Finite Group Databasebeta

← #47984211

Subgroups — #47984211

Order 35456.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×#22579908C212yesmaximal, complemented
2#31800583C211yesmaximal, characteristic, complemented
3C2×#22579806C212yesmaximal, complemented
4#31799903C211yesmaximal, characteristic, complemented
5#343×C277C211yesmaximal, characteristic, complemented
6C2×#17984563C2212yes—
7C22×D1108C2211yescharacteristic
8#22579908—24no—
9#22579908—24no—
10C2×#17984552—22no—
11C2×D2216—22no—
12#22579860—22no—
13#22579855—22no—
14#22579854—22no—
15C2×#17984540—22no—
16C2×C4×Dic277C2211yescharacteristic
17#22579806—24no—
18C2×M16×C277C2212yes—
19C2×C4⋊C4×C277C2211yescharacteristic
20C23×D277—21no—
21#17984563—22no—
22#17984563—22no—
23#17984563—22no—
24#17984563—22no—
25C2×Dic554D412yes—
26C2×D1108—22no—
27C2×D1108—22no—
28C2×D1108—22no—
29C2×D1108—21no—
30C2×D1108D412yes—
31C2×D1108D412yescomplemented
32C2×C22⋊D277—22no—
33C22×Dic277—21no—
34C2×C4×D277—22no—
35#17984552—28no—
36D2216—28no—
37C4⋊Dic277—22no—
38#17984540—24no—
39#17984540—44no—
40C4×Dic277—22no—
41C22×C4×C277D412yes—
42C22×C4×C277C2311yescharacteristic
43M16×C277—22no—
44M16×C277D414yescomplemented
45C2×C8×C277—22no—
46C4⋊C4×C277—22no—
47C22×D277—22no—
48C22×D277—22no—
49C22×D277—42no—
50C22×D277—42no—
51C22×D277—41no—
52C22×D277—41no—
53Dic554—22no—
54Dic554—22no—
55D1108—22no—
56D1108—24no—
57D1108—22no—
58D1108—42no—
59D1108—82no—
60C22⋊D277—42no—
61C22⋊D277—42no—
62C2×Dic277—22no—
63C2×Dic277—22no—
64C2×Dic277—41no—
65C2×Dic277—41no—
66C4×D277—42no—
67C4×D277—42no—
68C23×C277C2×D411yescharacteristic
69C2×C4×C277—22no—
70C2×C4×C277—42no—
71C2×C4×C277C2×D411yescharacteristic
72C2×C4×C277C2×D412yes—
73C2×C4×C277C2×D412yes—
74C2×C4×C277#4111yescharacteristic
75C8×C277—24no—
76C22×C277—21no—
77C22×C277—21no—
78C22×C277#12011yescharacteristic
79C22×C277#12111yescharacteristic
80C22×C277#12711yescharacteristic
81C2×D277—44no—
82C2×D277—42no—
83C2×D277—42no—
84C2×D277—42no—
85C2×D277—42no—
86C2×D277—82no—
87C2×D277—81no—
88C2×D277—81no—
89C4×C277—42no—
90C4×C277#12012yes—
91C4×C277#12112yes—
92Dic277—42no—
93Dic277—42no—
94C2×C277—21no—
95C2×C277—21no—
96C2×C277#39211yescharacteristic
97C2×C277#45311yescharacteristic
98C2×C277#45411yescharacteristic
99D277—82no—
100D277—82no—
101C277#200611yescharacteristic, complemented, Sylow
102#2006—2771nomaximal, Sylow
103C2×AGL(1,ℤ/8)—2772no—
104#537—2771no—
105C2×#104—2772no—
106#390—2771no—
107#343D27711yescharacteristic, complemented
108C2×#41—2772no—
109C22×D4—2771no—
110AGL(1,ℤ/8)—5544no—
111AGL(1,ℤ/8)—5544no—
112C2×SD16—5542no—
113C2×D8—5542no—
114C2×M16C2×D27712yes—
115C22⋊Q8—5542no—
116#121—5542no—
117#121—5542no—
118C2×C4⋊C4C2×D27711yescharacteristic
119C2×C22⋊C4—5542no—
120C2×C42—2771no—
121#104—5544no—
122C24—5541no—
123#41—5542no—
124#41—5542no—
125#41—5542no—
126#41—5542no—
127C2×Q8—2772no—
128C2×D4—2772no—
129C2×D4—2772no—
130C2×D4—5542no—
131C2×D4—5542no—
132C2×D4—5542no—
133C2×D4—5542no—
134C2×D4—5541no—
135C22×C4—5541no—
136C22×C4—5542no—
137C22×C4D110812yes—
138C22×C4C22×D27711yescharacteristic
139SD16—5548no—
140D8—5548no—
141M16—22no—
142M16D110814yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—5542no—
146C22⋊C4—5544no—
147C22⋊C4—11084no—
148C42—5542no—
149C23—5542no—
150C23—5542no—
151C23—11082no—
152C23—11082no—
153C23—11081no—
154C23—11081no—
155C23C2×D110811yescharacteristic
156Q8—5542no—
157Q8—5542no—
158D4—5542no—
159D4—5544no—
160D4—5542no—
161D4—11082no—
162D4—11082no—
163D4—11082no—
164D4—22162no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—5542no—
168C2×C4—5542no—
169C2×C4—11081no—
170C2×C4—11081no—
171C2×C4—11082no—
172C2×C4—11082no—
173C2×C4D4×D27711yescharacteristic
174C2×C4D4×D27712yes—
175C2×C4C2×D110812yes—
176C2×C4#1798456411yescharacteristic
177C8—24no—
178C22—21no—
179C22—21no—
180C22—11084no—
181C22—11082no—
182C22—11082no—
183C22—11082no—
184C22—11082no—
185C22—22162no—
186C22—22161no—
187C22—22161no—
188C22#2257985011yescharacteristic
189C22#2257985511yescharacteristic
190C22#2257987711yescharacteristic
191C4—42no—
192C4—11082no—
193C4—11082no—
194C4#2257985012yes—
195C4#2257985512yes—
196C2—21no—
197C2—21no—
198C2—22162no—
199C2—22162no—
200C2#3179991211yescharacteristic
201C2#3180017211yescharacteristic
202C2#3180017711yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#343×C277C2
socleC22×C277#120
hypercenter#343D277
hypocenterC277#2006
LCSG ▷ C22×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#22579908C2semidirect
2. #31800583C2semidirect
3. C2×#22579806C2semidirect
4. #31799903C2semidirect
5. #343×C277C2semidirect
31. C2×D1108D4semidirect
44. M16×C277D4semidirect
101. C277#2006semidirect
107. #343D277semidirect
142. M16D1108semidirect

Maximal subgroups

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

subgroupindex
C2×#225799082
#318005832
C2×#225798062
#317999032
#343×C2772
#2006277