Finite Group Databasebeta

← #18085589

Subgroups — #18085589

Order 4864.

452 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14568671C211yesmaximal, characteristic
2#14564582C211yesmaximal, characteristic
3#14564582C211yesmaximal, characteristic
4#14564436C211yesmaximal, characteristic
5#14561474C211yesmaximal, characteristic
6#14561474C211yesmaximal, characteristic
7C19×#1296C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×#10597336—21no—
10C2×#10597267—22no—
11C2×C4×C19⋊C8C2211yescharacteristic
12#11926477—22no—
13#11926443—21no—
14#11926440—21no—
15#11926413—21no—
16C4×C4⋊Dic19C2211yescharacteristic
17C4×C4⋊Dic19C2211yescharacteristic
18#11926307—21no—
19#11926307—21no—
20#11926307—21no—
21#11926307—21no—
22C2×C19×C4⋊C8C2211yescharacteristic
23C2×C19×C4⋊C8C2211yescharacteristic
24C19×#384C2211yescharacteristic
25C22×Dic38—21no—
26C22×C8×C19—21no—
27C22×C8×C19—21no—
28C2×C4⋊C4×C19—21no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19D412yes—
31C2×C42×C19C2311yescharacteristic
32C2×C4⋊Dic19—21no—
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19—22no—
35C2×C4⋊Dic19D411yescharacteristic
36C2×C4⋊Dic19D411yescharacteristic
37C2×C4⋊Dic19D411yescharacteristic
38C2×C4⋊Dic19D411yescharacteristic
39C2×Dic19⋊C4—22no—
40C2×Dic19⋊C4—22no—
41C2×C4×Dic19—21no—
42C2×C4×Dic19—21no—
43C22×C19⋊C8—21no—
44#10597336—42no—
45#10597336—42no—
46#10597315—21no—
47#10597315—21no—
48#10597315—21no—
49#10597315Q812yes—
50C19×C4⋊C8—21no—
51C19×C4⋊C8—21no—
52C19×C4⋊C8—21no—
53C19×C4⋊C8—21no—
54C19⋊#95—22no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57#10597267—44no—
58C4×C19⋊C8—21no—
59C4×C19⋊C8—21no—
60C22×C4×C19—22no—
61C22×C4×C19C2×D411yescharacteristic
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×Dic19—21no—
65C22×Dic19—21no—
66C22×Dic19—21no—
67C22×Dic19—21no—
68C22×Dic19—41no—
69C2×Dic38—22no—
70C2×Dic38—42no—
71C2×Dic38—42no—
72C2×Dic38—41no—
73C2×C8×C19—41no—
74C2×C8×C19—41no—
75C2×C8×C19—41no—
76C2×C8×C19—41no—
77C2×C8×C19—41no—
78C2×C8×C19—41no—
79C4⋊C4×C19—42no—
80C4⋊C4×C19—41no—
81C4⋊C4×C19—41no—
82C4⋊C4×C19—41no—
83C4⋊C4×C19—41no—
84C42×C19C2×Q811yescharacteristic
85C42×C19#4111yescharacteristic
86C42×C19#4111yescharacteristic
87C42×C19#4111yescharacteristic
88C4⋊Dic19—21no—
89C4⋊Dic19—21no—
90C4⋊Dic19—22no—
91C4⋊Dic19—22no—
92C4⋊Dic19—21no—
93C4⋊Dic19—21no—
94C4⋊Dic19—21no—
95C4⋊Dic19—21no—
96C4⋊Dic19—44no—
97C4⋊Dic19—41no—
98C4⋊Dic19—41no—
99C4⋊Dic19SD1612yes—
100C4⋊Dic19Q1612yes—
101Dic19⋊C4—44no—
102Dic19⋊C4—82no—
103C4×Dic19—41no—
104C4×Dic19—41no—
105C4×Dic19—41no—
106C4×Dic19—41no—
107C2×C19⋊C8—22no—
108C2×C19⋊C8—41no—
109C2×C19⋊C8—41no—
110#10355—191nomaximal, Sylow
111C23×C19#12011yescharacteristic
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19—42no—
117C2×C4×C19C22⋊Q811yescharacteristic
118C2×C4×C19C22⋊Q811yescharacteristic
