Finite Group Databasebeta

← #18079611

Subgroups — #18079611

Order 4864.

470 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572293C211yesmaximal, characteristic, complemented
2#14563730C211yesmaximal, characteristic, complemented
3#14562203C211yesmaximal, characteristic
4#14561995C211yesmaximal, characteristic
5#14561540C211yesmaximal, characteristic, complemented
6#14561522C211yesmaximal, characteristic, complemented
7C19×#3094C211yesmaximal, characteristic
8#11926605—22no—
9#11926601—21no—
10#11926597—21no—
11#11926571—21no—
12#11926508C2211yescharacteristic
13C2×C22⋊(C19⋊C8)C2211yescharacteristic
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15#11926500—21no—
16#11926404C2211yescharacteristic
17#11926306—21no—
18#11926306—21no—
19#11926278—21no—
20#11926278—21no—
21#11926268—22no—
22C2×C19×#121C2211yescharacteristic
23C2×C19×#117C2211yescharacteristic
24C19×#482—21no—
25C19×#482—21no—
26C19×#481—21no—
27C19×#480—21no—
28C19×#428C411yescharacteristic, complemented
29C19×#428C411yescharacteristic, complemented
30C19×#418C411yescharacteristic, complemented
31C19×#418C411yescharacteristic, complemented
32C19×#407C2211yescharacteristic
33C22×D4×C19—21no—
34C22×D4×C19C2×C411yescharacteristic
35C23×C4×C19C2311yescharacteristic
36C2×M16×C19C2×C411yescharacteristic
37C2×M16×C19C2×C411yescharacteristic
38C19×#121—21no—
39C19×#121—21no—
40C19×#121—21no—
41C19×#121—21no—
42C19×#117—21no—
43C19×#117—21no—
44C19×#117C2×C411yescharacteristic
45C19×#117C2×C411yescharacteristic
46C19×#117D411yescharacteristic
47C19×#117D411yescharacteristic
48C2×C4⋊C4×C19C2×C411yescharacteristic
49C2×C4⋊C4×C19D411yescharacteristic
50C2×C4⋊C4×C19D411yescharacteristic
51C2×C22⋊C4×C19—21no—
52C2×C22⋊C4×C19—21no—
53C2×C42×C19—21no—
54C2×C22⋊Dic19—21no—
55C2×C4⋊Dic19—21no—
56C2×#64520—21no—
57C22×C19⋊C8—21no—
58C22×C19⋊C8—21no—
59C19×#107—21no—
60C19×#107—21no—
61C19×#106—21no—
62C19×#106—21no—
63C19×#102—21no—
64C19×#102—21no—
65C19×#102—21no—
66C19×#102—21no—
67C19×C22⋊C8—21no—
68C19×C22⋊C8—21no—
69C19⋊#95—21no—
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)D411yescharacteristic
75C22⋊(C19⋊C8)D411yescharacteristic
76C22⋊(C19⋊C8)D412yes—
77C4⋊(C19⋊C8)—22no—
78C4⋊(C19⋊C8)—22no—
79#10597260—22no—
80C4×C19⋊C8—22no—
81C24×C19—21no—
82C24×C19#4111yescharacteristic
83C2×D4×C19—21no—
84C2×D4×C19—21no—
85C2×D4×C19—41no—
86C2×D4×C19—41no—
87C2×D4×C19—41no—
88C2×D4×C19—41no—
89C2×D4×C19—81no—
90C2×D4×C19—81no—
91C22×C4×C19—21no—
92C22×C4×C19—21no—
93C22×C4×C19—21no—
94C22×C4×C19—41no—
95C22×C4×C19—41no—
96C22×C4×C19C22×C411yescharacteristic
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19#4111yescharacteristic
102C22×Dic19—41no—
103M16×C19—41no—
104M16×C19—41no—
105C2×C8×C19—21no—
106C2×C8×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—21no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19C22⋊C411yescharacteristic
112C4⋊C4×C19C22⋊C411yescharacteristic
113C4⋊C4×C19C22⋊C411yescharacteristic
114C4⋊C4×C19C22⋊C411yescharacteristic
115C22⋊C4×C19—21no—
116C22⋊C4×C19—21no—
117C22⋊C4×C19—21no—
118C22⋊C4×C19—21no—
119C22⋊C4×C19—41no—
120C22⋊C4×C19—41no—
121C42×C19—21no—
122C42×C19—21no—
123C42×C19—21no—
124C42×C19—21no—
125C22⋊Dic19—81no—
126C4⋊Dic19—41no—
