Finite Group Databasebeta

← #18070906

Subgroups — #18070906

Order 4864.

442 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572010C211yesmaximal, characteristic
2#14563750C211yesmaximal, characteristic
3#14563483C211yesmaximal, characteristic
4#14561461C211yesmaximal, characteristic
5#14561460C211yesmaximal, characteristic
6#14561460C211yesmaximal, characteristic
7C19×#1272C211yesmaximal, characteristic
8C2×#10597334C411yescharacteristic
9C2×#10597390C411yescharacteristic
10C2×Dic19⋊C8—21no—
11C2×Dic19⋊C8—21no—
12C2×C8×Dic19—21no—
13#11926451C411yescharacteristic
14#11926450C2211yescharacteristic
15#11926449C411yescharacteristic
16#11926448—21no—
17#11926448—21no—
18#11926408—21no—
19#11926408—21no—
20C42×Dic19C2211yescharacteristic
21#11926299C2211yescharacteristic
22#11926299C2211yescharacteristic
23#11926298—21no—
24C19×#391C2211yescharacteristic
25C19×#336C2211yescharacteristic
26C19×#336C2211yescharacteristic
27C22×Q8×C19C2×C411yescharacteristic
28C22×Dic38—21no—
29C22×Dic38C2×C411yescharacteristic
30C22×C8×C19—21no—
31C22×C8×C19—21no—
32C2×C4⋊C4×C19C2×C411yescharacteristic
33C2×C42×C19C2311yescharacteristic
34#10597390—42no—
35C2×C4⋊Dic19C2×C411yescharacteristic
36C2×Dic19⋊C4—21no—
37C2×Dic19⋊C4—21no—
38C2×Dic19⋊C4—21no—
39C2×C4×Dic19C2×C411yescharacteristic
40C2×C4×Dic19C2×C411yescharacteristic
41C2×C4×Dic19D411yescharacteristic
42C2×C4×Dic19D411yescharacteristic
43C2×C4×Dic19D411yescharacteristic
44C2×C4×Dic19D411yescharacteristic
45C22×C19⋊C8—21no—
46C22×C19⋊C8—21no—
47#10597334—42no—
48C19×#95—21no—
49C19×#95—21no—
50C19⋊#95—21no—
51C19⋊#95—21no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56Dic19⋊C8—24no—
57Dic19⋊C8—42no—
58C8×Dic19—42no—
59C2×Q8×C19—21no—
60C2×Q8×C19—21no—
61C2×Q8×C19—41no—
62C2×Q8×C19—41no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19C22×C411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C22×Dic19—21no—
69C22×Dic19—21no—
70C22×Dic19C22⋊C411yescharacteristic
71C22×Dic19C22⋊C411yescharacteristic
72C22×Dic19C22⋊C411yescharacteristic
73C22×Dic19C22⋊C411yescharacteristic
74C2×Dic38—21no—
75C2×Dic38—21no—
76C2×Dic38—42no—
77C2×Dic38—42no—
78C2×Dic38—42no—
79C2×Dic38—41no—
80C2×Dic38—41no—
81C2×C8×C19—22no—
82C2×C8×C19—41no—
83C2×C8×C19—41no—
84C2×C8×C19—41no—
85C2×C8×C19—41no—
86C2×C8×C19—41no—
87C4⋊C4×C19—41no—
88C42×C19—41no—
89C4⋊Dic19—41no—
90Dic19⋊C4—42no—
91Dic19⋊C4—42no—
92Dic19⋊C4—42no—
93C4×Dic19—21no—
94C4×Dic19—21no—
95C4×Dic19—22no—
96C4×Dic19—22no—
97C4×Dic19—41no—
98C4×Dic19SD1612yes—
99C4×Dic19SD1612yes—
100C4×Dic19Q1612yes—
101C4×Dic19Q1612yes—
102C2×C19⋊C8—22no—
103C2×C19⋊C8—41no—
104C2×C19⋊C8—41no—
105C2×C19⋊C8—41no—
106C2×C19⋊C8—41no—
107C2×C19⋊C8—41no—
108#7662—191nomaximal, Sylow
109C23×C19C2×C22⋊C411yescharacteristic
110Q8×C19—81no—
111Q8×C19—81no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—41no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19#13111yescharacteristic
125C2×C4×C19#13111yescharacteristic
126C2×C4×C19C2×SD1611yescharacteristic
127C2×C4×C19C2×SD1611yescharacteristic
128C2×C4×C19C2×Q1611yescharacteristic
129C2×C4×C19C2×Q1611yescharacteristic
130C2×Dic19—21no—
131C2×Dic19—21no—
132C2×Dic19—21no—
133C2×Dic19—21no—
134C2×Dic19—21no—
135C2×Dic19—21no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19#10012yes—
143C2×Dic19#10312yes—
144C2×Dic19#10312yes—
145C2×Dic19#10312yes—
146C2×Dic19#10312yes—
147C2×Dic19#10412yes—
148Dic38—84no—
149Dic38—81no—
150Dic38—81no—
151C8×C19—42no—
152C8×C19—81no—
153C19⋊C8—42no—
154C19⋊C8—81no—
155#2862—191no—
156#1831—191no—
157C4×C4⋊C8—191no—
158#1272—191no—
159#1272—191no—
160#1272—191no—
161#1272D1911yescharacteristic
162C22×C19#40811yescharacteristic
163C22×C19#41011yescharacteristic
164C22×C19C2×#10011yescharacteristic
165C22×C19C2×#10311yescharacteristic
166C22×C19C2×#10311yescharacteristic
167C22×C19C2×#10411yescharacteristic
168C22×C19#42111yescharacteristic
169C4×C19—21no—
170C4×C19—21no—
