Finite Group Databasebeta

← #34068210

Subgroups — #34068210

Order 19328.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#23752877C211yesmaximal, characteristic, complemented
2#23752409C211yesmaximal, characteristic, complemented
3#23752404C211yesmaximal, characteristic
4#23751958C211yesmaximal, characteristic, complemented
5#23751944C211yesmaximal, characteristic, complemented
6#23751941C211yesmaximal, characteristic, complemented
7#486×C151C211yesmaximal, characteristic, complemented
8C2×Q8×D151—21no—
9C2×#14558992—21no—
10C2×#14558989—21no—
11#18012738—21no—
12#18012717—22no—
13#18012715—21no—
14C4×Dic302C2211yescharacteristic
15C4×D604C2211yescharacteristic
16#18012701—21no—
17C4⋊(C151⋊C8)C2211yescharacteristic
18C4⋊(C151⋊C8)C2211yescharacteristic
19#18012660—21no—
20#18012660—21no—
21C4⋊Q8×C151C2211yescharacteristic
22#127×C151C2211yescharacteristic
23#102×C151—22no—
24C4×C8×C151C2211yescharacteristic
25C2×Dic302—22no—
26C2×Dic302D411yescharacteristic
27Q8×D151—42no—
28Q8×D151—42no—
29C2×D604D411yescharacteristic
30C2×C4×D151—22no—
31C2×C4×D151—21no—
32#14558992—42no—
33#14558989—42no—
34C2×C151⋊C8—21no—
35C2×C151⋊C8—21no—
36C4⋊Dic151D411yescharacteristic
37C4⋊Dic151D411yescharacteristic
38Dic151⋊C4—22no—
39Dic151⋊C4—21no—
40(C2×D151)⋊C4—22no—
41(C2×D151)⋊C4—21no—
42C4×Dic151—21no—
43C2×Q8×C151—21no—
44C2×D4×C151—21no—
45C2×D4×C151—21no—
46C2×D4×C151—21no—
47C2×C8×C151—21no—
48C4⋊C4×C151—21no—
49C4⋊C4×C151D412yes—
50C42×C151C2311yescharacteristic
51C22×D151—21no—
52Dic302—21no—
53Dic302—44no—
54Dic302D812yescomplemented
55D604—21no—
56D604SD1612yescomplemented
57C2×Dic151—21no—
58C2×Dic151—21no—
59C2×Dic151—21no—
60C4×D151—44no—
61C4×D151—41no—
62C4×D151—41no—
63C151⋊C8—41no—
64C151⋊C8—41no—
65C23×C151—41no—
66Q8×C151—41no—
67Q8×C151—41no—
68D4×C151—42no—
69D4×C151—41no—
70D4×C151—41no—
71D4×C151—41no—
72D4×C151—41no—
73C2×C4×C151—22no—
74C2×C4×C151C2×D411yescharacteristic
75C2×C4×C151C2×D411yescharacteristic
76C2×C4×C151C2×D411yescharacteristic
77C8×C151—41no—
78C22×C151—81no—
79C22×C151—81no—
80C22×C151—81no—
81C22×C151#12011yescharacteristic
82C2×D151—22no—
83C2×D151—41no—
84C2×D151—41no—
85C4×C151—21no—
86C4×C151—42no—
87C4×C151C2×D811yescharacteristic
88C4×C151C2×SD1611yescharacteristic
89C4×C151AGL(1,ℤ/8)11yescharacteristic
90C4×C151#13711yescharacteristic
91Dic151—22no—
92Dic151—41no—
93Dic151—41no—
94C2×C151—161no—
95C2×C151#44711yescharacteristic
96C2×C151#44811yescharacteristic
97C2×C151#45411yescharacteristic
98D151—42no—
99C151#162711yescharacteristic, complemented, Sylow
100#1627—1511nomaximal, Sylow
101D4×Q8—1511no—
102#486D15111yescharacteristic, complemented
103#460—1511no—
104#459—1511no—
105#332—1511no—
106Q8⋊C8—1511no—
107D4⋊C8—1511no—
108C22×Q8—3021no—
109C2×SD16—3021no—
110C2×D8—3021no—
111C4⋊Q8—3021no—
112C4⋊Q8C2×D15111yescharacteristic
113#127C2×D15111yescharacteristic
114C22⋊Q8—3021no—
115C22⋊Q8—3022no—
116C4×Q8—1511no—
117C4×D4—3021no—
118C4×D4—1511no—
119C4⋊C8—1511no—
120C4⋊C8—1511no—
121#102—22no—
122#102—3021no—
123#102—3021no—
124C4×C8C2×D15111yescharacteristic
125C2×Q8—21no—
126C2×Q8—3022no—
127C2×Q8—6042no—
128C2×Q8—6042no—
129C2×Q8—1511no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—1511no—
134C22×C4—3022no—
135C22×C4—3021no—
136SD16—6042no—
137D8—6042no—
138C2×C8—21no—
139C2×C8—3021no—
140C2×C8—3021no—
141C4⋊C4—21no—
142C4⋊C4—3022no—
143C4⋊C4—3021no—
144C4⋊C4—1511no—
145C4⋊C4—1511no—
146C4⋊C4C22⋊D15112yes—
147C22⋊C4—3022no—
148C22⋊C4—3021no—
149C42—3021no—
150C42C22×D15111yescharacteristic
151C23—41no—
152C23—3021no—
153Q8—41no—
154Q8—41no—
155Q8—3021no—
156Q8—6044no—
157Q8—1512no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—3021no—
164D4—1512no—
165C2×C4—22no—
166C2×C4—3021no—
167C2×C4—3021no—
168C2×C4—3021no—
169C2×C4—6044no—
170C2×C4—6041no—
171C2×C4—6041no—
172C2×C4D4×D15111yescharacteristic
173C2×C4D4×D15111yescharacteristic
174C2×C4C2×C22⋊D15111yescharacteristic
175C8—41no—
176C8—6041no—
177C8—6041no—
178C22—81no—
179C22—81no—
180C22—81no—
181C22—3022no—
182C22—6041no—
183C22—6041no—
184C22#1801270711yescharacteristic
185C4—21no—
186C4—42no—
187C4—3022no—
188C4—6041no—
189C4—6041no—
190C4D8×D15111yescharacteristic
191C4SD16×D15111yescharacteristic
192C4#1801276311yescharacteristic
193C4#1801276811yescharacteristic
194C2—161no—
195C2—6042no—
196C2#2375234411yescharacteristic
197C2#2375234911yescharacteristic
198C2#2375238411yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#486×C151C2
socleC22×C151#120
prime radical#23752404C2
hypercenter#486D151
hypocenterC151#1627
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #23752877C2semidirect
2. #23752409C2semidirect
4. #23751958C2semidirect
5. #23751944C2semidirect
6. #23751941C2semidirect
7. #486×C151C2semidirect
54. Dic302D8semidirect
56. D604SD16semidirect
99. C151#1627semidirect
102. #486D151semidirect

Maximal subgroups

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

subgroupindex
#237528772
#237524092
#237524042
#237519582
#237519442
#237519412
#486×C1512
#1627151