Finite Group Databasebeta

← #18071823

Subgroups — #18071823

Order 4864.

358 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 85 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#14570587C211yesmaximal, characteristic
2#14565197C211yesmaximal, characteristic
3#14565197C211yesmaximal, characteristic
4#14561459C211yesmaximal, characteristic
5#14561459C211yesmaximal, characteristic
6#14561458C211yesmaximal, characteristic
7C19×#2100C211yesmaximal, characteristic
8C2×#10597335—21no—
9#11926476—21no—
10#11926474—21no—
11#11926474—21no—
12#11926443—21no—
13#11926442C2211yescharacteristic
14#11926442C2211yescharacteristic
15#11926429—21no—
16#11926306—21no—
17#11926306—21no—
18#11926306—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C19×#389C2211yescharacteristic
23C19×#384C2211yescharacteristic
24C19×#340—21no—
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⋊Dic19—21no—
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19D411yescharacteristic
38C2×C4⋊Dic19D411yescharacteristic
39C2×C4⋊Dic19D411yescharacteristic
40C2×C4⋊Dic19D411yescharacteristic
41C2×Dic19⋊C4—21no—
42C2×Dic19⋊C4—21no—
43C2×Dic19⋊C4—21no—
44C2×Dic19⋊C4—21no—
45C2×C4×Dic19—21no—
46C22×C19⋊C8—21no—
47C22×C19⋊C8—21no—
48#10597335—42no—
49#10597335—42no—
50C19×#95—21no—
51C19⋊#95—21no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55C19⋊#95—21no—
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—41no—
67C2×C8×C19—41no—
68C2×C8×C19—41no—
69C4⋊C4×C19—21no—
70C4⋊C4×C19—41no—
71C4⋊C4×C19—42no—
72C4⋊C4×C19—42no—
73C4⋊C4×C19—42no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—41no—
76C4⋊C4×C19SD1612yes—
77C42×C19—41no—
78C4⋊Dic19—21no—
79C4⋊Dic19—21no—
80C4⋊Dic19—21no—
81C4⋊Dic19—42no—
82C4⋊Dic19—41no—
83C4⋊Dic19—41no—
84C4⋊Dic19—81no—
85C4⋊Dic19Q1612yes—
86Dic19⋊C4—42no—
87Dic19⋊C4—42no—
88Dic19⋊C4—41no—
89Dic19⋊C4—41no—
90Dic19⋊C4—41no—
91Dic19⋊C4—41no—
92C4×Dic19—42no—
93C2×C19⋊C8—41no—
94C2×C19⋊C8—41no—
95C2×C19⋊C8—41no—
96C2×C19⋊C8—41no—
97C2×C19⋊C8—41no—
98C2×C19⋊C8—41no—
99#7827—191nomaximal, Sylow
100C23×C19#12011yescharacteristic
101C2×C4×C19—21no—
102C2×C4×C19—21no—
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—22no—
108C2×C4×C19—41no—
109C2×C4×C19—41no—
110C2×C4×C19—41no—
111C2×C4×C19—41no—
112C2×C4×C19—41no—
113C2×C4×C19—81no—
114C2×C4×C19—81no—
115C2×C4×C19—81no—
116C2×C4×C19C2×SD1611yescharacteristic
117C2×C4×C19C2×Q1611yescharacteristic
118C2×C4×C19#13511yescharacteristic
119C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C19#13711yescharacteristic
121C2×C4×C19#13711yescharacteristic
122C2×Dic19—22no—
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—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C8×C19—81no—
135C19⋊C8—81no—
136C19⋊C8—81no—
137#2726—191no—
138#2100—191no—
139#2100—191no—
140#2100D1911yescharacteristic
141#1271—191no—
142#1271—191no—
143#1271—191no—
144C22×C19#45011yescharacteristic
145C22×C19#45111yescharacteristic
146C22×C19#45211yescharacteristic
147C22×C19#45411yescharacteristic
148C22×C19#45411yescharacteristic
149C22×C19#45411yescharacteristic
150C22×C19#45811yescharacteristic
151C4×C19—21no—
152C4×C19—21no—
153C4×C19—21no—
154C4×C19—21no—
155C4×C19—21no—
156C4×C19—21no—
157C4×C19—42no—
158C4×C19—81no—
159C4×C19—161no—
160Dic19—42no—
161Dic19—81no—
162Dic19—81no—
163Dic19—81no—
164C2×#125—381no—
