Finite Group Databasebeta

← #47982249

Subgroups — #47982249

Order 35456.

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

normal subgroups only

This group has 240 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, complemented
2#31800374C211yesmaximal, characteristic, complemented
3#31800194C211yesmaximal, characteristic, complemented
4#31799750C211yesmaximal, characteristic, complemented
5D4⋊#14555660C211yesmaximal, characteristic, complemented
6#31799729C211yesmaximal, characteristic, complemented
7#459×C277C211yesmaximal, characteristic, complemented
8C2×#17984551—22no—
9C2×#17984548—21no—
10#22579880C2211yescharacteristic
11#22579866—22no—
12#22579854—21no—
13#22579851—21no—
14C4×D1108C2211yescharacteristic
15#22579839—21no—
16#22579838—21no—
17C4⋊#14555660C2211yescharacteristic
18#22579801—21no—
19C4×#14555660C2211yescharacteristic
20C2×D8×C277—21no—
21#127×C277C2211yescharacteristic
22C4×D4×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24#102×C277—21no—
25C2×Dic554D412yes—
26C2×D1108D411yescharacteristic
27C2×C22⋊D277—22no—
28C2×C4×D277—21no—
29#17984551—44no—
30#17984548—42no—
31C2×#14555660—21no—
32C2×#14555660—21no—
33C4⋊Dic277—21no—
34C4⋊Dic277—21no—
35C4⋊Dic277D411yescharacteristic
36C22⋊Dic277—22no—
37#17984540—22no—
38#17984540—21no—
39C4×Dic277—22no—
40C2×D4×C277—21no—
41C2×D4×C277—21no—
42C2×D4×C277—21no—
43C2×D4×C277D411yescharacteristic
44C22×C4×C277—21no—
45D8×C277—42no—
46C2×C8×C277—21no—
47C4⋊C4×C277D411yescharacteristic
48C22⋊C4×C277—21no—
49C42×C277C2311yescharacteristic
50C22×D277—21no—
51Dic554—42no—
52D1108—21no—
53D1108—21no—
54C22⋊D277—82no—
55C2×Dic277—21no—
56C2×Dic277—22no—
57C4×D277—41no—
58C4×D277—41no—
59#14555660—22no—
60#14555660—41no—
61C23×C277—21no—
62C23×C277—41no—
63D4×C277—21no—
64D4×C277—21no—
65D4×C277—42no—
66D4×C277—41no—
67D4×C277—41no—
68D4×C277—41no—
69D4×C277—41no—
70C2×C4×C277—21no—
71C2×C4×C277—41no—
72C2×C4×C277—41no—
73C2×C4×C277C2×D411yescharacteristic
74C2×C4×C277C2×D411yescharacteristic
75C2×C4×C277C2×D411yescharacteristic
76C8×C277—41no—
77C22×C277—41no—
78C22×C277—41no—
79C22×C277—41no—
80C22×C277—81no—
81C22×C277—81no—
82C22×C277—81no—
83C22×C277#12011yescharacteristic
84C2×D277—41no—
85C2×D277—41no—
86C2×D277—41no—
87C4×C277—21no—
88C4×C277—41no—
89C4×C277#13511yescharacteristic
90C4×C277#13511yescharacteristic
91C4×C277AGL(1,ℤ/8)11yescharacteristic
92C4×C277AGL(1,ℤ/8)11yescharacteristic
93Dic277—41no—
94Dic277—42no—
95C2×C277—81no—
96C2×C277—161no—
97C2×C277#44911yescharacteristic
98C2×C277#44911yescharacteristic
99C2×C277#45311yescharacteristic
100D277—81no—
101C277#162411yescharacteristic, complemented, Sylow
102#1624—2771nomaximal, Sylow
103#555—2771no—
104#492—2771no—
105#459—2771no—
106#459D27711yescharacteristic, complemented
107#333—2771no—
108D4⋊C8—2771no—
109D4⋊C8—2771no—
110C2×SD16—5542no—
111C2×D8—21no—
112C2×D8—5541no—
113C4⋊Q8—2771no—
114#127C2×D27711yescharacteristic
115#124—5542no—
116#121—5541no—
117#121—5541no—
118C4×D4—2771no—
119C4×D4C2×D27711yescharacteristic
120#117—5541no—
121#117—5541no—
122C4⋊C8—2771no—
123C4⋊C8C2×D27711yescharacteristic
124#102—21no—
125#102—5541no—
126C4×C8—2771no—
127C2×Q8—2772no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—2771no—
132C2×D4—5542no—
133C2×D4C22⋊D27711yescharacteristic
134C22×C4—21no—
135C22×C4—5541no—
136SD16—11084no—
137D8—42no—
138D8—11082no—
139C2×C8—21no—
140C2×C8—5541no—
141C2×C8—5541no—
142C4⋊C4—2771no—
143C4⋊C4—5541no—
144C4⋊C4—5541no—
145C4⋊C4C22⋊D27711yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—5542no—
148C22⋊C4—5542no—
149C22⋊C4—5541no—
150C42—5542no—
151C42C22×D27711yescharacteristic
152C23—21no—
153C23—41no—
154C23—5541no—
155Q8—11082no—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—5541no—
164D4—5541no—
165D4—22162no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—5541no—
170C2×C4—5542no—
171C2×C4—11081no—
172C2×C4—11081no—
173C2×C4D4×D27711yescharacteristic
174C2×C4D4×D27711yescharacteristic
175C2×C4C2×C22⋊D27711yescharacteristic
176C8—41no—
177C8—5542no—
178C8—11081no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—11081no—
186C22—11081no—
187C22—11081no—
188C22#2257984811yescharacteristic
189C4—21no—
190C4—41no—
191C4—11081no—
192C4—11082no—
193C4#2257989911yescharacteristic
194C4#2257990011yescharacteristic
195C4#2257990411yescharacteristic
196C4#2257990611yescharacteristic
197C2—81no—
198C2—161no—
199C2—22161no—
200C2#3180014411yescharacteristic
201C2#3180014511yescharacteristic
202C2#3180016811yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#459×C277C2
socleC22×C277#120
hypercenter#459D277
hypocenterC277#1624
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #31800717C2semidirect
2. #31800374C2semidirect
3. #31800194C2semidirect
4. #31799750C2semidirect
5. D4⋊#14555660C2semidirect
6. #31799729C2semidirect
7. #459×C277C2semidirect
101. C277#1624semidirect
106. #459D277semidirect

Maximal subgroups

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

subgroupindex
#318007172
#318003742
#318001942
#317997502
D4⋊#145556602
#317997292
#459×C2772
#1624277