Finite Group Databasebeta

← #18075717

Subgroups — #18075717

Order 4864.

432 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572596C211yesmaximal, characteristic
2#14563656C211yesmaximal, characteristic
3#14563652C211yesmaximal, characteristic
4C4×#10597265C211yesmaximal, characteristic, complemented
5#14562393C211yesmaximal, characteristic, complemented
6#14561537C211yesmaximal, characteristic, complemented
7C19×#1303C211yesmaximal, characteristic, complemented
8C4×#64541C2211yescharacteristic
9#11926671C411yescharacteristic, complemented
10#11926671C411yescharacteristic, complemented
11#11926621C411yescharacteristic, complemented
12#11926621C411yescharacteristic, complemented
13#11926612—21no—
14#11926612—21no—
15#11926595—21no—
16C2×#10597265—21no—
17#11926568C2211yescharacteristic
18C2×#10597262—21no—
19C2×#10597282—21no—
20C4×#64515—21no—
21C2×C4×C19⋊C8C2211yescharacteristic
22C4×C4⋊Dic19C2211yescharacteristic
23#11926306—21no—
24#11926305—21no—
25#11926304—21no—
26#11926296—21no—
27#11926296—21no—
28C19×#431C2211yescharacteristic
29C19×#423C2211yescharacteristic
30C4×C4⋊C4×C19C2211yescharacteristic
31C2×#64541D411yescharacteristic
32C2×M16×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C42×C19—21no—
35C2×C42×C19C2311yescharacteristic
36C4×C22⋊D19—21no—
37C4×C22⋊D19—21no—
38#10597372D411yescharacteristic
39C2×C4⋊Dic19—21no—
40C2×C4×Dic19—21no—
41C2×#64520—21no—
42C22×C19⋊C8D411yescharacteristic
43C22×C19⋊C8D411yescharacteristic
44C2×#64515—21no—
45C2×#64515—21no—
46C4×D76C2×C411yescharacteristic
47C4×D76Q811yescharacteristic
48#10597318—21no—
49C42×D19—21no—
50C4×Dic38C2×C411yescharacteristic
51C4×Dic38Q811yescharacteristic
52C19×C4⋊C8—21no—
53C19×C4⋊C8—21no—
54C19×C4⋊C8C2×C411yescharacteristic
55C19×C4⋊C8C2×C411yescharacteristic
56C19×C22⋊C8—21no—
57C4×C8×C19—21no—
58C19×#95—21no—
59C19⋊#95—21no—
60#10597282—42no—
61(C2×D19)⋊C8—21no—
62(C2×D19)⋊C8—21no—
63#10597272—21no—
64#10597272—21no—
65Dic19⋊C8—21no—
66Dic19⋊C8—21no—
67#10597265—24no—
68#10597262—42no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)—21no—
71C4×C19⋊C8C2×C411yescharacteristic
72C4×C19⋊C8C2×C411yescharacteristic
73C4×C19⋊C8D411yescharacteristic
74C4×C19⋊C8D411yescharacteristic
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#64541—21no—
84#64541—21no—
85C2×D76C4⋊C411yescharacteristic
86C2×C4×D19—21no—
87C2×C4×D19—21no—
88C2×C4×D19—21no—
89C2×Dic38C4⋊C411yescharacteristic
90M16×C19—41no—
91M16×C19—41no—
92C2×C8×C19—21no—
93C2×C8×C19—21no—
94C2×C8×C19—41no—
95C4⋊C4×C19—22no—
96C4⋊C4×C19—41no—
97C42×C19—41no—
98C42×C19—41no—
99C42×C19C22×C411yescharacteristic
100C42×C19C2×D411yescharacteristic
101C42×C19C2×Q811yescharacteristic
102C42×C19#4111yescharacteristic
103C22⋊Dic19—21no—
104(C2×D19)⋊C4—21no—
105(C2×D19)⋊C4—21no—
106C4⋊Dic19—22no—
107C4⋊Dic19—41no—
108C4⋊Dic19C4⋊C411yescharacteristic
109C4⋊Dic19C4⋊C411yescharacteristic
110Dic19⋊C4—21no—
111Dic19⋊C4—21no—
112C4×Dic19—21no—
113C4×Dic19—21no—
114C4×Dic19—21no—
115C4×Dic19—41no—
116C4×Dic19—41no—
117#64520—41no—
118#64520—41no—
119C2×C19⋊C8—22no—
120C2×C19⋊C8—41no—
121C2×C19⋊C8—41no—
122C2×C19⋊C8C22⋊C411yescharacteristic
