Finite Group Databasebeta

← #47982421

Subgroups — #47982421

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#31800405C211yesmaximal, characteristic, complemented
3#31800284C211yesmaximal, characteristic, complemented
4#31799749C211yesmaximal, characteristic, complemented
5#31799732C211yesmaximal, characteristic, complemented
6D4⋊#14555660C211yesmaximal, characteristic
7#461×C277C211yesmaximal, characteristic
8#22579880C2211yescharacteristic
9#22579873—22no—
10#22579867—21no—
11#22579859—21no—
12C4×Dic554C2211yescharacteristic
13#22579845—21no—
14#22579839—21no—
15#22579813—22no—
16#22579811—21no—
17C4⋊#14555660C2211yescharacteristic
18#22579803—21no—
19C4×#14555660C2211yescharacteristic
20C2×SD16×C277—21no—
21C4⋊Q8×C277C2211yescharacteristic
22C4×D4×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24#103×C277—21no—
25C2×Dic554—21no—
26C2×Dic554D411yescharacteristic
27C2×#14555660—21no—
28C2×#14555660—21no—
29C4⋊Dic277—21no—
30C4⋊Dic277D411yescharacteristic
31C4⋊Dic277D412yes—
32#17984542—22no—
33#17984542—21no—
34C22⋊Dic277—22no—
35C22⋊Dic277—22no—
36C4×Dic277—22no—
37C4×Dic277—21no—
38C2×Q8×C277—21no—
39C2×D4×C277D411yescharacteristic
40C22×C4×C277—21no—
41SD16×C277—42no—
42C2×C8×C277—21no—
43C4⋊C4×C277—21no—
44C4⋊C4×C277—21no—
45C4⋊C4×C277D411yescharacteristic
46C22⋊C4×C277—21no—
47C42×C277C2311yescharacteristic
48Dic554—21no—
49Dic554—21no—
50Dic554—41no—
51Dic554—41no—
52C2×Dic277—21no—
53C2×Dic277—21no—
54C2×Dic277—22no—
55#14555660—22no—
56#14555660—41no—
57C23×C277—21no—
58Q8×C277—41no—
59Q8×C277—41no—
60D4×C277—21no—
61D4×C277—21no—
62C2×C4×C277—21no—
63C2×C4×C277—41no—
64C2×C4×C277—41no—
65C2×C4×C277—41no—
66C2×C4×C277C2×D411yescharacteristic
67C2×C4×C277C2×D411yescharacteristic
68C2×C4×C277C2×D411yescharacteristic
69C8×C277—41no—
70C22×C277—41no—
71C22×C277—41no—
72C22×C277—41no—
73C22×C277#12011yescharacteristic
74C4×C277—21no—
75C4×C277—41no—
76C4×C277—81no—
77C4×C277#13511yescharacteristic
78C4×C277#13511yescharacteristic
79C4×C277AGL(1,ℤ/8)11yescharacteristic
80C4×C277#13711yescharacteristic
81Dic277—42no—
82Dic277—41no—
83Dic277—41no—
84C2×C277—81no—
85C2×C277#44911yescharacteristic
86C2×C277#45211yescharacteristic
87C2×C277#45611yescharacteristic
88C277#165011yescharacteristic, complemented, Sylow
89#1650—2771nomaximal, Sylow
90#556—2771no—
91#500—2771no—
92#475—2771no—
93#461D27711yescharacteristic
94#332—2771no—
95Q8⋊C8—2771no—
96D4⋊C8—2771no—
97C2×SD16—21no—
98C4⋊Q8—2771no—
99C4⋊Q8C2×D27711yescharacteristic
100#126—5542no—
101#124—5541no—
102C22⋊Q8—5541no—
103C4×Q8—2771no—
104C4×Q8—5541no—
105C4×D4C2×D27711yescharacteristic
106#117—5541no—
107#107—5542no—
108#106—5541no—
109C4⋊C8—2771no—
110C4⋊C8C2×D27711yescharacteristic
111#103—21no—
112#103—5541no—
113C4×C8—2771no—
114C2×Q8—21no—
115C2×Q8—2771no—
116C2×Q8—5541no—
117C2×D4C22⋊D27711yescharacteristic
118C22×C4—21no—
119SD16—42no—
120C2×C8—21no—
121C2×C8—5541no—
122C2×C8—5541no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—2771no—
126C4⋊C4—2772no—
127C4⋊C4—5542no—
128C4⋊C4—5541no—
129C4⋊C4—5541no—
130C4⋊C4C22⋊D27711yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—5542no—
133C22⋊C4—5542no—
134C42—5542no—
135C42—5541no—
136C42C22×D27711yescharacteristic
137C23—21no—
138Q8—41no—
139Q8—41no—
140Q8—5541no—
141Q8—5541no—
142Q8—11081no—
143Q8—11081no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—5541no—
151C2×C4—5542no—
152C2×C4—5541no—
153C2×C4D4×D27711yescharacteristic
154C2×C4D4×D27711yescharacteristic
155C2×C4C2×C22⋊D27711yescharacteristic
156C8—41no—
157C8—5542no—
158C8—11081no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#2257984811yescharacteristic
163C4—21no—
164C4—41no—
165C4—81no—
166C4—11082no—
167C4—11081no—
168C4—11081no—
169C4#2257990011yescharacteristic
170C4#2257990111yescharacteristic
171C4#2257990611yescharacteristic
172C4#2257990911yescharacteristic
173C2—81no—
174C2#3180014511yescharacteristic
175C2#3180016111yescharacteristic
176C2#3180018311yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#461×C277C2
socleC22×C277#120
prime radicalC2×D4×C277D4
hypercenter#461D277
hypocenterC277#1650
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #31800405C2semidirect
3. #31800284C2semidirect
4. #31799749C2semidirect
5. #31799732C2semidirect
88. C277#1650semidirect

Maximal subgroups

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

subgroupindex
#318007222
#318004052
#318002842
#317997492
#317997322
D4⋊#145556602
#461×C2772
#1650277