Finite Group Databasebeta

← #47983487

Subgroups — #47983487

Order 35456.

412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C2×#22579854C211yesmaximal, characteristic
2C2×#22579839C211yesmaximal, characteristic, complemented
3C2×#22579802C212yesmaximal, complemented
4#31799765C212yesmaximal, complemented
5C2×C22⋊C8×C277C211yesmaximal, characteristic, complemented
6C22×D1108C2211yescharacteristic
7C22×C22⋊D277—21no—
8#22579854—22no—
9#22579854C414yescomplemented
10#22579839—24no—
11C2×C4⋊Dic277C2211yescharacteristic
12C2×C4⋊Dic277C2212yes—
13C2×C22⋊Dic277—21no—
14C2×#17984540—21no—
15C2×C4×Dic277—21no—
16#22579802—24no—
17C23×C4×C277C2211yescharacteristic
18C22×C8×C277C2212yes—
19C22⋊C8×C277—22no—
20C23×D277—21no—
21C2×D1108—22no—
22C2×D1108—21no—
23C2×D1108—22no—
24C2×D1108C2×C412yes—
25C2×C22⋊D277—24no—
26C2×C22⋊D277—44no—
27C22×Dic277—22no—
28C22×Dic277—21no—
29C4⋊Dic277—22no—
30C4⋊Dic277—21no—
31C4⋊Dic277C2×C412yes—
32C4⋊Dic277D414yescomplemented
33C22⋊Dic277—24no—
34#17984540—24no—
35C4×Dic277—24no—
36C24×C277D411yescharacteristic
37C22×C4×C277—22no—
38C22×C4×C277—22no—
39C22×C4×C277C2×C412yes—
40C22×C4×C277D411yescharacteristic
41C22×C4×C277D412yes—
42C22×C4×C277C2311yescharacteristic
43C2×C8×C277—22no—
44C2×C8×C277—22no—
45C2×C8×C277—22no—
46C22×D277—22no—
47C22×D277—41no—
48C22×D277—41no—
49C22×D277—42no—
50C22×D277—42no—
51D1108—24no—
52D1108—42no—
53C22⋊D277—48no—
54C2×Dic277—22no—
55C2×Dic277—24no—
56C2×Dic277—42no—
57C2×Dic277—42no—
58C2×Dic277—42no—
59C23×C277—21no—
60C23×C277—21no—
61C23×C277—22no—
62C23×C277—22no—
63C23×C277C22⋊C412yes—
64C23×C277C2×D411yescharacteristic
65C2×C4×C277—21no—
66C2×C4×C277—21no—
67C2×C4×C277—24no—
68C2×C4×C277—24no—
69C2×C4×C277C22⋊C412yes—
70C2×C4×C277C22×C411yescharacteristic
71C2×C4×C277C2×D412yes—
72C2×C4×C277C2×D411yescharacteristic
73C2×C4×C277#4112yes—
74C8×C277—42no—
75C22×C277—22no—
76C22×C277—22no—
77C22×C277—22no—
78C22×C277—42no—
79C22×C277—42no—
80C22×C277C2×C22⋊C411yescharacteristic
81C22×C277#12011yescharacteristic
82C22×C277#12311yescharacteristic
83C22×C277#13512yes—
84C22×C277AGL(1,ℤ/8)12yes—
85C2×D277—42no—
86C2×D277—42no—
87C2×D277—42no—
88C2×D277—82no—
89C2×D277—82no—
90C4×C277—22no—
91C4×C277C4×D412yes—
92C4×C277#12112yes—
93Dic277—42no—
94Dic277—44no—
95C2×C277—42no—
96C2×C277#38611yescharacteristic
97C2×C277#41611yescharacteristic
98C2×C277#41811yescharacteristic
99C2×C277#44912yes—
100C2×C277#48212yes—
101D277—82no—
102C277#187511yescharacteristic, complemented, Sylow
103#1875—2771nomaximal, Sylow
104C2×#121—2771no—
105C2×#117—2771no—
106C2×#102—2772no—
107C2×C22⋊C8D27711yescharacteristic, complemented
108#340—2772no—
109C22×D4—2771no—
110C22×D4—5541no—
111C23×C4C2×D27711yescharacteristic
112C22×C8C2×D27712yes—
113#121—2774no—
114#121—5542no—
115#117—5544no—
116C2×C4⋊C4—2772no—
117C2×C4⋊C4—2771no—
118C2×C22⋊C4—5541no—
119C2×C22⋊C4—5541no—
120C2×C42—5541no—
121#102—5544no—
122C22⋊C8—22no—
123C24—5541no—
124C24D110811yescharacteristic
125C2×D4—2772no—
126C2×D4—5544no—
127C2×D4—5542no—
128C2×D4—5541no—
129C2×D4—5542no—
130C2×D4—11084no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—5542no—
134C22×C4—5541no—
135C22×C4C4×D27712yes—
136C22×C4C22⋊D27712yes—
137C22×C4D110811yescharacteristic
138C22×C4C22×D27711yescharacteristic
139C2×C8—22no—
140C2×C8—22no—
141C2×C8—22no—
142C4⋊C4—2772no—
143C4⋊C4—2774no—
144C4⋊C4—5542no—
145C4⋊C4—5541no—
146C22⋊C4—5544no—
147C22⋊C4—5544no—
148C42—5544no—
149C23—21no—
150C23—21no—
151C23—22no—
152C23—22no—
153C23—5542no—
154C23—11081no—
155C23—11081no—
156C23—11082no—
157C23—11082no—
158C23#1798454012yes—
159C23C2×D110811yescharacteristic
160D4—5544no—
161D4—11088no—
162D4—11082no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—5542no—
168C2×C4—5544no—
169C2×C4—11082no—
170C2×C4—11082no—
171C2×C4—11082no—
172C2×C4#1798454012yes—
173C2×C4C2×C4×D27711yescharacteristic
174C2×C4D4×D27712yes—
175C2×C4C2×C22⋊D27711yescharacteristic
176C2×C4#1798456212yes—
177C8—42no—
178C22—22no—
179C22—22no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—11082no—
184C22—11082no—
185C22—11082no—
186C22—22162no—
187C22—22162no—
188C22C2×#1798454011yescharacteristic
189C22#2257985011yescharacteristic
190C22#2257986411yescharacteristic
191C22#2257990212yes—
192C22#2257990812yes—
193C4—22no—
194C4—11084no—
195C4—11082no—
196C4#2257984012yes—
197C4#2257985212yes—
198C2—42no—
199C2—22162no—
200C2#3179987911yescharacteristic
201C2#3179999911yescharacteristic
202C2#3180000811yescharacteristic
203C2#3180014912yes—
204C2#3180032712yes—
subgroupG/H
centerC23C2×D1108
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
FittingC2×C22⋊C8×C277C2
socleC23×C277C2×D4
prime radicalC2×#22579854C2
cosocleC22×C4×C277C23
hypercenterC2×C22⋊C8D277
hypocenterC277#1875
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#22579839C2semidirect
3. C2×#22579802C2semidirect
4. #31799765C2semidirect
5. C2×C22⋊C8×C277C2semidirect
9. #22579854C4semidirect
32. C4⋊Dic277D4semidirect
102. C277#1875semidirect
107. C2×C22⋊C8D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225798542
C2×#225798392
C2×#225798022
#317997652
C2×C22⋊C8×C2772
#1875277