123C2×C19⋊C8C22⋊C411yescharacteristic
124C2×C19⋊C8C22⋊C411yescharacteristic
125C2×C19⋊C8C22⋊C411yescharacteristic
126#64515—42no—
127#64515—42no—
128#8669—191nomaximal, Sylow
129C23×C19#12111yescharacteristic
130C22×D19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—41no—
134C2×C4×C19—42no—
135C2×C4×C19—81no—
136C2×C4×C19—81no—
137C2×C4×C19C2×C22⋊C411yescharacteristic
138C2×C4×C19C2×C4⋊C411yescharacteristic
139C2×C4×C19#11711yescharacteristic
140C2×C4×C19#12111yescharacteristic
141C2×C4×C19C22⋊Q811yescharacteristic
142C2×C4×C19C22⋊Q811yescharacteristic
143C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C19#13711yescharacteristic
146C2×C4×C19#13711yescharacteristic
147C22⋊D19—41no—
148C22⋊D19—41no—
149C2×Dic19—21no—
150C2×Dic19—21no—
151C2×Dic19—21no—
152C2×Dic19—42no—
153C2×Dic19—81no—
154C2×Dic19—81no—
155D76—21no—
156D76—21no—
157C4×D19—42no—
158C4×D19—41no—
159C4×D19—41no—
160C4×D19—41no—
161C4×D19—41no—
162Dic38—21no—
163Dic38—21no—
164C8×C19—41no—
165C8×C19—41no—
166C8×C19—81no—
167C19⋊C8—21no—
168C19⋊C8—21no—
169C19⋊C8—21no—
170C19⋊C8—81no—
171C19⋊C8#10412yescomplemented
172#2965—191no—
173#1806—191no—
174#1806—191no—
175C4×#106—191no—
176#1567—191no—
177#1303—191no—
178#1303D1911yescharacteristic, complemented
179C22×C19—21no—
180C22×C19—21no—
181C22×C19#38011yescharacteristic
182C22×C19#46811yescharacteristic
183C22×C19#46811yescharacteristic
184C2×D19—41no—
185C2×D19—41no—
186C2×D19—41no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—21no—
190C4×C19—82no—
191C4×C19C2×#10411yescharacteristic
192C4×C19#42111yescharacteristic
193C4×C19#42811yescharacteristic
194C4×C19#42811yescharacteristic
195C4×C19#46911yescharacteristic
196C4×C19#47011yescharacteristic
197Dic19—41no—
198Dic19—41no—
199Dic19—41no—
200Dic19—82no—
201C4×#41—191no—
202#446—191no—
203#446—191no—
204#436—191no—
205#436—191no—
206#435—381no—
207#435—381no—
208#431—381no—
209#431C2×D1911yescharacteristic
210C2×#106—381no—
211#423—191no—
212#423C2×D1911yescharacteristic
213C2×#104—381no—
214C2×#104—381no—
215C4×M16—381no—
216C2×C4×C8—191no—
217C4×C4⋊C4—191no—
218C4×C4⋊C4C2×D1911yescharacteristic
219#340—381no—
220#339—381no—
221#339—381no—
222#335—381no—
223#335—381no—
224C2×C19—21no—
225C2×C19—21no—
226C2×C19#180611yescharacteristic
227C2×C19#180911yescharacteristic
228C2×C19#181411yescharacteristic
229D19—81no—
230C2×#41—191no—
231C2×M16—21no—
232C2×M16—381no—
233C2×M16—381no—
234C2×M16—381no—
235C22×C8—191no—
236C22×C8—191no—
237C4×Q8—191no—
238C4×Q8—191no—
239C4×D4—191no—
240C4×D4—191no—
241C4×D4—381no—
242C4×D4—381no—
243#117—191no—
244#117—381no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—381no—
247C2×C42—21no—
248C2×C42—381no—
249C2×C42—381no—
250C2×C42C22×D1911yescharacteristic
251#106—384no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—381no—
255C4⋊C8—381no—
256C4⋊C8—381no—
257C4⋊C8—381no—
258C4⋊C8C4×D1911yescharacteristic
259C4⋊C8C4×D1911yescharacteristic
260#104—762no—
261#104—762no—
262C22⋊C8—21no—
263C22⋊C8—381no—
264C22⋊C8—381no—
265#97—381no—
266#97—381no—
267C4×C8—21no—
268C4×C8—191no—
269C4×C8—191no—
270C4×C8—191no—
271C4×C8—191no—
272#95—21no—
273#95—381no—
