Finite Group Databasebeta

← #47981674

Subgroups — #47981674

Order 35456.

272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 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#31800552C211yesmaximal, characteristic
2#31800059C211yesmaximal, characteristic, complemented
3#31799735C214yesmaximal, complemented
4#376×C277C211yesmaximal, characteristic, complemented
5C2×#17984563—21no—
6#22579880C411yescharacteristic, complemented
7#22579877C411yescharacteristic, complemented
8#22579868—21no—
9#22579854—21no—
10#22579854C2212yes—
11C4×D1108—21no—
12C4×D1108C412yescomplemented
13C4⋊#14555660—21no—
14C22⋊#14555660C2212yes—
15#22579791—21no—
16C2×C42×C277—21no—
17C2×C42×C277C2211yescharacteristic
18#95×C277—21no—
19#95×C277C2212yes—
20#17984563—44no—
21C2×Dic554—21no—
22C2×D1108—21no—
23C2×D1108—21no—
24C2×D1108C2×C412yes—
25C2×C22⋊D277—22no—
26C2×C4×D277—22no—
27C2×#14555660—22no—
28C4⋊Dic277—21no—
29C4⋊Dic277C2×C412yes—
30#17984540—22no—
31#17984540—22no—
32C22×C4×C277—22no—
33C22×C4×C277D411yescharacteristic
34C22×C4×C277D411yescharacteristic
35C22×C4×C277C2311yescharacteristic
36C42×C277—24no—
37C42×C277C2×C411yescharacteristic
38C42×C277C2×C411yescharacteristic
39C42×C277D411yescharacteristic
40C42×C277D411yescharacteristic
41C22×D277—22no—
42Dic554—42no—
43D1108—42no—
44D1108—42no—
45D1108—42no—
46C22⋊D277—44no—
47C2×Dic277—22no—
48C4×D277—44no—
49#14555660—42no—
50C23×C277C2×D411yescharacteristic
51C2×C4×C277—22no—
52C2×C4×C277—22no—
53C2×C4×C277—24no—
54C2×C4×C277—41no—
55C2×C4×C277—42no—
56C2×C4×C277—42no—
57C2×C4×C277C22⋊C411yescharacteristic
58C2×C4×C277C22⋊C411yescharacteristic
59C2×C4×C277C22⋊C411yescharacteristic
60C2×C4×C277C22⋊C411yescharacteristic
61C2×C4×C277C22×C411yescharacteristic
62C2×C4×C277C2×D411yescharacteristic
63C22×C277—21no—
64C22×C277—21no—
65C22×C277C2×C22⋊C411yescharacteristic
66C22×C277AGL(1,ℤ/8)12yes—
67C2×D277—42no—
68C2×D277—42no—
69C2×D277—42no—
70C4×C277—21no—
71C4×C277—21no—
72C4×C277—21no—
73C4×C277—21no—
74C4×C277—21no—
75C4×C277—44no—
76C4×C277#10412yes—
77Dic277—42no—
78C2×C277—22no—
79C2×C277#41011yescharacteristic
80C2×C277#41811yescharacteristic
81C2×C277C2×#10411yescharacteristic
82D277—82no—
83C277#150511yescharacteristic, complemented, Sylow
84#1505—2771nomaximal, Sylow
85#532—2771no—
86#432—2771no—
87#376D27711yescharacteristic, complemented
88#327—2774no—
89C2×#41—5541no—
90C4⋊Q8—2771no—
91#127—2771no—
92#124—5541no—
93#121—2772no—
94#121—5541no—
95C4×D4—2772no—
96C4×D4—5541no—
97C2×C42—21no—
98C2×C42C2×D27711yescharacteristic
99C4⋊C8—5541no—
100C22⋊C8—2772no—
101#97—5541no—
102#95—21no—
103#95C2×D27712yes—
104#41—11084no—
105C2×Q8—5541no—
106C2×D4—2772no—
107C2×D4—5542no—
108C2×D4—5541no—
109C2×D4—5541no—
110C22×C4—22no—
111C22×C4—5542no—
112C22×C4C22⋊D27711yescharacteristic
113C22×C4C22⋊D27711yescharacteristic
114C22×C4C22×D27711yescharacteristic
115C2×C8—5542no—
116C4⋊C4—2772no—
117C4⋊C4—5541no—
118C22⋊C4—5542no—
119C22⋊C4—5542no—
120C42—24no—
121C42C4×D27711yescharacteristic
122C42C4×D27711yescharacteristic
123C42D110811yescharacteristic
124C42D110811yescharacteristic
125C23—5542no—
126C23C2×C22⋊D27711yescharacteristic
127Q8—11082no—
128D4—11082no—
129D4—11082no—
130D4—11084no—
131D4—11082no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—24no—
135C2×C4—41no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—5542no—
139C2×C4—11084no—
140C2×C4#1798454011yescharacteristic
141C2×C4#1798454011yescharacteristic
142C2×C4#1798454011yescharacteristic
143C2×C4#1798454011yescharacteristic
144C2×C4C2×C4×D27711yescharacteristic
145C2×C4C2×D110811yescharacteristic
146C8—11082no—
147C22—21no—
148C22—21no—
149C22—11082no—
150C22—11082no—
151C22—11082no—
152C22C2×#1798454011yescharacteristic
153C22#2257990512yes—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—44no—
160C4—11082no—
161C4#2257980812yes—
162C2—22no—
163C2—22162no—
164C2#3179997511yescharacteristic
165C2#3180000611yescharacteristic
166C2C2×#2257980811yescharacteristic
subgroupG/H
centerC22C2×#17984540
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
Fitting#376×C277C2
socleC22×C277C2×C22⋊C4
prime radical#31800552C2
cosocleC22×C4×C277C23
hypercenter#376D277
hypocenterC277#1505
LCSG ▷ C2×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #31800059C2semidirect
3. #31799735C2semidirect
4. #376×C277C2semidirect
6. #22579880C4semidirect
7. #22579877C4semidirect
12. C4×D1108C4semidirect
83. C277#1505semidirect
87. #376D277semidirect

Maximal subgroups

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

subgroupindex
#318005522
#318000592
#317997352
#376×C2772
#1505277