Finite Group Databasebeta

← #18077251

Subgroups — #18077251

Order 4864.

514 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573695C211yesmaximal, characteristic
2#14564462C211yesmaximal, characteristic, complemented
3C4×#10597294C211yesmaximal, characteristic, complemented
4#14562051C211yesmaximal, characteristic, complemented
5#14561524C211yesmaximal, characteristic, complemented
6#14561467C211yesmaximal, characteristic, complemented
7C19×#2991C211yesmaximal, characteristic, complemented
8#11927094C2211yescharacteristic
9#11926868—21no—
10#11926839C411yescharacteristic, complemented
11#11926834C411yescharacteristic, complemented
12#11926744C411yescharacteristic, complemented
13#11926739C411yescharacteristic, complemented
14#11926689—21no—
15C4×#64527—21no—
16C4×#64525—21no—
17#11926597C2211yescharacteristic
18C2×#10597294—21no—
19C2×#10597282—22no—
20C4×#64520C2211yescharacteristic
21C42×Dic19C2211yescharacteristic
22#11926303—21no—
23#11926271—21no—
24#11926271—21no—
25C4×#41×C19C2211yescharacteristic
26C8×Q8×C19—21no—
27C19×#436—22no—
28C19×#436—21no—
29C19×#431—21no—
30C19×#431C2211yescharacteristic
31C19×#423—21no—
32C19×#423C2211yescharacteristic
33C2×#41×C19D411yescharacteristic
34C2×#64541—21no—
35C2×M16×C19—22no—
36C2×M16×C19D412yes—
37C4×Q8×C19C2×C411yescharacteristic
38C4×Q8×C19D411yescharacteristic
39C4×D4×C19—21no—
40C4×D4×C19—21no—
41C4×D4×C19C2×C411yescharacteristic
42C4×D4×C19D411yescharacteristic
43C19×#117—21no—
44C19×#117D411yescharacteristic
45C2×C42×C19—21no—
46C2×C42×C19C2311yescharacteristic
47C2×#64527—21no—
48C2×#64525—21no—
49#10597376—21no—
50#10597376—21no—
51C2×C4×Dic19—21no—
52C2×C4×Dic19—21no—
53C2×C4×Dic19—21no—
54C2×#64520—21no—
55#10597321—21no—
56#10597320C2×C411yescharacteristic
57C4×D76—21no—
58C4×D76—21no—
59#10597315C2×C411yescharacteristic
60C19×C4⋊C8—22no—
61C19×C4⋊C8—21no—
62C19×C4⋊C8—21no—
63C19×C4⋊C8D411yescharacteristic
64C19×C4⋊C8D411yescharacteristic
65C19×C22⋊C8—22no—
66C19×C22⋊C8—21no—
67C4×C8×C19—22no—
68C4×C8×C19—21no—
69#10597294—24no—
70#10597292—21no—
71#10597289—21no—
72C22⋊(C19⋊C8)—21no—
73#10597282—44no—
74#10597266—21no—
75#10597266—21no—
76#10597265—21no—
77#10597264—21no—
78C4⋊(C19⋊C8)C2×C411yescharacteristic
79C4⋊(C19⋊C8)C2×C411yescharacteristic
80#10597260—21no—
81C4×C19⋊C8—21no—
82C4×C19⋊C8—21no—
83#41×C19—22no—
84#41×C19—41no—
85C2×Q8×C19C22⋊C411yescharacteristic
86C2×D4×C19—21no—
87C2×D4×C19C22⋊C411yescharacteristic
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19#4111yescharacteristic
94C2×C22⋊D19—41no—
95C22×Dic19—41no—
96#64541—42no—
97#64541—42no—
98C2×D76—21no—
99C2×D76—21no—
100C2×D76—21no—
101C2×C4×D19—41no—
102C2×Dic38—21no—
103M16×C19—42no—
104M16×C19—82no—
105C2×C8×C19—21no—
106C2×C8×C19—22no—
107C2×C8×C19—21no—
108C4⋊C4×C19—21no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19C22⋊C411yescharacteristic
111C4⋊C4×C19C22⋊C411yescharacteristic
112C22⋊C4×C19—21no—
113C22⋊C4×C19—21no—
114C22⋊C4×C19—21no—
115C42×C19—21no—
116C42×C19—21no—
117C42×C19—21no—
118C42×C19C22×C411yescharacteristic
119C42×C19C2×D411yescharacteristic
120C42×C19C2×D411yescharacteristic
121C42×C19#4111yescharacteristic
122#64527—42no—
123#64525—42no—
124(C2×D19)⋊C4—41no—
125(C2×D19)⋊C4—41no—
126C4⋊Dic19—21no—
127C4⋊Dic19—21no—
