Finite Group Databasebeta

← #18075943

Subgroups — #18075943

Order 4864.

482 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566028C211yesmaximal, characteristic
2#14563398C211yesmaximal, characteristic
3#14563398C211yesmaximal, characteristic
4#14561517C211yesmaximal, characteristic, complemented
5#14561517C211yesmaximal, characteristic, complemented
6#14561516C211yesmaximal, characteristic, complemented
7C19×#1295C211yesmaximal, characteristic, complemented
8C2×C42×D19C2211yescharacteristic
9C2×(C2×D19)⋊C8—21no—
10C2×(C2×D19)⋊C8—21no—
11C2×#10597260C2211yescharacteristic
12C2×#10597260C2211yescharacteristic
13#11926411—21no—
14#11926410C2211yescharacteristic
15#11926406—21no—
16#11926401C411yescharacteristic
17#11926401C411yescharacteristic
18C4⋊C4×Dic19C411yescharacteristic
19C4⋊C4×Dic19C411yescharacteristic
20#11926391—21no—
21#11926389—21no—
22#11926298—21no—
23#11926298—21no—
24C2×C19×#97C2211yescharacteristic
25C2×C19×#97C2211yescharacteristic
26C19×#382C2211yescharacteristic
27C22×C4×D19C2×C411yescharacteristic
28C22×C4×D19D411yescharacteristic
29C22×C4×D19D411yescharacteristic
30C22×C8×C19—21no—
31C22×C8×C19—21no—
32C2×C4⋊C4×C19C2×C411yescharacteristic
33C2×C4⋊C4×C19C2×C411yescharacteristic
34C2×C42×C19C2311yescharacteristic
35C2×(C2×D19)⋊C4—21no—
36C2×(C2×D19)⋊C4—21no—
37C2×C4⋊Dic19C2×C411yescharacteristic
38C2×C4⋊Dic19C2×C411yescharacteristic
39C2×C4×Dic19—21no—
40C2×C4×Dic19—21no—
41C2×C4×Dic19C2×C411yescharacteristic
42C2×C4×Dic19D411yescharacteristic
43C2×C4×Dic19D411yescharacteristic
44C22×C19⋊C8—21no—
45C22×C19⋊C8—21no—
46C42×D19—21no—
47C42×D19—21no—
48C42×D19—21no—
49C42×D19—21no—
50C19×#97—21no—
51C19×#97—21no—
52C19×#97—21no—
53C19×#97—21no—
54C19×#95—21no—
55C19×#95—21no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C19⋊#95—21no—
60C19⋊#95—21no—
61C19⋊#95—21no—
62(C2×D19)⋊C8—24no—
63(C2×D19)⋊C8—24no—
64#10597260—21no—
65#10597260—21no—
66#10597260—21no—
67#10597260—21no—
68C23×D19C22⋊C411yescharacteristic
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×Dic19—21no—
75C22×Dic19—21no—
76C22×Dic19C22⋊C411yescharacteristic
77C22×Dic19C22⋊C411yescharacteristic
78C22×Dic19C22⋊C411yescharacteristic
79C2×C4×D19—22no—
80C2×C4×D19—21no—
81C2×C4×D19—21no—
82C2×C4×D19—21no—
83C2×C4×D19—21no—
84C2×C4×D19—21no—
85C2×C4×D19—21no—
86C2×C4×D19—22no—
87C2×C4×D19—41no—
88C2×C4×D19—41no—
89C2×C4×D19—41no—
90C2×C4×D19—41no—
91C2×C8×C19—22no—
92C2×C8×C19—22no—
93C2×C8×C19—41no—
94C2×C8×C19—41no—
95C2×C8×C19—41no—
96C2×C8×C19—41no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19—41no—
99C42×C19#4111yescharacteristic
100C42×C19#4111yescharacteristic
101C42×C19#4111yescharacteristic
102C42×C19#4111yescharacteristic
103(C2×D19)⋊C4—42no—
104(C2×D19)⋊C4—42no—
105C4⋊Dic19—41no—
106C4⋊Dic19—41no—
107C4×Dic19—21no—
108C4×Dic19—21no—
109C4×Dic19—21no—
110C4×Dic19—21no—
111C4×Dic19—21no—
112C4×Dic19—21no—
113C4×Dic19—42no—
114C4×Dic19—42no—
115C2×C19⋊C8—22no—
116C2×C19⋊C8—22no—
117C2×C19⋊C8—41no—
118C2×C19⋊C8—41no—
