Finite Group Databasebeta

← #18081713

Subgroups — #18081713

Order 4864.

460 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574194C211yesmaximal, characteristic
2#14564578C211yesmaximal, characteristic, complemented
3#14564553C211yesmaximal, characteristic
4#14562133C211yesmaximal, characteristic, complemented
5#14562129C211yesmaximal, characteristic
6#14561924C211yesmaximal, characteristic, complemented
7C4×C19×#107C211yesmaximal, characteristic, complemented
8#11927101C2211yescharacteristic
9#11927094C2211yescharacteristic
10#11926942C411yescharacteristic, complemented
11#11926917C411yescharacteristic, complemented
12#11926895C411yescharacteristic, complemented
13#11926891C411yescharacteristic, complemented
14#11926773—21no—
15#11926773—21no—
16C4×#64516—21no—
17C4×#64516—21no—
18#11926597C2211yescharacteristic
19C2×#10597262—22no—
20C4×#64520C2211yescharacteristic
21#11926304—22no—
22#11926280—22no—
23#11926277—22no—
24#11926266—21no—
25#11926265—21no—
26C2×C19×#107—21no—
27C2×C4×C8×C19C2211yescharacteristic
28C4×C4⋊C4×C19C2211yescharacteristic
29C4×C4⋊C4×C19C2211yescharacteristic
30C19×#340—21no—
31C2×#64541—21no—
32C22×C8×C19D411yescharacteristic
33C22×C8×C19D411yescharacteristic
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C42×C19—21no—
37C2×C42×C19—21no—
38C2×C42×C19C2311yescharacteristic
39#10597376—21no—
40#10597376—21no—
41#10597372—21no—
42#10597370—21no—
43#10597370—21no—
44C2×#64520D412yes—
45C2×#64516—21no—
46C2×#64516—21no—
47#10597321—21no—
48#10597320C2×C411yescharacteristic
49C4×D76—21no—
50C4×D76—21no—
51#10597316—21no—
52#10597315C2×C411yescharacteristic
53#10597315C2×C411yescharacteristic
54#10597315C2×C411yescharacteristic
55C4×Dic38—21no—
56C4×Dic38—21no—
57C19×#107—24no—
58C4×C8×C19C2×C411yescharacteristic
59C4×C8×C19C2×C411yescharacteristic
60C4×C8×C19D411yescharacteristic
61C4×C8×C19D411yescharacteristic
62C19×#95—21no—
63C19×#95—21no—
64C22⋊(C19⋊C8)D412yes—
65#10597278—21no—
66#10597278—21no—
67#10597274—21no—
68#10597274—21no—
69#10597273—21no—
70#10597273—21no—
71#10597262—44no—
72C4⋊(C19⋊C8)—21no—
73#10597260—21no—
74C4×C19⋊C8—21no—
75C4×C19⋊C8—21no—
76C22×C4×C19—41no—
77C22×C4×C19—41no—
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C2×C22⋊D19—41no—
82#64541—42no—
83#64541—42no—
84C2×D76—21no—
85C2×D76—21no—
86C2×D76—21no—
87C2×C4×D19—41no—
88C2×Dic38—21no—
89C2×Dic38—21no—
90C2×Dic38—21no—
91C2×C8×C19—22no—
92C2×C8×C19—41no—
93C2×C8×C19C22⋊C411yescharacteristic
94C2×C8×C19C22⋊C411yescharacteristic
95C2×C8×C19C22⋊C411yescharacteristic
96C2×C8×C19C22⋊C411yescharacteristic
97C4⋊C4×C19—22no—
98C4⋊C4×C19—22no—
99C4⋊C4×C19—41no—
100C4⋊C4×C19—41no—
101C42×C19—42no—
102C42×C19—42no—
103C42×C19C22×C411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C42×C19#4111yescharacteristic
106C42×C19#4111yescharacteristic
107C22⋊Dic19—41no—
108(C2×D19)⋊C4—41no—
109(C2×D19)⋊C4—41no—
110C4⋊Dic19—21no—
111C4⋊Dic19—21no—
112C4⋊Dic19—21no—
113C4⋊Dic19—21no—
114C4⋊Dic19—21no—
