Finite Group Databasebeta

← #47982292

Subgroups — #47982292

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#31800674C211yesmaximal, characteristic
2#31800376C211yesmaximal, characteristic, complemented
3#31800289C211yesmaximal, characteristic, complemented
4#31799745C211yesmaximal, characteristic, complemented
5Q8⋊#14555660C211yesmaximal, characteristic, complemented
6#31799729C211yesmaximal, characteristic, complemented
7#477×C277C211yesmaximal, characteristic, complemented
8C2×#17984564—21no—
9C2×#17984550—22no—
10#22579877—21no—
11#22579877C2211yescharacteristic
12#22579855—22no—
13#22579855—21no—
14C4×D1108—21no—
15C4×D1108C2211yescharacteristic
16#22579811—21no—
17C4⋊#14555660C2211yescharacteristic
18#22579800—21no—
19C4×#14555660C2211yescharacteristic
20C4⋊Q8×C277C2211yescharacteristic
21C4×Q8×C277C2211yescharacteristic
22#107×C277—21no—
23C4⋊C8×C277C2211yescharacteristic
24#103×C277—21no—
25#17984564—42no—
26#17984564—42no—
27C2×D1108—22no—
28C2×D1108—22no—
29C2×D1108—21no—
30C2×D1108—21no—
31C2×D1108D411yescharacteristic
32C2×D1108D412yes—
33C2×C4×D277—22no—
34C2×C4×D277—21no—
35#17984550—44no—
36C2×#14555660—21no—
37C2×#14555660—21no—
38C4⋊Dic277D411yescharacteristic
39#17984540—22no—
40#17984540—21no—
41C2×Q8×C277—21no—
42C2×Q8×C277D411yescharacteristic
43C2×C8×C277—21no—
44C4⋊C4×C277—21no—
45C4⋊C4×C277—21no—
46C4⋊C4×C277—21no—
47C4⋊C4×C277D411yescharacteristic
48C42×C277—21no—
49C42×C277C2311yescharacteristic
50C22×D277—21no—
51C22×D277—22no—
52D1108—21no—
53D1108—21no—
54D1108—42no—
55D1108—44no—
56D1108—41no—
57D1108—41no—
58D1108—41no—
59D1108—41no—
60D1108—82no—
61C2×Dic277—21no—
62C4×D277—44no—
63C4×D277—41no—
64C4×D277—41no—
65#14555660—22no—
66#14555660—41no—
67Q8×C277—21no—
68Q8×C277—42no—
69Q8×C277SD1612yescomplemented
70C2×C4×C277—21no—
71C2×C4×C277—21no—
72C2×C4×C277—41no—
73C2×C4×C277C2×D411yescharacteristic
74C2×C4×C277C2×D411yescharacteristic
75C2×C4×C277C2×D411yescharacteristic
76C8×C277—41no—
77C22×C277#12011yescharacteristic
78C2×D277—42no—
79C2×D277—41no—
80C2×D277—41no—
81C2×D277—42no—
82C2×D277—42no—
83C2×D277—41no—
84C4×C277—22no—
85C4×C277—21no—
86C4×C277—41no—
87C4×C277—81no—
88C4×C277C2×SD1611yescharacteristic
89C4×C277#13511yescharacteristic
90C4×C277AGL(1,ℤ/8)11yescharacteristic
91C4×C277#13711yescharacteristic
92Dic277—41no—
93C2×C277#45011yescharacteristic
94C2×C277#45211yescharacteristic
95C2×C277#45311yescharacteristic
96D277—81no—
97D277—82no—
98C277#163111yescharacteristic, complemented, Sylow
99#1631—2771nomaximal, Sylow
100#550—2771no—
101#492—2771no—
102#477D27711yescharacteristic, complemented
103#476—2771no—
104#331—2771no—
105Q8⋊C8—2771no—
106D4⋊C8—2771no—
107C2×#41—5541no—
108C2×SD16—5542no—
109C4⋊Q8C2×D27711yescharacteristic
110#127—2771no—
111#127—5541no—
112#121—5542no—
113#121—5541no—
114C4×Q8C2×D27711yescharacteristic
115C4×D4—2771no—
116C4×D4—5541no—
117#107—21no—
118#106—5541no—
119C4⋊C8—2771no—
120C4⋊C8C2×D27711yescharacteristic
121#103—21no—
122#102—5541no—
123C4×C8—2771no—
124#41—11082no—
125#41—11082no—
126C2×Q8—21no—
127C2×Q8C22⋊D27711yescharacteristic
128C2×D4—2771no—
129C2×D4—2772no—
130C2×D4—5542no—
131C2×D4—5542no—
132C2×D4—5541no—
133C2×D4—5541no—
134C22×C4—5542no—
135C22×C4—5541no—
136SD16—11084no—
137C2×C8—21no—
138C2×C8—5541no—
139C2×C8—5541no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2771no—
144C4⋊C4C22⋊D27711yescharacteristic
145C22⋊C4—5542no—
146C22⋊C4—5541no—
147C42—21no—
148C42C22×D27711yescharacteristic
149C23—5541no—
150C23—5542no—
151Q8—21no—
152Q8—42no—
153Q8#1798455012yescomplemented
154D4—5541no—
155D4—5541no—
156D4—11082no—
157D4—11084no—
158D4—11081no—
159D4—11081no—
160D4—11081no—
161D4—11081no—
162D4—22162no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—5541no—
167C2×C4—11084no—
168C2×C4—11081no—
169C2×C4—11081no—
170C2×C4D4×D27711yescharacteristic
171C2×C4D4×D27711yescharacteristic
172C2×C4C2×C22⋊D27711yescharacteristic
173C8—41no—
174C8—5542no—
175C8—11081no—
176C22—11082no—
177C22—11081no—
178C22—11081no—
179C22—11082no—
180C22—11082no—
181C22—11081no—
182C22#2257984811yescharacteristic
183C4—22no—
184C4—21no—
185C4—41no—
186C4—81no—
187C4—11081no—
188C4C2×#1798455011yescharacteristic
189C4#2257990311yescharacteristic
190C4#2257990511yescharacteristic
191C4#2257991211yescharacteristic
192C2—22161no—
193C2—22162no—
194C2#3180015211yescharacteristic
195C2#3180016311yescharacteristic
196C2#3180016811yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#477×C277C2
socleC22×C277#120
prime radical#31800674C2
hypercenter#477D277
hypocenterC277#1631
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #31800376C2semidirect
3. #31800289C2semidirect
4. #31799745C2semidirect
5. Q8⋊#14555660C2semidirect
6. #31799729C2semidirect
7. #477×C277C2semidirect
69. Q8×C277SD16semidirect
98. C277#1631semidirect
102. #477D277semidirect
153. Q8#17984550semidirect

Maximal subgroups

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

subgroupindex
#318006742
#318003762
#318002892
#317997452
Q8⋊#145556602
#317997292
#477×C2772
#1631277