Finite Group Databasebeta

← #18083469

Subgroups — #18083469

Order 4864.

564 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 85 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#14573722C212yesmaximal, complemented
2#14564432C211yesmaximal, characteristic, complemented
3#14562246C212yesmaximal, complemented
4#14561505C211yesmaximal, characteristic, complemented
5C19×#3245C211yesmaximal, characteristic, complemented
6C2×C4×D76C2211yescharacteristic
7#11926860—22no—
8#11926831—22no—
9#11926736—22no—
10#11926677—22no—
11#11926654—24no—
12#11926601C2212yes—
13C2×(C2×D19)⋊C8—22no—
14C2×#10597260C2211yescharacteristic
15#11926284—24no—
16C19×#532C2212yes—
17C19×#474—22no—
18C19×#466—22no—
19C19×#459—22no—
20C2×C19×C4⋊C8C2211yescharacteristic
21C2×#41×C19—22no—
22C22×D76D411yescharacteristic
23C22×C4×D19—21no—
24C2×D8×C19—22no—
25C22×C8×C19D412yes—
26C19×C4⋊Q8D412yes—
27C19×#127D412yes—
28C19×#124—22no—
29C19×#121—22no—
30C19×#121—22no—
31C4×D4×C19—22no—
32C4×D4×C19—22no—
33C2×C42×C19C2311yescharacteristic
34C2×#64525—24no—
35C2×(C2×D19)⋊C4—21no—
36C2×C4⋊Dic19D411yescharacteristic
37C22×C19⋊C8—21no—
38C4×D76—22no—
39C4×D76—22no—
40C19×#107—22no—
41C19×C4⋊C8—22no—
42C19×#102—24no—
43#10597289—24no—
44C22⋊(C19⋊C8)—22no—
45(C2×D19)⋊C8—44no—
46#10597266—24no—
47#10597265—24no—
48C4⋊(C19⋊C8)—22no—
49#10597260—22no—
50#10597260D414yes—
51C23×D19—21no—
52#41×C19—84no—
53C2×Q8×C19—22no—
54C2×D4×C19—22no—
55C2×D4×C19—22no—
56C2×D4×C19—22no—
57C2×D4×C19—42no—
58C22×C4×C19—42no—
59C22×C4×C19C2×D411yescharacteristic
60C22×C4×C19C2×D411yescharacteristic
61C22×C4×C19#4111yescharacteristic
62C22×Dic19—21no—
63C2×D76—22no—
64C2×D76—42no—
65C2×C4×D19—42no—
66C2×C4×D19—42no—
67C2×C4×D19—41no—
68C2×C4×D19—41no—
69D8×C19—82no—
70C2×C8×C19—22no—
71C2×C8×C19—42no—
72C4⋊C4×C19—22no—
73C4⋊C4×C19—22no—
74C22⋊C4×C19—42no—
75C22⋊C4×C19—42no—
76C42×C19C2×D412yes—
77C42×C19C2×D412yes—
78#64525—48no—
79(C2×D19)⋊C4—42no—
80C4⋊Dic19—22no—
81C2×C19⋊C8—22no—
82C2×C19⋊C8—24no—
83C2×C19⋊C8—41no—
84C2×C19⋊C8—41no—
85#10026—191nomaximal, Sylow
86C23×C19—42no—
87C23×C19#12111yescharacteristic
88C22×D19—22no—
89C22×D19—42no—
90C22×D19—41no—
91C22×D19—41no—
92C22×D19—42no—
93Q8×C19—82no—
94D4×C19—44no—
95D4×C19—42no—
96D4×C19—42no—
97D4×C19—82no—
98D4×C19—84no—
99C2×C4×C19—22no—
100C2×C4×C19—21no—
101C2×C4×C19—21no—
102C2×C4×C19—41no—
103C2×C4×C19—42no—
104C2×C4×C19—84no—
105C2×C4×C19#12012yes—
106C2×C4×C19#12011yescharacteristic
107C2×C4×C19#12112yes—
108C2×C4×C19#12711yescharacteristic
109C2×Dic19—42no—
110C2×Dic19—41no—
111D76—24no—
112D76—42no—
113C4×D19—82no—
114C4×D19—81no—
115C4×D19—81no—
116C8×C19—42no—
117C19⋊C8—42no—
118C19⋊C8—44no—
119#3245D1911yescharacteristic, complemented
120#3109—192no—
121#1955—191no—
122#1530—192no—
123#1290—191no—
124C22×C19—21no—
125C22×C19—21no—
126C22×C19—82no—
127C22×C19—82no—
128C22×C19—82no—
129C22×C19#39211yescharacteristic
130C22×C19#47212yes—
131C2×D19—44no—
132C2×D19—42no—
133C2×D19—82no—
134C2×D19—81no—
135C2×D19—81no—
136C4×C19—21no—
137C4×C19—22no—
138C4×C19—22no—
139C4×C19—82no—
140C4×C19#45311yescharacteristic
141C4×C19#45411yescharacteristic
