Finite Group Databasebeta

← #30640232

Subgroups — #30640232

Order 16256.

224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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×C4⋊(C127⋊C8)C211yesmaximal, characteristic
3#22549774C211yesmaximal, characteristic
4#22549638C211yesmaximal, characteristic
5#22549638C211yesmaximal, characteristic
6#22549638C211yesmaximal, characteristic
7#389×C127C211yesmaximal, characteristic
8C22×C127⋊C8C2211yescharacteristic
9C22×C127⋊C8C2211yescharacteristic
10C2×C4⋊Dic127C2211yescharacteristic
11C2×C4⋊Dic127C2211yescharacteristic
12C2×Dic127⋊C4—21no—
13#16861140—22no—
14C4⋊(C127⋊C8)—22no—
15C127⋊#95—21no—
16C2×C4⋊C4×C127—21no—
17C2×C4⋊C4×C127C2211yescharacteristic
18C2×C4⋊C4×C127C2211yescharacteristic
19C2×C42×C127C2211yescharacteristic
20#95×C127—21no—
21C22×Dic127—21no—
22C22×Dic127—21no—
23C2×C127⋊C8—21no—
24C2×C127⋊C8—21no—
25C2×C127⋊C8—21no—
26C2×C127⋊C8—21no—
27C2×C127⋊C8—21no—
28C2×C127⋊C8D412yes—
29C4⋊Dic127—21no—
30C4⋊Dic127—21no—
31C4⋊Dic127—21no—
32C4⋊Dic127Q812yes—
33Dic127⋊C4—42no—
34C22×C4×C127—21no—
35C22×C4×C127—21no—
36C22×C4×C127D411yescharacteristic
37C22×C4×C127D411yescharacteristic
38C22×C4×C127C2311yescharacteristic
39C4⋊C4×C127—21no—
40C4⋊C4×C127—21no—
41C4⋊C4×C127—21no—
42C4⋊C4×C127—42no—
43C4⋊C4×C127Q812yes—
44C42×C127—21no—
45C42×C127—21no—
46C2×Dic127—22no—
47C2×Dic127—41no—
48C2×Dic127—41no—
49C2×Dic127—41no—
50C2×Dic127—41no—
51C2×Dic127—41no—
52C127⋊C8—22no—
53C127⋊C8—41no—
54C23×C127C2×D411yescharacteristic
55C2×C4×C127—21no—
56C2×C4×C127—21no—
57C2×C4×C127—21no—
58C2×C4×C127—22no—
59C2×C4×C127—21no—
60C2×C4×C127—21no—
61C2×C4×C127—41no—
62C2×C4×C127—41no—
63C2×C4×C127—41no—
64C2×C4×C127—41no—
65C2×C4×C127—41no—
66C2×C4×C127SD1612yes—
67C2×C4×C127C2×D411yescharacteristic
68C2×C4×C127C2×Q811yescharacteristic
69C2×C4×C127C2×Q811yescharacteristic
70C2×C4×C127#4111yescharacteristic
71C2×C4×C127#4111yescharacteristic
72C2×C4×C127#4111yescharacteristic
73C22×C127#12111yescharacteristic
74C22×C127C22⋊Q811yescharacteristic
75C22×C127C22⋊Q811yescharacteristic
76C22×C127C2×SD1611yescharacteristic
77C22×C127#13511yescharacteristic
78C22×C127AGL(1,ℤ/8)11yescharacteristic
79C22×C127#13711yescharacteristic
80C4×C127—22no—
81C4×C127—41no—
82C4×C127—42no—
83C4×C127—81no—
84C4×C127#12311yescharacteristic
85C4×C127#12511yescharacteristic
86C4×C127#12511yescharacteristic
87C4×C127C4⋊Q811yescharacteristic
88Dic127—42no—
89Dic127—81no—
90C2×C127#39811yescharacteristic
91C2×C127#46511yescharacteristic
92C2×C127#46811yescharacteristic
93C2×C127#47511yescharacteristic
94C2×C127#47611yescharacteristic
95C2×C127#47811yescharacteristic
96C2×C127#47911yescharacteristic
97#2088—1271nomaximal, Sylow
98C127#208811yescharacteristic, complemented, Sylow
99C2×#106—1271no—
100C2×C4⋊C8—1271no—
101#389—1271no—
102#389D12711yescharacteristic
103#340—1271no—
104#340—1271no—
105#340—1271no—
106C22×C8—1271no—
107C22×C8—1271no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—1271no—
110C2×C4⋊C4—1271no—
111C2×C4⋊C4—2541no—
112C2×C4⋊C4C2×D12711yescharacteristic
113C2×C4⋊C4C2×D12711yescharacteristic
114C2×C42C2×D12711yescharacteristic
115#106—2542no—
116C4⋊C8—2542no—
117#95—21no—
118#95—2541no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—2541no—
122C22×C4—2541no—
123C22×C4C22⋊D12711yescharacteristic
124C22×C4C22⋊D12711yescharacteristic
125C22×C4C22×D12711yescharacteristic
126C2×C8—1272no—
127C2×C8—2541no—
128C2×C8—2541no—
129C2×C8—2541no—
130C2×C8—2541no—
131C2×C8—2541no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—42no—
136C4⋊C4—1272no—
137C4⋊C4—5082no—
138C4⋊C4—2541no—
139C4⋊C4—2541no—
140C4⋊C4—2541no—
141C4⋊C4Dic25412yes—
142C42—21no—
143C42—21no—
144C23C2×C22⋊D12711yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—5081no—
157C2×C4—5081no—
158C2×C4—5081no—
159C2×C4—5081no—
160C2×C4—5081no—
161C2×C4—2542no—
162C2×C4#1452323512yes—
163C2×C4D4×D12711yescharacteristic
164C2×C4Q8×D12711yescharacteristic
165C2×C4C2×Dic25411yescharacteristic
166C2×C4#1452324711yescharacteristic
167C2×C4#1452324811yescharacteristic
168C2×C4#1452324911yescharacteristic
169C8—5081no—
170C8—2542no—
171C22#1686118111yescharacteristic
172C22#1686118511yescharacteristic
173C22#1686118811yescharacteristic
174C22C2×#1452323511yescharacteristic
175C22#1686122911yescharacteristic
176C22#1686123511yescharacteristic
177C22#1686123911yescharacteristic
178C4—22no—
179C4—41no—
180C4—42no—
181C4—81no—
182C4—10161no—
183C4—5082no—
184C4#1686119411yescharacteristic
185C4#1686119911yescharacteristic
186C4#1686120011yescharacteristic
187C4#1686120811yescharacteristic
188C2#2254980911yescharacteristic
189C2#2255010711yescharacteristic
190C2#2255012011yescharacteristic
191C2#2255016111yescharacteristic
192C2#2255016311yescharacteristic
193C2#2255017611yescharacteristic
194C2#2255018011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D127
commutator, cosocleC22×C4×C127C23
FrattiniC22×C4C22×D127
Fitting#389×C127C2
socle, prime radicalC23×C127C2×D4
hypercenter#389D127
hypocenterC127#2088
LCSG ▷ C22×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
98. C127#2088semidirect

Maximal subgroups

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

subgroupindex
C2×#168611402
C2×C4⋊(C127⋊C8)2
#225497742
#225496382
#389×C1272
#2088127