Finite Group Databasebeta

← #47982252

Subgroups — #47982252

Order 35456.

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

normal subgroups only

This group has 240 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#31800717C211yesmaximal, characteristic, complemented
2#31800375C211yesmaximal, characteristic, complemented
3#31800198C211yesmaximal, characteristic, complemented
4#31800197C211yesmaximal, characteristic, complemented
5#31799750C211yesmaximal, characteristic, complemented
6#31799731C211yesmaximal, characteristic, complemented
7D4⋊C8×C277C211yesmaximal, characteristic, complemented
8C2×#17984552—22no—
9C2×D2216—21no—
10C2×#17984548—21no—
11#22579880C2211yescharacteristic
12#22579877C2211yescharacteristic
13#22579866—22no—
14#22579854—21no—
15#22579851—21no—
16C4×D1108C2211yescharacteristic
17#22579839—21no—
18#22579838—21no—
19C4⋊#14555660C2211yescharacteristic
20#22579802—21no—
21#22579800—21no—
22C4×D4×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4×C8×C277C2211yescharacteristic
25C2×Dic554D412yes—
26C2×D1108—21no—
27C2×D1108—21no—
28C2×D1108—21no—
29C2×D1108D411yescharacteristic
30C2×C22⋊D277—22no—
31C2×C4×D277—21no—
32#17984552—44no—
33D2216—42no—
34#17984548—42no—
35C2×#14555660—21no—
36C4⋊Dic277—21no—
37C4⋊Dic277—21no—
38C4⋊Dic277D411yescharacteristic
39C22⋊Dic277—22no—
40#17984540—22no—
41#17984540—21no—
42C4×Dic277—22no—
43C2×D4×C277D411yescharacteristic
44C22×C4×C277—21no—
45C2×C8×C277—21no—
46C2×C8×C277—21no—
47C4⋊C4×C277D411yescharacteristic
48C22⋊C4×C277—21no—
49C42×C277C2311yescharacteristic
50C22×D277—21no—
51C22×D277—41no—
52Dic554—42no—
53D1108—21no—
54D1108—21no—
55D1108—42no—
56D1108—41no—
57D1108—41no—
58D1108—41no—
59D1108—41no—
60C22⋊D277—82no—
61C2×Dic277—21no—
62C2×Dic277—22no—
63C4×D277—41no—
64C4×D277—41no—
65#14555660—41no—
66C23×C277—21no—
67D4×C277—21no—
68D4×C277—21no—
69C2×C4×C277—21no—
70C2×C4×C277—41no—
71C2×C4×C277—41no—
72C2×C4×C277C2×D411yescharacteristic
73C2×C4×C277C2×D411yescharacteristic
74C2×C4×C277C2×D411yescharacteristic
75C8×C277—22no—
76C8×C277—41no—
77C22×C277—41no—
78C22×C277—41no—
79C22×C277—41no—
80C22×C277#12011yescharacteristic
81C2×D277—41no—
82C2×D277—41no—
83C2×D277—41no—
84C2×D277—81no—
85C2×D277—81no—
86C2×D277—81no—
87C4×C277—21no—
88C4×C277—41no—
89C4×C277#13511yescharacteristic
90C4×C277#13511yescharacteristic
91C4×C277AGL(1,ℤ/8)11yescharacteristic
92C4×C277AGL(1,ℤ/8)11yescharacteristic
93Dic277—41no—
94Dic277—42no—
95C2×C277—81no—
96C2×C277#44911yescharacteristic
97C2×C277#44911yescharacteristic
98C2×C277#45311yescharacteristic
99D277—81no—
100D277—161no—
101C277#162411yescharacteristic, complemented, Sylow
102#1624—2771nomaximal, Sylow
103#555—2771no—
104#492—2771no—
105#459—2771no—
106#459—2771no—
107#333—2771no—
108D4⋊C8—2771no—
109D4⋊C8D27711yescharacteristic, complemented
110C2×SD16—5542no—
111C2×D8—5541no—
112C2×D8—5541no—
113C4⋊Q8—2771no—
114#127—2771no—
115#124—5542no—
116#121—5541no—
117#121—5541no—
118C4×D4—2771no—
119C4×D4C2×D27711yescharacteristic
120#117—5541no—
121#117—5541no—
122C4⋊C8—2771no—
123C4⋊C8C2×D27711yescharacteristic
124#102—5541no—
125#102—5541no—
126C4×C8C2×D27711yescharacteristic
127C2×Q8—2772no—
128C2×D4—2771no—
129C2×D4—5542no—
130C2×D4—5541no—
131C2×D4—5541no—
132C2×D4—5541no—
133C2×D4D110811yescharacteristic
134C22×C4—21no—
135C22×C4—5541no—
136SD16—11084no—
137D8—11082no—
138D8—11082no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—5541no—
142C4⋊C4—2771no—
143C4⋊C4—5541no—
144C4⋊C4—5541no—
145C4⋊C4D110811yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—5542no—
148C22⋊C4—5542no—
149C22⋊C4—5541no—
150C42—5542no—
151C42C22×D27711yescharacteristic
152C23—21no—
153C23—5541no—
154C23—11081no—
155Q8—11082no—
156D4—21no—
157D4—21no—
158D4—5541no—
159D4—5541no—
160D4—11082no—
161D4—11081no—
162D4—11081no—
163D4—11081no—
164D4—11081no—
165D4—22162no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—5541no—
170C2×C4—5542no—
171C2×C4—11081no—
172C2×C4—11081no—
173C2×C4D4×D27711yescharacteristic
174C2×C4D4×D27711yescharacteristic
175C2×C4C2×D110811yescharacteristic
176C8—22no—
177C8—41no—
178C8—11081no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—11081no—
183C22—11081no—
184C22—11081no—
185C22—22161no—
186C22—22161no—
187C22—22161no—
188C22#2257985011yescharacteristic
189C4—21no—
190C4—41no—
191C4—11081no—
192C4—11082no—
193C4#2257990111yescharacteristic
194C4#2257990211yescharacteristic
195C4#2257990411yescharacteristic
196C4#2257990811yescharacteristic
197C2—81no—
198C2—44321no—
199C2—22161no—
200C2#3180014811yescharacteristic
201C2#3180014911yescharacteristic
202C2#3180017111yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
FittingD4⋊C8×C277C2
socleC22×C277#120
hypercenterD4⋊C8D277
hypocenterC277#1624
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #31800717C2semidirect
2. #31800375C2semidirect
3. #31800198C2semidirect
4. #31800197C2semidirect
5. #31799750C2semidirect
6. #31799731C2semidirect
7. D4⋊C8×C277C2semidirect
101. C277#1624semidirect
109. D4⋊C8D277semidirect

Maximal subgroups

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

subgroupindex
#318007172
#318003752
#318001982
#318001972
#317997502
#317997312
D4⋊C8×C2772
#1624277