128C4×Dic19—22no—
129C4×Dic19—22no—
130C4×Dic19—22no—
131C4×Dic19—41no—
132C4×Dic19—41no—
133C4×Dic19—41no—
134#64520—22no—
135#64520—41no—
136C2×C19⋊C8—21no—
137C2×C19⋊C8—21no—
138C2×C19⋊C8—41no—
139#8970—191nomaximal, Sylow
140C23×C19—21no—
141C23×C19#12111yescharacteristic
142C22×D19—41no—
143Q8×C19—21no—
144Q8×C19#10412yescomplemented
145D4×C19—21no—
146D4×C19—21no—
147D4×C19—42no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—21no—
152C2×C4×C19—21no—
153C2×C4×C19—21no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—42no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19C2×C22⋊C411yescharacteristic
163C2×C4×C19C4×D411yescharacteristic
164C2×C4×C19C4×D411yescharacteristic
165C2×C4×C19#12011yescharacteristic
166C2×C4×C19#12111yescharacteristic
167C2×C4×C19#12311yescharacteristic
168C22⋊D19—82no—
169C2×Dic19—42no—
170C2×Dic19—42no—
171C2×Dic19—42no—
172C2×Dic19—41no—
173D76—42no—
174D76—41no—
175D76—41no—
176D76—41no—
177D76—41no—
178C4×D19—81no—
179C4×D19—81no—
180Dic38—42no—
181C8×C19—42no—
182C8×C19—41no—
183C8×C19—41no—
184C19⋊C8—42no—
185C19⋊C8—41no—
186C19⋊C8—41no—
187#3106—191no—
188#2991D1911yescharacteristic, complemented
189#1962—191no—
190C4×#104—191no—
191#1484—191no—
192#1299—191no—
193#1276—191no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—41no—
198C22×C19—41no—
199C22×C19—41no—
200C22×C19#38611yescharacteristic
201C2×D19—81no—
202C2×D19—81no—
203C2×D19—81no—
204C4×C19—21no—
205C4×C19—22no—
206C4×C19—21no—
207C4×C19—21no—
208C4×C19—41no—
209C4×C19—41no—
210C4×C19C2×#10411yescharacteristic
211C4×C19#42111yescharacteristic
212C4×C19#44311yescharacteristic
213C4×C19#44411yescharacteristic
214C4×C19#45311yescharacteristic
215C4×C19#45411yescharacteristic
216Dic19—44no—
217Dic19—81no—
218#532—191no—
219C4×#41C2×D1911yescharacteristic
220#482—381no—
221#477—191no—
222#476—191no—
223#460—191no—
224#459—191no—
225#449—381no—
226C8×Q8—21no—
227C4×SD16—381no—
228C4×D8—381no—
229#436—22no—
230#436—21no—
231#431—21no—
232#431—191no—
233#431C2×D1911yescharacteristic
234#423—21no—
235#423C2×D1911yescharacteristic
236C2×#104—381no—
237C2×#104—382no—
238C4×M16—191no—
239C43—191no—
240#339—381no—
241D4⋊C8—381no—
242D4⋊C8—381no—
243C2×C19—41no—
244C2×C19—81no—
245C2×C19#187111yescharacteristic
246C2×C19#187611yescharacteristic
247C2×C19#188311yescharacteristic
248D19—161no—
249C2×#41—381no—
250C2×#41D7611yescharacteristic
251C2×SD16—381no—
252C2×D8—381no—
253C2×M16—22no—
254C2×M16—381no—
255C2×M16C22⋊D1912yes—
256C4⋊Q8—191no—
257#127—191no—
258#124—381no—
259#121—381no—
260#121—381no—
261C4×Q8C4×D1911yescharacteristic
262C4×Q8C22⋊D1911yescharacteristic
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—381no—
266C4×D4—381no—
267C4×D4C4×D1911yescharacteristic
268C4×D4C22⋊D1911yescharacteristic
269#117—21no—
270#117D7611yescharacteristic
271C2×C42—21no—
272C2×C42—381no—
273C2×C42—381no—
274C2×C42—381no—
275C2×C42C22×D1911yescharacteristic
276#107—381no—
277#106—381no—
278C4⋊C8—22no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—191no—
282C4⋊C8—191no—
283C4⋊C8C22⋊D1911yescharacteristic
284C4⋊C8C22⋊D1911yescharacteristic
285#104—384no—
286#104—764no—
287#103—381no—
288#102—381no—
289#102—381no—
290#102—381no—
291C22⋊C8—22no—
292C22⋊C8—21no—
293C22⋊C8—381no—
294#97—381no—
