Finite Group Databasebeta

← #47982315

Subgroups — #47982315

Order 35456.

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

normal subgroups only

This group has 234 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#31800655C211yesmaximal, characteristic
2#31800289C211yesmaximal, characteristic, complemented
3#31800289C211yesmaximal, characteristic, complemented
4#31799748C211yesmaximal, characteristic, complemented
5#31799731C211yesmaximal, characteristic, complemented
6#31799731C211yesmaximal, characteristic, complemented
7#487×C277C211yesmaximal, characteristic, complemented
8C2×#17984564—21no—
9#22579865—22no—
10#22579856—21no—
11#22579855—21no—
12C4×D1108C2211yescharacteristic
13C4×D1108C2211yescharacteristic
14C4⋊C4×D277—21no—
15#22579811—21no—
16#22579811—21no—
17C4⋊#14555660C2211yescharacteristic
18C4⋊#14555660C2211yescharacteristic
19#22579800—21no—
20#22579800—21no—
21C4⋊Q8×C277C2211yescharacteristic
22C4⋊Q8×C277C2211yescharacteristic
23#103×C277—22no—
24C4×C8×C277C2211yescharacteristic
25#17984564—42no—
26#17984564—42no—
27C2×D1108—22no—
28C2×D1108D411yescharacteristic
29C2×D1108D411yescharacteristic
30C2×C4×D277—22no—
31C2×C4×D277—21no—
32C2×C4×D277—21no—
33C2×#14555660—21no—
34C2×#14555660—21no—
35C4⋊Dic277D411yescharacteristic
36C4⋊Dic277D411yescharacteristic
37#17984542—22no—
38#17984540—22no—
39#17984540—21no—
40#17984540—21no—
41C2×Q8×C277—21no—
42C2×Q8×C277—21no—
43C2×C8×C277—21no—
44C4⋊C4×C277—21no—
45C4⋊C4×C277—21no—
46C4⋊C4×C277—21no—
47C4⋊C4×C277D412yes—
48C42×C277C2311yescharacteristic
49C22×D277—21no—
50C22×D277—21no—
51D1108—21no—
52D1108—21no—
53D1108—21no—
54D1108—44no—
55D1108SD1612yes—
56C2×Dic277—21no—
57C2×Dic277—21no—
58C4×D277—44no—
59C4×D277—41no—
60C4×D277—41no—
61C4×D277—41no—
62C4×D277—41no—
63#14555660—41no—
64#14555660—41no—
65Q8×C277—42no—
66Q8×C277—41no—
67Q8×C277—41no—
68C2×C4×C277—22no—
69C2×C4×C277—41no—
70C2×C4×C277C2×D411yescharacteristic
71C2×C4×C277C2×D411yescharacteristic
72C2×C4×C277C2×D411yescharacteristic
73C8×C277—41no—
74C22×C277#12011yescharacteristic
75C2×D277—22no—
76C2×D277—41no—
77C2×D277—41no—
78C2×D277—41no—
79C2×D277—41no—
80C2×D277—41no—
81C4×C277—21no—
82C4×C277—42no—
83C4×C277—81no—
84C4×C277C2×SD1611yescharacteristic
85C4×C277#13511yescharacteristic
86C4×C277AGL(1,ℤ/8)11yescharacteristic
87C4×C277#13711yescharacteristic
88Dic277—41no—
89Dic277—41no—
90C2×C277#45011yescharacteristic
91C2×C277#45211yescharacteristic
92C2×C277#45411yescharacteristic
93D277—42no—
94D277—81no—
95C277#163511yescharacteristic, complemented, Sylow
96#1635—2771nomaximal, Sylow
97#547—2771no—
98#487D27711yescharacteristic, complemented
99#476—2771no—
100#476—2771no—
101#332—2771no—
102D4⋊C8—2771no—
103D4⋊C8—2771no—
104C2×#41—5541no—
105C4⋊Q8C2×D27711yescharacteristic
106C4⋊Q8C2×D27711yescharacteristic
107#123—5542no—
108C22⋊Q8—5541no—
109#121—5541no—
110C4×D4—2771no—
111C4×D4—2771no—
112C2×C4⋊C4—5541no—
113#106—5541no—
114#106—5541no—
115C4⋊C8—2771no—
116C4⋊C8—2771no—
117#103—22no—
118#102—5541no—
119#102—5541no—
120C4×C8C2×D27711yescharacteristic
121#41—11082no—
122#41—11082no—
123C2×Q8—21no—
124C2×Q8—21no—
125C2×D4—2771no—
126C2×D4—2771no—
127C2×D4—5542no—
128C22×C4—5542no—
129C22×C4—5541no—
130C22×C4—5541no—
131C2×C8—21no—
132C2×C8—5541no—
133C2×C8—5541no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—2771no—
138C4⋊C4—2771no—
139C4⋊C4—5542no—
140C4⋊C4C22⋊D27712yes—
141C22⋊C4—5542no—
142C22⋊C4—5541no—
143C22⋊C4—5541no—
144C42C22×D27711yescharacteristic
145C23—5541no—
146C23—5541no—
147Q8—42no—
148Q8—41no—
149Q8—41no—
150D4—2772no—
151D4—5541no—
152D4—5541no—
153D4—5541no—
154D4—11084no—
155C2×C4—22no—
156C2×C4—41no—
157C2×C4—5541no—
158C2×C4—5541no—
159C2×C4—11084no—
160C2×C4—11081no—
161C2×C4—11081no—
162C2×C4—11081no—
163C2×C4—11081no—
164C2×C4D4×D27711yescharacteristic
165C2×C4D4×D27711yescharacteristic
166C2×C4C2×C22⋊D27711yescharacteristic
167C8—41no—
168C8—11081no—
169C8—11081no—
170C22—5542no—
171C22—11081no—
172C22—11081no—
173C22—11081no—
174C22—11081no—
175C22—11081no—
176C22#2257984811yescharacteristic
177C4—21no—
178C4—42no—
179C4—81no—
180C4—11081no—
181C4—11081no—
182C4SD16×D27711yescharacteristic
183C4#2257990311yescharacteristic
184C4#2257990711yescharacteristic
185C4#2257991211yescharacteristic
186C2—11082no—
187C2—22161no—
188C2#3180015111yescharacteristic
189C2#3180016311yescharacteristic
190C2#3180017411yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#487×C277C2
socleC22×C277#120
prime radical#31800655C2
hypercenter#487D277
hypocenterC277#1635
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #31800289C2semidirect
3. #31800289C2semidirect
4. #31799748C2semidirect
5. #31799731C2semidirect
6. #31799731C2semidirect
7. #487×C277C2semidirect
95. C277#1635semidirect
98. #487D277semidirect

Maximal subgroups

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

subgroupindex
#318006552
#318002892
#317997482
#317997312
#487×C2772
#1635277