Finite Group Databasebeta

← #34068243

Subgroups — #34068243

Order 19328.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#23752922C211yesmaximal, characteristic
2#23752591C211yesmaximal, characteristic, complemented
3#23752499C211yesmaximal, characteristic
4#23751960C211yesmaximal, characteristic, complemented
5Q8⋊(C151⋊C8)C211yesmaximal, characteristic, complemented
6#23751939C211yesmaximal, characteristic
7#477×C151C211yesmaximal, characteristic, complemented
8C2×#14558994—22no—
9#18012739C2211yescharacteristic
10#18012731—21no—
11#18012717—22no—
12#18012715—21no—
13C4×D604—21no—
14C4×D604C2211yescharacteristic
15C4⋊C4×D151—21no—
16#18012670—21no—
17C4⋊(C151⋊C8)C2211yescharacteristic
18#18012659—21no—
19C4×C151⋊C8C2211yescharacteristic
20C4⋊Q8×C151C2211yescharacteristic
21C4×Q8×C151C2211yescharacteristic
22#107×C151—21no—
23C4⋊C8×C151C2211yescharacteristic
24#103×C151—21no—
25C2×Dic302D412yes—
26C2×D604D411yescharacteristic
27C2×C4×D151—22no—
28C2×C4×D151—21no—
29#14558994—44no—
30C2×C151⋊C8—21no—
31C2×C151⋊C8—21no—
32C4⋊Dic151—21no—
33C4⋊Dic151—21no—
34C4⋊Dic151D411yescharacteristic
35Dic151⋊C4—22no—
36Dic151⋊C4—22no—
37(C2×D151)⋊C4—22no—
38(C2×D151)⋊C4—21no—
39C2×Q8×C151—21no—
40C2×Q8×C151D411yescharacteristic
41C2×C8×C151—21no—
42C4⋊C4×C151—21no—
43C4⋊C4×C151—21no—
44C4⋊C4×C151—21no—
45C4⋊C4×C151D411yescharacteristic
46C42×C151—21no—
47C42×C151C2311yescharacteristic
48C22×D151—21no—
49Dic302—42no—
50D604—21no—
51D604Q1612yescomplemented
52C2×Dic151—21no—
53C2×Dic151—22no—
54C4×D151—41no—
55C4×D151—41no—
56C4×D151—82no—
57C151⋊C8—22no—
58C151⋊C8—41no—
59Q8×C151—21no—
60Q8×C151—21no—
61Q8×C151—42no—
62C2×C4×C151—21no—
63C2×C4×C151—21no—
64C2×C4×C151—41no—
65C2×C4×C151C2×D411yescharacteristic
66C2×C4×C151C2×D411yescharacteristic
67C2×C4×C151C2×D411yescharacteristic
68C8×C151—41no—
69C22×C151#12011yescharacteristic
70C2×D151—22no—
71C2×D151—41no—
72C2×D151—41no—
73C4×C151—21no—
74C4×C151—41no—
75C4×C151—41no—
76C4×C151—81no—
77C4×C151C2×Q1611yescharacteristic
78C4×C151#13511yescharacteristic
79C4×C151#13711yescharacteristic
80C4×C151#13711yescharacteristic
81Dic151—41no—
82Dic151—42no—
83C2×C151#45111yescharacteristic
84C2×C151#45211yescharacteristic
85C2×C151#45311yescharacteristic
86D151—42no—
87C151#163211yescharacteristic, complemented, Sylow
88#1632—1511nomaximal, Sylow
89#554—1511no—
90#494—1511no—
91#477D15111yescharacteristic, complemented
92#476—1511no—
93#333—1511no—
94Q8⋊C8—1511no—
95D4⋊C8—1511no—
96C2×Q16—3022no—
97C4⋊Q8—1511no—
98C4⋊Q8C2×D15111yescharacteristic
99#125—3021no—
100C22⋊Q8—3022no—
101C22⋊Q8—3021no—
102C4×Q8C2×D15111yescharacteristic
103C4×D4—3021no—
104C4×D4—1511no—
105C2×C4⋊C4—3021no—
106#107—21no—
107#106—3021no—
108C4⋊C8—1511no—
109C4⋊C8C2×D15111yescharacteristic
110#103—21no—
111#102—3021no—
112C4×C8—1511no—
113C2×Q8—21no—
114C2×Q8—1512no—
115C2×Q8C22⋊D15111yescharacteristic
116C2×D4—1511no—
117C22×C4—3022no—
118C22×C4—3021no—
119Q16—6044no—
120C2×C8—21no—
121C2×C8—3021no—
122C2×C8—3021no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—3022no—
127C4⋊C4—3022no—
128C4⋊C4—3021no—
129C4⋊C4—3021no—
130C4⋊C4—1511no—
131C4⋊C4C22⋊D15111yescharacteristic
132C22⋊C4—3022no—
133C22⋊C4—3021no—
134C42—21no—
135C42C22×D15111yescharacteristic
136C23—3021no—
137Q8—21no—
138Q8—21no—
139Q8—42no—
140Q8—6042no—
141D4—3021no—
142D4—1512no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—3021no—
147C2×C4—3022no—
148C2×C4—6041no—
149C2×C4—6041no—
150C2×C4—12082no—
151C2×C4D4×D15111yescharacteristic
152C2×C4D4×D15111yescharacteristic
153C2×C4C2×C22⋊D15111yescharacteristic
154C8—41no—
155C8—3022no—
156C8—6041no—
157C22—3022no—
158C22—6041no—
159C22—6041no—
160C22#1801270711yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—6041no—
166C4—6042no—
167C4Q16×D15111yescharacteristic
168C4#1801275911yescharacteristic
169C4#1801277011yescharacteristic
170C4#1801277111yescharacteristic
171C2—6042no—
172C2#2375236611yescharacteristic
173C2#2375237211yescharacteristic
174C2#2375237811yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#477×C151C2
socleC22×C151#120
prime radicalC2×D604D4
hypercenter#477D151
hypocenterC151#1632
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #23752591C2semidirect
4. #23751960C2semidirect
5. Q8⋊(C151⋊C8)C2semidirect
7. #477×C151C2semidirect
51. D604Q16semidirect
87. C151#1632semidirect
91. #477D151semidirect

Maximal subgroups

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

subgroupindex
#237529222
#237525912
#237524992
#237519602
Q8⋊(C151⋊C8)2
#237519392
#477×C1512
#1632151