Finite Group Databasebeta

← #18081893

Subgroups — #18081893

Order 4864.

428 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573960C211yesmaximal, characteristic
2#14563500C211yesmaximal, characteristic, complemented
3#14562381C211yesmaximal, characteristic, complemented
4#14562134C211yesmaximal, characteristic, complemented
5#14562131C211yesmaximal, characteristic
6#14562033C211yesmaximal, characteristic
7C19×#1481C211yesmaximal, characteristic, complemented
8#11927094C2211yescharacteristic
9#11926901—21no—
10#11926901—21no—
11#11926896C411yescharacteristic, complemented
12#11926896C411yescharacteristic, complemented
13#11926892C411yescharacteristic, complemented
14#11926892C411yescharacteristic, complemented
15#11926597C2211yescharacteristic
16#11926538—21no—
17#11926538—21no—
18C2×C4×C19⋊C8C2211yescharacteristic
19C2×C8×Dic19—21no—
20C4×C4⋊Dic19C2211yescharacteristic
21#11926298—21no—
22#11926296—21no—
23#11926294—21no—
24#11926281—22no—
25#11926279—22no—
26#11926271—22no—
27C19×#533C2211yescharacteristic
28C19×#431C2211yescharacteristic
29C2×C19×C4⋊C8C2211yescharacteristic
30C19×Q8⋊C8—22no—
31C2×#64541—21no—
32C22×C8×C19—21no—
33C19×C4⋊Q8C2×C411yescharacteristic
34C19×C4⋊Q8C2×C411yescharacteristic
35C19×#125—21no—
36C19×C22⋊Q8—21no—
37C19×C22⋊Q8—21no—
38C4×Q8×C19—21no—
39C4×Q8×C19—21no—
40C19×#117—21no—
41C2×C42×C19C2311yescharacteristic
42#10597376—21no—
43#10597376—21no—
44C2×C4⋊Dic19—21no—
45C2×C4×Dic19—21no—
46C22×C19⋊C8D411yescharacteristic
47C22×C19⋊C8D411yescharacteristic
48#10597321—21no—
49#10597320C2×C411yescharacteristic
50C4×D76—21no—
51C4×D76—21no—
52#10597315C2×C411yescharacteristic
53C19×C4⋊C8—21no—
54C19×C4⋊C8—21no—
55C19×C4⋊C8D412yes—
56C19×C22⋊C8—21no—
57C4×C8×C19—21no—
58C19⋊#95D412yes—
59C22⋊(C19⋊C8)—21no—
60C8×Dic19—42no—
61#10597267—21no—
62#10597267—21no—
63#10597267—21no—
64#10597267—21no—
65#10597266—21no—
66#10597266—21no—
67#10597266—21no—
68#10597266—21no—
69C4⋊(C19⋊C8)—21no—
70C4×C19⋊C8—21no—
71C4×C19⋊C8C2×C411yescharacteristic
72C4×C19⋊C8C2×C411yescharacteristic
73C4×C19⋊C8D411yescharacteristic
74C4×C19⋊C8D411yescharacteristic
75C2×Q8×C19—21no—
76C2×Q8×C19—21no—
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19#4111yescharacteristic
80C2×C22⋊D19—41no—
81C22×Dic19—22no—
82#64541—41no—
83#64541—41no—
84#64541—41no—
85#64541—41no—
86C2×D76—21no—
87C2×D76—21no—
88C2×D76—21no—
89C2×C4×D19—41no—
90C2×Dic38—21no—
91C2×C8×C19—22no—
92C2×C8×C19—41no—
93C2×C8×C19—41no—
94C2×C8×C19—41no—
95C4⋊C4×C19—21no—
96C4⋊C4×C19—21no—
97C4⋊C4×C19—21no—
98C4⋊C4×C19—21no—
99C4⋊C4×C19—41no—
100C4⋊C4×C19—41no—
101C22⋊C4×C19—41no—
102C42×C19—41no—
103C42×C19C22×C411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C42×C19C2×D411yescharacteristic
106C42×C19#4111yescharacteristic
107(C2×D19)⋊C4—41no—
108(C2×D19)⋊C4—41no—
109C4⋊Dic19—24no—
110C4⋊Dic19—21no—
111C4⋊Dic19—21no—
112C4×Dic19—41no—
113C4×Dic19—41no—
114C2×C19⋊C8—21no—
115C2×C19⋊C8—21no—
116C2×C19⋊C8—21no—
117C2×C19⋊C8—21no—
