Finite Group Databasebeta

← #47985151

Subgroups — #47985151

Order 35456.

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

normal subgroups only

This group has 354 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#31800188C212yesmaximal, complemented
2#31800169C211yesmaximal, characteristic, complemented
3#31799795C211yesmaximal, characteristic, complemented
4#31799789C212yesmaximal, complemented
5D42×C277C211yesmaximal, characteristic, complemented
6#22579925C2211yescharacteristic, complemented
7#22579906—21no—
8#22579849—22no—
9#22579808—21no—
10#22579797C2211yescharacteristic, complemented
11#22579795C2212yescomplemented
12#22579794—22no—
13C22×D4×C277—22no—
14#127×C277C2211yescharacteristic
15#121×C277—22no—
16#120×C277—21no—
17#120×C277C2212yes—
18C4×D4×C277—21no—
19#17984563—21no—
20#17984562—41no—
21C2×C22⋊D277—22no—
22C2×C22⋊D277—42no—
23D4×D277—41no—
24#17984551—41no—
25#17984548—41no—
26#17984547—21no—
27C22⋊Dic277—22no—
28C22⋊Dic277—42no—
29C24×C277—21no—
30C24×C277D412yescomplemented
31C2×D4×C277—21no—
32C2×D4×C277—22no—
33C2×D4×C277—22no—
34C2×D4×C277—22no—
35C2×D4×C277—48no—
36C2×D4×C277D411yescharacteristic, complemented
37C2×D4×C277C2311yescharacteristic
38C22×C4×C277—22no—
39C4⋊C4×C277—21no—
40C22⋊C4×C277—21no—
41C22⋊C4×C277—22no—
42C22⋊C4×C277D412yescomplemented
43C42×C277D411yescharacteristic, complemented
44C22×D277—22no—
45Dic554—21no—
46D1108—21no—
47C22⋊D277—42no—
48C22⋊D277—41no—
49C22⋊D277—84no—
50C2×Dic277—22no—
51C2×Dic277—42no—
52C4×D277—41no—
53#14555660—41no—
54C23×C277—22no—
55C23×C277—21no—
56C23×C277—44no—
57C23×C277—42no—
58C23×C277—44no—
59C23×C277—81no—
60C23×C277C2×D412yes—
61D4×C277—24no—
62D4×C277—41no—
63D4×C277—41no—
64D4×C277—44no—
65D4×C277—44no—
66D4×C277—44no—
67C2×C4×C277—21no—
68C2×C4×C277—22no—
69C2×C4×C277—44no—
70C2×C4×C277C2×D411yescharacteristic
71C22×C277—24no—
72C22×C277—22no—
73C22×C277—42no—
74C22×C277—42no—
75C22×C277—42no—
76C22×C277—44no—
77C22×C277—42no—
78C22×C277—41no—
79C22×C277—82no—
80C22×C277—84no—
81C22×C277#12011yescharacteristic
82C2×D277—41no—
83C2×D277—82no—
84C4×C277—22no—
85C4×C277—21no—
86C4×C277—42no—
87Dic277—41no—
88Dic277—82no—
89C2×C277—21no—
90C2×C277—42no—
91C2×C277—44no—
92C2×C277—81no—
93C2×C277B(4,𝔽2)11yescharacteristic
94D277—81no—
95C277#219611yescharacteristic, complemented, Sylow
96#2196—2771nomaximal, Sylow
97D42D27711yescharacteristic, complemented
98B(4,𝔽2)—2772no—
99#453—2771no—
100#353—2771no—
101AΣL(1,𝔽16)—2772no—
102H(5,𝔽2)—2771no—
103C22×D4—22no—
104AGL(1,ℤ/8)—5541no—
105#127C2×D27711yescharacteristic
106#121—22no—
107#120—21no—
108#120—5542no—
109#120C2×D27712yes—
110C4×D4—21no—
111#104—5541no—
112#100—2771no—
113#99—2772no—
114#99—5542no—
115C24—21no—
116C24C22⋊D27712yescomplemented
117#41—5541no—
118#41—11081no—
119C2×D4—21no—
120C2×D4—22no—
121C2×D4—22no—
122C2×D4—22no—
123C2×D4—48no—
124C2×D4—5542no—
125C2×D4—11081no—
126C2×D4—11082no—
127C2×D4C22⋊D27711yescharacteristic, complemented
128C2×D4C22×D27711yescharacteristic
129C22×C4—22no—
130SD16—11081no—
131D8—11081no—
132M16—5541no—
133C4⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—22no—
136C22⋊C4—5542no—
137C22⋊C4—11082no—
138C22⋊C4C22⋊D27712yescomplemented
139C42C22⋊D27711yescharacteristic, complemented
140C23—22no—
141C23—21no—
142C23—42no—
143C23—44no—
144C23—44no—
145C23—81no—
146C23—5542no—
147C23C2×C22⋊D27712yes—
148Q8—5541no—
149D4—24no—
150D4—41no—
151D4—41no—
152D4—44no—
153D4—44no—
154D4—44no—
155D4—5541no—
156D4—11082no—
157D4—11081no—
158D4—22164no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—44no—
162C2×C4—5542no—
163C2×C4—11081no—
164C2×C4—11082no—
165C2×C4C2×C22⋊D27711yescharacteristic
166C8—11081no—
167C22—24no—
168C22—22no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—44no—
173C22—42no—
174C22—41no—
175C22—82no—
176C22—84no—
177C22—11081no—
178C22—22162no—
179C22#2257984911yescharacteristic
180C4—22no—
181C4—21no—
182C4—42no—
183C4—11081no—
184C4—22162no—
185C2—21no—
186C2—42no—
187C2—44no—
188C2—81no—
189C2—22161no—
190C2#3180018911yescharacteristic
subgroupG/H
centerC2#31800189
commutator, cosocleC2×D4×C277C23
FrattiniC2×D4C22×D277
FittingD42×C277C2
socleC2×C277B(4,𝔽2)
hypercenterD42D277
hypocenterC277#2196
LCSG ▷ C2×D4×C277 ▷ C22×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #31800188C2semidirect
2. #31800169C2semidirect
3. #31799795C2semidirect
4. #31799789C2semidirect
5. D42×C277C2semidirect
6. #22579925C22semidirect
10. #22579797C22semidirect
11. #22579795C22semidirect
30. C24×C277D4semidirect
36. C2×D4×C277D4semidirect
42. C22⋊C4×C277D4semidirect
43. C42×C277D4semidirect
95. C277#2196semidirect
97. D42D277semidirect
116. C24C22⋊D277semidirect
127. C2×D4C22⋊D277semidirect
138. C22⋊C4C22⋊D277semidirect
139. C42C22⋊D277semidirect

Maximal subgroups

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

subgroupindex
#318001882
#318001692
#317997952
#317997892
D42×C2772
#2196277