Finite Group Databasebeta

← #47982440

Subgroups — #47982440

Order 35456.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#31800722C211yesmaximal, characteristic
2#31800400C211yesmaximal, characteristic, complemented
3#31800282C211yesmaximal, characteristic
4#31800213C211yesmaximal, characteristic, complemented
5#31799747C211yesmaximal, characteristic, complemented
6#31799734C211yesmaximal, characteristic, complemented
7D4⋊C8×C277C211yesmaximal, characteristic
8C2×Dic1108—21no—
9#22579880C2211yescharacteristic
10#22579880C2211yescharacteristic
11#22579873—22no—
12#22579867—21no—
13#22579859—21no—
14C4×Dic554C2211yescharacteristic
15#22579845—21no—
16#22579839—21no—
17#22579813—21no—
18#22579812—22no—
19C4⋊#14555660C2211yescharacteristic
20#22579805—21no—
21#22579801—21no—
22C4×D4×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4×C8×C277C2211yescharacteristic
25C2×Dic554—21no—
26C2×Dic554—21no—
27C2×Dic554D411yescharacteristic
28Dic1108—42no—
29C2×#14555660—21no—
30C4⋊Dic277—21no—
31C4⋊Dic277—21no—
32C4⋊Dic277—21no—
33C4⋊Dic277D411yescharacteristic
34C4⋊Dic277D412yes—
35#17984542—22no—
36#17984542—21no—
37C22⋊Dic277—22no—
38C22⋊Dic277—22no—
39C4×Dic277—22no—
40C4×Dic277—21no—
41C2×D4×C277D411yescharacteristic
42C22×C4×C277—21no—
43C2×C8×C277—21no—
44C2×C8×C277—21no—
45C4⋊C4×C277D411yescharacteristic
46C22⋊C4×C277—21no—
47C42×C277C2311yescharacteristic
48Dic554—21no—
49Dic554—21no—
50Dic554—41no—
51Dic554—41no—
52Dic554—41no—
53Dic554—41no—
54C2×Dic277—21no—
55C2×Dic277—21no—
56C2×Dic277—22no—
57C2×Dic277—41no—
58#14555660—41no—
59C23×C277—21no—
60D4×C277—21no—
61D4×C277—21no—
62C2×C4×C277—21no—
63C2×C4×C277—41no—
64C2×C4×C277—41no—
65C2×C4×C277C2×D411yescharacteristic
66C2×C4×C277C2×D411yescharacteristic
67C2×C4×C277C2×D411yescharacteristic
68C8×C277—22no—
69C8×C277—41no—
70C22×C277—41no—
71C22×C277—41no—
72C22×C277—41no—
73C22×C277#12011yescharacteristic
74C4×C277—21no—
75C4×C277—41no—
76C4×C277#13511yescharacteristic
77C4×C277#13511yescharacteristic
78C4×C277AGL(1,ℤ/8)11yescharacteristic
79C4×C277#13711yescharacteristic
80Dic277—41no—
81Dic277—42no—
82Dic277—41no—
83Dic277—81no—
84C2×C277—81no—
85C2×C277#44911yescharacteristic
86C2×C277#45211yescharacteristic
87C2×C277#45611yescharacteristic
88C277#165211yescharacteristic, complemented, Sylow
89#1652—2771nomaximal, Sylow
90#556—2771no—
91#498—2771no—
92#474—2771no—
93#462—2771no—
94#332—2771no—
95Q8⋊C8—2771no—
96D4⋊C8D27711yescharacteristic
97C2×Q16—5541no—
98C4⋊Q8—2771no—
99C4⋊Q8—2771no—
100#126—5542no—
101#124—5541no—
102C22⋊Q8—5541no—
103C4×Q8—2771no—
104C4×Q8—5541no—
105C4×D4C2×D27711yescharacteristic
106#117—5541no—
107#107—5541no—
108#106—5542no—
109C4⋊C8—2771no—
110C4⋊C8C2×D27711yescharacteristic
111#103—5541no—
112#102—5541no—
113C4×C8C2×D27711yescharacteristic
114C2×Q8—2771no—
115C2×Q8—5541no—
116C2×Q8—5541no—
117C2×D4D110811yescharacteristic
118C22×C4—21no—
119Q16—11082no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—5541no—
123C4⋊C4—2771no—
124C4⋊C4—2772no—
125C4⋊C4—5542no—
126C4⋊C4—5541no—
127C4⋊C4—5541no—
128C4⋊C4—5541no—
129C4⋊C4—5541no—
130C4⋊C4D110811yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—5542no—
133C22⋊C4—5542no—
134C42—5542no—
135C42—5541no—
136C42C22×D27711yescharacteristic
137C23—21no—
138Q8—5541no—
139Q8—5541no—
140Q8—11081no—
141Q8—11081no—
142Q8—11081no—
143Q8—11081no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—5541no—
150C2×C4—5542no—
151C2×C4—5541no—
152C2×C4—11081no—
153C2×C4D4×D27711yescharacteristic
154C2×C4D4×D27711yescharacteristic
155C2×C4C2×D110811yescharacteristic
156C8—22no—
157C8—41no—
158C8—11081no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#2257985011yescharacteristic
163C4—21no—
164C4—41no—
165C4—11081no—
166C4—11082no—
167C4—11081no—
168C4—22161no—
169C4#2257990111yescharacteristic
170C4#2257990211yescharacteristic
171C4#2257990411yescharacteristic
172C4#2257991311yescharacteristic
173C2—81no—
174C2#3180014811yescharacteristic
175C2#3180016611yescharacteristic
176C2#3180018611yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
FittingD4⋊C8×C277C2
socleC22×C277#120
prime radicalC2×D4×C277D4
hypercenterD4⋊C8D277
hypocenterC277#1652
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
2. #31800400C2semidirect
4. #31800213C2semidirect
5. #31799747C2semidirect
6. #31799734C2semidirect
88. C277#1652semidirect

Maximal subgroups

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

subgroupindex
#318007222
#318004002
#318002822
#318002132
#317997472
#317997342
D4⋊C8×C2772
#1652277