127C4⋊Dic19—41no—
128#64520—41no—
129#64520—41no—
130C2×C19⋊C8—21no—
131C2×C19⋊C8—22no—
132C2×C19⋊C8—21no—
133C2×C19⋊C8—41no—
134C2×C19⋊C8—41no—
135C2×C19⋊C8—41no—
136C2×C19⋊C8—41no—
137C2×C19⋊C8—41no—
138#9348—191nomaximal, Sylow
139C23×C19—21no—
140C23×C19—21no—
141C23×C19—41no—
142C23×C19—41no—
143C23×C19—42no—
144C23×C19—41no—
145C23×C19—81no—
146C23×C19—81no—
147C23×C19C4×D411yescharacteristic
148C23×C19#12111yescharacteristic
149C23×C19#12311yescharacteristic
150D4×C19—41no—
151D4×C19—41no—
152D4×C19—81no—
153D4×C19—82no—
154D4×C19—81no—
155D4×C19—81no—
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—21no—
159C2×C4×C19—21no—
160C2×C4×C19—21no—
161C2×C4×C19—21no—
162C2×C4×C19—21no—
163C2×C4×C19—21no—
164C2×C4×C19—21no—
165C2×C4×C19—21no—
166C2×C4×C19—41no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19—41no—
170C2×C4×C19—41no—
171C2×C4×C19—41no—
172C2×C4×C19—81no—
173C2×C4×C19—81no—
174C2×C4×C19C2×C22⋊C411yescharacteristic
175C2×C4×C19C4×D411yescharacteristic
176C2×C4×C19#12011yescharacteristic
177C2×C4×C19#12111yescharacteristic
178C2×Dic19—81no—
179C2×Dic19—81no—
180C2×Dic19—81no—
181C8×C19—41no—
182C8×C19—41no—
183C19⋊C8—41no—
184C19⋊C8—41no—
185C19⋊C8—42no—
186C19⋊C8—81no—
187#3094D1911yescharacteristic
188#2924—191no—
189#1825—191no—
190#1519—191no—
191#1471—191no—
192#1305—191no—
193#1298—191no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—81no—
203C22×C19—81no—
204C22×C19—81no—
205C22×C19—81no—
206C22×C19—81no—
207C22×C19—162no—
208C22×C19#38611yescharacteristic
209C22×C19#47111yescharacteristic
210C22×C19#47211yescharacteristic
211C4×C19—21no—
212C4×C19—21no—
213C4×C19—21no—
214C4×C19—41no—
215C4×C19—41no—
216C4×C19—41no—
217C4×C19—41no—
218C4×C19—81no—
219C4×C19#41011yescharacteristic
220C4×C19#41011yescharacteristic
221Dic19—161no—
222C2×#121C2×D1911yescharacteristic
223C2×#117C2×D1911yescharacteristic
224#482—21no—
225#482—21no—
226#481—21no—
227#480—21no—
228#433—382no—
229#432—381no—
230#431—381no—
231#428Dic1911yescharacteristic, complemented
232#428Dic1911yescharacteristic, complemented
233#424—381no—
234#418Dic1911yescharacteristic, complemented
235#418Dic1911yescharacteristic, complemented
236#407—191no—
237#407C2×D1911yescharacteristic
238C2×C22⋊C8—191no—
239C2×C22⋊C8—191no—
240#405—381no—
241#380—191no—
242#340—381no—
243#340—381no—
244#327—381no—
245#327—381no—
246#323—382no—
247C2×C19—21no—
248C2×C19—21no—
249C2×C19—41no—
250C2×C19—41no—
251C2×C19—161no—
252C2×C19#188111yescharacteristic
253C2×C19#189911yescharacteristic
254C2×C19#190711yescharacteristic
255C22×D4—21no—
256C22×D4C2×Dic1911yescharacteristic
257C23×C4C22×D1911yescharacteristic
258C2×M16—381no—
259C2×M16C2×Dic1911yescharacteristic
260C2×M16C2×Dic1911yescharacteristic
261C22×C8—381no—
262C22×C8—381no—
263#121—21no—
264#121—21no—
265#121—21no—
266#121—21no—
267#117—21no—
268#117—21no—
269#117C2×Dic1911yescharacteristic
270#117C2×Dic1911yescharacteristic
271#117C22⋊D1911yescharacteristic
272#117C22⋊D1911yescharacteristic
273C2×C4⋊C4—381no—
274C2×C4⋊C4C2×Dic1911yescharacteristic
275C2×C4⋊C4C22⋊D1911yescharacteristic
276C2×C4⋊C4C22⋊D1911yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—381no—
280C2×C42—21no—
281#107—21no—
282#107—21no—
