Finite Group Databasebeta

← #47982314

Subgroups — #47982314

Order 35456.

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

normal subgroups only

This group has 218 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#31800717C211yesmaximal, characteristic
2#31800382C211yesmaximal, characteristic, complemented
3#31800293C211yesmaximal, characteristic, complemented
4#31800292C211yesmaximal, characteristic, complemented
5#31799750C211yesmaximal, characteristic, complemented
6#31799731C211yesmaximal, characteristic, complemented
7D4⋊C8×C277C211yesmaximal, characteristic, complemented
8C2×Dic1108—22no—
9#22579880C2211yescharacteristic
10#22579880C2211yescharacteristic
11#22579866—22no—
12#22579854—21no—
13#22579851—21no—
14C4×D1108C2211yescharacteristic
15#22579839—21no—
16#22579838—21no—
17#22579812—21no—
18#22579811—21no—
19C4⋊#14555660C2211yescharacteristic
20#22579802—21no—
21#22579801—21no—
22C4×D4×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4×C8×C277C2211yescharacteristic
25C2×Dic554—21no—
26C2×Dic554D412yes—
27C2×D1108D411yescharacteristic
28C2×C22⋊D277—22no—
29C2×C4×D277—21no—
30Dic1108—44no—
31C2×#14555660—21no—
32C4⋊Dic277—21no—
33C4⋊Dic277—21no—
34C4⋊Dic277—21no—
35C4⋊Dic277—21no—
36C4⋊Dic277D411yescharacteristic
37C22⋊Dic277—22no—
38#17984540—22no—
39#17984540—21no—
40C4×Dic277—22no—
41C2×D4×C277D411yescharacteristic
42C22×C4×C277—21no—
43C2×C8×C277—21no—
44C2×C8×C277—21no—
45C4⋊C4×C277D411yescharacteristic
46C22⋊C4×C277—21no—
47C42×C277C2311yescharacteristic
48C22×D277—21no—
49Dic554—42no—
50Dic554—42no—
51D1108—21no—
52D1108—21no—
53C22⋊D277—82no—
54C2×Dic277—21no—
55C2×Dic277—22no—
56C2×Dic277—41no—
57C4×D277—41no—
58C4×D277—41no—
59#14555660—41no—
60C23×C277—21no—
61D4×C277—21no—
62D4×C277—21no—
63C2×C4×C277—21no—
64C2×C4×C277—41no—
65C2×C4×C277—41no—
66C2×C4×C277C2×D411yescharacteristic
67C2×C4×C277C2×D411yescharacteristic
68C2×C4×C277C2×D411yescharacteristic
69C8×C277—22no—
70C8×C277—41no—
71C22×C277—41no—
72C22×C277—41no—
73C22×C277—41no—
74C22×C277#12011yescharacteristic
75C2×D277—41no—
76C2×D277—41no—
77C2×D277—41no—
78C4×C277—21no—
79C4×C277—41no—
80C4×C277#13511yescharacteristic
81C4×C277#13511yescharacteristic
82C4×C277#13711yescharacteristic
83C4×C277#13711yescharacteristic
84Dic277—41no—
85Dic277—42no—
86Dic277—81no—
87C2×C277—81no—
88C2×C277#45211yescharacteristic
89C2×C277#45211yescharacteristic
90C2×C277#45311yescharacteristic
91D277—81no—
92C277#163411yescharacteristic, complemented, Sylow
93#1634—2771nomaximal, Sylow
94#555—2771no—
95#494—2771no—
96#476—2771no—
97#476—2771no—
98#333—2771no—
99D4⋊C8—2771no—
100D4⋊C8D27711yescharacteristic, complemented
101C2×Q16—5542no—
102C4⋊Q8—2771no—
103C4⋊Q8—2771no—
104#124—5542no—
105#121—5541no—
106#121—5541no—
107C4×D4—2771no—
108C4×D4C2×D27711yescharacteristic
109#117—5541no—
110#117—5541no—
111#106—5541no—
112#106—5541no—
113C4⋊C8—2771no—
114C4⋊C8C2×D27711yescharacteristic
115#102—5541no—
116#102—5541no—
117C4×C8C2×D27711yescharacteristic
118C2×Q8—2772no—
119C2×Q8—5541no—
120C2×D4—2771no—
121C2×D4—5542no—
122C2×D4D110811yescharacteristic
123C22×C4—21no—
124C22×C4—5541no—
125Q16—11084no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—5541no—
129C4⋊C4—2771no—
130C4⋊C4—5541no—
131C4⋊C4—5541no—
132C4⋊C4—5541no—
133C4⋊C4—5541no—
134C4⋊C4D110811yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—5542no—
137C22⋊C4—5542no—
138C22⋊C4—5541no—
139C42—5542no—
140C42C22×D27711yescharacteristic
141C23—21no—
142C23—5541no—
143Q8—11082no—
144Q8—11082no—
145D4—21no—
146D4—21no—
147D4—5541no—
148D4—5541no—
149D4—22162no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—5541no—
154C2×C4—5542no—
155C2×C4—11081no—
156C2×C4—11081no—
157C2×C4—11081no—
158C2×C4D4×D27711yescharacteristic
159C2×C4D4×D27711yescharacteristic
160C2×C4C2×D110811yescharacteristic
161C8—22no—
162C8—41no—
163C8—11081no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—11081no—
168C22—11081no—
169C22—11081no—
170C22#2257985011yescharacteristic
171C4—21no—
172C4—41no—
173C4—11081no—
174C4—11082no—
175C4—22161no—
176C4#2257989911yescharacteristic
177C4#2257990211yescharacteristic
178C4#2257990911yescharacteristic
179C4#2257991311yescharacteristic
180C2—81no—
181C2—22161no—
182C2#3180016511yescharacteristic
183C2#3180016611yescharacteristic
184C2#3180017111yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
FittingD4⋊C8×C277C2
socleC22×C277#120
prime radical#31800717C2
hypercenterD4⋊C8D277
hypocenterC277#1634
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. #31800293C2semidirect
4. #31800292C2semidirect
5. #31799750C2semidirect
6. #31799731C2semidirect
7. D4⋊C8×C277C2semidirect
92. C277#1634semidirect
100. D4⋊C8D277semidirect

Maximal subgroups

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

subgroupindex
#318007172
#318003822
#318002932
#318002922
#317997502
#317997312
D4⋊C8×C2772
#1634277