Finite Group Databasebeta

← #18075080

Subgroups — #18075080

Order 4864.

656 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#11927155C211yesmaximal, characteristic
2#14562361C211yesmaximal, characteristic, complemented
3#14562261C212yesmaximal, complemented
4#14561967C212yesmaximal
5C19×#1558C211yesmaximal, characteristic, complemented
6#11927155—24no—
7#11927155—22no—
8#11927155—22no—
9C2×#10597344—22no—
10C2×#10597316C2211yescharacteristic
11C2×#10597335—22no—
12C2×#10597392C412yes—
13C2×Q8×Dic19C412yes—
14C2×#10597318C2211yescharacteristic
15#11926601C2212yes—
16#11926293—22no—
17#11926285—24no—
18#11926269—22no—
19#11926267—22no—
20C2×C19×C4⋊Q8C2211yescharacteristic
21C19×#432C2212yes—
22C19×#333—22no—
23C22×Q8×C19C2×C412yes—
24C22×C4×D19C2×C411yescharacteristic
25C19×C4⋊Q8—22no—
26C19×C4⋊Q8D412yes—
27C19×C4⋊Q8D412yes—
28C2×C4⋊C4×C19—22no—
29C2×C42×C19C2311yescharacteristic
30#10597392—24no—
31#10597392—24no—
32Q8×Dic19—24no—
33Q8×Dic19—24no—
34C2×(C2×D19)⋊C4—22no—
35C2×(C2×D19)⋊C4D412yes—
36C2×C4⋊Dic19—22no—
37C2×C4⋊Dic19C2×C412yes—
38C2×Dic19⋊C4—22no—
39C2×Dic19⋊C4—22no—
40C2×Dic19⋊C4D412yes—
41C2×C4×Dic19—22no—
42C2×C4×Dic19C2×C411yescharacteristic
43#10597344—28no—
44#10597344—28no—
45#10597335—28no—
46#10597335—28no—
47#10597318—21no—
48#10597318—22no—
49#10597318—21no—
50#10597316—21no—
51#10597316—21no—
52#10597316D414yes—
53C19×C4⋊C8—22no—
54C19×C22⋊C8—22no—
55C19×#97—22no—
56C22⋊(C19⋊C8)—22no—
57C4⋊(C19⋊C8)—22no—
58#10597260—22no—
59C23×D19C22⋊C411yescharacteristic
60C2×Q8×C19—22no—
61C2×Q8×C19—44no—
62C2×Q8×C19C22⋊C414yes—
63C22×C4×C19—22no—
64C22×C4×C19C22×C411yescharacteristic
65C22×C4×C19C2×D412yes—
66C22×Dic19—22no—
67C22×Dic19C22⋊C411yescharacteristic
68C22×Dic19C22⋊C412yes—
69C2×C4×D19—21no—
70C2×C4×D19—21no—
71C2×C4×D19—42no—
72C2×C8×C19—42no—
73C4⋊C4×C19—24no—
74C4⋊C4×C19—24no—
75C42×C19C2×D411yescharacteristic
76C42×C19C2×D412yes—
77C42×C19C2×D411yescharacteristic
78(C2×D19)⋊C4—28no—
79(C2×D19)⋊C4—22no—
80(C2×D19)⋊C4—22no—
81C4⋊Dic19—28no—
82C4⋊Dic19—22no—
83C4⋊Dic19C22⋊C414yes—
84Dic19⋊C4—28no—
85Dic19⋊C4—24no—
86Dic19⋊C4—24no—
87Dic19⋊C4—22no—
88Dic19⋊C4—22no—
89C4×Dic19—28no—
90C4×Dic19—21no—
91C4×Dic19—21no—
92C2×C19⋊C8—42no—
93#8527—191nomaximal, Sylow
94C23×C19C2×C22⋊C411yescharacteristic
95C22×D19—21no—
96C22×D19—22no—
97C22×D19—42no—
98Q8×C19—44no—
99Q8×C19—44no—
100C2×C4×C19—22no—
101C2×C4×C19—24no—
102C2×C4×C19—42no—
103C2×C4×C19—44no—
104C2×C4×C19C2×C22⋊C411yescharacteristic
105C2×C4×C19C2×C22⋊C411yescharacteristic
106C2×C4×C19#12012yes—
107C2×C4×C19#12012yes—
108C2×Dic19—22no—
109C2×Dic19—24no—
110C2×Dic19—21no—
111C2×Dic19—22no—
112C2×Dic19—44no—
113C2×Dic19—42no—
114C4×D19—42no—
115C4×D19—42no—
116C8×C19—82no—
117C19⋊C8—82no—
118C2×#541—191no—
119#1558—191no—
120#1558D1911yescharacteristic, complemented
121#1534—192no—
122#1464—192no—
123C22×C19—22no—
124C22×C19#37911yescharacteristic
125C22×C19#41312yes—
126C2×D19—42no—
127C2×D19—41no—
128C2×D19—82no—
129C4×C19—22no—
130C4×C19—22no—
131C4×C19—21no—
132C4×C19—21no—
133C4×C19—44no—
134Dic19—42no—
135Dic19—44no—
136Dic19—41no—
