Finite Group Databasebeta

← #47983697

Subgroups — #47983697

Order 35456.

362 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 85 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#31800569C211yesmaximal, characteristic
2#31800477C211yesmaximal, characteristic, complemented
3#31800018C212yesmaximal, complemented
4#31799759C212yesmaximal, complemented
5C2×#100×C277C211yesmaximal, characteristic, complemented
6C2×#17984563C2211yescharacteristic
7#22579876C412yescomplemented
8#22579867C412yescomplemented
9#22579851—22no—
10#22579849—22no—
11D4×Dic277—24no—
12#22579839C2211yescharacteristic
13#22579839C2212yes—
14C2×C22⋊Dic277—22no—
15#22579806—24no—
16C22×D4×C277C2211yescharacteristic
17C2×M16×C277C2212yes—
18#100×C277—22no—
19#17984563—22no—
20#17984563—22no—
21C2×Dic554C2×C411yescharacteristic, complemented
22C2×D1108C2×C411yescharacteristic, complemented
23C2×C22⋊D277—24no—
24C2×C22⋊D277—21no—
25C22×Dic277—24no—
26C2×C4×D277—21no—
27C4⋊Dic277—22no—
28C4⋊Dic277—21no—
29C22⋊Dic277—24no—
30C22⋊Dic277—24no—
31C22⋊Dic277—22no—
32C22⋊Dic277—21no—
33C4×Dic277C2×C412yescomplemented
34C4×Dic277D414yescomplemented
35C24×C277D412yes—
36C2×D4×C277—22no—
37C2×D4×C277—22no—
38C2×D4×C277C2×C412yes—
39C2×D4×C277D412yes—
40C22×C4×C277C2311yescharacteristic
41M16×C277—22no—
42M16×C277—22no—
43C2×C8×C277—22no—
44C22×D277—21no—
45Dic554—22no—
46D1108—22no—
47C22⋊D277—41no—
48C22⋊D277—41no—
49C22⋊D277—84no—
50C2×Dic277—22no—
51C2×Dic277—21no—
52C2×Dic277—24no—
53C2×Dic277—84no—
54C4×D277—42no—
55C23×C277—22no—
56C23×C277—22no—
57C23×C277—82no—
58C23×C277C22⋊C414yes—
59C23×C277C2×D411yescharacteristic
60D4×C277—24no—
61D4×C277—24no—
62C2×C4×C277C22×C411yescharacteristic
63C2×C4×C277C2×D412yes—
64C2×C4×C277C2×D411yescharacteristic
65C2×C4×C277#4112yes—
66C8×C277—42no—
67C22×C277—24no—
68C22×C277—41no—
69C22×C277—44no—
70C22×C277—44no—
71C22×C277—82no—
72C22×C277C2×C22⋊C411yescharacteristic
73C22×C277#12011yescharacteristic
74C22×C277#12311yescharacteristic
75C2×D277—42no—
76C2×D277—41no—
77C4×C277C4×D412yes—
78C4×C277#12112yes—
79Dic277—44no—
80Dic277—42no—
81Dic277—41no—
82C2×C277—21no—
83C2×C277—21no—
84C2×C277—21no—
85C2×C277—44no—
86C2×C277#38611yescharacteristic
87D277—81no—
88C277#191111yescharacteristic, complemented, Sylow
89#1911—2771nomaximal, Sylow
90#535—2771no—
91#518—2771no—
92#421—2772no—
93C2×#100D27711yescharacteristic, complemented
94H(3,ℤ/4)—2772no—
95C2×#41—2771no—
96C22×D4C2×D27711yescharacteristic
97C2×M16C2×D27712yes—
98#127—2772no—
99#124—2772no—
100#121—5542no—
101#120—5542no—
102C4×D4—5544no—
103#117—2772no—
104#117—2771no—
105C2×C22⋊C4—5542no—
106#104—5544no—
107#100—22no—
108C24D110812yes—
109#41—5542no—
110#41—5542no—
111C2×Q8—2771no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—2771no—
115C2×D4—5541no—
116C2×D4—5544no—
117C2×D4C4×D27712yes—
118C2×D4C22⋊D27712yes—
119C22×C4—5544no—
120C22×C4—5541no—
121C22×C4C22×D27711yescharacteristic
122M16—22no—
123M16—22no—
124C2×C8—22no—
125C4⋊C4—5542no—
126C4⋊C4—5541no—
127C22⋊C4—5544no—
128C22⋊C4—5544no—
129C22⋊C4—5542no—
130C22⋊C4—5541no—
131C42—2772no—
132C42—2774no—
133C23—22no—
134C23—22no—
135C23—82no—
136C23—5541no—
137C23#1798454014yes—
138C23C2×D110811yescharacteristic
139Q8—5542no—
140D4—24no—
141D4—24no—
142D4—5542no—
143D4—11081no—
144D4—11081no—
145D4—22164no—
146C2×C4—5542no—
147C2×C4—5541no—
148C2×C4—5544no—
149C2×C4—11082no—
150C2×C4—22164no—
151C2×C4C2×C4×D27711yescharacteristic
152C2×C4D4×D27712yes—
153C2×C4C2×C22⋊D27711yescharacteristic
154C2×C4#1798456212yes—
155C8—42no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—82no—
161C22—11082no—
162C22—11081no—
163C22C2×#1798454011yescharacteristic
164C22#2257985011yescharacteristic
165C22#2257986411yescharacteristic
166C4—11084no—
167C4—11082no—
168C4—11081no—
169C4#2257984012yes—
170C4#2257985212yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—22161no—
176C2#3179987911yescharacteristic
subgroupG/H
centerC2#31799879
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
FittingC2×#100×C277C2
socleC2×C277#386
prime radical#31800569C2
cosocleC22×C4×C277C23
hypercenterC2×#100D277
hypocenterC277#1911
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #31800477C2semidirect
3. #31800018C2semidirect
4. #31799759C2semidirect
5. C2×#100×C277C2semidirect
7. #22579876C4semidirect
8. #22579867C4semidirect
21. C2×Dic554C2×C4semidirect
22. C2×D1108C2×C4semidirect
33. C4×Dic277C2×C4semidirect
34. C4×Dic277D4semidirect
88. C277#1911semidirect
93. C2×#100D277semidirect

Maximal subgroups

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

subgroupindex
#318005692
#318004772
#318000182
#317997592
C2×#100×C2772
#1911277