Finite Group Databasebeta

← #18083495

Subgroups — #18083495

Order 4864.

520 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 83 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#14574980C211yesmaximal, characteristic, complemented
2#14573734C212yesmaximal
3#14562249C212yesmaximal, complemented
4#14561505C211yesmaximal, characteristic, complemented
5C19×#1955C211yesmaximal, characteristic
6#11927101C2212yes—
7#11926879—22no—
8#11926840—22no—
9#11926824—22no—
10#11926785—22no—
11#11926755—22no—
12#11926749—22no—
13#11926695—22no—
14#11926644—24no—
15#11926601C2212yes—
16#11926285—24no—
17C2×C4×D4×C19C2211yescharacteristic
18C2×C19×C4⋊C8C2211yescharacteristic
19C2×C19×C22⋊C8—22no—
20C2×C19×#97C2211yescharacteristic
21C22×D4×C19D411yescharacteristic
22C23×C4×C19—21no—
23C22×C8×C19—21no—
24C22×C8×C19D412yes—
25C4×D4×C19—22no—
26C4×D4×C19—22no—
27C2×C4⋊C4×C19D411yescharacteristic
28C2×C22⋊C4×C19—21no—
29C2×C42×C19C2311yescharacteristic
30C2×#64526—24no—
31#10597372—22no—
32#10597370—22no—
33#10597370—22no—
34C2×Dic76—22no—
35#10597316—22no—
36#10597315D412yes—
37#10597315D412yes—
38C4×Dic38—22no—
39C4×Dic38—22no—
40C19×C4⋊C8—22no—
41C19×C22⋊C8—44no—
42C19×#97—22no—
43#10597289—24no—
44C22⋊(C19⋊C8)—22no—
45#10597275—22no—
46#10597273—24no—
47#10597267—24no—
48#10597264—24no—
49C4⋊(C19⋊C8)—22no—
50#10597260D414yes—
51C24×C19—21no—
52C2×D4×C19—22no—
53C2×D4×C19—42no—
54C22×C4×C19—21no—
55C22×C4×C19—42no—
56C22×C4×C19—42no—
57C22×C4×C19—41no—
58C22×C4×C19—41no—
59C22×C4×C19C2×D411yescharacteristic
60C22×C4×C19C2×D411yescharacteristic
61C22×C4×C19#4111yescharacteristic
62C2×Dic38—22no—
63C2×Dic38—22no—
64C2×C8×C19—22no—
65C2×C8×C19—22no—
66C2×C8×C19—41no—
67C2×C8×C19—41no—
68C2×C8×C19—42no—
69C4⋊C4×C19—22no—
70C22⋊C4×C19—42no—
71C42×C19C2×D412yes—
72C42×C19C2×D412yes—
73C22⋊Dic19—42no—
74#64526—48no—
75C4⋊Dic19—22no—
76C4⋊Dic19—22no—
77C4⋊Dic19—22no—
78C4⋊Dic19—22no—
79Dic19⋊C4—42no—
80Dic19⋊C4—42no—
81C4×Dic19—42no—
82C2×C19⋊C8—24no—
83Dic76—82no—
84#10030—191nomaximal, Sylow
85C23×C19—22no—
86C23×C19—42no—
87C23×C19—41no—
88C23×C19—41no—
89C23×C19—42no—
90C23×C19#12111yescharacteristic
91D4×C19—24no—
92D4×C19—42no—
93C2×C4×C19—22no—
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19—41no—
97C2×C4×C19—42no—
98C2×C4×C19—41no—
99C2×C4×C19—82no—
100C2×C4×C19—81no—
101C2×C4×C19—81no—
102C2×C4×C19#12011yescharacteristic
103C2×C4×C19#12012yes—
104C2×C4×C19#12112yes—
105C2×C4×C19#12711yescharacteristic
106C2×Dic19—42no—
107C2×Dic19—42no—
108Dic38—44no—
109Dic38—42no—
110Dic38—42no—
111C8×C19—42no—
112C8×C19—42no—
113C19⋊C8—44no—
114#3249—191no—
115#3110—192no—
116#1955D1911yescharacteristic
117#1531—192no—
118#1290—191no—
119C22×C19—21no—
120C22×C19—21no—
121C22×C19—44no—
122C22×C19—42no—
123C22×C19—82no—
124C22×C19—81no—
125C22×C19—81no—
126C22×C19#39211yescharacteristic
127C22×C19#47312yes—
128C4×C19—21no—
129C4×C19—22no—
130C4×C19—22no—
131C4×C19—81no—
132C4×C19#45311yescharacteristic
