Finite Group Databasebeta

← #18085611

Subgroups — #18085611

Order 4864.

400 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 93 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#14564607C212yesmaximal
2#14564454C211yesmaximal, characteristic
3#14561516C211yesmaximal, characteristic
4#14561516C212yesmaximal
5C19×#2844C211yesmaximal, characteristic
6C2×#10597315C2211yescharacteristic
7C2×#10597267—21no—
8C2×#10597267—21no—
9C2×#10597260C2211yescharacteristic
10C2×#10597260C2212yes—
11#11926306—22no—
12#11926306—22no—
13C19×#400—21no—
14C19×#400—22no—
15C19×#395—21no—
16C19×#395—22no—
17C19×#382C2211yescharacteristic
18C19×#382C2212yes—
19C22×Q8×C19—21no—
20C22×Dic38—21no—
21C2×C4⋊C4×C19—21no—
22C2×C4⋊C4×C19—22no—
23C2×C4⋊C4×C19D411yescharacteristic
24C2×C4⋊C4×C19D411yescharacteristic
25C2×C4⋊C4×C19D412yes—
26C2×C4⋊C4×C19D412yes—
27C2×C42×C19C2311yescharacteristic
28C2×C4⋊Dic19—22no—
29C22×C19⋊C8—21no—
30C22×C19⋊C8—22no—
31#10597315—22no—
32#10597315—21no—
33#10597315Q812yescomplemented
34C19×#95—21no—
35C19×#95—22no—
36C19×#95—21no—
37C19×#95—22no—
38C19×#95—22no—
39C19×#95—22no—
40#10597267—42no—
41#10597267—42no—
42#10597260—22no—
43#10597260—22no—
44#10597260—22no—
45C2×Q8×C19—81no—
46C2×Q8×C19—82no—
47C22×C4×C19—21no—
48C22×C4×C19—22no—
49C22×C4×C19—21no—
50C22×C4×C19—22no—
51C22×C4×C19C2×D411yescharacteristic
52C22×C4×C19C2×D412yes—
53C22×Dic19—41no—
54C2×Dic38—22no—
55C2×Dic38—41no—
56C2×Dic38—41no—
57C2×Dic38—41no—
58C2×Dic38—41no—
59C2×Dic38—41no—
60C4⋊C4×C19—42no—
61C4⋊C4×C19—42no—
62C4⋊C4×C19—41no—
63C4⋊C4×C19—41no—
64C4⋊C4×C19—81no—
65C4⋊C4×C19—82no—
66C42×C19C2×Q811yescharacteristic
67C42×C19#4112yes—
68C42×C19#4111yescharacteristic
69C4⋊Dic19—24no—
70C4⋊Dic19—42no—
71C2×C19⋊C8—22no—
72C2×C19⋊C8—24no—
73C2×C19⋊C8—41no—
74C2×C19⋊C8—42no—
75C2×C19⋊C8—42no—
76C2×C19⋊C8—41no—
77#10359—191nomaximal, Sylow
78C23×C19#12011yescharacteristic
79Q8×C19—84no—
80C2×C4×C19—21no—
81C2×C4×C19—21no—
82C2×C4×C19—22no—
83C2×C4×C19—22no—
84C2×C4×C19—41no—
85C2×C4×C19—41no—
86C2×C4×C19—42no—
87C2×C4×C19—42no—
88C2×C4×C19—42no—
89C2×C4×C19—42no—
90C2×C4×C19—42no—
91C2×C4×C19—42no—
92C2×C4×C19—42no—
93C2×C4×C19—42no—
94C2×C4×C19C22⋊Q812yes—
95C2×C4×C19C22⋊Q811yescharacteristic
96C2×C4×C19#12412yes—
97C2×C4×C19#12411yescharacteristic
98C2×Dic19—42no—
99C2×Dic19—81no—
100C2×Dic19—81no—
101Dic38—42no—
102Dic38—42no—
103Dic38—81no—
104Dic38—81no—
105C19⋊C8—42no—
106C19⋊C8—44no—
107#2844D1911yescharacteristic
108#1993—192no—
109#1960—191no—
110#1295—191no—
111#1295—192no—
112C22×C19#39311yescharacteristic
113C22×C19#45311yescharacteristic
114C22×C19#45411yescharacteristic
115C22×C19#45512yes—
116C22×C19#45612yes—
117C4×C19—21no—
118C4×C19—21no—
119C4×C19—22no—
120C4×C19—22no—
121C4×C19—81no—
