Finite Group Databasebeta

← #34078641

Subgroups — #34078641

Order 19328.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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×#18012772C211yesmaximal, characteristic
2C22×Dic604C211yesmaximal, characteristic, complemented
3#23752788C211yesmaximal, characteristic
4#23752689C211yesmaximal, characteristic, complemented
5#23752435C214yesmaximal, complemented
6#23752423C214yesmaximal, complemented
7#23752222C211yesmaximal, characteristic, complemented
8#23752209C211yesmaximal, characteristic
9#424×C151C211yesmaximal, characteristic, complemented
10C2×#14559004C2211yescharacteristic
11C22×Dic302C2211yescharacteristic
12C22×Dic302C2211yescharacteristic
13#18012772—24no—
14C2×Dic604—24no—
15C2×Dic604C2214yes—
16C2×Dic604C2212yes—
17C2×#14558993C2212yes—
18#18012739C2212yes—
19#18012727C2212yes—
20#18012723—22no—
21#18012719—22no—
22C4×Dic302C2214yes—
23#18012704—22no—
24#18012698C2211yescharacteristic
25#18012695—22no—
26#18012664C2212yes—
27#18012664C2214yes—
28#18012661C2212yes—
29C2×M16×C151C2211yescharacteristic
30C22×C8×C151C2211yescharacteristic
31#117×C151C2211yescharacteristic
32C4⋊C8×C151C2214yes—
33#14559004—22no—
34#14559004—22no—
35C2×Dic302—21no—
36C2×Dic302—21no—
37C2×Dic302—22no—
38C2×Dic302—22no—
39C2×Dic302—22no—
40C2×Dic302D414yes—
41C2×Dic302C2312yes—
42C2×Dic302C2311yescharacteristic
43C2×Dic302C2312yes—
44C2×D604C2311yescharacteristic
45C2×C22⋊D151—21no—
46C22×Dic151—21no—
47C22×Dic151—21no—
48C2×C4×D151—21no—
49Dic604—28no—
50Dic604—24no—
51#14558993—24no—
52C4⋊Dic151—24no—
53C4⋊Dic151C2312yes—
54Dic151⋊C4—24no—
55C22⋊Dic151—21no—
56(C2×D151)⋊C4—24no—
57C4×Dic151—24no—
58C4×Dic151—21no—
59C22×C4×C151C2311yescharacteristic
60M16×C151—22no—
61C2×C8×C151—22no—
62C2×C8×C151C2312yes—
63C2×C8×C151C2312yes—
64C4⋊C4×C151D412yes—
65C22⋊C4×C151D412yes—
66C42×C151C2312yes—
67C22×D151—21no—
68Dic302—24no—
69Dic302—22no—
70Dic302—22no—
71Dic302—21no—
72Dic302—22no—
73Dic302—21no—
74Dic302—42no—
75Dic302C2×D414yes—
76D604—21no—
77D604—21no—
78C22⋊D151—42no—
79C2×Dic151—24no—
80C2×Dic151—22no—
81C2×Dic151—22no—
82C2×Dic151—22no—
83C2×Dic151—21no—
84C2×Dic151—42no—
85C4×D151—42no—
86C23×C151C2×D411yescharacteristic
87C2×C4×C151C2×D412yes—
88C2×C4×C151C2×D414yes—
89C2×C4×C151C2×D411yescharacteristic
90C2×C4×C151#4112yes—
91C2×C4×C151C2411yescharacteristic
92C8×C151—22no—
93C8×C151—22no—
94C22×C151—22no—
95C22×C151#12112yes—
96C22×C151C22×D411yescharacteristic
97C2×D151—41no—
98C2×D151—42no—
99C4×C151—24no—
100C4×C151#12112yes—
101C4×C151C22×D411yescharacteristic
102C4×C151C2×#4111yescharacteristic
103Dic151—24no—
104Dic151—41no—
105Dic151—42no—
106Dic151—42no—
107C2×C151—22no—
108C2×C151C2×#12111yescharacteristic