133C4×C19#45411yescharacteristic
134Dic19—82no—
135Dic19—82no—
136#533—192no—
137C2×C4×D4C2×D1911yescharacteristic
138#484—382no—
139#477—382no—
140#474—382no—
141#467—382no—
142#462—382no—
143#461—382no—
144#450—382no—
145#440—384no—
146#432—192no—
147C2×C4⋊C8C2×D1911yescharacteristic
148C2×C22⋊C8—22no—
149C2×#97C2×D1911yescharacteristic
150#330—384no—
151C2×C19—22no—
152C2×C19—82no—
153C2×C19#200611yescharacteristic
154C2×C19#201011yescharacteristic
155C2×C19#202011yescharacteristic
156C22×D4D7611yescharacteristic
157C23×C4—21no—
158C2×Q16—382no—
159C2×SD16—384no—
160C22×C8—21no—
161C22×C8C22⋊D1912yes—
162C4⋊Q8—192no—
163C4⋊Q8—192no—
164#125—382no—
165C22⋊Q8—382no—
166C22⋊Q8—382no—
167C4×Q8—382no—
168C4×Q8—382no—
169C4×D4—22no—
170C4×D4—22no—
171#117—382no—
172C2×C4⋊C4D7611yescharacteristic
173C2×C22⋊C4—21no—
174C2×C42C22×D1911yescharacteristic
175#107—384no—
176#107—382no—
177C4⋊C8—22no—
178C4⋊C8—382no—
179#103—384no—
180#103—384no—
181#102—384no—
182C22⋊C8—44no—
183C22⋊C8—382no—
184#97—22no—
185#97—194no—
186C19#1003011yescharacteristic, complemented, Sylow
187C24—21no—
188C2×Q8—382no—
189C2×Q8—382no—
190C2×D4—22no—
191C2×D4—42no—
192C22×C4—21no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4C2×D7611yescharacteristic
198C22×C4#6454111yescharacteristic
199C22×C4C2×C22⋊D1911yescharacteristic
200Q16—1522no—
201SD16—768no—
202C2×C8—22no—
203C2×C8—22no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—42no—
207C2×C8—384no—
208C4⋊C4—22no—
209C4⋊C4—382no—
210C4⋊C4—382no—
211C4⋊C4—382no—
212C4⋊C4—382no—
213C4⋊C4—762no—
214C4⋊C4—762no—
215C22⋊C4—42no—
216C22⋊C4—762no—
217C42—762no—
218C42D4×D1912yes—
219C42D4×D1912yes—
220C23—22no—
221C23—42no—
222C23—41no—
223C23—42no—
224C23—41no—
225C23#1059737611yescharacteristic
226Q8—764no—
227Q8—762no—
228Q8—762no—
229D4—24no—
230D4—42no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—82no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—762no—
241C2×C4—762no—
242C2×C4#1059732812yes—
243C2×C4#1059733012yes—
244C2×C4#1059738311yescharacteristic
245C2×C4#1059738611yescharacteristic
246C8—42no—
247C8—42no—
248C8—764no—
249C22—21no—
250C22—21no—
251C22—44no—
252C22—42no—
253C22—82no—
254C22—81no—
255C22—81no—
256C22#1192645311yescharacteristic
257C22#1192681912yes—
258C4—21no—
259C4—22no—
260C4—22no—
261C4—81no—
262C4—1522no—
263C4—1522no—
264C4#1192671111yescharacteristic
265C4#1192671611yescharacteristic
266C2—22no—
267C2—82no—
268C2#1456467611yescharacteristic
269C2#1456470211yescharacteristic
270C2#1456475611yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1955C2
socleC22×C19#392
prime radicalC22×D4×C19D4
hypercenter#1955D19
hypocenterC19#10030
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #14574980C2semidirect
3. #14562249C2semidirect
4. #14561505C2semidirect
186. C19#10030semidirect

Maximal subgroups

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

subgroupindex
#145749802
#145737342
#145622492
#145615052
C19×#19552
#1003019