Finite Group Databasebeta

← #49094410

Subgroups — #49094410

Order 35968.

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#31824187C211yesmaximal, characteristic, complemented
2#31823660C211yesmaximal, characteristic, complemented
3#31823655C211yesmaximal, characteristic
4#31823209C211yesmaximal, characteristic, complemented
5#31823195C211yesmaximal, characteristic, complemented
6#31823192C211yesmaximal, characteristic, complemented
7#486×C281C211yesmaximal, characteristic, complemented
8C2×#17985126—21no—
9C2×#17985123—21no—
10#22582874—22no—
11#22582868—21no—
12#22582859—21no—
13Q8×Dic281—21no—
14C4×Dic562C2211yescharacteristic
15C4×D1124C2211yescharacteristic
16#22582837—21no—
17C4⋊#14555886C2211yescharacteristic
18C4⋊#14555886C2211yescharacteristic
19#22582800—21no—
20#22582800—21no—
21C4⋊Q8×C281C2211yescharacteristic
22#127×C281C2211yescharacteristic
23#102×C281—22no—
24C4×C8×C281C2211yescharacteristic
25C2×Dic562D411yescharacteristic
26C2×D1124D411yescharacteristic
27C2×C4×D281—21no—
28#17985126—42no—
29#17985123—42no—
30C2×#14555886—21no—
31C2×#14555886—21no—
32C4⋊Dic281—22no—
33C4⋊Dic281D411yescharacteristic
34C4⋊Dic281D411yescharacteristic
35#17985117—21no—
36#17985115—22no—
37#17985115—22no—
38#17985115—21no—
39C4×Dic281—22no—
40C4×Dic281—21no—
41C2×Q8×C281—21no—
42C2×D4×C281—21no—
43C2×D4×C281—21no—
44C2×D4×C281—21no—
45C2×C8×C281—21no—
46C4⋊C4×C281—21no—
47C4⋊C4×C281D412yes—
48C42×C281C2311yescharacteristic
49C22×D281—21no—
50Dic562—21no—
51Dic562—21no—
52D1124—21no—
53D1124—21no—
54C2×Dic281—21no—
55C2×Dic281—21no—
56C2×Dic281—21no—
57C4×D281—41no—
58C4×D281—41no—
59#14555886—41no—
60#14555886—41no—
61C23×C281—41no—
62Q8×C281—41no—
63Q8×C281—41no—
64D4×C281—42no—
65D4×C281—41no—
66D4×C281—41no—
67D4×C281—41no—
68D4×C281—41no—
69C2×C4×C281—22no—
70C2×C4×C281C2×D411yescharacteristic
71C2×C4×C281C2×D411yescharacteristic
72C2×C4×C281C2×D411yescharacteristic
73C8×C281—41no—
74C22×C281—81no—
75C22×C281—81no—
76C22×C281—81no—
77C22×C281#12011yescharacteristic
78C2×D281—41no—
79C2×D281—41no—
80C2×D281—41no—
81C4×C281—21no—
82C4×C281—42no—
83C4×C281#13511yescharacteristic
84C4×C281#13511yescharacteristic
85C4×C281AGL(1,ℤ/8)11yescharacteristic
86C4×C281AGL(1,ℤ/8)11yescharacteristic
87Dic281—41no—
88Dic281—41no—
89Dic281—41no—
90C2×C281—161no—
91C2×C281#44911yescharacteristic
92C2×C281#44911yescharacteristic
93C2×C281#45411yescharacteristic
94D281—81no—
95C281#162811yescharacteristic, complemented, Sylow
96#1628—2811nomaximal, Sylow
97#556—2811no—
98#486D28111yescharacteristic, complemented
99#460—2811no—
100#459—2811no—
101#332—2811no—
102Q8⋊C8—2811no—
103D4⋊C8—2811no—
104C2×SD16—5621no—
105C2×D8—5621no—
106C4⋊Q8C2×D28111yescharacteristic
107#127C2×D28111yescharacteristic
108#126—5622no—
109#124—5621no—
110C22⋊Q8—5621no—
111C4×Q8—2811no—
112C4×Q8—5621no—
113C4×D4—2811no—
114#117—5621no—
115C4⋊C8—2811no—
116C4⋊C8—2811no—
117#102—22no—
118#102—5621no—
119#102—5621no—
120C4×C8C2×D28111yescharacteristic
121C2×Q8—21no—
122C2×Q8—2811no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—2811no—
127C22×C4—5621no—
128SD16—11242no—
129D8—11242no—
130C2×C8—21no—
131C2×C8—5621no—
132C2×C8—5621no—
133C4⋊C4—21no—
134C4⋊C4—2811no—
135C4⋊C4—2811no—
136C4⋊C4—5622no—
137C4⋊C4—5621no—
138C4⋊C4C22⋊D28112yes—
139C22⋊C4—5622no—
140C22⋊C4—5622no—
141C22⋊C4—5621no—
142C42—5622no—
143C42—5621no—
144C42C22×D28111yescharacteristic
145C23—41no—
146C23—5621no—
147Q8—41no—
148Q8—41no—
149Q8—5621no—
150Q8—5621no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—5621no—
157D4—5621no—
158C2×C4—22no—
159C2×C4—5621no—
160C2×C4—5621no—
161C2×C4—5621no—
162C2×C4—11241no—
163C2×C4—11241no—
164C2×C4D4×D28111yescharacteristic
165C2×C4D4×D28111yescharacteristic
166C2×C4C2×C22⋊D28111yescharacteristic
167C8—41no—
168C8—11241no—
169C8—11241no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—11241no—
174C22—11241no—
175C22—11241no—
176C22#2258284711yescharacteristic
177C4—21no—
178C4—42no—
179C4—11241no—
180C4—11241no—
181C4—11241no—
182C4#2258289811yescharacteristic
183C4#2258290011yescharacteristic
184C4#2258290311yescharacteristic
185C4#2258290611yescharacteristic
186C2—161no—
187C2—22481no—
188C2#3182360511yescharacteristic
189C2#3182360711yescharacteristic
190C2#3182363511yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#486×C281C2
socleC22×C281#120
prime radical#31823655C2
hypercenter#486D281
hypocenterC281#1628
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #31824187C2semidirect
2. #31823660C2semidirect
4. #31823209C2semidirect
5. #31823195C2semidirect
6. #31823192C2semidirect
7. #486×C281C2semidirect
95. C281#1628semidirect
98. #486D281semidirect

Maximal subgroups

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

subgroupindex
#318241872
#318236602
#318236552
#318232092
#318231952
#318231922
#486×C2812
#1628281