Finite Group Databasebeta

← #47982438

Subgroups — #47982438

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#31800726C211yesmaximal, characteristic
2#31800398C211yesmaximal, characteristic, complemented
3#31800283C211yesmaximal, characteristic
4#31800213C211yesmaximal, characteristic, complemented
5#31799732C211yesmaximal, characteristic, complemented
6#31799729C211yesmaximal, characteristic
7#332×C277C211yesmaximal, characteristic, complemented
8C2×Dic1108—21no—
9#22579880C2211yescharacteristic
10#22579875—22no—
11#22579869—21no—
12#22579860—21no—
13Q8×Dic277—21no—
14C4×Dic554C2211yescharacteristic
15C4×D1108C2211yescharacteristic
16#22579838—21no—
17#22579814—21no—
18#22579811—22no—
19#22579805—21no—
20#22579802—21no—
21C4×#14555660C2211yescharacteristic
22C4⋊Q8×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4⋊C8×C277C2211yescharacteristic
25C2×Dic554—21no—
26C2×Dic554D411yescharacteristic
27C2×D1108D411yescharacteristic
28C2×C4×D277—21no—
29Dic1108—42no—
30C2×#14555660—21no—
31C4⋊Dic277—22no—
32C4⋊Dic277—21no—
33C4⋊Dic277—21no—
34C4⋊Dic277D411yescharacteristic
35C4⋊Dic277D411yescharacteristic
36#17984542—21no—
37#17984540—22no—
38#17984540—22no—
39#17984540—21no—
40C4×Dic277—22no—
41C4×Dic277—21no—
42C2×Q8×C277—21no—
43C2×C8×C277—21no—
44C2×C8×C277—21no—
45C4⋊C4×C277—21no—
46C4⋊C4×C277D412yes—
47C42×C277C2311yescharacteristic
48C22×D277—21no—
49Dic554—21no—
50Dic554—21no—
51Dic554—41no—
52Dic554—41no—
53D1108—21no—
54D1108—21no—
55C2×Dic277—21no—
56C2×Dic277—21no—
57C2×Dic277—21no—
58C2×Dic277—41no—
59C4×D277—41no—
60C4×D277—41no—
61#14555660—22no—
62Q8×C277—41no—
63Q8×C277—41no—
64C2×C4×C277—22no—
65C2×C4×C277C2×D411yescharacteristic
66C2×C4×C277C2×D411yescharacteristic
67C2×C4×C277C2×D411yescharacteristic
68C8×C277—41no—
69C8×C277—41no—
70C22×C277#12011yescharacteristic
71C2×D277—41no—
72C2×D277—41no—
73C2×D277—41no—
74C4×C277—21no—
75C4×C277—42no—
76C4×C277#13511yescharacteristic
77C4×C277#13511yescharacteristic
78C4×C277AGL(1,ℤ/8)11yescharacteristic
79C4×C277#13711yescharacteristic
80Dic277—41no—
81Dic277—41no—
82Dic277—41no—
83Dic277—81no—
84C2×C277#44911yescharacteristic
85C2×C277#45211yescharacteristic
86C2×C277#45611yescharacteristic
87D277—81no—
88C277#165211yescharacteristic, complemented, Sylow
89#1652—2771nomaximal, Sylow
90#556—2771no—
91#498—2771no—
92#474—2771no—
93#462—2771no—
94#332D27711yescharacteristic, complemented
95Q8⋊C8—2771no—
96D4⋊C8—2771no—
97C2×Q16—5541no—
98C4⋊Q8—2771no—
99C4⋊Q8C2×D27711yescharacteristic
100#126—5542no—
101#124—5541no—
102C22⋊Q8—5541no—
103C4×Q8—2771no—
104C4×Q8—5541no—
105C4×D4—2771no—
106#117—5541no—
107#107—5541no—
108#106—5542no—
109C4⋊C8C2×D27711yescharacteristic
110C4⋊C8C2×D27711yescharacteristic
111#103—5541no—
112#102—5541no—
113C4×C8—2771no—
114C2×Q8—21no—
115C2×Q8—2771no—
116C2×Q8—5541no—
117C2×D4—2771no—
118C22×C4—5541no—
119Q16—11082no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—5541no—
123C4⋊C4—21no—
124C4⋊C4—2771no—
125C4⋊C4—2771no—
126C4⋊C4—5542no—
127C4⋊C4—5541no—
128C4⋊C4—5541no—
129C4⋊C4—5541no—
130C4⋊C4D110812yes—
131C22⋊C4—5542no—
132C22⋊C4—5542no—
133C22⋊C4—5541no—
134C42—5542no—
135C42—5541no—
136C42C22×D27711yescharacteristic
137C23—5541no—
138Q8—41no—
139Q8—41no—
140Q8—5541no—
141Q8—5541no—
142Q8—11081no—
143Q8—11081no—
144D4—5541no—
145D4—5541no—
146C2×C4—22no—
147C2×C4—5541no—
148C2×C4—5541no—
149C2×C4—5541no—
150C2×C4—11081no—
151C2×C4—11081no—
152C2×C4—11081no—
153C2×C4D4×D27711yescharacteristic
154C2×C4D4×D27711yescharacteristic
155C2×C4C2×D110811yescharacteristic
156C8—41no—
157C8—41no—
158C8—5542no—
159C22—11081no—
160C22—11081no—
161C22—11081no—
162C22#2257985011yescharacteristic
163C4—21no—
164C4—42no—
165C4—11081no—
166C4—11081no—
167C4—11081no—
168C4—22161no—
169C4#2257989911yescharacteristic
170C4#2257990311yescharacteristic
171C4#2257990711yescharacteristic
172C4#2257990911yescharacteristic
173C2—22161no—
174C2#3180015011yescharacteristic
175C2#3180016511yescharacteristic
176C2#3180018711yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#332×C277C2
socleC22×C277#120
prime radicalC2×D1108D4
hypercenter#332D277
hypocenterC277#1652
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #31800398C2semidirect
4. #31800213C2semidirect
5. #31799732C2semidirect
7. #332×C277C2semidirect
88. C277#1652semidirect
94. #332D277semidirect

Maximal subgroups

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

subgroupindex
#318007262
#318003982
#318002832
#318002132
#317997322
#317997292
#332×C2772
#1652277