Finite Group Databasebeta

← #18070332

Subgroups — #18070332

Order 4864.

260 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#11926343C211yesmaximal, characteristic
2#14564456C211yesmaximal, characteristic
3C2×C19×#356C211yesmaximal, characteristic
4C2×#10597292—21no—
5C2×#10597292—21no—
6C2×#10597293—21no—
7C2×#10597260C411yescharacteristic
8#11926410C411yescharacteristic
9#11926343—21no—
10#11926343C412yescomplemented
11C2×C19×C4⋊Q8C2211yescharacteristic
12C2×C19×#101—21no—
13C19×#356—21no—
14C19×#356C412yescomplemented
15C22×Q8×C19D411yescharacteristic
16C22×Q8×C19D411yescharacteristic
17C2×M16×C19—41no—
18C19×C4⋊Q8—41no—
19C19×C4⋊Q8C2×C411yescharacteristic
20C19×C4⋊Q8C2×C411yescharacteristic
21C19×C4⋊Q8D411yescharacteristic
22C19×C4⋊Q8Q811yescharacteristic
23C2×C4⋊C4×C19—41no—
24C2×C42×C19C2×C411yescharacteristic
25C2×C4⋊Dic19—21no—
26C2×#64520—41no—
27C22×C19⋊C8—21no—
28C19×#101—22no—
29C19×#101—41no—
30#10597293—22no—
31#10597293—41no—
32#10597292—42no—
33#10597292—42no—
34C19⋊#95—41no—
35#10597260—41no—
36C2×Q8×C19—21no—
37C2×Q8×C19—21no—
38C2×Q8×C19—41no—
39C2×Q8×C19—41no—
40C2×Q8×C19—41no—
41C2×Q8×C19—41no—
42C2×Q8×C19C22⋊C411yescharacteristic
43C2×Q8×C19C22⋊C411yescharacteristic
44C2×Q8×C19C4⋊C411yescharacteristic
45C2×Q8×C19C4⋊C411yescharacteristic
46C22×C4×C19—21no—
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19C22⋊C411yescharacteristic
50C22×Dic19—41no—
51M16×C19—42no—
52M16×C19—81no—
53C2×C8×C19—81no—
54C4⋊C4×C19—41no—
55C4⋊C4×C19—41no—
56C4⋊C4×C19—41no—
57C4⋊C4×C19—41no—
58C42×C19—21no—
59C42×C19C4211yescharacteristic
60C42×C19C4⋊C411yescharacteristic
61C4⋊Dic19—41no—
62C4⋊Dic19—41no—
63#64520—42no—
64#64520—81no—
65C2×C19⋊C8—22no—
66C2×C19⋊C8—41no—
67C2×C19⋊C8—41no—
68C2×C19⋊C8—81no—
69#7505—191nomaximal, Sylow
70C23×C19#9911yescharacteristic
71Q8×C19—41no—
72Q8×C19—41no—
73Q8×C19—41no—
74Q8×C19—41no—
75Q8×C19—81no—
76Q8×C19—81no—
77C2×C4×C19—21no—
78C2×C4×C19—21no—
79C2×C4×C19—21no—
80C2×C4×C19—21no—
81C2×C4×C19—21no—
82C2×C4×C19—21no—
83C2×C4×C19—21no—
84C2×C4×C19—21no—
85C2×C4×C19—42no—
86C2×C4×C19—41no—
87C2×C4×C19—41no—
88C2×C4×C19—41no—
89C2×C4×C19—41no—
90C2×C4×C19#9511yescharacteristic
91C2×C4×C19#9911yescharacteristic
92C2×Dic19—82no—
93C2×Dic19—81no—
94C8×C19—82no—
95C19⋊C8—42no—
96C19⋊C8—82no—
97C2×#356—191no—
98C2×#356D1911yescharacteristic
99#1960—191no—
100C22×C19—22no—
101C22×C19#34211yescharacteristic
102C22×C19#35311yescharacteristic
103C22×C19#35411yescharacteristic
104C4×C19—21no—
105C4×C19—21no—
106C4×C19—41no—
107C4×C19—41no—
108C4×C19—41no—
109C4×C19—41no—
110C4×C19—41no—
111C4×C19—41no—
112Dic19—161no—
113C2×C4⋊Q8C2×D1911yescharacteristic
114C2×#103—381no—
115C2×#103—381no—
116C2×#101—21no—
117C2×#101—381no—
118C2×#97—191no—
119#382—191no—
120#356—21no—
121#356—192no—
122#356—381no—
123#356Dic1912yescomplemented
124C2×C19—21no—
125C2×C19—21no—
126C2×C19#139311yescharacteristic
127C2×C19#141312yes—
128C22×Q8D7611yescharacteristic
129C22×Q8C22⋊D1911yescharacteristic
130C2×M16—41no—
131C2×M16—761no—
132C22×C8—381no—
133C4⋊Q8—41no—
134C4⋊Q8Dic3811yescharacteristic
135C4⋊Q8C4×D1911yescharacteristic
136C4⋊Q8C2×Dic1911yescharacteristic
137C4⋊Q8C22⋊D1911yescharacteristic
138C2×C4⋊C4—41no—
139C2×C4⋊C4—381no—
140C2×C42C4×D1911yescharacteristic
141#103—762no—
142#103—762no—
143#101—22no—
144#101—41no—
145#101—382no—
146#101—761no—
147#97—761no—
148#95—761no—
149C19#750511yescharacteristic, complemented, Sylow
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8Dic19⋊C411yescharacteristic
157C2×Q8C4⋊Dic1911yescharacteristic
158C2×Q8(C2×D19)⋊C411yescharacteristic
159C2×Q8C22⋊Dic1911yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—761no—
164C22×C4(C2×D19)⋊C411yescharacteristic
165M16—42no—
166M16—81no—
167M16—762no—
168M16—1521no—
169C2×C8—81no—
170C2×C8—382no—
171C2×C8—761no—
172C2×C8—761no—
173C2×C8—1521no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—761no—
179C4⋊C4—761no—
180C42—21no—
181C42C4×Dic1911yescharacteristic
182C42Dic19⋊C411yescharacteristic
183C23#1059726311yescharacteristic
184Q8—41no—
185Q8—41no—
186Q8—41no—
187Q8—41no—
188Q8—81no—
189Q8—81no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—42no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—1522no—
204C2×C4—1521no—
205C2×C4#1059726311yescharacteristic
206C2×C4C19⋊#9511yescharacteristic
207C8—82no—
208C8—762no—
209C8—1522no—
210C22—22no—
211C22#1192631011yescharacteristic
212C22#1192633611yescharacteristic
213C22#1192633811yescharacteristic
214C4—21no—
215C4—21no—
216C4—41no—
217C4—41no—
218C4—41no—
219C4—41no—
220C4—41no—
221C4—41no—
222C4—3041no—
223C2—21no—
224C2—21no—
225C2#1456175911yescharacteristic
226C2#1456180712yes—
subgroupG/H
centerC22#11926338
commutatorC42×C19C42
FrattiniC2×C4⋊Q8C2×D19
FittingC2×C19×#356C2
socleC22×C19#354
prime radicalC23×C19#99
cosocleC2×C19×C4⋊Q8C22
hypercenterC2×#356D19
hypocenterC19#7505
LCSG ▷ C42×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
10. #11926343C4semidirect
14. C19×#356C4semidirect
123. #356Dic19semidirect
149. C19#7505semidirect

Maximal subgroups

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

subgroupindex
C2×#119263432
#145644562
C2×C19×#3562
#750519