295C4×C8—22no—
296C4×C8—21no—
297C4×C8—381no—
298C4×C8—381no—
299C19#897011yescharacteristic, complemented, Sylow
300#41—22no—
301#41—41no—
302#41—762no—
303#41—762no—
304C2×Q8—381no—
305C2×Q8(C2×D19)⋊C411yescharacteristic
306C2×D4—21no—
307C2×D4—381no—
308C2×D4—381no—
309C2×D4—381no—
310C2×D4—761no—
311C2×D4(C2×D19)⋊C411yescharacteristic
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—761no—
316C22×C4—761no—
317C22×C4C2×D7611yescharacteristic
318C22×C4#6454111yescharacteristic
319C22×C4C2×C22⋊D1911yescharacteristic
320SD16—762no—
321D8—762no—
322M16—42no—
323M16—82no—
324M16—382no—
325M16—761no—
326C2×C8—21no—
327C2×C8—22no—
328C2×C8—21no—
329C2×C8—381no—
330C2×C8—381no—
331C2×C8—761no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—381no—
335C4⋊C4—381no—
336C4⋊C4(C2×D19)⋊C411yescharacteristic
337C4⋊C4(C2×D19)⋊C411yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—761no—
342C22⋊C4—761no—
343C42—21no—
344C42—21no—
345C42—21no—
346C42—382no—
347C42—382no—
348C42—382no—
349C42—761no—
350C42—761no—
351C42—761no—
352C42C2×C4×D1911yescharacteristic
353C42#6454111yescharacteristic
354C42C2×C22⋊D1911yescharacteristic
355C42C2×C22⋊D1911yescharacteristic
356C23—21no—
357C23—761no—
358C23#1059737611yescharacteristic
359Q8—21no—
360Q8—762no—
361Q8#1059728212yescomplemented
362D4—21no—
363D4—21no—
364D4—42no—
365D4—762no—
366D4—761no—
367D4—761no—
368D4—761no—
369D4—761no—
370D4—1522no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—762no—
386C2×C4—762no—
387C2×C4—762no—
388C2×C4—761no—
389C2×C4—1521no—
390C2×C4—1521no—
391C2×C4C2×(C2×D19)⋊C411yescharacteristic
392C2×C4C4×C22⋊D1911yescharacteristic
393C2×C4C4×C22⋊D1911yescharacteristic
394C2×C4#1059737511yescharacteristic
395C2×C4#1059737611yescharacteristic
396C2×C4#1059739911yescharacteristic
397C8—42no—
398C8—41no—
399C8—41no—
400C8—762no—
401C8—761no—
402C8—761no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—1521no—
410C22—1521no—
411C22—1521no—
412C22#1192642311yescharacteristic
413C4—21no—
414C4—22no—
415C4—21no—
416C4—21no—
417C4—41no—
418C4—41no—
419C4—764no—
420C4—1521no—
421C4C2×#1059728211yescharacteristic
422C4#1192656011yescharacteristic
423C4#1192665911yescharacteristic
424C4#1192666411yescharacteristic
425C4#1192671211yescharacteristic
426C4#1192671711yescharacteristic
427C2—41no—
428C2—81no—
429C2—3041no—
430C2#1456393711yescharacteristic
431C2#1456396211yescharacteristic
432C2#1456401111yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2991C2
socleC22×C19#386
prime radical#14573695C2
cosocleC2×C42×C19C23
hypercenter#2991D19
hypocenterC19#8970
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2991

Complements

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

NH ≅ G/Ntype
2. #14564462C2semidirect
3. C4×#10597294C2semidirect
4. #14562051C2semidirect
5. #14561524C2semidirect
6. #14561467C2semidirect
7. C19×#2991C2semidirect
10. #11926839C4semidirect
11. #11926834C4semidirect
12. #11926744C4semidirect
13. #11926739C4semidirect
144. Q8×C19#104semidirect
188. #2991D19semidirect
299. C19#8970semidirect
361. Q8#10597282semidirect

Maximal subgroups

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

subgroupindex
#145736952
#145644622
C4×#105972942
#145620512
#145615242
#145614672
C19×#29912
#897019