Finite Group Databasebeta

← #18079916

Subgroups — #18079916

Order 4864.

470 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 117 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#14572715C211yesmaximal, characteristic
2#14568851C211yesmaximal, characteristic
3#14563628C211yesmaximal, characteristic
4#14562320C211yesmaximal, characteristic
5#14561537C211yesmaximal, characteristic
6#14561536C211yesmaximal, characteristic
7C19×#1549C211yesmaximal, characteristic
8C2×C4×Dic38C2211yescharacteristic
9C8×Dic38—22no—
10#11926668—22no—
11#11926597C2211yescharacteristic
12#11926594—22no—
13#11926568C2211yescharacteristic
14C2×#10597281—21no—
15#11926482C414yes—
16#11926451—22no—
17#11926449—21no—
18#11926409—21no—
19C4×C4⋊Dic19C2211yescharacteristic
20#11926312—21no—
21#11926290—22no—
22C2×C19×C4⋊Q8C2211yescharacteristic
23C19×#431C2211yescharacteristic
24C19×#423C2211yescharacteristic
25C19×#332—22no—
26C22×Q8×C19—21no—
27C22×Dic38D411yescharacteristic
28C2×M16×C19—21no—
29C19×C4⋊Q8—21no—
30C19×C4⋊Q8—21no—
31C19×C4⋊Q8—21no—
32C19×C4⋊Q8—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19C2×C412yes—
35C2×C42×C19C2311yescharacteristic
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19D411yescharacteristic
38C2×Dic19⋊C4C2×C412yes—
39C2×C4×Dic19—21no—
40C2×C4×Dic19D412yes—
41C2×#64520—21no—
42C4×Dic38—21no—
43C4×Dic38—21no—
44C4×Dic38—21no—
45C4×Dic38—21no—
46C19×C4⋊C8—21no—
47C19×C4⋊C8—21no—
48C19×C4⋊C8D412yes—
49C19×C22⋊C8—21no—
50C4×C8×C19—21no—
51C19⋊#95—24no—
52C19⋊#95—24no—
53C19⋊#95C2×C412yes—
54C22⋊(C19⋊C8)—21no—
55#10597281—42no—
56Dic19⋊C8—24no—
57C8×Dic19—24no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)D412yes—
61C4×C19⋊C8—21no—
62C2×Q8×C19—44no—
63C2×Q8×C19—41no—
64C2×Q8×C19—41no—
65C22×C4×C19—22no—
66C22×C4×C19C22×C411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×Dic19—22no—
70C22×Dic19C22⋊C412yes—
71C22×Dic19C22⋊C412yes—
72C2×Dic38—21no—
73C2×Dic38—21no—
74C2×Dic38—21no—
75C2×Dic38—21no—
76C2×Dic38SD1612yes—
77C2×Dic38Q1612yes—
78M16×C19—41no—
79M16×C19—41no—
80C2×C8×C19—22no—
81C2×C8×C19—41no—
82C4⋊C4×C19—22no—
83C4⋊C4×C19—22no—
84C4⋊C4×C19—41no—
85C4⋊C4×C19—41no—
86C42×C19C2×D411yescharacteristic
87C42×C19C2×D411yescharacteristic
88C42×C19#4111yescharacteristic
89C42×C19#4111yescharacteristic
90C4⋊Dic19—21no—
91C4⋊Dic19—21no—
92C4⋊Dic19—42no—
93Dic19⋊C4—22no—
94Dic19⋊C4—22no—
95C4×Dic19—22no—
96C4×Dic19—22no—
97C4×Dic19—41no—
98C4×Dic19—41no—
99#64520—41no—
100#64520—41no—
101C2×C19⋊C8—22no—
102C2×C19⋊C8—41no—
103#9396—191nomaximal, Sylow
104C23×C19C2×C22⋊C411yescharacteristic
105Q8×C19—82no—
106Q8×C19—82no—
107C2×C4×C19—22no—
108C2×C4×C19—41no—
109C2×C4×C19—44no—
110C2×C4×C19—42no—
111C2×C4×C19C4×D411yescharacteristic
112C2×C4×C19C4×D411yescharacteristic
113C2×C4×C19#12011yescharacteristic
114C2×C4×C19#12111yescharacteristic
115C2×C4×C19#12111yescharacteristic
116C2×C4×C19#12311yescharacteristic
117C2×C4×C19C2×SD1611yescharacteristic
118C2×C4×C19C2×Q1611yescharacteristic
119C2×C4×C19#13511yescharacteristic
120C2×C4×C19#13511yescharacteristic
121C2×Dic19—22no—
122C2×Dic19—22no—
123C2×Dic19—22no—
124C2×Dic19—42no—
125C2×Dic19—42no—
126C2×Dic19—42no—
127C2×Dic19—42no—
128C2×Dic19#10314yes—
129Dic38—22no—
130Dic38—22no—
131Dic38—22no—
132Dic38—22no—
133C8×C19—42no—
134C8×C19—81no—
135C19⋊C8—42no—
136C19⋊C8—81no—
137#2982—191no—
138#2568—191no—
139#1801—191no—
140#1549—191no—
141#1549D1911yescharacteristic
142#1303—191no—
143#1303—191no—
144C22×C19—21no—
145C22×C19—21no—
146C22×C19#38611yescharacteristic
147C22×C19C2×#10311yescharacteristic
148C22×C19#41611yescharacteristic
149C4×C19—21no—
150C4×C19—21no—
151C4×C19—21no—
152C4×C19—82no—
153C4×C19#45412yes—
154C4×C19#46511yescharacteristic