119C2×C19⋊C8—41no—
120C2×C19⋊C8—41no—
121#8720—191nomaximal, Sylow
122C23×C19C2×C22⋊C411yescharacteristic
123C22×D19—21no—
124C22×D19—21no—
125C22×D19—21no—
126C22×D19—21no—
127C22×D19—21no—
128C22×D19—21no—
129C22×D19#10412yes—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19#11711yescharacteristic
143C2×C4×C19#11711yescharacteristic
144C2×C4×C19#12311yescharacteristic
145C2×C4×C19#12311yescharacteristic
146C2×C4×C19#12311yescharacteristic
147C2×C4×C19#12311yescharacteristic
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—21no—
151C2×Dic19—21no—
152C2×Dic19—21no—
153C2×Dic19—21no—
154C2×Dic19—21no—
155C2×Dic19—21no—
156C2×Dic19—41no—
157C2×Dic19—41no—
158C2×Dic19—41no—
159C2×Dic19—41no—
160C2×Dic19—41no—
161C2×Dic19—41no—
162C2×Dic19#10412yes—
163C4×D19—42no—
164C4×D19—42no—
165C4×D19—42no—
166C4×D19—42no—
167C4×D19—42no—
168C4×D19—42no—
169C8×C19—42no—
170C8×C19—42no—
171C19⋊C8—42no—
172C19⋊C8—42no—
173#2283—191no—
174#1749—191no—
175#1749—191no—
176#1295—191no—
177#1295—191no—
178#1295—191no—
179#1295D1911yescharacteristic, complemented
180C22×C19#38111yescharacteristic
181C22×C19#41311yescharacteristic
182C22×C19#41311yescharacteristic
183C22×C19C2×#10411yescharacteristic
184C22×C19C2×#10411yescharacteristic
185C22×C19#42111yescharacteristic
186C22×C19#42111yescharacteristic
187C2×D19—22no—
188C2×D19—22no—
189C2×D19—22no—
190C2×D19—41no—
191C2×D19—41no—
192C2×D19—41no—
193C2×D19—41no—
194C4×C19—21no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—21no—
199C4×C19—21no—
200C4×C19—81no—
201C4×C19—81no—
202Dic19—22no—
203Dic19—41no—
204Dic19—41no—
205Dic19—81no—
206Dic19—81no—
207C22×C42—191no—
208C2×C22⋊C8—381no—
209C2×C22⋊C8—381no—
210C2×#97—191no—
211C2×#97—191no—
212C2×#97C2×D1911yescharacteristic
213C2×#97C2×D1911yescharacteristic
214#383—381no—
215#382—191no—
216#382C2×D1911yescharacteristic
217#381—381no—
218#380—191no—
219#380—191no—
220C4×C4⋊C4—191no—
221C4×C4⋊C4—191no—
222C4×C22⋊C4—381no—
223#376—381no—
224#336—381no—
225#336—381no—
226C2×C19#152411yescharacteristic
227C2×C19#152911yescharacteristic
228C2×C19#153211yescharacteristic
229C2×C19#153511yescharacteristic
230C2×C19#182211yescharacteristic
231C2×C19#182611yescharacteristic
232C2×C19#182611yescharacteristic
233D19—42no—
234C23×C4—191no—
235C23×C4—191no—
236C23×C4—191no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—381no—
240C22×C8—381no—
241C2×C4⋊C4—191no—
242C2×C4⋊C4—191no—
243C2×C4⋊C4C4×D1911yescharacteristic
244C2×C4⋊C4C4×D1911yescharacteristic
245C2×C22⋊C4—381no—
246C2×C22⋊C4—381no—
247C2×C42—191no—
248C2×C42—191no—
249C2×C42—191no—
250C2×C42—381no—
251C2×C42—381no—
252C2×C42—381no—
253C2×C42—381no—
254C2×C42—381no—
255C2×C42—381no—
256C2×C42C22×D1911yescharacteristic
257C22⋊C8—384no—
258C22⋊C8—384no—
259#97—21no—
260#97—21no—
261#97—21no—
262#97—21no—
263#97—381no—
264#97—381no—
265#97—381no—
266#97—381no—
267#95—21no—
268#95—21no—
269#95—381no—
270#95—381no—
271#95—381no—
272#95—381no—
273#95—381no—
274#95—381no—
275C19#872011yescharacteristic, complemented, Sylow
