Finite Group Databasebeta

← #18079393

Subgroups — #18079393

Order 4864.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573451C211yesmaximal, characteristic
2#14572743C211yesmaximal, characteristic
3#14564558C211yesmaximal, characteristic, complemented
4#14563656C211yesmaximal, characteristic
5#14562319C211yesmaximal, characteristic, complemented
6#14561509C211yesmaximal, characteristic, complemented
7C19×#1303C211yesmaximal, characteristic, complemented
8C2×#10597315C2211yescharacteristic
9C4×#64541C2211yescharacteristic
10#11926840C412yescomplemented
11#11926835C412yescomplemented
12#11926830—21no—
13#11926825—21no—
14C8×Dic38—21no—
15C8×D76—21no—
16(C22⋊D19)⋊C8—22no—
17#11926596—21no—
18#11926586—21no—
19#11926568C2211yescharacteristic
20C2×C4⋊(C19⋊C8)C2211yescharacteristic
21C4⋊C8×D19—21no—
22C2×#10597262—21no—
23#11926546—21no—
24C2×#10597267—22no—
25#11926304—21no—
26#11926291—21no—
27#11926291—21no—
28C19×#431C2211yescharacteristic
29C19×#423C2211yescharacteristic
30C4×C4⋊C4×C19C2211yescharacteristic
31C2×#64541D411yescharacteristic
32C22×Dic38—21no—
33C2×M16×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C42×C19—21no—
36C2×C42×C19C2311yescharacteristic
37C4×C22⋊D19—21no—
38C4×C22⋊D19—21no—
39#10597372D411yescharacteristic
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19—21no—
42C2×#64520—21no—
43C22×C19⋊C8D412yes—
44C2×C8×D19—22no—
45C4×D76C2×C411yescharacteristic
46C4×D76D411yescharacteristic
47#10597318—21no—
48C42×D19—21no—
49#10597315—21no—
50#10597315—21no—
51#10597315—21no—
52#10597315C2×C412yes—
53C4×Dic38C2×C411yescharacteristic
54C4×Dic38D411yescharacteristic
55C19×C4⋊C8—21no—
56C19×C4⋊C8C2×C412yes—
57C19×C4⋊C8D411yescharacteristic
58C19×C4⋊C8D411yescharacteristic
59C19×C22⋊C8—21no—
60C4×C8×C19—21no—
61C19×#95—21no—
62#10597278—22no—
63(C2×D19)⋊C8—22no—
64#10597275—22no—
65#10597274—22no—
66#10597273—22no—
67Dic19⋊C8—22no—
68C8×Dic19—22no—
69#10597267—44no—
70#10597262—42no—
71C4⋊(C19⋊C8)—21no—
72C4⋊(C19⋊C8)—21no—
73C4⋊(C19⋊C8)—21no—
74C4⋊(C19⋊C8)—21no—
75C22×C4×C19—41no—
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19#4111yescharacteristic
79C2×C22⋊D19—21no—
80C22×Dic19—41no—
81#64541—21no—
82#64541—21no—
83#64541SD1612yes—
84#64541Q1612yes—
85C2×D76C22⋊C411yescharacteristic
86C2×C4×D19—21no—
87C2×C4×D19—21no—
88C2×C4×D19—21no—
89C2×Dic38—22no—
90C2×Dic38—42no—
91C2×Dic38—42no—
92C2×Dic38—41no—
93C2×Dic38C22⋊C411yescharacteristic
94M16×C19—41no—
95M16×C19—41no—
96C2×C8×C19—22no—
97C2×C8×C19—21no—
98C2×C8×C19—21no—
99C4⋊C4×C19—22no—
100C4⋊C4×C19—41no—
101C42×C19—41no—
102C42×C19—41no—
103C42×C19C22×C411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C42×C19C2×D411yescharacteristic
106C42×C19#4111yescharacteristic
107C22⋊Dic19—21no—
108(C2×D19)⋊C4—21no—
109(C2×D19)⋊C4—21no—
110C4⋊Dic19—22no—
111C4⋊Dic19—22no—
112C4⋊Dic19—41no—
113C4⋊Dic19—41no—
114C4⋊Dic19C22⋊C411yescharacteristic
115C4⋊Dic19C22⋊C411yescharacteristic
116Dic19⋊C4—21no—
117Dic19⋊C4—21no—
118C4×Dic19—21no—
119C4×Dic19—21no—
120C4×Dic19—21no—
121#64520—41no—
122#64520—41no—
