Finite Group Databasebeta

← #47982311

Subgroups — #47982311

Order 35456.

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

normal subgroups only

This group has 218 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#31800717C211yesmaximal, characteristic
2#31800381C211yesmaximal, characteristic, complemented
3#31800289C211yesmaximal, characteristic, complemented
4#31799750C211yesmaximal, characteristic, complemented
5D4⋊#14555660C211yesmaximal, characteristic, complemented
6#31799729C211yesmaximal, characteristic, complemented
7#476×C277C211yesmaximal, characteristic, complemented
8C2×#17984553—22no—
9#22579880C2211yescharacteristic
10#22579866—22no—
11#22579854—21no—
12#22579851—21no—
13C4×D1108C2211yescharacteristic
14#22579839—21no—
15#22579838—21no—
16#22579811—21no—
17C4⋊#14555660C2211yescharacteristic
18#22579800—21no—
19C4×#14555660C2211yescharacteristic
20C4⋊Q8×C277C2211yescharacteristic
21C4×D4×C277C2211yescharacteristic
22#106×C277—21no—
23C4⋊C8×C277C2211yescharacteristic
24#102×C277—21no—
25C2×Dic554D412yes—
26C2×D1108D411yescharacteristic
27C2×C22⋊D277—22no—
28C2×C4×D277—21no—
29#17984553—44no—
30C2×#14555660—21no—
31C2×#14555660—21no—
32C4⋊Dic277—21no—
33C4⋊Dic277—21no—
34C4⋊Dic277D411yescharacteristic
35C22⋊Dic277—22no—
36#17984540—22no—
37#17984540—21no—
38C4×Dic277—22no—
39C2×Q8×C277—21no—
40C2×D4×C277D411yescharacteristic
41C22×C4×C277—21no—
42C2×C8×C277—21no—
43C4⋊C4×C277—21no—
44C4⋊C4×C277—21no—
45C4⋊C4×C277D411yescharacteristic
46C22⋊C4×C277—21no—
47C42×C277C2311yescharacteristic
48C22×D277—21no—
49Dic554—42no—
50D1108—21no—
51D1108—21no—
52C22⋊D277—82no—
53C2×Dic277—21no—
54C2×Dic277—22no—
55C4×D277—41no—
56C4×D277—41no—
57#14555660—22no—
58#14555660—41no—
59C23×C277—21no—
60Q8×C277—42no—
61D4×C277—21no—
62D4×C277—21no—
63C2×C4×C277—21no—
64C2×C4×C277—41no—
65C2×C4×C277—41no—
66C2×C4×C277—41no—
67C2×C4×C277C2×D411yescharacteristic
68C2×C4×C277C2×D411yescharacteristic
69C2×C4×C277C2×D411yescharacteristic
70C8×C277—41no—
71C22×C277—41no—
72C22×C277—41no—
73C22×C277—41no—
74C22×C277#12011yescharacteristic
75C2×D277—41no—
76C2×D277—41no—
77C2×D277—41no—
78C4×C277—21no—
79C4×C277—41no—
80C4×C277—81no—
81C4×C277#13511yescharacteristic
82C4×C277#13511yescharacteristic
83C4×C277#13711yescharacteristic
84C4×C277#13711yescharacteristic
85Dic277—41no—
86Dic277—42no—
87C2×C277—81no—
88C2×C277#45211yescharacteristic
89C2×C277#45211yescharacteristic
90C2×C277#45311yescharacteristic
91D277—81no—
92C277#163411yescharacteristic, complemented, Sylow
93#1634—2771nomaximal, Sylow
94#555—2771no—
95#494—2771no—
96#476—2771no—
97#476D27711yescharacteristic, complemented
98#333—2771no—
99D4⋊C8—2771no—
100D4⋊C8—2771no—
101C2×Q16—5542no—
102C4⋊Q8—2771no—
103C4⋊Q8C2×D27711yescharacteristic
104#124—5542no—
105#121—5541no—
106#121—5541no—
107C4×D4—2771no—
108C4×D4C2×D27711yescharacteristic
109#117—5541no—
110#117—5541no—
111#106—21no—
112#106—5541no—
113C4⋊C8—2771no—
114C4⋊C8C2×D27711yescharacteristic
115#102—21no—
116#102—5541no—
117C4×C8—2771no—
118C2×Q8—21no—
119C2×Q8—2772no—
120C2×D4—2771no—
121C2×D4—5542no—
122C2×D4C22⋊D27711yescharacteristic
123C22×C4—21no—
124C22×C4—5541no—
125Q16—11084no—
126C2×C8—21no—
127C2×C8—5541no—
128C2×C8—5541no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—2771no—
132C4⋊C4—5541no—
133C4⋊C4—5541no—
134C4⋊C4C22⋊D27711yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—5542no—
137C22⋊C4—5542no—
138C22⋊C4—5541no—
139C42—5542no—
140C42C22×D27711yescharacteristic
141C23—21no—
142C23—5541no—
143Q8—42no—
144Q8—11082no—
145D4—21no—
146D4—21no—
147D4—5541no—
148D4—5541no—
149D4—22162no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—5541no—
155C2×C4—5542no—
156C2×C4—11081no—
157C2×C4—11081no—
158C2×C4D4×D27711yescharacteristic
159C2×C4D4×D27711yescharacteristic
160C2×C4C2×C22⋊D27711yescharacteristic
161C8—41no—
162C8—5542no—
163C8—11081no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—11081no—
168C22—11081no—
169C22—11081no—
170C22#2257984811yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—11081no—
175C4—11082no—
176C4#2257990011yescharacteristic
177C4#2257990111yescharacteristic
178C4#2257990911yescharacteristic
179C4#2257991111yescharacteristic
180C2—81no—
181C2—22161no—
182C2#3180016111yescharacteristic
183C2#3180016211yescharacteristic
184C2#3180016811yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#476×C277C2
socleC22×C277#120
prime radical#31800717C2
hypercenter#476D277
hypocenterC277#1634
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #31800381C2semidirect
3. #31800289C2semidirect
4. #31799750C2semidirect
5. D4⋊#14555660C2semidirect
6. #31799729C2semidirect
7. #476×C277C2semidirect
92. C277#1634semidirect
97. #476D277semidirect

Maximal subgroups

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

subgroupindex
#318007172
#318003812
#318002892
#317997502
D4⋊#145556602
#317997292
#476×C2772
#1634277