Finite Group Databasebeta

← #47983605

Subgroups — #47983605

Order 35456.

412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 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×#22579802C212yesmaximal, complemented
3#31799862C211yesmaximal, characteristic, complemented
4#31799765C212yesmaximal, complemented
5C22×M16×C277C211yesmaximal, characteristic, complemented
6C22×D1108C2211yescharacteristic
7C22×C22⋊D277—21no—
8#22579854—22no—
9#22579854C414yescomplemented
10C2×C4⋊Dic277C2212yes—
11C2×C4⋊Dic277C2211yescharacteristic
12C2×C22⋊Dic277—21no—
13C2×#17984540—21no—
14#22579802—24no—
15#22579787—21no—
16C23×C4×C277C2211yescharacteristic
17C2×M16×C277—22no—
18C2×M16×C277—24no—
19C22×C8×C277C2212yes—
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—21no—
28C22×Dic277—22no—
29C4⋊Dic277—21no—
30C4⋊Dic277—22no—
31C4⋊Dic277—22no—
32C4⋊Dic277C2×C412yes—
33C22⋊Dic277—42no—
34#17984540—24no—
35C24×C277D411yescharacteristic
36C22×C4×C277—22no—
37C22×C4×C277—22no—
38C22×C4×C277C2×C412yes—
39C22×C4×C277D411yescharacteristic
40C22×C4×C277D412yes—
41C22×C4×C277C2311yescharacteristic
42M16×C277—28no—
43C2×C8×C277—22no—
44C2×C8×C277—22no—
45C2×C8×C277D414yescomplemented
46C22×D277—22no—
47C22×D277—42no—
48C22×D277—42no—
49C22×D277—41no—
50C22×D277—41no—
51D1108—24no—
52D1108—41no—
53D1108—41no—
54C22⋊D277—48no—
55C2×Dic277—22no—
56C2×Dic277—42no—
57C2×Dic277—42no—
58C2×Dic277—42no—
59C2×Dic277—42no—
60C23×C277—22no—
61C23×C277—21no—
62C23×C277—22no—
63C23×C277—21no—
64C23×C277C22⋊C412yes—
65C23×C277C2×D411yescharacteristic
66C2×C4×C277—22no—
67C2×C4×C277—24no—
68C2×C4×C277—22no—
69C2×C4×C277—22no—
70C2×C4×C277C22⋊C412yes—
71C2×C4×C277C22×C411yescharacteristic
72C2×C4×C277C2×D412yes—
73C2×C4×C277C2×D411yescharacteristic
74C2×C4×C277#4112yes—
75C8×C277—24no—
76C22×C277—22no—
77C22×C277—22no—
78C22×C277—22no—
79C22×C277—42no—
80C22×C277—42no—
81C22×C277C2×C22⋊C411yescharacteristic
82C22×C277#12112yes—
83C22×C277AGL(1,ℤ/8)11yescharacteristic
84C22×C277AGL(1,ℤ/8)12yes—
85C22×C277#13711yescharacteristic
86C2×D277—42no—
87C2×D277—42no—
88C2×D277—42no—
89C2×D277—82no—
90C2×D277—82no—
91C4×C277—22no—
92C4×C277C4×D412yes—
93C4×C277#12011yescharacteristic
94C4×C277#12311yescharacteristic
95Dic277—42no—
96Dic277—82no—
97C2×C277—42no—
98C2×C277#38611yescharacteristic
99C2×C277#41711yescharacteristic
100C2×C277#41811yescharacteristic
101C2×C277#46812yes—
102C2×C277#46912yes—
103D277—82no—
104C277#189511yescharacteristic, complemented, Sylow
105#1895—2771nomaximal, Sylow
106C22×M16D27711yescharacteristic, complemented
107C2×#121—2771no—
108C2×#102—2772no—
109#380—2771no—
110#340—2772no—
111C22×D4—2771no—
112C22×D4—5541no—
113C23×C4C2×D27711yescharacteristic
114C2×M16—22no—
115C2×M16—24no—
116C22×C8C2×D27712yes—
117#121—2774no—
118#121—5542no—
119C2×C4⋊C4—2771no—
120C2×C4⋊C4—2772no—
121C2×C22⋊C4—5541no—
122C2×C22⋊C4—5541no—
123#102—5544no—
124#95—5541no—
125C24—5541no—
126C24D110811yescharacteristic
127C2×D4—2772no—
128C2×D4—5544no—
129C2×D4—5542no—
130C2×D4—5541no—
131C2×D4—5542no—
132C2×D4—11084no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—5541no—
136C22×C4—5542no—
137C22×C4C4×D27712yes—
138C22×C4C22⋊D27712yes—
139C22×C4D110811yescharacteristic
140C22×C4C22×D27711yescharacteristic
141M16—28no—
142C2×C8—22no—
143C2×C8—22no—
144C2×C8C22⋊D27714yescomplemented
145C4⋊C4—2772no—
146C4⋊C4—5541no—
147C4⋊C4—5542no—
148C4⋊C4—5542no—
149C22⋊C4—5544no—
150C22⋊C4—11082no—
151C23—22no—
152C23—21no—
153C23—22no—
154C23—21no—
155C23—5542no—
156C23—11082no—
157C23—11082no—
158C23—11081no—
159C23—11081no—
160C23#1798454012yes—
161C23C2×D110811yescharacteristic
162D4—5544no—
163D4—11088no—
164D4—11081no—
165D4—11081no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—5542no—
171C2×C4—11082no—
172C2×C4—11082no—
173C2×C4—11082no—
174C2×C4—11082no—
175C2×C4#1798454012yes—
176C2×C4C2×C4×D27711yescharacteristic
177C2×C4C2×C22⋊D27712yes—
178C2×C4C2×C22⋊D27711yescharacteristic
179C2×C4#1798456312yes—
180C8—24no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—11082no—
187C22—11082no—
188C22—11082no—
189C22—22162no—
190C22—22162no—
191C22C2×#1798454011yescharacteristic
192C22#2257985412yes—
193C22#2257990812yes—
194C22#2257990811yescharacteristic
195C22#2257991311yescharacteristic
196C4—22no—
197C4—11082no—
198C4—22162no—
199C4C4×C22⋊D27712yes—
200C4#2257984911yescharacteristic
201C4#2257986311yescharacteristic
202C2—42no—
203C2—22162no—
204C2#3179988111yescharacteristic
205C2#3180000411yescharacteristic
206C2#3180000811yescharacteristic
207C2#3180024812yes—
208C2#3180025512yes—
subgroupG/H
centerC23C2×D1108
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
FittingC22×M16×C277C2
socleC23×C277C2×D4
prime radicalC2×#22579854C2
cosocleC22×C4×C277C23
hypercenterC22×M16D277
hypocenterC277#1895
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#22579802C2semidirect
3. #31799862C2semidirect
4. #31799765C2semidirect
5. C22×M16×C277C2semidirect
9. #22579854C4semidirect
45. C2×C8×C277D4semidirect
104. C277#1895semidirect
106. C22×M16D277semidirect
144. C2×C8C22⋊D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225798542
C2×#225798022
#317998622
#317997652
C22×M16×C2772
#1895277