Finite Group Databasebeta

← #47985183

Subgroups — #47985183

Order 35456.

248 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 41 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#31800744C211yesmaximal, characteristic, complemented
2#31800175C212yesmaximal, complemented
3#31799799C211yesmaximal, characteristic, complemented
4#31799798C212yesmaximal, complemented
5#454×C277C211yesmaximal, characteristic, complemented
6#22579905—22no—
7#22579869C2212yes—
8#22579868—21no—
9#22579866—22no—
10#22579850—22no—
11#22579848—21no—
12#22579807—22no—
13#22579799C2212yescomplemented
142−1+4×C277C2211yescharacteristic, complemented
15AGL(1,ℤ/8)×C277—21no—
16#124×C277C2211yescharacteristic
17#104×C277—21no—
18#101×C277C2211yescharacteristic, complemented
19C23×D277—21no—
20C2×Dic554—21no—
21C2×D1108—21no—
22C2×D1108D412yes—
23C2×C22⋊D277—22no—
24#17984550—42no—
25#17984548—42no—
26#17984547—22no—
27C22⋊Dic277—21no—
28#17984540—22no—
29#17984540—22no—
30#17984540—22no—
31C4×Dic277D412yes—
32#41×C277—21no—
33#41×C277—22no—
34#41×C277—41no—
35C2×Q8×C277—41no—
36C2×Q8×C277C2311yescharacteristic
37C2×D4×C277D411yescharacteristic
38SD16×C277—41no—
39D8×C277—41no—
40M16×C277—21no—
41C22⋊C4×C277—22no—
42C42×C277D411yescharacteristic
43C22×D277—22no—
44C22×D277—82no—
45C22×D277—81no—
46Dic554—81no—
47D1108—42no—
48D1108—81no—
49C22⋊D277—82no—
50C2×Dic277—22no—
51#14555660—42no—
52C23×C277—21no—
53Q8×C277—21no—
54Q8×C277—22no—
55Q8×C277—41no—
56D4×C277—21no—
57D4×C277—22no—
58D4×C277—41no—
59D4×C277—41no—
60C2×C4×C277—21no—
61C2×C4×C277—41no—
62C2×C4×C277—42no—
63C2×C4×C277C2×D412yes—
64C2×C4×C277C2×D411yescharacteristic
65C8×C277—41no—
66C22×C277—42no—
67C22×C277—41no—
68C22×C277—41no—
69C22×C277#12011yescharacteristic
70C2×D277—42no—
71C2×D277—42no—
72C2×D277—42no—
73C2×D277—84no—
74C4×C277—21no—
75C4×C277—22no—
76C4×C277—41no—
77C4×C277—41no—
78Dic277—42no—
79C2×C277—21no—
80C2×C277—81no—
81C2×C277—81no—
82C2×C277B(4,𝔽2)11yescharacteristic
83D277—82no—
84C277#220211yescharacteristic, complemented, Sylow
85#2202—2771nomaximal, Sylow
86H(3,𝔽4)—2771no—
87#454—2772no—
88#454D27711yescharacteristic, complemented
89#355—2771no—
90#355—2772no—
912−1+4C2×D27711yescharacteristic, complemented
92AGL(1,ℤ/8)—21no—
93AGL(1,ℤ/8)—5542no—
94#124—2772no—
95#124—5542no—
96#124—5541no—
97#124C2×D27711yescharacteristic
98#120—5542no—
99#120—5541no—
100#104—21no—
101#104—5542no—
102#101—2772no—
103#101C2×D27711yescharacteristic, complemented
104C24—5541no—
105#41—22no—
106#41—21no—
107#41—41no—
108C2×Q8—41no—
109C2×Q8—5541no—
110C2×Q8C22×D27711yescharacteristic
111C2×D4—2772no—
112C2×D4—5541no—
113C2×D4—5542no—
114C2×D4C22⋊D27711yescharacteristic
115SD16—41no—
116SD16—11082no—
117D8—41no—
118D8—11082no—
119M16—21no—
120M16—5542no—
121C22⋊C4—22no—
122C22⋊C4—5542no—
123C22⋊C4—5541no—
124C22⋊C4—5542no—
125C22⋊C4—5542no—
126C42—2772no—
127C42C22⋊D27711yescharacteristic
128C23—21no—
129C23—5542no—
130C23—22162no—
131C23—22161no—
132Q8—21no—
133Q8—22no—
134Q8—41no—
135Q8—22161no—
136D4—21no—
137D4—22no—
138D4—41no—
139D4—41no—
140D4—11082no—
141D4—22161no—
142D4—22162no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—42no—
146C2×C4—5542no—
147C2×C4D4×D27712yes—
148C2×C4C2×C22⋊D27711yescharacteristic
149C8—41no—
150C8—11082no—
151C22—42no—
152C22—41no—
153C22—41no—
154C22—11082no—
155C22—11082no—
156C22—11082no—
157C22—22164no—
158C22#2257984811yescharacteristic
159C4—21no—
160C4—22no—
161C4—41no—
162C4—41no—
163C4—11082no—
164C2—21no—
165C2—81no—
166C2—81no—
167C2—22162no—
168C2#3180018811yescharacteristic
subgroupG/H
centerC2#31800188
commutator, cosocleC2×Q8×C277C23
FrattiniC2×Q8C22×D277
Fitting#454×C277C2
socleC2×C277B(4,𝔽2)
hypercenter#454D277
hypocenterC277#2202
LCSG ▷ C2×Q8×C277 ▷ C22×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #31800744C2semidirect
2. #31800175C2semidirect
3. #31799799C2semidirect
4. #31799798C2semidirect
5. #454×C277C2semidirect
13. #22579799C22semidirect
14. 2−1+4×C277C22semidirect
18. #101×C277C22semidirect
84. C277#2202semidirect
88. #454D277semidirect
91. 2−1+4C2×D277semidirect
103. #101C2×D277semidirect

Maximal subgroups

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

subgroupindex
#318007442
#318001752
#317997992
#317997982
#454×C2772
#2202277