Finite Group Databasebeta

← #18080221

Subgroups — #18080221

Order 4864.

468 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 103 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#14572720C211yesmaximal, characteristic
2#14568620C211yesmaximal, characteristic
3#14562360C212yesmaximal
4#14561490C212yesmaximal
5C19×#1467C211yesmaximal, characteristic
6C2×#10597315C2211yescharacteristic
7C2×#10597390C412yes—
8#11926675—24no—
9#11926601—21no—
10#11926601C2212yes—
11#11926597—21no—
12#11926474—21no—
13#11926474—21no—
14#11926449C412yes—
15#11926442—21no—
16#11926442—21no—
17C4×C4⋊Dic19C2211yescharacteristic
18#11926292—24no—
19C2×C4×Q8×C19C2211yescharacteristic
20C19×#432C2212yes—
21C19×#324—21no—
22C19×#324—21no—
23C22×Q8×C19C2×C411yescharacteristic
24C22×Dic38C2×C412yes—
25C4×Q8×C19—22no—
26C4×Q8×C19—22no—
27C2×C4⋊C4×C19C2×C411yescharacteristic
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C4⋊C4×C19D411yescharacteristic
30C2×C42×C19D411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19C2311yescharacteristic
33#10597390—44no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19—21no—
37C2×Dic19⋊C4—22no—
38C2×Dic19⋊C4—22no—
39C2×C4×Dic19C2×C412yes—
40#10597315—22no—
41#10597315—22no—
42C19×C4⋊C8—22no—
43C19×C22⋊C8—22no—
44C19×#97—22no—
45C19⋊#95—22no—
46C19⋊#95—22no—
47C19⋊#95—21no—
48C22⋊(C19⋊C8)—22no—
49C4⋊(C19⋊C8)—22no—
50C4⋊(C19⋊C8)—22no—
51C4⋊(C19⋊C8)D414yes—
52#10597260—22no—
53#10597260—22no—
54C4×C19⋊C8—22no—
55C2×Q8×C19—22no—
56C2×Q8×C19—22no—
57C2×Q8×C19—41no—
58C22×C4×C19C22⋊C411yescharacteristic
59C22×C4×C19C22⋊C411yescharacteristic
60C22×C4×C19C22⋊C411yescharacteristic
61C22×C4×C19C22⋊C411yescharacteristic
62C22×C4×C19C22×C411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19C2×D411yescharacteristic
65C22×Dic19—22no—
66C22×Dic19—22no—
67C2×Dic38—24no—
68C2×Dic38—42no—
69C2×Dic38—42no—
70C2×C8×C19—42no—
71C4⋊C4×C19—22no—
72C4⋊C4×C19—22no—
73C4⋊C4×C19—22no—
74C42×C19—21no—
75C42×C19—21no—
76C42×C19—21no—
77C42×C19—21no—
78C42×C19C2×D412yes—
79C42×C19#4112yes—
80C4⋊Dic19—24no—
81C4⋊Dic19—41no—
82C4⋊Dic19—42no—
83C4⋊Dic19—41no—
84Dic19⋊C4—44no—
85Dic19⋊C4—44no—
86C4×Dic19—42no—
87C2×C19⋊C8—24no—
88#9452—191nomaximal, Sylow
89C23×C19C2×C22⋊C411yescharacteristic
90Q8×C19—44no—
91C2×C4×C19—21no—
92C2×C4×C19—21no—
93C2×C4×C19—21no—
94C2×C4×C19—21no—
95C2×C4×C19—22no—
96C2×C4×C19—21no—
97C2×C4×C19—21no—
98C2×C4×C19—21no—
99C2×C4×C19—21no—
100C2×C4×C19—21no—
101C2×C4×C19—41no—
102C2×C4×C19—41no—
103C2×C4×C19—41no—
104C2×C4×C19#10012yes—
105C2×C4×C19C4×D412yes—
106C2×C4×C19#12011yescharacteristic
107C2×C4×C19#12112yes—
108C2×C4×C19#12311yescharacteristic
109C2×Dic19—24no—
110C2×Dic19—42no—
111C2×Dic19—42no—
112C2×Dic19—42no—
113C2×Dic19—42no—
114C2×Dic19—42no—
115Dic38—84no—
116C8×C19—82no—
117C19⋊C8—44no—
118#2983—191no—
119#2546—191no—
120#1558—192no—
121#1467D1911yescharacteristic
122#1285—192no—
123C22×C19—21no—
124C22×C19—21no—
125C22×C19#38611yescharacteristic
126C22×C19C2×#10011yescharacteristic
127C22×C19#41311yescharacteristic
128C4×C19—21no—
129C4×C19—22no—
130C4×C19—22no—
