Finite Group Databasebeta

← #18077657

Subgroups — #18077657

Order 4864.

468 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572683C211yesmaximal, characteristic
2#14563734C211yesmaximal, characteristic, complemented
3#14563706C211yesmaximal, characteristic, complemented
4#14562126C211yesmaximal, characteristic
5#14561523C211yesmaximal, characteristic, complemented
6#14561481C211yesmaximal, characteristic, complemented
7C19×#3091C211yesmaximal, characteristic
8#11926622—21no—
9#11926616—21no—
10#11926616—21no—
11D4×C19⋊C8—21no—
12#11926605—21no—
13#11926511—21no—
14#11926508C2211yescharacteristic
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16C2×C22⋊(C19⋊C8)C2211yescharacteristic
17C4×C22⋊Dic19C2211yescharacteristic
18#11926303—21no—
19#11926303—21no—
20#11926299—21no—
21#11926299—21no—
22#11926281—21no—
23#11926278—21no—
24C19×#525C2211yescharacteristic
25C2×C19×#117C2211yescharacteristic
26C19×#485—21no—
27C19×#484C411yescharacteristic, complemented
28C19×#483C411yescharacteristic, complemented
29C19×#482—21no—
30C19×#481C411yescharacteristic, complemented
31C19×#480C411yescharacteristic, complemented
32C19×#427—21no—
33C19×#416—21no—
34C2×C19×C22⋊C8C2211yescharacteristic
35C2×#41×C19D411yescharacteristic
36C23×C4×C19C2311yescharacteristic
37C22×C8×C19—21no—
38C19×#123—21no—
39C19×C22⋊Q8C2×C411yescharacteristic
40C19×C22⋊Q8D411yescharacteristic
41C19×#121C2×C411yescharacteristic
42C19×#121D411yescharacteristic
43C19×#120—21no—
44C4×D4×C19—21no—
45C4×D4×C19—21no—
46C19×#117—21no—
47C19×#117—21no—
48C19×#117—21no—
49C19×#117—21no—
50C19×#117D411yescharacteristic
51C2×C4⋊C4×C19C2×C411yescharacteristic
52C2×C4⋊C4×C19C2×C411yescharacteristic
53C2×C22⋊C4×C19—21no—
54C2×C42×C19—21no—
55C2×C22⋊Dic19—21no—
56C2×C4×Dic19—21no—
57C2×#64520—21no—
58C2×#64520D411yescharacteristic
59C2×#64520D411yescharacteristic
60C22×C19⋊C8—21no—
61C22×C19⋊C8—21no—
62C22×C19⋊C8D411yescharacteristic
63C22×C19⋊C8D411yescharacteristic
64C19×#107—21no—
65C19×#107—21no—
66C19×#106—21no—
67C19×#106—21no—
68C19×#103—21no—
69C19×#103—21no—
70C19×#102—21no—
71C19×#102—21no—
72C19×C22⋊C8—21no—
73C19×C22⋊C8C2×C411yescharacteristic
74C19×C22⋊C8C2×C411yescharacteristic
75C19⋊#95—21no—
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)—21no—
78C22⋊(C19⋊C8)—21no—
79C22⋊(C19⋊C8)—21no—
80C22⋊(C19⋊C8)—21no—
81C22⋊(C19⋊C8)—21no—
82C22⋊(C19⋊C8)—21no—
83C22⋊(C19⋊C8)—21no—
84C4⋊(C19⋊C8)—21no—
85C4⋊(C19⋊C8)—21no—
86#10597260—21no—
87C4×C19⋊C8—21no—
88C24×C19#4111yescharacteristic
89#41×C19—41no—
90#41×C19—41no—
91C2×Q8×C19C22⋊C411yescharacteristic
92C2×D4×C19—21no—
93C2×D4×C19—21no—
94C2×D4×C19—21no—
95C2×D4×C19C22⋊C411yescharacteristic
96C22×C4×C19—21no—
97C22×C4×C19—21no—
98C22×C4×C19—21no—
99C22×C4×C19—41no—
100C22×C4×C19—41no—
101C22×C4×C19C22×C411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19C2×D411yescharacteristic
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19C2×D411yescharacteristic
106C22×C4×C19#4111yescharacteristic
107C22×Dic19—41no—
108C2×C8×C19—21no—
109C2×C8×C19—21no—
110C2×C8×C19—41no—
111C2×C8×C19—41no—
112C4⋊C4×C19—21no—
113C4⋊C4×C19—21no—
114C4⋊C4×C19—21no—
115C4⋊C4×C19—21no—
116C4⋊C4×C19—21no—
117C4⋊C4×C19—21no—
118C4⋊C4×C19C22⋊C411yescharacteristic
119C4⋊C4×C19C22⋊C411yescharacteristic
120C22⋊C4×C19—21no—
121C22⋊C4×C19—21no—
122C22⋊C4×C19—21no—
123C22⋊C4×C19—21no—
124C22⋊C4×C19—21no—
125C22⋊C4×C19—41no—
126C22⋊C4×C19—41no—
127C42×C19—21no—