155C4×C19#46511yescharacteristic
156C4×C19#46711yescharacteristic
157C4×C19#46711yescharacteristic
158Dic19—24no—
159Dic19—42no—
160Dic19—82no—
161C2×C4⋊Q8C2×D1911yescharacteristic
162C2×C4×Q8—191no—
163C8×Q8—382no—
164C8×Q8—382no—
165#431—191no—
166#431—382no—
167#431C2×D1911yescharacteristic
168#423—191no—
169#423C2×D1911yescharacteristic
170C2×#101—381no—
171#400—194no—
172#391—382no—
173#391—381no—
174#382—381no—
175C4×C4⋊C4—191no—
176#343—381no—
177#332—22no—
178#332—382no—
179C2×C19—21no—
180C2×C19—21no—
181C2×C19#188811yescharacteristic
182C2×C19#189211yescharacteristic
183C2×C19#191511yescharacteristic
184C22×Q8—21no—
185C22×Q8—191no—
186C2×M16—21no—
187C2×M16—381no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4×Q8—381no—
193C4×Q8—381no—
194C4×Q8—381no—
195C4×Q8—381no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—192no—
198C2×C4⋊C4—191no—
199C2×C4⋊C4—381no—
200C2×C4⋊C4C4×D1912yes—
201C2×C42—192no—
202C2×C42—381no—
203C2×C42C22×D1911yescharacteristic
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—192no—
207C4⋊C8—384no—
208C4⋊C8—381no—
209C4⋊C8—381no—
210C4⋊C8C22⋊D1912yes—
211#101—762no—
212C22⋊C8—21no—
213C22⋊C8—381no—
214C4×C8—21no—
215C4×C8—384no—
216C4×C8—381no—
217#95—192no—
218#95—384no—
219#95—384no—
220C19#939611yescharacteristic, complemented, Sylow
221C2×Q8—44no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8—192no—
225C2×Q8—192no—
226C2×Q8—381no—
227C2×Q8—381no—
228C2×Q8—381no—
229C2×Q8—381no—
230C22×C4—22no—
231C22×C4—192no—
232C22×C4—192no—
233C22×C4—382no—
234C22×C4C2×C4×D1911yescharacteristic
235C22×C4D4×D1911yescharacteristic
236C22×C4D4×D1911yescharacteristic
237M16—41no—
238M16—41no—
239M16—761no—
240M16—761no—
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—382no—
244C2×C8—761no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—381no—
250C4⋊C4—382no—
251C4⋊C4—381no—
252C4⋊C4—382no—
253C4⋊C4—762no—
254C42—382no—
255C42—382no—
256C42—761no—
257C42—761no—
258C42#6454111yescharacteristic
259C42D4×D1911yescharacteristic
260C42#6454311yescharacteristic
261C42C2×C22⋊D1911yescharacteristic
262C23C22⋊C4×D1911yescharacteristic
263Q8—82no—
264Q8—82no—
265Q8—382no—
266Q8—382no—
267Q8—382no—
268Q8—382no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—44no—
272C2×C4—42no—
273C2×C4—194no—
274C2×C4—382no—
275C2×C4—382no—
276C2×C4—382no—
277C2×C4—762no—
278C2×C4—762no—
279C2×C4—762no—
280C2×C4—762no—
281C2×C4(C22⋊D19)⋊C411yescharacteristic
282C2×C4#1059732911yescharacteristic
283C2×C4#1059733011yescharacteristic
284C2×C4SD16×D1911yescharacteristic
285C2×C4#1059736211yescharacteristic
286C2×C4Q16×D1911yescharacteristic
287C2×C4#1059736511yescharacteristic
288C2×C4C4×C22⋊D1911yescharacteristic
289C2×C4#1059738311yescharacteristic
290C2×C4#1059738411yescharacteristic
291C8—42no—
292C8—81no—
293C8—762no—
294C8—1521no—
295C22—21no—
296C22—21no—
297C22#1192642011yescharacteristic
298C22#103×D1911yescharacteristic
299C22#1192653911yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—82no—
304C4—384no—
305C4—762no—
306C4—1522no—
307C4#1192671512yes—
308C4#1192677011yescharacteristic
309C4#1192677611yescharacteristic
310C4#1192678211yescharacteristic
311C4#1192678411yescharacteristic
312C2—21no—
313C2—21no—
314C2#1456403511yescharacteristic
315C2#1456405511yescharacteristic
316C2#1456418411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1549C2
socleC22×C19#386
prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1549D19
hypocenterC19#9396
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
220. C19#9396semidirect

Maximal subgroups

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

subgroupindex
#145727152
#145688512
#145636282
#145623202
#145615372
#145615362
C19×#15492
#939619