171C4×C19—21no—
172C4×C19—21no—
173C4×C19—21no—
174C4×C19—21no—
175C4×C19—81no—
176C4×C19—81no—
177Dic19—22no—
178Dic19—22no—
179Dic19—22no—
180Dic19—81no—
181Dic19—81no—
182Dic19#33314yes—
183C2×C4⋊Q8—191no—
184C2×C4⋊Q8—191no—
185C2×C4⋊C8—381no—
186C2×C4⋊C8—381no—
187C2×C4×C8—381no—
188#391—191no—
189#391—191no—
190#391—191no—
191#391—381no—
192#391—381no—
193#391C2×D1911yescharacteristic
194#382—381no—
195#382—381no—
196C43—191no—
197#336—191no—
198#336—191no—
199#336—381no—
200#336C2×D1911yescharacteristic
201#336C2×D1911yescharacteristic
202C2×C19#146911yescharacteristic
203C2×C19#148111yescharacteristic
204C2×C19#149311yescharacteristic
205C2×C19#150311yescharacteristic
206C2×C19#151811yescharacteristic
207C2×C19#152711yescharacteristic
208C2×C19C2×#33311yescharacteristic
209C22×Q8—191no—
210C22×Q8—381no—
211C22×Q8C4×D1911yescharacteristic
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—381no—
215C22×C8—381no—
216C4⋊Q8—762no—
217C4⋊Q8—762no—
218C2×C4⋊C4—191no—
219C2×C4⋊C4—381no—
220C2×C4⋊C4—381no—
221C2×C4⋊C4—381no—
222C2×C4⋊C4C4×D1911yescharacteristic
223C2×C42—191no—
224C2×C42—191no—
225C2×C42—191no—
226C2×C42—191no—
227C2×C42—191no—
228C2×C42—191no—
229C2×C42C22×D1911yescharacteristic
230C4⋊C8—384no—
231C4⋊C8—762no—
232C4×C8—762no—
233#95—21no—
234#95—21no—
235#95—381no—
236#95—381no—
237#95—381no—
238#95—381no—
239#95—381no—
240#95—381no—
241C19#766211yescharacteristic, complemented, Sylow
242C2×Q8—21no—
243C2×Q8—21no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—381no—
247C2×Q8—381no—
248C2×Q8—761no—
249C2×Q8—761no—
250C2×Q8—762no—
251C2×Q8—762no—
252C2×Q8—762no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—191no—
256C22×C4—191no—
257C22×C4—191no—
258C22×C4—191no—
259C22×C4—381no—
260C22×C4—381no—
261C22×C4C2×C4×D1911yescharacteristic
262C22×C4D4×D1911yescharacteristic
263C22×C4D4×D1911yescharacteristic
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—382no—
271C2×C8—761no—
272C2×C8—761no—
273C2×C8—761no—
274C2×C8—761no—
275C2×C8—761no—
276C4⋊C4—41no—
277C4⋊C4—761no—
278C4⋊C4—762no—
279C4⋊C4—762no—
280C4⋊C4—762no—
281C42—41no—
282C42—192no—
283C42—192no—
284C42—192no—
285C42—192no—
286C42—382no—
287C42—382no—
288C42—381no—
289C42—381no—
290C42—761no—
291C23C22⋊C4×D1911yescharacteristic
292Q8—81no—
293Q8—81no—
294Q8—1521no—
295Q8—1521no—
296Q8—1524no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—192no—
310C2×C4—192no—
311C2×C4—192no—
312C2×C4—192no—
313C2×C4—192no—
314C2×C4—192no—
315C2×C4—381no—
316C2×C4—381no—
317C2×C4—381no—
318C2×C4—381no—
319C2×C4—381no—
320C2×C4—381no—
321C2×C4—761no—
322C2×C4—761no—
323C2×C4—761no—
324C2×C4—761no—
325C2×C4—761no—
326C2×C4—761no—
327C2×C4#1059734711yescharacteristic
328C2×C4#1059735311yescharacteristic
329C2×C4SD16×D1911yescharacteristic
330C2×C4SD16×D1911yescharacteristic
331C2×C4Q16×D1911yescharacteristic
332C2×C4Q16×D1911yescharacteristic
333C8—42no—
334C8—81no—
335C8—762no—
336C8—1521no—
337C22#1192650911yescharacteristic
338C22#1192651611yescharacteristic
339C22#100×D1911yescharacteristic
340C22#103×D1911yescharacteristic
341C22#103×D1911yescharacteristic
342C22#104×D1911yescharacteristic
343C22#1192655911yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—81no—
351C4—81no—
352C4—194no—
353C4—382no—
354C4—382no—
355C4—382no—
356C4—1521no—
357C4—1521no—
358C2#1456198511yescharacteristic
359C2#1456203611yescharacteristic
360C2#1456208811yescharacteristic
361C2#1456213211yescharacteristic
362C2#1456219711yescharacteristic
363C2#1456223111yescharacteristic
364C2D19×#33311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1272C2
socle, prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1272D19
hypocenterC19#7662
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
241. C19#7662semidirect

Maximal subgroups

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

subgroupindex
#145720102
#145637502
#145634832
#145614612
#145614602
C19×#12722
#766219