Finite Group Databasebeta

← #47981843

Subgroups — #47981843

Order 35456.

260 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 73 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#31800553C211yesmaximal, characteristic
2#31800024C211yesmaximal, characteristic, complemented
3C4⋊C8×D277C211yesmaximal, characteristic, complemented
4#31799748C211yesmaximal, characteristic, complemented
5#31799745C211yesmaximal, characteristic, complemented
6#31799745C211yesmaximal, characteristic, complemented
7#332×C277C211yesmaximal, characteristic, complemented
8C2×#17984564—21no—
9C2×#17984546—21no—
10C2×C8×D277—21no—
11#22579877C2211yescharacteristic
12#22579869—21no—
13#22579855—21no—
14#22579855C412yes—
15#22579842—21no—
16#22579842C412yes—
17C42×D277C2211yescharacteristic
18C4⋊#14555660C2211yescharacteristic
19C4⋊#14555660C2211yescharacteristic
20#22579809—21no—
21#22579809—21no—
22C4⋊Q8×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4⋊C8×C277C2211yescharacteristic
25#17984564—42no—
26#17984564—42no—
27C2×D1108—22no—
28C2×D1108—21no—
29C2×D1108—21no—
30C2×D1108C2×C412yes—
31C2×C4×D277—22no—
32C2×C4×D277C2×C411yescharacteristic
33C2×C4×D277D411yescharacteristic
34C2×C4×D277D411yescharacteristic
35#17984546—42no—
36C2×#14555660—21no—
37C2×#14555660—21no—
38C8×D277—42no—
39#17984540—22no—
40#17984540—22no—
41C4×Dic277C2×C411yescharacteristic
42C4×Dic277D411yescharacteristic
43C4×Dic277D411yescharacteristic
44C2×Q8×C277—21no—
45C2×C8×C277—21no—
46C2×C8×C277—21no—
47C4⋊C4×C277—21no—
48C4⋊C4×C277C2×C412yes—
49C42×C277C2311yescharacteristic
50C22×D277—22no—
51C22×D277C22⋊C411yescharacteristic
52D1108—42no—
53D1108—44no—
54D1108—41no—
55D1108—41no—
56D1108—41no—
57D1108—41no—
58C2×Dic277C22⋊C411yescharacteristic
59C2×Dic277C22⋊C411yescharacteristic
60C2×Dic277C22⋊C411yescharacteristic
61C4×D277—21no—
62C4×D277—21no—
63C4×D277—41no—
64C4×D277—44no—
65C4×D277D812yes—
66C4×D277SD1612yes—
67#14555660—41no—
68#14555660—41no—
69Q8×C277—41no—
70Q8×C277—41no—
71C2×C4×C277—22no—
72C2×C4×C277C22×C411yescharacteristic
73C2×C4×C277C2×D411yescharacteristic
74C2×C4×C277C2×D411yescharacteristic
75C8×C277—41no—
76C8×C277—41no—
77C22×C277C2×C22⋊C411yescharacteristic
78C2×D277—21no—
79C2×D277—21no—
80C2×D277—42no—
81C2×D277—42no—
82C2×D277—42no—
83C2×D277#10212yes—
84C4×C277—21no—
85C4×C277—42no—
86C4×C277C2×D811yescharacteristic
87C4×C277C2×SD1611yescharacteristic
88C4×C277AGL(1,ℤ/8)11yescharacteristic
89C4×C277#13711yescharacteristic
90Dic277—21no—
91Dic277—21no—
92Dic277#10212yes—
93C2×C277#41311yescharacteristic
94C2×C277C2×#10211yescharacteristic
95C2×C277#41711yescharacteristic
96D277—22no—
97D277—82no—
98C277#154711yescharacteristic, complemented, Sylow
99#1547—2771nomaximal, Sylow
100#532—2771no—
101#423—2771no—
102C2×C4⋊C8—2771no—
103#332—2771no—
104#332D27711yescharacteristic, complemented
105#331—2771no—
106#331—2771no—
107C2×#41—5541no—
108C2×M16—5541no—
109C22×C8—5541no—
110C4⋊Q8C2×D27711yescharacteristic
111#127—2771no—
112#124—5541no—
113#121—2772no—
114#121—5541no—
115C4×D4—2772no—
116C4×D4—5541no—
117C2×C42—2771no—
118C4⋊C8—2771no—
119C4⋊C8—2771no—
120C4⋊C8—5541no—
121C4⋊C8—5541no—
122C4⋊C8C2×D27711yescharacteristic
123C4⋊C8C2×D27711yescharacteristic
124#41—11082no—
125#41—11082no—
126C2×Q8—21no—
127C2×D4—2772no—
128C2×D4—5542no—
129C2×D4—5541no—
130C2×D4—5541no—
131C22×C4—2771no—
132C22×C4—2771no—
133C22×C4—2771no—
134C22×C4—5542no—
135M16—11082no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—5541no—
139C2×C8—5541no—
140C2×C8—11082no—
141C4⋊C4—21no—
142C4⋊C4C4×D27712yes—
143C22⋊C4—5542no—
144C22⋊C4—5542no—
145C42—2771no—
146C42—2771no—
147C42—2771no—
148C42C22×D27711yescharacteristic
149C23—2771no—
150C23—5542no—
151Q8—41no—
152Q8—41no—
153D4—11082no—
154D4—11084no—
155D4—11081no—
156D4—11081no—
157D4—11081no—
158D4—11081no—
159C2×C4—22no—
160C2×C4—2771no—
161C2×C4—2772no—
162C2×C4—2772no—
163C2×C4—2771no—
164C2×C4—2771no—
165C2×C4—5541no—
166C2×C4—5541no—
167C2×C4—11081no—
168C2×C4—11084no—
169C2×C4C2×C4×D27711yescharacteristic
170C2×C4D4×D27711yescharacteristic
171C2×C4D4×D27711yescharacteristic
172C8—41no—
173C8—41no—
174C8—11081no—
175C8—11081no—
176C22—2772no—
177C22—5541no—
178C22—5541no—
179C22—11082no—
180C22—11082no—
181C22—11082no—
182C22C22⋊C4×D27711yescharacteristic
183C4—21no—
184C4—42no—
185C4—2772no—
186C4—5541no—
187C4—5541no—
188C4D8×D27711yescharacteristic
189C4SD16×D27711yescharacteristic
190C4#2257990711yescharacteristic
191C4#2257991211yescharacteristic
192C2—5542no—
193C2—22162no—
194C2#3179998511yescharacteristic
195C2#102×D27711yescharacteristic
196C2#3180000211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D277
commutatorC2×C4×C277C22×C4
FrattiniC42C22×D277
Fitting#332×C277C2
socleC22×C277C2×C22⋊C4
prime radical#31800553C2
cosocleC42×C277C23
hypercenter#332D277
hypocenterC277#1547
LCSG ▷ C2×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #31800024C2semidirect
3. C4⋊C8×D277C2semidirect
4. #31799748C2semidirect
5. #31799745C2semidirect
6. #31799745C2semidirect
7. #332×C277C2semidirect
98. C277#1547semidirect
104. #332D277semidirect

Maximal subgroups

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

subgroupindex
#318005532
#318000242
C4⋊C8×D2772
#317997482
#317997452
#332×C2772
#1547277