Finite Group Databasebeta

← #18083877

Subgroups — #18083877

Order 4864.

500 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11926953C212yesmaximal
2#14571703C211yesmaximal, characteristic
3#14564454C211yesmaximal, characteristic
4C2×#11926285C212yesmaximal
5C19×#1295C211yesmaximal, characteristic
6C2×#10597315C2211yescharacteristic
7C2×#10597316C2212yes—
8#11926953—24no—
9#11926953—24no—
10C2×#10597275—22no—
11C2×#10597274—22no—
12C2×#10597267—22no—
13C2×#10597260C2211yescharacteristic
14#11926484—22no—
15#11926476—22no—
16#11926474—22no—
17#11926285—24no—
18C2×C19×#97C2212yes—
19C19×#382C2211yescharacteristic
20C22×Dic38—21no—
21C22×C8×C19—22no—
22C2×C4⋊C4×C19D412yes—
23C2×C42×C19C2311yescharacteristic
24C2×C4⋊Dic19—22no—
25C2×C4⋊Dic19—22no—
26C2×C4⋊Dic19D412yes—
27C2×C4⋊Dic19D412yes—
28C2×Dic19⋊C4—22no—
29C2×Dic19⋊C4—22no—
30C22×C19⋊C8—21no—
31#10597316—22no—
32#10597316—22no—
33#10597316—22no—
34#10597316—22no—
35#10597315—22no—
36#10597315—21no—
37#10597315D412yes—
38C19×#97—22no—
39C19×#97D414yes—
40C19×#95—22no—
41C19⋊#95—24no—
42C19⋊#95—22no—
43#10597275—28no—
44#10597274—28no—
45#10597267—44no—
46#10597260—22no—
47C22×C4×C19—22no—
48C22×C4×C19C2×D411yescharacteristic
49C22×C4×C19C2×D412yes—
50C22×Dic19—22no—
51C22×Dic19—22no—
52C22×Dic19—41no—
53C2×Dic38—22no—
54C2×Dic38—42no—
55C2×Dic38—42no—
56C2×Dic38—41no—
57C2×C8×C19—28no—
58C2×C8×C19—24no—
59C4⋊C4×C19—42no—
60C42×C19C2×D412yes—
61C42×C19C2×D411yescharacteristic
62C42×C19#4111yescharacteristic
63C4⋊Dic19—22no—
64C4⋊Dic19—24no—
65C4⋊Dic19—22no—
66C4⋊Dic19—22no—
67C4⋊Dic19—22no—
68C4⋊Dic19—42no—
69C4⋊Dic19—82no—
70Dic19⋊C4—42no—
71Dic19⋊C4—42no—
72Dic19⋊C4—42no—
73Dic19⋊C4—42no—
74C2×C19⋊C8—22no—
75C2×C19⋊C8—41no—
76C2×C19⋊C8—41no—
77#10087—191nomaximal, Sylow
78C23×C19#12011yescharacteristic
79C2×C4×C19—21no—
80C2×C4×C19—21no—
81C2×C4×C19—24no—
82C2×C4×C19—42no—
83C2×C4×C19—44no—
84C2×C4×C19#12012yes—
85C2×C4×C19#12111yescharacteristic
86C2×C4×C19#12112yes—
87C2×C4×C19#12711yescharacteristic
88C2×Dic19—42no—
89C2×Dic19—42no—
90C2×Dic19—42no—
91C2×Dic19—42no—
92C2×Dic19—42no—
93C2×Dic19—44no—
94C2×Dic19—81no—
95C2×Dic19—81no—
96Dic38—44no—
97Dic38—82no—
98C8×C19—28no—
99C19⋊C8—42no—
100C2×#501—192no—
101#2822—191no—
102#1960—191no—
103C2×#330—192no—
104#1295D1911yescharacteristic
105C22×C19#39211yescharacteristic
106C22×C19#45311yescharacteristic
107C22×C19#45411yescharacteristic
108C22×C19#45614yes—
109C4×C19—22no—
110C4×C19—22no—
111C4×C19—21no—
112C4×C19—21no—
113C4×C19—82no—
114Dic19—82no—
115Dic19—82no—
116Dic19—82no—
117C2×C4⋊Q8—191no—
118C2×#125—192no—
119#501—384no—
120#501—384no—
121C2×#107—382no—
122C2×#106—382no—
123C2×#103—382no—
124C2×#97—191no—
125C2×#97C2×D1912yes—
126#400—382no—
127#398—382no—
128#398—382no—
129#382C2×D1911yescharacteristic
130#330—384no—
131C2×C19#166012yes—
132C2×C19#166312yes—
133C2×C19#200512yes—
134C2×C19#200611yescharacteristic
135C22×Q8—381no—
136C22×C8—22no—
137C22×C8—381no—
138C4⋊Q8—192no—
139C4⋊Q8—382no—
140C4⋊Q8—381no—
141#125—382no—
142#125—382no—
143#125—382no—
144#125—382no—
145C2×C4⋊C4—192no—
146C2×C4⋊C4—192no—
147C2×C4⋊C4—382no—
148C2×C4⋊C4—382no—
149C2×C4⋊C4—382no—
150C2×C4⋊C4—382no—
151C2×C4⋊C4D7612yes—
152C2×C42C22×D1911yescharacteristic
153#107—388no—
154#106—388no—
155#103—764no—
156#97—22no—
157#97—382no—
158#97D7614yes—
159#95—22no—
160#95—384no—
161#95—382no—
162C19#1008711yescharacteristic, complemented, Sylow
163C2×Q8—382no—
164C2×Q8—762no—
165C2×Q8—762no—
166C2×Q8—761no—
167C22×C4—22no—
168C22×C4—382no—
169C22×C4—382no—
170C22×C4—761no—
171C22×C4C2×D7611yescharacteristic
172C22×C4D4×D1912yes—
173C2×C8—28no—
174C2×C8—24no—
175C2×C8—382no—
176C2×C8—761no—
177C2×C8—761no—
178C4⋊C4—42no—
179C4⋊C4—382no—
180C4⋊C4—384no—
181C4⋊C4—382no—
182C4⋊C4—382no—
183C4⋊C4—382no—
184C4⋊C4—762no—
185C4⋊C4—762no—
186C4⋊C4—762no—
187C4⋊C4—762no—
188C4⋊C4—762no—
189C4⋊C4—1522no—
190C42C2×D7612yes—
191C42D4×D1911yescharacteristic
192C42#6454511yescharacteristic
193C23#1059732811yescharacteristic
194Q8—764no—
195Q8—1522no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—44no—
201C2×C4—762no—
202C2×C4—762no—
203C2×C4—762no—
204C2×C4—762no—
205C2×C4—762no—
206C2×C4—764no—
207C2×C4—1521no—
208C2×C4—1521no—
209C2×C4#1059732011yescharacteristic
210C2×C4#1059732812yes—
211C2×C4#1059734112yes—
212C2×C4#1059734111yescharacteristic
213C8—28no—
214C8—762no—
215C22#1192645411yescharacteristic
216C22#1192671411yescharacteristic
217C22#1192671911yescharacteristic
218C22#1192672814yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—1522no—
225C4—1522no—
226C4—1522no—
227C2#1456294712yes—
228C2#1456296412yes—
229C2#1456467412yes—
230C2#1456467911yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1295C2
socle, prime radicalC23×C19#120
hypercenter#1295D19
hypocenterC19#10087
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
162. C19#10087semidirect

Maximal subgroups

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

subgroupindex
C2×#119269532
#145717032
#145644542
C2×#119262852
C19×#12952
#1008719