Finite Group Databasebeta

← #30637900

Subgroups — #30637900

Order 16256.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#22550596C211yesmaximal, characteristic
2#22550226C211yesmaximal, characteristic, complemented
3#22550168C211yesmaximal, characteristic, complemented
4#22549623C211yesmaximal, characteristic, complemented
5#22549606C211yesmaximal, characteristic, complemented
6D4⋊(C127⋊C8)C211yesmaximal, characteristic
7#476×C127C211yesmaximal, characteristic
8#16861209C2211yescharacteristic
9#16861202—22no—
10#16861196—21no—
11#16861188—21no—
12C4×Dic254C2211yescharacteristic
13#16861174—21no—
14#16861168—21no—
15#16861142—21no—
16C4⋊(C127⋊C8)C2211yescharacteristic
17#16861133—22no—
18#16861132—21no—
19C4×C127⋊C8C2211yescharacteristic
20C4⋊Q8×C127C2211yescharacteristic
21C4×D4×C127C2211yescharacteristic
22#106×C127—21no—
23C4⋊C8×C127C2211yescharacteristic
24#102×C127—21no—
25C2×Dic254—21no—
26C2×Dic254D411yescharacteristic
27C2×C127⋊C8—21no—
28C2×C127⋊C8—21no—
29C4⋊Dic127—21no—
30C4⋊Dic127D412yes—
31C4⋊Dic127D411yescharacteristic
32Dic127⋊C4—22no—
33Dic127⋊C4—21no—
34C22⋊Dic127—22no—
35C22⋊Dic127—22no—
36C4×Dic127—22no—
37C4×Dic127—21no—
38C2×Q8×C127—21no—
39C2×D4×C127D411yescharacteristic
40C22×C4×C127—21no—
41C2×C8×C127—21no—
42C4⋊C4×C127—21no—
43C4⋊C4×C127—21no—
44C4⋊C4×C127D411yescharacteristic
45C22⋊C4×C127—21no—
46C42×C127C2311yescharacteristic
47Dic254—21no—
48Dic254—21no—
49Dic254—41no—
50Dic254—41no—
51C2×Dic127—21no—
52C2×Dic127—21no—
53C2×Dic127—22no—
54C127⋊C8—41no—
55C127⋊C8—41no—
56C23×C127—21no—
57Q8×C127—42no—
58D4×C127—21no—
59D4×C127—21no—
60C2×C4×C127—21no—
61C2×C4×C127—41no—
62C2×C4×C127—41no—
63C2×C4×C127—41no—
64C2×C4×C127C2×D411yescharacteristic
65C2×C4×C127C2×D411yescharacteristic
66C2×C4×C127C2×D411yescharacteristic
67C8×C127—41no—
68C22×C127—41no—
69C22×C127—41no—
70C22×C127—41no—
71C22×C127#12011yescharacteristic
72C4×C127—21no—
73C4×C127—41no—
74C4×C127—81no—
75C4×C127#13511yescharacteristic
76C4×C127#13511yescharacteristic
77C4×C127#13711yescharacteristic
78C4×C127#13711yescharacteristic
79Dic127—41no—
80Dic127—42no—
81Dic127—41no—
82C2×C127—81no—
83C2×C127#45211yescharacteristic
84C2×C127#45211yescharacteristic
85C2×C127#45411yescharacteristic
86#1638—1271nomaximal, Sylow
87C127#163811yescharacteristic, complemented, Sylow
88#556—1271no—
89#487—1271no—
90#477—1271no—
91#476D12711yescharacteristic
92#332—1271no—
93Q8⋊C8—1271no—
94D4⋊C8—1271no—
95C4⋊Q8—1271no—
96C4⋊Q8C2×D12711yescharacteristic
97#126—2542no—
98#124—2541no—
99C22⋊Q8—2541no—
100C4×Q8—1271no—
101C4×Q8—2541no—
102C4×D4C2×D12711yescharacteristic
103#117—2541no—
104#107—2541no—
105#106—21no—
106C4⋊C8—1271no—
107C4⋊C8C2×D12711yescharacteristic
108#103—2541no—
109#103—2542no—
110#102—21no—
111C4×C8—1271no—
112C2×Q8—21no—
113C2×Q8—1271no—
114C2×Q8—2541no—
115C2×D4C22⋊D12711yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—2541no—
119C2×C8—2541no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—1272no—
123C4⋊C4—1271no—
124C4⋊C4—2542no—
125C4⋊C4—2541no—
126C4⋊C4—2541no—
127C4⋊C4C22⋊D12711yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—2542no—
130C22⋊C4—2542no—
131C42—2542no—
132C42—2541no—
133C42C22×D12711yescharacteristic
134C23—21no—
135Q8—42no—
136Q8—5081no—
137Q8—5081no—
138Q8—2541no—
139Q8—2541no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—2541no—
147C2×C4—2542no—
148C2×C4—2541no—
149C2×C4D4×D12711yescharacteristic
150C2×C4D4×D12711yescharacteristic
151C2×C4C2×C22⋊D12711yescharacteristic
152C8—41no—
153C8—5081no—
154C8—5081no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#1686117711yescharacteristic
159C4—21no—
160C4—41no—
161C4—81no—
162C4—5081no—
163C4—5082no—
164C4—5081no—
165C4#1686122911yescharacteristic
166C4#1686123011yescharacteristic
167C4#1686123811yescharacteristic
168C4#1686124011yescharacteristic
169C2—81no—
170C2#2255003511yescharacteristic
171C2#2255003611yescharacteristic
172C2#2255004711yescharacteristic
subgroupG/H
centerC22#16861177
commutator, cosocleC42×C127C23
FrattiniC42C22×D127
Fitting#476×C127C2
socleC22×C127#120
prime radicalC2×D4×C127D4
hypercenter#476D127
hypocenterC127#1638
LCSG ▷ C42×C127 ▷ C22×C127 ▷ C127
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #22550226C2semidirect
3. #22550168C2semidirect
4. #22549623C2semidirect
5. #22549606C2semidirect
87. C127#1638semidirect

Maximal subgroups

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

subgroupindex
#225505962
#225502262
#225501682
#225496232
#225496062
D4⋊(C127⋊C8)2
#476×C1272
#1638127