Finite Group Databasebeta

← #18083471

Subgroups — #18083471

Order 4864.

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

normal subgroups only

This group has 564 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#14574945C211yesmaximal, characteristic, complemented
2#14573726C212yesmaximal, complemented
3#14562245C212yesmaximal, complemented
4#14561505C211yesmaximal, characteristic, complemented
5C19×#1955C211yesmaximal, characteristic, complemented
6#11927094C2212yes—
7#11926862—22no—
8#11926834—22no—
9#11926825—22no—
10#11926780—22no—
11#11926740—22no—
12#11926739—22no—
13#11926678—22no—
14#11926654—24no—
15#11926601C2212yes—
16#11926283—24no—
17C2×C4×D4×C19C2211yescharacteristic
18C2×C19×C4⋊C8C2211yescharacteristic
19C2×C19×C22⋊C8—22no—
20C2×C19×#97C2211yescharacteristic
21C22×D4×C19D411yescharacteristic
22C23×C4×C19—21no—
23C2×#64541—22no—
24C22×C8×C19—21no—
25C22×C8×C19D412yes—
26C4×D4×C19—22no—
27C4×D4×C19—22no—
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C22⋊C4×C19—21no—
30C2×C42×C19C2311yescharacteristic
31C2×#64525—24no—
32#10597376—22no—
33#10597376—22no—
34C2×D152—22no—
35#10597321—22no—
36#10597320D412yes—
37C4×D76—22no—
38C4×D76—22no—
39#10597315D412yes—
40C19×C4⋊C8—22no—
41C19×C22⋊C8—44no—
42C19×#97—22no—
43#10597289—24no—
44C22⋊(C19⋊C8)—22no—
45#10597278—24no—
46#10597275—22no—
47#10597266—24no—
48#10597265—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×C22⋊D19—42no—
63#64541—84no—
64C2×D76—22no—
65C2×D76—22no—
66C2×D76—22no—
67C2×C4×D19—42no—
68C2×Dic38—22no—
69C2×C8×C19—22no—
70C2×C8×C19—22no—
71C2×C8×C19—41no—
72C2×C8×C19—41no—
73C2×C8×C19—42no—
74C4⋊C4×C19—22no—
75C22⋊C4×C19—42no—
76C42×C19C2×D412yes—
77C42×C19C2×D412yes—
78#64525—48no—
79(C2×D19)⋊C4—42no—
80(C2×D19)⋊C4—42no—
81C4⋊Dic19—22no—
82C4⋊Dic19—22no—
83C2×C19⋊C8—24no—
84D152—82no—
85#10026—191nomaximal, Sylow
86C23×C19—22no—
87C23×C19—42no—
88C23×C19—41no—
89C23×C19—41no—
90C23×C19—42no—
91C23×C19#12111yescharacteristic
92C22×D19—42no—
93D4×C19—24no—
94D4×C19—42no—
95C2×C4×C19—22no—
96C2×C4×C19—21no—
97C2×C4×C19—21no—
98C2×C4×C19—41no—
99C2×C4×C19—42no—
100C2×C4×C19—41no—
101C2×C4×C19—82no—
102C2×C4×C19—81no—
103C2×C4×C19—81no—
104C2×C4×C19#12011yescharacteristic
105C2×C4×C19#12012yes—
106C2×C4×C19#12112yes—
107C2×C4×C19#12711yescharacteristic
108C22⋊D19—84no—
109C2×Dic19—42no—
110D76—44no—
111D76—42no—
112D76—42no—
113D76—82no—
114C4×D19—84no—
115Dic38—82no—
116C8×C19—42no—
117C8×C19—42no—
118C19⋊C8—44no—
119#3245—191no—
120#3109—192no—
121#1955D1911yescharacteristic, complemented
122#1530—192no—
123#1290—191no—
124C22×C19—21no—
125C22×C19—21no—
126C22×C19—44no—
127C22×C19—42no—
128C22×C19—82no—
129C22×C19—81no—
130C22×C19—81no—
131C22×C19#39211yescharacteristic
132C22×C19#47212yes—
133C2×D19—82no—
134C2×D19—82no—
135C2×D19—82no—
136C4×C19—21no—
137C4×C19—22no—
138C4×C19—22no—
139C4×C19—81no—
140C4×C19#45311yescharacteristic
141C4×C19#45411yescharacteristic
142Dic19—82no—
143#532—192no—
144C2×C4×D4C2×D1911yescharacteristic
145#481—382no—
