Finite Group Databasebeta

← #18070809

Subgroups — #18070809

Order 4864.

468 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 127 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#14563384C211yesmaximal, characteristic
2#14563384C211yesmaximal, characteristic
3#14561458C214yesmaximal
4C4×C19×C4⋊Q8C211yesmaximal, characteristic
5C2×#10597260—21no—
6C2×#10597260—21no—
7#11926299—21no—
8#11926299—21no—
9#11926299C2212yes—
10#11926299C2212yes—
11C2×C19×C4⋊Q8C411yescharacteristic
12C2×C4×Q8×C19—21no—
13C19×#391—21no—
14C19×#389—21no—
15C19×#389C2212yes—
16C19×#384C411yescharacteristic
17C4×C4⋊C4×C19—21no—
18C4×C4⋊C4×C19C412yes—
19C43×C19C2211yescharacteristic
20C22×Q8×C19—21no—
21C19×C4⋊Q8—24no—
22C4×Q8×C19—44no—
23C2×C4⋊C4×C19—21no—
24C2×C4⋊C4×C19—21no—
25C2×C4⋊C4×C19—21no—
26C2×C4⋊C4×C19—22no—
27C2×C4⋊C4×C19C2×C412yes—
28C2×C4⋊C4×C19C2×C412yes—
29C2×C42×C19—22no—
30C2×C42×C19C2×C411yescharacteristic
31C2×C42×C19C2×C411yescharacteristic
32C2×C42×C19D411yescharacteristic
33C2×C42×C19D411yescharacteristic
34C2×C42×C19D411yescharacteristic
35C2×C42×C19D411yescharacteristic
36C2×C42×C19C2311yescharacteristic
37C22×C19⋊C8—22no—
38C22×C19⋊C8—22no—
39C19×#95—22no—
40C19×#95—22no—
41#10597260—24no—
42#10597260—24no—
43C2×Q8×C19—24no—
44C2×Q8×C19—42no—
45C2×Q8×C19—42no—
46C22×C4×C19—22no—
47C22×C4×C19—22no—
48C22×C4×C19C22⋊C411yescharacteristic
49C22×C4×C19C22⋊C411yescharacteristic
50C22×C4×C19C22⋊C411yescharacteristic
51C22×C4×C19C22⋊C411yescharacteristic
52C22×C4×C19C22×C411yescharacteristic
53C22×C4×C19C2×D411yescharacteristic
54C22×C4×C19C2×D411yescharacteristic
55C4⋊C4×C19—24no—
56C4⋊C4×C19—22no—
57C4⋊C4×C19—42no—
58C4⋊C4×C19—42no—
59C4⋊C4×C19—42no—
60C4⋊C4×C19—44no—
61C4⋊C4×C19M1614yes—
62C42×C19—22no—
63C42×C19—22no—
64C42×C19—22no—
65C42×C19—22no—
66C42×C19—22no—
67C42×C19—22no—
68C42×C19—41no—
69C42×C19—44no—
70C2×C19⋊C8—24no—
71C2×C19⋊C8—24no—
72C2×C19⋊C8—42no—
73C2×C19⋊C8—42no—
74C2×C19⋊C8—42no—
75C2×C19⋊C8—42no—
76#7638—191nomaximal, Sylow
77C23×C19C2×C22⋊C411yescharacteristic
78Q8×C19—48no—
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—21no—
86C2×C4×C19—21no—
87C2×C4×C19—21no—
88C2×C4×C19—21no—
89C2×C4×C19—21no—
90C2×C4×C19—21no—
91C2×C4×C19—24no—
92C2×C4×C19—21no—
93C2×C4×C19—21no—
94C2×C4×C19—21no—
95C2×C4×C19—42no—
96C2×C4×C19—42no—
97C2×C4×C19—42no—
98C2×C4×C19—42no—
99C2×C4×C19—42no—
100C2×C4×C19#10112yes—
101C2×C4×C19#10412yes—
102C2×C4×C19#10412yes—
103C2×C4×C19C2×M1612yes—
104C2×C4×C19AGL(1,ℤ/8)12yes—
105C2×C4×C19#13712yes—
106C19⋊C8—44no—
107C19⋊C8—44no—
108C4×C4⋊Q8D1911yescharacteristic
109#1745—191no—
110#1745—191no—
111#1271—194no—
112C22×C19#40711yescharacteristic
113C22×C19#41011yescharacteristic
114C22×C19C2×#10111yescharacteristic
115C22×C19#41811yescharacteristic
116C22×C19#41911yescharacteristic
117C22×C19C2×#10411yescharacteristic
118C22×C19C2×#10411yescharacteristic
119C4×C19—22no—
120C4×C19—22no—
121C4×C19—22no—
122C4×C19—22no—
123C4×C19—22no—
124C4×C19—22no—
125C4×C19—44no—
126C4×C19—41no—
127C4×C19—82no—
128C2×C4⋊Q8Dic1911yescharacteristic