274C19#866911yescharacteristic, complemented, Sylow
275#41—381no—
276#41—381no—
277#41—381no—
278#41—381no—
279C2×Q8—191no—
280C2×D4—191no—
281C2×D4—381no—
282C22×C4—41no—
283C22×C4—381no—
284C22×C4—381no—
285C22×C4—381no—
286C22×C4—761no—
287C22×C4#6454111yescharacteristic
288C22×C4D4×D1911yescharacteristic
289C22×C4D4×D1911yescharacteristic
290M16—41no—
291M16—41no—
292M16—762no—
293M16—762no—
294M16—761no—
295M16—761no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—41no—
299C2×C8—191no—
300C2×C8—191no—
301C2×C8—191no—
302C2×C8—191no—
303C2×C8—382no—
304C2×C8—761no—
305C2×C8—761no—
306C4⋊C4—22no—
307C4⋊C4—41no—
308C4⋊C4—191no—
309C4⋊C4—191no—
310C4⋊C4—382no—
311C4⋊C4—381no—
312C4⋊C4—381no—
313C4⋊C4—761no—
314C22⋊C4—381no—
315C22⋊C4—381no—
316C22⋊C4—381no—
317C42—41no—
318C42—41no—
319C42—381no—
320C42—381no—
321C42—381no—
322C42—761no—
323C42—761no—
324C42C2×C4×D1911yescharacteristic
325C42#6454111yescharacteristic
326C42D4×D1911yescharacteristic
327C42Q8×D1911yescharacteristic
328C23—381no—
329C23#1059733011yescharacteristic
330Q8—381no—
331Q8—381no—
332D4—381no—
333D4—381no—
334D4—761no—
335D4—761no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—381no—
343C2×C4—381no—
344C2×C4—381no—
345C2×C4—762no—
346C2×C4—761no—
347C2×C4—761no—
348C2×C4—761no—
349C2×C4—761no—
350C2×C4—762no—
351C2×C4—1521no—
352C2×C4—1521no—
353C2×C4#1059731811yescharacteristic
354C2×C4C22⋊C4×D1911yescharacteristic
355C2×C4#1059733011yescharacteristic
356C2×C4C4⋊C4×D1911yescharacteristic
357C2×C4#1059734211yescharacteristic
358C2×C4#1059734211yescharacteristic
359C2×C4#1059735711yescharacteristic
360C2×C4#1059736011yescharacteristic
361C2×C4#1059736111yescharacteristic
362C2×C4#1059736411yescharacteristic
363C8—41no—
364C8—41no—
365C8—81no—
366C8—192no—
367C8—381no—
368C8—381no—
369C8—381no—
370C8—1521no—
371C22—21no—
372C22—21no—
373C22—761no—
374C22—761no—
375C22—761no—
376C22#1192640311yescharacteristic
377C22#1192678911yescharacteristic
378C22#1192679311yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—761no—
384C4—761no—
385C4—761no—
386C4—1522no—
387C4#104×D1911yescharacteristic
388C4#1192655911yescharacteristic
389C4#1192658311yescharacteristic
390C4#1192658511yescharacteristic
391C4#1192679611yescharacteristic
392C4#1192680111yescharacteristic
393C2—21no—
394C2—21no—
395C2—1521no—
396C2#1456365411yescharacteristic
397C2#1456366711yescharacteristic
398C2#1456368811yescharacteristic
subgroupG/H
centerC2×C4#10597330
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1303C2
socleC22×C19#380
prime radicalC2×#64541D4
cosocleC2×C42×C19C23
hypercenter#1303D19
hypocenterC19#8669
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
4. C4×#10597265C2semidirect
5. #14562393C2semidirect
6. #14561537C2semidirect
7. C19×#1303C2semidirect
9. #11926671C4semidirect
10. #11926671C4semidirect
11. #11926621C4semidirect
12. #11926621C4semidirect
171. C19⋊C8#104semidirect
178. #1303D19semidirect
274. C19#8669semidirect

Maximal subgroups

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

subgroupindex
#145725962
#145636562
#145636522
C4×#105972652
#145623932
#145615372
C19×#13032
#866919