Finite Group Databasebeta

← #47982811

Subgroups — #47982811

Order 35456.

164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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#31800405C211yesmaximal, characteristic
2#31800354C211yesmaximal, characteristic
3#31800353C211yesmaximal, characteristic
4#31800352C211yesmaximal, characteristic
5#31800352C211yesmaximal, characteristic
6#31799724C211yesmaximal, characteristic
7#498×C277C211yesmaximal, characteristic
8#22579880C2211yescharacteristic
9#22579880C2211yescharacteristic
10#22579813—22no—
11#22579805—22no—
12#22579804—22no—
13#22579804—22no—
14#22579803—22no—
15C4×#14555660C2211yescharacteristic
16C4×#14555660C2211yescharacteristic
17C4⋊Q8×C277C2211yescharacteristic
18C4⋊Q8×C277C2211yescharacteristic
19#106×C277—22no—
20C4×C8×C277C2211yescharacteristic
21C2×Dic554—21no—
22C2×Dic554—21no—
23C2×#14555660D412yes—
24C2×#14555660D412yes—
25C4⋊Dic277—21no—
26C4⋊Dic277—21no—
27C4⋊Dic277—21no—
28C4⋊Dic277—21no—
29C2×Q8×C277—21no—
30C2×Q8×C277—21no—
31C2×C8×C277D412yes—
32C4⋊C4×C277—21no—
33C4⋊C4×C277—21no—
34C4⋊C4×C277—21no—
35C4⋊C4×C277—21no—
36C42×C277C2311yescharacteristic
37Dic554—42no—
38Dic554—42no—
39C2×Dic277—41no—
40C2×Dic277—41no—
41#14555660—22no—
42#14555660—22no—
43Q8×C277—42no—
44Q8×C277—42no—
45C2×C4×C277—41no—
46C2×C4×C277—41no—
47C2×C4×C277C2×D411yescharacteristic
48C2×C4×C277C2×D411yescharacteristic
49C2×C4×C277C2×D411yescharacteristic
50C8×C277—22no—
51C22×C277#12711yescharacteristic
52C4×C277—81no—
53C4×C277—81no—
54C4×C277#13512yes—
55C4×C277#13712yes—
56C4×C277#13712yes—
57Dic277—81no—
58Dic277—81no—
59C2×C277#49511yescharacteristic
60C2×C277#49711yescharacteristic
61C2×C277#49711yescharacteristic
62C277#171811yescharacteristic, complemented, Sylow
63#1718—2771nomaximal, Sylow
64#500—2771no—
65#498D27711yescharacteristic
66#487—2771no—
67#487—2771no—
68#487—2771no—
69#487—2771no—
70#322—2771no—
71C4⋊Q8—2771no—
72C4⋊Q8—2771no—
73C4⋊Q8C2×D27711yescharacteristic
74C4⋊Q8C2×D27711yescharacteristic
75#107—5542no—
76#106—22no—
77#103—5542no—
78#103—5542no—
79#103—5542no—
80#103—5542no—
81C4×C8—2771no—
82C4×C8—2771no—
83C4×C8C2×D27711yescharacteristic
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—5541no—
87C2×Q8—5541no—
88C2×C8—2772no—
89C2×C8—2772no—
90C2×C8C22⋊D27712yes—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—5541no—
96C4⋊C4—5541no—
97C4⋊C4—5541no—
98C4⋊C4—5541no—
99C42C22×D27711yescharacteristic
100Q8—42no—
101Q8—42no—
102Q8—11082no—
103Q8—11082no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—11081no—
107C2×C4—11081no—
108C2×C4D4×D27711yescharacteristic
109C2×C4D4×D27711yescharacteristic
110C2×C4C2×C22⋊D27711yescharacteristic
111C8—22no—
112C8—5542no—
113C8—5542no—
114C22#2257987611yescharacteristic
115C4—81no—
116C4—81no—
117C4—22161no—
118C4—22161no—
119C4#2257990112yes—
120C4#2257990912yes—
121C4#2257991112yes—
122C2#3180038311yescharacteristic
123C2#3180039311yescharacteristic
124C2#3180039411yescharacteristic
subgroupG/H
centerC22#22579876
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#498×C277C2
socle, prime radicalC22×C277#127
hypercenter#498D277
hypocenterC277#1718
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
62. C277#1718semidirect

Maximal subgroups

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

subgroupindex
#318004052
#318003542
#318003532
#318003522
#317997242
#498×C2772
#1718277