165#398—381no—
166#398—381no—
167#398—381no—
168#389—191no—
169#389—191no—
170#389—381no—
171#389C2×D1911yescharacteristic
172#387—381no—
173#384C2×D1911yescharacteristic
174#340—21no—
175#340—21no—
176#340—381no—
177#340—381no—
178#340—381no—
179#340—381no—
180#336—191no—
181#336—191no—
182#336C2×D1911yescharacteristic
183C2×C19#161511yescharacteristic
184C2×C19#161611yescharacteristic
185C2×C19#161711yescharacteristic
186C2×C19#163511yescharacteristic
187C2×C19#163611yescharacteristic
188C2×C19#163711yescharacteristic
189C2×C19#165811yescharacteristic
190C22×C8—21no—
191C22×C8—381no—
192C22×C8—381no—
193#125—762no—
194#125—762no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—191no—
200C2×C4⋊C4—191no—
201C2×C4⋊C4—191no—
202C2×C4⋊C4—191no—
203C2×C4⋊C4—381no—
204C2×C4⋊C4—381no—
205C2×C4⋊C4—381no—
206C2×C4⋊C4—381no—
207C2×C4⋊C4—381no—
208C2×C4⋊C4—381no—
209C2×C4⋊C4C22⋊D1911yescharacteristic
210C2×C4⋊C4C22⋊D1911yescharacteristic
211C2×C42—381no—
212C2×C42C22×D1911yescharacteristic
213#95—21no—
214#95—381no—
215#95—381no—
216#95—381no—
217#95—381no—
218#95—381no—
219C19#782711yescharacteristic, complemented, Sylow
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—41no—
223C22×C4—381no—
224C22×C4—381no—
225C22×C4—381no—
226C22×C4—381no—
227C22×C4D4×D1911yescharacteristic
228C22×C4D4×D1911yescharacteristic
229C22×C4C2×C22⋊D1911yescharacteristic
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—761no—
234C2×C8—761no—
235C2×C8—761no—
236C2×C8—761no—
237C2×C8—761no—
238C2×C8—761no—
239C4⋊C4—21no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—192no—
247C4⋊C4—381no—
248C4⋊C4—381no—
249C4⋊C4—381no—
250C4⋊C4—761no—
251C4⋊C4—761no—
252C4⋊C4—762no—
253C4⋊C4—762no—
254C4⋊C4—762no—
255C4⋊C4—761no—
256C4⋊C4—761no—
257C4⋊C4—761no—
258C4⋊C4—761no—
259C4⋊C4—1521no—
260C4⋊C4#6452712yes—
261C42—41no—
262C42—762no—
263C23#1059738311yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—382no—
280C2×C4—761no—
281C2×C4—761no—
282C2×C4—761no—
283C2×C4—761no—
284C2×C4—761no—
285C2×C4—761no—
286C2×C4—761no—
287C2×C4—761no—
288C2×C4—761no—
289C2×C4—761no—
290C2×C4—761no—
291C2×C4#1059736111yescharacteristic
292C2×C4#1059736211yescharacteristic
293C2×C4Q16×D1911yescharacteristic
294C2×C4#1059736411yescharacteristic
295C2×C4C2×#6452711yescharacteristic
296C2×C4#1059739511yescharacteristic
297C8—81no—
298C8—1521no—
299C8—1521no—
300C22#1192669411yescharacteristic
301C22#1192669811yescharacteristic
302C22#1192670311yescharacteristic
303C22#1192671511yescharacteristic
304C22#1192671511yescharacteristic
305C22#1192671611yescharacteristic
306C22#1192673311yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—81no—
315C4—161no—
316C4—762no—
317C4—1521no—
318C4—1521no—
319C4—1521no—
320C2#1456266311yescharacteristic
321C2#1456267111yescharacteristic
322C2#1456267511yescharacteristic
323C2#1456278411yescharacteristic
324C2#1456279011yescharacteristic
325C2#1456279811yescharacteristic
326C2#1456293611yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2100C2
socle, prime radicalC23×C19#120
hypercenter#2100D19
hypocenterC19#7827
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
219. C19#7827semidirect

Maximal subgroups

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

subgroupindex
#145705872
#145651972
#145614592
#145614582
C19×#21002
#782719