142Dic19—81no—
143#532C2×D1912yes—
144C2×C4×D4—191no—
145#481—382no—
146#476—382no—
147#474—22no—
148#466—22no—
149#459—22no—
150#459—382no—
151#447—382no—
152#442—384no—
153#432—192no—
154C2×C4⋊C8C2×D1911yescharacteristic
155C2×C22⋊C8—382no—
156C2×#97—191no—
157#329—384no—
158C2×C19—22no—
159C2×C19—162no—
160C2×C19#200611yescharacteristic
161C2×C19#201011yescharacteristic
162C2×C19#201811yescharacteristic
163D19—82no—
164C2×#41—22no—
165C22×D4—191no—
166C23×C4—381no—
167C2×D8—22no—
168C2×D8—384no—
169C22×C8—381no—
170C22×C8C22⋊D1912yes—
171C4⋊Q8C22⋊D1912yes—
172#127C22⋊D1912yes—
173#124—22no—
174#121—22no—
175#121—22no—
176C4×D4—22no—
177C4×D4—22no—
178C4×D4—382no—
179C4×D4—382no—
180C2×C4⋊C4—191no—
181C2×C22⋊C4—381no—
182C2×C42C22×D1911yescharacteristic
183#107—22no—
184#106—384no—
185C4⋊C8—22no—
186C4⋊C8—382no—
187#102—24no—
188#102—384no—
189#102—384no—
190C22⋊C8—382no—
191C22⋊C8—764no—
192#97—194no—
193#97—382no—
194C19#1002611yescharacteristic, complemented, Sylow
195C24—381no—
196#41—84no—
197C2×Q8—22no—
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—22no—
201C2×D4—42no—
202C2×D4—382no—
203C2×D4—762no—
204C22×C4—42no—
205C22×C4—381no—
206C22×C4—762no—
207C22×C4—762no—
208C22×C4—761no—
209C22×C4—761no—
210C22×C4D4×D1911yescharacteristic
211C22×C4#6454311yescharacteristic
212C22×C4C2×C22⋊D1911yescharacteristic
213D8—82no—
214D8—768no—
215C2×C8—22no—
216C2×C8—42no—
217C2×C8—382no—
218C2×C8—384no—
219C2×C8—761no—
220C2×C8—761no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—382no—
224C22⋊C4—42no—
225C22⋊C4—42no—
226C22⋊C4—762no—
227C42D4×D1912yes—
228C42C2×C22⋊D1912yes—
229C23—42no—
230C23—382no—
231C23—762no—
232C23—761no—
233C23—762no—
234C23—761no—
235C23#1059738411yescharacteristic
236Q8—82no—
237D4—44no—
238D4—42no—
239D4—42no—
240D4—82no—
241D4—84no—
242D4—384no—
243D4—762no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—84no—
250C2×C4—762no—
251C2×C4—761no—
252C2×C4—1522no—
253C2×C4—1521no—
254C2×C4—1521no—
255C2×C4#1059738312yes—
256C2×C4#1059738512yes—
257C2×C4#1059738611yescharacteristic
258C2×C4#1059739911yescharacteristic
259C8—42no—
260C8—762no—
261C8—764no—
262C22—21no—
263C22—21no—
264C22—82no—
265C22—82no—
266C22—82no—
267C22—764no—
268C22—762no—
269C22—1522no—
270C22—1521no—
271C22—1521no—
272C22#1192645211yescharacteristic
273C22#1192681112yes—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—82no—
278C4—1521no—
279C4#1192671211yescharacteristic
280C4#1192671711yescharacteristic
281C2—22no—
282C2—162no—
283C2—1522no—
284C2#1456467711yescharacteristic
285C2#1456469911yescharacteristic
286C2#1456474211yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#3245C2
socleC22×C19#392
hypercenter#3245D19
hypocenterC19#10026
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #14573722C2semidirect
2. #14564432C2semidirect
3. #14562246C2semidirect
4. #14561505C2semidirect
5. C19×#3245C2semidirect
119. #3245D19semidirect
194. C19#10026semidirect

Maximal subgroups

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

subgroupindex
#145737222
#145644322
#145622462
#145615052
C19×#32452
#1002619