Finite Group Databasebeta

← #34080581

Subgroups — #34080581

Order 19328.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752833C212yesmaximal, complemented
2#23752503C212yesmaximal, complemented
3#23752498C212yesmaximal, complemented
4#23752470C211yesmaximal, characteristic, complemented
5#23752465C211yesmaximal, characteristic
6#23752441C212yesmaximal, complemented
7#23752435C212yesmaximal, complemented
8#23752428C212yesmaximal, complemented
9#424×C151C211yesmaximal, characteristic, complemented
10C2×Dic604C2211yescharacteristic
11C2×#14558993C2212yes—
12C2×D1208C2211yescharacteristic
13#18012739C2212yes—
14#18012734—22no—
15#18012727C2212yes—
16#18012725—22no—
17#18012721—22no—
18#18012718C2212yes—
19#18012717—22no—
20#18012713C2212yes—
21C4×Dic302C2212yes—
22C4×D604C2212yes—
23#18012671C2211yescharacteristic
24#18012671C2211yescharacteristic
25#18012671C2212yes—
26#18012664C2212yes—
27#18012664C2212yes—
28#18012661C2212yes—
29#18012661C2212yes—
30C2×M16×C151C2211yescharacteristic
31C22×C8×C151C2211yescharacteristic
32#117×C151C2211yescharacteristic
33C4⋊C8×C151C2212yes—
34C4⋊C8×C151C2212yes—
35C2×Dic302—22no—
36C2×Dic302C2312yes—
37C2×D604C2312yes—
38C2×C22⋊D151—22no—
39C2×C4×D151—22no—
40Dic604—41no—
41#14558993—42no—
42D1208—41no—
43C4⋊Dic151—22no—
44C4⋊Dic151C2312yes—
45C4⋊Dic151C2312yes—
46Dic151⋊C4—22no—
47Dic151⋊C4—22no—
48C22⋊Dic151—22no—
49(C2×D151)⋊C4—22no—
50(C2×D151)⋊C4—22no—
51(C2×D151)⋊C4—22no—
52(C2×D151)⋊C4—22no—
53C4×Dic151—22no—
54C22×C4×C151C2311yescharacteristic
55M16×C151—41no—
56C2×C8×C151—41no—
57C2×C8×C151C2311yescharacteristic
58C2×C8×C151C2312yes—
59C2×C8×C151C2311yescharacteristic
60C4⋊C4×C151D412yes—
61C22⋊C4×C151D411yescharacteristic
62C22⋊C4×C151D411yescharacteristic
63C42×C151C2312yes—
64C22×D151—22no—
65Dic302—22no—
66Dic302—22no—
67Dic302—82no—
68D604—22no—
69D604—22no—
70C22⋊D151—82no—
71C2×Dic151—22no—
72C2×Dic151—22no—
73C2×Dic151—22no—
74C4×D151—82no—
75C23×C151C2×D411yescharacteristic
76C2×C4×C151—21no—
77C2×C4×C151—21no—
78C2×C4×C151C2×D412yes—
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D412yes—
81C2×C4×C151C2411yescharacteristic
82C8×C151—21no—
83C8×C151—22no—
84C8×C151—21no—
85C22×C151—21no—
86C22×C151—22no—
87C22×C151C22×D411yescharacteristic
88C2×D151—42no—
89C2×D151—42no—
90C2×D151—42no—
91C4×C151—21no—
92C4×C151—22no—
93C4×C151—22no—
94C4×C151H(5,𝔽2)11yescharacteristic
95C4×C1512−1+411yescharacteristic
96Dic151—42no—
97Dic151—42no—
98Dic151—42no—
99C2×C151—41no—
100C2×C151#53711yescharacteristic
101C2×C151#57712yes—
102D151—82no—
103C151#326311yescharacteristic, complemented, Sylow
104#3263—1511nomaximal, Sylow
105#542—1512no—
106#476—1512no—
107#475—1512no—
108#470—1511no—
109#469—1511no—
110#465—1512no—
111#464—1512no—
112#463—1512no—
113#424D15111yescharacteristic, complemented
114C2×Q16—1511no—
115C2×SD16—1512no—
116C2×D8—1511no—
117C2×M16C2×D15111yescharacteristic
118C22×C8C2×D15111yescharacteristic
119C4⋊Q8—1512no—
120#126—3022no—
121#124—3022no—
122#124—1512no—
123#123—3022no—
124C22⋊Q8—3022no—
125C22⋊Q8—1512no—
126#121—1512no—
127C4×Q8—1512no—
128C4×D4—1512no—
129#117C2×D15111yescharacteristic
130#106—1512no—
131#106—1511no—
132#106—1511no—
133C4⋊C8C2×D15112yes—
134C4⋊C8C2×D15112yes—
135#103—1512no—
136#103—1512no—
137#102—1512no—
138#102—1512no—
139C2×Q8—3022no—
140C2×Q8—1512no—
141C2×D4—3022no—
142C2×D4—1512no—
143C22×C4—3022no—
144C22×C4C22×D15111yescharacteristic
145Q16—6041no—
146SD16—6042no—
147D8—6041no—
148M16—41no—
149C2×C8—41no—
150C2×C8C22×D15111yescharacteristic
151C2×C8C22×D15112yes—
152C2×C8C22×D15111yescharacteristic
153C4⋊C4—3022no—
154C4⋊C4—3022no—
155C4⋊C4—3022no—
156C4⋊C4—1512no—
157C4⋊C4—1512no—
158C4⋊C4D60412yes—
159C22⋊C4—3022no—
160C22⋊C4—3022no—
161C22⋊C4—3022no—
162C22⋊C4—3022no—
163C22⋊C4—3022no—
164C22⋊C4D60411yescharacteristic
165C22⋊C4D60411yescharacteristic
166C42—3022no—
167C42C22×D15112yes—
168C23—3022no—
169C23C2×D60411yescharacteristic
170Q8—3022no—
171Q8—3022no—
172Q8—12082no—
173D4—3022no—
174D4—3022no—
175D4—12082no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—3022no—
179C2×C4—3022no—
180C2×C4—3022no—
181C2×C4—12082no—
182C2×C4C2×D60412yes—
183C2×C4C2×D60412yes—
184C2×C4C2×D60411yescharacteristic
185C2×C4C23×D15111yescharacteristic
186C8—22no—
187C8—21no—
188C8—21no—
189C22—22no—
190C22—21no—
191C22—6042no—
192C22—6042no—
193C22—6042no—
194C22C22×D60411yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—6042no—
199C4—6042no—
200C4—6042no—
201C4#1801278411yescharacteristic
202C4#1801278711yescharacteristic
203C2—41no—
204C2—12082no—
205C2#2375279311yescharacteristic
206C2#2375302412yes—
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#424×C151C2
socleC22×C151C22×D4
prime radical#23752465C2
hypercenter#424D151
hypocenterC151#3263
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
1. #23752833C2semidirect
2. #23752503C2semidirect
3. #23752498C2semidirect
4. #23752470C2semidirect
6. #23752441C2semidirect
7. #23752435C2semidirect
8. #23752428C2semidirect
9. #424×C151C2semidirect
103. C151#3263semidirect
113. #424D151semidirect

Maximal subgroups

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

subgroupindex
#237528332
#237525032
#237524982
#237524702
#237524652
#237524412
#237524352
#237524282
#424×C1512
#3263151