Finite Group Databasebeta

← #47982253

Subgroups — #47982253

Order 35456.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#31800655C211yesmaximal, characteristic, complemented
2#31800194C211yesmaximal, characteristic, complemented
3#31800194C211yesmaximal, characteristic, complemented
4#31799748C211yesmaximal, characteristic, complemented
5#31799731C211yesmaximal, characteristic, complemented
6#31799731C211yesmaximal, characteristic, complemented
7#486×C277C211yesmaximal, characteristic, complemented
8C2×#17984564—21no—
9C2×#17984548—21no—
10C2×#17984548—21no—
11#22579865—22no—
12#22579856—21no—
13#22579855—21no—
14C4×D1108C2211yescharacteristic
15C4×D1108C2211yescharacteristic
16C4⋊C4×D277—21no—
17C4⋊#14555660C2211yescharacteristic
18C4⋊#14555660C2211yescharacteristic
19#22579801—21no—
20#22579801—21no—
21C4⋊Q8×C277C2211yescharacteristic
22#127×C277C2211yescharacteristic
23#102×C277—22no—
24C4×C8×C277C2211yescharacteristic
25#17984564—42no—
26#17984564—42no—
27C2×D1108—22no—
28C2×D1108D411yescharacteristic
29C2×D1108D411yescharacteristic
30C2×C4×D277—22no—
31C2×C4×D277—21no—
32C2×C4×D277—21no—
33#17984548—42no—
34#17984548—42no—
35C2×#14555660—21no—
36C2×#14555660—21no—
37C4⋊Dic277D411yescharacteristic
38C4⋊Dic277D411yescharacteristic
39#17984542—22no—
40#17984540—22no—
41#17984540—21no—
42#17984540—21no—
43C2×Q8×C277—21no—
44C2×D4×C277—21no—
45C2×D4×C277—21no—
46C2×D4×C277—21no—
47C2×C8×C277—21no—
48C4⋊C4×C277—21no—
49C4⋊C4×C277D412yes—
50C42×C277C2311yescharacteristic
51C22×D277—21no—
52C22×D277—21no—
53D1108—21no—
54D1108—21no—
55D1108—21no—
56D1108—44no—
57D1108D812yescomplemented
58C2×Dic277—21no—
59C2×Dic277—21no—
60C4×D277—44no—
61C4×D277—41no—
62C4×D277—41no—
63C4×D277—41no—
64C4×D277—41no—
65#14555660—41no—
66#14555660—41no—
67C23×C277—41no—
68Q8×C277—41no—
69Q8×C277—41no—
70D4×C277—42no—
71D4×C277—41no—
72D4×C277—41no—
73D4×C277—41no—
74D4×C277—41no—
75C2×C4×C277—22no—
76C2×C4×C277C2×D411yescharacteristic
77C2×C4×C277C2×D411yescharacteristic
78C2×C4×C277C2×D411yescharacteristic
79C8×C277—41no—
80C22×C277—81no—
81C22×C277—81no—
82C22×C277—81no—
83C22×C277#12011yescharacteristic
84C2×D277—22no—
85C2×D277—41no—
86C2×D277—41no—
87C2×D277—41no—
88C2×D277—41no—
89C2×D277—41no—
90C4×C277—21no—
91C4×C277—42no—
92C4×C277C2×D811yescharacteristic
93C4×C277#13511yescharacteristic
94C4×C277AGL(1,ℤ/8)11yescharacteristic
95C4×C277AGL(1,ℤ/8)11yescharacteristic
96Dic277—41no—
97Dic277—41no—
98C2×C277—161no—
99C2×C277#44711yescharacteristic
100C2×C277#44911yescharacteristic
101C2×C277#45411yescharacteristic
102D277—42no—
103D277—81no—
104C277#162511yescharacteristic, complemented, Sylow
105#1625—2771nomaximal, Sylow
106#547—2771no—
107#486D27711yescharacteristic, complemented
108#459—2771no—
109#459—2771no—
110#332—2771no—
111D4⋊C8—2771no—
112D4⋊C8—2771no—
113C2×#41—5541no—
114C2×D8—5541no—
115C2×D8—5541no—
116C4⋊Q8C2×D27711yescharacteristic
117#127C2×D27711yescharacteristic
118#123—5542no—
119C22⋊Q8—5541no—
120#121—5541no—
121C4×D4—2771no—
122C4×D4—2771no—
123C2×C4⋊C4—5541no—
124C4⋊C8—2771no—
125C4⋊C8—2771no—
126#102—22no—
127#102—5541no—
128#102—5541no—
129C4×C8C2×D27711yescharacteristic
130#41—11082no—
131#41—11082no—
132C2×Q8—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—2771no—
137C2×D4—2771no—
138C2×D4—5542no—
139C22×C4—5542no—
140C22×C4—5541no—
141C22×C4—5541no—
142D8—11082no—
143D8—11082no—
144C2×C8—21no—
145C2×C8—5541no—
146C2×C8—5541no—
147C4⋊C4—21no—
148C4⋊C4—2771no—
149C4⋊C4—2771no—
150C4⋊C4—5542no—
151C4⋊C4C22⋊D27712yes—
152C22⋊C4—5542no—
153C22⋊C4—5541no—
154C22⋊C4—5541no—
155C42C22×D27711yescharacteristic
156C23—41no—
157C23—5541no—
158C23—5541no—
159Q8—41no—
160Q8—41no—
161D4—42no—
162D4—41no—
163D4—41no—
164D4—41no—
165D4—41no—
166D4—2772no—
167D4—5541no—
168D4—5541no—
169D4—5541no—
170D4—11084no—
171C2×C4—22no—
172C2×C4—5541no—
173C2×C4—5541no—
174C2×C4—11084no—
175C2×C4—11081no—
176C2×C4—11081no—
177C2×C4—11081no—
178C2×C4—11081no—
179C2×C4D4×D27711yescharacteristic
180C2×C4D4×D27711yescharacteristic
181C2×C4C2×C22⋊D27711yescharacteristic
182C8—41no—
183C8—11081no—
184C8—11081no—
185C22—81no—
186C22—81no—
187C22—81no—
188C22—5542no—
189C22—11081no—
190C22—11081no—
191C22—11081no—
192C22—11081no—
193C22—11081no—
194C22#2257984811yescharacteristic
195C4—21no—
196C4—42no—
197C4—11081no—
198C4—11081no—
199C4D8×D27711yescharacteristic
200C4#2257990111yescharacteristic
201C4#2257990411yescharacteristic
202C4#2257990711yescharacteristic
203C2—161no—
204C2—11082no—
205C2—22161no—
206C2#3180013411yescharacteristic
207C2#3180014611yescharacteristic
208C2#3180017411yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#486×C277C2
socleC22×C277#120
hypercenter#486D277
hypocenterC277#1625
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #31800655C2semidirect
2. #31800194C2semidirect
3. #31800194C2semidirect
4. #31799748C2semidirect
5. #31799731C2semidirect
6. #31799731C2semidirect
7. #486×C277C2semidirect
57. D1108D8semidirect
104. C277#1625semidirect
107. #486D277semidirect

Maximal subgroups

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

subgroupindex
#318006552
#318001942
#317997482
#317997312
#486×C2772
#1625277