146#476—382no—
147#474—382no—
148#466—382no—
149#459—382no—
150#459—382no—
151#447—382no—
152#442—384no—
153#432—192no—
154C2×C4⋊C8C2×D1911yescharacteristic
155C2×C22⋊C8—22no—
156C2×#97C2×D1911yescharacteristic
157#329—384no—
158C2×C19—22no—
159C2×C19—82no—
160C2×C19#200611yescharacteristic
161C2×C19#201011yescharacteristic
162C2×C19#201811yescharacteristic
163D19—162no—
164C2×#41—382no—
165C22×D4D7611yescharacteristic
166C23×C4—21no—
167C2×D8—382no—
168C2×D8—384no—
169C22×C8—21no—
170C22×C8C22⋊D1912yes—
171C4⋊Q8—192no—
172#127—192no—
173#124—382no—
174#121—382no—
175#121—382no—
176C4×D4—22no—
177C4×D4—22no—
178C4×D4—382no—
179C4×D4—382no—
180C2×C4⋊C4D7611yescharacteristic
181C2×C22⋊C4—21no—
182C2×C42C22×D1911yescharacteristic
183#107—382no—
184#106—384no—
185C4⋊C8—22no—
186C4⋊C8—382no—
187#102—384no—
188#102—384no—
189#102—384no—
190C22⋊C8—44no—
191C22⋊C8—382no—
192#97—22no—
193#97—194no—
194C19#1002611yescharacteristic, complemented, Sylow
195C24—21no—
196#41—1524no—
197C2×Q8—382no—
198C2×D4—22no—
199C2×D4—42no—
200C2×D4—382no—
201C2×D4—382no—
202C2×D4—382no—
203C2×D4—762no—
204C22×C4—21no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—762no—
210C22×C4C2×D7611yescharacteristic
211C22×C4#6454111yescharacteristic
212C22×C4C2×C22⋊D1911yescharacteristic
213D8—768no—
214D8—1522no—
215C2×C8—22no—
216C2×C8—22no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—42no—
220C2×C8—384no—
221C4⋊C4—22no—
222C4⋊C4—382no—
223C4⋊C4—382no—
224C22⋊C4—42no—
225C22⋊C4—762no—
226C22⋊C4—762no—
227C42D4×D1912yes—
228C42D4×D1912yes—
229C23—22no—
230C23—42no—
231C23—41no—
232C23—42no—
233C23—41no—
234C23—762no—
235C23#1059737611yescharacteristic
236Q8—1522no—
237D4—24no—
238D4—42no—
239D4—764no—
240D4—762no—
241D4—762no—
242D4—1522no—
243D4—1524no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—82no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—762no—
254C2×C4—1524no—
255C2×C4#1059732812yes—
256C2×C4#1059733012yes—
257C2×C4#1059738311yescharacteristic
258C2×C4#1059738611yescharacteristic
259C8—42no—
260C8—42no—
261C8—764no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—42no—
266C22—82no—
267C22—81no—
268C22—81no—
269C22—1522no—
270C22—1522no—
271C22—1522no—
272C22#1192645311yescharacteristic
273C22#1192681412yes—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—81no—
278C4—1522no—
279C4#1192671111yescharacteristic
280C4#1192671611yescharacteristic
281C2—22no—
282C2—82no—
283C2—3042no—
284C2#1456467611yescharacteristic
285C2#1456470211yescharacteristic
286C2#1456474411yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1955C2
socleC22×C19#392
hypercenter#1955D19
hypocenterC19#10026
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. #14574945C2semidirect
2. #14573726C2semidirect
3. #14562245C2semidirect
4. #14561505C2semidirect
5. C19×#1955C2semidirect
121. #1955D19semidirect
194. C19#10026semidirect

Maximal subgroups

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

subgroupindex
#145749452
#145737262
#145622452
#145615052
C19×#19552
#1002619