Finite Group Databasebeta

← #18077249

Subgroups — #18077249

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#14572767C211yesmaximal, characteristic, complemented
3#14564463C211yesmaximal, characteristic, complemented
4#14562053C211yesmaximal, characteristic, complemented
5#14561525C211yesmaximal, characteristic, complemented
6#14561468C211yesmaximal, characteristic, complemented
7C4×C19×#104C211yesmaximal, characteristic, complemented
8#11927094C2211yescharacteristic
9#11926868—21no—
10#11926839C411yescharacteristic, complemented
11#11926834C411yescharacteristic, complemented
12#11926744C411yescharacteristic, complemented
13#11926739C411yescharacteristic, complemented
14#11926689—21no—
15Q8×C19⋊C8—21no—
16C4×#64527—21no—
17C4×#64525—21no—
18#11926622—22no—
19#11926622—21no—
20#11926597—21no—
21#11926597C2211yescharacteristic
22#11926597C2211yescharacteristic
23#11926568—21no—
24#11926568C2211yescharacteristic
25C2×#10597262—22no—
26#11926273—21no—
27#11926273—21no—
28C4×#41×C19C2211yescharacteristic
29C2×C19×#104—21no—
30C4×M16×C19C2211yescharacteristic
31C43×C19C2211yescharacteristic
32C19×#339—21no—
33C2×#41×C19D411yescharacteristic
34C2×#64541—21no—
35C2×M16×C19—21no—
36C4×Q8×C19C2×C411yescharacteristic
37C4×Q8×C19D411yescharacteristic
38C4×D4×C19—21no—
39C4×D4×C19—21no—
40C4×D4×C19C2×C411yescharacteristic
41C4×D4×C19D411yescharacteristic
42C19×#117—21no—
43C19×#117D411yescharacteristic
44C2×C42×C19—21no—
45C2×C42×C19—21no—
46C2×C42×C19—21no—
47C2×C42×C19—21no—
48C2×C42×C19C2311yescharacteristic
49C2×#64527—21no—
50C2×#64525—21no—
51#10597376—21no—
52#10597376—21no—
53C2×#64520—22no—
54C2×#64520D412yes—
55#10597321—21no—
56#10597320C2×C411yescharacteristic
57C4×D76—21no—
58C4×D76—21no—
59#10597315C2×C411yescharacteristic
60C19×#104—24no—
61C19×#97—21no—
62C4×C8×C19—21no—
63#10597292—21no—
64#10597289—21no—
65C22⋊(C19⋊C8)—22no—
66C22⋊(C19⋊C8)—21no—
67C22⋊(C19⋊C8)—21no—
68#10597266—21no—
69#10597266—21no—
70#10597265—21no—
71#10597264—21no—
72#10597262—44no—
73C4⋊(C19⋊C8)—22no—
74C4⋊(C19⋊C8)—21no—
75C4⋊(C19⋊C8)—21no—
76C4⋊(C19⋊C8)C2×C411yescharacteristic
77C4⋊(C19⋊C8)C2×C411yescharacteristic
78C4⋊(C19⋊C8)D411yescharacteristic
79C4⋊(C19⋊C8)D411yescharacteristic
80C4×C19⋊C8—22no—
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×C19—41no—
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19#4111yescharacteristic
95C2×C22⋊D19—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—22no—
104M16×C19—41no—
105C2×C8×C19—41no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19C22⋊C411yescharacteristic
109C4⋊C4×C19C22⋊C411yescharacteristic
110C22⋊C4×C19—21no—
111C22⋊C4×C19—21no—
112C22⋊C4×C19—21no—
113C42×C19—21no—
114C42×C19—21no—
115C42×C19—21no—
116C42×C19—22no—
117C42×C19—22no—
118C42×C19—22no—
119C42×C19—41no—
120C42×C19—41no—
121C42×C19—41no—
122C42×C19C22×C411yescharacteristic
123C42×C19C2×D411yescharacteristic
124C42×C19C2×D411yescharacteristic
125C42×C19#4111yescharacteristic
126#64527—42no—
127#64525—42no—
128(C2×D19)⋊C4—41no—
129(C2×D19)⋊C4—41no—
130C4⋊Dic19—21no—
131C4⋊Dic19—21no—
132#64520—42no—
133#64520—82no—
134C2×C19⋊C8—21no—
135C2×C19⋊C8—21no—
136C2×C19⋊C8—21no—
137C2×C19⋊C8—22no—
138C2×C19⋊C8—21no—
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—42no—
159C2×C4×C19—42no—
160C2×C4×C19—42no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—41no—
165C2×C4×C19C2×C22⋊C411yescharacteristic
166C2×C4×C19C4×D411yescharacteristic
167C2×C4×C19C4×D411yescharacteristic
168C2×C4×C19#12011yescharacteristic
169C2×C4×C19#12111yescharacteristic
170C2×C4×C19#12311yescharacteristic
171C22⋊D19—82no—
172C2×Dic19—41no—
173D76—42no—
174D76—41no—
175D76—41no—
176D76—41no—
177D76—41no—
178C4×D19—81no—
179C4×D19—81no—
180Dic38—42no—
181C8×C19—42no—
182C19⋊C8—41no—
183C19⋊C8—41no—
184C19⋊C8—42no—
185C19⋊C8—41no—
186C19⋊C8—41no—
187#3106—191no—
188#2991—191no—
189#1962—191no—
190C4×#104D1911yescharacteristic, complemented
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—44no—
209C4×C19—41no—
