Finite Group Databasebeta

← #47982467

Subgroups — #47982467

Order 35456.

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

normal subgroups only

This group has 206 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, complemented
2#31800391C211yesmaximal, characteristic
3#31800368C211yesmaximal, characteristic, complemented
4#31800367C211yesmaximal, characteristic, complemented
5#31799743C211yesmaximal, characteristic, complemented
6#31799741C211yesmaximal, characteristic, complemented
7#330×C277C211yesmaximal, characteristic, complemented
8C2×#17984552—21no—
9C2×D2216—21no—
10#22579879—21no—
11#22579877C2211yescharacteristic
12#22579875—21no—
13#22579875—21no—
14#22579872C2211yescharacteristic
15#22579868C2211yescharacteristic
16#22579865—21no—
17#22579860—21no—
18#22579858—21no—
19#22579802—21no—
20#22579802—21no—
21#22579800—21no—
22#22579800—21no—
23#22579791C2211yescharacteristic
24#125×C277C2211yescharacteristic
25#97×C277C2211yescharacteristic
26#97×C277C2211yescharacteristic
27C2×Dic554—21no—
28C2×Dic554D411yescharacteristic
29C2×D1108—21no—
30C2×D1108—21no—
31C2×D1108—21no—
32C2×D1108D411yescharacteristic
33C2×C4×D277—21no—
34#17984552—42no—
35D2216—42no—
36C2×#14555660—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—
57C22×D277—41no—
58Dic554—41no—
59Dic554—81no—
60D1108—41no—
61D1108—41no—
62D1108—41no—
63D1108—42no—
64D1108—42no—
65C2×Dic277—21no—
66C2×Dic277—21no—
67C2×Dic277—21no—
68C4×D277—81no—
69#14555660—41no—
70C2×C4×C277—21no—
71C2×C4×C277—21no—
72C2×C4×C277C2×D411yescharacteristic
73C2×C4×C277C2×D411yescharacteristic
74C2×C4×C277C2×D411yescharacteristic
75C8×C277—22no—
76C8×C277—41no—
77C22×C277#12011yescharacteristic
78C2×D277—41no—
79C2×D277—41no—
80C2×D277—41no—
81C2×D277—81no—
82C2×D277—81no—
83C2×D277—81no—
84C4×C277—21no—
85C4×C277—21no—
86C4×C277—21no—
87C4×C277—41no—
88C4×C277—41no—
89Dic277—41no—
90Dic277—41no—
91Dic277—41no—
92C2×C277#45311yescharacteristic
93C2×C277#45411yescharacteristic
94C2×C277#45411yescharacteristic
95D277—81no—
96D277—161no—
97C277#165711yescharacteristic, complemented, Sylow
98#1657—2771nomaximal, Sylow
99#563—2771no—
100#496—2771no—
101#490—2771no—
102#490—2771no—
103#330—2771no—
104#330D27711yescharacteristic, complemented
105#329—2771no—
106C2×SD16—5541no—
107C2×D8—5541no—
108C4⋊Q8—5541no—
109#127—2771no—
110#126—5541no—
111#126—5541no—
112#125—2771no—
113#125C2×D27711yescharacteristic
114#124—2771no—
115#123—5541no—
116C22⋊Q8—5541no—
117C22⋊Q8—5541no—
118#102—5541no—
119#102—5541no—
120#102—5541no—
121#102—5541no—
122#97—2771no—
123#97C2×D27711yescharacteristic
124#97C2×D27711yescharacteristic
125C2×Q8—2771no—
126C2×Q8—5541no—
127C2×D4—2771no—
128C2×D4—5541no—
129C2×D4—5541no—
130C2×D4—5541no—
131C22×C4—5541no—
132SD16—11082no—
133D8—11082no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—5541no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—2771no—
140C4⋊C4—2771no—
141C4⋊C4—5541no—
142C4⋊C4—5541no—
143C4⋊C4—5541no—
144C4⋊C4—5541no—
145C4⋊C4D110811yescharacteristic
146C4⋊C4D110811yescharacteristic
147C22⋊C4—5541no—
148C22⋊C4—5541no—
149C22⋊C4—5541no—
150C22⋊C4—5541no—
151C22⋊C4—5541no—
152C42—5541no—
153C42C22×D27711yescharacteristic
154C23—5541no—
155C23—11081no—
156Q8—11081no—
157Q8—22161no—
158D4—11081no—
159D4—11081no—
160D4—11081no—
161D4—11082no—
162D4—11082no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—5541no—
166C2×C4—5541no—
167C2×C4—5541no—
168C2×C4—22161no—
169C2×C4D4×D27711yescharacteristic
170C2×C4D4×D27711yescharacteristic
171C2×C4C2×D110811yescharacteristic
172C8—22no—
173C8—41no—
174C8—11081no—
175C22—11081no—
176C22—11081no—
177C22—11081no—
178C22—22161no—
179C22—22161no—
180C22—22161no—
181C22#2257985011yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—11081no—
188C4—11081no—
189C4—11081no—
190C2—44321no—
191C2—22161no—
192C2#3180017111yescharacteristic
193C2#3180017611yescharacteristic
194C2#3180017711yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#330×C277C2
socleC22×C277#120
prime radical#31800391C2
hypercenter#330D277
hypocenterC277#1657
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #31800756C2semidirect
3. #31800368C2semidirect
4. #31800367C2semidirect
5. #31799743C2semidirect
6. #31799741C2semidirect
7. #330×C277C2semidirect
97. C277#1657semidirect
104. #330D277semidirect

Maximal subgroups

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

subgroupindex
#318007562
#318003912
#318003682
#318003672
#317997432
#317997412
#330×C2772
#1657277