Finite Group Databasebeta

← #30640097

Subgroups — #30640097

Order 16256.

208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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×#16861144C211yesmaximal, characteristic
2#22549919C211yesmaximal, characteristic
3#22549903C211yesmaximal, characteristic
4C2×#16861133C211yesmaximal, characteristic
5C2×#16861128C211yesmaximal, characteristic
6#22549644C211yesmaximal, characteristic
7#419×C127C211yesmaximal, characteristic
8C2×#14523232C2211yescharacteristic
9C2×#14523232C2211yescharacteristic
10C22×C127⋊C8C2211yescharacteristic
11C2×C4⋊Dic127C2211yescharacteristic
12#16861144—22no—
13#16861142—21no—
14#16861140—21no—
15C4⋊(C127⋊C8)—22no—
16#16861133—22no—
17#16861128—22no—
18C22×Q8×C127C2211yescharacteristic
19C2×M16×C127C2211yescharacteristic
20#117×C127C2211yescharacteristic
21#103×C127—21no—
22#103×C127—21no—
23C22×Dic127—21no—
24#14523232—21no—
25#14523232—21no—
26#14523232—21no—
27#14523232D412yes—
28C2×C127⋊C8—21no—
29C2×C127⋊C8—21no—
30C2×C127⋊C8—21no—
31C2×C127⋊C8—21no—
32C2×C127⋊C8D412yes—
33C4⋊Dic127—21no—
34C4⋊Dic127—21no—
35C2×Q8×C127—21no—
36C2×Q8×C127—21no—
37C2×Q8×C127—21no—
38C2×Q8×C127—21no—
39C2×Q8×C127—21no—
40C2×Q8×C127Q812yes—
41C22×C4×C127—21no—
42C22×C4×C127C2311yescharacteristic
43M16×C127—21no—
44M16×C127—21no—
45C2×C8×C127—21no—
46C4⋊C4×C127D411yescharacteristic
47C4⋊C4×C127D411yescharacteristic
48C22⋊C4×C127—21no—
49C42×C127—21no—
50C2×Dic127—41no—
51C2×Dic127—81no—
52C127⋊C8—22no—
53C127⋊C8—22no—
54C127⋊C8—41no—
55C23×C127#4111yescharacteristic
56Q8×C127—22no—
57Q8×C127—22no—
58Q8×C127—41no—
59Q8×C127—41no—
60C2×C4×C127—21no—
61C2×C4×C127—21no—
62C2×C4×C127—22no—
63C2×C4×C127—41no—
64C2×C4×C127—41no—
65C2×C4×C127C2×D411yescharacteristic
66C2×C4×C127C2×D411yescharacteristic
67C2×C4×C127C2×D411yescharacteristic
68C2×C4×C127C2×Q811yescharacteristic
69C2×C4×C127#4111yescharacteristic
70C2×C4×C127#4111yescharacteristic
71C8×C127—41no—
72C22×C127—21no—
73C22×C127—21no—
74C22×C127#12111yescharacteristic
75C22×C127C22⋊Q811yescharacteristic
76C22×C127#12611yescharacteristic
77C4×C127—42no—
78C4×C127—41no—
79C4×C127—41no—
80C4×C127#12111yescharacteristic
81C4×C127#12111yescharacteristic
82C4×C127C22⋊Q811yescharacteristic
83C4×C127C22⋊Q811yescharacteristic
84Dic127—81no—
85C2×C127—21no—
86C2×C127—21no—
87C2×C127#39611yescharacteristic
88C2×C127#47111yescharacteristic
89C2×C127#47311yescharacteristic
90#2064—1271nomaximal, Sylow
91C127#206411yescharacteristic, complemented, Sylow
92C2×#108—1271no—
93#428—1271no—
94#424—1271no—
95#419D12711yescharacteristic
96C2×#103—1271no—
97C2×#101—1271no—
98#343—1271no—
99C22×Q8C2×D12711yescharacteristic
100C2×M16—1271no—
101C2×M16—1271no—
102C2×M16C2×D12711yescharacteristic
103C22×C8—1271no—
104#117C2×D12711yescharacteristic
105C2×C4⋊C4—1271no—
106#108—2542no—
107#107—2541no—
108#106—2541no—
109C4⋊C8—2542no—
110#103—21no—
111#103—21no—
112#103—2542no—
113#101—2542no—
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—21no—
119C2×Q8Dic25412yes—
120C22×C4—21no—
121C22×C4—2541no—
122C22×C4C22×D12711yescharacteristic
123M16—21no—
124M16—21no—
125M16—1272no—
126M16—2541no—
127M16—2541no—
128M16—2541no—
129C2×C8—21no—
130C2×C8—1272no—
131C2×C8—2541no—
132C2×C8—2541no—
133C2×C8—2541no—
134C2×C8—2541no—
135C4⋊C4—2541no—
136C4⋊C4—2541no—
137C4⋊C4C22⋊D12711yescharacteristic
138C4⋊C4C22⋊D12711yescharacteristic
139C22⋊C4—21no—
140C42—21no—
141C23#1452324711yescharacteristic
142Q8—22no—
143Q8—22no—
144Q8—41no—
145Q8—41no—
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—10161no—
152C2×C4—5081no—
153C2×C4D4×D12711yescharacteristic
154C2×C4D4×D12711yescharacteristic
155C2×C4C2×C22⋊D12711yescharacteristic
156C2×C4C2×Dic25411yescharacteristic
157C2×C4#1452324711yescharacteristic
158C2×C4#1452324811yescharacteristic
159C8—41no—
160C8—5081no—
161C8—2542no—
162C8—2542no—
163C22—21no—
164C22—21no—
165C22#1686118111yescharacteristic
166C22#1686118611yescharacteristic
167C22#1686120211yescharacteristic
168C4—42no—
169C4—41no—
170C4—41no—
171C4—10161no—
172C4#1686118011yescharacteristic
173C4#1686118211yescharacteristic
174C4#1686118611yescharacteristic
175C4#1686118811yescharacteristic
176C2—21no—
177C2—21no—
178C2#2254979911yescharacteristic
179C2#2255014111yescharacteristic
180C2#2255014911yescharacteristic
subgroupG/H
centerC22#16861181
commutator, cosocleC22×C4×C127C23
FrattiniC22×C4C22×D127
Fitting#419×C127C2
socleC22×C127#121
prime radicalC23×C127#41
hypercenter#419D127
hypocenterC127#2064
LCSG ▷ C22×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
91. C127#2064semidirect

Maximal subgroups

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

subgroupindex
C2×#168611442
#225499192
#225499032
C2×#168611332
C2×#168611282
#225496442
#419×C1272
#2064127