210C4×C19—41no—
211C4×C19C2×#10411yescharacteristic
212C4×C19#42111yescharacteristic
213C4×C19#44311yescharacteristic
214C4×C19#44411yescharacteristic
215C4×C19#45311yescharacteristic
216C4×C19#45411yescharacteristic
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—381no—
227C4×SD16—381no—
228C4×D8—381no—
229#436—382no—
230#436—381no—
231#431—191no—
232#431—191no—
233#431—381no—
234#423—191no—
235#423—381no—
236C2×#104—21no—
237C2×#104—382no—
238C4×M16C2×D1911yescharacteristic
239C43C2×D1911yescharacteristic
240#339—21no—
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×#41C22⋊D1911yescharacteristic
251C2×SD16—381no—
252C2×D8—381no—
253C2×M16—21no—
254C2×M16—192no—
255C2×M16—382no—
256C4⋊Q8—191no—
257#127—191no—
258#124—381no—
259#121—381no—
260#121—381no—
261C4×Q8C4×D1911yescharacteristic
262C4×Q8D7611yescharacteristic
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—381no—
266C4×D4—381no—
267C4×D4C4×D1911yescharacteristic
268C4×D4D7611yescharacteristic
269#117—21no—
270#117C22⋊D1911yescharacteristic
271C2×C42—21no—
272C2×C42—21no—
273C2×C42—21no—
274C2×C42—21no—
275C2×C42C22×D1911yescharacteristic
276#107—381no—
277#106—381no—
278C4⋊C8—191no—
279C4⋊C8—191no—
280C4⋊C8—191no—
281C4⋊C8—191no—
282C4⋊C8—382no—
283C4⋊C8—381no—
284C4⋊C8—381no—
285#104—24no—
286#104—764no—
287#103—381no—
288#102—381no—
289#102—381no—
290#102—381no—
291C22⋊C8—382no—
292C22⋊C8—381no—
293C22⋊C8—381no—
294#97—21no—
295C4×C8—21no—
296C4×C8—382no—
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—41no—
316C22×C4—761no—
317C22×C4D4×D1911yescharacteristic
318C22×C4#6454311yescharacteristic
319C22×C4C2×C22⋊D1911yescharacteristic
320SD16—762no—
321D8—762no—
322M16—22no—
323M16—41no—
324M16—762no—
325M16—1522no—
326C2×C8—41no—
327C2×C8—381no—
328C2×C8—381no—
329C2×C8—382no—
330C2×C8—381no—
331C2×C8—381no—
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—22no—
347C42—22no—
348C42—22no—
349C42—41no—
350C42—41no—
351C42—41no—
352C42C2×C4×D1911yescharacteristic
353C42C2×D7611yescharacteristic
354C42D4×D1911yescharacteristic
355C42#6454311yescharacteristic
356C23—21no—
357C23—761no—
358C23#1059738511yescharacteristic
359Q8—21no—
360Q8—762no—
361Q8#1059726212yescomplemented
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—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—761no—
389C2×C4—1521no—
390C2×C4—1521no—
391C2×C4(C22⋊D19)⋊C411yescharacteristic
392C2×C4(C22⋊D19)⋊C411yescharacteristic
393C2×C4#1059732811yescharacteristic
394C2×C4#1059733211yescharacteristic
395C2×C4C2×(C2×D19)⋊C411yescharacteristic
396C2×C4#1059738511yescharacteristic
397C8—42no—
398C8—761no—
399C8—761no—
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#1192642111yescharacteristic
413C4—21no—
414C4—22no—
415C4—21no—
416C4—21no—
417C4—44no—
418C4—41no—
419C4—41no—
420C4—1521no—
421C4C2×#1059726211yescharacteristic
422C4#1192656211yescharacteristic
423C4#1192665811yescharacteristic
424C4#1192666311yescharacteristic
425C4#1192671311yescharacteristic
426C4#1192671811yescharacteristic
427C2—41no—
428C2—81no—
429C2—3041no—
430C2#1456393511yescharacteristic
431C2#1456396011yescharacteristic
432C2#1456400911yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC4×C19×#104C2
socleC22×C19#386
prime radical#14573695C2
cosocleC2×C42×C19C23
hypercenterC4×#104D19
hypocenterC19#8970
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#104

Complements

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

NH ≅ G/Ntype
2. #14572767C2semidirect
3. #14564463C2semidirect
4. #14562053C2semidirect
5. #14561525C2semidirect
6. #14561468C2semidirect
7. C4×C19×#104C2semidirect
10. #11926839C4semidirect
11. #11926834C4semidirect
12. #11926744C4semidirect
13. #11926739C4semidirect
144. Q8×C19#104semidirect
190. C4×#104D19semidirect
299. C19#8970semidirect
361. Q8#10597262semidirect

Maximal subgroups

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

subgroupindex
#145736952
#145727672
#145644632
#145620532
#145615252
#145614682
C4×C19×#1042
#897019