Finite Group Databasebeta

← #34078640

Subgroups — #34078640

Order 19328.

458 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18012770C211yesmaximal, characteristic
2C22×#14558994C211yesmaximal, characteristic, complemented
3#23752788C211yesmaximal, characteristic
4#23752434C214yesmaximal, complemented
5#23752422C214yesmaximal, complemented
6#23752239C211yesmaximal, characteristic, complemented
7#23752220C211yesmaximal, characteristic, complemented
8#23752206C211yesmaximal, characteristic
9#519×C151C211yesmaximal, characteristic, complemented
10C2×#14559004C2211yescharacteristic
11C22×Dic302C2211yescharacteristic
12#18012770—24no—
13C2×#14558994—24no—
14C2×#14558994C2214yes—
15C2×#14558994C2212yes—
16C2×#14558991C2212yes—
17C2×#14558988C2211yescharacteristic
18C22×C151⋊C8C2211yescharacteristic
19#18012739C2212yes—
20#18012727C2212yes—
21#18012723—22no—
22#18012719—22no—
23C4⋊(C151⋊C8)C2214yes—
24#18012662C2212yes—
25#18012662C2214yes—
26#18012659C2212yes—
27C22×Q8×C151C2211yescharacteristic
28C4×Q8×C151—22no—
29C4×Q8×C151C2214yes—
30#117×C151—22no—
31#117×C151C2211yescharacteristic
32#117×C151C2211yescharacteristic
33#14559004—22no—
34#14559004—22no—
35C2×Dic302—21no—
36C2×Dic302—22no—
37C2×Dic302—22no—
38C2×Dic302C2312yes—
39C2×Dic302C2311yescharacteristic
40C2×D604C2311yescharacteristic
41C2×C22⋊D151—21no—
42C22×Dic151—21no—
43C2×C4×D151—21no—
44#14558994—28no—
45#14558994—24no—
46#14558991—24no—
47#14558988—22no—
48C2×C151⋊C8—22no—
49C2×C151⋊C8C2312yes—
50C2×C151⋊C8C2312yes—
51C4⋊Dic151—24no—
52(C2×D151)⋊C4—24no—
53C2×Q8×C151—21no—
54C2×Q8×C151—22no—
55C2×Q8×C151D414yes—
56C2×Q8×C151C2312yes—
57C22×C4×C151—21no—
58C22×C4×C151C2311yescharacteristic
59C4⋊C4×C151—24no—
60C4⋊C4×C151D412yes—
61C4⋊C4×C151C2312yes—
62C22⋊C4×C151—21no—
63C22⋊C4×C151D412yes—
64C42×C151—24no—
65C42×C151—21no—
66C42×C151C2312yes—
67C22×D151—21no—
68Dic302—22no—
69Dic302—21no—
70Dic302—22no—
71Dic302—21no—
72Dic302—42no—
73D604—21no—
74D604—21no—
75C22⋊D151—42no—
76C2×Dic151—22no—
77C2×Dic151—21no—
78C2×Dic151—42no—
79C4×D151—42no—
80C151⋊C8—22no—
81C151⋊C8—22no—
82C23×C151C2×D411yescharacteristic
83Q8×C151—24no—
84Q8×C151—22no—
85Q8×C151C2×D414yes—
86C2×C4×C151—24no—
87C2×C4×C151—22no—
88C2×C4×C151—22no—
89C2×C4×C151C2×D414yes—
90C2×C4×C151C2×D411yescharacteristic
91C2×C4×C151C2×D412yes—
92C2×C4×C151#4112yes—
93C2×C4×C151C2411yescharacteristic
94C22×C151—22no—
95C22×C151#12112yes—
96C22×C151C22×D411yescharacteristic
97C2×D151—41no—
98C2×D151—42no—
99C4×C151—24no—
100C4×C151—24no—
101C4×C151—42no—
102C4×C151#12112yes—
103C4×C151C22×D411yescharacteristic
104C4×C151C2×#4111yescharacteristic
105Dic151—41no—
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#519D15111yescharacteristic, complemented
117#464—1514no—
118#462—1514no—
119#424—1511no—
120#419—1511no—
121#416—1511no—
122C2×#41—1511no—
123C22×Q8—1511no—
124C22×Q8C2×D15111yescharacteristic
125#137—3024no—
126C2×Q16—3024no—
127C2×Q16—1514no—
128C2×Q16—1512no—
129C2×SD16—1512no—
130C2×M16—1511no—
131C22×C8—1511no—
132C4⋊Q8—1512no—
133#124—1512no—
134#123—3022no—
135C22⋊Q8—3022no—
136C4×Q8—22no—
137C4×Q8C2×D15114yes—
138#117—22no—
139#117C2×D15111yescharacteristic
140#117C2×D15111yescharacteristic
141C4⋊C8—1514no—
142#103—1512no—
143#103—1514no—
144#102—1512no—
145#41—3022no—
146#41—3022no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—3021no—
150C2×Q8—3022no—
151C2×Q8—3022no—
152C2×Q8—1512no—
153C2×Q8—1511no—
154C2×Q8D60414yes—
155C2×Q8C22×D15112yes—
156C2×D4—3021no—
157C2×D4—1511no—
158C22×C4—21no—
159C22×C4—3021no—
160C22×C4—3021no—
161C22×C4C22×D15111yescharacteristic
162Q16—3028no—
163Q16—3024no—
164SD16—3024no—
165M16—3022no—
166C2×C8—3022no—
167C2×C8—1512no—
168C2×C8—1512no—
169C4⋊C4—24no—
170C4⋊C4—3024no—
171C4⋊C4C22⋊D15112yes—
172C4⋊C4C22×D15112yes—
173C22⋊C4—21no—
174C22⋊C4—3024no—
175C22⋊C4C22⋊D15112yes—
176C42—24no—
177C42—21no—
178C42C22×D15112yes—
179C23—3021no—
180C23C2×C22⋊D15111yescharacteristic
181Q8—24no—
182Q8—22no—
183Q8—3022no—
184Q8—3021no—
185Q8—3022no—
186Q8—3021no—
187Q8—6042no—
188Q8C2×D60414yes—
189D4—3021no—
190D4—3021no—
191D4—6042no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—3022no—
196C2×C4—3021no—
197C2×C4—6042no—
198C2×C4—6042no—
199C2×C4C2×C22⋊D15114yes—
200C2×C4C2×C22⋊D15111yescharacteristic
201C2×C4C2×D60412yes—
202C2×C4#1455900412yes—
203C2×C4C23×D15111yescharacteristic
204C8—3022no—
205C8—3022no—
206C22—22no—
207C22—6041no—
208C22—6042no—
209C22#1801271312yes—
210C22C22×C22⋊D15111yescharacteristic
211C4—24no—
212C4—24no—
213C4—42no—
214C4—6041no—
215C4—6042no—
216C4#1801271312yes—
217C4C22×D60411yescharacteristic
218C4C2×#1455900411yescharacteristic
219C2—22no—
220C2—12081no—
221C2C2×#1801271311yescharacteristic
222C2#2375302712yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#519×C151C2
socleC22×C151C22×D4
prime radicalC2×#14559004C22
hypercenter#519D151
hypocenterC151#3044
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. C22×#14558994C2semidirect
4. #23752434C2semidirect
5. #23752422C2semidirect
6. #23752239C2semidirect
7. #23752220C2semidirect
9. #519×C151C2semidirect
111. C151#3044semidirect
116. #519D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127702
C22×#145589942
#237527882
#237524342
#237524222
#237522392
#237522202
#237522062
#519×C1512
#3044151