Finite Group Databasebeta

← #30640270

Subgroups — #30640270

Order 16256.

254 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 87 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×#16861140C211yesmaximal, characteristic
2C2×#16861134C211yesmaximal, characteristic
3C2×#16861132C211yesmaximal, characteristic
4#22549781C211yesmaximal, characteristic
5#22549745C211yesmaximal, characteristic
6#22549630C211yesmaximal, characteristic
7C2×#106×C127C211yesmaximal, characteristic
8C22×Dic254C2211yescharacteristic
9C22×C127⋊C8C2211yescharacteristic
10C2×C4⋊Dic127C2211yescharacteristic
11C2×Dic127⋊C4—22no—
12C2×C4×Dic127C2211yescharacteristic
13#16861140—22no—
14#16861134—22no—
15#16861132—22no—
16C127⋊#95—22no—
17C22×C8×C127C2211yescharacteristic
18C2×C4⋊C4×C127C2211yescharacteristic
19C2×C4⋊C4×C127C2211yescharacteristic
20#106×C127—22no—
21C2×Dic254—21no—
22C2×Dic254—21no—
23C2×Dic254—21no—
24C2×Dic254—21no—
25C2×Dic254—21no—
26C2×Dic254Q812yes—
27C22×Dic127—21no—
28C22×Dic127—21no—
29C22×Dic127D412yes—
30C2×C127⋊C8—21no—
31C2×C127⋊C8—21no—
32C2×C127⋊C8D412yes—
33C4⋊Dic127—21no—
34C4⋊Dic127—21no—
35Dic127⋊C4—44no—
36C4×Dic127—21no—
37C4×Dic127—21no—
38C22×C4×C127—21no—
39C22×C4×C127—21no—
40C22×C4×C127C2311yescharacteristic
41C2×C8×C127—21no—
42C2×C8×C127—21no—
43C2×C8×C127D412yes—
44C4⋊C4×C127—21no—
45C4⋊C4×C127—21no—
46C4⋊C4×C127—21no—
47C4⋊C4×C127—21no—
48Dic254—22no—
49Dic254—22no—
50Dic254—41no—
51Dic254—41no—
52C2×Dic127—22no—
53C2×Dic127—22no—
54C2×Dic127—22no—
55C2×Dic127—41no—
56C2×Dic127—41no—
57C2×Dic127—41no—
58C2×Dic127—42no—
59C2×Dic127SD1614yes—
60C127⋊C8—22no—
61C23×C127C2×D411yescharacteristic
62C2×C4×C127—41no—
63C2×C4×C127—41no—
64C2×C4×C127—42no—
65C2×C4×C127—42no—
66C2×C4×C127C2×D411yescharacteristic
67C2×C4×C127C2×D411yescharacteristic
68C2×C4×C127C2×Q811yescharacteristic
69C2×C4×C127#4111yescharacteristic
70C2×C4×C127#4111yescharacteristic
71C2×C4×C127#4111yescharacteristic
72C8×C127—22no—
73C22×C127C22⋊Q811yescharacteristic
74C22×C127#12311yescharacteristic
75C22×C127#12711yescharacteristic
76C22×C127C2×SD1612yes—
77C22×C127#13712yes—
78C4×C127—81no—
79C4×C127—81no—
80C4×C127C22⋊Q811yescharacteristic
81C4×C127C22⋊Q811yescharacteristic
82C4×C127#12311yescharacteristic
83C4×C127#12311yescharacteristic
84Dic127—24no—
85Dic127—42no—
86Dic127—81no—
87C2×C127#39911yescharacteristic
88C2×C127#47512yes—
89C2×C127#48312yes—
90C2×C127#49211yescharacteristic
91C2×C127#49711yescharacteristic
92#2096—1271nomaximal, Sylow
93C127#209611yescharacteristic, complemented, Sylow
94C2×#106—1271no—
95C2×#106D12711yescharacteristic
96C2×#103—1271no—
97C2×#103—1271no—
98#391—1271no—
99#384—1271no—
100#336—1271no—
101C22×Q8—1271no—
102C22×C8—1271no—
103C22×C8C2×D12711yescharacteristic
104C2×C4⋊C4—1271no—
105C2×C4⋊C4—2542no—
106C2×C4⋊C4C2×D12711yescharacteristic
107C2×C4⋊C4C2×D12711yescharacteristic
108C2×C42—1271no—
109#106—22no—
110#106—2542no—
111#103—2542no—
112#103—2542no—
113#95—2542no—
114C2×Q8—1272no—
115C2×Q8—2541no—
116C2×Q8—2541no—
117C2×Q8—2541no—
118C2×Q8—2541no—
119C2×Q8—2541no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—1272no—
123C22×C4—2541no—
124C22×C4—2541no—
125C22×C4C22×D12711yescharacteristic
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—1272no—
129C2×C8—2541no—
130C2×C8—2541no—
131C2×C8C22⋊D12712yes—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—5084no—
137C4⋊C4—2541no—
138C4⋊C4—2541no—
139C42—2541no—
140C42—2541no—
141C23D4×D12711yescharacteristic
142Q8—5081no—
143Q8—5081no—
144Q8—2542no—
145Q8—2542no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—1274no—
151C2×C4—5081no—
152C2×C4—5082no—
153C2×C4—5081no—
154C2×C4—5081no—
155C2×C4—2542no—
156C2×C4—2542no—
157C2×C4—2542no—
158C2×C4D4×D12711yescharacteristic
159C2×C4C2×C22⋊D12711yescharacteristic
160C2×C4Q8×D12711yescharacteristic
161C2×C4#1452324811yescharacteristic
162C2×C4#1452324811yescharacteristic
163C2×C4#1452324911yescharacteristic
164C8—22no—
165C8—2542no—
166C22#1686118711yescharacteristic
167C22#1686119411yescharacteristic
168C22#1686120511yescharacteristic
169C22SD16×D12712yes—
170C22#1686123812yes—
171C4—81no—
172C4—81no—
173C4—10161no—
174C4—5082no—
175C4—2544no—
176C4#1686118511yescharacteristic
177C4#1686118711yescharacteristic
178C4#1686119211yescharacteristic
179C4#1686119411yescharacteristic
180C2#2254981111yescharacteristic
181C2#2255016012yes—
182C2#2255020812yes—
183C2#2255024711yescharacteristic
184C2#2255026711yescharacteristic
subgroupG/H
centerC23D4×D127
commutator, cosocleC22×C4×C127C23
FrattiniC22×C4C22×D127
FittingC2×#106×C127C2
socle, prime radicalC23×C127C2×D4
hypercenterC2×#106D127
hypocenterC127#2096
LCSG ▷ C22×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
93. C127#2096semidirect

Maximal subgroups

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

subgroupindex
C2×#168611402
C2×#168611342
C2×#168611322
#225497812
#225497452
#225496302
C2×#106×C1272
#2096127