115C4⋊Dic19—21no—
116Dic19⋊C4—41no—
117Dic19⋊C4—41no—
118C4×Dic19—41no—
119#64520—22no—
120#64520—22no—
121C2×C19⋊C8—22no—
122C2×C19⋊C8—22no—
123#64516—42no—
124#64516—42no—
125#9722—191nomaximal, Sylow
126C23×C19#12711yescharacteristic
127C22×D19—41no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—41no—
131C2×C4×C19—42no—
132C2×C4×C19—42no—
133C2×C4×C19—81no—
134C2×C4×C19—81no—
135C2×C4×C19—81no—
136C2×C4×C19—81no—
137C2×C4×C19C2×C22⋊C411yescharacteristic
138C2×C4×C19C4×D411yescharacteristic
139C2×C4×C19C4×D411yescharacteristic
140C2×C4×C19#12111yescharacteristic
141C2×C4×C19#12111yescharacteristic
142C2×C4×C19#12411yescharacteristic
143C2×C4×C19AGL(1,ℤ/8)12yes—
144C2×C4×C19#13712yes—
145C22⋊D19—81no—
146C22⋊D19—81no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150D76—41no—
151D76—41no—
152D76—42no—
153D76—81no—
154C4×D19—82no—
155Dic38—41no—
156Dic38—41no—
157Dic38—42no—
158Dic38—81no—
159C8×C19—21no—
160C8×C19—21no—
161C8×C19—21no—
162C8×C19#10412yescomplemented
163C19⋊C8—42no—
164C19⋊C8—42no—
165#3167—191no—
166#1986—191no—
167#1980—191no—
168C4×#107D1911yescharacteristic, complemented
169#1503—191no—
170#1502—191no—
171#1451—191no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19#39011yescharacteristic
175C22×C19#49611yescharacteristic
176C22×C19#49711yescharacteristic
177C2×D19—81no—
178C2×D19—81no—
179C2×D19—81no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—82no—
184C4×C19—82no—
185C4×C19C2×#10411yescharacteristic
186C4×C19#42111yescharacteristic
187C4×C19#44012yes—
188C4×C19#46812yes—
189Dic19—81no—
190Dic19—81no—
191Dic19—81no—
192#533—191no—
193#532—191no—
194#498—191no—
195#492—191no—
196#487—191no—
197#486—191no—
198#465—381no—
199#465—381no—
200C4×SD16—381no—
201C4×SD16—381no—
202#431—191no—
203C2×#107—21no—
204C2×#104—382no—
205C4×M16—191no—
206C2×C4×C8C2×D1911yescharacteristic
207C4×C4⋊C4C2×D1911yescharacteristic
208C4×C4⋊C4C2×D1911yescharacteristic
209#340—21no—
210#339—382no—
211#328—382no—
212#327—382no—
213#322—381no—
214#322—381no—
215C2×C19—21no—
216C2×C19—21no—
217C2×C19#197311yescharacteristic
218C2×C19#197611yescharacteristic
219C2×C19#198011yescharacteristic
220D19—161no—
221C2×#41—381no—
222C2×SD16—381no—
223C2×SD16—381no—
224C2×M16—192no—
225C22×C8C22⋊D1911yescharacteristic
226C22×C8C22⋊D1911yescharacteristic
227C4⋊Q8—191no—
228C4⋊Q8—191no—
229C4⋊Q8—191no—
230#127—191no—
231#125—381no—
232#124—381no—
233C22⋊Q8—381no—
234C22⋊Q8—381no—
235#121—381no—
236#121—381no—
237C4×Q8—381no—
238C4×Q8—381no—
239C4×D4—381no—
240C4×D4—381no—
241#117—381no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C42—21no—
245C2×C42—21no—
246C2×C42C22×D1911yescharacteristic
247#107—24no—
248#106—381no—
249#106—381no—
250C4⋊C8—381no—
251#104—764no—
252#103—381no—
253#103—381no—
254#102—381no—
255#102—381no—
256C22⋊C8—192no—
257#97—381no—
258C4×C8—381no—
259C4×C8—381no—
260C4×C8C4×D1911yescharacteristic
261C4×C8C4×D1911yescharacteristic
262C4×C8D7611yescharacteristic
263C4×C8D7611yescharacteristic
