Finite Group Databasebeta

← #30640211

Subgroups — #30640211

Order 16256.

214 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 85 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×#16861142C211yesmaximal, characteristic
2C2×#16861140C211yesmaximal, characteristic
3#22549742C211yesmaximal, characteristic
4#22549638C211yesmaximal, characteristic
5#22549638C211yesmaximal, characteristic
6#22549631C211yesmaximal, characteristic
7#389×C127C211yesmaximal, characteristic
8C22×C127⋊C8C2211yescharacteristic
9C22×C127⋊C8C2211yescharacteristic
10C2×C4⋊Dic127C2211yescharacteristic
11C2×C4⋊Dic127C2211yescharacteristic
12#16861142—22no—
13#16861140—22no—
14C127⋊#95—21no—
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⋊C8Q812yes—
28C2×C127⋊C8Q812yes—
29C4⋊Dic127—21no—
30C4⋊Dic127—21no—
31C4⋊Dic127—21no—
32C4⋊Dic127—21no—
33C22×C4×C127—21no—
34C22×C4×C127—21no—
35C22×C4×C127D411yescharacteristic
36C22×C4×C127D411yescharacteristic
37C22×C4×C127C2311yescharacteristic
38C4⋊C4×C127—21no—
39C4⋊C4×C127—21no—
40C4⋊C4×C127—21no—
41C4⋊C4×C127—42no—
42C4⋊C4×C127D412yes—
43C42×C127—21no—
44C42×C127—21no—
45C2×Dic127—41no—
46C2×Dic127—41no—
47C2×Dic127—41no—
48C2×Dic127—41no—
49C2×Dic127—41no—
50C2×Dic127—41no—
51C127⋊C8—22no—
52C127⋊C8—22no—
53C23×C127C2×D411yescharacteristic
54C2×C4×C127—22no—
55C2×C4×C127—21no—
56C2×C4×C127—21no—
57C2×C4×C127—21no—
58C2×C4×C127—21no—
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×C127C2×D411yescharacteristic
67C2×C4×C127C2×Q811yescharacteristic
68C2×C4×C127C2×Q811yescharacteristic
69C2×C4×C127#4111yescharacteristic
70C2×C4×C127#4111yescharacteristic
71C2×C4×C127#4111yescharacteristic
72C22×C127#12111yescharacteristic
73C22×C127#12311yescharacteristic
74C22×C127C4⋊Q811yescharacteristic
75C22×C127#13511yescharacteristic
76C22×C127#13511yescharacteristic
77C22×C127AGL(1,ℤ/8)11yescharacteristic
78C22×C127#13711yescharacteristic
79C4×C127—42no—
80C4×C127—41no—
81C4×C127—41no—
82C4×C127—81no—
83C4×C127C22⋊Q811yescharacteristic
84C4×C127C22⋊Q811yescharacteristic
85C4×C127#12511yescharacteristic
86C4×C127#12511yescharacteristic
87Dic127—81no—
88Dic127—81no—
89C2×C127#39811yescharacteristic
90C2×C127#46311yescharacteristic
91C2×C127#46411yescharacteristic
92C2×C127#48211yescharacteristic
93C2×C127#48511yescharacteristic
94C2×C127#49911yescharacteristic
95C2×C127#50111yescharacteristic
96#2085—1271nomaximal, Sylow
97C127#208511yescharacteristic, complemented, Sylow
98C2×#107—1271no—
99C2×#106—1271no—
100#389D12711yescharacteristic
101#382—1271no—
102#340—1271no—
103#340—1271no—
104#336—1271no—
105C22×C8—1271no—
106C22×C8—1271no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—1271no—
109C2×C4⋊C4—1271no—
110C2×C4⋊C4C2×D12711yescharacteristic
111C2×C4⋊C4C2×D12711yescharacteristic
112C2×C42C2×D12711yescharacteristic
113#107—2542no—
114#106—2542no—
115#95—21no—
116#95—2541no—
117#95—2541no—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—2541no—
121C22×C4—2541no—
122C22×C4C22⋊D12711yescharacteristic
123C22×C4C22⋊D12711yescharacteristic
124C22×C4C22×D12711yescharacteristic
125C2×C8—1272no—
126C2×C8—1272no—
127C2×C8—2541no—
128C2×C8—2541no—
129C2×C8—2541no—
130C2×C8—2541no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—42no—
135C4⋊C4—2541no—
136C4⋊C4—2541no—
137C4⋊C4—2541no—
138C4⋊C4—2541no—
139C4⋊C4D50812yes—
140C42—21no—
141C42—21no—
142C23C2×C22⋊D12711yescharacteristic
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—5081no—
156C2×C4—5081no—
157C2×C4—5081no—
158C2×C4—5081no—
159C2×C4—5081no—
160C2×C4—5081no—
161C2×C4C2×D50811yescharacteristic
162C2×C4Q8×D12711yescharacteristic
163C2×C4Q8×D12711yescharacteristic
164C2×C4#1452324711yescharacteristic
165C2×C4#1452324711yescharacteristic
166C2×C4#1452324811yescharacteristic
167C8—2542no—
168C8—2542no—
169C22#1686118311yescharacteristic
170C22#1686119011yescharacteristic
171C22#1686120711yescharacteristic
172C22#1686122911yescharacteristic
173C22#1686122911yescharacteristic
174C22#1686123511yescharacteristic
175C22#1686124011yescharacteristic
176C4—42no—
177C4—41no—
178C4—41no—
179C4—81no—
180C4—10161no—
181C4—10161no—
182C4#1686118911yescharacteristic
183C4#1686118911yescharacteristic
184C4#1686119911yescharacteristic
185C4#1686119911yescharacteristic
186C2#2254980611yescharacteristic
187C2#2255009111yescharacteristic
188C2#2255009811yescharacteristic
189C2#2255019711yescharacteristic
190C2#2255021411yescharacteristic
191C2#2255027511yescharacteristic
192C2#2255028211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D127
commutator, cosocleC22×C4×C127C23
FrattiniC22×C4C22×D127
Fitting#389×C127C2
socle, prime radicalC23×C127C2×D4
hypercenter#389D127
hypocenterC127#2085
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
97. C127#2085semidirect

Maximal subgroups

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

subgroupindex
C2×#168611422
C2×#168611402
#225497422
#225496382
#225496312
#389×C1272
#2085127