Finite Group Databasebeta

← #47982479

Subgroups — #47982479

Order 35456.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#31800752C211yesmaximal, characteristic
2#31800411C212yesmaximal, complemented
3#31800397C211yesmaximal, characteristic
4#31799743C212yesmaximal, complemented
5#329×C277C211yesmaximal, characteristic
6C2×#17984553—21no—
7C2×#17984551—21no—
8#22579880C2211yescharacteristic
9#22579878—21no—
10#22579873—22no—
11#22579872C2212yes—
12#22579861—21no—
13#22579857—22no—
14#22579814—22no—
15#22579812—22no—
16#22579791C2211yescharacteristic
17#124×C277C2211yescharacteristic
18#97×C277C2212yes—
19C2×Dic554—21no—
20C2×Dic554—21no—
21C22×Dic277—21no—
22#17984553—42no—
23#17984551—42no—
24C2×#14555660—21no—
25C4⋊Dic277—22no—
26C4⋊Dic277D412yes—
27C4⋊Dic277D412yes—
28#17984542—22no—
29#17984542—22no—
30#17984542—22no—
31C22⋊Dic277—22no—
32C22⋊Dic277—21no—
33C4×Dic277—21no—
34C2×Q8×C277D411yescharacteristic
35C2×D4×C277D411yescharacteristic
36C2×C8×C277—22no—
37C22⋊C4×C277—22no—
38C42×C277C2311yescharacteristic
39Dic554—41no—
40Dic554—41no—
41Dic554—81no—
42C2×Dic277—22no—
43C2×Dic277—22no—
44C2×Dic277—41no—
45C2×Dic277—81no—
46#14555660—22no—
47C23×C277—21no—
48Q8×C277—41no—
49D4×C277—41no—
50C2×C4×C277—21no—
51C2×C4×C277C2×D412yes—
52C2×C4×C277C2×D411yescharacteristic
53C8×C277—24no—
54C22×C277—41no—
55C22×C277—42no—
56C22×C277#12011yescharacteristic
57C4×C277—21no—
58C4×C277—22no—
59C4×C277—41no—
60Dic277—42no—
61Dic277—42no—
62Dic277—81no—
63C2×C277—81no—
64C2×C277#45311yescharacteristic
65C2×C277#45612yes—
66C277#166011yescharacteristic, complemented, Sylow
67#1660—2771nomaximal, Sylow
68#563—2771no—
69#501—2772no—
70#497—2771no—
71#330—2772no—
72#329D27711yescharacteristic
73C2×Q16—5541no—
74C2×SD16—5541no—
75C4⋊Q8—2771no—
76C4⋊Q8—5541no—
77#126—5542no—
78#125—2772no—
79#124C2×D27711yescharacteristic
80#123—5541no—
81C22⋊Q8—5542no—
82#107—5542no—
83#106—5542no—
84#97—2771no—
85#97C2×D27712yes—
86C2×Q8—5541no—
87C2×Q8—5541no—
88C2×Q8D110811yescharacteristic
89C2×D4D110811yescharacteristic
90C22×C4—5541no—
91Q16—11082no—
92SD16—11082no—
93C2×C8—22no—
94C2×C8—5541no—
95C4⋊C4—2772no—
96C4⋊C4—2772no—
97C4⋊C4—5542no—
98C4⋊C4—5542no—
99C4⋊C4—5542no—
100C4⋊C4—5542no—
101C22⋊C4—22no—
102C22⋊C4—5542no—
103C22⋊C4—5541no—
104C42—5541no—
105C42C22×D27711yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—11081no—
109Q8—11081no—
110Q8—22161no—
111D4—41no—
112C2×C4—21no—
113C2×C4—5542no—
114C2×C4—5542no—
115C2×C4—11081no—
116C2×C4—22161no—
117C2×C4D4×D27712yes—
118C2×C4C2×D110811yescharacteristic
119C8—24no—
120C8—5542no—
121C22—41no—
122C22—42no—
123C22#2257985011yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—11082no—
128C4—11082no—
129C4—22161no—
130C2—81no—
131C2#3180017211yescharacteristic
132C2#3180018612yes—
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#329×C277C2
socleC22×C277#120
prime radicalC2×D4×C277D4
hypercenter#329D277
hypocenterC277#1660
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31800411C2semidirect
4. #31799743C2semidirect
66. C277#1660semidirect

Maximal subgroups

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

subgroupindex
#318007522
#318004112
#318003972
#317997432
#329×C2772
#1660277