109C2×C151#57812yes—
110D151—81no—
111C151#304411yescharacteristic, complemented, Sylow
112#3044—1511nomaximal, Sylow
113C2×#137—1511no—
114C22×Q16—1511no—
115#536—1511no—
116#519—1511no—
117#464—1514no—
118#462—1514no—
119#424D15111yescharacteristic, complemented
120#419—1511no—
121#416—1511no—
122C2×#41—1511no—
123C22×Q8—1511no—
124C22×Q8—1511no—
125#137—3024no—
126C2×Q16—3024no—
127C2×Q16—1514no—
128C2×Q16—1512no—
129C2×SD16—1512no—
130C2×M16C2×D15111yescharacteristic
131C22×C8C2×D15111yescharacteristic
132C4⋊Q8—1512no—
133#124—1512no—
134#123—3022no—
135C22⋊Q8—3022no—
136C4×Q8—3022no—
137C4×Q8—1514no—
138#117—3022no—
139#117—1511no—
140#117C2×D15111yescharacteristic
141C4⋊C8C2×D15114yes—
142#103—1512no—
143#103—1514no—
144#102—1512no—
145#41—3022no—
146#41—3022no—
147C2×Q8—3021no—
148C2×Q8—3021no—
149C2×Q8—3022no—
150C2×Q8—3022no—
151C2×Q8—3022no—
152C2×Q8—1514no—
153C2×Q8—1512no—
154C2×Q8—1511no—
155C2×Q8—1512no—
156C2×D4—3021no—
157C2×D4—1511no—
158C22×C4—3021no—
159C22×C4—3021no—
160C22×C4—3021no—
161C22×C4C22×D15111yescharacteristic
162Q16—3028no—
163Q16—3024no—
164SD16—3024no—
165M16—22no—
166C2×C8—22no—
167C2×C8C22×D15112yes—
168C2×C8C22×D15112yes—
169C4⋊C4—3024no—
170C4⋊C4—3024no—
171C4⋊C4—1512no—
172C4⋊C4D60412yes—
173C22⋊C4—3021no—
174C22⋊C4—3024no—
175C22⋊C4D60412yes—
176C42—3024no—
177C42—3021no—
178C42C22×D15112yes—
179C23—3021no—
180C23C2×D60411yescharacteristic
181Q8—3024no—
182Q8—3022no—
183Q8—3022no—
184Q8—3021no—
185Q8—3022no—
186Q8—3021no—
187Q8—6042no—
188Q8—1514no—
189D4—3021no—
190D4—3021no—
191D4—6042no—
192C2×C4—3024no—
193C2×C4—3022no—
194C2×C4—3022no—
195C2×C4—3022no—
196C2×C4—3021no—
197C2×C4—6042no—
198C2×C4—6042no—
199C2×C4D4×D15112yes—
200C2×C4C2×D60414yes—
201C2×C4C2×D60411yescharacteristic
202C2×C4#1455900512yes—
203C2×C4C23×D15111yescharacteristic
204C8—22no—
205C8—22no—
206C22—22no—
207C22—6041no—
208C22—6042no—
209C22#1801271412yes—
210C22C22×D60411yescharacteristic
211C4—24no—
212C4—3024no—
213C4—6041no—
214C4—6042no—
215C4—6042no—
216C4#1801271412yes—
217C4C2×D4×D15111yescharacteristic
218C4C2×#1455900511yescharacteristic
219C2—22no—
220C2—12081no—
221C2C2×#1801271411yescharacteristic
222C2#2375302912yes—
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#424×C151C2
socleC22×C151C22×D4
prime radicalC2×#14559004C22
hypercenter#424D151
hypocenterC151#3044
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. C22×Dic604C2semidirect
4. #23752689C2semidirect
5. #23752435C2semidirect
6. #23752423C2semidirect
7. #23752222C2semidirect
9. #424×C151C2semidirect
111. C151#3044semidirect
119. #424D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127722
C22×Dic6042
#237527882
#237526892
#237524352
#237524232
#237522222
#237522092
#424×C1512
#3044151