119C2×C4×C19C22⋊Q811yescharacteristic
120C2×C4×C19#12411yescharacteristic
121C2×C4×C19#12411yescharacteristic
122C2×C4×C19#12411yescharacteristic
123C2×C4×C19C2×SD1611yescharacteristic
124C2×C4×C19C2×Q1611yescharacteristic
125C2×C4×C19#13511yescharacteristic
126C2×C4×C19#13511yescharacteristic
127C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C19#13711yescharacteristic
129C2×C4×C19#13711yescharacteristic
130C2×C4×C19#13711yescharacteristic
131C2×Dic19—22no—
132C2×Dic19—22no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—42no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144C2×Dic19—81no—
145C2×Dic19—81no—
146Dic38—44no—
147Dic38—82no—
148C8×C19—81no—
149C8×C19—81no—
150C19⋊C8—42no—
151#2552—191no—
152#1987—191no—
153#1987—191no—
154#1956—191no—
155#1296D1911yescharacteristic
156#1279—191no—
157#1279—191no—
158C22×C19#39311yescharacteristic
159C22×C19#45011yescharacteristic
160C22×C19#45111yescharacteristic
161C22×C19#45211yescharacteristic
162C22×C19#45211yescharacteristic
163C22×C19#45311yescharacteristic
164C22×C19#45411yescharacteristic
165C4×C19—21no—
166C4×C19—21no—
167C4×C19—82no—
168C4×C19#47511yescharacteristic
169C4×C19#47711yescharacteristic
170C4×C19#47911yescharacteristic
171C4×C19#47911yescharacteristic
172C4×C19#48711yescharacteristic
173C4×C19#48811yescharacteristic
174C4×C19#48911yescharacteristic
175C4×C19#49111yescharacteristic
176Dic19—42no—
177Dic19—42no—
178Dic19—81no—
179Dic19—81no—
180Dic19—82no—
181C2×C4⋊Q8—191no—
182C2×#125—381no—
183C2×C4⋊C8C2×D1911yescharacteristic
184C2×C4⋊C8C2×D1911yescharacteristic
185C2×#103—382no—
186C2×C4×C8—191no—
187#398—382no—
188#389—381no—
189#389—381no—
190#384—381no—
191#384C2×D1911yescharacteristic
192C4×C4⋊C4—191no—
193C4×C4⋊C4—191no—
194#340—381no—
195#340—381no—
196#340—381no—
197#340—381no—
198C2×C19#163111yescharacteristic
199C2×C19#163211yescharacteristic
200C2×C19#163511yescharacteristic
201C2×C19#163611yescharacteristic
202C2×C19#202411yescharacteristic
203C2×C19#202611yescharacteristic
204C2×C19#202711yescharacteristic
205C22×Q8—381no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—381no—
209C4⋊Q8—192no—
210C4⋊Q8—381no—
211C4⋊Q8—381no—
212C4⋊Q8—381no—
213#125—762no—
214#125—762no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—191no—
218C2×C4⋊C4—191no—
219C2×C4⋊C4—191no—
220C2×C4⋊C4—191no—
221C2×C4⋊C4—381no—
222C2×C4⋊C4—381no—
223C2×C4⋊C4—382no—
224C2×C4⋊C4—382no—
225C2×C4⋊C4—382no—
226C2×C4⋊C4D7612yes—
227C2×C42—381no—
228C2×C42—381no—
229C2×C42C22×D1911yescharacteristic
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234#103—764no—
235C4×C8—381no—
236C4×C8—381no—
237#95—382no—
238#95—381no—
239#95—381no—
240C19#1035511yescharacteristic, complemented, Sylow
241C2×Q8—382no—
242C2×Q8—762no—
243C2×Q8—762no—
244C2×Q8—761no—
245C22×C4—22no—
246C22×C4—381no—
247C22×C4—381no—
248C22×C4—381no—
