Finite Group Databasebeta

← #18086993

Subgroups — #18086993

Order 4864.

406 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14568874C211yesmaximal, characteristic
2#14564396C211yesmaximal, characteristic
3#14563794C211yesmaximal, characteristic
4#14561519C211yesmaximal, characteristic
5#14561476C211yesmaximal, characteristic
6#14561474C211yesmaximal, characteristic
7C19×#1948C211yesmaximal, characteristic
8C2×#10597264—22no—
9C2×#10597265—21no—
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×C4×C19⋊C8C2211yescharacteristic
12#11926486—22no—
13#11926442—21no—
14#11926440—21no—
15#11926414C2211yescharacteristic
16#11926410—21no—
17#11926409—21no—
18C4×C4⋊Dic19C2211yescharacteristic
19#11926306—21no—
20C2×C19×#106—21no—
21C2×C19×C4⋊C8C2211yescharacteristic
22C19×#384C2211yescharacteristic
23C4×C4⋊C4×C19C2211yescharacteristic
24C19×#340—21no—
25C22×C8×C19—21no—
26C2×C4⋊C4×C19—21no—
27C2×C4⋊C4×C19—21no—
28C2×C4⋊C4×C19—21no—
29C2×C4⋊C4×C19D411yescharacteristic
30C2×C4⋊C4×C19D411yescharacteristic
31C2×C42×C19—21no—
32C2×C42×C19C2311yescharacteristic
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19D411yescharacteristic
36C2×C4⋊Dic19D411yescharacteristic
37C2×C4⋊Dic19D412yes—
38C2×Dic19⋊C4—22no—
39C2×C4×Dic19—21no—
40C22×C19⋊C8—21no—
41C22×C19⋊C8—21no—
42C19×#106—42no—
43C19×C4⋊C8—21no—
44C19×C4⋊C8Q812yes—
45C19×#95—21no—
46C19⋊#95—22no—
47C19⋊#95—22no—
48C19⋊#95—22no—
49C19⋊#95—21no—
50#10597265—42no—
51#10597264—44no—
52C4⋊(C19⋊C8)—21no—
53C4⋊(C19⋊C8)Q812yes—
54C4×C19⋊C8—21no—
55C4×C19⋊C8Q812yes—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—41no—
59C22×C4×C19C2×D411yescharacteristic
60C22×C4×C19C2×D411yescharacteristic
61C22×C4×C19C2×D411yescharacteristic
62C22×Dic19—21no—
63C22×Dic19—21no—
64C22×Dic19—22no—
65C2×C8×C19—22no—
66C2×C8×C19—41no—
67C2×C8×C19—41no—
68C4⋊C4×C19—21no—
69C4⋊C4×C19—21no—
70C4⋊C4×C19—21no—
71C4⋊C4×C19—21no—
72C4⋊C4×C19—42no—
73C4⋊C4×C19—41no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—41no—
76C4⋊C4×C19—41no—
77C42×C19—41no—
78C42×C19—41no—
79C42×C19C2×Q811yescharacteristic
80C42×C19C2×Q811yescharacteristic
81C42×C19C2×Q811yescharacteristic
82C42×C19#4111yescharacteristic
83C4⋊Dic19—21no—
84C4⋊Dic19—21no—
85C4⋊Dic19—21no—
86C4⋊Dic19—21no—
87C4⋊Dic19—41no—
88C4⋊Dic19—41no—
89C4⋊Dic19—41no—
90C4⋊Dic19—41no—
91C4⋊Dic19—42no—
92Dic19⋊C4—82no—
93C4×Dic19—41no—
94C4×Dic19—41no—
95C2×C19⋊C8—22no—
96C2×C19⋊C8—22no—
97C2×C19⋊C8—22no—
98C2×C19⋊C8—22no—
99C2×C19⋊C8—41no—
100C2×C19⋊C8—41no—
101#10576—191nomaximal, Sylow
102C23×C19#12011yescharacteristic
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19—41no—
106C2×C4×C19—41no—
107C2×C4×C19—41no—
108C2×C4×C19—41no—
109C2×C4×C19—41no—
110C2×C4×C19—41no—
111C2×C4×C19—81no—
112C2×C4×C19—81no—
113C2×C4×C19—81no—
114C2×C4×C19C22⋊Q811yescharacteristic
115C2×C4×C19C22⋊Q811yescharacteristic
116C2×C4×C19C22⋊Q811yescharacteristic
117C2×C4×C19C4⋊Q811yescharacteristic
118C2×C4×C19C4⋊Q811yescharacteristic
119C2×C4×C19C4⋊Q811yescharacteristic
120C2×C4×C19#13511yescharacteristic
121C2×C4×C19#13511yescharacteristic
122C2×C4×C19#13511yescharacteristic
123C2×C4×C19#13511yescharacteristic
124C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C19#13711yescharacteristic
127C2×C4×C19#13711yescharacteristic
128C2×Dic19—41no—
129C2×Dic19—42no—
130C2×Dic19—42no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—42no—
136C2×Dic19—41no—
137C8×C19—42no—
138C19⋊C8—24no—
139C19⋊C8—42no—
140#2571—191no—
141#1948—191no—
142#1948D1911yescharacteristic
143#1845—191no—
144#1296—191no—
145#1279—191no—
146#1279—191no—
147C22×C19#39511yescharacteristic
148C22×C19#44911yescharacteristic
149C22×C19#44911yescharacteristic
150C22×C19#45211yescharacteristic
151C22×C19#45211yescharacteristic
152C22×C19#45311yescharacteristic
153C22×C19#45611yescharacteristic
154C4×C19—21no—
155C4×C19—21no—
156C4×C19—81no—
157C4×C19—81no—
158C4×C19—161no—
159C4×C19#47811yescharacteristic
160C4×C19#47811yescharacteristic
161C4×C19#47911yescharacteristic
162C4×C19#47911yescharacteristic
163C4×C19#49911yescharacteristic
164C4×C19#49911yescharacteristic
