Finite Group Databasebeta

← #18083483

Subgroups — #18083483

Order 4864.

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

normal subgroups only

This group has 512 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
2#14573757C212yesmaximal, complemented
3#14562245C212yesmaximal, complemented
4#14561505C211yesmaximal, characteristic, complemented
5C19×#1985C211yesmaximal, characteristic, complemented
6#11927094C2212yes—
7#11926857—22no—
8#11926839—22no—
9#11926825—22no—
10#11926780—22no—
11#11926744—22no—
12#11926740—22no—
13#11926683—22no—
14#11926642—24no—
15#11926601C2212yes—
16#11926283—24no—
17C2×C4×Q8×C19C2211yescharacteristic
18C2×C19×C4⋊C8C2211yescharacteristic
19C2×C19×#97C2211yescharacteristic
20C19×#336—22no—
21C22×Q8×C19D411yescharacteristic
22C2×#64541—22no—
23C22×C8×C19—21no—
24C22×C8×C19D412yes—
25C4×Q8×C19—22no—
26C4×Q8×C19—22no—
27C2×C4⋊C4×C19—21no—
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C42×C19—21no—
30C2×C42×C19C2311yescharacteristic
31C2×#64527—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×#97—22no—
42#10597292—24no—
43C22⋊(C19⋊C8)—22no—
44#10597278—24no—
45#10597275—22no—
46#10597266—24no—
47#10597264—24no—
48C4⋊(C19⋊C8)—22no—
49#10597260D414yes—
50C2×Q8×C19—22no—
51C2×Q8×C19—42no—
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19C2×D411yescharacteristic
55C22×C4×C19C2×D411yescharacteristic
56C22×C4×C19#4111yescharacteristic
57C2×C22⋊D19—42no—
58#64541—84no—
59C2×D76—22no—
60C2×D76—22no—
61C2×D76—22no—
62C2×C4×D19—42no—
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—
70C4⋊C4×C19—42no—
71C42×C19—41no—
72C42×C19—41no—
73C42×C19C2×D412yes—
74C42×C19C2×D412yes—
75#64527—48no—
76(C2×D19)⋊C4—42no—
77(C2×D19)⋊C4—42no—
78C4⋊Dic19—22no—
79C4⋊Dic19—22no—
80C2×C19⋊C8—24no—
81D152—82no—
82#10028—191nomaximal, Sylow
83C23×C19#12111yescharacteristic
84C22×D19—42no—
85Q8×C19—24no—
86Q8×C19—42no—
87C2×C4×C19—22no—
88C2×C4×C19—21no—
89C2×C4×C19—21no—
90C2×C4×C19—22no—
91C2×C4×C19—41no—
92C2×C4×C19—41no—
93C2×C4×C19—41no—
94C2×C4×C19—41no—
95C2×C4×C19—42no—
96C2×C4×C19#12011yescharacteristic
97C2×C4×C19#12012yes—
98C2×C4×C19#12112yes—
99C2×C4×C19#12711yescharacteristic
100C22⋊D19—84no—
101C2×Dic19—42no—
102D76—44no—
103D76—42no—
104D76—42no—
105D76—82no—
106C4×D19—84no—
107Dic38—82no—
108C8×C19—42no—
109C8×C19—42no—
110C19⋊C8—44no—
111#3245—191no—
112#3112—192no—
113#1985D1911yescharacteristic, complemented
114#1530—192no—
115#1290—191no—
116C22×C19—21no—
117C22×C19—21no—
118C22×C19#39211yescharacteristic
119C22×C19#47212yes—
120C2×D19—82no—
121C2×D19—82no—
122C2×D19—82no—
123C4×C19—21no—
124C4×C19—22no—
125C4×C19—22no—
126C4×C19—42no—
127C4×C19—81no—
128C4×C19#45511yescharacteristic
129C4×C19#45611yescharacteristic
130Dic19—82no—
131#532—192no—
132C2×C4×Q8C2×D1911yescharacteristic
133#480—382no—
134#477—382no—
135#474—382no—
136#466—382no—
137#460—382no—
138#459—382no—
139#448—382no—
140#440—384no—
141#432—192no—
142C2×C4⋊C8C2×D1911yescharacteristic
143C2×#97C2×D1911yescharacteristic
144#336—22no—
145#329—384no—
146C2×C19—22no—
147C2×C19#200711yescharacteristic
148C2×C19#201011yescharacteristic
149C2×C19#201811yescharacteristic
150D19—162no—
151C2×#41—382no—
152C22×Q8D7611yescharacteristic
153C2×SD16—384no—
154C2×D8—382no—
155C22×C8—21no—
156C22×C8C22⋊D1912yes—
157C4⋊Q8—192no—
158#127—192no—
159#124—382no—
160#121—382no—
161#121—382no—
162C4×Q8—22no—
163C4×Q8—22no—
164C4×D4—382no—
165C4×D4—382no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4D7611yescharacteristic
168C2×C42—21no—
169C2×C42C22×D1911yescharacteristic
170#107—384no—
171#107—382no—
172C4⋊C8—22no—
173C4⋊C8—382no—
174#103—384no—
175#102—384no—
176#102—384no—
177C22⋊C8—382no—
178#97—22no—
179#97—194no—
180C19#1002811yescharacteristic, complemented, Sylow
181#41—1524no—
182C2×Q8—22no—
183C2×Q8—42no—
184C2×Q8—382no—
185C2×D4—382no—
186C2×D4—382no—
187C2×D4—382no—
188C2×D4—762no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—762no—
192C22×C4C2×D7611yescharacteristic
193C22×C4#6454111yescharacteristic
194C22×C4C2×C22⋊D1911yescharacteristic
195SD16—768no—
196D8—1522no—
197C2×C8—22no—
198C2×C8—22no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—42no—
202C2×C8—384no—
203C4⋊C4—22no—
204C4⋊C4—42no—
205C4⋊C4—382no—
206C4⋊C4—382no—
207C22⋊C4—762no—
208C22⋊C4—762no—
209C42—41no—
210C42—41no—
211C42D4×D1912yes—
212C42D4×D1912yes—
213C23—762no—
214C23#1059737611yescharacteristic
215Q8—24no—
216Q8—42no—
217Q8—1522no—
218D4—764no—
219D4—762no—
220D4—762no—
221D4—1522no—
222D4—1524no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—762no—
233C2×C4—1524no—
234C2×C4#1059732812yes—
235C2×C4#1059733012yes—
236C2×C4#1059738311yescharacteristic
237C2×C4#1059738611yescharacteristic
238C8—42no—
239C8—42no—
240C8—764no—
241C22—21no—
242C22—21no—
243C22—1522no—
244C22—1522no—
245C22—1522no—
246C22#1192645311yescharacteristic
247C22#1192681412yes—
248C4—21no—
249C4—22no—
250C4—22no—
251C4—42no—
252C4—81no—
253C4—1522no—
254C4#1192672111yescharacteristic
255C4#1192672611yescharacteristic
256C2—22no—
257C2—3042no—
258C2#1456468111yescharacteristic
259C2#1456470211yescharacteristic
260C2#1456474411yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1985C2
socleC22×C19#392
prime radical#14574945C2
hypercenter#1985D19
hypocenterC19#10028
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
2. #14573757C2semidirect
3. #14562245C2semidirect
4. #14561505C2semidirect
5. C19×#1985C2semidirect
113. #1985D19semidirect
180. C19#10028semidirect

Maximal subgroups

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

subgroupindex
#145749452
#145737572
#145622452
#145615052
C19×#19852
#1002819