128C42×C19—41no—
129C42×C19—41no—
130C22⋊Dic19—22no—
131C22⋊Dic19—41no—
132C4×Dic19—41no—
133C4×Dic19—41no—
134#64520—41no—
135#64520—41no—
136#64520—81no—
137C2×C19⋊C8—21no—
138C2×C19⋊C8—21no—
139C2×C19⋊C8—21no—
140C2×C19⋊C8—21no—
141C2×C19⋊C8—41no—
142C2×C19⋊C8—41no—
143C2×C19⋊C8—41no—
144C2×C19⋊C8—41no—
145C2×C19⋊C8—41no—
146C2×C19⋊C8—81no—
147#9038—191nomaximal, Sylow
148C23×C19—21no—
149C23×C19—21no—
150C23×C19—21no—
151C23×C19—41no—
152C23×C19—41no—
153C23×C19C4×D411yescharacteristic
154C23×C19#12111yescharacteristic
155C23×C19#12311yescharacteristic
156Q8×C19—41no—
157D4×C19—41no—
158D4×C19—41no—
159D4×C19—41no—
160D4×C19—81no—
161D4×C19—81no—
162C2×C4×C19—21no—
163C2×C4×C19—21no—
164C2×C4×C19—21no—
165C2×C4×C19—21no—
166C2×C4×C19—21no—
167C2×C4×C19—21no—
168C2×C4×C19—21no—
169C2×C4×C19—21no—
170C2×C4×C19—21no—
171C2×C4×C19—41no—
172C2×C4×C19—41no—
173C2×C4×C19—41no—
174C2×C4×C19—41no—
175C2×C4×C19—41no—
176C2×C4×C19—42no—
177C2×C4×C19—41no—
178C2×C4×C19—41no—
179C2×C4×C19—41no—
180C2×C4×C19—41no—
181C2×C4×C19C2×C22⋊C411yescharacteristic
182C2×C4×C19C4×D411yescharacteristic
183C2×C4×C19#12011yescharacteristic
184C2×C4×C19#12111yescharacteristic
185C2×Dic19—42no—
186C2×Dic19—81no—
187C2×Dic19—81no—
188C8×C19—41no—
189C8×C19—41no—
190C19⋊C8—41no—
191C19⋊C8—41no—
192C19⋊C8—41no—
193C19⋊C8—41no—
194C19⋊C8—81no—
195#3091D1911yescharacteristic
196#2976—191no—
197#1826—191no—
198#1818—191no—
199#1501—191no—
200#1298—191no—
201#1282—191no—
202C22×C19—21no—
203C22×C19—21no—
204C22×C19—21no—
205C22×C19—21no—
206C22×C19—21no—
207C22×C19—21no—
208C22×C19—21no—
209C22×C19—21no—
210C22×C19—41no—
211C22×C19—41no—
212C22×C19—41no—
213C22×C19—81no—
214C22×C19—81no—
215C22×C19#38611yescharacteristic
216C22×C19#44311yescharacteristic
217C22×C19#44411yescharacteristic
218C4×C19—21no—
219C4×C19—21no—
220C4×C19—21no—
221C4×C19—41no—
222C4×C19—41no—
223C4×C19—41no—
224C4×C19—81no—
225C4×C19—81no—
226C4×C19#45811yescharacteristic
227C4×C19#45811yescharacteristic
228Dic19—82no—
229#525C2×D1911yescharacteristic
230C2×#117C2×D1911yescharacteristic
231#485—21no—
232#484Dic1911yescharacteristic, complemented
233#483Dic1911yescharacteristic, complemented
234#482—21no—
235#481Dic1911yescharacteristic, complemented
236#480Dic1911yescharacteristic, complemented
237#436—381no—
238#435—381no—
239#435—381no—
240C8×D4—381no—
241#433—381no—
242#427—21no—
243#416—21no—
244#408—381no—
245#407—191no—
246C2×C22⋊C8—191no—
247C2×C22⋊C8—191no—
248C2×C22⋊C8C2×D1911yescharacteristic
249C4×C22⋊C4—191no—
250#339—381no—
251#339—381no—
252#336—381no—
253#336—381no—
254#328—381no—
255#327—381no—
256C2×C19—21no—
257C2×C19—21no—
258C2×C19—41no—
259C2×C19—41no—
260C2×C19—81no—
261C2×C19#187611yescharacteristic
262C2×C19#188111yescharacteristic
263C2×C19#189011yescharacteristic
264C2×#41C22⋊D1911yescharacteristic
265C23×C4C22×D1911yescharacteristic
266C2×M16—191no—
267C2×M16—191no—
268C2×M16—381no—
269C22×C8—21no—
270C22×C8—191no—
271C22×C8—191no—
272C22×C8—381no—
273C22×C8—381no—
274#123—21no—
275C22⋊Q8C2×Dic1911yescharacteristic
276C22⋊Q8C22⋊D1911yescharacteristic
277#121C2×Dic1911yescharacteristic
278#121C22⋊D1911yescharacteristic
279#120—21no—
280C4×D4—21no—
281C4×D4—21no—
282#117—21no—
283#117—21no—
284#117—21no—
285#117—21no—
286#117C22⋊D1911yescharacteristic
287C2×C4⋊C4C2×Dic1911yescharacteristic
288C2×C4⋊C4C2×Dic1911yescharacteristic
289C2×C22⋊C4—21no—
290C2×C22⋊C4—381no—
