Finite Group Databasebeta

← #34080546

Subgroups — #34080546

Order 19328.

370 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 109 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#23752815C212yesmaximal, complemented
2#23752514C212yesmaximal, complemented
3#23752511C212yesmaximal, complemented
4#23752465C211yesmaximal, characteristic, complemented
5#23752446C212yesmaximal, complemented
6#23752406C212yesmaximal, complemented
7#23752405C212yesmaximal, complemented
8#23752240C211yesmaximal, characteristic, complemented
9#469×C151C211yesmaximal, characteristic, complemented
10C2×D1208C2211yescharacteristic
11C2×#14558989C2212yes—
12C22×C151⋊C8C2211yescharacteristic
13#18012735C2212yes—
14#18012730C2212yes—
15#18012723—22no—
16#18012721—22no—
17#18012713C2212yes—
18#18012711—22no—
19#18012710—22no—
20D4×Dic151C2212yes—
21#18012701C2212yes—
22#18012698C2211yescharacteristic
23#18012672C2212yes—
24#18012671C2211yescharacteristic
25Dic151⋊C8C2212yes—
26Dic151⋊C8C2212yes—
27#18012661C2212yes—
28#18012660C2212yes—
29#18012659C2212yes—
30C2×D8×C151C2211yescharacteristic
31C2×M16×C151C2211yescharacteristic
32#121×C151C2212yes—
33#106×C151C2211yescharacteristic
34#102×C151C2212yes—
35C2×D604C2312yes—
36C2×C22⋊D151—22no—
37C2×C22⋊D151—22no—
38C2×C22⋊D151—22no—
39C22×Dic151—22no—
40C2×C4×D151—22no—
41D1208—41no—
42#14558989—42no—
43C2×C151⋊C8—41no—
44C2×C151⋊C8C2312yes—
45C4⋊Dic151—22no—
46C4⋊Dic151D412yes—
47C4⋊Dic151C2312yes—
48Dic151⋊C4—22no—
49C22⋊Dic151—22no—
50C22⋊Dic151D411yescharacteristic
51C22⋊Dic151D411yescharacteristic
52(C2×D151)⋊C4—22no—
53(C2×D151)⋊C4—22no—
54C4×Dic151C2312yes—
55C2×D4×C151—22no—
56C2×D4×C151C2312yes—
57C22×C4×C151C2311yescharacteristic
58D8×C151—41no—
59M16×C151—41no—
60C2×C8×C151C2311yescharacteristic
61C2×C8×C151C2311yescharacteristic
62C4⋊C4×C151C2312yes—
63C22⋊C4×C151—22no—
64C22×D151—22no—
65D604—22no—
66D604—22no—
67C22⋊D151—82no—
68C22⋊D151—82no—
69C22⋊D151—82no—
70C2×Dic151—22no—
71C2×Dic151—82no—
72C2×Dic151C2×D412yes—
73C2×Dic151C2×D412yes—
74C4×D151—82no—
75C151⋊C8—22no—
76C23×C151—22no—
77C23×C151C2×D411yescharacteristic
78D4×C151—22no—
79D4×C151—22no—
80D4×C151—82no—
81C2×C4×C151—21no—
82C2×C4×C151—21no—
83C2×C4×C151—22no—
84C2×C4×C151C2×D411yescharacteristic
85C2×C4×C151C2411yescharacteristic
86C8×C151—21no—
87C8×C151—21no—
88C22×C151—21no—
89C22×C151—22no—
90C22×C151—42no—
91C22×C151—42no—
92C22×C151—42no—
93C22×C151C22×D411yescharacteristic
94C2×D151—42no—
95C2×D151—42no—
96C2×D151—42no—
97C4×C151—21no—
98C4×C151—42no—
99C4×C151H(5,𝔽2)11yescharacteristic
100C4×C1512−1+411yescharacteristic
101Dic151—22no—
102Dic151—22no—
103Dic151—42no—
104C2×C151—41no—
105C2×C151—82no—
106C2×C151#53711yescharacteristic
107C2×C151#57612yes—
108D151—82no—
109C151#325911yescharacteristic, complemented, Sylow
110#3259—1511nomaximal, Sylow
111#540—1512no—
112#478—1512no—
113#478—1512no—
114#469—1511no—
115#469D15111yescharacteristic, complemented
116#466—1512no—
117#459—1512no—
118#459—1512no—
119#424—1511no—
120C2×D8—1512no—
121C2×D8—1511no—
122C2×D8C2×D15111yescharacteristic
123C2×M16C2×D15111yescharacteristic
124C22×C8—1511no—
125#127—1512no—
126#125—1512no—
127#123—3022no—
128#123—3022no—
129#121—3022no—
130#121—3022no—
131#121—1512no—
132#121C2×D15112yes—
133C4×D4—1512no—
134C4×D4—1512no—
135#117—1511no—
136#107—1512no—
137#106—1511no—
138#106C2×D15111yescharacteristic
139C4⋊C8—1512no—
140C4⋊C8—1512no—
141#102—1512no—
142#102—1512no—
143#102—1512no—
144#102C2×D15112yes—
145C2×D4—22no—
146C2×D4—3022no—
147C2×D4—3022no—
148C2×D4—3022no—
149C2×D4—1512no—
150C2×D4C22×D15112yes—
151C22×C4—3022no—
152C22×C4—3022no—
153C22×C4C22×D15111yescharacteristic
154D8—41no—
155D8—6041no—
156D8—6042no—
157M16—41no—
158C2×C8—6041no—
159C2×C8—1512no—
160C2×C8C22×D15111yescharacteristic
161C2×C8C22×D15111yescharacteristic
162C4⋊C4—3022no—
163C4⋊C4—3022no—
164C4⋊C4—1512no—
165C4⋊C4—1512no—
166C4⋊C4C22×D15112yes—
167C22⋊C4—22no—
168C22⋊C4—3022no—
169C22⋊C4—3022no—
170C22⋊C4—3022no—
171C22⋊C4—1511no—
172C22⋊C4—1511no—
173C42—1512no—
174C23—22no—
175C23—3022no—
176C23D4×D15111yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—3022no—
181D4—3022no—
182D4—12082no—
183D4—12082no—
184D4—12082no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—3022no—
189C2×C4—1512no—
190C2×C4—1512no—
191C2×C4—12082no—
192C2×C4—12082no—
193C2×C4D4×D15111yescharacteristic
194C2×C4C23×D15111yescharacteristic
195C8—21no—
196C8—21no—
197C8—3022no—
198C22—22no—
199C22—21no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—6042no—
204C22—6042no—
205C22—6042no—
206C22C2×D4×D15111yescharacteristic
207C4—21no—
208C4—42no—
209C4—3022no—
210C4—3022no—
211C4—6042no—
212C4#1801278411yescharacteristic
213C4#1801278611yescharacteristic
214C2—41no—
215C2—82no—
216C2—12082no—
217C2#2375278911yescharacteristic
218C2#2375301612yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#469×C151C2
socleC22×C151C22×D4
hypercenter#469D151
hypocenterC151#3259
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #23752815C2semidirect
2. #23752514C2semidirect
3. #23752511C2semidirect
4. #23752465C2semidirect
5. #23752446C2semidirect
6. #23752406C2semidirect
7. #23752405C2semidirect
8. #23752240C2semidirect
9. #469×C151C2semidirect
109. C151#3259semidirect
115. #469D151semidirect

Maximal subgroups

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

subgroupindex
#237528152
#237525142
#237525112
#237524652
#237524462
#237524062
#237524052
#237522402
#469×C1512
#3259151