Finite Group Databasebeta

← #47985118

Subgroups — #47985118

Order 35456.

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

normal subgroups only

This group has 216 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#31800442C212yesmaximal, complemented
2#31800260C211yesmaximal, characteristic, complemented
3#31799812C212yesmaximal, complemented
4#31799784C211yesmaximal, characteristic, complemented
5#575×C277C211yesmaximal, characteristic
6C2×Dic1108C2211yescharacteristic, complemented
7#22579859—21no—
8#22579826—22no—
9#22579824—22no—
10#22579820C2212yescomplemented
11#22579812C2211yescharacteristic, complemented
12#22579805—21no—
13C2×#41×C277—21no—
14#137×C277—22no—
15AGL(1,ℤ/8)×C277—22no—
16#135×C277—21no—
17#135×C277C2212yes—
18C2×M16×C277C2211yescharacteristic
19C2×Dic554—21no—
20Dic1108—22no—
21C4⋊Dic277—21no—
22#17984542—41no—
23C22⋊Dic277—41no—
24#17984538—22no—
25#41×C277—22no—
26#41×C277—22no—
27#41×C277—41no—
28#41×C277—41no—
29C2×Q8×C277—21no—
30C2×D4×C277—21no—
31C2×D4×C277—41no—
32C22×C4×C277—41no—
33C22×C4×C277D411yescharacteristic
34Q16×C277—21no—
35Q16×C277D412yes—
36SD16×C277—22no—
37SD16×C277—22no—
38D8×C277—21no—
39D8×C277D412yes—
40M16×C277—22no—
41C2×C8×C277D411yescharacteristic
42C2×C8×C277C2311yescharacteristic
43Dic554—41no—
44Dic554—41no—
45C2×Dic277—41no—
46C2×Dic277—41no—
47C23×C277—41no—
48C23×C277D811yescharacteristic
49Q8×C277—22no—
50Q8×C277—41no—
51D4×C277—22no—
52D4×C277—41no—
53D4×C277—42no—
54D4×C277—42no—
55C2×C4×C277—21no—
56C2×C4×C277—21no—
57C2×C4×C277—42no—
58C2×C4×C277—41no—
59C2×C4×C277—42no—
60C2×C4×C277D811yescharacteristic
61C2×C4×C277C2×D411yescharacteristic
62C8×C277—21no—
63C8×C277C2×D412yes—
64C22×C277—21no—
65C22×C277—41no—
66C22×C277—42no—
67C22×C277—82no—
68C22×C277C2×D811yescharacteristic
69C4×C277—21no—
70C4×C277—42no—
71C4×C277#12011yescharacteristic
72C4×C277AGL(1,ℤ/8)11yescharacteristic
73Dic277—81no—
74Dic277—81no—
75C2×C277—21no—
76C2×C277—41no—
77C2×C277—82no—
78C2×C277#44711yescharacteristic
79C277#219111yescharacteristic, complemented, Sylow
80#2191—2771nomaximal, Sylow
81#575D27711yescharacteristic
82#510—2772no—
83#470—2771no—
84#360—2772no—
85#349—2771no—
86C2×#41—21no—
87#137—22no—
88AGL(1,ℤ/8)—22no—
89#135—21no—
90#135C2×D27712yes—
91C2×Q16—2771no—
92C2×M16C2×D27711yescharacteristic
93C22⋊Q8—5541no—
94Q32—5542no—
95SD32—5542no—
96M32—2772no—
97#106—2771no—
98#103—5541no—
99#41—22no—
100#41—22no—
101#41—41no—
102#41—41no—
103C2×Q8—21no—
104C2×Q8—5541no—
105C2×D4—21no—
106C2×D4—41no—
107C22×C4—41no—
108C22×C4C22⋊D27711yescharacteristic
109Q16—21no—
110Q16—5542no—
111Q16C22⋊D27712yes—
112SD16—22no—
113SD16—22no—
114D8—21no—
115D8C22⋊D27712yes—
116M16—22no—
117C2×C8C22⋊D27711yescharacteristic
118C2×C8C22×D27711yescharacteristic
119C4⋊C4—5541no—
120C4⋊C4—11081no—
121C22⋊C4—11081no—
122C16—5542no—
123C23—41no—
124C23#1798454811yescharacteristic
125Q8—22no—
126Q8—41no—
127Q8—11081no—
128Q8—11081no—
129D4—22no—
130D4—41no—
131D4—42no—
132D4—42no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—42no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—11081no—
139C2×C4—11081no—
140C2×C4#1798454811yescharacteristic
141C2×C4C2×C22⋊D27711yescharacteristic
142C8—21no—
143C8C2×C22⋊D27712yes—
144C22—21no—
145C22—41no—
146C22—42no—
147C22—82no—
148C22C2×#1798454811yescharacteristic
149C4—21no—
150C4—42no—
151C4—22161no—
152C4—22161no—
153C4#2257984911yescharacteristic
154C4#2257990611yescharacteristic
155C2—21no—
156C2—41no—
157C2—82no—
158C2#3180013611yescharacteristic
subgroupG/H
centerC2#31800136
commutator, cosocleC2×C8×C277C23
FrattiniC2×C8C22×D277
Fitting, prime radical#575×C277C2
socleC2×C277#447
hypercenter#575D277
hypocenterC277#2191
LCSG ▷ C2×C8×C277 ▷ C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #31800442C2semidirect
2. #31800260C2semidirect
3. #31799812C2semidirect
4. #31799784C2semidirect
6. C2×Dic1108C22semidirect
10. #22579820C22semidirect
11. #22579812C22semidirect
79. C277#2191semidirect

Maximal subgroups

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

subgroupindex
#318004422
#318002602
#317998122
#317997842
#575×C2772
#2191277