118C2×C19⋊C8—41no—
119C2×C19⋊C8C22⋊C411yescharacteristic
120C2×C19⋊C8C22⋊C411yescharacteristic
121C2×C19⋊C8C22⋊C411yescharacteristic
122C2×C19⋊C8C22⋊C411yescharacteristic
123#9751—191nomaximal, Sylow
124C23×C19#12111yescharacteristic
125C22×D19—41no—
126Q8×C19—42no—
127Q8×C19—81no—
128C2×C4×C19—22no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19C2×C22⋊C411yescharacteristic
133C2×C4×C19C4×D411yescharacteristic
134C2×C4×C19C4×D411yescharacteristic
135C2×C4×C19#12111yescharacteristic
136C2×C4×C19#12411yescharacteristic
137C2×C4×C19#12711yescharacteristic
138C2×C4×C19#13511yescharacteristic
139C2×C4×C19#13511yescharacteristic
140C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C19#13711yescharacteristic
142C22⋊D19—81no—
143C22⋊D19—81no—
144C2×Dic19—24no—
145C2×Dic19—42no—
146C2×Dic19—42no—
147C2×Dic19—41no—
148D76—41no—
149D76—41no—
150D76—42no—
151D76—81no—
152C4×D19—81no—
153C4×D19—81no—
154Dic38—41no—
155Dic38—41no—
156C8×C19—42no—
157C8×C19—81no—
158C19⋊C8—21no—
159C19⋊C8—21no—
160C19⋊C8—21no—
161C19⋊C8—21no—
162C19⋊C8—81no—
163#3131—191no—
164C8×C4⋊C4—191no—
165#1564—191no—
166#1503—191no—
167#1502—191no—
168#1481D1911yescharacteristic, complemented
169#1480—191no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19#39011yescharacteristic
173C22×C19#46311yescharacteristic
174C22×C19#46411yescharacteristic
175C2×D19—81no—
176C2×D19—81no—
177C2×D19—81no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—81no—
182C4×C19—81no—
183C4×C19#41611yescharacteristic
184C4×C19#41711yescharacteristic
185C4×C19#44312yes—
186C4×C19#46311yescharacteristic
187C4×C19#46411yescharacteristic
188Dic19—44no—
189Dic19—81no—
190#533C2×D1911yescharacteristic
191#532—191no—
192#488—381no—
193#488—381no—
194#487—191no—
195#487—191no—
196#486—191no—
197#486—191no—
198#431—191no—
199#431C2×D1911yescharacteristic
200C2×C4⋊C8C2×D1911yescharacteristic
201#416—381no—
202#416—381no—
203C2×C4×C8—191no—
204C2×C4×C8—381no—
205C4×C4⋊C4—191no—
206#336—381no—
207#335—381no—
208#334—381no—
209#328—382no—
210#327—382no—
211Q8⋊C8—22no—
212D4⋊C8—382no—
213C2×C19—21no—
214C2×C19—21no—
215C2×C19#197411yescharacteristic
216C2×C19#197611yescharacteristic
217C2×C19#198311yescharacteristic
218D19—161no—
219C2×#41—381no—
220C22×C8—21no—
221C22×C8—191no—
222C22×C8—191no—
223C4⋊Q8—191no—
224C4⋊Q8C4×D1911yescharacteristic
225C4⋊Q8C4×D1911yescharacteristic
226#127—191no—
227#125—21no—
228#124—381no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231#121—381no—
232#121—381no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—381no—
236C4×D4—381no—
237#117—21no—
238C2×C4⋊C4—381no—
239C2×C42—381no—
240C2×C42C22×D1911yescharacteristic
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—381no—
244C4⋊C8C22⋊D1912yes—
245#103—381no—
246#103—381no—
247#103—381no—
248#103—381no—
249#102—381no—
250#102—381no—
251#102—381no—
252#102—381no—
253C22⋊C8—21no—
254C22⋊C8—381no—
255C4×C8—21no—
256C4×C8—191no—
257C4×C8—191no—
258C4×C8—191no—