165C4×C19#50111yescharacteristic
166C4×C19#50111yescharacteristic
167Dic19—82no—
168Dic19—81no—
169Dic19—81no—
170C2×#107—382no—
171C2×#106—21no—
172C2×#106—381no—
173C2×C4⋊C8—191no—
174C2×C4⋊C8C2×D1911yescharacteristic
175C2×C4×C8—191no—
176#400—382no—
177#389—381no—
178#389—381no—
179#384—191no—
180#384C2×D1911yescharacteristic
181#382—381no—
182#382—381no—
183C4×C4⋊C4—191no—
184C4×C4⋊C4C2×D1911yescharacteristic
185#340—21no—
186#340—381no—
187C2×C19#162011yescharacteristic
188C2×C19#163411yescharacteristic
189C2×C19#165011yescharacteristic
190C2×C19#165011yescharacteristic
191C2×C19#205911yescharacteristic
192C2×C19#205911yescharacteristic
193C2×C19#206011yescharacteristic
194C22×C8—21no—
195C22×C8—381no—
196C22×C8—381no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—191no—
201C2×C4⋊C4—191no—
202C2×C4⋊C4—192no—
203C2×C4⋊C4—381no—
204C2×C4⋊C4—381no—
205C2×C4⋊C4—382no—
206C2×C4⋊C4C22⋊D1911yescharacteristic
207C2×C4⋊C4C22⋊D1911yescharacteristic
208C2×C42—21no—
209C2×C42—381no—
210C2×C42C22×D1911yescharacteristic
211#107—764no—
212#106—42no—
213#106—762no—
214C4⋊C8—21no—
215C4⋊C8—192no—
216C4⋊C8—381no—
217C4⋊C8Dic3812yes—
218C4×C8—192no—
219C4×C8—381no—
220#95—21no—
221#95—382no—
222#95—382no—
223#95—382no—
224#95—381no—
225C19#1057611yescharacteristic, complemented, Sylow
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—381no—
230C22×C4—381no—
231C22×C4—382no—
232C22×C4D4×D1911yescharacteristic
233C22×C4D4×D1911yescharacteristic
234C22×C4C2×C22⋊D1911yescharacteristic
235C2×C8—22no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—382no—
239C2×C8—382no—
240C2×C8—382no—
241C2×C8—382no—
242C2×C8—761no—
243C2×C8—761no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—42no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—381no—
254C4⋊C4—381no—
255C4⋊C4—381no—
256C4⋊C4—381no—
257C4⋊C4—762no—
258C4⋊C4—761no—
259C4⋊C4—761no—
260C4⋊C4—761no—
261C4⋊C4—761no—
262C4⋊C4—1522no—
263C42—41no—
264C42—41no—
265C42—761no—
266C42—761no—
267C42C2×Dic3811yescharacteristic
268C42#6454111yescharacteristic
269C42Q8×D1911yescharacteristic
270C42Q8×D1911yescharacteristic
271C23#1059738311yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—762no—
284C2×C4—761no—
285C2×C4—762no—
286C2×C4—761no—
287C2×C4—761no—
288C2×C4—761no—
289C2×C4—762no—
290C2×C4—761no—
291C2×C4—761no—
292C2×C4#1059733411yescharacteristic
293C2×C4#1059733411yescharacteristic
294C2×C4#1059734211yescharacteristic
295C2×C4#1059734211yescharacteristic
296C2×C4#1059736011yescharacteristic
297C2×C4#1059736111yescharacteristic
298C2×C4#1059736211yescharacteristic
299C2×C4#1059736211yescharacteristic
300C2×C4#1059737011yescharacteristic
301C2×C4#1059737811yescharacteristic
302C2×C4#1059738811yescharacteristic
303C2×C4#1059739011yescharacteristic
304C2×C4#1059739611yescharacteristic
305C2×C4#1059739611yescharacteristic
306C8—42no—
307C8—384no—
308C8—762no—
309C22#1192646411yescharacteristic
310C22#1192668711yescharacteristic
311C22#1192668811yescharacteristic
312C22#1192670311yescharacteristic
313C22#1192670411yescharacteristic
314C22#1192671011yescharacteristic
315C22#1192672511yescharacteristic
316C4—21no—
317C4—21no—
318C4—81no—
319C4—81no—
320C4—161no—
321C4—1521no—
322C4—1522no—
323C4—1521no—
324C4#1192684311yescharacteristic
325C4#1192684411yescharacteristic
326C4#1192685111yescharacteristic
327C4#1192685411yescharacteristic
328C4#1192694311yescharacteristic
329C4#1192694411yescharacteristic
330C4#1192695011yescharacteristic
331C4#1192695111yescharacteristic
332C2#1456269311yescharacteristic
333C2#1456277911yescharacteristic
334C2#1456288911yescharacteristic
335C2#1456289011yescharacteristic
336C2#1456497311yescharacteristic
337C2#1456497511yescharacteristic
338C2#1456497811yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1948C2
socle, prime radicalC23×C19#120
hypercenter#1948D19
hypocenterC19#10576
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
225. C19#10576semidirect

Maximal subgroups

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

subgroupindex
#145688742
#145643962
#145637942
#145615192
#145614762
#145614742
C19×#19482
#1057619