Finite Group Databasebeta

← #18071674

Subgroups — #18071674

Order 4864.

338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14571626C211yesmaximal, characteristic
2#14565192C211yesmaximal, characteristic
3#14565112C211yesmaximal, characteristic
4#14561459C211yesmaximal, characteristic
5#14561458C211yesmaximal, characteristic
6#14561457C211yesmaximal, characteristic
7C19×#2083C211yesmaximal, characteristic
8C2×#10597265—21no—
9#11926484—21no—
10#11926483—21no—
11#11926482—21no—
12#11926442C2211yescharacteristic
13#11926442C2211yescharacteristic
14#11926431—21no—
15#11926430—21no—
16#11926425—21no—
17#11926306—21no—
18#11926306—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C2×C19×#107—21no—
23C19×#389C2211yescharacteristic
24C19×#384C2211yescharacteristic
25C19×#340—21no—
26C19×#336C2211yescharacteristic
27C22×C8×C19—21no—
28C2×C4⋊C4×C19—21no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19D411yescharacteristic
33C2×C4⋊C4×C19D411yescharacteristic
34C2×C42×C19C2311yescharacteristic
35C2×C4⋊Dic19D411yescharacteristic
36C2×C4⋊Dic19D411yescharacteristic
37C2×C4⋊Dic19D411yescharacteristic
38C2×C4⋊Dic19D411yescharacteristic
39C2×Dic19⋊C4—21no—
40C2×Dic19⋊C4—21no—
41C2×C4×Dic19—21no—
42C22×C19⋊C8—21no—
43C22×C19⋊C8—21no—
44C19×#107—42no—
45C19×#95—21no—
46C19⋊#95—21no—
47C19⋊#95—21no—
48C19⋊#95—21no—
49C19⋊#95—21no—
50C19⋊#95—21no—
51C19⋊#95—21no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55#10597265—42no—
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—21no—
65C22×Dic19—21no—
66C2×C8×C19—22no—
67C2×C8×C19—41no—
68C2×C8×C19—41no—
69C4⋊C4×C19—21no—
70C4⋊C4×C19—21no—
71C4⋊C4×C19—41no—
72C4⋊C4×C19—42no—
73C4⋊C4×C19—41no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—41no—
76C4⋊C4×C19—41no—
77C4⋊C4×C19—41no—
78C4⋊C4×C19—41no—
79C42×C19—41no—
80C4⋊Dic19—21no—
81C4⋊Dic19—21no—
82C4⋊Dic19—21no—
83C4⋊Dic19—21no—
84C4⋊Dic19—41no—
85C4⋊Dic19—41no—
86Dic19⋊C4—41no—
87Dic19⋊C4—41no—
88Dic19⋊C4—41no—
89Dic19⋊C4—41no—
90C4×Dic19—81no—
91C2×C19⋊C8—22no—
92C2×C19⋊C8—41no—
93C2×C19⋊C8—41no—
94C2×C19⋊C8—41no—
95C2×C19⋊C8—41no—
96C2×C19⋊C8—41no—
97#7803—191nomaximal, Sylow
98C23×C19#12011yescharacteristic
99C2×C4×C19—21no—
100C2×C4×C19—21no—
101C2×C4×C19—21no—
102C2×C4×C19—21no—
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×C19#13511yescharacteristic
115C2×C4×C19#13511yescharacteristic
116C2×C4×C19#13511yescharacteristic
117C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C19#13711yescharacteristic
120C2×Dic19—41no—
121C2×Dic19—41no—
122C2×Dic19—41no—
123C2×Dic19—41no—
124C2×Dic19—41no—
125C2×Dic19—41no—
126C2×Dic19—41no—
127C2×Dic19—41no—
128C2×Dic19—41no—
129C2×Dic19—41no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C8×C19—42no—
133C19⋊C8—42no—
134C19⋊C8—81no—
135#2810—191no—
136#2099—191no—
137#2084—191no—
138#2083D1911yescharacteristic
139#1271—191no—
140#1271—191no—
141#1271—191no—
142C22×C19#44911yescharacteristic
143C22×C19#44911yescharacteristic
144C22×C19#45211yescharacteristic
145C22×C19#45411yescharacteristic
146C22×C19#45611yescharacteristic
147C22×C19#45611yescharacteristic
148C22×C19#45811yescharacteristic
149C4×C19—21no—
150C4×C19—21no—
151C4×C19—21no—
152C4×C19—21no—
153C4×C19—21no—
154C4×C19—21no—
155C4×C19—81no—
156C4×C19—81no—
157C4×C19—161no—
158Dic19—81no—
159Dic19—81no—
160Dic19—81no—
161Dic19—81no—
