Finite Group Databasebeta

← #47982300

Subgroups — #47982300

Order 35456.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#31800712C211yesmaximal, characteristic
2#31800381C211yesmaximal, characteristic, complemented
3#31800289C211yesmaximal, characteristic
4#31799750C211yesmaximal, characteristic, complemented
5Q8⋊#14555660C211yesmaximal, characteristic, complemented
6#31799729C211yesmaximal, characteristic
7#477×C277C211yesmaximal, characteristic, complemented
8C2×#17984553—22no—
9#22579880C2211yescharacteristic
10#22579872—21no—
11#22579858—22no—
12#22579856—21no—
13C4×D1108—21no—
14C4×D1108C2211yescharacteristic
15C4⋊C4×D277—21no—
16#22579811—21no—
17C4⋊#14555660C2211yescharacteristic
18#22579800—21no—
19C4×#14555660C2211yescharacteristic
20C4⋊Q8×C277C2211yescharacteristic
21C4×Q8×C277C2211yescharacteristic
22#107×C277—21no—
23C4⋊C8×C277C2211yescharacteristic
24#103×C277—21no—
25C2×Dic554D412yes—
26C2×D1108D411yescharacteristic
27C2×C4×D277—22no—
28C2×C4×D277—21no—
29#17984553—44no—
30C2×#14555660—21no—
31C2×#14555660—21no—
32C4⋊Dic277—21no—
33C4⋊Dic277—21no—
34C4⋊Dic277D411yescharacteristic
35#17984542—22no—
36#17984542—22no—
37#17984540—22no—
38#17984540—21no—
39C2×Q8×C277—21no—
40C2×Q8×C277D411yescharacteristic
41C2×C8×C277—21no—
42C4⋊C4×C277—21no—
43C4⋊C4×C277—21no—
44C4⋊C4×C277—21no—
45C4⋊C4×C277D411yescharacteristic
46C42×C277—21no—
47C42×C277C2311yescharacteristic
48C22×D277—21no—
49Dic554—42no—
50D1108—21no—
51D1108Q1612yescomplemented
52C2×Dic277—21no—
53C2×Dic277—22no—
54C4×D277—41no—
55C4×D277—41no—
56C4×D277—82no—
57#14555660—22no—
58#14555660—41no—
59Q8×C277—21no—
60Q8×C277—21no—
61Q8×C277—42no—
62C2×C4×C277—21no—
63C2×C4×C277—21no—
64C2×C4×C277—41no—
65C2×C4×C277C2×D411yescharacteristic
66C2×C4×C277C2×D411yescharacteristic
67C2×C4×C277C2×D411yescharacteristic
68C8×C277—41no—
69C22×C277#12011yescharacteristic
70C2×D277—22no—
71C2×D277—41no—
72C2×D277—41no—
73C4×C277—21no—
74C4×C277—41no—
75C4×C277—41no—
76C4×C277—81no—
77C4×C277C2×Q1611yescharacteristic
78C4×C277#13511yescharacteristic
79C4×C277#13711yescharacteristic
80C4×C277#13711yescharacteristic
81Dic277—41no—
82Dic277—42no—
83C2×C277#45111yescharacteristic
84C2×C277#45211yescharacteristic
85C2×C277#45311yescharacteristic
86D277—42no—
87C277#163211yescharacteristic, complemented, Sylow
88#1632—2771nomaximal, Sylow
89#554—2771no—
90#494—2771no—
91#477D27711yescharacteristic, complemented
92#476—2771no—
93#333—2771no—
94Q8⋊C8—2771no—
95D4⋊C8—2771no—
96C2×Q16—5542no—
97C4⋊Q8—2771no—
98C4⋊Q8C2×D27711yescharacteristic
99#125—5541no—
100C22⋊Q8—5542no—
101C22⋊Q8—5541no—
102C4×Q8C2×D27711yescharacteristic
103C4×D4—2771no—
104C4×D4—5541no—
105C2×C4⋊C4—5541no—
106#107—21no—
107#106—5541no—
108C4⋊C8—2771no—
109C4⋊C8C2×D27711yescharacteristic
110#103—21no—
111#102—5541no—
112C4×C8—2771no—
113C2×Q8—21no—
114C2×Q8—2772no—
115C2×Q8C22⋊D27711yescharacteristic
116C2×D4—2771no—
117C22×C4—5542no—
118C22×C4—5541no—
119Q16—11084no—
120C2×C8—21no—
121C2×C8—5541no—
122C2×C8—5541no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—2771no—
127C4⋊C4—5542no—
128C4⋊C4—5542no—
129C4⋊C4—5541no—
130C4⋊C4—5541no—
131C4⋊C4C22⋊D27711yescharacteristic
132C22⋊C4—5542no—
133C22⋊C4—5541no—
134C42—21no—
135C42C22×D27711yescharacteristic
136C23—5541no—
137Q8—21no—
138Q8—21no—
139Q8—42no—
140Q8—11082no—
141D4—2772no—
142D4—5541no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—5541no—
147C2×C4—5542no—
148C2×C4—11081no—
149C2×C4—11081no—
150C2×C4—22162no—
151C2×C4D4×D27711yescharacteristic
152C2×C4D4×D27711yescharacteristic
153C2×C4C2×C22⋊D27711yescharacteristic
154C8—41no—
155C8—5542no—
156C8—11081no—
157C22—5542no—
158C22—11081no—
159C22—11081no—
160C22#2257984811yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—11081no—
166C4—11082no—
167C4Q16×D27711yescharacteristic
168C4#2257990011yescharacteristic
169C4#2257991111yescharacteristic
170C4#2257991211yescharacteristic
171C2—11082no—
172C2#3180015611yescharacteristic
173C2#3180016211yescharacteristic
174C2#3180016811yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#477×C277C2
socleC22×C277#120
prime radicalC2×D1108D4
hypercenter#477D277
hypocenterC277#1632
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #31800381C2semidirect
4. #31799750C2semidirect
5. Q8⋊#14555660C2semidirect
7. #477×C277C2semidirect
51. D1108Q16semidirect
87. C277#1632semidirect
91. #477D277semidirect

Maximal subgroups

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

subgroupindex
#318007122
#318003812
#318002892
#317997502
Q8⋊#145556602
#317997292
#477×C2772
#1632277