Finite Group Databasebeta

← #1616×C277 #47979005

Subgroups — #1616×C277 #47979005

Order 35456.

246 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 68 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#537×C277C211yesmaximal, characteristic
2#481×C277C212yesmaximal, complemented
3#400×C277C211yesmaximal, characteristic, complemented
4#327×C277C212yesmaximal, complemented
5#324×C277C211yesmaximal, characteristic, complemented
6C2×#41×C277—21no—
7C22⋊Q8×C277—22no—
8#121×C277—22no—
9#121×C277—21no—
10#121×C277C2212yes—
11C2×C4⋊C4×C277C2211yescharacteristic
12C2×C4⋊C4×C277C2211yescharacteristic
13#106×C277—22no—
14#102×C277—22no—
15C22⋊C8×C277C2212yes—
16#95×C277—21no—
17#95×C277—21no—
18#95×C277C2211yescharacteristic
19#41×C277—42no—
20#41×C277—42no—
21C2×Q8×C277—21no—
22C2×D4×C277—21no—
23C2×D4×C277—22no—
24C2×D4×C277—21no—
25C2×D4×C277D412yes—
26C22×C4×C277—22no—
27C22×C4×C277—21no—
28C22×C4×C277—21no—
29C22×C4×C277D411yescharacteristic
30C22×C4×C277D411yescharacteristic
31C22×C4×C277C2311yescharacteristic
32C2×C8×C277—22no—
33C4⋊C4×C277—21no—
34C4⋊C4×C277—22no—
35C4⋊C4×C277—22no—
36C4⋊C4×C277D412yes—
37C22⋊C4×C277—22no—
38C22⋊C4×C277—22no—
39C23×C277—22no—
40C23×C277C2×D411yescharacteristic
41Q8×C277—42no—
42D4×C277—42no—
43D4×C277—42no—
44D4×C277—42no—
45D4×C277—42no—
46D4×C277—81no—
47C2×C4×C277—21no—
48C2×C4×C277—21no—
49C2×C4×C277—21no—
50C2×C4×C277—22no—
51C2×C4×C277—41no—
52C2×C4×C277—44no—
53C2×C4×C277—41no—
54C2×C4×C277—41no—
55C2×C4×C277—41no—
56C2×C4×C277—42no—
57C2×C4×C277—41no—
58C2×C4×C277—41no—
59C2×C4×C277SD1612yes—
60C2×C4×C277C2×D412yes—
61C8×C277—42no—
62C22×C277—21no—
63C22×C277—21no—
64C22×C277—42no—
65C22×C277—42no—
66C22×C277—42no—
67C22×C277#12011yescharacteristic
68C22×C277C2×SD1611yescharacteristic
69C22×C277AGL(1,ℤ/8)11yescharacteristic
70C4×C277—22no—
71C4×C277—22no—
72C4×C277—42no—
73C4×C277—41no—
74C4×C277—81no—
75C4×C277—81no—
76C2×C277—21no—
77C2×C277—21no—
78C2×C277—82no—
79C2×C277#45011yescharacteristic
80C2×C277#45411yescharacteristic
81C2×C277#45811yescharacteristic
82C277#161611yescharacteristic, direct product factor, Sylow
83#1616C27711yesmaximal, characteristic, direct product factor, Sylow
84#537C2×C27711yescharacteristic
85#481C2×C27712yescomplemented
86#400C2×C27711yescharacteristic, complemented
87#327C2×C27712yescomplemented
88#324C2×C27711yescharacteristic, complemented
89C2×#41—21no—
90C22⋊Q8—22no—
91#121—22no—
92#121—21no—
93#121C22×C27712yes—
94C2×C4⋊C4C22×C27711yescharacteristic
95C2×C4⋊C4C22×C27711yescharacteristic
96#106—22no—
97#102—22no—
98C22⋊C8C22×C27712yes—
99#95—21no—
100#95—21no—
101#95C22×C27711yescharacteristic
102#41—42no—
103#41—42no—
104C2×Q8—21no—
105C2×D4—21no—
106C2×D4—22no—
107C2×D4—21no—
108C2×D4D4×C27712yes—
109C22×C4—22no—
110C22×C4—21no—
111C22×C4—21no—
112C22×C4D4×C27711yescharacteristic
113C22×C4D4×C27711yescharacteristic
114C22×C4C23×C27711yescharacteristic
115C2×C8—22no—
116C4⋊C4—21no—
117C4⋊C4—22no—
118C4⋊C4—22no—
119C4⋊C4D4×C27712yes—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C23—22no—
123C23C2×D4×C27711yescharacteristic
124Q8—42no—
125D4—42no—
126D4—42no—
127D4—42no—
128D4—42no—
129D4—81no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—22no—
134C2×C4—41no—
135C2×C4—44no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—42no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4SD16×C27712yes—
143C2×C4C2×D4×C27712yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—42no—
148C22—42no—
149C22—42no—
150C22#120×C27711yescharacteristic
151C22C2×SD16×C27711yescharacteristic
152C22AGL(1,ℤ/8)×C27711yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—41no—
157C4—81no—
158C4—81no—
159C2—21no—
160C2—21no—
161C2—82no—
162C2#450×C27711yescharacteristic
163C2#454×C27711yescharacteristic
164C2#458×C27711yescharacteristic
subgroupG/H
center, socleC22×C277#120
commutator, Frattini, cosocleC22×C4C23×C277
prime radical#537×C277C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C277 ◁ C22×C4×C277 ◁ G

Complements

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

NH ≅ G/Ntype
2. #481×C277C2semidirect
3. #400×C277C2semidirect
4. #327×C277C2semidirect
5. #324×C277C2semidirect
82. C277#1616direct (N × H)
83. #1616C277direct (N × H)
85. #481C2×C277semidirect
86. #400C2×C277semidirect
87. #327C2×C277semidirect
88. #324C2×C277semidirect

Maximal subgroups

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

subgroupindex
#537×C2772
#481×C2772
#400×C2772
#327×C2772
#324×C2772
#1616277