Finite Group Databasebeta

← #47985141

Subgroups — #47985141

Order 35456.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#31800803C211yesmaximal, characteristic
2#31800445C211yesmaximal, characteristic, complemented
3C2×#22579824C211yesmaximal, characteristic, complemented
4#31800278C211yesmaximal, characteristic, complemented
5#31799808C211yesmaximal, characteristic, complemented
6#31799787C211yesmaximal, characteristic, complemented
7#361×C277C211yesmaximal, characteristic, complemented
8#22579925—21no—
9#22579913—21no—
10#22579906—21no—
11#22579904—22no—
12#22579902C2211yescharacteristic
13#22579899—21no—
14C2×Dic1108C2211yescharacteristic, complemented
15D8×D277—21no—
16#22579886C2211yescharacteristic
17Dic2216—21no—
18#22579825—21no—
19#22579824—22no—
20C2×#17984538C2211yescharacteristic, complemented
21#22579798—21no—
22C2×D8×C277C2211yescharacteristic
23M32×C277C2211yescharacteristic, complemented
24#108×C277C2211yescharacteristic, complemented
25#17984563—21no—
26#17984563D411yescharacteristic
27#17984562—22no—
28#17984562—41no—
29C2×Dic554—21no—
30C2×C22⋊D277—42no—
31D4×D277—22no—
32D4×D277—41no—
33Dic1108—21no—
34Dic1108—21no—
35Dic1108—41no—
36Dic1108D411yescharacteristic
37#17984552—21no—
38#17984552—41no—
39#17984551—22no—
40D2216D411yescharacteristic
41#17984548—22no—
42#17984547D411yescharacteristic
43#17984546—21no—
44C8×D277—21no—
45#17984538—21no—
46C2×D4×C277—21no—
47D8×C277—21no—
48D8×C277D412yes—
49M16×C277—21no—
50C2×C8×C277C2311yescharacteristic
51C16×C277—21no—
52C22×D277—42no—
53Dic554—21no—
54Dic554—41no—
55Dic554—41no—
56Dic554D811yescharacteristic
57D1108—21no—
58D1108D811yescharacteristic
59C22⋊D277—21no—
60C22⋊D277—42no—
61C22⋊D277—42no—
62C22⋊D277—41no—
63C2×Dic277—42no—
64C2×Dic277—41no—
65C4×D277—21no—
66C4×D277—41no—
67#14555660—21no—
68C23×C277—41no—
69D4×C277—22no—
70D4×C277—41no—
71C2×C4×C277C2×D411yescharacteristic
72C8×C277—41no—
73C8×C277C2×D411yescharacteristic
74C8×C277C2×D411yescharacteristic
75C22×C277—42no—
76C22×C277—161no—
77C22×C277AGL(1,ℤ/8)11yescharacteristic
78C2×D277—21no—
79C2×D277—41no—
80C2×D277—162no—
81C4×C277#12011yescharacteristic
82C4×C277C2×D811yescharacteristic
83Dic277—21no—
84Dic277—41no—
85Dic277—81no—
86C2×C277—21no—
87C2×C277—82no—
88C2×C277#44711yescharacteristic
89D277—41no—
90D277—81no—
91C277#219411yescharacteristic, complemented, Sylow
92#2194—2771nomaximal, Sylow
93#576—2771no—
94#510—2771no—
95C2×SD32—2771no—
96#473—2771no—
97#361D27711yescharacteristic, complemented
98#359—2771no—
99#350—2771no—
100H(5,𝔽2)—5541no—
101#137—5541no—
102AGL(1,ℤ/8)—5541no—
103AGL(1,ℤ/8)—5542no—
104#135—2771no—
105#135—5541no—
106C2×Q16—2771no—
107C2×D8—5541no—
108C2×D8C2×D27711yescharacteristic
109#131—2771no—
110Q32—5541no—
111SD32—5541no—
112SD32—5542no—
113M32C2×D27711yescharacteristic, complemented
114C2×C16—2771no—
115#108C2×D27711yescharacteristic, complemented
116#101—5541no—
117#41—2771no—
118#41—5542no—
119#41—5541no—
120#41—11081no—
121C2×Q8—5541no—
122C2×D4—21no—
123C2×D4—5542no—
124C2×D4—11081no—
125C2×D4—11082no—
126Q16—2771no—
127Q16—5541no—
128Q16—5541no—
129Q16—11081no—
130SD16—5542no—
131SD16—5541no—
132SD16—11081no—
133D8—21no—
134D8—2771no—
135D8—5542no—
136D8D110812yes—
137M16—21no—
138M16—2771no—
139M16—5541no—
140C2×C8—5541no—
141C2×C8C22×D27711yescharacteristic
142C16—21no—
143C16—5541no—
144C23—41no—
145C23—11082no—
146Q8—2771no—
147Q8—5541no—
148Q8—11081no—
149Q8—11081no—
150D4—22no—
151D4—41no—
152D4—2771no—
153D4—5541no—
154D4—5541no—
155D4—11082no—
156D4—11082no—
157D4—11081no—
158C2×C4—5541no—
159C2×C4—11082no—
160C2×C4—11081no—
161C2×C4—11081no—
162C2×C4D4×D27711yescharacteristic
163C8—41no—
164C8—5541no—
165C8D4×D27711yescharacteristic
166C8C2×D110811yescharacteristic
167C22—42no—
168C22—161no—
169C22—5541no—
170C22—44322no—
171C22—11081no—
172C22#2257990711yescharacteristic
173C4—5541no—
174C4—11081no—
175C4—22161no—
176C4#2257985011yescharacteristic
177C4D8×D27711yescharacteristic
178C2—21no—
179C2—82no—
180C2—11081no—
181C2—22161no—
182C2#3180013711yescharacteristic
subgroupG/H
centerC2#31800137
commutator, cosocleC2×C8×C277C23
FrattiniC2×C8C22×D277
Fitting#361×C277C2
socleC2×C277#447
prime radical#31800803C2
hypercenter#361D277
hypocenterC277#2194
LCSG ▷ C2×C8×C277 ▷ C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
2. #31800445C2semidirect
3. C2×#22579824C2semidirect
4. #31800278C2semidirect
5. #31799808C2semidirect
6. #31799787C2semidirect
7. #361×C277C2semidirect
14. C2×Dic1108C22semidirect
20. C2×#17984538C22semidirect
23. M32×C277C22semidirect
24. #108×C277C22semidirect
91. C277#2194semidirect
97. #361D277semidirect
113. M32C2×D277semidirect
115. #108C2×D277semidirect

Maximal subgroups

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

subgroupindex
#318008032
#318004452
C2×#225798242
#318002782
#317998082
#317997872
#361×C2772
#2194277