Finite Group Databasebeta

← #47982432

Subgroups — #47982432

Order 35456.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic554C211yesmaximal, characteristic
2#31800400C211yesmaximal, characteristic, complemented
3#31800288C211yesmaximal, characteristic, complemented
4#31800207C211yesmaximal, characteristic
5#31799749C211yesmaximal, characteristic, complemented
6#31799734C211yesmaximal, characteristic, complemented
7D4⋊C8×C277C211yesmaximal, characteristic
8C22×Dic554—21no—
9C2×#17984551—21no—
10#22579880C2211yescharacteristic
11#22579880C2211yescharacteristic
12#22579879—21no—
13#22579859—21no—
14#22579857—22no—
15C4×Dic554C2211yescharacteristic
16D4×Dic277—21no—
17#22579812—22no—
18#22579812—21no—
19C4⋊#14555660C2211yescharacteristic
20#22579805—21no—
21#22579803—21no—
22C4×D4×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4×C8×C277C2211yescharacteristic
25C2×Dic554—22no—
26C2×Dic554—21no—
27C2×Dic554—21no—
28C2×Dic554—42no—
29C2×Dic554—42no—
30C2×Dic554D411yescharacteristic
31C22×Dic277—22no—
32#17984551—42no—
33C2×#14555660—21no—
34C4⋊Dic277—21no—
35C4⋊Dic277—21no—
36C4⋊Dic277—21no—
37C4⋊Dic277D411yescharacteristic
38C4⋊Dic277D412yes—
39#17984542—22no—
40#17984542—21no—
41C22⋊Dic277—22no—
42C4×Dic277—21no—
43C2×D4×C277D411yescharacteristic
44C22×C4×C277—21no—
45C2×C8×C277—21no—
46C2×C8×C277—21no—
47C4⋊C4×C277D411yescharacteristic
48C22⋊C4×C277—21no—
49C42×C277C2311yescharacteristic
50Dic554—21no—
51Dic554—44no—
52Dic554—41no—
53Dic554—41no—
54Dic554—41no—
55Dic554—41no—
56Dic554SD1612yescomplemented
57C2×Dic277—21no—
58C2×Dic277—21no—
59C2×Dic277—22no—
60C2×Dic277—44no—
61C2×Dic277—41no—
62#14555660—41no—
63C23×C277—21no—
64D4×C277—21no—
65D4×C277SD1612yes—
66C2×C4×C277—21no—
67C2×C4×C277—41no—
68C2×C4×C277—41no—
69C2×C4×C277C2×D411yescharacteristic
70C2×C4×C277C2×D411yescharacteristic
71C2×C4×C277C2×D411yescharacteristic
72C8×C277—22no—
73C8×C277—41no—
74C22×C277—22no—
75C22×C277—41no—
76C22×C277—41no—
77C22×C277#12011yescharacteristic
78C4×C277—21no—
79C4×C277—41no—
80C4×C277C2×SD1611yescharacteristic
81C4×C277C2×SD1611yescharacteristic
82C4×C277AGL(1,ℤ/8)11yescharacteristic
83C4×C277#13711yescharacteristic
84Dic277—22no—
85Dic277—42no—
86Dic277—41no—
87Dic277—81no—
88C2×C277—42no—
89C2×C277#44811yescharacteristic
90C2×C277#45011yescharacteristic
91C2×C277#45611yescharacteristic
92C277#165111yescharacteristic, complemented, Sylow
93#1651—2771nomaximal, Sylow
94D4×Q8—2771no—
95#498—2771no—
96#475—2771no—
97#461—2771no—
98#332—2771no—
99Q8⋊C8—2771no—
100D4⋊C8D27711yescharacteristic
101C22×Q8—5541no—
102C2×SD16—5541no—
103C4⋊Q8—2771no—
104C4⋊Q8—2771no—
105C4⋊Q8—5541no—
106C22⋊Q8—5542no—
107C22⋊Q8—5541no—
108C4×Q8—2771no—
109C4×D4—5541no—
110C4×D4C2×D27711yescharacteristic
111#106—5541no—
112#106—5542no—
113C4⋊C8—2771no—
114C4⋊C8C2×D27711yescharacteristic
115#103—5541no—
116#103—5541no—
117C4×C8C2×D27711yescharacteristic
118C2×Q8—2771no—
119C2×Q8—5542no—
120C2×Q8—5541no—
121C2×Q8—5541no—
122C2×Q8—11082no—
123C2×Q8—11082no—
124C2×D4D110811yescharacteristic
125C22×C4—21no—
126C22×C4—5542no—
127SD16—11082no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—5541no—
131C4⋊C4—2771no—
132C4⋊C4—2772no—
133C4⋊C4—5542no—
134C4⋊C4—5541no—
135C4⋊C4—5541no—
136C4⋊C4—5541no—
137C4⋊C4—5541no—
138C4⋊C4D110811yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—5542no—
141C42—5541no—
142C42C22×D27711yescharacteristic
143C23—21no—
144Q8—2772no—
145Q8—5541no—
146Q8—11084no—
147Q8—11081no—
148Q8—11081no—
149Q8—11081no—
150Q8—11081no—
151D4—21no—
152D4#1798455212yes—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—5541no—
157C2×C4—5541no—
158C2×C4—5542no—
159C2×C4—11084no—
160C2×C4—11081no—
161C2×C4D4×D27711yescharacteristic
162C2×C4D4×D27711yescharacteristic
163C2×C4C2×D110811yescharacteristic
164C8—22no—
165C8—41no—
166C8—11081no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#2257985011yescharacteristic
171C4—21no—
172C4—41no—
173C4—5542no—
174C4—11082no—
175C4—11081no—
176C4—22161no—
177C4SD16×D27711yescharacteristic
178C4C2×#1798455211yescharacteristic
179C4#2257990411yescharacteristic
180C4#2257991311yescharacteristic
181C2—42no—
182C2#3180014311yescharacteristic
183C2#3180015411yescharacteristic
184C2#3180018611yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
FittingD4⋊C8×C277C2
socleC22×C277#120
prime radicalC2×D4×C277D4
hypercenterD4⋊C8D277
hypocenterC277#1651
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. #31800400C2semidirect
3. #31800288C2semidirect
5. #31799749C2semidirect
6. #31799734C2semidirect
56. Dic554SD16semidirect
92. C277#1651semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5542
#318004002
#318002882
#318002072
#317997492
#317997342
D4⋊C8×C2772
#1651277