Finite Group Databasebeta

← #18079523

Subgroups — #18079523

Order 4864.

360 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 91 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#14574837C211yesmaximal, characteristic
2#14572741C211yesmaximal, characteristic
3#14562261C211yesmaximal, characteristic
4#14561990C211yesmaximal, characteristic
5C19⋊#1308C211yesmaximal, characteristic
6#14561497C211yesmaximal, characteristic
7C19×#1554C211yesmaximal, characteristic
8C2×#10597316C2211yescharacteristic
9#11926950—21no—
10#11926912—21no—
11#11926877C412yes—
12#11926872C412yes—
13#11926851—22no—
14#11926675—22no—
15#11926675—22no—
16#11926605—22no—
17#11926601C2211yescharacteristic
18#11926601C2211yescharacteristic
19#11926601C2211yescharacteristic
20#11926285—22no—
21#11926269—22no—
22C19×#533C2211yescharacteristic
23C19×#432C2211yescharacteristic
24C19×#431C2211yescharacteristic
25C19×#333—21no—
26C19×#332—21no—
27C19×C4⋊Q8D411yescharacteristic
28C19×C4⋊Q8D411yescharacteristic
29C19×#125—21no—
30C19×C22⋊Q8—21no—
31C19×C22⋊Q8C2×C412yes—
32C4×Q8×C19—21no—
33C4×Q8×C19D412yes—
34C19×#117—21no—
35C2×C42×C19C2311yescharacteristic
36C2×C4⋊Dic19C2×C411yescharacteristic
37C2×C4⋊Dic19C2×C411yescharacteristic
38C2×Dic19⋊C4—21no—
39C2×Dic19⋊C4—21no—
40#10597316—21no—
41#10597316—21no—
42#10597316—21no—
43#10597316—21no—
44C19×C4⋊C8—21no—
45C19×C4⋊C8—21no—
46C19×C22⋊C8—21no—
47C19×C22⋊C8—21no—
48C19×#97—21no—
49C4×C8×C19—21no—
50#10597292—22no—
51#10597292—22no—
52C22⋊(C19⋊C8)—21no—
53C22⋊(C19⋊C8)C2×C412yes—
54C22⋊(C19⋊C8)D412yes—
55#10597265—22no—
56#10597264—22no—
57C4⋊(C19⋊C8)—24no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)—21no—
61#10597260—22no—
62#10597260—21no—
63#10597260—21no—
64#10597260D412yes—
65C4×C19⋊C8—22no—
66C2×Q8×C19—21no—
67C2×Q8×C19C22⋊C412yes—
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19#4111yescharacteristic
71C22×Dic19—21no—
72C22×Dic19—21no—
73C2×C8×C19—41no—
74C2×C8×C19—41no—
75C4⋊C4×C19—22no—
76C4⋊C4×C19—21no—
77C4⋊C4×C19—21no—
78C4⋊C4×C19—21no—
79C4⋊C4×C19—22no—
80C4⋊C4×C19C22⋊C412yes—
81C22⋊C4×C19—22no—
82C42×C19—22no—
83C42×C19C2×D411yescharacteristic
84C42×C19C2×D411yescharacteristic
85C42×C19C2×D411yescharacteristic
86C42×C19#4111yescharacteristic
87C4⋊Dic19—21no—
88C4⋊Dic19—21no—
89C4⋊Dic19—21no—
90C4⋊Dic19—21no—
91Dic19⋊C4—41no—
92Dic19⋊C4—41no—
93Dic19⋊C4—41no—
94Dic19⋊C4—41no—
95C2×C19⋊C8—22no—
96C2×C19⋊C8—22no—
97C2×C19⋊C8—22no—
98#9336—191nomaximal, Sylow
99C23×C19C4×D411yescharacteristic
100Q8×C19—42no—
101Q8×C19—81no—
102C2×C4×C19—22no—
103C2×C4×C19—22no—
104C2×C4×C19—41no—
105C2×C4×C19—41no—
106C2×C4×C19—41no—
107C2×C4×C19C2×C22⋊C411yescharacteristic
108C2×C4×C19C4×D411yescharacteristic
109C2×C4×C19#12011yescharacteristic
110C2×C4×C19#12111yescharacteristic
111C2×C4×C19#12111yescharacteristic
112C2×C4×C19#12311yescharacteristic
113C2×Dic19—42no—
114C2×Dic19—41no—
115C2×Dic19—41no—
116C2×Dic19—81no—
117C8×C19—81no—
118C8×C19—81no—
119C19⋊C8—42no—
120C19⋊C8—42no—
121C19⋊C8—42no—
122#3236—191no—
123#2987—191no—
124#1554D1911yescharacteristic
125#1534—191no—
126#1470—191no—
127#1308—191no—
128#1287—191no—
129C22×C19—21no—
130C22×C19—21no—
131C22×C19—21no—
132C22×C19#38611yescharacteristic
133C4×C19—21no—