123C2×C19⋊C8—22no—
124C2×C19⋊C8—42no—
125C2×C19⋊C8—41no—
126C8×D19—82no—
127#9317—191nomaximal, Sylow
128C23×C19#12111yescharacteristic
129C22×D19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—41no—
133C2×C4×C19—42no—
134C2×C4×C19—81no—
135C2×C4×C19—81no—
136C2×C4×C19C2×C22⋊C411yescharacteristic
137C2×C4×C19C4×D411yescharacteristic
138C2×C4×C19C4×D411yescharacteristic
139C2×C4×C19#12011yescharacteristic
140C2×C4×C19#12111yescharacteristic
141C2×C4×C19#12311yescharacteristic
142C2×C4×C19C2×SD1611yescharacteristic
143C2×C4×C19C2×Q1611yescharacteristic
144C2×C4×C19#13511yescharacteristic
145C2×C4×C19#13511yescharacteristic
146C22⋊D19—22no—
147C22⋊D19—22no—
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—21no—
151C2×Dic19—42no—
152C2×Dic19—82no—
153D76—21no—
154D76#10312yescomplemented
155C4×D19—22no—
156C4×D19—22no—
157C4×D19—41no—
158C4×D19—41no—
159C4×D19—81no—
160Dic38—21no—
161Dic38—44no—
162Dic38—81no—
163Dic38—81no—
164Dic38#10312yescomplemented
165C8×C19—42no—
166C8×C19—41no—
167C8×C19—41no—
168C19⋊C8—42no—
169C19⋊C8—81no—
170#3079—191no—
171#2988—191no—
172#1981—191no—
173#1806—191no—
174#1549—191no—
175#1303D1911yescharacteristic, complemented
176#1292—191no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19#38611yescharacteristic
180C22×C19#46511yescharacteristic
181C22×C19#46711yescharacteristic
182C2×D19—22no—
183C2×D19—41no—
184C2×D19—41no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—82no—
189C4×C19C2×#10311yescharacteristic
190C4×C19#41611yescharacteristic
191C4×C19#45311yescharacteristic
192C4×C19#45411yescharacteristic
193C4×C19#46511yescharacteristic
194C4×C19#46711yescharacteristic
195Dic19—22no—
196Dic19—41no—
197Dic19—41no—
198Dic19—82no—
199C2×C4⋊Q8—191no—
200C4×#41—191no—
201#477—192no—
202#476—192no—
203#475—381no—
204#474—381no—
205C8×Q8—381no—
206C8×D4—381no—
207C8×D4—382no—
208#431—381no—
209#431C2×D1911yescharacteristic
210#428—381no—
211#423—191no—
212#423C2×D1911yescharacteristic
213C2×C4⋊C8—191no—
214C2×C4⋊C8—381no—
215C2×#104—381no—
216#417—381no—
217C2×#103—382no—
218C4×C4⋊C4C2×D1911yescharacteristic
219#339—381no—
220#332—381no—
221#332—381no—
222C2×C19—21no—
223C2×C19—21no—
224C2×C19#188311yescharacteristic
225C2×C19#189211yescharacteristic
226C2×C19#190211yescharacteristic
227D19—42no—
228C2×#41—191no—
229C22×Q8—381no—
230C2×M16—21no—
231C2×M16—381no—
232C22×C8—192no—
233C22×C8—382no—
234C4⋊Q8—192no—
235C4⋊Q8—381no—
236C4⋊Q8—381no—
237C4⋊Q8—381no—
238C4×Q8—191no—
239C4×Q8—191no—
240C4×D4—191no—
241C4×D4—191no—
242C4×D4—381no—
243C4×D4—381no—
244#117—191no—
245#117—381no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—381no—
248C2×C4⋊C4—381no—
249C2×C42—21no—
250C2×C42—381no—
251C2×C42C22×D1911yescharacteristic
252#107—382no—
253#106—382no—
254C4⋊C8—21no—
255C4⋊C8—382no—
256C4⋊C8—381no—
257C4⋊C8—381no—
258C4⋊C8—381no—
259C4⋊C8—381no—
260C4⋊C8C4×D1912yes—
261C4⋊C8D7611yescharacteristic
262C4⋊C8D7611yescharacteristic
263#104—762no—
264#103—382no—
265#103—764no—
266#102—382no—
267C22⋊C8—21no—
268C22⋊C8—382no—
269C4×C8—21no—
270C4×C8—382no—
