Finite Group Databasebeta

← #47982371

Subgroups — #47982371

Order 35456.

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

normal subgroups only

This group has 208 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#31800713C211yesmaximal, characteristic
2#31800284C211yesmaximal, characteristic, complemented
3#31800204C211yesmaximal, characteristic
4#31799751C211yesmaximal, characteristic, complemented
5#31799734C211yesmaximal, characteristic, complemented
6#31799731C211yesmaximal, characteristic
7#487×C277C211yesmaximal, characteristic, complemented
8C2×#17984550—21no—
9#22579871—21no—
10#22579860—21no—
11#22579856—22no—
12C4×Dic554C2211yescharacteristic
13C4×D1108C2211yescharacteristic
14#22579842—21no—
15C4⋊C4×D277—21no—
16#22579811—21no—
17C4⋊#14555660C2211yescharacteristic
18C4⋊#14555660C2211yescharacteristic
19#22579804—21no—
20#22579803—21no—
21C4⋊Q8×C277C2211yescharacteristic
22C4⋊Q8×C277C2211yescharacteristic
23#103×C277—22no—
24C4×C8×C277C2211yescharacteristic
25C2×Dic554D411yescharacteristic
26C2×D1108D411yescharacteristic
27C2×C4×D277—22no—
28C2×C4×D277—21no—
29#17984550—42no—
30C2×#14555660—21no—
31C2×#14555660—21no—
32C4⋊Dic277—22no—
33C4⋊Dic277D411yescharacteristic
34C4⋊Dic277D411yescharacteristic
35#17984542—22no—
36#17984542—21no—
37#17984540—22no—
38#17984540—21no—
39C4×Dic277—21no—
40C2×Q8×C277—21no—
41C2×Q8×C277D412yes—
42C2×C8×C277—21no—
43C4⋊C4×C277—21no—
44C4⋊C4×C277—21no—
45C4⋊C4×C277—21no—
46C4⋊C4×C277—21no—
47C42×C277C2311yescharacteristic
48C22×D277—21no—
49Dic554—21no—
50Dic554—21no—
51D1108—21no—
52D1108SD1612yes—
53C2×Dic277—21no—
54C2×Dic277—21no—
55C2×Dic277—21no—
56C4×D277—41no—
57C4×D277—41no—
58C4×D277—82no—
59#14555660—41no—
60#14555660—41no—
61Q8×C277—42no—
62Q8×C277—41no—
63Q8×C277—41no—
64C2×C4×C277—22no—
65C2×C4×C277—41no—
66C2×C4×C277C2×D411yescharacteristic
67C2×C4×C277C2×D411yescharacteristic
68C2×C4×C277C2×D411yescharacteristic
69C8×C277—41no—
70C22×C277#12011yescharacteristic
71C2×D277—22no—
72C2×D277—41no—
73C2×D277—41no—
74C4×C277—21no—
75C4×C277—42no—
76C4×C277—81no—
77C4×C277C2×SD1611yescharacteristic
78C4×C277#13511yescharacteristic
79C4×C277#13711yescharacteristic
80C4×C277#13711yescharacteristic
81Dic277—41no—
82Dic277—41no—
83Dic277—41no—
84C2×C277#44811yescharacteristic
85C2×C277#45211yescharacteristic
86C2×C277#45511yescharacteristic
87D277—42no—
88C277#164311yescharacteristic, complemented, Sylow
89#1643—2771nomaximal, Sylow
90#554—2771no—
91#487D27711yescharacteristic, complemented
92#475—2771no—
93#461—2771no—
94#333—2771no—
95Q8⋊C8—2771no—
96D4⋊C8—2771no—
97C2×SD16—5541no—
98C4⋊Q8C2×D27711yescharacteristic
99C4⋊Q8C2×D27711yescharacteristic
100#125—5541no—
101C22⋊Q8—5541no—
102C22⋊Q8—5542no—
103C4×Q8—2771no—
104C4×D4—2771no—
105C4×D4—5541no—
106C2×C4⋊C4—5541no—
107#106—5541no—
108C4⋊C8—2771no—
109C4⋊C8—2771no—
110#103—22no—
111#103—5541no—
112#103—5541no—
113C4×C8C2×D27711yescharacteristic
114C2×Q8—21no—
115C2×Q8—2771no—
116C2×Q8C22⋊D27712yes—
117C2×D4—2771no—
118C22×C4—5542no—
119C22×C4—5541no—
120SD16—11082no—
121C2×C8—21no—
122C2×C8—5541no—
123C2×C8—5541no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—2771no—
129C4⋊C4—2771no—
130C4⋊C4—5542no—
131C4⋊C4—5542no—
132C4⋊C4—5541no—
133C22⋊C4—5542no—
134C22⋊C4—5541no—
135C42—5541no—
136C42C22×D27711yescharacteristic
137C23—5541no—
138Q8—42no—
139Q8—41no—
140Q8—41no—
141Q8—5541no—
142Q8—5541no—
143D4—2772no—
144D4—5541no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—5541no—
148C2×C4—5541no—
149C2×C4—5541no—
150C2×C4—11081no—
151C2×C4—11081no—
152C2×C4—22162no—
153C2×C4D4×D27711yescharacteristic
154C2×C4D4×D27711yescharacteristic
155C2×C4C2×C22⋊D27711yescharacteristic
156C8—41no—
157C8—11081no—
158C8—11081no—
159C22—5542no—
160C22—11081no—
161C22—11081no—
162C22#2257984811yescharacteristic
163C4—21no—
164C4—42no—
165C4—81no—
166C4—11081no—
167C4—11081no—
168C4—11081no—
169C4SD16×D27711yescharacteristic
170C4#2257990311yescharacteristic
171C4#2257990911yescharacteristic
172C4#2257991211yescharacteristic
173C2—11082no—
174C2#3180013911yescharacteristic
175C2#3180016311yescharacteristic
176C2#3180017911yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#487×C277C2
socleC22×C277#120
prime radicalC2×D1108D4
hypercenter#487D277
hypocenterC277#1643
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #31800284C2semidirect
4. #31799751C2semidirect
5. #31799734C2semidirect
7. #487×C277C2semidirect
88. C277#1643semidirect
91. #487D277semidirect

Maximal subgroups

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

subgroupindex
#318007132
#318002842
#318002042
#317997512
#317997342
#317997312
#487×C2772
#1643277