Finite Group Databasebeta

← #47982274

Subgroups — #47982274

Order 35456.

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

normal subgroups only

This group has 216 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#31800726C211yesmaximal, characteristic, complemented
2#31800199C211yesmaximal, characteristic, complemented
3#31800194C211yesmaximal, characteristic
4#31799748C211yesmaximal, characteristic, complemented
5#31799734C211yesmaximal, characteristic, complemented
6#31799731C211yesmaximal, characteristic, complemented
7#486×C277C211yesmaximal, characteristic, complemented
8C2×#17984551—21no—
9C2×#17984548—21no—
10#22579875—22no—
11#22579869—21no—
12#22579860—21no—
13Q8×Dic277—21no—
14C4×Dic554C2211yescharacteristic
15C4×D1108C2211yescharacteristic
16#22579838—21no—
17C4⋊#14555660C2211yescharacteristic
18C4⋊#14555660C2211yescharacteristic
19#22579801—21no—
20#22579801—21no—
21C4⋊Q8×C277C2211yescharacteristic
22#127×C277C2211yescharacteristic
23#102×C277—22no—
24C4×C8×C277C2211yescharacteristic
25C2×Dic554D411yescharacteristic
26C2×D1108D411yescharacteristic
27C2×C4×D277—21no—
28#17984551—42no—
29#17984548—42no—
30C2×#14555660—21no—
31C2×#14555660—21no—
32C4⋊Dic277—22no—
33C4⋊Dic277D411yescharacteristic
34C4⋊Dic277D411yescharacteristic
35#17984542—21no—
36#17984540—22no—
37#17984540—22no—
38#17984540—21no—
39C4×Dic277—22no—
40C4×Dic277—21no—
41C2×Q8×C277—21no—
42C2×D4×C277—21no—
43C2×D4×C277—21no—
44C2×D4×C277—21no—
45C2×C8×C277—21no—
46C4⋊C4×C277—21no—
47C4⋊C4×C277D412yes—
48C42×C277C2311yescharacteristic
49C22×D277—21no—
50Dic554—21no—
51Dic554—21no—
52D1108—21no—
53D1108—21no—
54C2×Dic277—21no—
55C2×Dic277—21no—
56C2×Dic277—21no—
57C4×D277—41no—
58C4×D277—41no—
59#14555660—41no—
60#14555660—41no—
61C23×C277—41no—
62Q8×C277—41no—
63Q8×C277—41no—
64D4×C277—42no—
65D4×C277—41no—
66D4×C277—41no—
67D4×C277—41no—
68D4×C277—41no—
69C2×C4×C277—22no—
70C2×C4×C277C2×D411yescharacteristic
71C2×C4×C277C2×D411yescharacteristic
72C2×C4×C277C2×D411yescharacteristic
73C8×C277—41no—
74C22×C277—81no—
75C22×C277—81no—
76C22×C277—81no—
77C22×C277#12011yescharacteristic
78C2×D277—41no—
79C2×D277—41no—
80C2×D277—41no—
81C4×C277—21no—
82C4×C277—42no—
83C4×C277#13511yescharacteristic
84C4×C277#13511yescharacteristic
85C4×C277AGL(1,ℤ/8)11yescharacteristic
86C4×C277AGL(1,ℤ/8)11yescharacteristic
87Dic277—41no—
88Dic277—41no—
89Dic277—41no—
90C2×C277—161no—
91C2×C277#44911yescharacteristic
92C2×C277#44911yescharacteristic
93C2×C277#45411yescharacteristic
94D277—81no—
95C277#162811yescharacteristic, complemented, Sylow
96#1628—2771nomaximal, Sylow
97#556—2771no—
98#486D27711yescharacteristic, complemented
99#460—2771no—
100#459—2771no—
101#332—2771no—
102Q8⋊C8—2771no—
103D4⋊C8—2771no—
104C2×SD16—5541no—
105C2×D8—5541no—
106C4⋊Q8C2×D27711yescharacteristic
107#127C2×D27711yescharacteristic
108#126—5542no—
109#124—5541no—
110C22⋊Q8—5541no—
111C4×Q8—2771no—
112C4×Q8—5541no—
113C4×D4—2771no—
114#117—5541no—
115C4⋊C8—2771no—
116C4⋊C8—2771no—
117#102—22no—
118#102—5541no—
119#102—5541no—
120C4×C8C2×D27711yescharacteristic
121C2×Q8—21no—
122C2×Q8—2771no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—2771no—
127C22×C4—5541no—
128SD16—11082no—
129D8—11082no—
130C2×C8—21no—
131C2×C8—5541no—
132C2×C8—5541no—
133C4⋊C4—21no—
134C4⋊C4—2771no—
135C4⋊C4—2771no—
136C4⋊C4—5542no—
137C4⋊C4—5541no—
138C4⋊C4C22⋊D27712yes—
139C22⋊C4—5542no—
140C22⋊C4—5542no—
141C22⋊C4—5541no—
142C42—5542no—
143C42—5541no—
144C42C22×D27711yescharacteristic
145C23—41no—
146C23—5541no—
147Q8—41no—
148Q8—41no—
149Q8—5541no—
150Q8—5541no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—5541no—
157D4—5541no—
158C2×C4—22no—
159C2×C4—5541no—
160C2×C4—5541no—
161C2×C4—5541no—
162C2×C4—11081no—
163C2×C4—11081no—
164C2×C4D4×D27711yescharacteristic
165C2×C4D4×D27711yescharacteristic
166C2×C4C2×C22⋊D27711yescharacteristic
167C8—41no—
168C8—11081no—
169C8—11081no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—11081no—
174C22—11081no—
175C22—11081no—
176C22#2257984811yescharacteristic
177C4—21no—
178C4—42no—
179C4—11081no—
180C4—11081no—
181C4—11081no—
182C4#2257989911yescharacteristic
183C4#2257990111yescharacteristic
184C4#2257990411yescharacteristic
185C4#2257990711yescharacteristic
186C2—161no—
187C2—22161no—
188C2#3180014411yescharacteristic
189C2#3180014611yescharacteristic
190C2#3180017411yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#486×C277C2
socleC22×C277#120
prime radical#31800194C2
hypercenter#486D277
hypocenterC277#1628
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #31800726C2semidirect
2. #31800199C2semidirect
4. #31799748C2semidirect
5. #31799734C2semidirect
6. #31799731C2semidirect
7. #486×C277C2semidirect
95. C277#1628semidirect
98. #486D277semidirect

Maximal subgroups

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

subgroupindex
#318007262
#318001992
#318001942
#317997482
#317997342
#317997312
#486×C2772
#1628277