Finite Group Databasebeta

← #47982500

Subgroups — #47982500

Order 35456.

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

normal subgroups only

This group has 184 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#31800752C211yesmaximal, characteristic
2#31800408C211yesmaximal, characteristic, complemented
3#31800370C211yesmaximal, characteristic, complemented
4#31799743C211yesmaximal, characteristic, complemented
5#31799743C211yesmaximal, characteristic, complemented
6#31799742C211yesmaximal, characteristic
7#489×C277C211yesmaximal, characteristic
8#22579878—21no—
9#22579873—21no—
10#22579873—21no—
11#22579872C2211yescharacteristic
12#22579872C2211yescharacteristic
13#22579861—21no—
14#22579857—21no—
15#22579857—21no—
16#22579813—21no—
17#22579811—21no—
18#22579804—21no—
19#22579804—21no—
20#22579791C2211yescharacteristic
21#22579791C2211yescharacteristic
22C4⋊Q8×C277C2211yescharacteristic
23#124×C277C2211yescharacteristic
24#103×C277—21no—
25#102×C277—21no—
26#97×C277C2211yescharacteristic
27C2×Dic554—21no—
28C22×Dic277—21no—
29C2×#14555660—21no—
30C2×#14555660—21no—
31C4⋊Dic277D411yescharacteristic
32C4⋊Dic277D411yescharacteristic
33C4⋊Dic277D411yescharacteristic
34C4⋊Dic277D411yescharacteristic
35#17984542—21no—
36#17984542—21no—
37#17984542—21no—
38#17984542—21no—
39#17984542—21no—
40#17984542—21no—
41C22⋊Dic277—21no—
42C22⋊Dic277—21no—
43C22⋊Dic277—21no—
44C4×Dic277—21no—
45C2×Q8×C277—21no—
46C2×Q8×C277D411yescharacteristic
47C2×D4×C277D411yescharacteristic
48C2×C8×C277—21no—
49C4⋊C4×C277—21no—
50C4⋊C4×C277—21no—
51C22⋊C4×C277—21no—
52C22⋊C4×C277—21no—
53C42×C277C2311yescharacteristic
54Dic554—81no—
55C2×Dic277—21no—
56C2×Dic277—21no—
57C2×Dic277—21no—
58C2×Dic277—21no—
59C2×Dic277—81no—
60#14555660—22no—
61#14555660—41no—
62C23×C277—21no—
63Q8×C277—41no—
64Q8×C277—42no—
65D4×C277—41no—
66C2×C4×C277—21no—
67C2×C4×C277—41no—
68C2×C4×C277C2×D411yescharacteristic
69C2×C4×C277C2×D411yescharacteristic
70C2×C4×C277C2×D411yescharacteristic
71C8×C277—41no—
72C22×C277—41no—
73C22×C277—41no—
74C22×C277—41no—
75C22×C277#12011yescharacteristic
76C4×C277—21no—
77C4×C277—21no—
78C4×C277—21no—
79C4×C277—41no—
80C4×C277—81no—
81Dic277—41no—
82Dic277—41no—
83Dic277—41no—
84Dic277—41no—
85C2×C277—81no—
86C2×C277#45411yescharacteristic
87C2×C277#45511yescharacteristic
88C2×C277#45611yescharacteristic
89C277#166411yescharacteristic, complemented, Sylow
90#1664—2771nomaximal, Sylow
91#563—2771no—
92#501—2771no—
93#491—2771no—
94#489D27711yescharacteristic
95#330—2771no—
96#330—2771no—
97#329—2771no—
98C4⋊Q8—5541no—
99C4⋊Q8C2×D27711yescharacteristic
100#126—5541no—
101#126—5541no—
102#125—2771no—
103#125—2771no—
104#124C2×D27711yescharacteristic
105#123—5541no—
106C22⋊Q8—5541no—
107C22⋊Q8—5541no—
108#107—5541no—
109#106—5541no—
110#103—21no—
111#103—5541no—
112#103—5541no—
113#102—21no—
114#97—2771no—
115#97—2771no—
116#97C2×D27711yescharacteristic
117C2×Q8—21no—
118C2×Q8—5541no—
119C2×Q8C22⋊D27711yescharacteristic
120C2×D4C22⋊D27711yescharacteristic
121C22×C4—5541no—
122C2×C8—21no—
123C2×C8—5541no—
124C2×C8—5541no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—2771no—
128C4⋊C4—2771no—
129C4⋊C4—2771no—
130C4⋊C4—2771no—
131C4⋊C4—5541no—
132C4⋊C4—5541no—
133C4⋊C4—5541no—
134C4⋊C4—5541no—
135C4⋊C4—5541no—
136C4⋊C4—5541no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—5541no—
140C22⋊C4—5541no—
141C22⋊C4—5541no—
142C42—5541no—
143C42C22×D27711yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—42no—
147Q8—22161no—
148D4—41no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—5541no—
152C2×C4—5541no—
153C2×C4—5541no—
154C2×C4—5541no—
155C2×C4—22161no—
156C2×C4D4×D27711yescharacteristic
157C2×C4D4×D27711yescharacteristic
158C2×C4C2×C22⋊D27711yescharacteristic
159C8—41no—
160C8—5542no—
161C8—11081no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#2257984811yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—81no—
171C4—11081no—
172C4—11081no—
173C4—11081no—
174C4—11081no—
175C2—81no—
176C2#3180017311yescharacteristic
177C2#3180017911yescharacteristic
178C2#3180018311yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#489×C277C2
socleC22×C277#120
prime radicalC2×D4×C277D4
hypercenter#489D277
hypocenterC277#1664
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #31800408C2semidirect
3. #31800370C2semidirect
4. #31799743C2semidirect
5. #31799743C2semidirect
89. C277#1664semidirect

Maximal subgroups

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

subgroupindex
#318007522
#318004082
#318003702
#317997432
#317997422
#489×C2772
#1664277