249C22×C4—381no—
250C22×C4—761no—
251C22×C4C2×D7611yescharacteristic
252C22×C4D4×D1911yescharacteristic
253C22×C4D4×D1911yescharacteristic
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—382no—
261C2×C8—761no—
262C2×C8—761no—
263C4⋊C4—42no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—192no—
269C4⋊C4—192no—
270C4⋊C4—381no—
271C4⋊C4—381no—
272C4⋊C4—382no—
273C4⋊C4—382no—
274C4⋊C4—381no—
275C4⋊C4—381no—
276C4⋊C4—381no—
277C4⋊C4—381no—
278C4⋊C4—764no—
279C4⋊C4—764no—
280C4⋊C4—761no—
281C4⋊C4—761no—
282C4⋊C4—1522no—
283C42—761no—
284C42—761no—
285C42—761no—
286C42—761no—
287C42#6454111yescharacteristic
288C42#6454111yescharacteristic
289C42#6454311yescharacteristic
290C42Q8×D1911yescharacteristic
291C23#1059732811yescharacteristic
292Q8—764no—
293Q8—1522no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—382no—
300C2×C4—382no—
301C2×C4—761no—
302C2×C4—761no—
303C2×C4—761no—
304C2×C4—761no—
305C2×C4—761no—
306C2×C4—761no—
307C2×C4—761no—
308C2×C4—761no—
309C2×C4—762no—
310C2×C4—761no—
311C2×C4—761no—
312C2×C4—1521no—
313C2×C4—1521no—
314C2×C4#1059732111yescharacteristic
315C2×C4#1059733111yescharacteristic
316C2×C4#1059733111yescharacteristic
317C2×C4#1059734211yescharacteristic
318C2×C4#1059734211yescharacteristic
319C2×C4#1059734311yescharacteristic
320C2×C4#1059735711yescharacteristic
321C2×C4#1059735811yescharacteristic
322C2×C4SD16×D1911yescharacteristic
323C2×C4#1059736111yescharacteristic
324C2×C4#1059736111yescharacteristic
325C2×C4#1059736211yescharacteristic
326C2×C4Q16×D1911yescharacteristic
327C2×C4#1059736411yescharacteristic
328C8—81no—
329C8—81no—
330C8—762no—
331C22#1192645711yescharacteristic
332C22#1192669611yescharacteristic
333C22#1192670111yescharacteristic
334C22#1192670711yescharacteristic
335C22#1192670911yescharacteristic
336C22#1192671411yescharacteristic
337C22#1192671911yescharacteristic
338C4—21no—
339C4—21no—
340C4—82no—
341C4—762no—
342C4—762no—
343C4—1522no—
344C4—1521no—
345C4—1521no—
346C4#1192682811yescharacteristic
347C4#1192683811yescharacteristic
348C4#1192685011yescharacteristic
349C4#1192685411yescharacteristic
350C4#1192689311yescharacteristic
351C4#1192689711yescharacteristic
352C4#1192690211yescharacteristic
353C4#1192691111yescharacteristic
354C2#1456276311yescharacteristic
355C2#1456277011yescharacteristic
356C2#1456278711yescharacteristic
357C2#1456279411yescharacteristic
358C2#1456477511yescharacteristic
359C2#1456478511yescharacteristic
360C2#1456479211yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1296C2
socle, prime radicalC23×C19#120
hypercenter#1296D19
hypocenterC19#10355
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
240. C19#10355semidirect

Maximal subgroups

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

subgroupindex
#145686712
#145645822
#145644362
#145614742
C19×#12962
#1035519