122C4×C19—82no—
123C4×C19—81no—
124C4×C19—82no—
125Dic19—82no—
126C2×C4⋊Q8—191no—
127C2×#103—381no—
128C2×#103—381no—
129C2×#97—191no—
130C2×#97—192no—
131#400—22no—
132#400—21no—
133#395—22no—
134#395—21no—
135#382C2×D1911yescharacteristic
136#382C2×D1912yes—
137#340—382no—
138#340—382no—
139C2×C19#165911yescharacteristic
140C2×C19#166011yescharacteristic
141C2×C19#166412yes—
142C2×C19#202711yescharacteristic
143C2×C19#202812yes—
144C22×Q8—21no—
145C22×Q8—381no—
146C22×C8—382no—
147C22×C8—381no—
148C4⋊Q8—192no—
149C4⋊Q8—382no—
150C4⋊Q8—381no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—382no—
154C2×C4⋊C4C22⋊D1912yes—
155C2×C4⋊C4C22⋊D1912yes—
156C2×C4⋊C4C22⋊D1911yescharacteristic
157C2×C4⋊C4C22⋊D1911yescharacteristic
158C2×C42C22×D1911yescharacteristic
159#103—762no—
160#103—762no—
161#97—382no—
162#97—382no—
163#97—382no—
164#95—22no—
165#95—21no—
166#95—21no—
167#95—22no—
168#95—22no—
169#95—22no—
170C19#1035911yescharacteristic, complemented, Sylow
171C2×Q8—81no—
172C2×Q8—82no—
173C2×Q8—382no—
174C2×Q8—761no—
175C2×Q8—761no—
176C2×Q8—761no—
177C2×Q8—761no—
178C2×Q8—761no—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—21no—
182C22×C4—22no—
183C22×C4—761no—
184C22×C4C2×C22⋊D1912yes—
185C22×C4C2×C22⋊D1911yescharacteristic
186C2×C8—382no—
187C2×C8—384no—
188C2×C8—761no—
189C2×C8—762no—
190C2×C8—762no—
191C2×C8—761no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—81no—
197C4⋊C4—82no—
198C4⋊C4—384no—
199C4⋊C4—762no—
200C42Q8×D1911yescharacteristic
201C42#6454512yes—
202C42#6454511yescharacteristic
203C23#1059739911yescharacteristic
204Q8—84no—
205Q8—762no—
206Q8—762no—
207Q8—1521no—
208Q8—1521no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—762no—
224C2×C4—1521no—
225C2×C4—1521no—
226C2×C4#1059739212yes—
227C2×C4#1059739211yescharacteristic
228C2×C4#1059739312yes—
229C2×C4#1059739311yescharacteristic
230C8—762no—
231C8—764no—
232C22#1192645511yescharacteristic
233C22#1192671211yescharacteristic
234C22#1192671711yescharacteristic
235C22#1192672212yes—
236C22#1192672712yes—
237C4—21no—
238C4—21no—
239C4—22no—
240C4—22no—
241C4—81no—
242C4—82no—
243C4—81no—
244C4—82no—
245C4—1522no—
246C2#1456294111yescharacteristic
247C2#1456294611yescharacteristic
248C2#1456296912yes—
249C2#1456478811yescharacteristic
250C2#1456479312yes—
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2844C2
socle, prime radicalC23×C19#120
hypercenter#2844D19
hypocenterC19#10359
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2844

Complements

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

NH ≅ G/Ntype
33. #10597315Q8semidirect
170. C19#10359semidirect

Maximal subgroups

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

subgroupindex
#145646072
#145644542
#145615162
C19×#28442
#1035919