋊Dic19—41no—
108C4⋊Dic19—41no—
109C4⋊Dic19—41no—
110C4⋊Dic19—41no—
111C4⋊Dic19—42no—
112Dic19⋊C4—82no—
113C4×Dic19—41no—
114C4×Dic19—41no—
115C2×C19⋊C8—41no—
116C2×C19⋊C8—41no—
117C2×C19⋊C8—41no—
118#10351—191nomaximal, Sylow
119C23×C19#12011yescharacteristic
120C22×D19—42no—
121C22×D19—81no—
122C22×D19—81no—
123C22×D19—81no—
124C22×D19—81no—
125C22×D19—81no—
126C22×D19—81no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19C22⋊Q811yescharacteristic
136C2×C4×C19C22⋊Q811yescharacteristic
137C2×C4×C19C22⋊Q811yescharacteristic
138C2×C4×C19#12411yescharacteristic
139C2×C4×C19#12411yescharacteristic
140C2×C4×C19#12411yescharacteristic
141C2×C4×C19#13511yescharacteristic
142C2×C4×C19#13511yescharacteristic
143C2×C4×C19#13511yescharacteristic
144C2×C4×C19#13511yescharacteristic
145C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
149C2×Dic19—41no—
150C2×Dic19—41no—
151C2×Dic19—41no—
152C2×Dic19—41no—
153C2×Dic19—42no—
154C2×Dic19—42no—
155C2×Dic19—41no—
156C2×Dic19—42no—
157C2×Dic19—41no—
158D76—44no—
159D76—42no—
160D76—42no—
161D76—42no—
162D76—42no—
163D76—82no—
164D76—81no—
165D76—81no—
166D76—81no—
167D76—81no—
168C8×C19—42no—
169C8×C19—81no—
170C19⋊C8—81no—
171#2571—191no—
172#1982—191no—
173#1982—191no—
174#1957—191no—
175#1296—191no—
176#1279—191no—
177#1279D1911yescharacteristic, complemented
178C22×C19#39311yescharacteristic
179C22×C19#44911yescharacteristic
180C22×C19#44911yescharacteristic
181C22×C19#44911yescharacteristic
182C22×C19#44911yescharacteristic
183C22×C19#45311yescharacteristic
184C22×C19#45411yescharacteristic
185C2×D19—82no—
186C2×D19—82no—
187C2×D19—82no—
188C2×D19—161no—
189C2×D19—161no—
190C2×D19—161no—
191C2×D19—161no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—81no—
195C4×C19—81no—
196C4×C19#47811yescharacteristic
197C4×C19#47811yescharacteristic
198C4×C19#47811yescharacteristic
199C4×C19#47811yescharacteristic
200C4×C19#48811yescharacteristic
201C4×C19#48811yescharacteristic
202C4×C19#49011yescharacteristic
203C4×C19#49011yescharacteristic
204Dic19—82no—
205Dic19—81no—
206Dic19—81no—
207C2×#127—191no—
208C2×C4⋊C8—191no—
209C2×C4⋊C8C2×D1911yescharacteristic
210C2×#102—382no—
211C2×#102—381no—
212C2×#102—381no—
213C2×#102—381no—
214C2×#102—381no—
215C2×C4×C8C2×D1911yescharacteristic
216#400—382no—
217#389—381no—
218#389—381no—
219#384—191no—
220#382—381no—
221#382—381no—
222C4×C4⋊C4—191no—
223C4×C4⋊C4C2×D1911yescharacteristic
224C2×C19#162011yescharacteristic
225C2×C19#162411yescharacteristic
226C2×C19#162811yescharacteristic
227C2×C19#162811yescharacteristic
228C2×C19#202511yescharacteristic
229C2×C19#202511yescharacteristic
230C2×C19#202711yescharacteristic
231D19—162no—
232C22×D4—381no—
233C22×D4—381no—
234C22×D4—381no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—381no—
238#127—192no—
239#127—381no—
240#127—381no—
241#127—381no—
242C2×C4⋊C4—191no—
243C2×C4⋊C4—191no—
244C2×C4⋊C4—192no—
245C2×C4⋊C4—381no—
246C2×C4⋊C4—381no—
247C2×C4⋊C4—382no—
248C2×C4⋊C4D7611yescharacteristic
249C2×C4⋊C4D7611yescharacteristic
250C2×C42—21no—
251C2×C42—381no—
252C2×C42C22×D1911yescharacteristic
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—381no—
256C4⋊C8—381no—
257#102—762no—
258#102—762no—
259#102—762no—
260#102—762no—
261#102—764no—
262C4×C8—21no—
263C4×C8—21no—
264#95—21no—
265#95—382no—
266#95—382no—
267#95—382no—
268#95—381no—
269C19#1035111yescharacteristic, complemented, Sylow
270C24—761no—
271C2×D4—382no—