291C2×C42—21no—
292C2×C42—381no—
293#107—21no—
294#107—21no—
295#106—21no—
296#106—21no—
297C4⋊C8—381no—
298C4⋊C8—381no—
299#103—21no—
300#103—21no—
301#102—21no—
302#102—21no—
303C22⋊C8—21no—
304C22⋊C8—381no—
305C22⋊C8—381no—
306C22⋊C8—381no—
307C22⋊C8—381no—
308C22⋊C8—381no—
309C22⋊C8—381no—
310C22⋊C8—381no—
311C22⋊C8—381no—
312C22⋊C8C2×Dic1911yescharacteristic
313C22⋊C8C2×Dic1911yescharacteristic
314#97—381no—
315C4×C8—381no—
316#95—381no—
317C19#903811yescharacteristic, complemented, Sylow
318C24#6454311yescharacteristic
319#41—41no—
320#41—41no—
321C2×Q8C22⋊Dic1911yescharacteristic
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4C22⋊Dic1911yescharacteristic
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—761no—
332C22×C4D4×D1911yescharacteristic
333C22×C4D4×D1911yescharacteristic
334C22×C4#6454311yescharacteristic
335C22×C4C22×Dic1911yescharacteristic
336C22×C4C2×C22⋊D1911yescharacteristic
337C22×C4C2×C22⋊D1911yescharacteristic
338M16—761no—
339M16—761no—
340M16—1521no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—381no—
346C2×C8—381no—
347C2×C8—381no—
348C2×C8—381no—
349C2×C8—761no—
350C2×C8—761no—
351C2×C8—761no—
352C2×C8—761no—
353C2×C8—761no—
354C2×C8—1521no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4C22⋊Dic1911yescharacteristic
362C4⋊C4C22⋊Dic1911yescharacteristic
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—21no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—382no—
371C22⋊C4—761no—
372C42—21no—
373C42—41no—
374C42—41no—
375C42—761no—
376C42—761no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—41no—
381C23—41no—
382C23D4×Dic1911yescharacteristic
383C23#1059738111yescharacteristic
384C23#1059738511yescharacteristic
385Q8—41no—
386D4—41no—
387D4—41no—
388D4—41no—
389D4—81no—
390D4—81no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—762no—
411C2×C4—1521no—
412C2×C4—1521no—
413C2×C4D4×Dic1911yescharacteristic
414C2×C4#1059738311yescharacteristic
415C2×C4#1059738511yescharacteristic
416C2×C4C2×C22⋊Dic1911yescharacteristic
417C8—41no—
418C8—41no—
419C8—761no—
420C8—761no—
421C8—761no—
422C8—761no—
423C8—1521no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—81no—
436C22—81no—
437C22#1192642411yescharacteristic
438C22#1192666111yescharacteristic
439C22#1192666611yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—41no—
444C4—41no—
445C4—41no—
446C4—81no—
447C4—81no—
448C4—1522no—
449C4#1192673311yescharacteristic
450C4#1192673311yescharacteristic
451C2—21no—
452C2—21no—
453C2—41no—
454C2—41no—
455C2—81no—
456C2#1456396411yescharacteristic
457C2#1456399911yescharacteristic
458C2#1456404911yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#3091C2
socleC22×C19#386
prime radicalC19×#525C22
cosocleC23×C4×C19C23
hypercenter#3091D19
hypocenterC19#9038
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3091

Complements

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

NH ≅ G/Ntype
2. #14563734C2semidirect
3. #14563706C2semidirect
5. #14561523C2semidirect
6. #14561481C2semidirect
27. C19×#484C4semidirect
28. C19×#483C4semidirect
30. C19×#481C4semidirect
31. C19×#480C4semidirect
232. #484Dic19semidirect
233. #483Dic19semidirect
235. #481Dic19semidirect
236. #480Dic19semidirect
317. C19#9038semidirect

Maximal subgroups

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

subgroupindex
#145726832
#145637342
#145637062
#145621262
#145615232
#145614812
C19×#30912
#903819