162C2×#107—21no—
163C2×#106—381no—
164#400—381no—
165#400—381no—
166#400—381no—
167#389—191no—
168#389—191no—
169#389C2×D1911yescharacteristic
170#387—381no—
171#387—381no—
172#387—381no—
173#384C2×D1911yescharacteristic
174#340—21no—
175#340—381no—
176#340—381no—
177#340—381no—
178#336—191no—
179#336—191no—
180#336C2×D1911yescharacteristic
181C2×C19#160911yescharacteristic
182C2×C19#160911yescharacteristic
183C2×C19#161511yescharacteristic
184C2×C19#162811yescharacteristic
185C2×C19#165011yescharacteristic
186C2×C19#165211yescharacteristic
187C2×C19#166311yescharacteristic
188C22×C8—21no—
189C22×C8—381no—
190C22×C8—381no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—191no—
196C2×C4⋊C4—191no—
197C2×C4⋊C4—191no—
198C2×C4⋊C4—191no—
199C2×C4⋊C4—381no—
200C2×C4⋊C4—381no—
201C2×C4⋊C4C22⋊D1911yescharacteristic
202C2×C4⋊C4C22⋊D1911yescharacteristic
203C2×C42—381no—
204C2×C42C22×D1911yescharacteristic
205#107—42no—
206#106—762no—
207#95—21no—
208#95—381no—
209#95—381no—
210#95—381no—
211#95—381no—
212#95—381no—
213#95—381no—
214#95—381no—
215#95—381no—
216#95—381no—
217C19#780311yescharacteristic, complemented, Sylow
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—41no—
221C22×C4—381no—
222C22×C4—381no—
223C22×C4—381no—
224C22×C4—381no—
225C22×C4D4×D1911yescharacteristic
226C22×C4D4×D1911yescharacteristic
227C22×C4C2×C22⋊D1911yescharacteristic
228C2×C8—22no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—382no—
232C2×C8—761no—
233C2×C8—761no—
234C2×C8—761no—
235C2×C8—761no—
236C2×C8—761no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—381no—
248C4⋊C4—381no—
249C4⋊C4—381no—
250C4⋊C4—381no—
251C4⋊C4—761no—
252C4⋊C4—761no—
253C4⋊C4—761no—
254C4⋊C4—761no—
255C4⋊C4—761no—
256C4⋊C4—761no—
257C42—41no—
258C42—1521no—
259C23#1059738311yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—761no—
276C2×C4—761no—
277C2×C4—761no—
278C2×C4—761no—
279C2×C4—761no—
280C2×C4—761no—
281C2×C4—761no—
282C2×C4—761no—
283C2×C4—761no—
284C2×C4—761no—
285C2×C4—761no—
286C2×C4—761no—
287C2×C4#1059735711yescharacteristic
288C2×C4#1059735811yescharacteristic
289C2×C4#1059736411yescharacteristic
290C2×C4#1059736511yescharacteristic
291C2×C4#1059737811yescharacteristic
292C2×C4#1059739611yescharacteristic
293C8—42no—
294C8—762no—
295C8—1521no—
296C22#1192668611yescharacteristic
297C22#1192668711yescharacteristic
298C22#1192670511yescharacteristic
299C22#1192671511yescharacteristic
300C22#1192672511yescharacteristic
301C22#1192672611yescharacteristic
302C22#1192673311yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—161no—
312C4—1521no—
313C4—1521no—
314C4—1521no—
315C4—1521no—
316C2#1456262911yescharacteristic
317C2#1456263011yescharacteristic
318C2#1456266511yescharacteristic
319C2#1456274311yescharacteristic
320C2#1456288811yescharacteristic
321C2#1456290311yescharacteristic
322C2#1456296211yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2083C2
socle, prime radicalC23×C19#120
hypercenter#2083D19
hypocenterC19#7803
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2083

Complements

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

NH ≅ G/Ntype
217. C19#7803semidirect

Maximal subgroups

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

subgroupindex
#145716262
#145651922
#145651122
#145614592
#145614582
#145614572
C19×#20832
#780319