137#541—384no—
138#541—382no—
139#541—382no—
140C2×C4⋊Q8C2×D1911yescharacteristic
141C2×#126—382no—
142C2×#125—191no—
143C2×#125—382no—
144C2×C22⋊Q8—192no—
145C2×C4×Q8—192no—
146C2×#117—191no—
147#432—192no—
148#432C2×D1912yes—
149#333—22no—
150#333—382no—
151#330—384no—
152#324—382no—
153#323—382no—
154C2×C19—22no—
155C2×C19#178511yescharacteristic
156C2×C19#179612yes—
157D19—81no—
158C22×Q8C4×D1912yes—
159C23×C4—191no—
160C4⋊Q8—22no—
161C4⋊Q8D7612yes—
162C4⋊Q8C22⋊D1912yes—
163#126—388no—
164#126—388no—
165#125—194no—
166#125—388no—
167#125—388no—
168#125—381no—
169#125—381no—
170C22⋊Q8—384no—
171C22⋊Q8—384no—
172C4×Q8—384no—
173C4×Q8—384no—
174#117—381no—
175#117—382no—
176#117—381no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—192no—
179C2×C4⋊C4—192no—
180C2×C4⋊C4—382no—
181C2×C4⋊C4—382no—
182C2×C4⋊C4—382no—
183C2×C22⋊C4—192no—
184C2×C22⋊C4—382no—
185C2×C42—191no—
186C2×C42—382no—
187C2×C42C22×D1911yescharacteristic
188C4⋊C8—22no—
189C4⋊C8—382no—
190C22⋊C8—22no—
191C22⋊C8—382no—
192#97—22no—
193#97—382no—
194C19#852711yescharacteristic, complemented, Sylow
195C24—191no—
196C2×Q8—22no—
197C2×Q8—44no—
198C2×Q8(C2×D19)⋊C414yes—
199C22×C4—22no—
200C22×C4—191no—
201C22×C4—192no—
202C22×C4—382no—
203C22×C4—381no—
204C22×C4—381no—
205C22×C4—762no—
206C22×C4C2×C4×D1911yescharacteristic
207C22×C4D4×D1912yes—
208C2×C8—42no—
209C2×C8—762no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—194no—
213C4⋊C4—388no—
214C4⋊C4—388no—
215C4⋊C4—382no—
216C4⋊C4—384no—
217C4⋊C4—382no—
218C4⋊C4—384no—
219C4⋊C4—382no—
220C22⋊C4—388no—
221C22⋊C4—382no—
222C22⋊C4—382no—
223C42—388no—
224C42—381no—
225C42—381no—
226C42C2×D7611yescharacteristic
227C42D4×D1912yes—
228C42C2×C22⋊D1911yescharacteristic
229C23—381no—
230C23—382no—
231C23—762no—
232C23C22⋊C4×D1911yescharacteristic
233Q8—44no—
234Q8—44no—
235C2×C4—22no—
236C2×C4—24no—
237C2×C4—42no—
238C2×C4—44no—
239C2×C4—382no—
240C2×C4—384no—
241C2×C4—381no—
242C2×C4—382no—
243C2×C4—762no—
244C2×C4—762no—
245C2×C4—764no—
246C2×C4—762no—
247C2×C4C22⋊C4×D1911yescharacteristic
248C2×C4#1059732812yes—
249C2×C4C2×(C2×D19)⋊C411yescharacteristic
250C2×C4#1059738312yes—
251C8—82no—
252C8—1522no—
253C22—22no—
254C22—762no—
255C22—761no—
256C22—1522no—
257C22#1192639911yescharacteristic
258C22#1192652512yes—
259C4—22no—
260C4—22no—
261C4—21no—
262C4—21no—
263C4—44no—
264C4—764no—
265C4—762no—
266C4—761no—
267C2—22no—
268C2—1521no—
269C2#1456356011yescharacteristic
270C2#1456360712yes—
subgroupG/H
centerC22#11926399
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1558C2
socleC22×C19#379
prime radicalC23×D19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1558D19
hypocenterC19#8527
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1558

Complements

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

NH ≅ G/Ntype
2. #14562361C2semidirect
3. #14562261C2semidirect
5. C19×#1558C2semidirect
120. #1558D19semidirect
194. C19#8527semidirect

Maximal subgroups

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

subgroupindex
C2×#119271552
#145623612
#145622612
#145619672
C19×#15582
#852719