Finite Group Databasebeta

← #47982480

Subgroups — #47982480

Order 35456.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#31800756C211yesmaximal, characteristic
2#31800412C211yesmaximal, characteristic, complemented
3#31800411C211yesmaximal, characteristic, complemented
4#31800396C211yesmaximal, characteristic
5#31799743C211yesmaximal, characteristic, complemented
6#31799741C211yesmaximal, characteristic
7#330×C277C211yesmaximal, characteristic, complemented
8C2×Dic1108—21no—
9C2×#17984552—21no—
10#22579880C2211yescharacteristic
11#22579879—21no—
12#22579875—21no—
13#22579875—21no—
14#22579872C2211yescharacteristic
15#22579868C2211yescharacteristic
16#22579865—21no—
17#22579860—21no—
18#22579858—21no—
19#22579814—21no—
20#22579813—21no—
21#22579812—21no—
22#22579811—21no—
23#22579791C2211yescharacteristic
24#125×C277C2211yescharacteristic
25#97×C277C2211yescharacteristic
26#97×C277C2211yescharacteristic
27C2×Dic554—21no—
28C2×Dic554—21no—
29C2×Dic554D411yescharacteristic
30C2×D1108D411yescharacteristic
31C2×C4×D277—21no—
32Dic1108—42no—
33#17984552—42no—
34C2×#14555660—21no—
35C4⋊Dic277—21no—
36C4⋊Dic277—21no—
37C4⋊Dic277—21no—
38C4⋊Dic277D411yescharacteristic
39C4⋊Dic277D411yescharacteristic
40#17984542—21no—
41#17984542—21no—
42#17984542—21no—
43#17984540—21no—
44#17984540—21no—
45#17984540—21no—
46#17984540—21no—
47#17984540—21no—
48C4×Dic277—21no—
49C2×C8×C277—21no—
50C2×C8×C277—21no—
51C4⋊C4×C277—21no—
52C4⋊C4×C277—21no—
53C4⋊C4×C277D411yescharacteristic
54C4⋊C4×C277D411yescharacteristic
55C42×C277C2311yescharacteristic
56C22×D277—21no—
57Dic554—41no—
58Dic554—41no—
59Dic554—41no—
60Dic554—81no—
61D1108—41no—
62C2×Dic277—21no—
63C2×Dic277—21no—
64C2×Dic277—21no—
65C2×Dic277—41no—
66C4×D277—81no—
67#14555660—22no—
68C2×C4×C277—21no—
69C2×C4×C277—21no—
70C2×C4×C277C2×D411yescharacteristic
71C2×C4×C277C2×D411yescharacteristic
72C2×C4×C277C2×D411yescharacteristic
73C8×C277—22no—
74C8×C277—22no—
75C22×C277#12011yescharacteristic
76C2×D277—41no—
77C2×D277—41no—
78C2×D277—41no—
79C4×C277—21no—
80C4×C277—21no—
81C4×C277—21no—
82C4×C277—41no—
83C4×C277—41no—
84Dic277—41no—
85Dic277—41no—
86Dic277—41no—
87Dic277—81no—
88C2×C277#45311yescharacteristic
89C2×C277#45611yescharacteristic
90C2×C277#45611yescharacteristic
91D277—81no—
92C277#166011yescharacteristic, complemented, Sylow
93#1660—2771nomaximal, Sylow
94#563—2771no—
95#501—2771no—
96#501—2771no—
97#497—2771no—
98#330—2771no—
99#330D27711yescharacteristic, complemented
100#329—2771no—
101C2×Q16—5541no—
102C2×SD16—5541no—
103C4⋊Q8—2771no—
104C4⋊Q8—5541no—
105#126—5541no—
106#126—5541no—
107#125—2771no—
108#125C2×D27711yescharacteristic
109#124—2771no—
110#123—5541no—
111C22⋊Q8—5541no—
112C22⋊Q8—5541no—
113#107—5541no—
114#107—5541no—
115#106—5541no—
116#106—5541no—
117#97—2771no—
118#97C2×D27711yescharacteristic
119#97C2×D27711yescharacteristic
120C2×Q8—2771no—
121C2×Q8—5541no—
122C2×Q8—5541no—
123C2×D4—2771no—
124C22×C4—5541no—
125Q16—11082no—
126SD16—11082no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—5541no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—2771no—
133C4⋊C4—2771no—
134C4⋊C4—5541no—
135C4⋊C4—5541no—
136C4⋊C4—5541no—
137C4⋊C4—5541no—
138C4⋊C4—5541no—
139C4⋊C4—5541no—
140C4⋊C4D110811yescharacteristic
141C4⋊C4D110811yescharacteristic
142C22⋊C4—5541no—
143C22⋊C4—5541no—
144C22⋊C4—5541no—
145C22⋊C4—5541no—
146C22⋊C4—5541no—
147C42—5541no—
148C42C22×D27711yescharacteristic
149C23—5541no—
150Q8—11081no—
151Q8—11081no—
152Q8—11081no—
153Q8—22161no—
154D4—11081no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—5541no—
158C2×C4—5541no—
159C2×C4—5541no—
160C2×C4—11081no—
161C2×C4—22161no—
162C2×C4D4×D27711yescharacteristic
163C2×C4D4×D27711yescharacteristic
164C2×C4C2×D110811yescharacteristic
165C8—22no—
166C8—22no—
167C8—5542no—
168C22—11081no—
169C22—11081no—
170C22—11081no—
171C22#2257985011yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—11081no—
178C4—11081no—
179C4—11081no—
180C4—22161no—
181C2—22161no—
182C2#3180017111yescharacteristic
183C2#3180018611yescharacteristic
184C2#3180018711yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#330×C277C2
socleC22×C277#120
prime radicalC2×D1108D4
hypercenter#330D277
hypocenterC277#1660
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #31800412C2semidirect
3. #31800411C2semidirect
5. #31799743C2semidirect
7. #330×C277C2semidirect
92. C277#1660semidirect
99. #330D277semidirect

Maximal subgroups

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

subgroupindex
#318007562
#318004122
#318004112
#318003962
#317997432
#317997412
#330×C2772
#1660277