Finite Group Databasebeta

← #47982104

Subgroups — #47982104

Order 35456.

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

normal subgroups only

This group has 310 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#31800583C211yesmaximal, characteristic, complemented
2#31800138C212yesmaximal, complemented
3#31799919C211yesmaximal, characteristic, complemented
4#31799737C212yesmaximal, complemented
5#324×C277C211yesmaximal, characteristic, complemented
6C2×#17984563—21no—
7C22×D1108C2211yescharacteristic
8C2×D2216—22no—
9#22579860—22no—
10#22579855—22no—
11#22579854—21no—
12#22579854C2212yes—
13C2×#17984540—21no—
14C2×#17984540—21no—
15#22579802—22no—
16#22579787C2211yescharacteristic
17C2×C4⋊C4×C277C2211yescharacteristic
18C22⋊C8×C277C2212yes—
19C23×D277—21no—
20#17984563—42no—
21#17984563—42no—
22C2×Dic554—21no—
23C2×D1108—21no—
24C2×D1108—21no—
25C2×D1108—22no—
26C2×D1108—42no—
27C2×D1108D412yes—
28C2×C22⋊D277—22no—
29C22×Dic277—21no—
30C2×C4×D277—22no—
31D2216—44no—
32C4⋊Dic277—21no—
33C4⋊Dic277D412yes—
34#17984540—22no—
35#17984540—22no—
36#17984540—42no—
37#17984540—42no—
38C22×C4×C277D411yescharacteristic
39C22×C4×C277D411yescharacteristic
40C22×C4×C277C2311yescharacteristic
41C2×C8×C277—22no—
42C4⋊C4×C277—22no—
43C22×D277—22no—
44C22×D277—22no—
45C22×D277—41no—
46C22×D277—41no—
47C22×D277—41no—
48C22×D277—41no—
49C22×D277—41no—
50C22×D277—41no—
51Dic554—42no—
52D1108—24no—
53D1108—42no—
54D1108—42no—
55D1108—42no—
56D1108—81no—
57C22⋊D277—42no—
58C22⋊D277—42no—
59C2×Dic277—22no—
60C2×Dic277—41no—
61C2×Dic277—41no—
62C2×Dic277—41no—
63C4×D277—44no—
64C23×C277C2×D411yescharacteristic
65C2×C4×C277—21no—
66C2×C4×C277—21no—
67C2×C4×C277—21no—
68C2×C4×C277—41no—
69C2×C4×C277—41no—
70C2×C4×C277D812yescomplemented
71C2×C4×C277C2×D412yes—
72C8×C277—42no—
73C22×C277—21no—
74C22×C277—21no—
75C22×C277#12011yescharacteristic
76C22×C277C2×D811yescharacteristic
77C22×C277AGL(1,ℤ/8)11yescharacteristic
78C2×D277—42no—
79C2×D277—42no—
80C2×D277—42no—
81C2×D277—42no—
82C2×D277—42no—
83C2×D277—42no—
84C2×D277—81no—
85C2×D277—81no—
86C2×D277—81no—
87C2×D277—81no—
88C4×C277—22no—
89C4×C277—22no—
90C4×C277—41no—
91Dic277—42no—
92Dic277—81no—
93C2×C277—21no—
94C2×C277—21no—
95C2×C277#44711yescharacteristic
96C2×C277#45411yescharacteristic
97C2×C277B(4,𝔽2)11yescharacteristic
98D277—82no—
99D277—82no—
100C277#159811yescharacteristic, complemented, Sylow
101#1598—2771nomaximal, Sylow
102#537—2771no—
103#447—2772no—
104#394—2771no—
105#327—2772no—
106#324D27711yescharacteristic, complemented
107C2×#41—5541no—
108C22×D4—2771no—
109C2×D8—5542no—
110C22⋊Q8—5542no—
111#121—2772no—
112#121—5542no—
113#121—5541no—
114C2×C4⋊C4C2×D27711yescharacteristic
115C2×C22⋊C4—5541no—
116C2×C22⋊C4—5541no—
117#102—5542no—
118C22⋊C8C2×D27712yes—
119#95—2771no—
120C24—5541no—
121#41—11082no—
122#41—11082no—
123C2×Q8—5541no—
124C2×D4—2772no—
125C2×D4—5541no—
126C2×D4—5541no—
127C2×D4—5542no—
128C2×D4—5542no—
129C2×D4—11082no—
130C22×C4—5542no—
131C22×C4—5541no—
132C22×C4D110811yescharacteristic
133C22×C4D110811yescharacteristic
134C22×C4C22×D27711yescharacteristic
135D8—11084no—
136C2×C8—22no—
137C4⋊C4—22no—
138C4⋊C4—2772no—
139C4⋊C4—5541no—
140C22⋊C4—5542no—
141C22⋊C4—5542no—
142C22⋊C4—11082no—
143C22⋊C4—11082no—
144C23—5542no—
145C23—5542no—
146C23—11081no—
147C23—11081no—
148C23—11081no—
149C23—11081no—
150C23—11081no—
151C23—11081no—
152C23C2×D110811yescharacteristic
153Q8—11082no—
154D4—5544no—
155D4—11082no—
156D4—11082no—
157D4—11082no—
158D4—11082no—
159D4—11082no—
160D4—22161no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—5542no—
167C2×C4—11084no—
168C2×C4—11081no—
169C2×C4—11081no—
170C2×C4—11081no—
171C2×C4D221612yescomplemented
172C2×C4D4×D27712yes—
173C8—42no—
174C22—21no—
175C22—21no—
176C22—11082no—
177C22—11082no—
178C22—11082no—
179C22—11082no—
180C22—11082no—
181C22—11082no—
182C22—22161no—
183C22—22161no—
184C22—22161no—
185C22—22161no—
186C22#2257985011yescharacteristic
187C22C2×D221611yescharacteristic
188C22#2257990811yescharacteristic
189C4—22no—
190C4—22no—
191C4—41no—
192C4—11082no—
193C4—22161no—
194C2—21no—
195C2—21no—
196C2—22162no—
197C2—22162no—
198C2#3180013811yescharacteristic
199C2#3180017711yescharacteristic
200C2#3180019011yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#324×C277C2
socleC22×C277#120
hypercenter#324D277
hypocenterC277#1598
LCSG ▷ C22×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
1. #31800583C2semidirect
2. #31800138C2semidirect
3. #31799919C2semidirect
4. #31799737C2semidirect
5. #324×C277C2semidirect
70. C2×C4×C277D8semidirect
100. C277#1598semidirect
106. #324D277semidirect
171. C2×C4D2216semidirect

Maximal subgroups

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

subgroupindex
#318005832
#318001382
#317999192
#317997372
#324×C2772
#1598277