283#106—21no—
284#106—21no—
285C4⋊C8—382no—
286C4⋊C8—382no—
287#102—21no—
288#102—21no—
289#102—21no—
290#102—21no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—192no—
294C22⋊C8—191no—
295C22⋊C8—191no—
296C22⋊C8—381no—
297C22⋊C8—381no—
298C22⋊C8—381no—
299C22⋊C8—381no—
300#97—382no—
301C4×C8—382no—
302#95—381no—
303C19#934811yescharacteristic, complemented, Sylow
304C24—21no—
305C24#6454311yescharacteristic
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—81no—
313C2×D4—81no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—761no—
320C22×C4D4×D1911yescharacteristic
321C22×C4D4×D1911yescharacteristic
322C22×C4#6454311yescharacteristic
323C22×C4C22×Dic1911yescharacteristic
324C22×C4C2×C22⋊D1911yescharacteristic
325C22×C4C2×C22⋊D1911yescharacteristic
326M16—41no—
327M16—41no—
328M16—761no—
329M16—761no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—381no—
333C2×C8—382no—
334C2×C8—381no—
335C2×C8—761no—
336C2×C8—761no—
337C2×C8—761no—
338C2×C8—761no—
339C2×C8—761no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—761no—
345C4⋊C4—761no—
346C4⋊C4C22⋊Dic1911yescharacteristic
347C4⋊C4C22⋊Dic1911yescharacteristic
348C4⋊C4C22⋊Dic1911yescharacteristic
349C4⋊C4C22⋊Dic1911yescharacteristic
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—21no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—1521no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—21no—
361C23—21no—
362C23—21no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—41no—
367C23—81no—
368C23—81no—
369C23D4×Dic1911yescharacteristic
370C23#1059738111yescharacteristic
371C23#1059738511yescharacteristic
372D4—41no—
373D4—41no—
374D4—81no—
375D4—82no—
376D4—81no—
377D4—81no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—1521no—
397C2×C4—1521no—
398C2×C4—1521no—
399C2×C4D4×Dic1911yescharacteristic
400C2×C4#1059738311yescharacteristic
401C2×C4#1059738511yescharacteristic
402C2×C4C2×C22⋊Dic1911yescharacteristic
403C8—41no—
404C8—41no—
405C8—761no—
406C8—761no—
407C8—762no—
408C8—1521no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—162no—
423C22#1192642411yescharacteristic
424C22#1192680511yescharacteristic
425C22#1192681211yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—41no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—81no—
434C4—3041no—
435C4#1192651811yescharacteristic
436C4#1192651811yescharacteristic
437C2—21no—
438C2—21no—
439C2—41no—
440C2—41no—
441C2—161no—
442C2#1456399911yescharacteristic
443C2#1456409411yescharacteristic
444C2#1456414511yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#3094C2
socleC22×C19#386
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#3094D19
hypocenterC19#9348
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. #14572293C2semidirect
2. #14563730C2semidirect
5. #14561540C2semidirect
6. #14561522C2semidirect
28. C19×#428C4semidirect
29. C19×#428C4semidirect
30. C19×#418C4semidirect
31. C19×#418C4semidirect
231. #428Dic19semidirect
232. #428Dic19semidirect
234. #418Dic19semidirect
235. #418Dic19semidirect
303. C19#9348semidirect

Maximal subgroups

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

subgroupindex
#145722932
#145637302
#145622032
#145619952
#145615402
#145615222
C19×#30942
#934819