259C4×C8—191no—
260C4×C8—381no—
261C4×C8—762no—
262#95—192no—
263C19#975111yescharacteristic, complemented, Sylow
264#41—761no—
265#41—761no—
266#41—761no—
267#41—761no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—381no—
271C2×D4—381no—
272C2×D4—381no—
273C2×D4—381no—
274C2×D4—761no—
275C22×C4—382no—
276C22×C4—761no—
277C22×C4#6454111yescharacteristic
278C22×C4D4×D1911yescharacteristic
279C22×C4D4×D1911yescharacteristic
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—191no—
285C2×C8—191no—
286C2×C8—191no—
287C2×C8—191no—
288C2×C8—381no—
289C2×C8—381no—
290C2×C8—381no—
291C2×C8—381no—
292C2×C8—761no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—384no—
300C4⋊C4—381no—
301C4⋊C4—381no—
302C22⋊C4—41no—
303C22⋊C4—761no—
304C22⋊C4—761no—
305C42—41no—
306C42—761no—
307C42—761no—
308C42C2×C4×D1911yescharacteristic
309C42D4×D1911yescharacteristic
310C42#6454311yescharacteristic
311C42C2×C22⋊D1911yescharacteristic
312C23—761no—
313C23#1059733011yescharacteristic
314Q8—42no—
315Q8—81no—
316Q8—761no—
317Q8—761no—
318D4—761no—
319D4—761no—
320D4—762no—
321D4—1521no—
322D4—1521no—
323D4—1521no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—384no—
329C2×C4—762no—
330C2×C4—762no—
331C2×C4—761no—
332C2×C4—1521no—
333C2×C4—1521no—
334C2×C4C22⋊C4×D1911yescharacteristic
335C2×C4(C22⋊D19)⋊C411yescharacteristic
336C2×C4#1059733111yescharacteristic
337C2×C4#1059736011yescharacteristic
338C2×C4#1059736211yescharacteristic
339C2×C4#1059736411yescharacteristic
340C2×C4#1059736511yescharacteristic
341C2×C4C4×C22⋊D1911yescharacteristic
342C2×C4#1059738511yescharacteristic
343C2×C4#1059738611yescharacteristic
344C8—42no—
345C8—81no—
346C8—381no—
347C8—381no—
348C8—381no—
349C8—381no—
350C8—1521no—
351C22—21no—
352C22—21no—
353C22—1521no—
354C22—1521no—
355C22—1521no—
356C22#1192644411yescharacteristic
357C22#1192676211yescharacteristic
358C22#1192676911yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—81no—
364C4—764no—
365C4—1521no—
366C4#1192653911yescharacteristic
367C4#1192654411yescharacteristic
368C4#1192665912yes—
369C4#1192676111yescharacteristic
370C4#1192676811yescharacteristic
371C2—21no—
372C2—21no—
373C2—3041no—
374C2#1456452211yescharacteristic
375C2#1456453211yescharacteristic
376C2#1456456411yescharacteristic
subgroupG/H
centerC2×C4#10597385
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1481C2
socleC22×C19#390
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenter#1481D19
hypocenterC19#9751
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
2. #14563500C2semidirect
3. #14562381C2semidirect
4. #14562134C2semidirect
7. C19×#1481C2semidirect
11. #11926896C4semidirect
12. #11926896C4semidirect
13. #11926892C4semidirect
14. #11926892C4semidirect
168. #1481D19semidirect
263. C19#9751semidirect

Maximal subgroups

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

subgroupindex
#145739602
#145635002
#145623812
#145621342
#145621312
#145620332
C19×#14812
#975119