Finite Group Databasebeta

← #47982303

Subgroups — #47982303

Order 35456.

214 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 57 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#31800709C211yesmaximal, characteristic
2#31800382C211yesmaximal, characteristic, complemented
3#31800298C211yesmaximal, characteristic, complemented
4#31800292C211yesmaximal, characteristic
5#31799750C211yesmaximal, characteristic, complemented
6#31799734C211yesmaximal, characteristic, complemented
7D4⋊C8×C277C211yesmaximal, characteristic
8C2×Dic1108—22no—
9#22579880C2211yescharacteristic
10#22579880C2211yescharacteristic
11#22579871—21no—
12#22579859—21no—
13#22579857—22no—
14C4×Dic554C2211yescharacteristic
15D4×Dic277—21no—
16C2×C4⋊Dic277—21no—
17#22579814—21no—
18#22579811—21no—
19C4⋊#14555660C2211yescharacteristic
20#22579805—21no—
21#22579801—21no—
22C4×D4×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4×C8×C277C2211yescharacteristic
25C2×Dic554—21no—
26C2×Dic554D411yescharacteristic
27C2×Dic554D412yes—
28C22×Dic277—22no—
29Dic1108—44no—
30C2×#14555660—21no—
31C4⋊Dic277—22no—
32C4⋊Dic277—21no—
33C4⋊Dic277—21no—
34C4⋊Dic277—21no—
35C4⋊Dic277—21no—
36C4⋊Dic277D411yescharacteristic
37#17984542—22no—
38#17984542—21no—
39C22⋊Dic277—22no—
40C4×Dic277—21no—
41C2×D4×C277D411yescharacteristic
42C22×C4×C277—21no—
43C2×C8×C277—21no—
44C2×C8×C277—21no—
45C4⋊C4×C277D411yescharacteristic
46C22⋊C4×C277—21no—
47C42×C277C2311yescharacteristic
48Dic554—21no—
49Dic554—21no—
50Dic554—42no—
51Dic554—42no—
52C2×Dic277—21no—
53C2×Dic277—21no—
54C2×Dic277—22no—
55C2×Dic277—41no—
56C2×Dic277—82no—
57#14555660—41no—
58C23×C277—21no—
59D4×C277—21no—
60D4×C277Q1612yescomplemented
61C2×C4×C277—21no—
62C2×C4×C277—41no—
63C2×C4×C277—41no—
64C2×C4×C277C2×D411yescharacteristic
65C2×C4×C277C2×D411yescharacteristic
66C2×C4×C277C2×D411yescharacteristic
67C8×C277—22no—
68C8×C277—41no—
69C22×C277—22no—
70C22×C277—41no—
71C22×C277—41no—
72C22×C277#12011yescharacteristic
73C4×C277—21no—
74C4×C277—41no—
75C4×C277C2×Q1611yescharacteristic
76C4×C277#13511yescharacteristic
77C4×C277#13711yescharacteristic
78C4×C277#13711yescharacteristic
79Dic277—41no—
80Dic277—41no—
81Dic277—42no—
82Dic277—81no—
83C2×C277—42no—
84C2×C277#45111yescharacteristic
85C2×C277#45211yescharacteristic
86C2×C277#45311yescharacteristic
87C277#163211yescharacteristic, complemented, Sylow
88#1632—2771nomaximal, Sylow
89#554—2771no—
90#494—2771no—
91#477—2771no—
92#476—2771no—
93#333—2771no—
94Q8⋊C8—2771no—
95D4⋊C8D27711yescharacteristic
96C2×Q16—5542no—
97C4⋊Q8—2771no—
98C4⋊Q8—2771no—
99#125—5541no—
100C22⋊Q8—5542no—
101C22⋊Q8—5541no—
102C4×Q8—2771no—
103C4×D4—5541no—
104C4×D4C2×D27711yescharacteristic
105C2×C4⋊C4—5541no—
106#107—5541no—
107#106—5541no—
108C4⋊C8—2771no—
109C4⋊C8C2×D27711yescharacteristic
110#103—5541no—
111#102—5541no—
112C4×C8C2×D27711yescharacteristic
113C2×Q8—2771no—
114C2×Q8—2772no—
115C2×Q8—5541no—
116C2×D4D110811yescharacteristic
117C22×C4—21no—
118C22×C4—5542no—
119Q16—11084no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—5541no—
123C4⋊C4—2771no—
124C4⋊C4—5542no—
125C4⋊C4—5542no—
126C4⋊C4—5541no—
127C4⋊C4—5541no—
128C4⋊C4—5541no—
129C4⋊C4—5541no—
130C4⋊C4—5541no—
131C4⋊C4D110811yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—5542no—
134C42—5541no—
135C42C22×D27711yescharacteristic
136C23—21no—
137Q8—5541no—
138Q8—5541no—
139Q8—11082no—
140Q8—11082no—
141D4—21no—
142D4Dic110812yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—5541no—
147C2×C4—5541no—
148C2×C4—5542no—
149C2×C4—11081no—
150C2×C4—22162no—
151C2×C4D4×D27711yescharacteristic
152C2×C4D4×D27711yescharacteristic
153C2×C4C2×D110811yescharacteristic
154C8—22no—
155C8—41no—
156C8—11081no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#2257985011yescharacteristic
161C4—21no—
162C4—41no—
163C4—11081no—
164C4—11081no—
165C4—11082no—
166C4—22161no—
167C4C2×Dic110811yescharacteristic
168C4#2257989911yescharacteristic
169C4#2257990911yescharacteristic
170C4#2257991311yescharacteristic
171C2—42no—
172C2#3180016011yescharacteristic
173C2#3180016511yescharacteristic
174C2#3180017111yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
FittingD4⋊C8×C277C2
socleC22×C277#120
prime radicalC2×D4×C277D4
hypercenterD4⋊C8D277
hypocenterC277#1632
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #31800382C2semidirect
3. #31800298C2semidirect
5. #31799750C2semidirect
6. #31799734C2semidirect
60. D4×C277Q16semidirect
87. C277#1632semidirect
142. D4Dic1108semidirect

Maximal subgroups

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

subgroupindex
#318007092
#318003822
#318002982
#318002922
#317997502
#317997342
D4⋊C8×C2772
#1632277