134C4×C19—21no—
135C4×C19—21no—
136C4×C19—21no—
137C4×C19—21no—
138C4×C19—21no—
139C4×C19—42no—
140C4×C19—42no—
141Dic19—81no—
142Dic19—81no—
143#533C2×D1911yescharacteristic
144C2×#125—191no—
145#501—381no—
146#491—381no—
147#484—192no—
148#483—192no—
149#479—382no—
150#446—382no—
151#446—382no—
152#433—382no—
153#432—191no—
154#432—191no—
155#432—191no—
156#432C2×D1911yescharacteristic
157#431C2×D1911yescharacteristic
158#333—21no—
159#332—21no—
160#330—382no—
161#324—382no—
162C2×C19—41no—
163C2×C19#188111yescharacteristic
164C2×C19#190511yescharacteristic
165C2×C19#191511yescharacteristic
166C4⋊Q8C22⋊D1911yescharacteristic
167C4⋊Q8C22⋊D1911yescharacteristic
168#125—21no—
169#125—381no—
170#125—381no—
171#125—381no—
172#125—381no—
173C22⋊Q8—21no—
174C22⋊Q8C4×D1912yes—
175C4×Q8—21no—
176C4×Q8D7612yes—
177#117—21no—
178C2×C4⋊C4—191no—
179C2×C4⋊C4—191no—
180C2×C4⋊C4—381no—
181C2×C4⋊C4—381no—
182C2×C42C22×D1911yescharacteristic
183#107—382no—
184#106—382no—
185C4⋊C8—21no—
186C4⋊C8—21no—
187C4⋊C8—384no—
188C4⋊C8—381no—
189C4⋊C8—381no—
190C4⋊C8—381no—
191#103—382no—
192#103—382no—
193C22⋊C8—21no—
194C22⋊C8—21no—
195C22⋊C8—192no—
196C22⋊C8—192no—
197C22⋊C8—381no—
198#97—21no—
199#97—192no—
200#97—382no—
201#97—381no—
202#97—381no—
203C4×C8—21no—
204C4×C8—382no—
205C19#933611yescharacteristic, complemented, Sylow
206C2×Q8—21no—
207C2×Q8(C2×D19)⋊C412yes—
208C22×C4—381no—
209C22×C4—381no—
210C22×C4C2×C4×D1911yescharacteristic
211C22×C4D4×D1911yescharacteristic
212C22×C4#6454311yescharacteristic
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—382no—
216C2×C8—382no—
217C2×C8—382no—
218C4⋊C4—21no—
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—381no—
224C4⋊C4—381no—
225C4⋊C4—381no—
226C4⋊C4—381no—
227C4⋊C4—761no—
228C4⋊C4—761no—
229C4⋊C4—761no—
230C4⋊C4—761no—
231C4⋊C4(C2×D19)⋊C412yes—
232C22⋊C4—22no—
233C42—22no—
234C42C2×D7611yescharacteristic
235C42D4×D1911yescharacteristic
236C42#6454311yescharacteristic
237C42C2×C22⋊D1911yescharacteristic
238C23(C22⋊D19)⋊C411yescharacteristic
239Q8—42no—
240Q8—81no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—762no—
247C2×C4—761no—
248C2×C4—761no—
249C2×C4—1521no—
250C2×C4(C22⋊D19)⋊C411yescharacteristic
251C2×C4#1059732811yescharacteristic
252C2×C4#1059733211yescharacteristic
253C2×C4C2×(C2×D19)⋊C411yescharacteristic
254C2×C4#1059738511yescharacteristic
255C2×C4#1059738511yescharacteristic
256C8—81no—
257C8—81no—
258C8—762no—
259C8—762no—
260C8—762no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22#1192642111yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—21no—
271C4—42no—
272C4—42no—
273C4—1521no—
274C4—1521no—
275C2—41no—
276C2#1456399511yescharacteristic
277C2#1456412711yescharacteristic
278C2#1456418511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1554C2
socleC22×C19#386
prime radicalC23×C19C4×D4
cosocleC2×C42×C19C23
hypercenter#1554D19
hypocenterC19#9336
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1554

Complements

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

NH ≅ G/Ntype
205. C19#9336semidirect

Maximal subgroups

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

subgroupindex
#145748372
#145727412
#145622612
#145619902
C19⋊#13082
#145614972
C19×#15542
#933619