264#95—21no—
265#95—21no—
266C19#972211yescharacteristic, complemented, Sylow
267#41—762no—
268#41—762no—
269C2×Q8—381no—
270C2×Q8—381no—
271C2×Q8—381no—
272C2×D4—381no—
273C2×D4—381no—
274C2×D4—381no—
275C2×D4—761no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—761no—
279C22×C4D4×D1911yescharacteristic
280C22×C4D4×D1911yescharacteristic
281C22×C4C2×C22⋊D1911yescharacteristic
282SD16—762no—
283SD16—762no—
284M16—382no—
285M16—382no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—382no—
289C2×C8—382no—
290C2×C8(C2×D19)⋊C411yescharacteristic
291C2×C8(C2×D19)⋊C411yescharacteristic
292C2×C8(C2×D19)⋊C411yescharacteristic
293C2×C8(C2×D19)⋊C411yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—381no—
299C4⋊C4—381no—
300C4⋊C4—381no—
301C4⋊C4—381no—
302C4⋊C4—381no—
303C4⋊C4—381no—
304C4⋊C4—761no—
305C4⋊C4—761no—
306C22⋊C4—761no—
307C22⋊C4—761no—
308C22⋊C4—761no—
309C42—42no—
310C42—42no—
311C42—761no—
312C42C2×C4×D1911yescharacteristic
313C42C2×D7611yescharacteristic
314C42#6454511yescharacteristic
315C42#6454511yescharacteristic
316C23—761no—
317C23#1059738611yescharacteristic
318Q8—761no—
319Q8—761no—
320Q8—762no—
321Q8—1521no—
322D4—761no—
323D4—761no—
324D4—762no—
325D4—1521no—
326D4—1521no—
327D4—1521no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—761no—
338C2×C4—761no—
339C2×C4—761no—
340C2×C4—1522no—
341C2×C4#1059733911yescharacteristic
342C2×C4#1059733911yescharacteristic
343C2×C4#1059734111yescharacteristic
344C2×C4#1059734111yescharacteristic
345C2×C4#1059735712yes—
346C2×C4#1059736412yes—
347C2×C4C2×(C2×D19)⋊C411yescharacteristic
348C2×C4#1059739311yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—762no—
353C8—762no—
354C8#1059726212yescomplemented
355C22—21no—
356C22—21no—
357C22—1521no—
358C22—1521no—
359C22—1521no—
360C22#1192644511yescharacteristic
361C22#1192693211yescharacteristic
362C22#1192693711yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—82no—
368C4—1521no—
369C4—1521no—
370C4—1521no—
371C4C2×#1059726211yescharacteristic
372C4#1192656211yescharacteristic
373C4#1192664312yes—
374C4#1192679112yes—
375C2—21no—
376C2—21no—
377C2—3041no—
378C2#1456451411yescharacteristic
379C2#1456453111yescharacteristic
380C2#1456455311yescharacteristic
subgroupG/H
centerC2×C4#10597341
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC4×C19×#107C2
socleC22×C19#390
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenterC4×#107D19
hypocenterC19#9722
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
2. #14564578C2semidirect
4. #14562133C2semidirect
6. #14561924C2semidirect
7. C4×C19×#107C2semidirect
10. #11926942C4semidirect
11. #11926917C4semidirect
12. #11926895C4semidirect
13. #11926891C4semidirect
162. C8×C19#104semidirect
168. C4×#107D19semidirect
266. C19#9722semidirect
354. C8#10597262semidirect

Maximal subgroups

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

subgroupindex
#145741942
#145645782
#145645532
#145621332
#145621292
#145619242
C4×C19×#1072
#972219