271#95—21no—
272C19#931711yescharacteristic, complemented, Sylow
273#41—192no—
274#41—192no—
275#41—381no—
276#41—381no—
277C2×Q8—191no—
278C2×Q8—382no—
279C2×Q8—762no—
280C2×Q8—762no—
281C2×Q8—761no—
282C2×D4—191no—
283C2×D4—381no—
284C22×C4—41no—
285C22×C4—381no—
286C22×C4—381no—
287C22×C4—381no—
288C22×C4—761no—
289C22×C4#6454111yescharacteristic
290C22×C4D4×D1911yescharacteristic
291C22×C4D4×D1911yescharacteristic
292M16—41no—
293M16—41no—
294M16—761no—
295M16—761no—
296C2×C8—22no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—382no—
300C2×C8—762no—
301C2×C8—761no—
302C2×C8—1522no—
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—191no—
306C4⋊C4—191no—
307C4⋊C4—381no—
308C4⋊C4—381no—
309C4⋊C4—382no—
310C4⋊C4—382no—
311C4⋊C4—761no—
312C4⋊C4—761no—
313C22⋊C4—381no—
314C22⋊C4—381no—
315C22⋊C4—381no—
316C42—41no—
317C42—41no—
318C42—381no—
319C42—381no—
320C42—381no—
321C42C2×C4×D1911yescharacteristic
322C42C2×D7611yescharacteristic
323C42D4×D1911yescharacteristic
324C42#6454511yescharacteristic
325C23—381no—
326C23#1059733011yescharacteristic
327Q8—192no—
328Q8—381no—
329Q8—764no—
330Q8—1521no—
331Q8—1521no—
332D4—192no—
333D4—382no—
334D4—382no—
335D4—381no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—381no—
343C2×C4—382no—
344C2×C4—382no—
345C2×C4—381no—
346C2×C4—381no—
347C2×C4—761no—
348C2×C4—761no—
349C2×C4—762no—
350C2×C4—1521no—
351C2×C4—1522no—
352C2×C4C4×D7611yescharacteristic
353C2×C4C22⋊C4×D1911yescharacteristic
354C2×C4#1059732811yescharacteristic
355C2×C4#1059733911yescharacteristic
356C2×C4#1059734011yescharacteristic
357C2×C4#1059734111yescharacteristic
358C2×C4#1059735811yescharacteristic
359C2×C4SD16×D1911yescharacteristic
360C2×C4#1059736211yescharacteristic
361C2×C4Q16×D1911yescharacteristic
362C8—42no—
363C8—41no—
364C8—41no—
365C8—762no—
366C8—1521no—
367C22—21no—
368C22—21no—
369C22—382no—
370C22—761no—
371C22—761no—
372C22#1192642211yescharacteristic
373C22#1192677211yescharacteristic
374C22#1192678411yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—82no—
379C4—382no—
380C4—761no—
381C4—761no—
382C4—1522no—
383C4#103×D1911yescharacteristic
384C4#1192653711yescharacteristic
385C4#1192671311yescharacteristic
386C4#1192671811yescharacteristic
387C4#1192677411yescharacteristic
388C4#1192678611yescharacteristic
389C2—21no—
390C2—21no—
391C2—762no—
392C2#1456401211yescharacteristic
393C2#1456405711yescharacteristic
394C2#1456410711yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1303C2
socleC22×C19#386
prime radicalC2×#64541D4
cosocleC2×C42×C19C23
hypercenter#1303D19
hypocenterC19#9317
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #14564558C2semidirect
5. #14562319C2semidirect
6. #14561509C2semidirect
7. C19×#1303C2semidirect
10. #11926840C4semidirect
11. #11926835C4semidirect
154. D76#103semidirect
164. Dic38#103semidirect
175. #1303D19semidirect
272. C19#9317semidirect

Maximal subgroups

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

subgroupindex
#145734512
#145727432
#145645582
#145636562
#145623192
#145615092
C19×#13032
#931719