Finite Group Databasebeta

← #18085295

Subgroups — #18085295

Order 4864.

554 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 89 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#14575022C212yesmaximal, complemented
2#14564611C211yesmaximal, characteristic, complemented
3#14564464C212yesmaximal, complemented
4C19⋊#1309C211yesmaximal, characteristic, complemented
5C19×#3253C211yesmaximal, characteristic
6#11927101C2211yescharacteristic
7#11926836—22no—
8#11926824—22no—
9#11926788—24no—
10#11926749—22no—
11#11926741—22no—
12#11926568C2212yes—
13C2×#10597294—24no—
14C42×Dic19C2211yescharacteristic
15#11926305—22no—
16C19×#532C2212yes—
17C19×#476—22no—
18C19×#469—22no—
19C19×#459—22no—
20C19×#423C2211yescharacteristic
21C2×#41×C19—22no—
22C2×D8×C19—22no—
23C2×M16×C19D412yes—
24C19×C4⋊Q8D412yes—
25C19×#127D412yes—
26C19×#124—22no—
27C19×#121—22no—
28C19×#121—22no—
29C4×D4×C19—22no—
30C4×D4×C19—22no—
31C2×C42×C19C2311yescharacteristic
32C2×#64526—24no—
33#10597372—21no—
34#10597370—22no—
35C2×C4×Dic19—22no—
36C2×C4×Dic19—21no—
37C2×#64520D414yes—
38#10597316—21no—
39#10597315D412yes—
40C4×Dic38—22no—
41C19×#106—22no—
42C19×C4⋊C8—22no—
43C19×#102—24no—
44#10597294—48no—
45#10597289—24no—
46#10597267—24no—
47#10597264—24no—
48C4⋊(C19⋊C8)—22no—
49C4⋊(C19⋊C8)—22no—
50#41×C19—44no—
51#41×C19—44no—
52C2×Q8×C19—22no—
53C2×D4×C19—22no—
54C2×D4×C19—22no—
55C2×D4×C19—22no—
56C2×D4×C19—42no—
57C22×C4×C19—42no—
58C22×C4×C19C2×D412yes—
59C22×C4×C19C2×D411yescharacteristic
60C22×Dic19—41no—
61C2×Dic38—22no—
62D8×C19—82no—
63M16×C19—42no—
64C2×C8×C19—22no—
65C4⋊C4×C19—22no—
66C4⋊C4×C19—22no—
67C22⋊C4×C19—42no—
68C22⋊C4×C19—42no—
69C42×C19C2×D411yescharacteristic
70C42×C19C2×D412yes—
71C42×C19#4111yescharacteristic
72C22⋊Dic19—41no—
73#64526—84no—
74C4⋊Dic19—22no—
75C4⋊Dic19—22no—
76Dic19⋊C4—42no—
77C4×Dic19—24no—
78C4×Dic19—22no—
79C4×Dic19—42no—
80C4×Dic19—41no—
81C4×Dic19—41no—
82#64520—44no—
83C2×C19⋊C8—24no—
84#10301—191nomaximal, Sylow
85C23×C19—42no—
86C23×C19#12711yescharacteristic
87Q8×C19—44no—
88D4×C19—44no—
89D4×C19—42no—
90D4×C19—42no—
91D4×C19—42no—
92D4×C19—42no—
93D4×C19—84no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—21no—
97C2×C4×C19—21no—
98C2×C4×C19—42no—
99C2×C4×C19—82no—
100C2×C4×C19—82no—
101C2×C4×C19#12012yes—
102C2×C4×C19#12011yescharacteristic
103C2×C4×C19#12111yescharacteristic
104C2×C4×C19#12112yes—
105C2×Dic19—44no—
106C2×Dic19—42no—
107C2×Dic19—42no—
108Dic38—42no—
109Dic38—42no—
110C8×C19—42no—
111C19⋊C8—44no—
112#3254—192no—
113#3253D1911yescharacteristic
114#1994—191no—
115#1962—192no—
116#1309—191no—
117C22×C19—22no—
118C22×C19—21no—
119C22×C19—82no—
120C22×C19—82no—
121C22×C19—82no—
122C22×C19#39211yescharacteristic
123C4×C19—22no—
124C4×C19—21no—
125C4×C19—82no—
126C4×C19#45312yes—
127C4×C19#45412yes—