276C24—191no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—191no—
280C22×C4—191no—
281C22×C4—191no—
282C22×C4—382no—
283C22×C4—382no—
284C22×C4—381no—
285C22×C4—381no—
286C22×C4—381no—
287C22×C4—381no—
288C22×C4—381no—
289C22×C4—381no—
290C22×C4—381no—
291C22×C4—381no—
292C22×C4—761no—
293C22×C4—761no—
294C22×C4—761no—
295C22×C4—761no—
296C22×C4C2×C4×D1911yescharacteristic
297C22×C4D4×D1911yescharacteristic
298C22×C4D4×D1911yescharacteristic
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—382no—
306C2×C8—382no—
307C2×C8—761no—
308C2×C8—761no—
309C2×C8—761no—
310C2×C8—761no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—761no—
314C4⋊C4—761no—
315C22⋊C4—762no—
316C22⋊C4—762no—
317C42—381no—
318C42—381no—
319C42—381no—
320C42—381no—
321C42—381no—
322C42—381no—
323C42—762no—
324C42—762no—
325C42#6454111yescharacteristic
326C42#6454111yescharacteristic
327C42#6454311yescharacteristic
328C42#6454511yescharacteristic
329C23—192no—
330C23—381no—
331C23—381no—
332C23—381no—
333C23—381no—
334C23—381no—
335C23—381no—
336C23C22⋊C4×D1911yescharacteristic
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—192no—
350C2×C4—381no—
351C2×C4—381no—
352C2×C4—381no—
353C2×C4—381no—
354C2×C4—381no—
355C2×C4—381no—
356C2×C4—381no—
357C2×C4—381no—
358C2×C4—762no—
359C2×C4—762no—
360C2×C4—762no—
361C2×C4—762no—
362C2×C4—762no—
363C2×C4—762no—
364C2×C4—761no—
365C2×C4—761no—
366C2×C4—761no—
367C2×C4—761no—
368C2×C4—761no—
369C2×C4—761no—
370C2×C4#1059731811yescharacteristic
371C2×C4#1059732911yescharacteristic
372C2×C4#1059732911yescharacteristic
373C2×C4#1059733811yescharacteristic
374C2×C4#1059734011yescharacteristic
375C2×C4#1059734011yescharacteristic
376C8—42no—
377C8—42no—
378C8—762no—
379C8—762no—
380C22—382no—
381C22—382no—
382C22—382no—
383C22—761no—
384C22—761no—
385C22—761no—
386C22—761no—
387C22#1192640611yescharacteristic
388C22#1192652511yescharacteristic
389C22#1192652711yescharacteristic
390C22#104×D1911yescharacteristic
391C22#104×D1911yescharacteristic
392C22#1192655911yescharacteristic
393C22#1192655911yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—81no—
401C4—81no—
402C4—382no—
403C4—761no—
404C4—761no—
405C4—1521no—
406C4—1521no—
407C2—762no—
408C2#1456222011yescharacteristic
409C2#1456224111yescharacteristic
410C2#1456225411yescharacteristic
411C2#1456226311yescharacteristic
412C2#1456371711yescharacteristic
413C2#1456373311yescharacteristic
414C2#1456373311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1295C2
socleC23×C19C2×C22⋊C4
prime radicalC23×D19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1295D19
hypocenterC19#8720
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
4. #14561517C2semidirect
5. #14561517C2semidirect
6. #14561516C2semidirect
7. C19×#1295C2semidirect
179. #1295D19semidirect
275. C19#8720semidirect

Maximal subgroups

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

subgroupindex
#145660282
#145633982
#145615172
#145615162
C19×#12952
#872019