131C4×C19—22no—
132C4×C19—41no—
133C4×C19—41no—
134C4×C19—41no—
135C4×C19#45612yes—
136Dic19—44no—
137Dic19—82no—
138C2×C4⋊Q8—192no—
139C2×C4⋊Q8—191no—
140C2×C4×Q8C2×D1911yescharacteristic
141#446—384no—
142#432—192no—
143#432—381no—
144#432C2×D1912yes—
145#431—381no—
146#398—381no—
147#398—381no—
148#391—192no—
149#389—381no—
150#389—381no—
151C4×C4⋊C4—191no—
152#333—384no—
153#324—21no—
154#324—21no—
155C2×C19—21no—
156C2×C19—21no—
157C2×C19#188611yescharacteristic
158C2×C19#190011yescharacteristic
159C2×C19#190911yescharacteristic
160C22×Q8—192no—
161C22×Q8C4×D1911yescharacteristic
162C4⋊Q8—382no—
163C4⋊Q8—382no—
164C4⋊Q8—764no—
165C4×Q8—22no—
166C4×Q8—22no—
167C2×C4⋊C4—381no—
168C2×C4⋊C4—382no—
169C2×C4⋊C4—382no—
170C2×C4⋊C4—381no—
171C2×C4⋊C4—381no—
172C2×C4⋊C4C4×D1911yescharacteristic
173C2×C4⋊C4C22⋊D1911yescharacteristic
174C2×C4⋊C4C22⋊D1911yescharacteristic
175C2×C42—192no—
176C2×C42D7611yescharacteristic
177C2×C42D7611yescharacteristic
178C2×C42C22×D1911yescharacteristic
179C4⋊C8—22no—
180C4⋊C8—194no—
181C4⋊C8—382no—
182C4⋊C8—382no—
183C22⋊C8—22no—
184C22⋊C8—382no—
185#97—22no—
186#97—382no—
187#97—382no—
188C4×C8—382no—
189#95—382no—
190#95—382no—
191#95—381no—
192C19#945211yescharacteristic, complemented, Sylow
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—41no—
196C2×Q8—384no—
197C2×Q8—762no—
198C2×Q8—762no—
199C22×C4—382no—
200C22×C4—382no—
201C22×C4(C2×D19)⋊C411yescharacteristic
202C22×C4(C2×D19)⋊C411yescharacteristic
203C22×C4(C2×D19)⋊C411yescharacteristic
204C22×C4(C2×D19)⋊C411yescharacteristic
205C22×C4C2×C4×D1911yescharacteristic
206C22×C4C2×D7611yescharacteristic
207C22×C4C2×C22⋊D1911yescharacteristic
208C2×C8—42no—
209C2×C8—384no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—384no—
214C4⋊C4—764no—
215C4⋊C4—762no—
216C4⋊C4—764no—
217C4⋊C4—761no—
218C4⋊C4—761no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—762no—
224C42D4×D1912yes—
225C42#6454312yes—
226C23C2×(C2×D19)⋊C411yescharacteristic
227Q8—44no—
228Q8—1524no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—384no—
243C2×C4—762no—
244C2×C4—762no—
245C2×C4—762no—
246C2×C4—762no—
247C2×C4—762no—
248C2×C4#1059728012yes—
249C2×C4(C22⋊D19)⋊C412yes—
250C2×C4#1059732811yescharacteristic
251C2×C4#1059733211yescharacteristic
252C2×C4#1059738512yes—
253C8—82no—
254C8—764no—
255C22—21no—
256C22—21no—
257C22#1192642111yescharacteristic
258C22C2×#1059728011yescharacteristic
259C22#1192652611yescharacteristic
260C4—22no—
261C4—22no—
262C4—22no—
263C4—21no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—764no—
268C4—1522no—
269C4#1192672912yes—
270C2—21no—
271C2—21no—
272C2#1456402611yescharacteristic
273C2#1456409611yescharacteristic
274C2#1456415511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1467C2
socleC22×C19#386
prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1467D19
hypocenterC19#9452
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
192. C19#9452semidirect

Maximal subgroups

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

subgroupindex
#145727202
#145686202
#145623602
#145614902
C19×#14672
#945219