Finite Group Databasebeta

← #18086614

Subgroups — #18086614

Order 4864.

388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 79 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#14562328C212yesmaximal, complemented
3#14562142C212yesmaximal, complemented
4#14561505C211yesmaximal, characteristic, complemented
5C19×#1832C211yesmaximal, characteristic, complemented
6#11927094C2212yes—
7#11926825—22no—
8#11926780—22no—
9#11926740—22no—
10#11926601C2212yes—
11#11926292—22no—
12#11926287—22no—
13#11926277—24no—
14C2×C19×C4⋊C8C2211yescharacteristic
15C2×C19×C4⋊C8C2211yescharacteristic
16C19×#376C2211yescharacteristic
17C19×#336—22no—
18C2×#64541—22no—
19C22×C8×C19—21no—
20C22×C8×C19D412yes—
21C2×C42×C19—21no—
22C2×C42×C19C2311yescharacteristic
23#10597376—22no—
24#10597376—22no—
25C2×D152—22no—
26#10597321—22no—
27#10597320D412yes—
28C4×D76—22no—
29C4×D76—22no—
30#10597315D412yes—
31C19×C4⋊C8—22no—
32C19×C4⋊C8—22no—
33C19×#95—21no—
34C19×#95D412yes—
35C22⋊(C19⋊C8)—22no—
36#10597278—24no—
37#10597275—22no—
38C4⋊(C19⋊C8)—22no—
39#10597260—22no—
40C22×C4×C19—22no—
41C22×C4×C19C2×D411yescharacteristic
42C22×C4×C19C2×D411yescharacteristic
43C22×C4×C19#4111yescharacteristic
44C2×C22⋊D19—42no—
45#64541—84no—
46C2×D76—22no—
47C2×D76—22no—
48C2×D76—22no—
49C2×C4×D19—42no—
50C2×Dic38—22no—
51C2×C8×C19—22no—
52C2×C8×C19—42no—
53C2×C8×C19—42no—
54C2×C8×C19—41no—
55C42×C19—41no—
56C42×C19—41no—
57C42×C19C2×D412yes—
58C42×C19#4112yes—
59(C2×D19)⋊C4—42no—
60(C2×D19)⋊C4—42no—
61C4⋊Dic19—22no—
62C4⋊Dic19—22no—
63C2×C19⋊C8—42no—
64D152—82no—
65#10513—191nomaximal, Sylow
66C23×C19#12111yescharacteristic
67C22×D19—42no—
68C2×C4×C19—22no—
69C2×C4×C19—21no—
70C2×C4×C19—21no—
71C2×C4×C19—41no—
72C2×C4×C19—42no—
73C2×C4×C19—42no—
74C2×C4×C19—42no—
75C2×C4×C19#12011yescharacteristic
76C2×C4×C19#12112yes—
77C2×C4×C19#12312yes—
78C2×C4×C19#12411yescharacteristic
79C22⋊D19—84no—
80C2×Dic19—42no—
81D76—42no—
82D76—42no—
83D76—82no—
84D76—82no—
85C4×D19—84no—
86Dic38—82no—
87C8×C19—42no—
88C8×C19—81no—
89C19⋊C8—82no—
90#3245—191no—
91#1832D1911yescharacteristic, complemented
92#1551—192no—
93#1505—192no—
94#1290—191no—
95C22×C19—21no—
96C22×C19—21no—
97C22×C19#39411yescharacteristic
98C22×C19#47212yes—
99C2×D19—82no—
100C2×D19—82no—
101C2×D19—82no—
102C4×C19—22no—
103C4×C19—21no—
104C4×C19—22no—
105C4×C19—82no—
106C4×C19#45411yescharacteristic
107C4×C19#45511yescharacteristic
108Dic19—82no—
109#532—192no—
110#474—382no—
111#466—382no—
112#459—382no—
113#432—192no—
114C2×C4⋊C8C2×D1911yescharacteristic
115C2×C4⋊C8C2×D1911yescharacteristic
116#376C2×D1911yescharacteristic
117#336—22no—
118#333—382no—
119#331—382no—
120#327—384no—
121C2×C19—22no—
122C2×C19#204011yescharacteristic
123C2×C19#204511yescharacteristic
124C2×C19#205311yescharacteristic
125D19—162no—
126C2×#41—382no—
127C2×D8—382no—
128C22×C8—21no—
129C22×C8C22⋊D1912yes—
130C4⋊Q8—192no—
131#127—192no—
132#124—382no—
133#121—382no—
134#121—382no—
135C4×D4—382no—
136C4×D4—382no—
137C2×C42—21no—
138C2×C42C22×D1911yescharacteristic
139#107—382no—
140C4⋊C8—22no—
141C4⋊C8—22no—
142C4⋊C8—382no—
143#102—384no—
144C22⋊C8—382no—
145#97—382no—
146#95—21no—
147#95D7612yes—
148C19#1051311yescharacteristic, complemented, Sylow
149#41—1524no—
150C2×Q8—382no—
151C2×D4—382no—
152C2×D4—382no—
153C2×D4—382no—
154C2×D4—762no—
155C22×C4—22no—
156C22×C4—762no—
157C22×C4C2×D7611yescharacteristic
158C22×C4#6454111yescharacteristic
159C22×C4C2×C22⋊D1911yescharacteristic
160D8—1522no—
161C2×C8—22no—
162C2×C8—42no—
163C2×C8—42no—
164C2×C8—41no—
165C2×C8—762no—
166C4⋊C4—382no—
167C4⋊C4—382no—
168C22⋊C4—762no—
169C22⋊C4—762no—
170C42—41no—
171C42—41no—
172C42D4×D1912yes—
173C42#6454512yes—
174C23—762no—
175C23#1059737611yescharacteristic
176Q8—1522no—
177D4—762no—
178D4—762no—
179D4—1522no—
180D4—1522no—
181D4—1524no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—762no—
190C2×C4—1524no—
191C2×C4#1059734012yes—
192C2×C4#1059734112yes—
193C2×C4#1059738311yescharacteristic
194C2×C4#1059739311yescharacteristic
195C8—42no—
196C8—81no—
197C8—1522no—
198C22—21no—
199C22—21no—
200C22—1522no—
201C22—1522no—
202C22—1522no—
203C22#1192646111yescharacteristic
204C22#1192681412yes—
205C4—21no—
206C4—22no—
207C4—22no—
208C4—82no—
209C4—1522no—
210C4#1192671611yescharacteristic
211C4#1192672111yescharacteristic
212C2—22no—
213C2—3042no—
214C2#1456486411yescharacteristic
215C2#1456489111yescharacteristic
216C2#1456494111yescharacteristic
subgroupG/H
centerC22#11926461
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1832C2
socleC22×C19#394
prime radical#14574945C2
hypercenter#1832D19
hypocenterC19#10513
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1832

Complements

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

NH ≅ G/Ntype
2. #14562328C2semidirect
3. #14562142C2semidirect
4. #14561505C2semidirect
5. C19×#1832C2semidirect
91. #1832D19semidirect
148. C19#10513semidirect

Maximal subgroups

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

subgroupindex
#145749452
#145623282
#145621422
#145615052
C19×#18322
#1051319