Finite Group Databasebeta

← #47982258

Subgroups — #47982258

Order 35456.

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

normal subgroups only

This group has 256 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#31800656C211yesmaximal, characteristic, complemented
2#31800349C211yesmaximal, characteristic, complemented
3#31800198C211yesmaximal, characteristic, complemented
4#31800197C211yesmaximal, characteristic, complemented
5#31799747C211yesmaximal, characteristic, complemented
6#31799731C211yesmaximal, characteristic, complemented
7D4⋊C8×C277C211yesmaximal, characteristic, complemented
8C2×#17984562—21no—
9C2×D2216—21no—
10C2×#17984548—21no—
11#22579880C2211yescharacteristic
12#22579877C2211yescharacteristic
13#22579864—22no—
14#22579860—21no—
15#22579854—21no—
16C4×D1108C2211yescharacteristic
17C2×C4⋊Dic277—21no—
18C4⋊#14555660C2211yescharacteristic
19#22579802—22no—
20#22579802—21no—
21#22579800—21no—
22C4×D4×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4×C8×C277C2211yescharacteristic
25#17984562—42no—
26#17984562—42no—
27C2×Dic554—21no—
28C2×D1108—21no—
29C2×D1108—21no—
30C2×D1108—21no—
31C2×D1108D411yescharacteristic
32C2×C22⋊D277—22no—
33C22×Dic277—22no—
34C2×C4×D277—21no—
35D2216—42no—
36#17984548—42no—
37C2×#14555660—21no—
38C4⋊Dic277—22no—
39C4⋊Dic277—21no—
40C4⋊Dic277D411yescharacteristic
41C4⋊Dic277D412yes—
42#17984540—22no—
43#17984540—21no—
44C2×D4×C277D411yescharacteristic
45C22×C4×C277—21no—
46C2×C8×C277—21no—
47C2×C8×C277—21no—
48C4⋊C4×C277D411yescharacteristic
49C22⋊C4×C277—21no—
50C42×C277C2311yescharacteristic
51C22×D277—21no—
52C22×D277—41no—
53Dic554—41no—
54Dic554—41no—
55D1108—21no—
56D1108—21no—
57D1108—42no—
58D1108—41no—
59D1108—41no—
60D1108—41no—
61D1108—41no—
62C22⋊D277—44no—
63C2×Dic277—21no—
64C2×Dic277—22no—
65C2×Dic277—44no—
66C4×D277—41no—
67C4×D277—41no—
68#14555660—41no—
69C23×C277—21no—
70D4×C277—21no—
71D4×C277D812yescomplemented
72C2×C4×C277—21no—
73C2×C4×C277—41no—
74C2×C4×C277—41no—
75C2×C4×C277C2×D411yescharacteristic
76C2×C4×C277C2×D411yescharacteristic
77C2×C4×C277C2×D411yescharacteristic
78C8×C277—41no—
79C8×C277—41no—
80C22×C277—22no—
81C22×C277—41no—
82C22×C277—41no—
83C22×C277#12011yescharacteristic
84C2×D277—41no—
85C2×D277—41no—
86C2×D277—41no—
87C2×D277—81no—
88C2×D277—81no—
89C2×D277—81no—
90C4×C277—21no—
91C4×C277—41no—
92C4×C277C2×D811yescharacteristic
93C4×C277#13511yescharacteristic
94C4×C277AGL(1,ℤ/8)11yescharacteristic
95C4×C277AGL(1,ℤ/8)11yescharacteristic
96Dic277—41no—
97Dic277—42no—
98C2×C277—42no—
99C2×C277#44711yescharacteristic
100C2×C277#44911yescharacteristic
101C2×C277#45411yescharacteristic
102D277—81no—
103D277—161no—
104C277#162511yescharacteristic, complemented, Sylow
105#1625—2771nomaximal, Sylow
106#547—2771no—
107#486—2771no—
108#459—2771no—
109#459—2771no—
110#332—2771no—
111D4⋊C8—2771no—
112D4⋊C8D27711yescharacteristic, complemented
113C2×#41—5541no—
114C2×D8—5541no—
115C2×D8—5541no—
116C4⋊Q8—2771no—
117#127—2771no—
118#123—5542no—
119C22⋊Q8—5541no—
120#121—5541no—
121C4×D4—2771no—
122C4×D4C2×D27711yescharacteristic
123C2×C4⋊C4—5541no—
124C4⋊C8—2771no—
125C4⋊C8C2×D27711yescharacteristic
126#102—5541no—
127#102—5542no—
128#102—5541no—
129C4×C8C2×D27711yescharacteristic
130#41—11082no—
131#41—11082no—
132C2×Q8—5541no—
133C2×D4—2771no—
134C2×D4—5542no—
135C2×D4—5541no—
136C2×D4—5541no—
137C2×D4—5541no—
138C2×D4D110811yescharacteristic
139C22×C4—21no—
140C22×C4—5542no—
141C22×C4—5541no—
142D8—11082no—
143D8—11082no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—5541no—
147C4⋊C4—2771no—
148C4⋊C4—2772no—
149C4⋊C4—5542no—
150C4⋊C4—5541no—
151C4⋊C4D110811yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—5542no—
154C22⋊C4—5541no—
155C42C22×D27711yescharacteristic
156C23—21no—
157C23—5541no—
158C23—11081no—
159Q8—11081no—
160Q8—11081no—
161D4—21no—
162D4—5541no—
163D4—5541no—
164D4—11082no—
165D4—11084no—
166D4—11081no—
167D4—11081no—
168D4—11081no—
169D4—11081no—
170D4D221612yescomplemented
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—5541no—
175C2×C4—5542no—
176C2×C4—11084no—
177C2×C4—11081no—
178C2×C4—11081no—
179C2×C4D4×D27711yescharacteristic
180C2×C4D4×D27711yescharacteristic
181C2×C4C2×D110811yescharacteristic
182C8—41no—
183C8—41no—
184C8—11081no—
185C22—22no—
186C22—41no—
187C22—41no—
188C22—11081no—
189C22—11081no—
190C22—11081no—
191C22—22161no—
192C22—22161no—
193C22—22161no—
194C22#2257985011yescharacteristic
195C4—21no—
196C4—41no—
197C4—11081no—
198C4—11082no—
199C4C2×D221611yescharacteristic
200C4#2257990111yescharacteristic
201C4#2257990411yescharacteristic
202C4#2257990811yescharacteristic
203C2—42no—
204C2—44321no—
205C2—22161no—
206C2#3180013811yescharacteristic
207C2#3180014811yescharacteristic
208C2#3180017611yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
FittingD4⋊C8×C277C2
socleC22×C277#120
hypercenterD4⋊C8D277
hypocenterC277#1625
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. #31800656C2semidirect
2. #31800349C2semidirect
3. #31800198C2semidirect
4. #31800197C2semidirect
5. #31799747C2semidirect
6. #31799731C2semidirect
7. D4⋊C8×C277C2semidirect
71. D4×C277D8semidirect
104. C277#1625semidirect
112. D4⋊C8D277semidirect
170. D4D2216semidirect

Maximal subgroups

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

subgroupindex
#318006562
#318003492
#318001982
#318001972
#317997472
#317997312
D4⋊C8×C2772
#1625277