129C2×C4×Q8—21no—
130C2×#97—381no—
131C2×#97—381no—
132#391—21no—
133#389—21no—
134#389C2×D1912yes—
135#384Dic1911yescharacteristic
136C4×C4⋊C4—21no—
137C4×C4⋊C4Dic1912yes—
138C43C2×D1911yescharacteristic
139#336—192no—
140#336—192no—
141#336—381no—
142#336—381no—
143C2×C19#146711yescharacteristic
144C2×C19#149011yescharacteristic
145C2×C19#149111yescharacteristic
146C2×C19#150511yescharacteristic
147C2×C19#150611yescharacteristic
148C2×C19#152611yescharacteristic
149C2×C19#155611yescharacteristic
150C22×Q8—21no—
151C22×C8—382no—
152C22×C8—382no—
153C4⋊Q8—24no—
154C4×Q8—44no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4C2×Dic1912yes—
160C2×C4⋊C4C2×Dic1912yes—
161C2×C42—22no—
162C2×C42C2×Dic1911yescharacteristic
163C2×C42C2×Dic1911yescharacteristic
164C2×C42C22⋊D1911yescharacteristic
165C2×C42C22⋊D1911yescharacteristic
166C2×C42C22⋊D1911yescharacteristic
167C2×C42C22⋊D1911yescharacteristic
168C2×C42C22×D1911yescharacteristic
169#97—384no—
170#97—384no—
171#95—22no—
172#95—22no—
173C19#763811yescharacteristic, complemented, Sylow
174C2×Q8—24no—
175C2×Q8—42no—
176C2×Q8—42no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4C22⋊Dic1911yescharacteristic
180C22×C4C22⋊Dic1911yescharacteristic
181C22×C4C22⋊Dic1911yescharacteristic
182C22×C4C22⋊Dic1911yescharacteristic
183C22×C4C22×Dic1911yescharacteristic
184C22×C4C2×C22⋊D1911yescharacteristic
185C22×C4C2×C22⋊D1911yescharacteristic
186C2×C8—384no—
187C2×C8—384no—
188C2×C8—762no—
189C2×C8—762no—
190C2×C8—762no—
191C2×C8—762no—
192C4⋊C4—24no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—44no—
197C4⋊C4—42no—
198C4⋊C4#6452014yes—
199C42—22no—
200C42—22no—
201C42—22no—
202C42—22no—
203C42—22no—
204C42—22no—
205C42—41no—
206C42—44no—
207C23C2×C22⋊Dic1911yescharacteristic
208Q8—48no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—24no—
224C2×C4—21no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4#1059729312yes—
231C2×C4#1059729412yes—
232C2×C4#1059729412yes—
233C2×C4C2×#6452012yes—
234C2×C4#1059737812yes—
235C2×C4#1059738812yes—
236C8—764no—
237C8—764no—
238C22#1192650811yescharacteristic
239C22#1192651811yescharacteristic
240C22C2×#1059729311yescharacteristic
241C22#1192654911yescharacteristic
242C22#1192655311yescharacteristic
243C22C2×#1059729411yescharacteristic
244C22C2×#1059729411yescharacteristic
245C4—22no—
246C4—22no—
247C4—22no—
248C4—22no—
249C4—22no—
250C4—22no—
251C4—44no—
252C4—41no—
253C4—82no—
254C2#1456197911yescharacteristic
255C2#1456207811yescharacteristic
256C2#1456208211yescharacteristic
257C2#1456214311yescharacteristic
258C2#1456214711yescharacteristic
259C2#1456223011yescharacteristic
260C2#1456235211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC4×C19×C4⋊Q8C2
socle, prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenterC4×C4⋊Q8D19
hypocenterC19#7638
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
173. C19#7638semidirect

Maximal subgroups

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

subgroupindex
#145633842
#145614582
C4×C19×C4⋊Q82
#763819