272C2×D4—382no—
273C2×D4—382no—
274C2×D4—762no—
275C2×D4—762no—
276C2×D4—761no—
277C2×D4—761no—
278C2×D4—761no—
279C2×D4—761no—
280C2×D4—761no—
281C2×D4—761no—
282C2×D4—761no—
283C2×D4—761no—
284C2×D4—761no—
285C2×D4—761no—
286C2×D4—761no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—381no—
290C22×C4—381no—
291C22×C4—382no—
292C22×C4C2×D7611yescharacteristic
293C22×C4D4×D1911yescharacteristic
294C22×C4D4×D1911yescharacteristic
295C2×C8—22no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—761no—
302C2×C8—761no—
303C2×C8—761no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—381no—
309C4⋊C4—381no—
310C4⋊C4—381no—
311C4⋊C4—381no—
312C4⋊C4—762no—
313C4⋊C4—761no—
314C4⋊C4—761no—
315C4⋊C4—761no—
316C4⋊C4—761no—
317C4⋊C4—1522no—
318C42—41no—
319C42—41no—
320C42—761no—
321C42—761no—
322C42#6454111yescharacteristic
323C42#6454111yescharacteristic
324C42#6454311yescharacteristic
325C42Q8×D1911yescharacteristic
326C23—762no—
327C23—1521no—
328C23—1521no—
329C23—1521no—
330C23—1521no—
331C23—1521no—
332C23—1521no—
333C23#1059732811yescharacteristic
334D4—764no—
335D4—762no—
336D4—762no—
337D4—762no—
338D4—762no—
339D4—1522no—
340D4—1521no—
341D4—1521no—
342D4—1521no—
343D4—1521no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—761no—
353C2×C4—761no—
354C2×C4—761no—
355C2×C4—762no—
356C2×C4—761no—
357C2×C4—762no—
358C2×C4—762no—
359C2×C4—761no—
360C2×C4—761no—
361C2×C4#1059732111yescharacteristic
362C2×C4#1059733111yescharacteristic
363C2×C4#1059733111yescharacteristic
364C2×C4#1059734211yescharacteristic
365C2×C4#1059734211yescharacteristic
366C2×C4#1059734311yescharacteristic
367C2×C4#1059735011yescharacteristic
368C2×C4#1059735011yescharacteristic
369C2×C4#1059735411yescharacteristic
370C2×C4#1059735411yescharacteristic
371C2×C4#1059735711yescharacteristic
372C2×C4#1059736011yescharacteristic
373C2×C4#1059736211yescharacteristic
374C2×C4#1059736511yescharacteristic
375C8—42no—
376C8—81no—
377C8—1521no—
378C22—3041no—
379C22—3041no—
380C22—3041no—
381C22—3041no—
382C22—1522no—
383C22—1522no—
384C22—1522no—
385C22#1192645711yescharacteristic
386C22#1192669011yescharacteristic
387C22#1192669111yescharacteristic
388C22#1192669111yescharacteristic
389C22#1192669211yescharacteristic
390C22#1192671311yescharacteristic
391C22#1192671811yescharacteristic
392C4—21no—
393C4—21no—
394C4—81no—
395C4—81no—
396C4—1522no—
397C4—1521no—
398C4—1521no—
399C4#1192684311yescharacteristic
400C4#1192684511yescharacteristic
401C4#1192684511yescharacteristic
402C4#1192684711yescharacteristic
403C4#1192689911yescharacteristic
404C4#1192690011yescharacteristic
405C4#1192690711yescharacteristic
406C4#1192690911yescharacteristic
407C2—3042no—
408C2#1456269611yescharacteristic
409C2#1456272011yescharacteristic
410C2#1456274711yescharacteristic
411C2#1456274811yescharacteristic
412C2#1456478011yescharacteristic
413C2#1456478211yescharacteristic
414C2#1456479011yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1279C2
socleC23×C19#120
prime radicalC2×#10597320C22
hypercenter#1279D19
hypocenterC19#10351
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
1. #14568874C2semidirect
5. #14561519C2semidirect
6. #14561475C2semidirect
7. C19×#1279C2semidirect
177. #1279D19semidirect
269. C19#10351semidirect

Maximal subgroups

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

subgroupindex
#145688742
#145645622
#145645612
#145644412
#145615192
#145614752
C19×#12792
#1035119