128C4×C19#45511yescharacteristic
129C4×C19#45611yescharacteristic
130Dic19—44no—
131Dic19—82no—
132#533—191no—
133#532C2×D1912yes—
134#477—382no—
135#476—22no—
136#474—382no—
137#469—22no—
138#468—384no—
139#461—382no—
140#460—382no—
141#459—22no—
142#423—192no—
143#423C2×D1911yescharacteristic
144C2×#104—384no—
145C43—191no—
146#339—382no—
147C2×C19—41no—
148C2×C19—162no—
149C2×C19#200612yes—
150C2×C19#200711yescharacteristic
151C2×#41—22no—
152C2×SD16—384no—
153C2×D8—22no—
154C2×M16—194no—
155C2×M16C22⋊D1912yes—
156C4⋊Q8—192no—
157C4⋊Q8C22⋊D1912yes—
158#127C22⋊D1912yes—
159#125—381no—
160#124—22no—
161C22⋊Q8—382no—
162#121—22no—
163#121—22no—
164C4×Q8—382no—
165C4×D4—22no—
166C4×D4—22no—
167#117—381no—
168C2×C42—382no—
169C2×C42—381no—
170C2×C42C22×D1911yescharacteristic
171#107—384no—
172#106—22no—
173C4⋊C8—22no—
174C4⋊C8—382no—
175C4⋊C8—382no—
176#104—768no—
177#103—384no—
178#102—24no—
179#102—384no—
180C19#1030111yescharacteristic, complemented, Sylow
181#41—44no—
182#41—44no—
183C2×Q8—22no—
184C2×Q8—382no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—22no—
188C2×D4—42no—
189C22×C4—42no—
190C22×C4—761no—
191C22×C4D4×D1912yes—
192C22×C4C2×C22⋊D1911yescharacteristic
193SD16—1524no—
194D8—82no—
195M16—42no—
196M16—764no—
197C2×C8—22no—
198C2×C8—384no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—382no—
202C4⋊C4—382no—
203C4⋊C4—762no—
204C22⋊C4—42no—
205C22⋊C4—42no—
206C22⋊C4—761no—
207C42—384no—
208C42—382no—
209C42—762no—
210C42—761no—
211C42—761no—
212C42D4×D1911yescharacteristic
213C42#6454311yescharacteristic
214C42C2×C22⋊D1912yes—
215C23—42no—
216C23#1059738611yescharacteristic
217Q8—44no—
218Q8—762no—
219Q8—762no—
220D4—44no—
221D4—42no—
222D4—42no—
223D4—42no—
224D4—42no—
225D4—84no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—42no—
231C2×C4—82no—
232C2×C4—82no—
233C2×C4—764no—
234C2×C4—762no—
235C2×C4—762no—
236C2×C4#1059738312yes—
237C2×C4#1059738411yescharacteristic
238C2×C4#1059738512yes—
239C2×C4#1059739911yescharacteristic
240C8—42no—
241C8—764no—
242C22—22no—
243C22—21no—
244C22—82no—
245C22—82no—
246C22—82no—
247C22#1192645211yescharacteristic
248C4—22no—
249C4—21no—
250C4—82no—
251C4—764no—
252C4—1522no—
253C4#1192671012yes—
254C4#1192671512yes—
255C4#1192672211yescharacteristic
256C4#1192672711yescharacteristic
257C2—41no—
258C2—162no—
259C2#1456467512yes—
260C2#1456468211yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3253C2
socleC22×C19#392
hypercenter#3253D19
hypocenterC19#10301
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #14575022C2semidirect
2. #14564611C2semidirect
3. #14564464C2semidirect
4. C19⋊#1309C2semidirect
180. C19#10301semidirect

Maximal subgroups

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

subgroupindex
#145750222
#145646112
#145644642
C19⋊#13092
C19×#32532
#1030119